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int64 | request_idx
int64 | task_name
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi has prepared N dishes for Snuke.\nThe dishes are numbered from 1 to N, and dish i has a sweetness of A_i and a saltiness of B_i.\nTakahashi can arrange these dishes in any order he likes.\nSnuke will eat the dishes in the order they are arranged, but if at any point the total sweetness of the dishes he has eaten so far exceeds X or the total saltiness exceeds Y, he will not eat any further dishes.\nTakahashi wants Snuke to eat as many dishes as possible.\nFind the maximum number of dishes Snuke will eat if Takahashi arranges the dishes optimally.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN X Y\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N\n\nOutput\n\nPrint the answer as an integer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 80\n- 1 \\leq A_i, B_i \\leq 10000\n- 1 \\leq X, Y \\leq 10000\n- All input values are integers.\n\nSample Input 1\n\n4 8 4\n1 5\n3 2\n4 1\n5 3\n\nSample Output 1\n\n3\n\nConsider the scenario where Takahashi arranges the dishes in the order 2, 3, 1, 4.\n\n- First, Snuke eats dish 2. The total sweetness so far is 3, and the total saltiness is 2.\n- Next, Snuke eats dish 3. The total sweetness so far is 7, and the total saltiness is 3.\n- Next, Snuke eats dish 1. The total sweetness so far is 8, and the total saltiness is 8.\n- The total saltiness has exceeded Y=4, so Snuke will not eat any further dishes.\n\nThus, in this arrangement, Snuke will eat three dishes.\nNo matter how Takahashi arranges the dishes, Snuke will not eat all four dishes, so the answer is 3.\n\nSample Input 2\n\n2 1 1\n3 2\n3 2\n\nSample Output 2\n\n1\n\nSample Input 3\n\n2 100 100\n3 2\n3 2\n\nSample Output 3\n\n2\n\nSample Input 4\n\n6 364 463\n230 381\n154 200\n328 407\n339 94\n193 10\n115 309\n\nSample Output 4\n\n3",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N people, and the current hair length of the i-th person (1 \\leq i \\leq N) is L_i.\nEach person's hair grows by 1 per day.\nPrint the number of days after which the number of people whose hair length is at least T becomes P or more for the first time.\nIf there are already P or more people whose hair length is at least T now, print 0.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN T P\nL_1 L_2 \\ldots L_N\n\nOutput\n\nPrint the number of days after which the number of people whose hair length is at least T becomes P or more for the first time. \nIf this condition is already satisfied now, print 0.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- 1 \\leq L_i \\leq 100\n- 1 \\leq T \\leq 100\n- 1 \\leq P \\leq N\n- All input values are integers.\n\nSample Input 1\n\n5 10 3\n3 11 1 6 2\n\nSample Output 1\n\n7\n\nThere are five people, and their current hair lengths are 3, 11, 1, 6, 2, so there is one person whose hair length is at least 10.\nAfter seven days, the hair lengths of the people will be 10, 18, 8, 13, 9, respectively, and there will be three people whose hair length is at least 10.\nAfter six days, there are only two people whose hair length is at least 10, not satisfying the condition, so print 7.\n\nSample Input 2\n\n2 5 2\n10 10\n\nSample Output 2\n\n0\n\nSince there are already two people whose hair length is at least 5 now, satisfying the condition, so print 0.\n\nSample Input 3\n\n3 10 1\n1 2 3\n\nSample Output 3\n\n7",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are playing a game.\nThere are N enemies lined up in a row, and the i-th enemy from the front has a health of H_i.\nYou will repeat the following action until the healths of all enemies become 0 or less, using a variable T initialized to 0.\n\n- Increase T by 1. Then, attack the frontmost enemy with health 1 or more. If T is a multiple of 3, the enemy's health decreases by 3; otherwise, it decreases by 1.\n\nFind the value of T when the healths of all enemies become 0 or less.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nH_1 H_2 \\ldots H_N\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2\\times 10^5\n- 1 \\leq H_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n3\r\n6 2 2\n\nSample Output 1\n\n8\r\n\nThe actions are performed as follows:\n\n- T becomes 1. Attack the 1st enemy, and its health becomes 6-1=5.\n- T becomes 2. Attack the 1st enemy, and its health becomes 5-1=4.\n- T becomes 3. Attack the 1st enemy, and its health becomes 4-3=1.\n- T becomes 4. Attack the 1st enemy, and its health becomes 1-1=0.\n- T becomes 5. Attack the 2nd enemy, and its health becomes 2-1=1.\n- T becomes 6. Attack the 2nd enemy, and its health becomes 1-3=-2.\n- T becomes 7. Attack the 3rd enemy, and its health becomes 2-1=1.\n- T becomes 8. Attack the 3rd enemy, and its health becomes 1-1=0.\n\nSample Input 2\n\n9\r\n1 12 123 1234 12345 123456 1234567 12345678 123456789\n\nSample Output 2\n\n82304529\n\nSample Input 3\n\n5\r\n1000000000 1000000000 1000000000 1000000000 1000000000\n\nSample Output 3\n\n3000000000\r\n\nBeware of integer overflow.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given three integers n, x, and y.\nAn event is being held for n performers. When a performer arrives, they are assigned to one of the x stages. All performers assigned to the same stage will perform together as a band, though some stages might remain empty.\nAfter all performances are completed, the jury will award each band a score in the range [1, y].\nReturn the total number of possible ways the event can take place.\nSince the answer may be very large, return it modulo 10^9 + 7.\nNote that two events are considered to have been held differently if either of the following conditions is satisfied:\n\nAny performer is assigned a different stage.\nAny band is awarded a different score.\n\n \nExample 1:\n\nInput: n = 1, x = 2, y = 3\nOutput: 6\nExplanation:\n\nThere are 2 ways to assign a stage to the performer.\nThe jury can award a score of either 1, 2, or 3 to the only band.\n\n\nExample 2:\n\nInput: n = 5, x = 2, y = 1\nOutput: 32\nExplanation:\n\nEach performer will be assigned either stage 1 or stage 2.\nAll bands will be awarded a score of 1.\n\n\nExample 3:\n\nInput: n = 3, x = 3, y = 4\nOutput: 684\n\n \nConstraints:\n\n1 <= n, x, y <= 1000",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Alice and Bob are playing a game on a string.\nYou are given a string s, Alice and Bob will take turns playing the following game where Alice starts first:\n\nOn Alice's turn, she has to remove any non-empty substring from s that contains an odd number of vowels.\nOn Bob's turn, he has to remove any non-empty substring from s that contains an even number of vowels.\n\nThe first player who cannot make a move on their turn loses the game. We assume that both Alice and Bob play optimally.\nReturn true if Alice wins the game, and false otherwise.\nThe English vowels are: a, e, i, o, and u.\n \nExample 1:\n\nInput: s = \"leetcoder\"\nOutput: true\nExplanation:\nAlice can win the game as follows:\n\nAlice plays first, she can delete the underlined substring in s = \"leetcoder\" which contains 3 vowels. The resulting string is s = \"der\".\nBob plays second, he can delete the underlined substring in s = \"der\" which contains 0 vowels. The resulting string is s = \"er\".\nAlice plays third, she can delete the whole string s = \"er\" which contains 1 vowel.\nBob plays fourth, since the string is empty, there is no valid play for Bob. So Alice wins the game.\n\n\nExample 2:\n\nInput: s = \"bbcd\"\nOutput: false\nExplanation:\nThere is no valid play for Alice in her first turn, so Alice loses the game.\n\n \nConstraints:\n\n1 <= s.length <= 10^5\ns consists only of lowercase English letters.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Alice and Bob are playing a fantasy battle game consisting of n rounds where they summon one of three magical creatures each round: a Fire Dragon, a Water Serpent, or an Earth Golem. In each round, players simultaneously summon their creature and are awarded points as follows:\n\nIf one player summons a Fire Dragon and the other summons an Earth Golem, the player who summoned the Fire Dragon is awarded a point.\nIf one player summons a Water Serpent and the other summons a Fire Dragon, the player who summoned the Water Serpent is awarded a point.\nIf one player summons an Earth Golem and the other summons a Water Serpent, the player who summoned the Earth Golem is awarded a point.\nIf both players summon the same creature, no player is awarded a point.\n\nYou are given a string s consisting of n characters 'F', 'W', and 'E', representing the sequence of creatures Alice will summon in each round:\n\nIf s[i] == 'F', Alice summons a Fire Dragon.\nIf s[i] == 'W', Alice summons a Water Serpent.\nIf s[i] == 'E', Alice summons an Earth Golem.\n\nBob’s sequence of moves is unknown, but it is guaranteed that Bob will never summon the same creature in two consecutive rounds. Bob beats Alice if the total number of points awarded to Bob after n rounds is strictly greater than the points awarded to Alice.\nReturn the number of distinct sequences Bob can use to beat Alice.\nSince the answer may be very large, return it modulo 10^9 + 7.