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[ { "content": "Question:\nWatson gives a square of side length 1 to Sherlock. Now, after each second, each square of some arbitrary side $\\boldsymbol{\\mbox{I}}$ will break into four squares each of side $L/2$(as shown in the image below). \n\nNow, Watson asks Sherlock: What will be the sum of length of solid l...
[ { "content": "Question:\nWatson gives a square of side length 1 to Sherlock. Now, after each second, each square of some arbitrary side $\\boldsymbol{\\mbox{I}}$ will break into four squares each of side $L/2$(as shown in the image below). \n\nNow, Watson asks Sherlock: What will be the sum of length of solid l...
[ { "content": "Question:\nRead problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.\n\nThere are $N$ frogs (numbered $1$ through $N$) in a line. For each valid $i$, the $i$-th frog is initially at the position $i$, it has weight $W_{i}$, and whenever you hit its back...
[ { "content": "Question:\nRead problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.\n\nThere are $N$ frogs (numbered $1$ through $N$) in a line. For each valid $i$, the $i$-th frog is initially at the position $i$, it has weight $W_{i}$, and whenever you hit its back...
[ { "content": "Question:\nThe AtCoder company office can be represented as a grid of H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nThe state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell contains a desk; if S_{i,j} i...
[ { "content": "Question:\nThe AtCoder company office can be represented as a grid of H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nThe state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell contains a desk; if S_{i,j} i...
[ { "content": "Question:\nWatson gives a square of side length 1 to Sherlock. Now, after each second, each square of some arbitrary side $\\boldsymbol{\\mbox{I}}$ will break into four squares each of side $L/2$(as shown in the image below). \n\nNow, Watson asks Sherlock: What will be the sum of length of solid l...
[ { "content": "Question:\nWatson gives a square of side length 1 to Sherlock. Now, after each second, each square of some arbitrary side $\\boldsymbol{\\mbox{I}}$ will break into four squares each of side $L/2$(as shown in the image below). \n\nNow, Watson asks Sherlock: What will be the sum of length of solid l...
[ { "content": "Question:\nThe AtCoder company office can be represented as a grid of H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nThe state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell contains a desk; if S_{i,j} i...
[ { "content": "Question:\nThe AtCoder company office can be represented as a grid of H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nThe state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell contains a desk; if S_{i,j} i...
[ { "content": "Question:\nYou have a board represented as a grid with $2 \\times n$ cells.\n\nThe first $k_1$ cells on the first row and first $k_2$ cells on the second row are colored in white. All other cells are colored in black.\n\nYou have $w$ white dominoes ($2 \\times 1$ tiles, both cells are colored in w...
[ { "content": "Question:\nYou have a board represented as a grid with $2 \\times n$ cells.\n\nThe first $k_1$ cells on the first row and first $k_2$ cells on the second row are colored in white. All other cells are colored in black.\n\nYou have $w$ white dominoes ($2 \\times 1$ tiles, both cells are colored in w...
[ { "content": "Question:\n\\documentclass{article}\n\\usepackage{graphicx} % Required for inserting images\n\n\\title{test}\n\\author{z1284537530 }\n\\date{March 2023}\n\n\\begin{document}\n\n\\maketitle\n\nAfter their success in coming up with Fun Game, Kyle and Mike invented another game having the following r...
[ { "content": "Question:\n\\documentclass{article}\n\\usepackage{graphicx} % Required for inserting images\n\n\\title{test}\n\\author{z1284537530 }\n\\date{March 2023}\n\n\\begin{document}\n\n\\maketitle\n\nAfter their success in coming up with Fun Game, Kyle and Mike invented another game having the following r...
[ { "content": "Question:\nYou are given a string $s$ consisting of the characters 0, 1, and ?.\n\nLet's call a string unstable if it consists of the characters 0 and 1 and any two adjacent characters are different (i. e. it has the form 010101... or 101010...).\n\nLet's call a string beautiful if it consists of ...
[ { "content": "Question:\nYou are given a string $s$ consisting of the characters 0, 1, and ?.\n\nLet's call a string unstable if it consists of the characters 0 and 1 and any two adjacent characters are different (i. e. it has the form 010101... or 101010...).\n\nLet's call a string beautiful if it consists of ...
[ { "content": "Question:\nPasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. \n\nPasha likes rectangles but hates squares, so he wonde...
[ { "content": "Question:\nPasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. \n\nPasha likes rectangles but hates squares, so he wonde...
