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Solve the programming task below in a Python markdown code block. As Famil Door’s birthday is coming, some of his friends (like Gabi) decided to buy a present for him. His friends are going to buy a string consisted of round brackets since Famil Door loves string of brackets of length n more than any other strings! The sequence of round brackets is called valid if and only if: 1. the total number of opening brackets is equal to the total number of closing brackets; 2. for any prefix of the sequence, the number of opening brackets is greater or equal than the number of closing brackets. Gabi bought a string s of length m (m ≤ n) and want to complete it to obtain a valid sequence of brackets of length n. He is going to pick some strings p and q consisting of round brackets and merge them in a string p + s + q, that is add the string p at the beginning of the string s and string q at the end of the string s. Now he wonders, how many pairs of strings p and q exists, such that the string p + s + q is a valid sequence of round brackets. As this number may be pretty large, he wants to calculate it modulo 109 + 7. Input First line contains n and m (1 ≤ m ≤ n ≤ 100 000, n - m ≤ 2000) — the desired length of the string and the length of the string bought by Gabi, respectively. The second line contains string s of length m consisting of characters '(' and ')' only. Output Print the number of pairs of string p and q such that p + s + q is a valid sequence of round brackets modulo 109 + 7. Examples Input 4 1 ( Output 4 Input 4 4 (()) Output 1 Input 4 3 ((( Output 0 Note In the first sample there are four different valid pairs: 1. p = "(", q = "))" 2. p = "()", q = ")" 3. p = "", q = "())" 4. p = "", q = ")()" In the second sample the only way to obtain a desired string is choose empty p and q. In the third sample there is no way to get a valid sequence of brackets. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Niwel is a little golden bear. As everyone knows, bears live in forests, but Niwel got tired of seeing all the trees so he decided to move to the city. In the city, Niwel took on a job managing bears to deliver goods. The city that he lives in can be represented as a directed graph with n nodes and m edges. Each edge has a weight capacity. A delivery consists of a bear carrying weights with their bear hands on a simple path from node 1 to node n. The total weight that travels across a particular edge must not exceed the weight capacity of that edge. Niwel has exactly x bears. In the interest of fairness, no bear can rest, and the weight that each bear carries must be exactly the same. However, each bear may take different paths if they like. Niwel would like to determine, what is the maximum amount of weight he can deliver (it's the sum of weights carried by bears). Find the maximum weight. Input The first line contains three integers n, m and x (2 ≤ n ≤ 50, 1 ≤ m ≤ 500, 1 ≤ x ≤ 100 000) — the number of nodes, the number of directed edges and the number of bears, respectively. Each of the following m lines contains three integers ai, bi and ci (1 ≤ ai, bi ≤ n, ai ≠ bi, 1 ≤ ci ≤ 1 000 000). This represents a directed edge from node ai to bi with weight capacity ci. There are no self loops and no multiple edges from one city to the other city. More formally, for each i and j that i ≠ j it's guaranteed that ai ≠ aj or bi ≠ bj. It is also guaranteed that there is at least one path from node 1 to node n. Output Print one real value on a single line — the maximum amount of weight Niwel can deliver if he uses exactly x bears. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6. Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct if <image>. Examples Input 4 4 3 1 2 2 2 4 1 1 3 1 3 4 2 Output 1.5000000000 Input 5 11 23 1 2 3 2 3 4 3 4 5 4 5 6 1 3 4 2 4 5 3 5 6 1 4 2 2 5 3 1 5 2 3 2 30 Output 10.2222222222 Note In the first sample, Niwel has three bears. Two bears can choose the path <image>, while one bear can choose the path <image>. Even though the bear that goes on the path <image> can carry one unit of weight, in the interest of fairness, he is restricted to carry 0.5 units of weight. Thus, the total weight is 1.5 units overall. Note that even though Niwel can deliver more weight with just 2 bears, he must use exactly 3 bears on this day. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The map of Berland is a rectangle of the size n × m, which consists of cells of size 1 × 1. Each cell is either land or water. The map is surrounded by the ocean. Lakes are the maximal regions of water cells, connected by sides, which are not connected with the ocean. Formally, lake is a set of water cells, such that it's possible to get from any cell of the set to any other without leaving the set and moving only to cells adjacent by the side, none of them is located on the border of the rectangle, and it's impossible to add one more water cell to the set such that it will be connected with any other cell. You task is to fill up with the earth the minimum number of water cells so that there will be exactly k lakes in Berland. Note that the initial number of lakes on the map is not less than k. Input The first line of the input contains three integers n, m and k (1 ≤ n, m ≤ 50, 0 ≤ k ≤ 50) — the sizes of the map and the number of lakes which should be left on the map. The next n lines contain m characters each — the description of the map. Each of the characters is either '.' (it means that the corresponding cell is water) or '' (it means that the corresponding cell is land). It is guaranteed that the map contain at least k lakes. Output In the first line print the minimum number of cells which should be transformed from water to land. In the next n lines print m symbols — the map after the changes. The format must strictly follow the format of the map in the input data (there is no need to print the size of the map). If there are several answers, print any of them. It is guaranteed that the answer exists on the given data. Examples Input 5 4 1 *** .. ** .* .. Output 1 ** .. ** .. Input 3 3 0 *** . * Output 1 * * * Note In the first example there are only two lakes — the first consists of the cells (2, 2) and (2, 3), the second consists of the cell (4, 3). It is profitable to cover the second lake because it is smaller. Pay attention that the area of water in the lower left corner is not a lake because this area share a border with the ocean. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Hongcow is ruler of the world. As ruler of the world, he wants to make it easier for people to travel by road within their own countries. The world can be modeled as an undirected graph with n nodes and m edges. k of the nodes are home to the governments of the k countries that make up the world. There is at most one edge connecting any two nodes and no edge connects a node to itself. Furthermore, for any two nodes corresponding to governments, there is no path between those two nodes. Any graph that satisfies all of these conditions is stable. Hongcow wants to add as many edges as possible to the graph while keeping it stable. Determine the maximum number of edges Hongcow can add. Input The first line of input will contain three integers n, m and k (1 ≤ n ≤ 1 000, 0 ≤ m ≤ 100 000, 1 ≤ k ≤ n) — the number of vertices and edges in the graph, and the number of vertices that are homes of the government. The next line of input will contain k integers c1, c2, ..., ck (1 ≤ ci ≤ n). These integers will be pairwise distinct and denote the nodes that are home to the governments in this world. The following m lines of input will contain two integers ui and vi (1 ≤ ui, vi ≤ n). This denotes an undirected edge between nodes ui and vi. It is guaranteed that the graph described by the input is stable. Output Output a single integer, the maximum number of edges Hongcow can add to the graph while keeping it stable. Examples Input 4 1 2 1 3 1 2 Output 2 Input 3 3 1 2 1 2 1 3 2 3 Output 0 Note For the first sample test, the graph looks like this: <image> Vertices 1 and 3 are special. The optimal solution is to connect vertex 4 to vertices 1 and 2. This adds a total of 2 edges. We cannot add any more edges, since vertices 1 and 3 cannot have any path between them. For the second sample test, the graph looks like this: <image> We cannot add any more edges to this graph. Note that we are not allowed to add self-loops, and the graph must be simple. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Sam has been teaching Jon the Game of Stones to sharpen his mind and help him devise a strategy to fight the white walkers. The rules of this game are quite simple: * The game starts with n piles of stones indexed from 1 to n. The i-th pile contains si stones. * The players make their moves alternatively. A move is considered as removal of some number of stones from a pile. Removal of 0 stones does not count as a move. * The player who is unable to make a move loses. Now Jon believes that he is ready for battle, but Sam does not think so. To prove his argument, Sam suggested that they play a modified version of the game. In this modified version, no move can be made more than once on a pile. For example, if 4 stones are removed from a pile, 4 stones cannot be removed from that pile again. Sam sets up the game and makes the first move. Jon believes that Sam is just trying to prevent him from going to battle. Jon wants to know if he can win if both play optimally. Input First line consists of a single integer n (1 ≤ n ≤ 106) — the number of piles. Each of next n lines contains an integer si (1 ≤ si ≤ 60) — the number of stones in i-th pile. Output Print a single line containing "YES" (without quotes) if Jon wins, otherwise print "NO" (without quotes) Examples Input 1 5 Output NO Input 2 1 2 Output YES Note In the first case, Sam removes all the stones and Jon loses. In second case, the following moves are possible by Sam: <image> In each of these cases, last move can be made by Jon to win the game as follows: <image> The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. T is a complete binary tree consisting of n vertices. It means that exactly one vertex is a root, and each vertex is either a leaf (and doesn't have children) or an inner node (and has exactly two children). All leaves of a complete binary tree have the same depth (distance from the root). So n is a number such that n + 1 is a power of 2. In the picture you can see a complete binary tree with n = 15. <image> Vertices are numbered from 1 to n in a special recursive way: we recursively assign numbers to all vertices from the left subtree (if current vertex is not a leaf), then assign a number to the current vertex, and then recursively assign numbers to all vertices from the right subtree (if it exists). In the picture vertices are numbered exactly using this algorithm. It is clear that for each size of a complete binary tree exists exactly one way to give numbers to all vertices. This way of numbering is called symmetric. You have to write a program that for given n answers q queries to the tree. Each query consists of an integer number ui (1 ≤ ui ≤ n) and a string si, where ui is the number of vertex, and si represents the path starting from this vertex. String si doesn't contain any characters other than 'L', 'R' and 'U', which mean traverse to the left child, to the right child and to the parent, respectively. Characters from si have to be processed from left to right, considering that ui is the vertex where the path starts. If it's impossible to process a character (for example, to go to the left child of a leaf), then you have to skip it. The answer is the number of vertex where the path represented by si ends. For example, if ui = 4 and si = «UURL», then the answer is 10. Input The first line contains two integer numbers n and q (1 ≤ n ≤ 1018, q ≥ 1). n is such that n + 1 is a power of 2. The next 2q lines represent queries; each query consists of two consecutive lines. The first of these two lines contains ui (1 ≤ ui ≤ n), the second contains non-empty string si. si doesn't contain any characters other than 'L', 'R' and 'U'. It is guaranteed that the sum of lengths of si (for each i such that 1 ≤ i ≤ q) doesn't exceed 105. Output Print q numbers, i-th number must be the answer to the i-th query. Example Input 15 2 4 UURL 8 LRLLLLLLLL Output 10 5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Pasha is participating in a contest on one well-known website. This time he wants to win the contest and will do anything to get to the first place! This contest consists of n problems, and Pasha solves ith problem in ai time units (his solutions are always correct). At any moment of time he can be thinking about a solution to only one of the problems (that is, he cannot be solving two problems at the same time). The time Pasha spends to send his solutions is negligible. Pasha can send any number of solutions at the same moment. Unfortunately, there are too many participants, and the website is not always working. Pasha received the information that the website will be working only during m time periods, jth period is represented by its starting moment lj and ending moment rj. Of course, Pasha can send his solution only when the website is working. In other words, Pasha can send his solution at some moment T iff there exists a period x such that lx ≤ T ≤ rx. Pasha wants to know his best possible result. We need to tell him the minimal moment of time by which he is able to have solutions to all problems submitted, if he acts optimally, or say that it's impossible no matter how Pasha solves the problems. Input The first line contains one integer n (1 ≤ n ≤ 1000) — the number of problems. The second line contains n integers ai (1 ≤ ai ≤ 105) — the time Pasha needs to solve ith problem. The third line contains one integer m (0 ≤ m ≤ 1000) — the number of periods of time when the website is working. Next m lines represent these periods. jth line contains two numbers lj and rj (1 ≤ lj < rj ≤ 105) — the starting and the ending moment of jth period. It is guaranteed that the periods are not intersecting and are given in chronological order, so for every j > 1 the condition lj > rj - 1 is met. Output If Pasha can solve and submit all the problems before the end of the contest, print the minimal moment of time by which he can have all the solutions submitted. Otherwise print "-1" (without brackets). Examples Input 2 3 4 2 1 4 7 9 Output 7 Input 1 5 1 1 4 Output -1 Input 1 5 1 1 5 Output 5 Note In the first example Pasha can act like this: he solves the second problem in 4 units of time and sends it immediately. Then he spends 3 time units to solve the first problem and sends it 7 time units after the contest starts, because at this moment the website starts working again. In the second example Pasha invents the solution only after the website stops working for the last time. In the third example Pasha sends the solution exactly at the end of the first period. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You may have heard of the pie rule before. It states that if two people wish to fairly share a slice of pie, one person should cut the slice in half, and the other person should choose who gets which slice. Alice and Bob have many slices of pie, and rather than cutting the slices in half, each individual slice will be eaten by just one person. The way Alice and Bob decide who eats each slice is as follows. First, the order in which the pies are to be handed out is decided. There is a special token called the "decider" token, initially held by Bob. Until all the pie is handed out, whoever has the decider token will give the next slice of pie to one of the participants, and the decider token to the other participant. They continue until no slices of pie are left. All of the slices are of excellent quality, so each participant obviously wants to maximize the total amount of pie they get to eat. Assuming both players make their decisions optimally, how much pie will each participant receive? Input Input will begin with an integer N (1 ≤ N ≤ 50), the number of slices of pie. Following this is a line with N integers indicating the sizes of the slices (each between 1 and 100000, inclusive), in the order in which they must be handed out. Output Print two integers. First, the sum of the sizes of slices eaten by Alice, then the sum of the sizes of the slices eaten by Bob, assuming both players make their decisions optimally. Examples Input 3 141 592 653 Output 653 733 Input 5 10 21 10 21 10 Output 31 41 Note In the first example, Bob takes the size 141 slice for himself and gives the decider token to Alice. Then Alice gives the size 592 slice to Bob and keeps the decider token for herself, so that she can then give the size 653 slice to herself. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A one-dimensional Japanese crossword can be represented as a binary string of length x. An encoding of this crossword is an array a of size n, where n is the number of segments formed completely of 1's, and ai is the length of i-th segment. No two segments touch or intersect. For example: * If x = 6 and the crossword is 111011, then its encoding is an array {3, 2}; * If x = 8 and the crossword is 01101010, then its encoding is an array {2, 1, 1}; * If x = 5 and the crossword is 11111, then its encoding is an array {5}; * If x = 5 and the crossword is 00000, then its encoding is an empty array. Mishka wants to create a new one-dimensional Japanese crossword. He has already picked the length and the encoding for this crossword. And now he needs to check if there is exactly one crossword such that its length and encoding are equal to the length and encoding he picked. Help him to check it! Input The first line contains two integer numbers n and x (1 ≤ n ≤ 100000, 1 ≤ x ≤ 109) — the number of elements in the encoding and the length of the crossword Mishka picked. The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 10000) — the encoding. Output Print YES if there exists exaclty one crossword with chosen length and encoding. Otherwise, print NO. Examples Input 2 4 1 3 Output NO Input 3 10 3 3 2 Output YES Input 2 10 1 3 Output NO The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A newspaper is published in Walrusland. Its heading is s1, it consists of lowercase Latin letters. Fangy the little walrus wants to buy several such newspapers, cut out their headings, glue them one to another in order to get one big string. After that walrus erase several letters from this string in order to get a new word s2. It is considered that when Fangy erases some letter, there's no whitespace formed instead of the letter. That is, the string remains unbroken and it still only consists of lowercase Latin letters. For example, the heading is "abc". If we take two such headings and glue them one to the other one, we get "abcabc". If we erase the letters on positions 1 and 5, we get a word "bcac". Which least number of newspaper headings s1 will Fangy need to glue them, erase several letters and get word s2? Input The input data contain two lines. The first line contain the heading s1, the second line contains the word s2. The lines only consist of lowercase Latin letters (1 ≤ \|s1\| ≤ 104, 1 ≤ \|s2\| ≤ 106). Output If it is impossible to get the word s2 in the above-described manner, print "-1" (without the quotes). Otherwise, print the least number of newspaper headings s1, which Fangy will need to receive the word s2. Examples Input abc xyz Output -1 Input abcd dabc Output 2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Resistance is trying to take control over all planets in a particular solar system. This solar system is shaped like a tree. More precisely, some planets are connected by bidirectional hyperspace tunnels in such a way that there is a path between every pair of the planets, but removing any tunnel would disconnect some of them. The Resistance already has measures in place that will, when the time is right, enable them to control every planet that is not remote. A planet is considered to be remote if it is connected to the rest of the planets only via a single hyperspace tunnel. How much work is there left to be done: that is, how many remote planets are there? Input The first line of the input contains an integer N (2 ≤ N ≤ 1000) – the number of planets in the galaxy. The next N - 1 lines describe the hyperspace tunnels between the planets. Each of the N - 1 lines contains two space-separated integers u and v (1 ≤ u, v ≤ N) indicating that there is a bidirectional hyperspace tunnel between the planets u and v. It is guaranteed that every two planets are connected by a path of tunnels, and that each tunnel connects a different pair of planets. Output A single integer denoting the number of remote planets. Examples Input 5 4 1 4 2 1 3 1 5 Output 3 Input 4 1 2 4 3 1 4 Output 2 Note In the first example, only planets 2, 3 and 5 are connected by a single tunnel. In the second example, the remote planets are 2 and 3. Note that this problem has only two versions – easy and medium. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You work in a big office. It is a 9 floor building with an elevator that can accommodate up to 4 people. It is your responsibility to manage this elevator. Today you are late, so there are queues on some floors already. For each person you know the floor where he currently is and the floor he wants to reach. Also, you know the order in which people came to the elevator. According to the company's rules, if an employee comes to the elevator earlier than another one, he has to enter the elevator earlier too (even if these employees stay on different floors). Note that the employees are allowed to leave the elevator in arbitrary order. The elevator has two commands: * Go up or down one floor. The movement takes 1 second. * Open the doors on the current floor. During this operation all the employees who have reached their destination get out of the elevator. Then all the employees on the floor get in the elevator in the order they are queued up while it doesn't contradict the company's rules and there is enough space in the elevator. Each employee spends 1 second to get inside and outside the elevator. Initially the elevator is empty and is located on the floor 1. You are interested what is the minimum possible time you need to spend to deliver all the employees to their destination. It is not necessary to return the elevator to the floor 1. Input The first line contains an integer n (1 ≤ n ≤ 2000) — the number of employees. The i-th of the next n lines contains two integers ai and bi (1 ≤ ai, bi ≤ 9, ai ≠ bi) — the floor on which an employee initially is, and the floor he wants to reach. The employees are given in the order they came to the elevator. Output Print a single integer — the minimal possible time in seconds. Examples Input 2 3 5 5 3 Output 10 Input 2 5 3 3 5 Output 12 Note Explaination for the first sample <image> t = 0 <image> t = 2 <image> t = 3 <image> t = 5 <image> t = 6 <image> t = 7 <image> t = 9 <image> t = 10 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given a string S of length N consisting of only lower-case English alphabets, you will be asked to process Q queries over it . In each query you will be given two lower case characters X and Y. Your task is to find out the number of such substrings of the the string S which have the characters X and Y on either of its end points, both X...Y and Y...X are considered to be valid. Note : Substrings length should be greater than 1. Input: The first line of the input will contain N , the length of the string. Next line will contain as string of length N. Next line will will contain Q , the number of queries. Then Q subsequent lines will contain two lowercase characters X and Y separated by a space. Output: For each query , output the answer in a separate line. Constraints: 1 ≤ N ≤ 10^6 1 ≤ Q ≤ 10^3 SAMPLE INPUT 5 aacbb 2 a c a b SAMPLE OUTPUT 2 4 Explanation For the first query, the possible substrings are aac and ac . Hence the answer is 2. For the second query, the possible substrings are aacbb , aacb , acbb , and acb , hence making a total of 4 substrings. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Abhimanyu simply drew two triangles, as shown in the picture below: He says this, Amazing painting 1. Then he drew two more triangles, as shown in the picture below: He says this, Amazing painting 2. Similarly he defined Amazing painting 3, 4, 5, ..., N. Now he starts finding the points where two lines meet or intersect in the every amazing painting. He names these points as A, B, C, ..., X, Y, Z in Top to Down and Left to Right order and in Cyclic order, i.e., after naming 26th point as Z, he will name 27th point as A, and next points as B, C, D, ... Every letter A-Z has a self increment cost to it and has initial value equal to CK for 1 ≤ K ≤ 26. Self increment cost means that the cost of any letter is incremented by 1 whenever it comes during naming process again. For example, say you have total 28 points in the painting, and cost of letters A, B is 4, 5 respectively, then when you name the 27th point as A, the cost of letter A will be 5 and similarly when naming 28th point as B, the cost of letter B it will be 6. This way any painting costs to C, total sum of costs of each letter appeared during naming process. You need to tell Abhimanyu the cost of painting so that he can sell it. Input: First line of input is an integer T, total number of test cases. Each test case consists of two lines. First line of each test case is an integer N, the amazing painting id. Second line contains 26 space separated integers, the initial cost of letters CK. Output: For each test case print the cost of painting in single line. Constraints: There are two types of test files: Type1: 1 ≤ T ≤ 100000 (10^5) 1 ≤ N ≤ 100000 (10^5) 1 ≤ CK ≤ 100000 (10^5) Type2: 1 ≤ T ≤ 1000 (10^3) 100000 (10^5) < N ≤ 1000000000 (10^9) 1 ≤ CK ≤ 10000 (10^4) SAMPLE INPUT 1 1 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 SAMPLE OUTPUT 24 Explanation As Letters A to L used once, so answer is 1+2+3+1+2+3+1+2+3+1+2+3 = 24 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Jiva is a self driven car and is out on its very first drive. It aims to earn some revenue by serving as taxi driver. It starts its journey from a point and travels in a line for 100 Km. It picks and drops passenger on the way,but can accommodate a maximum of M passengers at once. Jiva wants be very economical & intends to equally split the fare among the number of passengers as the following : - The normal rate being - 10 INR/Km for every passenger - If there are 2 passengers in the car at any part of journey, it gives a 5% discount to both the passengers for that part of the journey. - If there are 3 or more passengers in the car at any part of journey, it gives a 7% discount to all of them for that part of the journey. Also note that if the cab was full at any point in the journey,Jiva can not take any more passengers at that time and reports "Cab was full" to its engineers in the end. Given, a total of N passengers that board Jiva at different points. Find the total revenue earned after the journey completes. (See N.B. Section) Input: The first line contains an integer T. T test cases follow. Second line of each test case contains 2 space-separated integers N and M. Next N lines contain 2 space-separated integers ( Si and Ei ), the pick up and drop point of the i'th passenger w.r.t the starting point. Output: Print the revenue earned (Rounded to the nearest integer) followed by "Cab was full" (without the quotes) ,if applicable, in a new line for each test case. N.B. If at a particular point of time, Jiva can take some people to fulfill the capacity then it would take the people in preference of the order in which they are mentioned in the problem statement. Suppose, The input is: 2 1 0 20 0 100 At time T = 0, there are 2 people, but Jiva can take only one of them. It will give higher priority to the person mentioned first i.e. The person with time 0-20. Constraints: 1 ≤ T ≤ 10 0 ≤ N, M ≤ 1000 0 ≤ Si ≤ Ei ≤ 100 Note: Candidates need to attempt only one of the given problems SAMPLE INPUT 2 4 3 0 100 0 20 30 50 40 80 6 4 10 55 10 20 40 60 55 60 60 70 75 95 SAMPLE OUTPUT 1719 Cab was full 1070 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Chester Bennington, being a skinny kid as we all know, is always bullied since he was a child. This time its just unacceptable. Mike Shinoda, the second vocalist to his band, tried to bully him. Chester was never a bright student and Mike, being a high school graduate, gave him a tough mathematical problem. He gave Chester a number N. His task is to find all the prime numbers under N(inclusive) which can be written as the sum of two primes and list them. Help Chester so that this time he is not bullied....... Again !!! Input: First line contains t, the number of test cases. t lines follow after that which contain an integer N. Output: For each test case, you have to print all the prime numbers that meet the above mentioned condition in a single line in a space separated format. For each test-case use a new line. Constraints: 1 ≤ t ≤ 100 1 ≤ N ≤ 10000 Note: 1 and 0 are not considered Primes Problem Setter: Rohit Mishra SAMPLE INPUT 3 7 17 29 SAMPLE OUTPUT 5 7 5 7 13 5 7 13 19 Explanation Consider test case - 2 N=17 Prime Numbers under 17 are 2,3,5,7,11,13,17 Output is 5,7,13 As 1+10 = 2+9 = 3+8 = 4+7 = 5+6 = 11 None of the above mentioned pairs meets the required criteria. Same is the case with the other numbers which are not mentioned in the output. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Agon Packers and Movers specialize in moving large number luggages from one place to another. The luggages are packed by the Packers, and after they're done with the job, the Movers take over. First, the Packers put the packages they have packed in a single line, one behind the other, and then the Movers come one by one to pick the packages. A Mover can come only once, can only pick the first few packages in the line, and then take them with him. He might also choose not to pick any. Another Mover comes, and repeats the process, till all the packages are taken. The Movers need to carry of all the packages. The Movers are a friendly lot, and care about each other - so their goal is to minimize the maximum load that any Mover gets. You are given the number of movers M in the first line. The next line contains the number of packages P. The next line contains the weight of the P package (in Kilograms) in order - first weight representing of first package in the line, separated by space. You need to print the maximum load any mover carries in the best possible case, in accordance with their goal. Constraints: 1 ≤ M ≤ 15 1 ≤ P ≤ 250 Weight of each Package (W): 1 ≤ W ≤ 10000 Examples: 1) INPUT 5 5 1 1 1 2 1 OUTPUT 2 Explanation: There are 5 movers, and doesn't matter what the split is, one mover needs to carry at least 2 kilograms 2) INPUT 2 4 5 10 21 20 OUTPUT 36 Explanation: 36 is the best case among all the splits possible (happens when the first guy picks 5, 10 and 21) SAMPLE INPUT 2 5 200 25 974 564 429 SAMPLE OUTPUT 1199 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a string of length N. Calculate the number of distinct substrings of S. Constraints * 1 \leq N \leq 500,000 * S consists of lowercase English letters. Input Input is given from Standard Input in the following format: S Output Print the answer. Examples Input abcbcba Output 21 Input mississippi Output 53 Input ababacaca Output 33 Input aaaaa Output 5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given is an integer S. Find a combination of six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfies all of the following conditions: * 0 \leq X_1,Y_1,X_2,Y_2,X_3,Y_3 \leq 10^9 * The area of the triangle in a two-dimensional plane whose vertices are (X_1,Y_1),(X_2,Y_2), and (X_3,Y_3) is S/2. We can prove that there always exist six integers that satisfy the conditions under the constraints of this problem. Constraints * 1 \leq S \leq 10^{18} * All values in input are integers. Input Input is given from Standard Input in the following format: S Output Print six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfy the conditions, in this order, with spaces in between. If multiple solutions exist, any of them will be accepted. Examples Input 3 Output 1 0 2 2 0 1 Input 100 Output 0 0 10 0 0 10 Input 311114770564041497 Output 314159265 358979323 846264338 327950288 419716939 937510582 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A serious incident happened at Taro's house, which loves steamed buns. One of the three steamed buns offered at the Buddhist altar in the Japanese-style room was gone. When Taro, who was aiming for a snack someday, started an investigation to find the criminal, it turned out that there were many people who entered the Japanese-style room that day. So I decided to ask everyone to give the following form of testimony to find out the order in which these suspects entered the room. Suspect A's testimony "I entered the room before Suspect B." One of the suspects (?) Is a calico cat, so I can't testify, but fortunately Taro saw the last time he entered the room. From these testimonies, Taro decided to guess the order in which he entered the room and use it for the investigation. For example, if there are 6 suspects and Tama is suspect 2, the following testimony is obtained. Testimony of Suspect 5 "I entered the room before 2." Suspect 1's testimony "I entered the room before 4." Testimony of Suspect 3 "I entered the room before 5." Suspect 4's testimony "I entered the room before 2." Suspect 1's testimony "I entered the room before 6." Suspect 6's testimony "I entered the room before 4." Testimony of Suspect 3 "I entered the room before 4." Putting this testimony together, the order in which they entered the room * 3 → 5 → 1 → 6 → 4 → 2 * 1 → 6 → 3 → 4 → 5 → 2 * 3 → 1 → 6 → 5 → 4 → 2 You can narrow down to several possibilities. From the testimony of all suspects except Tama (Suspect 2), estimate the order in which they entered the room and write a program that outputs one of the possible orders. However, although some suspects may give multiple testimonies, all testimonies shall be true and consistent. Input The input is given in the following format: m n x1 y1 x2 y2 :: xn yn The first line gives the number of suspects m (m ≤ 20), and the second line gives the number of testimonies n (n ≤ 100). The following n lines are given the contents of the i-th testimony, xi and yi, respectively, on the first line. xi yi represents the testimony that "suspect xi (I) entered before suspect yi". Output Print the number of the suspect who entered the room first, the number of the suspect who entered the room second, ..., and the number of the suspect who entered the room second, in order on one line. Example Input 6 7 5 2 1 4 3 5 4 2 1 6 6 4 3 4 Output 3 5 1 6 4 2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. To get on the Shinkansen, you need two tickets, a "ticket" and a "limited express ticket". These are separate tickets because some of the routes may not use the Shinkansen, but for routes that use only the Shinkansen, one ticket can be used as both a ticket and a limited express ticket. It may also be issued. Automatic ticket gates must read these tickets and open the gate only when the correct ticket is inserted. Create a program that determines whether one "ticket" and one "limited express ticket" or both, or one "boarding / limited express ticket" has been inserted, and determines whether the door of the automatic ticket gate is open or closed. please do it. input The input is given in the following format. b1 b2 b3 The input consists of one line and contains three integers separated by one space. b1 indicates the state in which the "ticket" is inserted, b2 indicates the state in which the "limited express ticket" is inserted, and b3 indicates the state in which the "boarding / limited express ticket" is inserted. The turned-in state is represented by 0 or 1, where 0 indicates a non-charged state, and 1 indicates a loaded state. However, the combination of expected input states is limited to the following cases. Input \| Input state \| Door operation for input --- \| --- \| --- 1 0 0 \| Insert only "ticket" \| Close 0 1 0 \| Only "Limited Express Ticket" is introduced \| Close 1 1 0 \| Introducing "tickets" and "express tickets" \| Open 0 0 1 \| Introducing "Boarding / Limited Express Tickets" \| Open 0 0 0 \| No input \| Close output Outputs Open or Close, which indicates the opening and closing of the automatic ticket gate, on one line. Example Input 0 0 1 Output Open The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. problem You are in charge of quality control at a machine manufacturing plant. This machine requires a power supply, a motor, and a cable as parts. The manufacturing plant has a power supply, b motors, and c cables, numbered from 1 to a, a + 1 to a + b, and a + b + 1 to a + b + c, respectively. attached. The trouble is that some parts may be out of order. I want to know which parts are out of order and which parts are normal in the factory. Therefore, the factory inspected the parts by the following method. Bring the power supply, motor, and cable one by one, connect them, and try to operate them. At this time, if all three parts are normal, it operates correctly and is recognized as "passed". If any of the three parts is out of order, it will not operate properly and will be recognized as "failed". (Since the machines made in the factory are so precise, it does not happen that the broken parts are mixed and operate correctly by accident.) You will be given a list of test results. Each line in the list of test results shows the numbers of the power supply, motor, and cable used for the test, and whether the test passed or failed. Given a list of inspection results, all parts are either faulty or normal from the inspection results, some are definitely faulty, some are definitely normal. Create a program to classify parts that are not decided. input The input consists of multiple datasets. The format of each data set is as follows. The input ends on a line containing three zeros. Three integers are written on the first line, separated by blanks, and represent the number of power supplies a, the number of motors b, and the number of cables c in order. One integer is written on the second line, and the number of tests N included in the list of test results is written. The next N lines represent a list of test results. On each line, four integers i, j, k, r are written with one blank as a delimiter, and the result of inspection by connecting the power supply i, the motor j, and the cable k is "pass" (r = 1). (When) or "Fail" (when r = 0). a, b, c, N satisfy 1 ≤ a, b, c ≤ 100, 1 ≤ N ≤ 1000. The number of datasets does not exceed 5. output Output in the following format for each data set. The output of each dataset consists of lines a + b + c. Line i (1 ≤ i ≤ a + b + c): * If the inspection result shows that the part i is out of order, 0 is output. * If the inspection result shows that the part i is normal, 1 is output. * Output 2 if the inspection result does not determine whether part i is defective or normal. Examples Input 2 2 2 4 2 4 5 0 2 3 6 0 1 4 5 0 2 3 5 1 0 0 0 Output 2 1 1 0 1 0 Input None Output None The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In order to participate in the Asian Regional Qualifiers of the International Collegiate Programming Contest held every year in Japan, we must break through the strict domestic qualifiers. Even though it is a university competition, multiple teams from one school will participate. Therefore, the following selection rules apply to the selection of breakthrough teams so that as many schools as possible can participate in the Asian Qualifiers: Let A be the team and apply the following rules in order of best grade: * Rule 1: If the number of selected teams at that time is less than 10: If the number of teams in the same affiliation as A and selected at that time is less than 3, A will be selected. * Rule 2: If the number of selected teams at that time is less than 20: If the number of teams in the same affiliation as A and selected at that time is less than 2, A will be selected. * Rule 3: If the number of selected teams at that time is less than 26: If there is no team in the same affiliation as A and selected at that time, A will be selected. In addition, the order of grades is determined by the following rules: * The team that solved more problems will be ranked higher. * If the number of problems solved is the same, the team with the smaller penalty will be ranked higher. Enter the ID (integer), affiliation (integer), number of correct answers (integer), and penalty (integer) of each team, and create a program that outputs the ID of the selected team in the order of selection. Please note that teams are not always given in order of grade, so selection rules must be applied after ranking. In this question, if there is a team with the same number of correct answers and the same penalty, the one with the smaller ID will be ranked higher. Input Multiple datasets are given as input. Each dataset is given in the following format: n (number of teams: integer) I1 U1 A1 P1 (ID of first team, affiliation, number of correct answers, penalty: 4 integers separated by blanks) I2 U2 A2 P2 (ID of second team, affiliation, number of correct answers, penalty: 4 integers separated by blanks) .. .. In Un An Pn (ID of nth team, affiliation, number of correct answers, penalty: 4 integers separated by blanks) n is 300 or less, and Ii and Ui are 1 or more and 1000 or less. You can assume that there are no teams with the same ID in a dataset. Ai should be 10 or less