\n \nExample 1:\n\nInput: s = \"FFF\"\nOutput: 3\nExplanation:\nBob can beat Alice by making one of the following sequences of moves: \"WFW\", \"FWF\", or \"WEW\". Note that other winning sequences like \"WWE\" or \"EWW\" are invalid since Bob cannot make the same move twice in a row.\n\nExample 2:\n\nInput: s = \"FWEFW\"\nOutput: 18\nExplanation:\nBob can beat Alice by making one of the following sequences of moves: \"FWFWF\", \"FWFWE\", \"FWEFE\", \"FWEWE\", \"FEFWF\", \"FEFWE\", \"FEFEW\", \"FEWFE\", \"WFEFE\", \"WFEWE\", \"WEFWF\", \"WEFWE\", \"WEFEF\", \"WEFEW\", \"WEWFW\", \"WEWFE\", \"EWFWE\", or \"EWEWE\".\n\n \nConstraints:\n\n1 <= s.length <= 1000\ns[i] is one of 'F', 'W', or 'E'.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer n and a 2D array requirements, where requirements[i] = [end_i, cnt_i] represents the end index and the inversion count of each requirement.\nA pair of indices (i, j) from an integer array nums is called an inversion if:\n\ni < j and nums[i] > nums[j]\n\nReturn the number of permutations perm of [0, 1, 2, ..., n - 1] such that for all requirements[i], perm[0..end_i] has exactly cnt_i inversions.\nSince the answer may be very large, return it modulo 10^9 + 7.\n \nExample 1:\n\nInput: n = 3, requirements = [[2,2],[0,0]]\nOutput: 2\nExplanation:\nThe two permutations are:\n\n[2, 0, 1]\n\nPrefix [2, 0, 1] has inversions (0, 1) and (0, 2).\nPrefix [2] has 0 inversions.\n\n\n[1, 2, 0]\n\nPrefix [1, 2, 0] has inversions (0, 2) and (1, 2).\nPrefix [1] has 0 inversions.\n\n\n\n\nExample 2:\n\nInput: n = 3, requirements = [[2,2],[1,1],[0,0]]\nOutput: 1\nExplanation:\nThe only satisfying permutation is [2, 0, 1]:\n\nPrefix [2, 0, 1] has inversions (0, 1) and (0, 2).\nPrefix [2, 0] has an inversion (0, 1).\nPrefix [2] has 0 inversions.\n\n\nExample 3:\n\nInput: n = 2, requirements = [[0,0],[1,0]]\nOutput: 1\nExplanation:\nThe only satisfying permutation is [0, 1]:\n\nPrefix [0] has 0 inversions.\nPrefix [0, 1] has an inversion (0, 1).\n\n\n \nConstraints:\n\n2 <= n <= 300\n1 <= requirements.length <= n\nrequirements[i] = [end_i, cnt_i]\n0 <= end_i <= n - 1\n0 <= cnt_i <= 400\nThe input is generated such that there is at least one i such that end_i == n - 1.\nThe input is generated such that all end_i are unique.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N pairs of integers (L_1, R_1), (L_2, R_2), \\ldots, (L_N, R_N).\nDetermine whether there exists a sequence of N integers X = (X_1, X_2, \\ldots, X_N) that satisfies the following conditions, and print one such sequence if it exists.\n\n- L_i \\leq X_i \\leq R_i for each i = 1, 2, \\ldots, N.\n- \\displaystyle \\sum_{i=1}^N X_i = 0.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nL_1 R_1\r\nL_2 R_2\r\n\\vdots\r\nL_N R_N\n\nOutput\n\nIf no solution exists, print No. Otherwise, print an integer sequence X that satisfies the conditions in the following format:\nYes\r\nX_1 X_2 \\ldots X_N\r\n\nIf multiple solutions exist, any of them will be considered correct.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- -10^9 \\leq L_i \\leq R_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n3\r\n3 5\r\n-4 1\r\n-2 3\n\nSample Output 1\n\nYes\r\n4 -3 -1\r\n\nThe sequence X = (4, -3, -1) satisfies all the conditions. Other valid sequences include (3, -3, 0) and (5, -4, -1).\n\nSample Input 2\n\n3\r\n1 2\r\n1 2\r\n1 2\n\nSample Output 2\n\nNo\r\n\nNo sequence X satisfies the conditions.\n\nSample Input 3\n\n6\r\n-87 12\r\n-60 -54\r\n2 38\r\n-76 6\r\n87 96\r\n-17 38\n\nSample Output 3\n\nYes\r\n-66 -57 31 -6 89 9",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Note: This problem has almost the same setting as Problem B. Only the parts in bold in the main text and constraints differ.\nYou are holding a ring with both hands.\nThis ring consists of N\\ (N \\geq 3) parts numbered 1,2,\\dots,N, where parts i and i+1 (1 \\leq i \\leq N-1) are adjacent, and parts 1 and N are also adjacent.\nInitially, your left hand is holding part 1, and your right hand is holding part 2.\nIn one operation, you can do the following:\n\n- Move one of your hands to an adjacent part of the part it is currently holding. However, you can do this only if the other hand is not on the destination part.\n\nThe following figure shows the initial state and examples of operations that can and cannot be made from there. The number written on each part of the ring represents the part number, and the circles labeled L and R represent your left and right hands, respectively.\n\nYou need to follow Q instructions given to you in order.\nThe i-th (1 \\leq i \\leq Q) instruction is represented by a character H_i and an integer T_i, meaning the following:\n\n- Perform some number of operations (possibly zero) so that your left hand (if H_i is L) or your right hand (if H_i is R) is holding part T_i.\n Here, you may move the other hand not specified by H_i.\n\nUnder the settings and constraints of this problem, it can be proved that any instructions are achievable.\nFind the minimum total number of operations required to follow all the instructions.\n\nInput\n\nThe Input is given from Standard Input in the following format:\nN Q\nH_1 T_1\nH_2 T_2\n\\vdots\nH_Q T_Q\n\nOutput\n\nPrint the minimum total number of operations required to follow all the instructions.\n\nConstraints\n\n\n- 3\\leq N \\leq 3000\n- 1\\leq Q \\leq 3000\n- H_i is L or R.\n- 1 \\leq T_i \\leq N\n- N, Q, and T_i are integers.\n\nSample Input 1\n\n6 3\nR 4\nL 5\nR 5\n\nSample Output 1\n\n6\n\n\nBy performing the following operations, you can follow all Q instructions in order.\n\n- Move your right hand as part 2 \\rightarrow 3 \\rightarrow 4 to follow the first instruction.\n- Move your left hand as part 1 \\rightarrow 6 \\rightarrow 5 to follow the second instruction.\n- Move your left hand as part 5 \\rightarrow 6, then move your right hand as part 4 \\rightarrow 5 to follow the third instruction.\n\nIn this case, the total number of operations is 2+2+1+1=6, which is the minimum.\n\nSample Input 2\n\n100 2\nL 1\nR 2\n\nSample Output 2\n\n0\n\nThere are cases where you can follow the instructions without performing any operations.\n\nSample Input 3\n\n30 8\nR 23\nR 26\nR 29\nL 20\nR 29\nR 19\nL 7\nL 16\n\nSample Output 3\n\n58",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.AtCoder Regular Contest (ARC) is divided into two divisions.\n\n- In ARC Div. 1, participants whose rating at the start of the contest is between 1600 and 2799, inclusive, are subject to rating updates.\n- In ARC Div. 2, participants whose rating at the start of the contest is between 1200 and 2399, inclusive, are subject to rating updates.\n\nTakahashi decided to participate in N ARCs.\nInitially, his rating is R.\nThe i-th (1\\leq i\\leq N) ARC is Div. D _ i, and his performance in that contest is represented by an integer A _ i.\nIf he is subject to a rating update in the i-th ARC, let T be his rating at the start of that contest. Then, after the contest, his rating becomes T+A _ i.\nIf his is not subject to a rating update, his rating does not change.\nRating updates for ARCs are performed immediately after the contest ends, and whether he is subject to rating updates in the next contest is determined based on his rating after the update.\nFind his rating after finishing the N ARCs.\nHe does not participate in any contests other than these N ARCs, and his rating does not change in other ways.\n\nInput\n\nThe input is given in the following format from Standard Input:\nN R\r\nD _ 1 A _ 1\r\nD _ 2 A _ 2\r\n\\vdots\r\nD _ N A _ N\n\nOutput\n\nPrint Takahashi's rating after finishing the N ARCs.\n\nConstraints\n\n\n- 1\\leq N\\leq 100\n- 0\\leq R\\leq 4229\n- 1\\leq D _ i\\leq 2\\ (1\\leq i\\leq N)\n- -1000\\leq A _ i\\leq 1000\\ (1\\leq i\\leq N)\n- All input values are integers.\n\nSample Input 1\n\n4 1255\r\n2 900\r\n1 521\r\n2 600\r\n1 52\n\nSample Output 1\n\n2728\r\n\nInitially, Takahashi's rating is 1255.\nFor each contest, Takahashi's rating changes as follows:\n\n- The 1st ARC is Div. 2. He is subject to rating updates, so his rating becomes 1255+900=2155.\n- The 2nd ARC is Div. 1. He is subject to rating updates, so his rating becomes 2155+521=2676.\n- The 3rd ARC is Div. 2. He is not subject to rating updates, so his rating does not change.\n- The 4th ARC is Div. 1. He is subject to rating updates, so his rating becomes 2676+52=2728.\n\nAfter the four ARCs, his rating is 2728, so print 2728.\n\nSample Input 2\n\n2 3031\r\n1 1000\r\n2 -1000\n\nSample Output 2\n\n3031\r\n\nHe is a Red coder, so his rating does not change upon his performance in ARC.\n\nSample Input 3\n\n15 2352\r\n2 -889\r\n2 420\r\n2 -275\r\n1 957\r\n1 -411\r\n1 -363\r\n1 151\r\n2 -193\r\n2 289\r\n2 -770\r\n2 109\r\n1 345\r\n2 551\r\n1 -702\r\n1 355\n\nSample Output 3\n\n1226",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a road extending east and west, and N persons are on the road.\nThe road extends infinitely long to the east and west from a point called the origin.\nThe i-th person (1\\leq i\\leq N) is initially at a position X_i meters east from the origin.\nThe persons can move along the road to the east or west.\nSpecifically, they can perform the following movement any number of times.