[ { "content": "Question:\nYou are given a string S consisting of uppercase and lowercase English letters. \nWe perform the following operation on S 10^{100} times:\n\n- First, create a string T by changing uppercase letters in S to lowercase, and lowercase letters to uppercase.\n- Then, concatenate S and T in t...
[ { "content": "Question:\nYou are given a string S consisting of uppercase and lowercase English letters. \nWe perform the following operation on S 10^{100} times:\n\n- First, create a string T by changing uppercase letters in S to lowercase, and lowercase letters to uppercase.\n- Then, concatenate S and T in t...
[ { "content": "Question:\nThere are N people participating in an event, and the transportation cost for the i-th person is A_i yen.\nTakahashi, the organizer of the event, decided to set a maximum limit x for the transportation subsidy. The subsidy for person i will be \\min(x, A_i) yen. Here, x must be a non-ne...
[ { "content": "Question:\nThere are N people participating in an event, and the transportation cost for the i-th person is A_i yen.\nTakahashi, the organizer of the event, decided to set a maximum limit x for the transportation subsidy. The subsidy for person i will be \\min(x, A_i) yen. Here, x must be a non-ne...
[ { "content": "Question:\nThe Berland language consists of words having exactly two letters. Moreover, the first letter of a word is different from the second letter. Any combination of two different Berland letters (which, by the way, are the same as the lowercase letters of Latin alphabet) is a correct word in...
[ { "content": "Question:\nThe Berland language consists of words having exactly two letters. Moreover, the first letter of a word is different from the second letter. Any combination of two different Berland letters (which, by the way, are the same as the lowercase letters of Latin alphabet) is a correct word in...
[ { "content": "Question:\nIn Arcady's garden there grows a peculiar apple-tree that fruits one time per year. Its peculiarity can be explained in following way: there are n inflorescences, numbered from 1 to n. Inflorescence number 1 is situated near base of tree and any other inflorescence with number i (i > 1)...
[ { "content": "Question:\nIn Arcady's garden there grows a peculiar apple-tree that fruits one time per year. Its peculiarity can be explained in following way: there are n inflorescences, numbered from 1 to n. Inflorescence number 1 is situated near base of tree and any other inflorescence with number i (i > 1)...
[ { "content": "Question:\nIn Ciel's restaurant, a waiter is training.\nSince the waiter isn't good at arithmetic, sometimes he gives guests wrong change.\nCiel gives him a simple problem.\nWhat is A-B (A minus B) ?\n\nSurprisingly, his answer is wrong.\nTo be more precise, his answer has exactly one wrong digit....
[ { "content": "Question:\nIn Ciel's restaurant, a waiter is training.\nSince the waiter isn't good at arithmetic, sometimes he gives guests wrong change.\nCiel gives him a simple problem.\nWhat is A-B (A minus B) ?\n\nSurprisingly, his answer is wrong.\nTo be more precise, his answer has exactly one wrong digit....
[ { "content": "Question:\nGiven a positive integer N, find a possible arrangement of the integers from 0 to N -1 such that the binary representation of every number (except the first) differs at most at one bit from the binary representation of the number before it. Or tell that it’s impossible to get such an ar...
[ { "content": "Question:\nGiven a positive integer N, find a possible arrangement of the integers from 0 to N -1 such that the binary representation of every number (except the first) differs at most at one bit from the binary representation of the number before it. Or tell that it’s impossible to get such an ar...
[ { "content": "Question:\nThe only difference between easy and hard versions is the constraints.\n\nPolycarp has to write a coursework. The coursework consists of $m$ pages.\n\nPolycarp also has $n$ cups of coffee. The coffee in the $i$-th cup has $a_i$ caffeine in it. Polycarp can drink some cups of coffee (eac...
[ { "content": "Question:\nThe only difference between easy and hard versions is the constraints.\n\nPolycarp has to write a coursework. The coursework consists of $m$ pages.\n\nPolycarp also has $n$ cups of coffee. The coffee in the $i$-th cup has $a_i$ caffeine in it. Polycarp can drink some cups of coffee (eac...
[ { "content": "Question:\nDuring the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started le...
[ { "content": "Question:\nDuring the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started le...
[ { "content": "Question:\nThe AtCoder company office can be represented as a grid of H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nThe state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell contains a desk; if S_{i,j} i...
[ { "content": "Question:\nThe AtCoder company office can be represented as a grid of H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nThe state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell contains a desk; if S_{i,j} i...