and Pi should be 100,000 or less. When n is 0, it is the end of input. Output For each dataset, output the IDs of the selected teams in the order in which they were selected. Please output one ID on one line. Example Input 6 1 1 6 200 2 1 6 300 3 1 6 400 4 2 5 1200 5 1 5 1400 6 3 4 800 3 777 1 5 300 808 2 4 20 123 3 6 500 2 2 1 3 100 1 1 3 100 0 Output 1 2 3 4 6 123 777 808 1 2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Tax Rate Changed VAT (value-added tax) is a tax imposed at a certain rate proportional to the sale price. Our store uses the following rules to calculate the after-tax prices. * When the VAT rate is x%, for an item with the before-tax price of p yen, its after-tax price of the item is p (100+x) / 100 yen, fractions rounded off. * The total after-tax price of multiple items paid at once is the sum of after-tax prices of the items. The VAT rate is changed quite often. Our accountant has become aware that "different pairs of items that had the same total after-tax price may have different total after-tax prices after VAT rate changes." For example, when the VAT rate rises from 5% to 8%, a pair of items that had the total after-tax prices of 105 yen before can now have after-tax prices either of 107, 108, or 109 yen, as shown in the table below. Before-tax prices of two items\| After-tax price with 5% VAT\| After-tax price with 8% VAT ---\|---\|--- 20, 80\| 21 + 84 = 105\| 21 + 86 = 107 2, 99\| 2 + 103 = 105\| 2 + 106 = 108 13, 88\| 13 + 92 = 105\| 14 + 95 = 109 Our accountant is examining effects of VAT-rate changes on after-tax prices. You are asked to write a program that calculates the possible maximum total after-tax price of two items with the new VAT rate, knowing their total after-tax price before the VAT rate change. Input The input consists of multiple datasets. Each dataset is in one line, which consists of three integers x, y, and s separated by a space. x is the VAT rate in percent before the VAT-rate change, y is the VAT rate in percent after the VAT-rate change, and s is the sum of after-tax prices of two items before the VAT-rate change. For these integers, 0 < x < 100, 0 < y < 100, 10 < s < 1000, and x ≠ y hold. For before-tax prices of items, all possibilities of 1 yen through s-1 yen should be considered. The end of the input is specified by three zeros separated by a space. Output For each dataset, output in a line the possible maximum total after-tax price when the VAT rate is changed to y%. Sample Input 5 8 105 8 5 105 1 2 24 99 98 24 12 13 26 1 22 23 1 13 201 13 16 112 2 24 50 1 82 61 1 84 125 1 99 999 99 1 999 98 99 999 1 99 11 99 1 12 0 0 0 Output for the Sample Input 109 103 24 24 26 27 225 116 62 111 230 1972 508 1004 20 7 Hints In the following table, an instance of a before-tax price pair that has the maximum after-tax price after the VAT-rate change is given for each dataset of the sample input. Dataset\| Before-tax prices\| After-tax price with y% VAT ---\|---\|--- 5 8 105 \| 13, 88\| 14 + 95 = 109 8 5 105 \| 12, 87\| 12 + 91 = 103 1 2 24 \| 1, 23\| 1 + 23 = 24 99 98 24 \| 1, 12\| 1 + 23 = 24 12 13 26 \| 1, 23\| 1 + 25 = 26 1 22 23 \| 1, 22\| 1 + 26 = 27 1 13 201 \| 1,199\| 1 +224 = 225 13 16 112\| 25, 75\| 29 + 87 = 116 2 24 50 \| 25, 25\| 31 + 31 = 62 1 82 61 \| 11, 50\| 20 + 91 = 111 1 84 125 \| 50, 75\| 92 +138 = 230 1 99 999 \| 92,899\| 183+1789 =1972 99 1 999 \| 1,502\| 1 +507 = 508 98 99 999\| 5,500\| 9 +995 =1004 1 99 11 \| 1, 10\| 1 + 19 = 20 99 1 12 \| 1, 6\| 1 + 6 = 7 Example Input 5 8 105 8 5 105 1 2 24 99 98 24 12 13 26 1 22 23 1 13 201 13 16 112 2 24 50 1 82 61 1 84 125 1 99 999 99 1 999 98 99 999 1 99 11 99 1 12 0 0 0 Output 109 103 24 24 26 27 225 116 62 111 230 1972 508 1004 20 7 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. We will define Ginkgo numbers and multiplication on Ginkgo numbers. A Ginkgo number is a pair <m, n> where m and n are integers. For example, <1, 1>, <-2, 1> and <-3,-1> are Ginkgo numbers. The multiplication on Ginkgo numbers is defined by <m, n> * <x, y> = <mx − ny, my + nx>. For example, <1, 1> * <-2, 1> = <-3,-1>. A Ginkgo number <m, n> is called a divisor of a Ginkgo number <p, q> if there exists a Ginkgo number <x, y> such that <m, n> * <x, y> = <p, q>. For any Ginkgo number <m, n>, Ginkgo numbers <1, 0>, <0, 1>, <-1, 0>, <0,-1>, <m, n>, <-n,m>, <-m,-n> and <n,-m> are divisors of <m, n>. If m2+n2 > 1, these Ginkgo numbers are distinct. In other words, any Ginkgo number such that m2 + n2 > 1 has at least eight divisors. A Ginkgo number <m, n> is called a prime if m2+n2 > 1 and it has exactly eight divisors. Your mission is to check whether a given Ginkgo number is a prime or not. The following two facts might be useful to check whether a Ginkgo number is a divisor of another Ginkgo number. * Suppose m2 + n2 > 0. Then, <m, n> is a divisor of <p, q> if and only if the integer m2 + n2 is a common divisor of mp + nq and mq − np. * If <m, n> * <x, y> = <p, q>, then (m2 + n2)(x2 + y2) = p2 + q2. Input The first line of the input contains a single integer, which is the number of datasets. The rest of the input is a sequence of datasets. Each dataset is a line containing two integers m and n, separated by a space. They designate the Ginkgo number <m, n>. You can assume 1 < m2 + n2 < 20000. Output For each dataset, output a character 'P' in a line if the Ginkgo number is a prime. Output a character 'C' in a line otherwise. Example Input 8 10 0 0 2 -3 0 4 2 0 -13 -4 1 -2 -1 3 -1 Output C C P C C P P C The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Background The site of Mr. A's house, which lives in a certain city, is surrounded by white walls. Feeling unsatisfied with the wall, Mr. A decided to invite the children in the neighborhood to paint the wall freely. Ask the children to choose their favorite section of the wall and paint it. So how was the wall painted? Problem There is a circular white wall as shown below, which consists of sections 0 to N-1. Figure 1 M children specify the starting position a of this wall and the length L from the starting position, and paint counterclockwise from a to (a + L) mod N (however, a mod N is Represents the remainder when a is divided by N). Here, it is possible to paint over the section painted by another person, in which case it is regarded as one section painted with color. Output the colored sections in descending order. Also, output at the same time how many sections of that size are. Constrains Input meets the following conditions * 2 ≤ N ≤ 100 * 1 ≤ M ≤ 50 * 0 ≤ ai <N * 1 ≤ Li ≤ N Input The input is given in the following format. N M a0 L0 a1 L1 ... aM−1 LM−1 The first line is given two integers N, M, separated by blanks, which represent the length of the wall and the number of people who paint the wall, respectively. The following M line is given the start position ai and the length Li of the section to be painted by each person. Output The length of the colored section and the total number of the lengths are output in descending order of the colored section. Examples Input 5 3 0 1 2 1 3 1 Output 2 1 1 1 Input 4 2 0 2 1 2 Output 3 1 Input 10 3 2 1 4 1 9 2 Output 2 1 1 2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Everlasting Sa-Ga, a new, hot and very popular role-playing game, is out on October 19, 2008. Fans have been looking forward to a new title of Everlasting Sa-Ga. Little Jimmy is in trouble. He is a seven-year-old boy, and he obtained the Everlasting Sa-Ga and is attempting to reach the end of the game before his friends. However, he is facing difficulty solving the riddle of the first maze in this game -- Everlasting Sa-Ga is notorious in extremely hard riddles like Neverending Fantasy and Forever Quest. The riddle is as follows. There are two doors on the last floor of the maze: the door to the treasure repository and the gate to the hell. If he wrongly opens the door to the hell, the game is over and his save data will be deleted. Therefore, he should never open the wrong door. So now, how can he find the door to the next stage? There is a positive integer given for each door -- it is a great hint to this riddle. The door to the treasure repository has the integer that gives the larger key number. The key number of a positive integer n is the largest prime factor minus the total sum of any other prime factors, where the prime factors are the prime numbers that divide into n without leaving a remainder. Note that each prime factor should be counted only once. As an example, suppose there are doors with integers 30 and 20 respectively. Since 30 has three prime factors 2, 3 and 5, its key number is 5 - (2 + 3) = 0. Similarly, since 20 has two prime factors 2 and 5, its key number 20 is 5 - 2 = 3. Jimmy therefore should open the door with 20. Your job is to write a program to help Jimmy by solving this riddle. Input The input is a sequence of datasets. Each dataset consists of a line that contains two integers a and b separated by a space (2 ≤ a, b ≤ 106 ). It is guaranteed that key numbers of these integers are always different. The input is terminated by a line with two zeros. This line is not part of any datasets and thus should not be processed. Output For each dataset, print in a line ‘a’ (without quotes) if the door with the integer a is connected to the treasure repository; print ‘b’ otherwise. No extra space or character is allowed. Example Input 10 15 30 20 0 0 Output a b The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. When Mr. Kay was browsing a certain SNS as usual, the problem that "there are people who can solve IQ150 or more" came to the timeline. Mr. Kay has an IQ of over 150, so he solved the problem in an instant without even looking at it. For him, he doesn't have to work on such a mystery. It is enough to leave it to the computer. problem The following mysterious mathematical formula was written in the problem. * \\ (5 + 3 = 28 \\) * \\ (9 + 1 = 810 \\) * \\ (8 + 6 = 214 \\) * \\ (5 + 4 = 19 \\) * \\ (2 + 2 = 4 \\) * \\ (15 + 8 = 723 \\) * \\ (7 + 9 = -216 \\) * \\ (3 + 0 = 33 \\) When thinking about the above operator \\ (+ \\), for a positive integer \\ (a \\) \\ (x \ geq 0, y \ geq 0 \\) and \\ (x + y =) Find the number of integer pairs \\ (x, y \\) such that a \\). input A positive integer \\ (a \\) is given on one line. output Output the number of pairs \\ ((x, y) \\) that satisfy \\ (a = x + y, x \ geq 0, y \ geq 0 \\) on one line. Constraint * \\ (1 \ leq a \ leq 10 ^ 9 (= 1000000000) \\) Input / output example Input 1 19 Output 1 1 There is one way of \\ (5 + 4 \\). Input 2 twenty two Output 2 2 There are two types: \\ (11 + 11 \\) and \\ (2 + 0 \\). Input 3 1 Output 3 0 \\ (1 + 0 = 11, 0 + 1 = -11 \\). \\ (1 \\) cannot be generated. Input 4 101 Output 4 0 Note that \\ (1 --0 \\) is not \\ (101 \\). Input 5 660233276 Output 5 Four Example Input 19 Output 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. JAG mock qualifying practice session The ACM-ICPC OB / OG Association (Japanese Alumni Group; JAG) has N questions in stock of questions to be asked in the mock contest, and each question is numbered with an integer from 1 to N. Difficulty evaluation and recommendation voting are conducted for each problem. Problem i has a difficulty level of di and a recommendation level of vi. The maximum difficulty level is M. In the next contest, we plan to ask a total of M questions, one for each of the difficulty levels 1 to M. In order to improve the quality of the contest, I would like to select the questions so that the total recommendation level is maximized. However, since JAG's questioning ability is tremendous, it can be assumed that there is at least one question for each difficulty level. Your job is to create a program that finds the maximum sum of the sums of recommendations when the questions are selected to meet the conditions. Input The input consists of multiple datasets. Each dataset is represented in the following format. > N M > d1 v1 > ... > dN vN > The first line of the dataset is given an integer N, which represents the number of problem stocks, and a maximum difficulty value, M, separated by blanks. These numbers satisfy 1 ≤ M ≤ N ≤ 100. On the i-th line of the following N lines, the integers di and vi representing the difficulty level and recommendation level of problem i are given, separated by blanks. These numbers satisfy 1 ≤ di ≤ M and 0 ≤ vi ≤ 100. Also, for each 1 ≤ j ≤ M, it is guaranteed that there is at least one i such that di = j. > The end of the input is represented by two zeros separated by a blank. Also, the number of datasets does not exceed 50. > ### Output For each data set, output the maximum value of the sum of the recommendation levels of the questions to be asked when one question is asked from each difficulty level on one line. > ### Sample Input 5 3 1 1 twenty three 3 2 3 5 twenty one 4 2 1 7 twenty one 13 1 5 6 1 13 1 2 1 8 1 2 1 7 1 6 20 9 4 10 twenty four 5 3 6 6 6 3 7 4 8 10 4 6 7 5 1 8 5 7 1 5 6 6 9 9 5 8 6 7 14 6 4 7 10 3 5 19 6 4 1 6 5 5 10 1 10 3 10 4 6 twenty three 5 4 2 10 1 8 3 4 3 1 5 4 1 10 13 5 6 5 2 1 10 twenty three 0 0 There are 5 sample datasets, in order Lines 1 to 6 are the first (N = 5, M = 3) test cases, Lines 7 to 11 are the second (N = 4, M = 2) test case, Lines 12-18 are the third (N = 6, M = 1) test case, The fourth (N = 20, M = 9) test case from line 19 to line 39, Lines 40 to 59 represent the fifth test case (N = 19, M = 6). Output for Sample Input 9 8 8 71 51 Example Input 5 3 1 1 2 3 3 2 3 5 2 1 4 2 1 7 2 1 1 3 1 5 6 1 1 3 1 2 1 8 1 2 1 7 1 6 20 9 4 10 2 4 5 3 6 6 6 3 7 4 8 10 4 6 7 5 1 8 5 7 1 5 6 6 9 9 5 8 6 7 1 4 6 4 7 10 3 5 19 6 4 1 6 5 5 10 1 10 3 10 4 6 2 3 5 4 2 10 1 8 3 4 3 1 5 4 1 10 1 3 5 6 5 2 1 10 2 3 0 0 Output 9 8 8 71 51 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Auction square1001 You were watching a certain auction. An auction is a transaction in which when there are a large number of buyers and the number of items is limited, the one with the highest price is given the right to buy. (From the 7th edition of the Shinmei Kokugo Dictionary) The rules of the auction here are as follows. 1. Repeat steps 2 to 6 below until the item is exhausted. 2. Bring out new items and show them to customers 3. One of the customers puts the item at the price they like 4. Price higher than the price currently on the item by one of the customers 5. Repeat step 4 until there are no more customers to perform the action of 4. 6. The customer who puts the highest price on the item wins the bid square1001 You recorded all the prices attached to the items during this auction in chronological order. According to the record, $ N $ items are priced, starting from the beginning with $ A_1, A_2, A_3, \ dots, A_N $. E869120 You are wondering how many items were put up for sale in this auction. square1001 From the list you made, find the minimum and maximum possible number of items for sale in this auction. input Input is given from standard input in the following format. $ N $ $ A_1 $ $ A_2 $ $ A_3 $ $ \ cdots $ $ A_N $ output Please output the minimum and maximum possible number of items listed in this auction in this order, separated by line breaks. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 100000 \ (= 10 ^ 5) $ * $ 1 \ leq A_i \ leq 1000000000 \ (= 10 ^ 9) $ * All inputs are integers. Input example 1 Five 8 6 9 1 20 Output example 1 3 Five When three items are sold in order at price 8, price 9, and price 20, the minimum number of items is 3. Input example 2 6 3 3 4 3 3 4 Output example 2 Four 6 Input example 3 8 5 5 4 4 3 3 2 2 Output example 3 8 8 Example Input 5 8 6 9 1 20 Output 3 5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively. Constraints * $1 \leq N \leq 10^6$ * $1 \leq L \leq 10^6$ * $1 \leq a_i \leq 10^9$ * $L \leq N$ Input The input is given in the following format. $N$ $L$ $a_1$ $a_2$ ... $a_N$ Output Print a sequence of the minimum in a line. Print a space character between adjacent elements. Example Input 7 3 1 7 7 4 8 1 6 Output 1 4 4 1 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Head Chef has received his id from the Association of Byteland . He wants to know the numerical rank of his number among the numbers that can be formed by the exact same digits ( i.e. among numbers having same number of 0's , 1's ... 9's as his id ) . Note that id's can start with 0 . Given a number, find the rank of the number . Input The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. Each test case contains a single integer N denoting the id the chef has received . Output For each test case, output a single line containing the answer to the given test case . Constraints 1 ≤ T ≤ 10000 1 ≤ number of digits in N ≤ 18 Example Input: 2 276 762 Output: 2 6 Explanation Example case 1.The numbers that can be formed with one '2' ; one '7' and one '6' in increasing order are : 267 276 627 672 726 762 The rank for 276 is 2 and rank for 762 is 6. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Panic is rising in the committee for doggo standardization — the puppies of the new brood have been born multi-colored! In total there are 26 possible colors of puppies in the nature and they are denoted by letters from 'a' to 'z' inclusive. The committee rules strictly prohibit even the smallest diversity between doggos and hence all the puppies should be of the same color. Thus Slava, the committee employee, has been assigned the task to recolor some puppies into other colors in order to eliminate the difference and make all the puppies have one common color. Unfortunately, due to bureaucratic reasons and restricted budget, there's only one operation Slava can perform: he can choose a color x such that there are currently at least two puppies of color x and recolor all puppies of the color x into some arbitrary color y. Luckily, this operation can be applied multiple times (including zero). For example, if the number of puppies is 7 and their colors are represented as the string "abababc", then in one operation Slava can get the results "zbzbzbc", "bbbbbbc", "aaaaaac", "acacacc" and others. However, if the current color sequence is "abababc", then he can't choose x='c' right now, because currently only one puppy has the color 'c'. Help Slava and the committee determine whether it is possible to standardize all the puppies, i.e. after Slava's operations all the puppies should have the same color. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of puppies. The second line contains a string s of length n consisting of lowercase Latin letters, where the i-th symbol denotes the i-th puppy's color. Output If it's possible to recolor all puppies into one color, print "Yes". Otherwise print "No". Output the answer without quotation signs. Examples Input 6 aabddc Output Yes Input 3 abc Output No Input 3 jjj Output Yes Note In the first example Slava can perform the following steps: 1. take all puppies of color 'a' (a total of two) and recolor them into 'b'; 2. take all puppies of color 'd' (a total of two) and recolor them into 'c'; 3. take all puppies of color 'b' (three puppies for now) and recolor them into 'c'. In the second example it's impossible to recolor any of the puppies. In the third example all the puppies' colors are the same; thus there's no need to recolor anything. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A conglomerate consists of n companies. To make managing easier, their owners have decided to merge all companies into one. By law, it is only possible to merge two companies, so the owners plan to select two companies, merge them into one, and continue doing so until there is only one company left. But anti-monopoly service forbids to merge companies if they suspect unfriendly absorption. The criterion they use is the difference in maximum salaries between two companies. Merging is allowed only if the maximum salaries are equal. To fulfill the anti-monopoly requirements, the owners can change salaries in their companies before merging. But the labor union insists on two conditions: it is only allowed to increase salaries, moreover all the employees in one company must get the same increase. Sure enough, the owners want to minimize the total increase of all salaries in all companies. Help them find the minimal possible increase that will allow them to merge companies into one. Input The first line contains a single integer n — the number of companies in the conglomerate (1 ≤ n ≤ 2 ⋅ 10^5). Each of the next n lines describes a company. A company description start with an integer m_i — the number of its employees (1 ≤ m_i ≤ 2 ⋅ 10^5). Then m_i integers follow: the salaries of the employees. All salaries are positive and do not exceed 10^9. The total number of employees in all companies does not exceed 2 ⋅ 10^5. Output Output a single integer — the minimal total increase of all employees that allows to merge all companies. Example Input 3 2 4 3 2 2 1 3 1 1 1 Output 13 Note One of the optimal merging strategies is the following. First increase all salaries in the second company by 2, and merge the first and the second companies. Now the conglomerate consists of two companies with salaries [4, 3, 4, 3] and [1, 1, 1]. To merge them, increase the salaries in the second of those by 3. The total increase is 2 + 2 + 3 + 3 + 3 = 13. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You went to the store, selling n types of chocolates. There are a_i chocolates of type i in stock. You have unlimited amount of cash (so you are not restricted by any prices) and want to buy as many chocolates as possible. However if you buy x_i chocolates of type i (clearly, 0 ≤ x_i ≤ a_i), then for all 1 ≤ j < i at least one of the following must hold: * x_j = 0 (you bought zero chocolates of type j) * x_j < x_i (you bought less chocolates of type j than of type i) For example, the array x = [0, 0, 1, 2, 10] satisfies the requirement above (assuming that all a_i ≥ x_i), while arrays x = [0, 1, 0], x = [5, 5] and x = [3, 2] don't. Calculate the maximum number of chocolates you can buy. Input The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5), denoting the number of types of chocolate. The next line contains n integers a_i (1 ≤ a_i ≤ 10^9), denoting the number of chocolates of each type. Output Print the maximum number of chocolates you can buy. Examples Input 5 1 2 1 3 6 Output 10 Input 5 3 2 5 4 10 Output 20 Input 4 1 1 1 1 Output 1 Note In the first example, it is optimal to buy: 0 + 0 + 1 + 3 + 6 chocolates. In the second example, it is optimal to buy: 1 + 2 + 3 + 4 + 10 chocolates. In the third example, it is optimal to buy: 0 + 0 + 0 + 1 chocolates. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given two integers x and y (it is guaranteed that x > y). You may choose any prime integer p and subtract it any number of times from x. Is it possible to make x equal to y? Recall that a prime number is a positive integer that has exactly two positive divisors: 1 and this integer itself. The sequence of prime numbers starts with 2, 3, 5, 7, 11. Your program should solve t independent test cases. Input The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t lines follow, each describing a test case. Each line contains two integers x and y (1 ≤ y < x ≤ 10^{18}). Output For each test case, print YES if it is possible to choose a prime number p and subtract it any number of times from x so that x becomes equal to y. Otherwise, print NO. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes, and YES will all be recognized as positive answer). Example Input 4 100 98 42 32 1000000000000000000 1 41 40 Output YES YES YES NO Note In the first test of the example you may choose p = 2 and subtract it once. In the second test of the example you may choose p = 5 and subtract it twice. Note that you cannot choose p = 7, subtract it, then choose p = 3 and subtract it again. In the third test of the example you may choose p = 3 and subtract it 333333333333333333 times. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a permutation of length n. Recall that the permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2, 3, 1, 5, 4] is a permutation, but [1, 2, 2] is not a permutation (2 appears twice in the array) and [1, 3, 4] is also not a permutation (n=3 but there is 4 in the array). You can perform at most n-1 operations with the given permutation (it is possible that you don't perform any operations at all). The i-th operation allows you to swap elements of the given permutation on positions i and i+1. Each operation can be performed at most once. The operations can be performed in arbitrary order. Your task is to find the lexicographically minimum possible permutation obtained by performing some of the given operations in some order. You can see the definition of the lexicographical order in the notes section. You have to answer q independent test cases. For example, let's consider the permutation [5, 4, 1, 3, 2]. The minimum possible permutation we can obtain is [1, 5, 2, 4, 3] and we can do it in the following way: 1. perform the second operation (swap the second and the third elements) and obtain the permutation [5, 1, 4, 3, 2]; 2. perform the fourth operation (swap the fourth and the fifth elements) and obtain the permutation [5, 1, 4, 2, 3]; 3. perform the third operation (swap the third and the fourth elements) and obtain the permutation [5, 1, 2, 4, 3]. 4. perform the first operation (swap the first and the second elements) and obtain the permutation [1, 5, 2, 4, 3]; Another example is [1, 2, 4, 3]. The minimum possible permutation we can obtain is [1, 2, 3, 4] by performing the third operation (swap the third and the fourth elements). Input The first line of the input contains one integer q (1 ≤ q ≤ 100) — the number of test cases. Then q test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 100) — the number of elements in the permutation. The second line of the test case contains n distinct integers from 1 to n — the given permutation. Output For each test case, print the answer on it — the lexicograhically minimum possible permutation obtained by performing some of the given operations in some order. Example Input 4 5 5 4 1 3 2 4 1 2 4 3 1 1 4 4 3 2 1 Output 1 5 2 4 3 1 2 3 4 1 1 4 3 2 Note Recall that the permutation p of length n is lexicographically less than the permutation q of length n if there is such index i ≤ n that for all j from 1 to i - 1 the condition p_j = q_j is satisfied, and p_i < q_i. For example: * p = [1, 3, 5, 2, 4] is less than q = [1, 3, 5, 4, 2] (such i=4 exists, that p_i < q_i and for each j < i holds p_j = q_j), * p = [1, 2] is less than q = [2, 1] (such i=1 exists, that p_i < q_i and for each j < i holds p_j = q_j). The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There is a very secret base in Potatoland where potato mash is made according to a special recipe. The neighbours from Porridgia decided to seize this recipe and to sell it to Pilauland. For this mission they have been preparing special agent Pearlo for many years. When, finally, Pearlo learned all secrets of espionage, he penetrated into the Potatoland territory and reached the secret base. Now he is standing at the entrance, but to get inside he need to pass combination lock. Minute ago one of the workers entered the password on the terminal and opened the door. The terminal is a square digital keyboard 3 × 3 with digits from 1 to 9. Pearlo knows that the password consists from distinct digits and is probably symmetric with respect to the central button of the terminal. He has heat sensor which allowed him to detect the digits which the worker pressed. Now he wants to check whether the password entered by the worker is symmetric with respect to the central button of the terminal. This fact can Help Pearlo to reduce the number of different possible password combinations. Input Input contains the matrix of three rows of three symbols each. Symbol «X» means that the corresponding button was pressed, and «.» means that is was not pressed. The matrix may contain no «X», also it may contain no «.». Output Print YES if the password is symmetric with respect to the central button of the terminal and NO otherwise. Examples Input XX. ... .XX Output YES Input X.X X.. ... Output NO Note If you are not familiar with the term «central symmetry», you may look into http://en.wikipedia.org/wiki/Central_symmetry The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A bracketed sequence is called correct (regular) if by inserting "+" and "1" you can get a well-formed mathematical expression from it. For example, sequences "(())()", "()" and "(()(()))" are correct, while ")(", "(()" and "(()))(" are not. The teacher gave Dmitry's class a very strange task — she asked every student to come up with a sequence of arbitrary length, consisting only of opening and closing brackets. After that all the students took turns naming the sequences they had invented. When Dima's turn came, he suddenly realized that all his classmates got the correct bracketed sequence, and whether he got the correct bracketed sequence, he did not know. Dima suspects now that he simply missed the word "correct" in the task statement, so now he wants to save the situation by modifying his sequence slightly. More precisely, he can the arbitrary number of times (possibly zero) perform the reorder operation. The reorder operation consists of choosing an arbitrary consecutive subsegment (substring) of the sequence and then reordering all the characters in it in an arbitrary way. Such operation takes l nanoseconds, where l is the length of the subsegment being reordered. It's easy to see that reorder operation doesn't change the number of opening and closing brackets. For example for "))((" he can choose the substring ")(" and do reorder ")()(" (this operation will take 2 nanoseconds). Since Dima will soon have to answer, he wants to make his sequence correct as fast as possible. Help him to do this, or determine that it's impossible. Input The first line contains a single integer n (1 ≤ n ≤ 10^6) — the length of Dima's sequence. The second line contains string of length n, consisting of characters "(" and ")" only. Output Print a single integer — the minimum number of nanoseconds to make the sequence correct or "-1" if it is impossible to do so. Examples Input 8 ))((())( Output 6 Input 3 (() Output -1 Note In the first example we can firstly reorder the segment from first to the fourth character, replacing it with "()()", the whole sequence will be "()()())(". And then reorder the segment from the seventh to eighth character, replacing it with "()". In the end the sequence will be "()()()()", while the total time spent is 4 + 2 = 6 nanoseconds. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given a permutation p of length n, find its subsequence s_1, s_2, …, s_k of length at least 2 such that: * \|s_1-s_2\|+\|s_2-s_3\|+…+\|s_{k-1}-s_k\| is as big as possible over all subsequences of p with length at least 2. * Among all such subsequences, choose the one whose length, k, is as small as possible. If multiple subsequences satisfy these conditions, you are allowed to find any of them. A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements. A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once. Input The first line contains an integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows. The first line of each test case contains an integer n (2 ≤ n ≤ 10^5) — the length of the permutation p. The second line of each test case contains n integers p_1, p_2, …, p_{n} (1 ≤ p_i ≤ n, p_i are distinct) — the elements of the permutation p. The sum of n across the test cases doesn't exceed 10^5. Output For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, …, s_k — its elements. If multiple subsequences satisfy these conditions, you are allowed to find any of them. Example Input 2 3 3 2 1 4 1 3 4 2 Output 2 3 1 3 1 4 2 Note In the first test case, there are 4 subsequences of length at least 2: * [3,2] which gives us \|3-2\|=1. * [3,1] which gives us \|3-1\|=2. * [2,1] which gives us \|2-1\|=1. * [3,2,1] which gives us \|3-2\|+\|2-1\|=2. So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Note that the only difference between String Transformation 1 and String Transformation 2 is in the move Koa does. In this version the letter y Koa selects must be strictly greater alphabetically than x (read statement for better understanding). You can make hacks in these problems independently. Koa the Koala has two strings A and B of the same length n (\|A\|=\|B\|=n) consisting of the first 20 lowercase English alphabet letters (ie. from a to t). In one move Koa: 1. selects some subset of positions p_1, p_2, …, p_k (k ≥ 1; 1 ≤ p_i ≤ n; p_i ≠ p_j if i ≠ j) of A such that A_{p_1} = A_{p_2} = … = A_{p_k} = x (ie. all letters on this positions are equal to some letter x). 2. selects a letter y (from the first 20 lowercase letters in English alphabet) such that y>x (ie. letter y is strictly greater alphabetically than x). 3. sets each letter in positions p_1, p_2, …, p_k to letter y. More formally: for each i (1 ≤ i ≤ k) Koa sets A_{p_i} = y. Note that you can only modify letters in string A. Koa wants to know the smallest number of moves she has to do to make strings equal to each other (A = B) or to determine that there is no way to make them equal. Help her! Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10) — the number of test cases. Description of the test cases follows. The first line of each test case contains one integer n (1 ≤ n ≤ 10^5) — the length of strings A and B. The second line of each test case contains string A (\|A\|=n). The third line of each test case contains string B (\|B\|=n). Both strings consists of the first 20 lowercase English alphabet letters (ie. from a to t). It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case: Print on a single line the smallest number of moves she has to do to make strings equal to each other (A = B) or -1 if there is no way to make them equal. Example Input 5 3 aab bcc 4 cabc abcb 3 abc tsr 4 aabd cccd 5 abcbd bcdda Output 2 -1 3 2 -1 Note * In the 1-st test case Koa: 1. selects positions 1 and 2 and sets A_1 = A_2 = b (\color{red}{aa}b → \color{blue}{bb}b). 2. selects positions 2 and 3 and sets A_2 = A_3 = c (b\color{red}{bb} → b\color{blue}{cc}). * In the 2-nd test case Koa has no way to make string A equal B. * In the 3-rd test case Koa: 1. selects position 1 and sets A_1 = t (\color{red}{a}bc → \color{blue}{t}bc). 2. selects position 2 and sets A_2 = s (t\color{red}{b}c → t\color{blue}{s}c). 3. selects position 3 and sets A_3 = r (ts\color{red}{c} → ts\color{blue}{r}). The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given an array of n integers a_1,a_2,...,a_n. You have to create an array of n integers b_1,b_2,...,b_n such that: * The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal. For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a. * For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+⋅⋅⋅+b_knot=0 .$$$ If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 1000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains one integer n (1≤ n≤ 50) — the length of the array a. The second line of each testcase contains n integers a_1,a_2,..., a_n (-50≤ a_i≤ 50) — the elements of a. Output For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO. Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n. If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them. Example Input 4 4 1 -2 3 -4 3 0 0 0 5 1 -1 1 -1 1 6 40 -31 -9 0 13 -40 Output YES 1 -2 3 -4 NO YES 1 1 -1 1 -1 YES -40 13 40 0 -9 -31 Note Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds: * The first element of b is 1. * The sum of the first two elements of b is -1. * The sum of the first three elements of b is 2. * The sum of the first four elements of b is -2. Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO. Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds: * The first element of b is 1. * The sum of the first two elements of b is 2. * The sum of the first three elements of b is 1. * The sum of the first four elements of b is 2. * The sum of the first five elements of b is 1. Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds: * The first element of b is -40. * The sum of the first two elements of b is -27. * The sum of the first three elements of b is 13. * The sum of the first four elements of b is 13. * The sum of the first five elements of b is 4. * The sum of the first six elements of b is -27. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A string b is a subsequence of a string a if b can be obtained from a by deletion of several (possibly, zero or all) characters. For example, "xy" is a subsequence of "xzyw" and "xy", but not "yx". You are given a string a. Your task is to reorder the characters of a so that "trygub" is not a subsequence of the resulting string. In other words, you should find a string b which is a permutation of symbols of the string a and "trygub" is not a subsequence of b. We have a truly marvelous proof that any string can be arranged not to contain "trygub" as a subsequence, but this problem statement is too short to contain it. Input The first line contains a single integer t (1≤ t≤ 100) — the number of test cases. The first line of each test case contains a single integer n (1≤ n≤ 200) — the length of a. The next line contains the string a of length n, consisting of lowercase English letters. Output For each test case, output a string b of length n which is a permutation of characters of the string a, and such that "trygub" is not a subsequence of it. If there exist multiple possible strings b, you can print any. Example Input 3 11 antontrygub 15 bestcoordinator 19 trywatchinggurabruh Output bugyrtnotna bestcoordinator bruhtrywatchinggura Note In the first test case, "bugyrtnotna" does not contain "trygub" as a subsequence. It does contain the letters of "trygub", but not in the correct order, so it is not a subsequence. In the second test case, we did not change the order of characters because it is not needed. In the third test case, "bruhtrywatchinggura" does contain "trygu" as a subsequence, but not "trygub". The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Note that the memory limit is unusual. You are given an integer n and two sequences a_1, a_2, ..., a_n and b_1, b_2, ..., b_n. Let's call a set of integers S such that S ⊆ \{1, 2, 3, ..., n\} strange, if, for every element i of S, the following condition is met: for every j ∈ [1, i - 1], if a_j divides a_i, then j is also included in S. An empty set is always strange. The cost of the set S is ∑_{i ∈ S} b_i. You have to calculate the maximum possible cost of a strange set. Input The first line contains one integer n (1 ≤ n ≤ 3000). The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100). The third line contains n integers b_1, b_2, ..., b_n (-10^5 ≤ b_i ≤ 10^5). Output Print one integer — the maximum cost of a strange set. Examples Input 9 4 7 3 4 5 6 7 8 13 -2 3 -19 5 -6 7 -8 9 1 Output 16 Input 2 42 42 -37 13 Output 0 Input 2 42 42 13 -37 Output 13 Note The strange set with the maximum cost in the first example is \{1, 2, 4, 8, 9\}. The strange set with the maximum cost in the second example is empty. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. What joy! Petya's parents went on a business trip for the whole year and the playful kid is left all by himself. Petya got absolutely happy. He jumped on the bed and threw pillows all day long, until... Today Petya opened the cupboard and found a scary note there. His parents had left him with duties: he should water their favourite flower all year, each day, in the morning, in the afternoon and in the evening. "Wait a second!" — thought Petya. He know for a fact that if he fulfills the parents' task in the i-th (1 ≤ i ≤ 12) month of the year, then the flower will grow by ai centimeters, and if he doesn't water the flower in the i-th month, then the flower won't grow this month. Petya also knows that try as he might, his parents won't believe that he has been watering the flower if it grows strictly less than by k centimeters. Help Petya choose the minimum number of months when he will water the flower, given that the flower should grow no less than by k centimeters. Input The first line contains exactly one integer k (0 ≤ k ≤ 100). The next line contains twelve space-separated integers: the i-th (1 ≤ i ≤ 12) number in the line represents ai (0 ≤ ai ≤ 100). Output Print the only integer — the minimum number of months when Petya has to water the flower so that the flower grows no less than by k centimeters. If the flower can't grow by k centimeters in a year, print -1. Examples Input 5 1 1 1 1 2 2 3 2 2 1 1 1 Output 2 Input 0 0 0 0 0 0 0 0 1 1 2 3 0 Output 0 Input 11 1 1 4 1 1 5 1 1 4 1 1 1 Output 3 Note Let's consider the first sample test. There it is enough to water the flower during the seventh and the ninth month. Then the flower grows by exactly five centimeters. In the second sample Petya's parents will believe him even if the flower doesn't grow at all (k = 0). So, it is possible for Petya not to water the flower at all. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. <image> William really likes the cellular automaton called "Game of Life" so he decided to make his own version. For simplicity, William decided to define his cellular automaton on an array containing n cells, with each cell either being alive or dead. Evolution of the array in William's cellular automaton occurs iteratively in the following way: * If the element is dead and it has exactly 1 alive neighbor in the current state of the array, then on the next iteration it will become alive. For an element at index i the neighbors would be elements with indices i - 1 and i + 1. If there is no element at that index, it is considered to be a dead neighbor. * William is a humane person so all alive elements stay alive. Check the note section for examples of the evolution. You are given some initial state of all elements and you need to help William find the state of the array after m iterations of evolution. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^3). Description of the test cases follows. The first line of each test case contains two integers n and m (2 ≤ n ≤ 10^3, 1 ≤ m ≤ 10^9), which are the total number of cells in the array and the number of iterations. The second line of each test case contains a string of length n made up of characters "0" and "1" and defines the initial state of the array. "1" means a cell is alive and "0" means it is dead. It is guaranteed that the sum of n over all test cases does not exceed 10^4. Output In each test case output a string of length n, made up of characters "0" and "1" — the state of the array after m iterations of evolution. Example Input 4 11 3 01000000001 10 2 0110100101 5 2 10101 3 100 000 Output 11111001111 1110111101 10101 000 Note Sequence of iterations of evolution for the first test case * 01000000001 — initial state * 11100000011 — first iteration of evolution * 11110000111 — second iteration of evolution * 11111001111 — third iteration of evolution Sequence of iterations of evolution for the second test case * 0110100101 — initial state * 1110111101 — first iteration of evolution * 1110111101 — second iteration of evolution The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has n pebbles. He arranges them in a equal rows, each row has b pebbles (a > 1). Note that the Beaver must use all the pebbles he has, i. e. n = a·b. <image> 10 pebbles are arranged in two rows, each row has 5 pebbles Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, b pebbles) and discards all other pebbles. Then he arranges all his pebbles again (possibly choosing other values of a and b) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. The game process can be represented as a finite sequence of integers c1, ..., ck, where: * c1 = n * ci + 1 is the number of pebbles that the Beaver ends up with after the i-th move, that is, the number of pebbles in a row after some arrangement of ci pebbles (1 ≤ i < k). Note that ci > ci + 1. * ck = 1 The result of the game is the sum of numbers ci. You are given n. Find the maximum possible result of the game. Input The single line of the input contains a single integer n — the initial number of pebbles the Smart Beaver has. The input limitations for getting 30 points are: * 2 ≤ n ≤ 50 The input limitations for getting 100 points are: * 2 ≤ n ≤ 109 Output Print a single number — the maximum possible result of the game. Examples Input 10 Output 16 Input 8 Output 15 Note Consider the first example (c1 = 10). The possible options for the game development are: * Arrange the pebbles in 10 rows, one pebble per row. Then c2 = 1, and the game ends after the first move with the result of 11. * Arrange the pebbles in 5 rows, two pebbles per row. Then c2 = 2, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. c3 = 1, and the game ends with the result of 13. * Finally, arrange the pebbles in two rows, five pebbles per row. The same logic leads us to c2 = 5, c3 = 1, and the game ends with the result of 16 — the maximum possible result. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high. At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into k bacteria. After that some abnormal effects create b more bacteria in the test tube. Thus, if at the beginning of some second the test tube had x bacteria, then at the end of the second it will have kx + b bacteria. The experiment showed that after n seconds there were exactly z bacteria and the experiment ended at this point. For the second experiment Qwerty is going to sterilize the test tube and put there t bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least z bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. Help Qwerty and find the minimum number of seconds needed to get a tube with at least z bacteria in the second experiment. Input The first line contains four space-separated integers k, b, n and t (1 ≤ k, b, n, t ≤ 106) — the parameters of bacterial growth, the time Qwerty needed to grow z bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly. Output Print a single number — the minimum number of seconds Qwerty needs to grow at least z bacteria in the tube. Examples Input 3 1 3 5 Output 2 Input 1 4 4 7 Output 3 Input 2 2 4 100 Output 0 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Little Elephant loves numbers. He has a positive integer x. The Little Elephant wants to find the number of positive integers d, such that d is the divisor of x, and x and d have at least one common (the same) digit in their decimal representations. Help the Little Elephant to find the described number. Input A single line contains a single integer x (1 ≤ x ≤ 109). Output In a single line print an integer — the answer to the problem. Examples Input 1 Output 1 Input 10 Output 2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Iahub is a big fan of tourists. He wants to become a tourist himself, so he planned a trip. There are n destinations on a straight road that Iahub wants to visit. Iahub starts the excursion from kilometer 0. The n destinations are described by a non-negative integers sequence a1, a2, ..., an. The number ak represents that the kth destination is at distance ak kilometers from the starting point. No two destinations are located in the same place. Iahub wants to visit each destination only once. Note that, crossing through a destination is not considered visiting, unless Iahub explicitly wants to visit it at that point. Also, after Iahub visits his last destination, he doesn't come back to kilometer 0, as he stops his trip at the last destination. The distance between destination located at kilometer x and next destination, located at kilometer y, is \|x - y\| kilometers. We call a "route" an order of visiting the destinations. Iahub can visit destinations in any order he wants, as long as he visits all n destinations and he doesn't visit a destination more than once. Iahub starts writing out on a paper all possible routes and for each of them, he notes the total distance he would walk. He's interested in the average number of kilometers he would walk by choosing a route. As he got bored of writing out all the routes, he asks you to help him. Input The first line contains integer n (2 ≤ n ≤ 105). Next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ 107). Output Output two integers — the numerator and denominator of a fraction which is equal to the wanted average number. The fraction must be irreducible. Examples Input 3 2 3 5 Output 22 3 Note Consider 6 possible routes: * [2, 3, 5]: total distance traveled: \|2 – 0\| + \|3 – 2\| + \|5 – 3\| = 5; * [2, 5, 3]: \|2 – 0\| + \|5 – 2\| + \|3 – 5\| = 7; * [3, 2, 5]: \|3 – 0\| + \|2 – 3\| + \|5 – 2\| = 7; * [3, 5, 2]: \|3 – 0\| + \|5 – 3\| + \|2 – 5\| = 8; * [5, 2, 3]: \|5 – 0\| + \|2 – 5\| + \|3 – 2\| = 9; * [5, 3, 2]: \|5 – 0\| + \|3 – 5\| + \|2 – 3\| = 8. The average travel distance is <image> = <image> = <image>. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with n vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2." Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to k? Input The first line contains a single integer k (1 ≤ k ≤ 109). Output You should output a graph G with n vertexes (2 ≤ n ≤ 1000). There must be exactly k shortest paths between vertex 1 and vertex 2 of the graph. The first line must contain an integer n. Then adjacency matrix G with n rows and n columns must follow. Each element of the matrix must be 'N' or 'Y'. If Gij is 'Y', then graph G has a edge connecting vertex i and vertex j. Consider the graph vertexes are numbered from 1 to n. The graph must be undirected and simple: Gii = 'N' and Gij = Gji must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them. Examples Input 2 Output 4 NNYY NNYY YYNN YYNN Input 9 Output 8 NNYYYNNN NNNNNYYY YNNNNYYY YNNNNYYY YNNNNYYY NYYYYNNN NYYYYNNN NYYYYNNN Input 1 Output 2 NY YN Note In first example, there are 2 shortest paths: 1-3-2 and 1-4-2. In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The hero of the Cut the Rope game is a little monster named Om Nom. He loves candies. And what a coincidence! He also is the hero of today's problem. <image> One day, Om Nom visited his friend Evan. Evan has n candies of two types (fruit drops and caramel drops), the i-th candy hangs at the height of hi centimeters above the floor of the house, its mass is mi. Om Nom wants to eat as many candies as possible. At the beginning Om Nom can make at most x centimeter high jumps. When Om Nom eats a candy of mass y, he gets stronger and the height of his jump increases by y centimeters. What maximum number of candies can Om Nom eat if he never eats two candies of the same type in a row (Om Nom finds it too boring)? Input The first line contains two integers, n and x (1 ≤ n, x ≤ 2000) — the number of sweets Evan has and the initial height of Om Nom's jump. Each of the following n lines contains three integers ti, hi, mi (0 ≤ ti ≤ 1; 1 ≤ hi, mi ≤ 2000) — the type, height and the mass of the i-th candy. If number ti equals 0, then the current candy is a caramel drop, otherwise it is a fruit drop. Output Print a single integer — the maximum number of candies Om Nom can eat. Examples Input 5 3 0 2 4 1 3 1 0 8 3 0 20 10 1 5 5 Output 4 Note One of the possible ways to eat 4 candies is to eat them in the order: 1, 5, 3, 2. Let's assume the following scenario: 1. Initially, the height of Om Nom's jump equals 3. He can reach candies 1 and 2. Let's assume that he eats candy 1. As the mass of this candy equals 4, the height of his jump will rise to 3 + 4 = 7. 2. Now Om Nom can reach candies 2 and 5. Let's assume that he eats candy 5. Then the height of his jump will be 7 + 5 = 12. 3. At this moment, Om Nom can reach two candies, 2 and 3. He won't eat candy 2 as its type matches the type of the previously eaten candy. Om Nom eats candy 3, the height of his jump is 12 + 3 = 15. 4. Om Nom eats candy 2, the height of his jump is 15 + 1 = 16. He cannot reach candy 4. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Student Valera is an undergraduate student at the University. His end of term exams are approaching and he is to pass exactly n exams. Valera is a smart guy, so he will be able to pass any exam he takes on his first try. Besides, he can take several exams on one day, and in any order. According to the schedule, a student can take the exam for the i-th subject on the day number ai. However, Valera has made an arrangement with each teacher and the teacher of the i-th subject allowed him to take an exam before the schedule time on day bi (bi < ai). Thus, Valera can take an exam for the i-th subject either on day ai, or on day bi. All the teachers put the record of the exam in the student's record book on the day of the actual exam and write down the date of the mark as number ai. Valera believes that it would be rather strange if the entries in the record book did not go in the order of non-decreasing date. Therefore Valera asks you to help him. Find the minimum possible value of the day when Valera can take the final exam if he takes exams so that all the records in his record book go in the order of non-decreasing date. Input The first line contains a single positive integer n (1 ≤ n ≤ 5000) — the number of exams Valera will take. Each of the next n lines contains two positive space-separated integers ai and bi (1 ≤ bi < ai ≤ 109) — the date of the exam in the schedule and the early date of passing the i-th exam, correspondingly. Output Print a single integer — the minimum possible number of the day when Valera can take the last exam if he takes all the exams so that all the records in his record book go in the order of non-decreasing date. Examples Input 3 5 2 3 1 4 2 Output 2 Input 3 6 1 5 2 4 3 Output 6 Note In the first sample Valera first takes an exam in the second subject on the first day (the teacher writes down the schedule date that is 3). On the next day he takes an exam in the third subject (the teacher writes down the schedule date, 4), then he takes an exam in the first subject (the teacher writes down the mark with date 5). Thus, Valera takes the last exam on the second day and the dates will go in the non-decreasing order: 3, 4, 5. In the second sample Valera first takes an exam in the third subject on the fourth day. Then he takes an exam in the second subject on the fifth day. After that on the sixth day Valera takes an exam in the first subject. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Ohana Matsumae is trying to clean a room, which is divided up into an n by n grid of squares. Each square is initially either clean or dirty. Ohana can sweep her broom over columns of the grid. Her broom is very strange: if she sweeps over a clean square, it will become dirty, and if she sweeps over a dirty square, it will become clean. She wants to sweep some columns of the room to maximize the number of rows that are completely clean. It is not allowed to sweep over the part of the column, Ohana can only sweep the whole column. Return the maximum number of rows that she can make completely clean. Input The first line of input will be a single integer n (1 ≤ n ≤ 100). The next n lines will describe the state of the room. The i-th line will contain a binary string with n characters denoting the state of the i-th row of the room. The j-th character on this line is '1' if the j-th square in the i-th row is clean, and '0' if it is dirty. Output The output should be a single line containing an integer equal to a maximum possible number of rows that are completely clean. Examples Input 4 0101 1000 1111 0101 Output 2 Input 3 111 111 111 Output 3 Note In the first sample, Ohana can sweep the 1st and 3rd columns. This will make the 1st and 4th row be completely clean. In the second sample, everything is already clean, so Ohana doesn't need to do anything. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 ≤ i ≤ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order. Help Kefa cope with this task! Input The first line contains integer n (1 ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109). Output Print a single integer — the length of the maximum non-decreasing subsegment of sequence a. Examples Input 6 2 2 1 3 4 1 Output 3 Input 3 2 2 9 Output 3 Note In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one. In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. One day student Vasya was sitting on a lecture and mentioned a string s1s2... sn, consisting of letters "a", "b" and "c" that was written on his desk. As the lecture was boring, Vasya decided to complete the picture by composing a graph G with the following properties: * G has exactly n vertices, numbered from 1 to n. * For all pairs of vertices i and j, where i ≠ j, there is an edge connecting them if and only if characters si and sj are either equal or neighbouring in the alphabet. That is, letters in pairs "a"-"b" and "b"-"c" are neighbouring, while letters "a"-"c" are not. Vasya painted the resulting graph near the string and then erased the string. Next day Vasya's friend Petya came to a lecture and found some graph at his desk. He had heard of Vasya's adventure and now he wants to find out whether it could be the original graph G, painted by Vasya. In order to verify this, Petya needs to know whether there exists a string s, such that if Vasya used this s he would produce the given graph G. Input The first line of the input contains two integers n and m <image> — the number of vertices and edges in the graph found by Petya, respectively. Each of the next m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the edges of the graph G. It is guaranteed, that there are no multiple edges, that is any pair of vertexes appear in this list no more than once. Output In the first line print "Yes" (without the quotes), if the string s Petya is interested in really exists and "No" (without the quotes) otherwise. If the string s exists, then print it on the second line of the output. The length of s must be exactly n, it must consist of only letters "a", "b" and "c" only, and the graph built using this string must coincide with G. If there are multiple possible answers, you may print any of them. Examples Input 2 1 1 2 Output Yes aa Input 4 3 1 2 1 3 1 4 Output No Note In the first sample you are given a graph made of two vertices with an edge between them. So, these vertices can correspond to both the same and adjacent letters. Any of the following strings "aa", "ab", "ba", "bb", "bc", "cb", "cc" meets the graph's conditions. In the second sample the first vertex is connected to all three other vertices, but these three vertices are not connected with each other. That means that they must correspond to distinct letters that are not adjacent, but that is impossible as there are only two such letters: a and c. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Every summer Vitya comes to visit his grandmother in the countryside. This summer, he got a huge wart. Every grandma knows that one should treat warts when the moon goes down. Thus, Vitya has to catch the moment when the moon is down. Moon cycle lasts 30 days. The size of the visible part of the moon (in Vitya's units) for each day is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and then cycle repeats, thus after the second 1 again goes 0. As there is no internet in the countryside, Vitya has been watching the moon for n consecutive days and for each of these days he wrote down the size of the visible part of the moon. Help him find out whether the moon will be up or down next day, or this cannot be determined by the data he has. Input The first line of the input contains a single integer n (1 ≤ n ≤ 92) — the number of consecutive days Vitya was watching the size of the visible part of the moon. The second line contains n integers ai (0 ≤ ai ≤ 15) — Vitya's records. It's guaranteed that the input data is consistent. Output If Vitya can be sure that the size of visible part of the moon on day n + 1 will be less than the size of the visible part on day n, then print "DOWN" at the only line of the output. If he might be sure that the size of the visible part will increase, then print "UP". If it's impossible to determine what exactly will happen with the moon, print -1. Examples Input 5 3 4 5 6 7 Output UP Input 7 12 13 14 15 14 13 12 Output DOWN Input 1 8 Output -1 Note In the first sample, the size of the moon on the next day will be equal to 8, thus the answer is "UP". In the second sample, the size of the moon on the next day will be 11, thus the answer is "DOWN". In the third sample, there is no way to determine whether the size of the moon on the next day will be 7 or 9, thus the answer is -1. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vasya has an array a consisting of positive integer numbers. Vasya wants to divide this array into two non-empty consecutive parts (the prefix and the suffix) so that the sum of all elements in the first part equals to the sum of elements in the second part. It is not always possible, so Vasya will move some element before dividing the array (Vasya will erase some element and insert it into an arbitrary position). Inserting an element in the same position he was erased from is also considered moving. Can Vasya divide the array after choosing the right element to move and its new position? Input The first line contains single integer n (1 ≤ n ≤ 100000) — the size of the array. The second line contains n integers a1, a2... an (1 ≤ ai ≤ 109) — the elements of the array. Output Print YES if Vasya can divide the array after moving one element. Otherwise print NO. Examples Input 3 1 3 2 Output YES Input 5 1 2 3 4 5 Output NO Input 5 2 2 3 4 5 Output YES Note In the first example Vasya can move the second element to the end of the array. In the second example no move can make the division possible. In the third example Vasya can move the fourth element by one position to the left. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well. In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned. Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023. Input The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines. Next n lines contain commands. A command consists of a character that represents the operation ("&", "\|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023. Output Output an integer k (0 ≤ k ≤ 5) — the length of your program. Next k lines must contain commands in the same format as in the input. Examples Input 3 \| 3 ^ 2 \| 1 Output 2 \| 3 ^ 2 Input 3 & 1 & 3 & 5 Output 1 & 1 Input 3 ^ 1 ^ 2 ^ 3 Output 0 Note You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>. Second sample: Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given an undirected graph with n vertices. There are no edge-simple cycles with the even length in it. In other words, there are no cycles of even length that pass each edge at most once. Let's enumerate vertices from 1 to n. You have to answer q queries. Each query is described by a segment of vertices [l; r], and you have to count the number of its subsegments [x; y] (l ≤ x ≤ y ≤ r), such that if we delete all vertices except the segment of vertices [x; y] (including x and y) and edges between them, the resulting graph is bipartite. Input The first line contains two integers n and m (1 ≤ n ≤ 3·105, 1 ≤ m ≤ 3·105) — the number of vertices and the number of edges in the graph. The next m lines describe edges in the graph. The i-th of these lines contains two integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi), denoting an edge between vertices ai and bi. It is guaranteed that this graph does not contain edge-simple cycles of even length. The next line contains a single integer q (1 ≤ q ≤ 3·105) — the number of queries. The next q lines contain queries. The i-th of these lines contains two integers li and ri (1 ≤ li ≤ ri ≤ n) — the query parameters. Output Print q numbers, each in new line: the i-th of them should be the number of subsegments [x; y] (li ≤ x ≤ y ≤ ri), such that the graph that only includes vertices from segment [x; y] and edges between them is bipartite. Examples Input 6 6 1 2 2 3 3 1 4 5 5 6 6 4 3 1 3 4 6 1 6 Output 5 5 14 Input 8 9 1 2 2 3 3 1 4 5 5 6 6 7 7 8 8 4 7 2 3 1 8 1 4 3 8 Output 27 8 19 Note The first example is shown on the picture below: <image> For the first query, all subsegments of [1; 3], except this segment itself, are suitable. For the first query, all subsegments of [4; 6], except this segment itself, are suitable. For the third query, all subsegments of [1; 6] are suitable, except [1; 3], [1; 4], [1; 5], [1; 6], [2; 6], [3; 6], [4; 6]. The second example is shown on the picture below: <image> The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are n cities and m roads in Berland. Each road connects a pair of cities. The roads in Berland are one-way. What is the minimum number of new roads that need to be built to make all the cities reachable from the capital? New roads will also be one-way. Input The first line of input consists of three integers n, m and s (1 ≤ n ≤ 5000, 0 ≤ m ≤ 5000, 1 ≤ s ≤ n) — the number of cities, the number of roads and the index of the capital. Cities are indexed from 1 to n. The following m lines contain roads: road i is given as a pair of cities u_i, v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i). For each pair of cities (u, v), there can be at most one road from u to v. Roads in opposite directions between a pair of cities are allowed (i.e. from u to v and from v to u). Output Print one integer — the minimum number of extra roads needed to make all the cities reachable from city s. If all the cities are already reachable from s, print 0. Examples Input 9 9 1 1 2 1 3 2 3 1 5 5 6 6 1 1 8 9 8 7 1 Output 3 Input 5 4 5 1 2 2 3 3 4 4 1 Output 1 Note The first example is illustrated by the following: <image> For example, you can add roads (6, 4), (7, 9), (1, 7) to make all the cities reachable from s = 1. The second example is illustrated by the following: <image> In this example, you can add any one of the roads (5, 1), (5, 2), (5, 3), (5, 4) to make all the cities reachable from s = 5. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M. Road i connects City A_i and City B_i. Snuke can perform the following operation zero or more times: * Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities. After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times). What is the minimum number of roads he must build to achieve the goal? Constraints * 2 \leq N \leq 100,000 * 1 \leq M \leq 100,000 * 1 \leq A_i < B_i \leq N * No two roads connect the same pair of cities. * All values in input are integers. Input Input is given from Standard Input in the following format: N M A_1 B_1 : A_M B_M Output Print the answer. Example Input 3 1 1 2 Output 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a string S of length N consisting of lowercase English letters, and an integer K. Print the string obtained by replacing every character in S that differs from the K-th character of S, with ``. Constraints 1 \leq K \leq N\leq 10 * S is a string of length N consisting of lowercase English letters. * N and K are integers. Input Input is given from Standard Input in the following format: N S K Output Print the string obtained by replacing every character in S that differs from the K-th character of S, with ``. Examples Input 5 error 2 Output rrr Input 6 eleven 5 Output eee Input 9 education 7 Output ****i The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There is a string S consisting of digits `1`, `2`, ..., `9`. Lunlun, the Dachshund, will take out three consecutive digits from S, treat them as a single integer X and bring it to her master. (She cannot rearrange the digits.) The master's favorite number is 753. The closer to this number, the better. What is the minimum possible (absolute) difference between X and 753? Constraints * S is a string of length between 4 and 10 (inclusive). * Each character in S is `1`, `2`, ..., or `9`. Input Input is given from Standard Input in the following format: S Output Print the minimum possible difference between X and 753. Examples Input 1234567876 Output 34 Input 35753 Output 0 Input 1111111111 Output 642 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are three positive integers A, B and C written on a blackboard. E869120 performs the following operation K times: * Choose one integer written on the blackboard and let the chosen integer be n. Replace the chosen integer with 2n. What is the largest possible sum of the integers written on the blackboard after K operations? Constraints * A, B and C are integers between 1 and 50 (inclusive). * K is an integer between 1 and 10 (inclusive). Input Input is given from Standard Input in the following format: A B C K Output Print the largest possible sum of the integers written on the blackboard after K operations by E869220. Examples Input 5 3 11 1 Output 30 Input 3 3 4 2 Output 22 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Snuke has N dogs and M monkeys. He wants them to line up in a row. As a Japanese saying goes, these dogs and monkeys are on bad terms. ("ken'en no naka", literally "the relationship of dogs and monkeys", means a relationship of mutual hatred.) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys. How many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that). Here, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished. Constraints * 1 ≤ N,M ≤ 10^5 Input Input is given from Standard Input in the following format: N M Output Print the number of possible arrangements, modulo 10^9+7. Examples Input 2 2 Output 8 Input 3 2 Output 12 Input 1 8 Output 0 Input 100000 100000 Output 530123477 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Dolphin resides in two-dimensional Cartesian plane, with the positive x-axis pointing right and the positive y-axis pointing up. Currently, he is located at the point (sx,sy). In each second, he can move up, down, left or right by a distance of 1. Here, both the x- and y-coordinates before and after each movement must be integers. He will first visit the point (tx,ty) where sx < tx and sy < ty, then go back to the point (sx,sy), then visit the point (tx,ty) again, and lastly go back to the point (sx,sy). Here, during the whole travel, he is not allowed to pass through the same point more than once, except the points (sx,sy) and (tx,ty). Under this condition, find a shortest path for him. Constraints * -1000 ≤ sx < tx ≤ 1000 * -1000 ≤ sy < ty ≤ 1000 * sx,sy,tx and ty are integers. Input The input is given from Standard Input in the following format: sx sy tx ty Output Print a string S that represents a shortest path for Dolphin. The i-th character in S should correspond to his i-th movement. The directions of the movements should be indicated by the following characters: * `U`: Up * `D`: Down * `L`: Left * `R`: Right If there exist multiple shortest paths under the condition, print any of them. Examples Input 0 0 1 2 Output UURDDLLUUURRDRDDDLLU Input -2 -2 1 1 Output UURRURRDDDLLDLLULUUURRURRDDDLLDL The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There is a game that uses numbers called "Fizz Buzz". In this game, multiple players count the numbers one by one, starting with 1, and each player says only one number after the previous player. At that time, you must say "Fizz" if it is divisible by 3, "Buzz" if it is divisible by 5, and "FizzBuzz" if it is divisible by both. For example, the first 16 statements are as follows: 1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz, 16, ・・・ Taro decided to play "Fizz Buzz" with his friends. Taro and his colleagues decided the rules as follows. "The wrong person will drop out. The next person will start with the next number after the wrong number. That is, if you say 1, 2, 3, you made a mistake with 3, so you will start with 4." I play the game according to this rule, but because I am not used to the game, I sometimes do not notice that I made a mistake, and I cannot make a fair decision. So you decided to create a program that outputs the remaining people at the end of the set number of remarks so that Taro and his friends can enjoy this game. Create a program that inputs the number of players, the number of times spoken during the game, and each statement, and outputs the number of the remaining players at the end of the input in ascending order. However, the players are numbered from 1, and the order of speaking is also from the first player, and when the speaking is completed, the first player will speak again. If the player in turn has already dropped out, the next player will speak. Also, the program must ignore subsequent statements when the player is alone. Input A sequence of multiple datasets is given as input. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format: m n s1 s2 :: sn The first line gives the number of players m (2 ≤ m ≤ 1000) and the number of remarks n (1 ≤ n ≤ 10000). The next n lines are given the i-th statement s1. si is an integer, Fizz, Buzz, or a string (up to 8 characters) that indicates FizzBuzz. The number of datasets does not exceed 50. Output For each input dataset, the number of the player remaining when the specified number of remarks is input is output in ascending order. Example Input 5 7 1 2 Fizz 4 Buzz 6 7 3 5 1 2 3 4 5 0 0 Output 2 3 4 5 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Chief Judge's log, stardate 48642.5. We have decided to make a problem from elementary number theory. The problem looks like finding all prime factors of a positive integer, but it is not. A positive integer whose remainder divided by 7 is either 1 or 6 is called a 7N+{1,6} number. But as it is hard to pronounce, we shall call it a Monday-Saturday number. For Monday-Saturday numbers a and b, we say a is a Monday-Saturday divisor of b if there exists a Monday-Saturday number x such that ax = b. It is easy to show that for any Monday-Saturday numbers a and b, it holds that a is a Monday-Saturday divisor of b if and only if a is a divisor of b in the usual sense. We call a Monday-Saturday number a Monday-Saturday prime if it is greater than 1 and has no Monday-Saturday divisors other than itself and 1. A Monday-Saturday number which is a prime in the usual sense is a Monday-Saturday prime but the converse does not always hold. For example, 27 is a Monday-Saturday prime although it is not a prime in the usual sense. We call a Monday-Saturday prime which is a Monday-Saturday divisor of a Monday-Saturday number a a Monday-Saturday prime factor of a. For example, 27 is one of the Monday-Saturday prime factors of 216, since 27 is a Monday-Saturday prime and 216 = 27 × 8 holds. Any Monday-Saturday number greater than 1 can be expressed as a product of one or more Monday-Saturday primes. The expression is not always unique even if differences in order are ignored. For example, 216 = 6 × 6 × 6 = 8 × 27 holds. Our contestants should write a program that outputs all Monday-Saturday prime factors of each input Monday-Saturday number. Input The input is a sequence of lines each of which contains a single Monday-Saturday number. Each Monday-Saturday number is greater than 1 and less than 300000 (three hundred thousand). The end of the input is indicated by a line containing a single digit 1. Output For each input Monday-Saturday number, it should be printed, followed by a colon `:' and the list of its Monday-Saturday prime factors on a single line. Monday-Saturday prime factors should be listed in ascending order and each should be preceded by a space. All the Monday-Saturday prime factors should be printed only once even if they divide the input Monday-Saturday number more than once. Sample Input 205920 262144 262200 279936 299998 1 Output for the Sample Input 205920: 6 8 13 15 20 22 55 99 262144: 8 262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185 279936: 6 8 27 299998: 299998 Example Input 205920 262144 262200 279936 299998 1 Output 205920: 6 8 13 15 20 22 55 99 262144: 8 262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185 279936: 6 8 27 299998: 299998 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Do you know "sed," a tool provided with Unix? Its most popular use is to substitute every occurrence of a string contained in the input string (actually each input line) with another string β. More precisely, it proceeds as follows. 1. Within the input string, every non-overlapping (but possibly adjacent) occurrences of α are marked. If there is more than one possibility for non-overlapping matching, the leftmost one is chosen. 2. Each of the marked occurrences is substituted with β to obtain the output string; other parts of the input string remain intact. For example, when α is "aa" and β is "bca", an input string "aaxaaa" will produce "bcaxbcaa", but not "aaxbcaa" nor "bcaxabca". Further application of the same substitution to the string "bcaxbcaa" will result in "bcaxbcbca", but this is another substitution, which is counted as the second one. In this problem, a set of substitution pairs (αi, βi) (i = 1, 2, ... , n), an initial string γ, and a final string δ are given, and you must investigate how to produce δ from γ with a minimum number of substitutions. A single substitution (αi, βi) here means simultaneously substituting all the non-overlapping occurrences of αi, in the sense described above, with βi. You may use a specific substitution (αi, βi ) multiple times, including zero times. Input The input consists of multiple datasets, each in the following format. n α1 β1 α2 β2 . . . αn βn γ δ n is a positive integer indicating the number of pairs. αi and βi are separated by a single space. You may assume that 1 ≤ \|αi\| < \|βi\| ≤ 10 for any i (\|s\| means the length of the string s), αi ≠ αj for any i ≠ j, n ≤ 10 and 1 ≤ \|γ\| < \|δ\| ≤ 10. All the strings consist solely of lowercase letters. The end of the input is indicated by a line containing a single zero. Output For each dataset, output the minimum number of substitutions to obtain δ from γ. If δ cannot be produced from γ with the given set of substitutions, output -1. Example Input 2 a bb b aa a bbbbbbbb 1 a aa a aaaaa 3 ab aab abc aadc ad dee abc deeeeeeeec 10 a abc b bai c acf d bed e abh f fag g abe h bag i aaj j bbb a abacfaabe 0 Output 3 -1 7 4 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Osaki Osaki English text is not available in this practice contest. The Yamanote Line is a circular railway line laid in the 23 wards of Tokyo. The total route distance is 34.5km, and one lap takes about one hour. There are 29 stations in total. The line color is Uguisu color. The peak congestion rate exceeds 200%, making it one of the busiest railway lines in Japan. One train runs every three minutes during the busiest hours, and people who come to Tokyo for the first time are amazed at the sight. Mr. Tetsuko loves the Yamanote Line and loves genuine railways. One day, she came up with the following question while reading her favorite book, the JR timetable. "How many vehicles are used a day on the Yamanote Line?" She tried to figure out the minimum number of vehicles required for operation from the timetable. However, the number of trains was so large that she couldn't count it by herself. So she turned to you, a good programmer, for help. Your job is to write a program to find the minimum number of cars required to operate the Yamanote Line from a given timetable. Since the Yamanote Line is a circular line, the timetable is often written with "Osaki Station" as the starting and ending stations for convenience. Therefore, only the departure and arrival times of each train at Osaki Station are recorded in the timetable given by her. Although this cannot happen on the actual Yamanote Line, in order to simplify the situation setting, we will consider that the train can depart from Osaki Station immediately after it arrives at Osaki Station. In addition, there are cases where the time taken by Mr. Tetsuko is incorrect, or the train added by Mr. Tetsuko's delusion is mixed in the timetable, but you can not see them, so to the last The number must be calculated for the time as written. If you write a program that works, she may invite you to a date on the train. However, it is up to you to accept or decline the invitation. Input The input consists of multiple datasets. Each dataset has the following format. > n > hh: mm: ss hh: mm: ss > hh: mm: ss hh: mm: ss > ... > hh: mm: ss hh: mm: ss The integer n in the first line is the number of trains included in the timetable. This value is guaranteed not to exceed 10,000. The departure time and arrival time of each train at Osaki Station are given in this order on the n lines from the 2nd line to the n + 1st line, and the departure time and arrival time are separated by a single space. Each time is expressed in the format hh: mm: ss, where hh is the hour, mm is the minute, and ss is the second. The range of each value is 0 ≤ hh <24, 0 ≤ mm <60, 0 ≤ ss <60. All of these numbers are prefixed with 0s as needed to be two digits. Trains that run across 24:00 at night are not included. Therefore, the departure time is always before the arrival time. The end of input is indicated by n = 0. It is not included in the dataset. Output For each dataset, output the minimum number of vehicles required on one line. Sample Input 3 05:47:15 09:54:40 12:12:59 12:13:00 16:30:20 21:18:53 6 00:00:00 03:00:00 01:00:00 03:00:00 02:00:00 03:00:00 03:00:00 04:00:00 03:00:00 05:00:00 03:00:00 06:00:00 0 Output for the Sample Input 1 3 Example Input 3 05:47:15 09:54:40 12:12:59 12:13:00 16:30:20 21:18:53 6 00:00:00 03:00:00 01:00:00 03:00:00 02:00:00 03:00:00 03:00:00 04:00:00 03:00:00 05:00:00 03:00:00 06:00:00 0 Output 1 3 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Open Binary and Object Group organizes a programming contest every year. Mr. Hex belongs to this group and joins the judge team of the contest. This year, he created a geometric problem with its solution for the contest. The problem required a set of points forming a line-symmetric polygon for the input. Preparing the input for this problem was also his task. The input was expected to cover all edge cases, so he spent much time and attention to make them satisfactory. However, since he worked with lots of care and for a long time, he got tired before he finished. So He might have made mistakes - there might be polygons not meeting the condition. It was not reasonable to prepare the input again from scratch. The judge team thus decided to find all line-asymmetric polygons in his input and fix them as soon as possible. They asked a programmer, just you, to write a program to find incorrect polygons. You can assume the following: * Edges of the polygon must not cross or touch each other except for the end points of adjacent edges. * It is acceptable for the polygon to have adjacent three vertexes on a line, but in such a case, there must be the vertex symmetric to each of them. Input The input consists of a set of points in the following format. N x1 y1 x2 y2 ... xN yN The first line of the input contains an integer N (3 ≤ N ≤ 1000), which denotes the number of points. The following N lines describe each point. The i-th line contains two integers x1, y1 (-10000 ≤ xi, yi ≤ 10000), which denote the coordinates of the i-th point. Note that, although the points are the vertexes of a polygon, they are given in an artibrary order, not necessarily clockwise or counterclockwise. Output Output "Yes" in a line if the points can form a line-symmetric polygon, otherwise output "No". Examples Input 4 0 1 1 0 0 0 1 1 Output Yes Input 4 0 1 1 -1 0 0 1 1 Output No Input 9 -1 1 0 1 1 1 -1 0 0 0 1 0 -1 -1 0 -1 1 -1 Output No Input 3 -1 -1 0 0 1 1 Output No Input 4 0 2 0 0 -1 0 1 0 Output Yes The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Quarkgo Empire Expeditionary Force is an evil organization that plans to invade the