\n\n- Choose one person. If there is no other person at the destination, move the chosen person 1 meter east or west.\n\nThey have Q tasks in total, and the i-th task (1\\leq i\\leq Q) is as follows.\n\n- The T_i-th person arrives at coordinate G_i.\n\nFind the minimum total number of movements required to complete all Q tasks in order.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nX_1 X_2 \\ldots X_N\nQ\nT_1 G_1\nT_2 G_2\n\\vdots\nT_Q G_Q\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1\\leq N\\leq2\\times10^5\n- 0\\leq X_1 < X_2 < \\dotsb < X_N \\leq10^8\n- 1\\leq Q\\leq2\\times10^5\n- 1\\leq T_i\\leq N\\ (1\\leq i\\leq Q)\n- 0\\leq G_i\\leq10^8\\ (1\\leq i\\leq Q)\n- All input values are integers.\n\nSample Input 1\n\n5\n10 20 30 40 50\n4\n3 45\n4 20\n1 35\n2 60\n\nSample Output 1\n\n239\n\nAn optimal sequence of movements for the persons is as follows (the positions of the persons are not necessarily drawn to scale):\n\nFor each task, the persons move as follows.\n\n- The 4th person moves 6 steps east, and the 3rd person moves 15 steps east.\n- The 2nd person moves 2 steps west, the 3rd person moves 26 steps west, and the 4th person moves 26 steps west.\n- The 4th person moves 18 steps east, the 3rd person moves 18 steps east, the 2nd person moves 18 steps east, and the 1st person moves 25 steps east.\n- The 5th person moves 13 steps east, the 4th person moves 24 steps east, the 3rd person moves 24 steps east, and the 2nd person moves 24 steps east.\n\nThe total number of movements is 21+54+79+85=239.\nYou cannot complete all tasks with a total movement count of 238 or less, so print 239.\n\nSample Input 2\n\n8\n0 1 2 3 4 5 6 100000000\n6\n1 100000000\n8 0\n1 100000000\n8 4\n1 100000000\n5 21006578\n\nSample Output 2\n\n4294967297\n\nNote that some persons may need to move to the west of the origin or more than 10^8 meters to the east of it.\nAlso, note that the answer may exceed 2^{32}.\n\nSample Input 3\n\n12\n1558 3536 3755 3881 4042 4657 5062 7558 7721 8330 8542 9845\n8\n9 1694\n7 3296\n12 5299\n5 5195\n5 5871\n1 2491\n8 1149\n8 2996\n\nSample Output 3\n\n89644",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given positive integers N, L, and R.\r\nFor a sequence A = (1, 2, \\dots, N) of length N, an operation of reversing the L-th through R-th elements was performed once.\r\nPrint the sequence after this operation.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN L R\n\nOutput\n\nLet A' = (A'_1, A'_2, \\dots, A'_N) be the sequence after the operation. Print it in the following format:\nA'_1 A'_2 \\dots A'_N\n\nConstraints\n\n\n- All input values are integers.\n- 1 \\leq L \\leq R \\leq N \\leq 100\n\nSample Input 1\n\n5 2 3\n\nSample Output 1\n\n1 3 2 4 5\r\n\nInitially, A = (1, 2, 3, 4, 5).\r\nAfter reversing the second through third elements, the sequence becomes (1, 3, 2, 4, 5), which should be printed.\n\nSample Input 2\n\n7 1 1\n\nSample Output 2\n\n1 2 3 4 5 6 7\r\n\nIt is possible that L = R.\n\nSample Input 3\n\n10 1 10\n\nSample Output 3\n\n10 9 8 7 6 5 4 3 2 1\r\n\nIt is possible that L = 1 or R = N.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.For strings S and T consisting of lowercase English letters, and a string X consisting of 0 and 1, define the string f(S,T,X) consisting of lowercase English letters as follows:\n\n- Starting with an empty string, for each i=1,2,\\dots,|X|, append S to the end if the i-th character of X is 0, and append T to the end if it is 1.\n\nYou are given a string S consisting of lowercase English letters, and strings X and Y consisting of 0 and 1.\nDetermine if there exists a string T (which can be empty) such that f(S,T,X)=f(S,T,Y).\nYou have t test cases to solve.\n\nInput\n\nThe input is given from Standard Input in the following format:\nt\r\n\\mathrm{case}_1\r\n\\vdots\r\n\\mathrm{case}_t\r\n\nEach case is given in the following format:\nS\r\nX\r\nY\n\nOutput\n\nPrint t lines. The i-th line should contain Yes if there exists a T that satisfies the condition for the i-th test case, and No otherwise.\n\nConstraints\n\n\n- 1 \\leq t \\leq 5 \\times 10^5\n- 1 \\leq |S| \\leq 5\\times 10^5\n- 1 \\leq |X|,|Y| \\leq 5\\times 10^5\n- S is a string consisting of lowercase English letters.\n- X and Y are strings consisting of 0 and 1.\n- The sum of |S| across all test cases in a single input is at most 5 \\times 10^5.\n- The sum of |X| across all test cases in a single input is at most 5 \\times 10^5.\n- The sum of |Y| across all test cases in a single input is at most 5 \\times 10^5.\n\nSample Input 1\n\n3\r\naraara\r\n01\r\n111\r\naraaaa\r\n100100\r\n0010111\r\nabacabac\r\n0\r\n1111\n\nSample Output 1\n\nYes\r\nNo\r\nNo\r\n\nBelow, string concatenation is represented using +.\nFor the 1st test case, if T=ara, then f(S,T,X)=S+T=araaraara and f(S,T,Y)=T+T+T=araaraara, so f(S,T,X)=f(S,T,Y).\nFor the 2nd and 3rd test cases, there is no T that satisfies the condition.\n\nSample Input 2\n\n2\r\nempty\r\n10101\r\n00\r\nempty\r\n11111\r\n111\n\nSample Output 2\n\nYes\r\nYes\r\n\nT can be empty.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.How many integers x between 1 and N, inclusive, can be expressed as x = a^b using some positive integer a and a positive integer b not less than 2?\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint the answer as an integer.\n\nConstraints\n\n\n- All input values are integers.\n- 1 \\le N \\le 10^{18}\n\nSample Input 1\n\n99\n\nSample Output 1\n\n12\r\n\nThe integers that satisfy the conditions in the problem statement are 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81: there are 12.\n\nSample Input 2\n\n1000000000000000000\n\nSample Output 2\n\n1001003332",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.In the nation of Atcoder, there are N cities numbered 1 to N, and M trains numbered 1 to M.\r\nTrain i departs from city A_i at time S_i and arrives at city B_i at time T_i.\nGiven a positive integer X_1, find a way to set non-negative integers X_2,\\ldots,X_M that satisfies the following condition with the minimum possible value of X_2+\\ldots+X_M.\n\n- Condition: For all pairs (i,j) satisfying 1 \\leq i,j \\leq M, if B_i=A_j and T_i \\leq S_j, then T_i+X_i \\leq S_j+X_j.\n- In other words, for any pair of trains that are originally possible to transfer between, it is still possible to transfer even after delaying the departure and arrival times of each train i by X_i.\n\n\n\nIt can be proved that such a way to set X_2,\\ldots,X_M with the minimum possible value of X_2+\\ldots+X_M is unique.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M X_1\r\nA_1 B_1 S_1 T_1\r\n\\vdots\r\nA_M B_M S_M T_M\n\nOutput\n\nPrint X_2,\\ldots,X_M that satisfy the condition with the minimum possible sum, in that order, separated by spaces.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2\\times 10^5\n- 2 \\leq M \\leq 2\\times 10^5\n- 1 \\leq A_i,B_i \\leq N\n- A_i \\neq B_i\n- 0 \\leq S_i < T_i \\leq 10^9\n- 1 \\leq X_1 \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n3 6 15\r\n1 2 10 20\r\n1 2 20 30\r\n2 3 25 40\r\n2 3 35 50\r\n3 1 15 30\r\n3 1 45 60\n\nSample Output 1\n\n0 10 0 0 5\r\n\nThe arrival of train 1 from city 1 to 2 is delayed by 15 and becomes time 35.\r\nTo allow transfer from train 1 to 3 in city 2, the departure of train 3 is delayed by 10, making it depart at time 35 and arrive at time 50.\r\nFurther, to allow transfer from train 3 to 6 in city 3, the departure of train 6 is delayed by 5, making it depart at time 50.\r\nOther trains can operate without delay while still allowing transfers between originally transferable trains, so (X_2,X_3,X_4,X_5,X_6)=(0,10,0,0,5) satisfies the condition.\r\nMoreover, there is no solution with a smaller sum that satisfies the condition, so this is the answer.\n\nSample Input 2\n\n10 9 100\r\n1 10 0 1\r\n10 2 1 100\r\n10 3 1 100\r\n10 4 1 100\r\n10 5 1 100\r\n10 6 1 100\r\n10 7 1 100\r\n10 8 1 100\r\n10 9 1 100\n\nSample Output 2\n\n100 100 100 100 100 100 100 100\n\nSample Input 3\n\n4 4 10\r\n1 2 0 1\r\n1 2 0 10\r\n2 3 100 200\r\n2 4 100 200\n\nSample Output 3\n\n0 0 0",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.AtCoder Regular Contest (ARC) is divided into two divisions.\n\n- In ARC Div. 1, participants whose rating at the start of the contest is between 1600 and 2799, inclusive, are subject to rating updates.\n- In ARC Div. 2, participants whose rating at the start of the contest is between 1200 and 2399, inclusive, are subject to rating updates.\n\nTakahashi decided to participate in N ARCs.\nInitially, his rating is R.\nThe i-th (1\\leq i\\leq N) ARC is Div. D _ i, and his performance in that contest is represented by an integer A _ i.\nIf he is subject to a rating update in the i-th ARC, let T be his rating at the start of that contest. Then, after the contest, his rating becomes T+A _ i.\nIf his is not subject to a rating update, his rating does not change.\nRating updates for ARCs are performed immediately after the contest ends, and whether he is subject to rating updates in the next contest is determined based on his rating after the update.\nFind his rating after finishing the N ARCs.