[ { "content": "Question:\nSardar Khan has finally decided to attack Ramadhir - he will bomb one of Ramadhir's businesses in Wasseypur. Sardar Khan knows that Ramadhir has N businesses (numbered 1 to N) and that there are N - 1 roads connecting pairs of these businesses in such a way that all businesses are conne...
[ { "content": "Question:\nSardar Khan has finally decided to attack Ramadhir - he will bomb one of Ramadhir's businesses in Wasseypur. Sardar Khan knows that Ramadhir has N businesses (numbered 1 to N) and that there are N - 1 roads connecting pairs of these businesses in such a way that all businesses are conne...
[ { "content": "Question:\n$n$ distinct integers $x_1,x_2,\\ldots,x_n$ are written on the board. Nezzar can perform the following operation multiple times.\n\nSelect two integers $x,y$ (not necessarily distinct) on the board, and write down $2x-y$. Note that you don't remove selected numbers.\n\nNow, Nezzar wonde...
[ { "content": "Question:\n$n$ distinct integers $x_1,x_2,\\ldots,x_n$ are written on the board. Nezzar can perform the following operation multiple times.\n\nSelect two integers $x,y$ (not necessarily distinct) on the board, and write down $2x-y$. Note that you don't remove selected numbers.\n\nNow, Nezzar wonde...
[ { "content": "Question:\nRead problem statements in [Russian], [Bengali], and [Mandarin Chinese] as well.\n\nAnn is going to take part in a race. At the start, she has $X$ units of energy. For each subsequent second, she can decide to run or to rest (she must perform the chosen action during the whole second). ...
[ { "content": "Question:\nRead problem statements in [Russian], [Bengali], and [Mandarin Chinese] as well.\n\nAnn is going to take part in a race. At the start, she has $X$ units of energy. For each subsequent second, she can decide to run or to rest (she must perform the chosen action during the whole second). ...
[ { "content": "Question:\nWatchmen are in a danger and Doctor Manhattan together with his friend Daniel Dreiberg should warn them as soon as possible. There are n watchmen on a plane, the i-th watchman is located at point (x_{i}, y_{i}).\n\nThey need to arrange a plan, but there are some difficulties on their wa...
[ { "content": "Question:\nWatchmen are in a danger and Doctor Manhattan together with his friend Daniel Dreiberg should warn them as soon as possible. There are n watchmen on a plane, the i-th watchman is located at point (x_{i}, y_{i}).\n\nThey need to arrange a plan, but there are some difficulties on their wa...
[ { "content": "Question:\nSasha and Kolya decided to get drunk with Coke, again. This time they have k types of Coke. i-th type is characterised by its carbon dioxide concentration <image>. Today, on the party in honour of Sergiy of Vancouver they decided to prepare a glass of Coke with carbon dioxide concentrat...
[ { "content": "Question:\nSasha and Kolya decided to get drunk with Coke, again. This time they have k types of Coke. i-th type is characterised by its carbon dioxide concentration <image>. Today, on the party in honour of Sergiy of Vancouver they decided to prepare a glass of Coke with carbon dioxide concentrat...
[ { "content": "Question:\nOne industrial factory is reforming working plan. The director suggested to set a mythical detail production norm. If at the beginning of the day there were x details in the factory storage, then by the end of the day the factory has to produce $x \\operatorname{mod} m$ (remainder after...
[ { "content": "Question:\nOne industrial factory is reforming working plan. The director suggested to set a mythical detail production norm. If at the beginning of the day there were x details in the factory storage, then by the end of the day the factory has to produce $x \\operatorname{mod} m$ (remainder after...
[ { "content": "Question:\nPasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. \n\nPasha likes rectangles but hates squares, so he wonde...
[ { "content": "Question:\nPasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. \n\nPasha likes rectangles but hates squares, so he wonde...
[ { "content": "Question:\nOne warm and sunny day king Copa decided to visit the shooting gallery, located at the Central Park, and try to win the main prize — big pink plush panda. The king is not good at shooting, so he invited you to help him.\n\nThe shooting gallery is an infinite vertical plane with Cartesia...
[ { "content": "Question:\nOne warm and sunny day king Copa decided to visit the shooting gallery, located at the Central Park, and try to win the main prize — big pink plush panda. The king is not good at shooting, so he invited you to help him.\n\nThe shooting gallery is an infinite vertical plane with Cartesia...
[ { "content": "Question:\nThe only difference between easy and hard versions is constraints.\n\nNow elections are held in Berland and you want to win them. More precisely, you want everyone to vote for you.\n\nThere are $n$ voters, and two ways to convince each of them to vote for you. The first way to convince ...