Earth. In keeping with the tradition of the invaders, they continued to send monsters at a pace of one every week, targeting the area around Tokyo in Japan. However, each time, five warriors calling themselves the Human Squadron Earth Five appeared, and the monster who was rampaging in the city was easily defeated. Walzard Thru (Earth name: Genmasa) is a female executive of the Quarkgo Empire Expeditionary Force who is seriously worried about such a situation. She had a headache under a commander who wouldn't learn anything from her weekly defeat, or a genius scientist who repeated some misplaced inventions. Meanwhile, the next operation was decided to send the blood-sucking monster Dracula to Japan. Dracula is a terrifying monster who turns a blood-sucking human into Dracula. Humans who have been sucked by Dracula also suck the blood of other humans to increase their fellow Dracula. In this way, the strategy is to fill the entire earth with Dracula. Upon hearing this, Walzard soon realized. This strategy is different from the usual sequel strategy such as taking over a kindergarten bus. It's rare for that bad commander to have devised it, and it has the potential to really conquer the Earth. The momentum of the game is terrifying. Dracula, who landed on the ground, quickly increased the number of friends. If we went on like this, the invasion of the earth seemed to be just a stone's throw away. However, at that moment, a strong and unpleasant premonition ran through Walzard's mind. No way, if this monster, the original is defeated, his friends will not be wiped out, right? When I asked the scientist who designed and developed Dracula in a hurry, he was still worried about Walzard. It is designed so that when the original Dracula is destroyed, all humans who have sucked blood will return to their original state. Don't be foolish developer. Why did you add such an extra function! Walzard jumped to the developer and decided to kick his knee, and immediately started the original recovery work. No matter how much the original and the fake look exactly the same, if nothing is done, it is visible that the rushed Earth Five will see through the original for some reason and be defeated. According to the developers, all Draculaized humans weigh the same, but the original Dracula is a little heavier. Then you should be able to find the original by using only the balance. You must find and retrieve the original Dracula as soon as possible before the Earth Five appears. Input N The integer N (2 ≤ N ≤ 2,000,000,000) is written on the first line of the input. This represents the total number of Draculas, both original and fake. Output In the worst case, how many times is it enough to use the balance to find one original from the N Draculas using the balance? Output the minimum value. However, comparing the weights of several Draculas placed on the left and right plates of the balance is counted as one time. Examples Input 8 Output 2 Input 30 Output 4 Input 2000000000 Output 20 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In 20XX AD, a school competition was held. The tournament has finally left only the final competition. You are one of the athletes in the competition. The competition you participate in is to compete for the time it takes to destroy all the blue objects placed in the space. Athletes are allowed to bring in competition guns. In the space, there are multiple blue objects, the same number of red objects, and multiple obstacles. There is a one-to-one correspondence between the blue object and the red object, and the blue object must be destroyed by shooting a bullet at the blue object from the coordinates where the red object is placed. The obstacles placed in the space are spherical and the composition is slightly different, but if it is a normal bullet, the bullet will stop there when it touches the obstacle. The bullet used in the competition is a special bullet called Magic Bullet. This bullet can store magical power, and when the bullet touches an obstacle, it automatically consumes the magical power, and the magic that the bullet penetrates is activated. Due to the difference in the composition of obstacles, the amount of magic required to penetrate and the amount of magic power consumed to activate it are different. Therefore, even after the magic for one obstacle is activated, it is necessary to activate another magic in order to penetrate another obstacle. Also, if the bullet touches multiple obstacles at the same time, magic will be activated at the same time. The amount of magical power contained in the bullet decreases with each magic activation. While the position and size of obstacles and the amount of magical power required to activate the penetrating magic have already been disclosed, the positions of the red and blue objects have not been disclosed. However, the position of the object could be predicted to some extent from the information of the same competition in the past. You want to save as much magical power as you can, because putting magical power into a bullet is very exhausting. Therefore, assuming the position of the red object and the corresponding blue object, the minimum amount of magical power required to be loaded in the bullet at that time, that is, the magical power remaining in the bullet when reaching the blue object is 0. Let's find the amount of magical power that becomes. Constraints * 0 ≤ N ≤ 50 * 1 ≤ Q ≤ 50 * -500 ≤ xi, yi, zi ≤ 500 * 1 ≤ ri ≤ 1,000 * 1 ≤ li ≤ 1016 * -500 ≤ sxj, syj, szj ≤ 500 * -500 ≤ dxj, dyj, dzj ≤ 500 * Obstacles are never stuck in other obstacles * The coordinates of the object are not inside or on the surface of the obstacle * Under each assumption, the coordinates of the red object and the blue object do not match. Input All inputs are integers. Each number is separated by a single space. N Q x1 y1 z1 r1 l1 :: xN yN zN rN lN sx1 sy1 sz1 dx1 dy1 dz1 :: sxQ syQ szQ dxQ dyQ dzQ * N is the number of obstacles, and Q is the number of coordinates of the assumed blue and red objects. * xi, yi, and zi are the x-coordinate, y-coordinate, and z-coordinate that represent the position of the center of the i-th obstacle, respectively. * ri is the radius of the i-th obstacle. * li is the amount of magical power consumed by magic to penetrate the i-th obstacle. * sxj, syj, and szj are the x-coordinate, y-coordinate, and z-coordinate that represent the position of the red object in the jth assumption, respectively. * dxj, dyj, and dzj are the x-coordinate, y-coordinate, and z-coordinate that represent the position of the blue object in the jth assumption, respectively. Output Assuming the position of each pair of red objects and the corresponding blue objects, the amount of magical power to be loaded in the bullet is output on one line, assuming that there are only obstacles, red objects, and one pair of blue objects in space. Let's do it. The bullet is supposed to fly in a straight line from the position of the red object to the position of the blue object, and since the size of the bullet is very small, it is treated as a point. Examples Input 5 1 0 10 0 5 2 0 20 0 5 12 0 30 0 5 22 0 40 0 5 32 0 50 0 5 42 0 0 0 0 60 0 Output 110 Input 1 1 10 5 0 5 9 0 0 0 9 12 0 Output 9 Input 5 5 -38 -71 -293 75 1 -158 -38 -405 66 1 -236 -303 157 266 1 316 26 411 190 1 207 -312 -27 196 1 -50 292 -375 -401 389 -389 460 278 409 -329 -303 411 215 -220 -200 309 -474 300 261 -494 -87 -300 123 -463 386 378 486 -443 -64 299 Output 0 2 1 3 0 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Problem statement You and AOR Ika are preparing for a graph problem in competitive programming. Generating input cases is AOR Ika-chan's job. The input case for that problem is a directed graph of the $ N $ vertices. The vertices are numbered from $ 1 $ to $ N $. Edges may contain self-loops, but not multiple edges. However, AOR Ika suddenly lost communication and couldn't get the original graph. All that remains is the following information: * The number of vertices with degree $ i $ is $ a_i $. That is, the number of vertices ending in $ i $ is $ a_i $. * The number of vertices with degree $ i $ is $ b_i $. That is, the number of vertices starting from $ i $ is $ b_i $. Is there a directed graph that is consistent with the information left behind? Judge it, output YES if it exists, and then output one consistent directed graph. If there are more than one, any one may be output. If it does not exist, output NO. Input constraints $ 1 \ leq n \ leq 50 $ $ 0 \ leq a_i \ leq n $ $ 0 \ leq b_i \ leq n $ sample Sample input 1 3 1 2 0 0 1 2 0 0 Sample output 1 YES YES 0 1 0 0 0 1 0 0 0 Sample input 2 1 Ten Ten Sample output 2 YES YES 0 Sample input 3 2 0 2 0 0 2 0 Sample output 3 YES YES 0 1 Ten Sample input 4 Four 1 3 0 0 0 3 0 0 1 0 Sample output 4 YES YES 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 Sample input 5 1 1 1 0 0 Sample output 5 NO input $ n $ $ a_0 \ cdots a_n $ $ b_0 \ cdots b_n $ output If there is a graph that meets the conditions, output it in the following format. $ e_ {ij} $ should be 1 if there is a directed edge from $ i $ to $ j $, or 0 otherwise. Be careful not to print a blank at the end of the line. YES YES $ e_ {11} \ e_ {12} \ cdots e_ {1n} $ $ e_ {21} \ e_ {22} \ cdots e_ {2n} $ $ \ vdots $ $ e_ {n1} \ e_ {n2} \ cdots e_ {nn} $ If not, output as follows. NO Example Input 3 1 2 0 0 1 2 0 0 Output YES 0 1 0 0 0 1 0 0 0 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A: Information Search problem The posting list is a list in which there is a correspondence between the search term and the appearing document ID. For example * Hokkaido: 1, 2, 4, 9 * Sightseeing: 1, 3, 4, 7 And so on. From the above posting list, if you search for and, the document with ID 1, 4 will be hit, and if you search for or, ID 1, 2, 3, 4, 7, 9 will be hit. Here, and search means "listing elements contained in either list", or search means "listing elements contained in at least one of the lists". Since the posting list is given, output the results of and search and or search respectively. Input format n m a_1 a_2 $ \ ldots $ a_n b_1 b_2 $ \ ldots $ b_m All inputs consist of integers. The first line gives the lengths n and m of the two posting lists to search, separated by spaces. The second and third lines are given the IDs contained in their respective posting lists, separated by blanks. Constraint * 1 \ leq n, m \ leq 2 \ times 10 ^ 5 * a_i <a_j (i <j) * b_i <b_j (i <j) * 1 \ leq a_i, b_i \ leq 10 ^ 9 Output format Let A be the number of hits in the and search, and B be the number of hits in the or search. Print on the first line in the order A B, separated by blanks. Output the IDs hit by and search on the following line A in ascending order. Output the IDs hit by or search on the following B line in ascending order. Input example 1 4 4 1 2 4 9 1 3 4 7 Output example 1 2 6 1 Four 1 2 3 Four 7 9 Input example 2 4 4 1 3 5 7 2 4 6 8 Output example 2 0 8 1 2 3 Four Five 6 7 8 Input example 3 3 5 one two Three 1 2 3 4 5 Output example 3 3 5 1 2 3 1 2 3 Four Five Example Input 4 4 1 2 4 9 1 3 4 7 Output 2 6 1 4 1 2 3 4 7 9 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique. * insert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$. * get($key$): Print the value with the specified $key$. Print 0 if there is no such element. * delete($key$): Delete the element with the specified $key$. * dump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order. Constraints * $1 \leq q \leq 200,000$ * $1 \leq x \leq 1,000,000,000$ * $1 \leq $ length of $key$ $ \leq 20$ * $key$ consists of lower-case letters * $L \leq R$ in lexicographic order * The total number of elements printed by dump operations does not exceed $1,000,000$ Input The input is given in the following format. $q$ $query_1$ $query_2$ : $query_q$ Each query $query_i$ is given by 0 $key$ $x$ or 1 $key$ or 2 $key$ or 3 $L$ $R$ where the first digits 0, 1, 2 and 3 represent insert, get, delete and dump operations. Output For each get operation, print the corresponding value. For each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements (a pair of key and value separated by a space character) in ascending order of the keys. Example Input 9 0 blue 4 0 red 1 0 white 5 1 red 1 blue 2 red 1 black 1 red 3 w z Output 1 4 0 0 white 5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given two binary strings, A (of length 10) and B (of length 5), output 1 if B is a substring of A and 0 otherwise. Input The first line contains the number of test cases n. This is followed by n lines each consisting of pairs of binary strings A and B separated by a single space. Output output 1 if B is a substring of A and 0 otherwise. Example Input: 1 1010110010 10110 Output: 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given an array of n non-negative integers: A1, A2, …, AN. Your mission is finding a pair of integers Au, Av (1 ≤ u < v ≤ N) such that (Au and Av) is as large as possible. And is a bit-wise operation which is corresponding to & in C++ and Java. Input The first line of the input contains a single integer N. The ith line in the next N lines contains the Ai. Output Contains a single integer which is the largest value of Au and Av where 1 ≤ u < v ≤ N. Constraints 50 points: 2 ≤ N ≤ 5000 0 ≤ Ai ≤ 10^9 50 points: 2 ≤ N ≤ 3 × 10^5 0 ≤ Ai ≤ 10^9 Example Input: 4 2 4 8 10 Output: 8 Explanation 2 and 4 = 0 2 and 8 = 0 2 and 10 = 2 4 and 8 = 0 4 and 10 = 0 8 and 10 = 8 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. This is an interactive problem. Natasha is going to fly to Mars. Finally, Natasha sat in the rocket. She flies, flies... but gets bored. She wishes to arrive to Mars already! So she decides to find something to occupy herself. She couldn't think of anything better to do than to calculate the distance to the red planet. Let's define x as the distance to Mars. Unfortunately, Natasha does not know x. But it is known that 1 ≤ x ≤ m, where Natasha knows the number m. Besides, x and m are positive integers. Natasha can ask the rocket questions. Every question is an integer y (1 ≤ y ≤ m). The correct answer to the question is -1, if x<y, 0, if x=y, and 1, if x>y. But the rocket is broken — it does not always answer correctly. Precisely: let the correct answer to the current question be equal to t, then, if the rocket answers this question correctly, then it will answer t, otherwise it will answer -t. In addition, the rocket has a sequence p of length n. Each element of the sequence is either 0 or 1. The rocket processes this sequence in the cyclic order, that is 1-st element, 2-nd, 3-rd, …, (n-1)-th, n-th, 1-st, 2-nd, 3-rd, …, (n-1)-th, n-th, …. If the current element is 1, the rocket answers correctly, if 0 — lies. Natasha doesn't know the sequence p, but she knows its length — n. You can ask the rocket no more than 60 questions. Help Natasha find the distance to Mars. Assume, that the distance to Mars does not change while Natasha is asking questions. Your solution will not be accepted, if it does not receive an answer 0 from the rocket (even if the distance to Mars is uniquely determined by the already received rocket's answers). Input The first line contains two integers m and n (1 ≤ m ≤ 10^9, 1 ≤ n ≤ 30) — the maximum distance to Mars and the number of elements in the sequence p. Interaction You can ask the rocket no more than 60 questions. To ask a question, print a number y (1≤ y≤ m) and an end-of-line character, then do the operation flush and read the answer to the question. If the program reads 0, then the distance is correct and you must immediately terminate the program (for example, by calling exit(0)). If you ignore this, you can get any verdict, since your program will continue to read from the closed input stream. If at some point your program reads -2 as an answer, it must immediately end (for example, by calling exit(0)). You will receive the "Wrong answer" verdict, and this will mean that the request is incorrect or the number of requests exceeds 60. If you ignore this, you can get any verdict, since your program will continue to read from the closed input stream. If your program's request is not a valid integer between -2^{31} and 2^{31}-1 (inclusive) without leading zeros, then you can get any verdict. You can get "Idleness limit exceeded" if you don't print anything or if you forget to flush the output. To flush the output buffer you can use (after printing a query and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking Use the following format for hacking: In the first line, print 3 integers m,n,x (1≤ x≤ m≤ 10^9, 1≤ n≤ 30) — the maximum distance to Mars, the number of elements in the sequence p and the current distance to Mars. In the second line, enter n numbers, each of which is equal to 0 or 1 — sequence p. The hacked solution will not have access to the number x and sequence p. Example Input 5 2 1 -1 -1 1 0 Output 1 2 4 5 3 Note In the example, hacking would look like this: 5 2 3 1 0 This means that the current distance to Mars is equal to 3, Natasha knows that it does not exceed 5, and the rocket answers in order: correctly, incorrectly, correctly, incorrectly ... Really: on the first query (1) the correct answer is 1, the rocket answered correctly: 1; on the second query (2) the correct answer is 1, the rocket answered incorrectly: -1; on the third query (4) the correct answer is -1, the rocket answered correctly: -1; on the fourth query (5) the correct answer is -1, the rocket answered incorrectly: 1; on the fifth query (3) the correct and incorrect answer is 0. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The letters shop showcase is a string s, consisting of n lowercase Latin letters. As the name tells, letters are sold in the shop. Letters are sold one by one from the leftmost to the rightmost. Any customer can only buy some prefix of letters from the string s. There are m friends, the i-th of them is named t_i. Each of them is planning to estimate the following value: how many letters (the length of the shortest prefix) would s/he need to buy if s/he wanted to construct her/his name of bought letters. The name can be constructed if each letter is presented in the equal or greater amount. * For example, for s="arrayhead" and t_i="arya" 5 letters have to be bought ("arrayhead"). * For example, for s="arrayhead" and t_i="harry" 6 letters have to be bought ("arrayhead"). * For example, for s="arrayhead" and t_i="ray" 5 letters have to be bought ("arrayhead"). * For example, for s="arrayhead" and t_i="r" 2 letters have to be bought ("arrayhead"). * For example, for s="arrayhead" and t_i="areahydra" all 9 letters have to be bought ("arrayhead"). It is guaranteed that every friend can construct her/his name using the letters from the string s. Note that the values for friends are independent, friends are only estimating them but not actually buying the letters. Input The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of showcase string s. The second line contains string s, consisting of exactly n lowercase Latin letters. The third line contains one integer m (1 ≤ m ≤ 5 ⋅ 10^4) — the number of friends. The i-th of the next m lines contains t_i (1 ≤ \|t_i\| ≤ 2 ⋅ 10^5) — the name of the i-th friend. It is guaranteed that ∑ _{i=1}^m \|t_i\| ≤ 2 ⋅ 10^5. Output For each friend print the length of the shortest prefix of letters from s s/he would need to buy to be able to construct her/his name of them. The name can be constructed if each letter is presented in the equal or greater amount. It is guaranteed that every friend can construct her/his name using the letters from the string s. Example Input 9 arrayhead 5 arya harry ray r areahydra Output 5 6 5 2 9 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that: * No two students i and j such that \|a_i - a_j\| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1); * the number of teams is the minimum possible. You have to answer q independent queries. Input The first line of the input contains one integer q (1 ≤ q ≤ 100) — the number of queries. Then q queries follow. The first line of the query contains one integer n (1 ≤ n ≤ 100) — the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100, all a_i are distinct), where a_i is the programming skill of the i-th student. Output For each query, print the answer on it — the minimum number of teams you can form if no two students i and j such that \|a_i - a_j\| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1) Example Input 4 4 2 10 1 20 2 3 6 5 2 3 4 99 100 1 42 Output 2 1 2 1 Note In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of \|a_1 - a_3\|=\|2-1\|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team. In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 × 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone — neither any other statues, nor Anna, nor Maria. Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is — to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared. At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner. Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error. Input You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one — for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S". It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S". Output If Maria wins, print string "WIN". If the statues win, print string "LOSE". Examples Input .......A ........ ........ ........ ........ ........ ........ M....... Output WIN Input .......A ........ ........ ........ ........ ........ SS...... M....... Output LOSE Input .......A ........ ........ ........ ........ .S...... S....... MS...... Output LOSE The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97. Alice is given a sequence of n composite numbers a_1,a_2,…,a_n. She wants to choose an integer m ≤ 11 and color each element one of m colors from 1 to m so that: * for each color from 1 to m there is at least one element of this color; * each element is colored and colored exactly one color; * the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color. Note that equal elements can be colored different colors — you just have to choose one of m colors for each of the indices from 1 to n. Alice showed already that if all a_i ≤ 1000 then she can always solve the task by choosing some m ≤ 11. Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11. Input The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. Then the descriptions of the test cases follow. The first line of the test case contains a single integer n (1 ≤ n ≤ 1000) — the amount of numbers in a sequence a. The second line of the test case contains n composite integers a_1,a_2,…,a_n (4 ≤ a_i ≤ 1000). It is guaranteed that the sum of n over all test cases doesn't exceed 10^4. Output For each test case print 2 lines. The first line should contain a single integer m (1 ≤ m ≤ 11) — the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11. Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1). Example Input 3 3 6 10 15 2 4 9 23 437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961 Output 1 1 1 1 2 2 1 11 4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6 Note In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case. In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Pay attention to the non-standard memory limit in this problem. In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution. The array a=[a_1, a_2, …, a_n] (1 ≤ a_i ≤ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 ≤ l < r ≤ n) such that a_i = a_l + a_{l+1} + … + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not). Print the number of special elements of the given array a. For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5: * a_3=4 is a special element, since a_3=4=a_1+a_2=3+1; * a_5=5 is a special element, since a_5=5=a_2+a_3=1+4; * a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1; * a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1; * a_9=5 is a special element, since a_9=5=a_2+a_3=1+4. Please note that some of the elements of the array a may be equal — if several elements are equal and special, then all of them should be counted in the answer. Input The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Then t test cases follow. Each test case is given in two lines. The first line contains an integer n (1 ≤ n ≤ 8000) — the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n). It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000. Output Print t numbers — the number of special elements for each of the given arrays. Example Input 5 9 3 1 4 1 5 9 2 6 5 3 1 1 2 5 1 1 1 1 1 8 8 7 6 5 4 3 2 1 1 1 Output 5 1 0 4 0 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up! Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position. Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}. An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows. The first line of each test case contains integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation. The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ n) — the initial permutation. It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5. Output For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation. Example Input 2 5 1 2 3 4 5 7 3 2 4 5 1 6 7 Output 0 2 Note In the first permutation, it is already sorted so no exchanges are needed. It can be shown that you need at least 2 exchanges to sort the second permutation. [3, 2, 4, 5, 1, 6, 7] Perform special exchange on range (1, 5) [4, 1, 2, 3, 5, 6, 7] Perform special exchange on range (1, 4) [1, 2, 3, 4, 5, 6, 7] The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n. In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b. Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible. Input The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9). Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped. Output If it is impossible to make the array a increasing using the given operations, print -1. Otherwise, print one integer — the minimum number of operations you have to perform. Examples Input 7 2 1 2 1 1 3 5 1 3 5 Output 4 Input 3 3 1 3 2 1 2 3 Output -1 Input 5 0 4 3 1 2 3 Output 2 Input 10 3 1 3 5 6 12 9 8 10 13 15 2 4 9 Output 3 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5). Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b. Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple. When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples. Input The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9). Output For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with. Example Input 3 3 6 9 Output 0 1 1 Note The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote. However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes. n reviewers enter the site one by one. Each reviewer is one of the following types: * type 1: a reviewer has watched the movie, and they like it — they press the upvote button; * type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button; * type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie. Each reviewer votes on the movie exactly once. Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one. What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to? Input The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases. Then the descriptions of t testcases follow. The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers. The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site. Output For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to. Example Input 4 1 2 3 1 2 3 5 1 1 1 1 1 3 3 3 2 Output 0 2 5 2 Note In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes. In the second testcase of the example you can send all reviewers to the first server: * the first reviewer upvotes; * the second reviewer downvotes; * the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves. There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server: * the first reviewer upvotes on the first server; * the second reviewer downvotes on the first server; * the last reviewer sees no upvotes or downvotes on the second server — upvote themselves. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. One day Vasya painted a Cartesian coordinate system on a piece of paper and marked some set of points (x1, y1), (x2, y2), ..., (xn, yn). Let's define neighbors for some fixed point from the given set (x, y): * point (x', y') is (x, y)'s right neighbor, if x' > x and y' = y * point (x', y') is (x, y)'s left neighbor, if x' < x and y' = y * point (x', y') is (x, y)'s lower neighbor, if x' = x and y' < y * point (x', y') is (x, y)'s upper neighbor, if x' = x and y' > y We'll consider point (x, y) from the given set supercentral, if it has at least one upper, at least one lower, at least one left and at least one right neighbor among this set's points. Vasya marked quite many points on the paper. Analyzing the picture manually is rather a challenge, so Vasya asked you to help him. Your task is to find the number of supercentral points in the given set. Input The first input line contains the only integer n (1 ≤ n ≤ 200) — the number of points in the given set. Next n lines contain the coordinates of the points written as "x y" (without the quotes) (\|x\|, \|y\| ≤ 1000), all coordinates are integers. The numbers in the line are separated by exactly one space. It is guaranteed that all points are different. Output Print the only number — the number of supercentral points of the given set. Examples Input 8 1 1 4 2 3 1 1 2 0 2 0 1 1 0 1 3 Output 2 Input 5 0 0 0 1 1 0 0 -1 -1 0 Output 1 Note In the first sample the supercentral points are only points (1, 1) and (1, 2). In the second sample there is one supercental point — point (0, 0). The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Each year in the castle of Dwarven King there is a competition in growing mushrooms among the dwarves. The competition is one of the most prestigious ones, and the winner gets a wooden salad bowl. This year's event brought together the best mushroom growers from around the world, so we had to slightly change the rules so that the event gets more interesting to watch. Each mushroom grower has a mushroom that he will grow on the competition. Under the new rules, the competition consists of two parts. The first part lasts t1 seconds and the second part lasts t2 seconds. The first and the second part are separated by a little break. After the starting whistle the first part of the contest starts, and all mushroom growers start growing mushrooms at once, each at his individual speed of vi meters per second. After t1 seconds, the mushroom growers stop growing mushrooms and go to have a break. During the break, for unexplained reasons, the growth of all mushrooms is reduced by k percent. After the break the second part of the contest starts and all mushrooms growers at the same time continue to grow mushrooms, each at his individual speed of ui meters per second. After a t2 seconds after the end of the break, the competition ends. Note that the speeds before and after the break may vary. Before the match dwarf Pasha learned from all participants, what two speeds they have chosen. However, the participants did not want to disclose to him all their strategy and therefore, did not say in what order they will be using these speeds. That is, if a participant chose speeds ai and bi, then there are two strategies: he either uses speed ai before the break and speed bi after it, or vice versa. Dwarf Pasha really wants to win the totalizer. He knows that each participant chooses the strategy that maximizes the height of the mushroom. Help Dwarf Pasha make the final table of competition results. The participants are sorted in the result table by the mushroom height (the participants with higher mushrooms follow earlier in the table). In case of equal mushroom heights, the participants are sorted by their numbers (the participants with a smaller number follow earlier). Input The first input line contains four integer numbers n, t1, t2, k (1 ≤ n, t1, t2 ≤ 1000; 1 ≤ k ≤ 100) — the number of participants, the time before the break, the time after the break and the percentage, by which the mushroom growth drops during the break, correspondingly. Each of the following n lines contains two integers. The i-th (1 ≤ i ≤ n) line contains space-separated integers ai, bi (1 ≤ ai, bi ≤ 1000) — the speeds which the participant number i chose. Output Print the final results' table: n lines, each line should contain the number of the corresponding dwarf and the final maximum height of his mushroom with exactly two digits after the decimal point. The answer will be considered correct if it is absolutely accurate. Examples Input 2 3 3 50 2 4 4 2 Output 1 15.00 2 15.00 Input 4 1 1 1 544 397 280 101 280 101 693 970 Output 4 1656.07 1 937.03 2 379.99 3 379.99 Note * First example: for each contestant it is optimal to use firstly speed 2 and afterwards speed 4, because 2·3·0.5 + 4·3 > 4·3·0.5 + 2·3. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Smart Beaver from ABBYY came up with another splendid problem for the ABBYY Cup participants! This time the Beaver invites the contest participants to check out a problem on sorting documents by their subjects. Let's describe the problem: You've got some training set of documents. For each document you know its subject. The subject in this problem is an integer from 1 to 3. Each of these numbers has a physical meaning. For instance, all documents with subject 3 are about trade. You can download the training set of documents at the following link: http://download4.abbyy.com/a2/X2RZ2ZWXBG5VYWAL61H76ZQM/train.zip. The archive contains three directories with names "1", "2", "3". Directory named "1" contains documents on the 1-st subject, directory "2" contains documents on the 2-nd subject, and directory "3" contains documents on the 3-rd subject. Each document corresponds to exactly one file from some directory. All documents have the following format: the first line contains the document identifier, the second line contains the name of the document, all subsequent lines contain the text of the document. The document identifier is used to make installing the problem more convenient and has no useful information for the participants. You need to write a program that should indicate the subject for a given document. It is guaranteed that all documents given as input to your program correspond to one of the three subjects of the training set. Input The first line contains integer id (0 ≤ id ≤ 106) — the document identifier. The second line contains the name of the document. The third and the subsequent lines contain the text of the document. It is guaranteed that the size of any given document will not exceed 10 kilobytes. The tests for this problem are divided into 10 groups. Documents of groups 1 and 2 are taken from the training set, but their identifiers will not match the identifiers specified in the training set. Groups from the 3-rd to the 10-th are roughly sorted by the author in ascending order of difficulty (these groups contain documents which aren't present in the training set). Output Print an integer from 1 to 3, inclusive — the number of the subject the given document corresponds to. Examples The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n. Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image> is as minimal as possible. If there are multiple "nearest" fractions, choose the one with the minimum denominator. If there are multiple "nearest" fractions with the minimum denominator, choose the one with the minimum numerator. Input A single line contains three integers x, y, n (1 ≤ x, y, n ≤ 105). Output Print the required fraction in the format "a/b" (without quotes). Examples Input 3 7 6 Output 2/5 Input 7 2 4 Output 7/2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In mathematics, the Pythagorean theorem — is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states: In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation: a2 + b2 = c2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. <image> Given n, your task is to count how many right-angled triangles with side-lengths a, b and c that satisfied an inequality 1 ≤ a ≤ b ≤ c ≤ n. Input The only line contains one integer n (1 ≤ n ≤ 104) as we mentioned above. Output Print a single integer — the answer to the problem. Examples Input 5 Output 1 Input 74 Output 35 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Jeff's friends know full well that the boy likes to get sequences and arrays for his birthday. Thus, Jeff got sequence p1, p2, ..., pn for his birthday. Jeff hates inversions in sequences. An inversion in sequence a1, a2, ..., an is a pair of indexes i, j (1 ≤ i < j ≤ n), such that an inequality ai > aj holds. Jeff can multiply some numbers of the sequence p by -1. At that, he wants the number of inversions in the sequence to be minimum. Help Jeff and find the minimum number of inversions he manages to get. Input The first line contains integer n (1 ≤ n ≤ 2000). The next line contains n integers — sequence p1, p2, ..., pn (\|pi\| ≤ 105). The numbers are separated by spaces. Output In a single line print the answer to the problem — the minimum number of inversions Jeff can get. Examples Input 2 2 1 Output 0 Input 9 -2 0 -1 0 -1 2 1 0 -1 Output 6 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The employees of the F company have lots of ways to entertain themselves. Today they invited a famous magician who shows a trick with plastic cups and a marble. The point is to trick the spectator's attention. Initially, the spectator stands in front of a line of n plastic cups. Then the magician places a small marble under one cup and shuffles the cups. Then the spectator should guess which cup hides the marble. But the head coder of the F company isn't easy to trick. When he saw the performance, he noticed several important facts: * each cup contains a mark — a number from 1 to n; all marks on the cups are distinct; * the magician shuffles the cups in m operations, each operation looks like that: take a cup marked xi, sitting at position yi in the row of cups (the positions are numbered from left to right, starting from 1) and shift it to the very beginning of the cup row (on the first position). When the head coder came home after work he wanted to re-do the trick. Unfortunately, he didn't remember the starting or the final position of the cups. He only remembered which operations the magician performed. Help the coder: given the operations in the order they were made find at least one initial permutation of the cups that can go through the described operations in the given order. Otherwise, state that such permutation doesn't exist. Input The first line contains integers n and m (1 ≤ n, m ≤ 106). Each of the next m lines contains a couple of integers. The i-th line contains integers xi, yi (1 ≤ xi, yi ≤ n) — the description of the i-th operation of the magician. Note that the operations are given in the order in which the magician made them and the coder wants to make them in the same order. Output If the described permutation doesn't exist (the programmer remembered wrong operations), print -1. Otherwise, print n distinct integers, each from 1 to n: the i-th number should represent the mark on the cup that initially is in the row in position i. If there are multiple correct answers, you should print the lexicographically minimum one. Examples Input 2 1 2 1 Output 2 1 Input 3 2 1 2 1 1 Output 2 1 3 Input 3 3 1 3 2 3 1 3 Output -1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. DZY loves collecting special strings which only contain lowercase letters. For each lowercase letter c DZY knows its value wc. For each special string s = s1s2... s\|s\| (\|s\| is the length of the string) he represents its value with a function f(s), where <image> Now DZY has a string s. He wants to insert k lowercase letters into this string in order to get the largest possible value of the resulting string. Can you help him calculate the largest possible value he could get? Input The first line contains a single string s (1 ≤ \|s\| ≤ 103). The second line contains a single integer k (0 ≤ k ≤ 103). The third line contains twenty-six integers from wa to wz. Each such number is non-negative and doesn't exceed 1000. Output Print a single integer — the largest possible value of the resulting string DZY could get. Examples Input abc 3 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Output 41 Note In the test sample DZY can obtain "abcbbc", value = 1·1 + 2·2 + 3·2 + 4·2 + 5·2 + 6·2 = 41. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Little X used to play a card game called "24 Game", but recently he has found it too easy. So he invented a new game. Initially you have a sequence of n integers: 1, 2, ..., n. In a single step, you can pick two of them, let's denote them a and b, erase them from the sequence, and append to the sequence either a + b, or a - b, or a × b. After n - 1 steps there is only one number left. Can you make this number equal to 24? Input The first line contains a single integer n (1 ≤ n ≤ 105). Output If it's possible, print "YES" in the first line. Otherwise, print "NO" (without the quotes). If there is a way to obtain 24 as the result number, in the following n - 1 lines print the required operations an operation per line. Each operation should be in form: "a op b = c". Where a and b are the numbers you've picked at this operation; op is either "+", or "-", or ""; c is the result of corresponding operation. Note, that the absolute value of c mustn't be greater than 1018. The result of the last operation must be equal to 24. Separate operator sign and equality sign from numbers with spaces. If there are multiple valid answers, you may print any of them. Examples Input 1 Output NO Input 8 Output YES 8 7 = 56 6 * 5 = 30 3 - 4 = -1 1 - 2 = -1 30 - -1 = 31 56 - 31 = 25 25 + -1 = 24 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.

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