\nHe does not participate in any contests other than these N ARCs, and his rating does not change in other ways.\n\nInput\n\nThe input is given in the following format from Standard Input:\nN R\r\nD _ 1 A _ 1\r\nD _ 2 A _ 2\r\n\\vdots\r\nD _ N A _ N\n\nOutput\n\nPrint Takahashi's rating after finishing the N ARCs.\n\nConstraints\n\n\n- 1\\leq N\\leq 100\n- 0\\leq R\\leq 4229\n- 1\\leq D _ i\\leq 2\\ (1\\leq i\\leq N)\n- -1000\\leq A _ i\\leq 1000\\ (1\\leq i\\leq N)\n- All input values are integers.\n\nSample Input 1\n\n4 1255\r\n2 900\r\n1 521\r\n2 600\r\n1 52\n\nSample Output 1\n\n2728\r\n\nInitially, Takahashi's rating is 1255.\nFor each contest, Takahashi's rating changes as follows:\n\n- The 1st ARC is Div. 2. He is subject to rating updates, so his rating becomes 1255+900=2155.\n- The 2nd ARC is Div. 1. He is subject to rating updates, so his rating becomes 2155+521=2676.\n- The 3rd ARC is Div. 2. He is not subject to rating updates, so his rating does not change.\n- The 4th ARC is Div. 1. He is subject to rating updates, so his rating becomes 2676+52=2728.\n\nAfter the four ARCs, his rating is 2728, so print 2728.\n\nSample Input 2\n\n2 3031\r\n1 1000\r\n2 -1000\n\nSample Output 2\n\n3031\r\n\nHe is a Red coder, so his rating does not change upon his performance in ARC.\n\nSample Input 3\n\n15 2352\r\n2 -889\r\n2 420\r\n2 -275\r\n1 957\r\n1 -411\r\n1 -363\r\n1 151\r\n2 -193\r\n2 289\r\n2 -770\r\n2 109\r\n1 345\r\n2 551\r\n1 -702\r\n1 355\n\nSample Output 3\n\n1226",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given simple undirected graphs G and H, each with N vertices: vertices 1, 2, \\ldots, N.\nGraph G has M_G edges, and its i-th edge (1\\leq i\\leq M_G) connects vertices u_i and v_i.\nGraph H has M_H edges, and its i-th edge (1\\leq i\\leq M_H) connects vertices a_i and b_i.\nYou can perform the following operation on graph H any number of times, possibly zero.\n\n- Choose a pair of integers (i,j) satisfying 1\\leq i<j\\leq N. Pay A_{i,j} yen, and if there is no edge between vertices i and j in H, add one; if there is, remove it.\n\nFind the minimum total cost required to make G and H isomorphic.\nWhat is a simple undirected graph?\n A simple undirected graph is a graph without self-loops or multi-edges, where edges have no direction.\n\nWhat does it mean for graphs to be isomorphic?\n Two graphs G and H with N vertices are isomorphic if and only if there exists a permutation (P_1,P_2,\\ldots,P_N) of (1,2,\\ldots,N) such that for all 1\\leq i\\lt j\\leq N:\n\n- an edge exists between vertices i and j in G if and only if an edge exists between vertices P_i and P_j in H.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nM _ G\nu _ 1 v _ 1\nu _ 2 v _ 2\n\\vdots\nu _ {M _ G} v _ {M _ G}\nM _ H\na _ 1 b _ 1\na _ 2 b _ 2\n\\vdots\na _ {M _ H} b _ {M _ H}\nA _ {1,2} A _ {1,3} \\ldots A _ {1,N}\nA _ {2,3} \\ldots A _ {2,N}\n\\vdots\nA _ {N-1,N}\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1\\leq N\\leq8\n- 0\\leq M _ G\\leq\\dfrac{N(N-1)}2\n- 0\\leq M _ H\\leq\\dfrac{N(N-1)}2\n- 1\\leq u _ i\\lt v _ i\\leq N\\ (1\\leq i\\leq M _ G)\n- (u _ i,v _ i)\\neq(u _ j,v _ j)\\ (1\\leq i\\lt j\\leq M _ G)\n- 1\\leq a _ i\\lt b _ i\\leq N\\ (1\\leq i\\leq M _ H)\n- (a _ i,b _ i)\\neq(a _ j,b _ j)\\ (1\\leq i\\lt j\\leq M _ H)\n- 1\\leq A _ {i,j}\\leq 10 ^ 6\\ (1\\leq i\\lt j\\leq N)\n- All input values are integers.\n\nSample Input 1\n\n5\n4\n1 2\n2 3\n3 4\n4 5\n4\n1 2\n1 3\n1 4\n1 5\n3 1 4 1\n5 9 2\n6 5\n3\n\nSample Output 1\n\n9\n\nThe given graphs are as follows:\n\nFor example, you can perform the following four operations on H to make it isomorphic to G at a cost of 9 yen.\n\n- Choose (i,j)=(1,3). There is an edge between vertices 1 and 3 in H, so pay 1 yen to remove it.\n- Choose (i,j)=(2,5). There is no edge between vertices 2 and 5 in H, so pay 2 yen to add it.\n- Choose (i,j)=(1,5). There is an edge between vertices 1 and 5 in H, so pay 1 yen to remove it.\n- Choose (i,j)=(3,5). There is no edge between vertices 3 and 5 in H, so pay 5 yen to add it.\n\nAfter these operations, H becomes:\n\nYou cannot make G and H isomorphic at a cost less than 9 yen, so print 9.\n\nSample Input 2\n\n5\n3\n1 2\n2 3\n3 4\n4\n1 2\n2 3\n3 4\n4 5\n9 1 1 1\n1 1 1\n1 1\n9\n\nSample Output 2\n\n3\n\nFor example, performing the operations (i,j)=(2,3),(2,4),(3,4) on H will make it isomorphic to G.\n\nSample Input 3\n\n5\n3\n1 2\n2 3\n3 4\n4\n1 2\n2 3\n3 4\n4 5\n5 4 4 4\n4 4 4\n4 4\n5\n\nSample Output 3\n\n5\n\nFor example, performing the operation (i,j)=(4,5) once will make G and H isomorphic.\n\nSample Input 4\n\n2\n0\n0\n371\n\nSample Output 4\n\n0\n\nNote that G and H may have no edges.\nAlso, it is possible that no operations are needed.\n\nSample Input 5\n\n8\n13\n1 8\n5 7\n4 6\n1 5\n7 8\n1 6\n1 2\n5 8\n2 6\n5 6\n6 7\n3 7\n4 8\n15\n3 5\n1 7\n4 6\n3 8\n7 8\n1 2\n5 6\n1 6\n1 5\n1 4\n2 8\n2 6\n2 4\n4 7\n1 3\n7483 1694 5868 3296 9723 5299 4326\n5195 4088 5871 1384 2491 6562\n1149 6326 2996 9845 7557\n4041 7720 1554 5060\n8329 8541 3530\n4652 3874\n3748\n\nSample Output 5\n\n21214",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given an array nums of n integers and an integer k, determine whether there exist two adjacent subarrays of length k such that both subarrays are strictly increasing. Specifically, check if there are two subarrays starting at indices a and b (a < b), where:\n\nBoth subarrays nums[a..a + k - 1] and nums[b..b + k - 1] are strictly increasing.\nThe subarrays must be adjacent, meaning b = a + k.\n\nReturn true if it is possible to find two such subarrays, and false otherwise.\n \nExample 1:\n\nInput: nums = [2,5,7,8,9,2,3,4,3,1], k = 3\nOutput: true\nExplanation:\n\nThe subarray starting at index 2 is [7, 8, 9], which is strictly increasing.\nThe subarray starting at index 5 is [2, 3, 4], which is also strictly increasing.\nThese two subarrays are adjacent, so the result is true.\n\n\nExample 2:\n\nInput: nums = [1,2,3,4,4,4,4,5,6,7], k = 5\nOutput: false\n\n \nConstraints:\n\n2 <= nums.length <= 100\n1 < 2 * k <= nums.length\n-1000 <= nums[i] <= 1000",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s.\nA string t is called good if all characters of t occur the same number of times.\nYou can perform the following operations any number of times:\n\nDelete a character from s.\nInsert a character in s.\nChange a character in s to its next letter in the alphabet.\n\nNote that you cannot change 'z' to 'a' using the third operation.\nReturn the minimum number of operations required to make s good.\n \nExample 1:\n\nInput: s = \"acab\"\nOutput: 1\nExplanation:\nWe can make s good by deleting one occurrence of character 'a'.\n\nExample 2:\n\nInput: s = \"wddw\"\nOutput: 0\nExplanation:\nWe do not need to perform any operations since s is initially good.\n\nExample 3:\n\nInput: s = \"aaabc\"\nOutput: 2\nExplanation:\nWe can make s good by applying these operations:\n\nChange one occurrence of 'a' to 'b'\nInsert one occurrence of 'c' into s\n\n\n \nConstraints:\n\n3 <= s.length <= 2 * 10^4\ns contains only lowercase English letters.",
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{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi and Aoki played rock-paper-scissors N times. [Note: In this game, Rock beats Scissors, Scissors beats Paper, and Paper beats Rock.]\nAoki's moves are represented by a string S of length N consisting of the characters R, P, and S.\r\nThe i-th character of S indicates Aoki's move in the i-th game: R for Rock, P for Paper, and S for Scissors.\nTakahashi's moves satisfy the following conditions:\n\n- Takahashi never lost to Aoki.\n- For i=1,2,\\ldots,N-1, Takahashi's move in the i-th game is different from his move in the (i+1)-th game.\n\nDetermine the maximum number of games Takahashi could have won.\nIt is guaranteed that there exists a sequence of moves for Takahashi that satisfies these conditions.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nS\n\nOutput\n\nPrint the maximum number of games Takahashi could have won.\n\nConstraints\n\n\n- 1\\leq N\\leq2\\times10 ^ 5\n- S is a string of length N consisting of R, P, and S.\n- N is an integer.\n\nSample Input 1\n\n6\r\nPRSSRS\n\nSample Output 1\n\n5\r\n\nIn the six games of rock-paper-scissors, Aoki played Paper, Rock, Scissors, Scissors, Rock, and Scissors.\nTakahashi can play Scissors, Paper, Rock, Scissors, Paper, and Rock to win the 1st, 2nd, 3rd, 5th, and 6th games.\nThere is no sequence of moves for Takahashi that satisfies the conditions and wins all six games, so print 5.\n\nSample Input 2\n\n10\r\nSSSSSSSSSS\n\nSample Output 2\n\n5\n\nSample Input 3\n\n24\r\nSPRPSRRRRRPPRPRPSSRSPRSS\n\nSample Output 3\n\n18",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N buildings numbered 1 to N on a number line.\nBuilding i is at coordinate X_i and has height H_i. The size in directions other than height is negligible.\nFrom a point P with coordinate x and height h, building i is considered visible if there exists a point Q on building i such that the line segment PQ does not intersect with any other building.\nFind the maximum height at coordinate 0 from which it is not possible to see all buildings. Height must be non-negative; if it is possible to see all buildings at height 0 at coordinate 0, report -1 instead.