[ { "content": "Question:\nThe only difference between easy and hard versions is constraints.\n\nNow elections are held in Berland and you want to win them. More precisely, you want everyone to vote for you.\n\nThere are $n$ voters, and two ways to convince each of them to vote for you. The first way to convince ...
[ { "content": "Question:\nIahub is training for the IOI. What is a better way to train than playing a Zuma-like game? \n\nThere are n balls put in a row. Each ball is colored in one of k colors. Initially the row doesn't contain three or more contiguous balls with the same color. Iahub has a single ball of color...
[ { "content": "Question:\nIahub is training for the IOI. What is a better way to train than playing a Zuma-like game? \n\nThere are n balls put in a row. Each ball is colored in one of k colors. Initially the row doesn't contain three or more contiguous balls with the same color. Iahub has a single ball of color...
[ { "content": "Question:\nDexter and Debra are playing a game. They have N containers each having one or more chocolates. Containers are numbered from 1 to N, where i^{th} container has A[i] number of chocolates.\n\nThe game goes like this. First player will choose a container and take one or more chocolates fro...
[ { "content": "Question:\nDexter and Debra are playing a game. They have N containers each having one or more chocolates. Containers are numbered from 1 to N, where i^{th} container has A[i] number of chocolates.\n\nThe game goes like this. First player will choose a container and take one or more chocolates fro...
[ { "content": "Question:\nYou are given a horizontally written text. Convert it to vertical writing, filling spaces with *.\n\nYou are given N strings S_1, S_2, \\dots, S_N consisting of lowercase English letters. Let M be the maximum length of these strings.\nPrint M strings T_1, T_2, \\dots, T_M that satisfy t...
[ { "content": "Question:\nYou are given a horizontally written text. Convert it to vertical writing, filling spaces with *.\n\nYou are given N strings S_1, S_2, \\dots, S_N consisting of lowercase English letters. Let M be the maximum length of these strings.\nPrint M strings T_1, T_2, \\dots, T_M that satisfy t...
[ { "content": "Question:\nYou are given an array of integers nums of size n and a positive integer threshold.\nThere is a graph consisting of n nodes with the i^th node having a value of nums[i]. Two nodes i and j in the graph are connected via an undirected edge if lcm(nums[i], nums[j]) <= threshold.\nReturn th...
[ { "content": "Question:\nYou are given an array of integers nums of size n and a positive integer threshold.\nThere is a graph consisting of n nodes with the i^th node having a value of nums[i]. Two nodes i and j in the graph are connected via an undirected edge if lcm(nums[i], nums[j]) <= threshold.\nReturn th...
[ { "content": "Question:\nRead problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.\n\nIn Chefland, each citizen has their own personal string. Chef is no exception. Recently, his string broke and he went to a shop to get a new one.\n\nThere are two strings in the sh...
[ { "content": "Question:\nRead problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.\n\nIn Chefland, each citizen has their own personal string. Chef is no exception. Recently, his string broke and he went to a shop to get a new one.\n\nThere are two strings in the sh...
[ { "content": "Question:\nA magician has various spells.\nYou are given an array power, where each element represents the damage of a spell. Multiple spells can have the same damage value.\nIt is a known fact that if a magician decides to cast a spell with a damage of power[i], they cannot cast any spell with a ...
[ { "content": "Question:\nA magician has various spells.\nYou are given an array power, where each element represents the damage of a spell. Multiple spells can have the same damage value.\nIt is a known fact that if a magician decides to cast a spell with a damage of power[i], they cannot cast any spell with a ...
[ { "content": "Question:\nYou are given three integers A,B,C. Determine whether it is possible to divide these three integers into two or more groups so that these groups have equal sums.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA B C\n\nOutput\n\nIf it is possible to divide A...
[ { "content": "Question:\nYou are given three integers A,B,C. Determine whether it is possible to divide these three integers into two or more groups so that these groups have equal sums.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA B C\n\nOutput\n\nIf it is possible to divide A...
[ { "content": "Question:\nThe statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, $n$ is always even, and in C2, $n$ is always odd.\n\nYou are given a regular polygon with $2 \\cdot n$ vertices (it's convex and has equal sides and equal angles) and al...
[ { "content": "Question:\nThe statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, $n$ is always even, and in C2, $n$ is always odd.\n\nYou are given a regular polygon with $2 \\cdot n$ vertices (it's convex and has equal sides and equal angles) and al...
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