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nX_1 H_1\n\\vdots\nX_N H_N\n\nOutput\n\nIf it is possible to see all buildings from coordinate 0 and height 0, print -1. Otherwise, print the maximum height at coordinate 0 from which it is not possible to see all buildings. Answers with an absolute or relative error of at most 10^{-9} from the true answer will be considered correct.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq X_1 < \\dots < X_N \\leq 10^9\n- 1 \\leq H_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n3\n3 2\n5 4\n7 5\n\nSample Output 1\n\n1.500000000000000000\n\nFrom coordinate 0 and height 1.5, building 3 cannot be seen. If the height is even slightly greater than 1.5, all buildings including building 3 can be seen. Thus, the answer is 1.5.\n\nSample Input 2\n\n2\n1 1\n2 100\n\nSample Output 2\n\n-1\n\nNote that -1.000 or similar outputs would be considered incorrect.\n\nSample Input 3\n\n3\n1 1\n2 2\n3 3\n\nSample Output 3\n\n0.000000000000000000\n\nSample Input 4\n\n4\n10 10\n17 5\n20 100\n27 270\n\nSample Output 4\n\n17.142857142857142350",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a m x n 2D array board representing a chessboard, where board[i][j] represents the value of the cell (i, j).\nRooks in the same row or column attack each other. You need to place three rooks on the chessboard such that the rooks do not attack each other.\nReturn the maximum sum of the cell values on which the rooks are placed.\n \nExample 1:\n\nInput: board = [[-3,1,1,1],[-3,1,-3,1],[-3,2,1,1]]\nOutput: 4\nExplanation:\n\nWe can place the rooks in the cells (0, 2), (1, 3), and (2, 1) for a sum of 1 + 1 + 2 = 4.\n\nExample 2:\n\nInput: board = [[1,2,3],[4,5,6],[7,8,9]]\nOutput: 15\nExplanation:\nWe can place the rooks in the cells (0, 0), (1, 1), and (2, 2) for a sum of 1 + 5 + 9 = 15.\n\nExample 3:\n\nInput: board = [[1,1,1],[1,1,1],[1,1,1]]\nOutput: 3\nExplanation:\nWe can place the rooks in the cells (0, 2), (1, 1), and (2, 0) for a sum of 1 + 1 + 1 = 3.\n\n \nConstraints:\n\n3 <= m == board.length <= 100\n3 <= n == board[i].length <= 100\n-10^9 <= board[i][j] <= 10^9",
"role": "user"
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|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N linear functions f_1, f_2, \\ldots, f_N, where f_i(x) = A_i x + B_i.\nFind the maximum possible value of f_{p_1}(f_{p_2}(\\ldots f_{p_K}(1) \\ldots )) for a sequence p = (p_1, p_2, \\ldots, p_K) of K distinct integers between 1 and N, inclusive.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN K\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N\n\nOutput\n\nPrint the answer as an integer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^{5}\n- 1 \\leq K \\leq \\text{min}(N,10)\n- 1 \\leq A_i, B_i \\leq 50 (1 \\leq i \\leq N)\n- All input values are integers.\n\nSample Input 1\n\n3 2\n2 3\n1 5\n4 2\n\nSample Output 1\n\n26\n\nHere are all possible p and the corresponding values of f_{p_1}(f_{p_2}(1)):\n\n- p= ( 1,2 ) : f_1(f_2(1))=15\n- p= ( 1,3 ) : f_1(f_3(1))=15\n- p= ( 2,1 ) : f_2(f_1(1))=10\n- p= ( 2,3 ) : f_2(f_3(1))=11\n- p= ( 3,1 ) : f_3(f_1(1))=22\n- p= ( 3,2 ) : f_3(f_2(1))=26\n\nTherefore, print 26.\n\nSample Input 2\n\n10 3\n48 40\n34 22\n24 37\n45 40\n48 31\n49 44\n45 40\n44 6\n35 22\n39 28\n\nSample Output 2\n\n216223",
"role": "user"
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The coordinate plane is covered with 2\\times1 tiles. The tiles are laid out according to the following rules:\n\n- For an integer pair (i,j), the square A _ {i,j}=\\lbrace(x,y)\\mid i\\leq x\\leq i+1\\wedge j\\leq y\\leq j+1\\rbrace is contained in one tile.\n- When i+j is even, A _ {i,j} and A _ {i + 1,j} are contained in the same tile.\n\nTiles include their boundaries, and no two different tiles share a positive area.\nNear the origin, the tiles are laid out as follows:\n\nTakahashi starts at the point (S _ x+0.5,S _ y+0.5) on the coordinate plane.\nHe can repeat the following move as many times as he likes:\n\n- Choose a direction (up, down, left, or right) and a positive integer n. Move n units in that direction.\n\nEach time he enters a tile, he pays a toll of 1.\nFind the minimum toll he must pay to reach the point (T _ x+0.5,T _ y+0.5).\n\nInput\n\nThe input is given from Standard Input in the following format:\nS _ x S _ y\r\nT _ x T _ y\n\nOutput\n\nPrint the minimum toll Takahashi must pay.\n\nConstraints\n\n\n- 0\\leq S _ x\\leq2\\times10 ^ {16}\n- 0\\leq S _ y\\leq2\\times10 ^ {16}\n- 0\\leq T _ x\\leq2\\times10 ^ {16}\n- 0\\leq T _ y\\leq2\\times10 ^ {16}\n- All input values are integers.\n\nSample Input 1\n\n5 0\r\n2 5\n\nSample Output 1\n\n5\r\n\nFor example, Takahashi can pay a toll of 5 by moving as follows:\n\n\n- Move left by 1. Pay a toll of 0.\n- Move up by 1. Pay a toll of 1.\n- Move left by 1. Pay a toll of 0.\n- Move up by 3. Pay a toll of 3.\n- Move left by 1. Pay a toll of 0.\n- Move up by 1. Pay a toll of 1.\n\nIt is impossible to reduce the toll to 4 or less, so print 5.\n\nSample Input 2\n\n3 1\r\n4 1\n\nSample Output 2\n\n0\r\n\nThere are cases where no toll needs to be paid.\n\nSample Input 3\n\n2552608206527595 5411232866732612\r\n771856005518028 7206210729152763\n\nSample Output 3\n\n1794977862420151\r\n\nNote that the value to be output may exceed the range of a 32-bit integer.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums consisting of n prime integers.\nYou need to construct an array ans of length n, such that, for each index i, the bitwise OR of ans[i] and ans[i] + 1 is equal to nums[i], i.e. ans[i] OR (ans[i] + 1) == nums[i].\nAdditionally, you must minimize each value of ans[i] in the resulting array.\nIf it is not possible to find such a value for ans[i] that satisfies the condition, then set ans[i] = -1.\n \nExample 1:\n\nInput: nums = [2,3,5,7]\nOutput: [-1,1,4,3]\nExplanation:\n\nFor i = 0, as there is no value for ans[0] that satisfies ans[0] OR (ans[0] + 1) = 2, so ans[0] = -1.\nFor i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 3 is 1, because 1 OR (1 + 1) = 3.\nFor i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 5 is 4, because 4 OR (4 + 1) = 5.\nFor i = 3, the smallest ans[3] that satisfies ans[3] OR (ans[3] + 1) = 7 is 3, because 3 OR (3 + 1) = 7.\n\n\nExample 2:\n\nInput: nums = [11,13,31]\nOutput: [9,12,15]\nExplanation:\n\nFor i = 0, the smallest ans[0] that satisfies ans[0] OR (ans[0] + 1) = 11 is 9, because 9 OR (9 + 1) = 11.\nFor i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 13 is 12, because 12 OR (12 + 1) = 13.\nFor i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 31 is 15, because 15 OR (15 + 1) = 31.\n\n\n \nConstraints:\n\n1 <= nums.length <= 100\n2 <= nums[i] <= 1000\nnums[i] is a prime number.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer mountainHeight denoting the height of a mountain.\nYou are also given an integer array workerTimes representing the work time of workers in seconds.\nThe workers work simultaneously to reduce the height of the mountain. For worker i:\n\nTo decrease the mountain's height by x, it takes workerTimes[i] + workerTimes[i] * 2 + ... + workerTimes[i] * x seconds. For example:\n\n\t\nTo reduce the height of the mountain by 1, it takes workerTimes[i] seconds.\nTo reduce the height of the mountain by 2, it takes workerTimes[i] + workerTimes[i] * 2 seconds, and so on.\n\n\n\nReturn an integer representing the minimum number of seconds required for the workers to make the height of the mountain 0.\n \nExample 1:\n\nInput: mountainHeight = 4, workerTimes = [2,1,1]\nOutput: 3\nExplanation:\nOne way the height of the mountain can be reduced to 0 is:\n\nWorker 0 reduces the height by 1, taking workerTimes[0] = 2 seconds.\nWorker 1 reduces the height by 2, taking workerTimes[1] + workerTimes[1] * 2 = 3 seconds.\nWorker 2 reduces the height by 1, taking workerTimes[2] = 1 second.\n\nSince they work simultaneously, the minimum time needed is max(2, 3, 1) = 3 seconds.\n\nExample 2:\n\nInput: mountainHeight = 10, workerTimes = [3,2,2,4]\nOutput: 12\nExplanation:\n\nWorker 0 reduces the height by 2, taking workerTimes[0] + workerTimes[0] * 2 = 9 seconds.\nWorker 1 reduces the height by 3, taking workerTimes[1] + workerTimes[1] * 2 + workerTimes[1] * 3 = 12 seconds.\nWorker 2 reduces the height by 3, taking workerTimes[2] + workerTimes[2] * 2 + workerTimes[2] * 3 = 12 seconds.\nWorker 3 reduces the height by 2, taking workerTimes[3] + workerTimes[3] * 2 = 12 seconds.\n\nThe number of seconds needed is max(9, 12, 12, 12) = 12 seconds.\n\nExample 3:\n\nInput: mountainHeight = 5, workerTimes = [1]\nOutput: 15\nExplanation:\nThere is only one worker in this example, so the answer is workerTimes[0] + workerTimes[0] * 2 + workerTimes[0] * 3 + workerTimes[0] * 4 + workerTimes[0] * 5 = 15.\n\n \nConstraints:\n\n1 <= mountainHeight <= 10^5\n1 <= workerTimes.length <= 10^4\n1 <= workerTimes[i] <= 10^6",
"role": "user"
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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|
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array of positive integers nums of length n.\nWe call a pair of non-negative integer arrays (arr1, arr2) monotonic if:\n\nThe lengths of both arrays are n.\narr1 is monotonically non-decreasing, in other words, arr1[0] <= arr1[1] <= ... <= arr1[n - 1].\narr2 is monotonically non-increasing, in other words, arr2[0] >= arr2[1] >= ... >= arr2[n - 1].\narr1[i] + arr2[i] == nums[i] for all 0 <= i <= n - 1.\n\nReturn the count of monotonic pairs.\nSince the answer may be very large, return it modulo 10^9 + 7.\n \nExample 1:\n\nInput: nums = [2,3,2]\nOutput: 4\nExplanation:\nThe good pairs are:\n\n([0, 1, 1], [2, 2, 1])\n([0, 1, 2], [2, 2, 0])\n([0, 2, 2], [2, 1, 0])\n([1, 2, 2], [1, 1, 0])\n\n\nExample 2:\n\nInput: nums = [5,5,5,5]\nOutput: 126\n\n \nConstraints:\n\n1 <= n == nums.length <= 2000\n1 <= nums[i] <= 50",
"role": "user"
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| 1 | 85 |
LiveCodeBenchV5
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[
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence A = (A_1, A_2, \\dots, A_N) of length N. For each k = 1, 2, \\dots, N, find the number, modulo 998244353, of (not necessarily contiguous) subsequences of A of length k that are arithmetic sequences. Two subsequences are distinguished if they are taken from different positions, even if they are equal as sequences.\n\nWhat is a subsequence?\nA subsequence of a sequence A is a sequence obtained by deleting zero or more elements from A and arranging the remaining elements without changing the order.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nA_1 A_2 \\dots A_N\n\nOutput\n\nPrint the answers for k = 1, 2, \\dots, N in this order, in a single line, separated by spaces.\n\nConstraints\n\n\n- 1 \\leq N \\leq 80\n- 1 \\leq A_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n5\n1 2 3 2 3\n\nSample Output 1\n\n5 10 3 0 0\n\n\n- There are 5 subsequences of length 1, all of which are arithmetic sequences.\n- There are 10 subsequences of length 2, all of which are arithmetic sequences.\n- There are 3 subsequences of length 3 that are arithmetic sequences: (A_1, A_2, A_3), (A_1, A_2, A_5), and (A_1, A_4, A_5).\n- There are no arithmetic subsequences of length 4 or more.\n\nSample Input 2\n\n4\n1 2 3 4\n\nSample Output 2\n\n4 6 2 1\n\nSample Input 3\n\n1\n100\n\nSample Output 3\n\n1",
"role": "user"
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LiveCodeBenchV5
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"expected_answer": "",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given an array of integers nums and an integer k, return the number of subarrays of nums where the bitwise AND of the elements of the subarray equals k.\n \nExample 1:\n\nInput: nums = [1,1,1], k = 1\nOutput: 6\nExplanation:\nAll subarrays contain only 1's.\n\nExample 2:\n\nInput: nums = [1,1,2], k = 1\nOutput: 3\nExplanation:\nSubarrays having an AND value of 1 are: [1,1,2], [1,1,2], [1,1,2].\n\nExample 3:\n\nInput: nums = [1,2,3], k = 2\nOutput: 2\nExplanation:\nSubarrays having an AND value of 2 are: [1,2,3], [1,2,3].\n\n \nConstraints:\n\n1 <= nums.length <= 10^5\n0 <= nums[i], k <= 10^9",
"role": "user"
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"do_sample": false,
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| 2 | 94 |
LiveCodeBenchV5
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A 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 damage of power[i] - 2, power[i] - 1, power[i] + 1, or power[i] + 2.\nEach spell can be cast only once.\nReturn the maximum possible total damage that a magician can cast.\n \nExample 1:\n\nInput: power = [1,1,3,4]\nOutput: 6\nExplanation:\nThe maximum possible damage of 6 is produced by casting spells 0, 1, 3 with damage 1, 1, 4.\n\nExample 2:\n\nInput: power = [7,1,6,6]\nOutput: 13\nExplanation:\nThe maximum possible damage of 13 is produced by casting spells 1, 2, 3 with damage 1, 6, 6.\n\n \nConstraints:\n\n1 <= power.length <= 10^5\n1 <= power[i] <= 10^9",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A mayoral election is being held in AtCoder City. The candidates are Takahashi and Aoki.\nThere are N valid votes cast for either of the two candidates, and the counting is currently underway. Here, N is an odd number.\nThe current vote count is T votes for Takahashi and A votes for Aoki.\nDetermine if the outcome of the election is already decided at this point.\n\nInput\n\nThe input is given from standard input in the following format:\nN T A\n\nOutput\n\nPrint Yes if the outcome of the election is already decided, and No otherwise.\n\nConstraints\n\n\n- 1 \\leq N \\leq 99\n- N is an odd number.\n- 0 \\leq T, A \\leq N\n- T + A \\leq N\n- All input values are integers.\n\nSample Input 1\n\n7 4 2\n\nSample Output 1\n\nYes\r\n\nEven if the remaining one vote goes to Aoki, Takahashi will still win. That is, his victory is decided, so print Yes.\n\nSample Input 2\n\n99 12 48\n\nSample Output 2\n\nNo\r\n\nAlthough Aoki currently has more votes, Takahashi would win if he receives the remaining 39 votes. Therefore, print No.\n\nSample Input 3\n\n1 0 0\n\nSample Output 3\n\nNo",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns.\r\nLet (i,j) denote the cell at the i-th row from the top and the j-th column from the left.\nThere are N horizontal bars numbered from 1 to N placed on the grid.\r\nBar i consists of L_i blocks of size 1 \\times 1 connected horizontally, and its leftmost block is initially at cell (R_i, C_i).\r\nThat is, initially, bar i occupies the cells (R_i, C_i), (R_i, C_i + 1), \\dots, (R_i, C_i + L_i - 1).\r\nIt is guaranteed that there is no cell occupied by two different bars.\nThe current time is t = 0.\r\nAt every time t = 0.5 + n for some non-negative integer n, the following occurs in order of i = 1, 2, \\dots, N:\n\n- If bar i is not on the bottom row (the H-th row), and none of the cells directly below the cells occupied by bar i is occupied by any bar, then bar i moves down by one cell. That is, if at that time bar i occupies the cells (r,C_i),(r,C_i+1),\\dots,(r,C_i+L_i-1)\\ (r < H), and the cell (r + 1, C_i + j) is not occupied by any bar for all j (0 \\leq j \\leq L_i - 1), then bar i now occupies (r + 1, C_i), (r + 1, C_i + 1), \\dots, (r + 1, C_i + L_i - 1).\n- Otherwise, nothing happens.\n\nLet (R'_i, C_i), (R'_i, C_i + 1), \\dots, (R'_i, C_i + L_i - 1) be the cells occupied by bar i at time t = 10^{100}. Find R'_1, R'_2, \\dots, R'_N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W N\r\nR_1 C_1 L_1\r\nR_2 C_2 L_2\r\n\\vdots\r\nR_N C_N L_N\n\nOutput\n\nPrint N lines.\r\nThe i-th line (1 \\leq i \\leq N) should contain R'_i.\n\nConstraints\n\n\n- 1 \\leq H, W \\leq 2 \\times 10^5\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq R_i \\leq H\n- 1 \\leq C_i \\leq W\n- 1 \\leq L_i \\leq W - C_i + 1\n- In the initial state, there is no cell occupied by two different bars.\n- All input values are integers.\n\nSample Input 1\n\n4 4 4\r\n1 2 3\r\n3 2 2\r\n2 1 2\r\n2 4 1\n\nSample Output 1\n\n2\r\n4\r\n3\r\n4\r\n\nThe following three diagrams represent the grid at times t = 0, 1, and 2 from left to right.\r\nColored rectangles represent the bars, and the number inside each rectangle indicates its bar number.\n\nThe changes in the grid state are explained as follows:\n\n- At t = 0.5:\n- i = 1: The cells directly below bar 1 are (2,2),(2,3),(2,4). Among these, (2,2) is occupied by bar 3 and (2,4) is occupied by bar 4, so nothing happens.\n- i = 2: The cells directly below bar 2 are (4,2),(4,3), which are not occupied by any other bar, so bar 2 moves down by one cell.\n- i = 3: The cells directly below bar 3 are (3,1),(3,2), which are not occupied by any other bar, so bar 3 moves down by one cell.\n- i = 4: The cell directly below bar 4 is (3,4), which is not occupied by any other bar, so bar 4 moves down by one cell.\n\n\n- At t = 1.5:\n- i = 1: The cells directly below bar 1 are (2,2),(2,3),(2,4), which are not occupied by any other bar, so bar 1 moves down by one cell.\n- i = 2: Bar 2 is on the bottom row, so nothing happens.\n- i = 3: The cells directly below bar 3 are (4,1),(4,2). Among these, (4,2) is occupied by bar 2, so nothing happens.\n- i = 4: The cell directly below bar 4 is (4,4), which is not occupied by any other bar, so bar 4 moves down by one cell.\n\n\n\nAt times t = 2.5, 3.5, \\dots, there is no bar such that the cells directly below it are all unoccupied, so nothing happens. Thus, the grid at time t = 10^{100} is the same as at t = 2 (the rightmost diagram above).\nTherefore, R'_1 = 2, R'_2 = 4, R'_3 = 3, R'_4 = 4.\n\nSample Input 2\n\n382 382 3\r\n3 3 3\r\n8 8 8\r\n2 2 2\n\nSample Output 2\n\n382\r\n382\r\n381\n\nSample Input 3\n\n5 10 8\r\n2 2 1\r\n4 3 1\r\n4 8 2\r\n1 2 2\r\n2 5 3\r\n5 4 3\r\n4 5 2\r\n1 5 2\n\nSample Output 3\n\n5\r\n5\r\n5\r\n4\r\n3\r\n5\r\n4\r\n2",
"role": "user"
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.For strings S and T consisting of lowercase English letters, and a string X consisting of 0 and 1, define the string f(S,T,X) consisting of lowercase English letters as follows:\n\n- Starting with an empty string, for each i=1,2,\\dots,|X|, append S to the end if the i-th character of X is 0, and append T to the end if it is 1.\n\nYou are given a string S consisting of lowercase English letters, and strings X and Y consisting of 0 and 1.\nDetermine if there exists a string T (which can be empty) such that f(S,T,X)=f(S,T,Y).\nYou have t test cases to solve.\n\nInput\n\nThe input is given from Standard Input in the following format:\nt\r\n\\mathrm{case}_1\r\n\\vdots\r\n\\mathrm{case}_t\r\n\nEach case is given in the following format:\nS\r\nX\r\nY\n\nOutput\n\nPrint t lines. The i-th line should contain Yes if there exists a T that satisfies the condition for the i-th test case, and No otherwise.\n\nConstraints\n\n\n- 1 \\leq t \\leq 5 \\times 10^5\n- 1 \\leq |S| \\leq 5\\times 10^5\n- 1 \\leq |X|,|Y| \\leq 5\\times 10^5\n- S is a string consisting of lowercase English letters.\n- X and Y are strings consisting of 0 and 1.\n- The sum of |S| across all test cases in a single input is at most 5 \\times 10^5.\n- The sum of |X| across all test cases in a single input is at most 5 \\times 10^5.\n- The sum of |Y| across all test cases in a single input is at most 5 \\times 10^5.\n\nSample Input 1\n\n3\r\naraara\r\n01\r\n111\r\naraaaa\r\n100100\r\n0010111\r\nabacabac\r\n0\r\n1111\n\nSample Output 1\n\nYes\r\nNo\r\nNo\r\n\nBelow, string concatenation is represented using +.\nFor the 1st test case, if T=ara, then f(S,T,X)=S+T=araaraara and f(S,T,Y)=T+T+T=araaraara, so f(S,T,X)=f(S,T,Y).\nFor the 2nd and 3rd test cases, there is no T that satisfies the condition.\n\nSample Input 2\n\n2\r\nempty\r\n10101\r\n00\r\nempty\r\n11111\r\n111\n\nSample Output 2\n\nYes\r\nYes\r\n\nT can be empty.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given positive integers N and K.\nAn integer sequence of length NK where each integer from 1 to N appears exactly K times is called a good integer sequence.\nLet S be the number of good integer sequences.\r\nFind the \\operatorname{floor}((S+1)/2)-th good integer sequence in lexicographical order.\r\nHere, \\operatorname{floor}(x) represents the largest integer not exceeding x.\n What is lexicographical order for sequences?\nA sequence S = (S_1,S_2,\\ldots,S_{|S|}) is lexicographically smaller than a sequence T = (T_1,T_2,\\ldots,T_{|T|}) if either 1. or 2. below holds.\r\nHere, |S| and |T| represent the lengths of S and T, respectively.\n\n- |S| \\lt |T| and (S_1,S_2,\\ldots,S_{|S|}) = (T_1,T_2,\\ldots,T_{|S|}). \n- There exists an integer 1 \\leq i \\leq \\min\\lbrace |S|, |T| \\rbrace such that both of the following hold:\r\n\n- (S_1,S_2,\\ldots,S_{i-1}) = (T_1,T_2,\\ldots,T_{i-1})\n- S_i is (numerically) smaller than T_i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN K\n\nOutput\n\nPrint the desired integer sequence, with elements separated by spaces.\n\nConstraints\n\n\n- 1 \\leq N \\leq 500\n- 1 \\leq K \\leq 500\n- All input values are integers.\n\nSample Input 1\n\n2 2\n\nSample Output 1\n\n1 2 2 1\r\n\nThere are six good integer sequences:\n\n- (1,1,2,2)\n- (1,2,1,2)\n- (1,2,2,1)\n- (2,1,1,2)\n- (2,1,2,1)\n- (2,2,1,1)\n\nTherefore, the answer is the 3rd sequence in lexicographical order, (1,2,2,1).\n\nSample Input 2\n\n1 5\n\nSample Output 2\n\n1 1 1 1 1\n\nSample Input 3\n\n6 1\n\nSample Output 3\n\n3 6 5 4 2 1\n\nSample Input 4\n\n3 3\n\nSample Output 4\n\n2 2 2 1 3 3 3 1 1",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cells in a row, numbered 1 to N.\nFor each 1 \\leq i < N, cells i and i+1 are adjacent.\nInitially, cell i is painted with color i.\nYou are given Q queries. Process them in order. Each query is of one of the following two types.\n\n- 1 x c: Repaint the following to color c: all reachable cells reachable from cell x by repeatedly moving to an adjacent cell painted in the same color as the current cell.\n- 2 c: Print the number of cells painted with color c.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN Q\n\\mathrm{query}_1\n\\vdots\n\\mathrm{query}_Q\n\nEach query is given in one of the following two formats:\n1 x c\n\n2 c\n\nOutput\n\nLet q be the number of queries of the second type. Print q lines.\nThe i-th line should contain the answer to the i-th such query.\n\nConstraints\n\n\n- 1 \\leq N \\leq 5 \\times 10^5\n- 1 \\leq Q \\leq 2 \\times 10^5\n- In queries of the first type, 1 \\leq x \\leq N.\n- In queries of the first and second types, 1 \\leq c \\leq N.\n- There is at least one query of the second type.\n- All input values are integers.\n\nSample Input 1\n\n5 6\n1 5 4\n1 4 2\n2 2\n1 3 2\n1 2 3\n2 3\n\nSample Output 1\n\n3\n4\n\nThe queries recolor the cells as shown in the figure.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two strings, coordinate1 and coordinate2, representing the coordinates of a square on an 8 x 8 chessboard.\nBelow is the chessboard for reference.\n\nReturn true if these two squares have the same color and false otherwise.\nThe coordinate will always represent a valid chessboard square. The coordinate will always have the letter first (indicating its column), and the number second (indicating its row).\n \nExample 1:\n\nInput: coordinate1 = \"a1\", coordinate2 = \"c3\"\nOutput: true\nExplanation:\nBoth squares are black.\n\nExample 2:\n\nInput: coordinate1 = \"a1\", coordinate2 = \"h3\"\nOutput: false\nExplanation:\nSquare \"a1\" is black and \"h3\" is white.\n\n \nConstraints:\n\ncoordinate1.length == coordinate2.length == 2\n'a' <= coordinate1[0], coordinate2[0] <= 'h'\n'1' <= coordinate1[1], coordinate2[1] <= '8'",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a tree with N vertices.\r\nThe vertices are numbered 1, 2, \\ldots, N.\r\nThe i-th edge (1\\leq i\\leq N-1) connects vertices U_i and V_i, with a length of L_i.\nFor each K=1,2,\\ldots, N, solve the following problem.\n\nTakahashi and Aoki play a game. The game proceeds as follows.\n\n- First, Aoki specifies K distinct vertices on the tree.\n- Then, Takahashi constructs a walk that starts and ends at vertex 1, and passes through all the vertices specified by Aoki.\n\nThe score is defined as the length of the walk constructed by Takahashi. Takahashi wants to minimize the score, while Aoki wants to maximize it.\r\nFind the score when both players play optimally.\n\n\nDefinition of a walk\r\n A walk on an undirected graph (possibly a tree) is a sequence of k vertices and k-1 edges v_1,e_1,v_2,\\ldots,v_{k-1},e_{k-1},v_k (where k is a positive integer)\r\n such that edge e_i connects vertices v_i and v_{i+1}. The same vertex or edge can appear multiple times in the sequence. \r\n A walk is said to pass through vertex x if there exists at least one i (1\\leq i\\leq k) such that v_i=x. (There can be multiple such i.) \r\n The walk is said to start and end at v_1 and v_k, respectively, and the length of the walk is the sum of the lengths of e_1, e_2, \\ldots, e_{k-1}.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nU_1 V_1 L_1\r\nU_2 V_2 L_2\r\n\\vdots\r\nU_{N-1} V_{N-1} L_{N-1}\n\nOutput\n\nPrint N lines.\r\nThe i-th line (1\\leq i\\leq N) should contain the answer to the problem for K=i.\n\nConstraints\n\n\n- 2\\leq N\\leq 2\\times 10^5\n- 1\\leq U_i<V_i\\leq N\n- 1\\leq L_i\\leq 10^9\n- All input values are integers.\n- The given graph is a tree.\n\nSample Input 1\n\n5\r\n1 2 3\r\n2 3 5\r\n2 4 2\r\n1 5 3\n\nSample Output 1\n\n16\r\n22\r\n26\r\n26\r\n26\r\n\nFor K=1, Aoki's optimal move is to specify vertex 3, and Takahashi's optimal move is to construct a path vertex 1 \\to vertex 2 \\to vertex 3 \\to vertex 2 \\to vertex 1, resulting in a score of 16.\nFor K=2, Aoki's optimal move is to specify vertices 3 and 5, and Takahashi's optimal move is to construct a path such as vertex 1 \\to vertex 5 \\to vertex 1 \\to vertex 2 \\to vertex 3 \\to vertex 2 \\to vertex 1, resulting in a score of 22.\nFor K\\geq 3, the score when both players play optimally is 26.\n\nSample Input 2\n\n3\r\n1 2 1000000000\r\n2 3 1000000000\n\nSample Output 2\n\n4000000000\r\n4000000000\r\n4000000000\r\n\nBeware that the answer may not fit in a 32-bit integer.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two integers red and blue representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1^st row will have 1 ball, the 2^nd row will have 2 balls, the 3^rd row will have 3 balls, and so on.\nAll the balls in a particular row should be the same color, and adjacent rows should have different colors.\nReturn the maximum height of the triangle that can be achieved.\n \nExample 1:\n\nInput: red = 2, blue = 4\nOutput: 3\nExplanation:\n\nThe only possible arrangement is shown above.\n\nExample 2:\n\nInput: red = 2, blue = 1\nOutput: 2\nExplanation:\n\nThe only possible arrangement is shown above.\n\nExample 3:\n\nInput: red = 1, blue = 1\nOutput: 1\n\nExample 4:\n\nInput: red = 10, blue = 1\nOutput: 2\nExplanation:\n\nThe only possible arrangement is shown above.\n\n \nConstraints:\n\n1 <= red, blue <= 100",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given simple undirected graphs G and H, each with N vertices: vertices 1, 2, \\ldots, N.\nGraph G has M_G edges, and its i-th edge (1\\leq i\\leq M_G) connects vertices u_i and v_i.\nGraph H has M_H edges, and its i-th edge (1\\leq i\\leq M_H) connects vertices a_i and b_i.\nYou can perform the following operation on graph H any number of times, possibly zero.\n\n- Choose a pair of integers (i,j) satisfying 1\\leq i<j\\leq N. Pay A_{i,j} yen, and if there is no edge between vertices i and j in H, add one; if there is, remove it.\n\nFind the minimum total cost required to make G and H isomorphic.\nWhat is a simple undirected graph?\n A simple undirected graph is a graph without self-loops or multi-edges, where edges have no direction.\n\nWhat does it mean for graphs to be isomorphic?\n Two graphs G and H with N vertices are isomorphic if and only if there exists a permutation (P_1,P_2,\\ldots,P_N) of (1,2,\\ldots,N) such that for all 1\\leq i\\lt j\\leq N:\n\n- an edge exists between vertices i and j in G if and only if an edge exists between vertices P_i and P_j in H.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nM _ G\nu _ 1 v _ 1\nu _ 2 v _ 2\n\\vdots\nu _ {M _ G} v _ {M _ G}\nM _ H\na _ 1 b _ 1\na _ 2 b _ 2\n\\vdots\na _ {M _ H} b _ {M _ H}\nA _ {1,2} A _ {1,3} \\ldots A _ {1,N}\nA _ {2,3} \\ldots A _ {2,N}\n\\vdots\nA _ {N-1,N}\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1\\leq N\\leq8\n- 0\\leq M _ G\\leq\\dfrac{N(N-1)}2\n- 0\\leq M _ H\\leq\\dfrac{N(N-1)}2\n- 1\\leq u _ i\\lt v _ i\\leq N\\ (1\\leq i\\leq M _ G)\n- (u _ i,v _ i)\\neq(u _ j,v _ j)\\ (1\\leq i\\lt j\\leq M _ G)\n- 1\\leq a _ i\\lt b _ i\\leq N\\ (1\\leq i\\leq M _ H)\n- (a _ i,b _ i)\\neq(a _ j,b _ j)\\ (1\\leq i\\lt j\\leq M _ H)\n- 1\\leq A _ {i,j}\\leq 10 ^ 6\\ (1\\leq i\\lt j\\leq N)\n- All input values are integers.\n\nSample Input 1\n\n5\n4\n1 2\n2 3\n3 4\n4 5\n4\n1 2\n1 3\n1 4\n1 5\n3 1 4 1\n5 9 2\n6 5\n3\n\nSample Output 1\n\n9\n\nThe given graphs are as follows:\n\nFor example, you can perform the following four operations on H to make it isomorphic to G at a cost of 9 yen.\n\n- Choose (i,j)=(1,3). There is an edge between vertices 1 and 3 in H, so pay 1 yen to remove it.\n- Choose (i,j)=(2,5). There is no edge between vertices 2 and 5 in H, so pay 2 yen to add it.\n- Choose (i,j)=(1,5). There is an edge between vertices 1 and 5 in H, so pay 1 yen to remove it.\n- Choose (i,j)=(3,5). There is no edge between vertices 3 and 5 in H, so pay 5 yen to add it.\n\nAfter these operations, H becomes:\n\nYou cannot make G and H isomorphic at a cost less than 9 yen, so print 9.\n\nSample Input 2\n\n5\n3\n1 2\n2 3\n3 4\n4\n1 2\n2 3\n3 4\n4 5\n9 1 1 1\n1 1 1\n1 1\n9\n\nSample Output 2\n\n3\n\nFor example, performing the operations (i,j)=(2,3),(2,4),(3,4) on H will make it isomorphic to G.\n\nSample Input 3\n\n5\n3\n1 2\n2 3\n3 4\n4\n1 2\n2 3\n3 4\n4 5\n5 4 4 4\n4 4 4\n4 4\n5\n\nSample Output 3\n\n5\n\nFor example, performing the operation (i,j)=(4,5) once will make G and H isomorphic.\n\nSample Input 4\n\n2\n0\n0\n371\n\nSample Output 4\n\n0\n\nNote that G and H may have no edges.\nAlso, it is possible that no operations are needed.\n\nSample Input 5\n\n8\n13\n1 8\n5 7\n4 6\n1 5\n7 8\n1 6\n1 2\n5 8\n2 6\n5 6\n6 7\n3 7\n4 8\n15\n3 5\n1 7\n4 6\n3 8\n7 8\n1 2\n5 6\n1 6\n1 5\n1 4\n2 8\n2 6\n2 4\n4 7\n1 3\n7483 1694 5868 3296 9723 5299 4326\n5195 4088 5871 1384 2491 6562\n1149 6326 2996 9845 7557\n4041 7720 1554 5060\n8329 8541 3530\n4652 3874\n3748\n\nSample Output 5\n\n21214",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N people numbered from 1 to N visiting a conveyor belt sushi restaurant.\r\nThe gourmet level of person i is A_i.\nNow, M pieces of sushi will be placed on the conveyor belt.\r\nThe deliciousness of the j-th sushi is B_j.\r\nEach piece of sushi passes in front of people 1, 2, \\dots, N in this order.\r\nEach person, when a sushi whose deliciousness is not less than their gourmet level passes in front of them, will take and eat that sushi; otherwise, they do nothing.\r\nA sushi that person i takes and eats will no longer pass in front of person j\\ (j > i).\nFor each of the M pieces of sushi, determine who eats that sushi, or if nobody eats it.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nA_1 A_2 \\dots A_N\r\nB_1 B_2 \\dots B_M\n\nOutput\n\nPrint M lines.\r\nThe j-th line (1 \\leq j \\leq M) should contain the number representing the person who eats the j-th sushi, or -1 if nobody eats it.\n\nConstraints\n\n\n- 1 \\leq N, M \\leq 2 \\times 10^5\n- 1 \\leq A_i, B_i \\leq 2 \\times 10^5\n- All input values are integers.\n\nSample Input 1\n\n3 3\r\n3 8 2\r\n5 2 1\n\nSample Output 1\n\n1\r\n3\r\n-1\r\n\n\n- For the 1st sushi:\n- It first passes in front of person 1. Since B_1 \\geq A_1, person 1 takes and eats it.\n- It will not pass in front of person 2 and 3.\n\n\n- For the 2nd sushi:\n- It first passes in front of person 1. Since B_2 < A_1, person 1 does nothing.\n- Next, it passes in front of person 2. Since B_2 < A_2, person 2 does nothing.\n- Finally, it passes in front of person 3. Since B_2 \\geq A_3, person 3 takes and eats it.\n\n\n- For the 3rd sushi:\n- It first passes in front of person 1. Since B_3 < A_1, person 1 does nothing.\n- Next, it passes in front of person 2. Since B_3 < A_2, person 2 does nothing.\n- Finally, it passes in front of person 3. Since B_3 < A_3, person 3 does nothing.\n- Therefore, nobody eats this sushi.\n\nSample Input 2\n\n3 3\r\n1 1 1\r\n1 1 1\n\nSample Output 2\n\n1\r\n1\r\n1\n\nSample Input 3\n\n10 5\r\n60 83 76 45 70 91 37 58 94 22\r\n70 39 52 33 18\n\nSample Output 3\n\n1\r\n7\r\n4\r\n10\r\n-1",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is an undirected graph with N vertices and 0 edges. The vertices are numbered 1 to N.\nYou are given Q queries to process in order. Each query is of one of the following two types:\n\n- Type 1: Given in the format 1 u v. Add an edge between vertices u and v.\n- Type 2: Given in the format 2 v k. Print the k-th largest vertex number among the vertices connected to vertex v. If there are fewer than k vertices connected to v, print -1.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN Q\r\n\\mathrm{query}_1\r\n\\mathrm{query}_2\r\n\\vdots\r\n\\mathrm{query}_Q\r\n\nHere, \\mathrm{query}_i is the i-th query and is given in one of the following formats:\n1 u v\r\n\n2 v k\n\nOutput\n\nLet q be the number of Type 2 queries. Print q lines.\r\nThe i-th line should contain the answer to the i-th Type 2 query.\n\nConstraints\n\n\n- 1 \\leq N, Q \\leq 2 \\times 10^5\n- In a Type 1 query, 1 \\leq u < v \\leq N.\n- In a Type 2 query, 1 \\leq v \\leq N, 1 \\leq k \\leq 10.\n- All input values are integers.\n\nSample Input 1\n\n4 10\r\n1 1 2\r\n2 1 1\r\n2 1 2\r\n2 1 3\r\n1 1 3\r\n1 2 3\r\n1 3 4\r\n2 1 1\r\n2 1 3\r\n2 1 5\n\nSample Output 1\n\n2\r\n1\r\n-1\r\n4\r\n2\r\n-1\r\n\n\n- In the first query, an edge is added between vertices 1 and 2.\n- In the second query, two vertices are connected to vertex 1: 1 and 2. Among them, the 1-st largest vertex number is 2, which should be printed.\n- In the third query, two vertices are connected to vertex 1: 1 and 2. Among them, the 2-nd largest vertex number is 1, which should be printed.\n- In the fourth query, two vertices are connected to vertex 1: 1 and 2, which is fewer than 3, so print -1.\n- In the fifth query, an edge is added between vertices 1 and 3.\n- In the sixth query, an edge is added between vertices 2 and 3.\n- In the seventh query, an edge is added between vertices 3 and 4.\n- In the eighth query, four vertices are connected to vertex 1: 1,2,3,4. Among them, the 1-st largest vertex number is 4, which should be printed.\n- In the ninth query, four vertices are connected to vertex 1: 1,2,3,4. Among them, the 3-rd largest vertex number is 2, which should be printed.\n- In the tenth query, four vertices are connected to vertex 1: 1,2,3,4, which is fewer than 5, so print -1.\n\nSample Input 2\n\n6 20\r\n1 3 4\r\n1 3 5\r\n2 1 1\r\n2 3 1\r\n1 1 5\r\n2 6 9\r\n2 1 3\r\n2 6 1\r\n1 4 6\r\n2 2 1\r\n2 6 2\r\n2 4 7\r\n1 1 4\r\n2 6 2\r\n2 3 4\r\n1 2 5\r\n2 4 1\r\n1 1 6\r\n2 3 3\r\n2 1 3\n\nSample Output 2\n\n1\r\n5\r\n-1\r\n3\r\n6\r\n2\r\n5\r\n-1\r\n5\r\n3\r\n6\r\n4\r\n4",
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LiveCodeBenchV5
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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[
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A non-negative integer X is called a palindrome number if its decimal representation (without leading zeros) is a palindrome.\r\nFor example, 363, 12344321, and 0 are all palindrome numbers. \nFind the N-th smallest palindrome number.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint the N-th smallest palindrome number.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^{18}\n- N is an integer.\n\nSample Input 1\n\n46\n\nSample Output 1\n\n363\r\n\nThe 46th smallest palindrome number is 363.\n\nSample Input 2\n\n1\n\nSample Output 2\n\n0\n\nSample Input 3\n\n1000000000000000000\n\nSample Output 3\n\n90000000000000000000000000000000009",
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"do_sample": false,
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"seed": 1,
"temperature": 0.7
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| 1 | 40 |
LiveCodeBenchV5
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"expected_answer": "",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a graph with N + Q vertices, numbered 1, 2, \\ldots, N + Q. Initially, the graph has no edges.\nFor this graph, perform the following operation for i = 1, 2, \\ldots, Q in order:\n\n- For each integer j satisfying L_i \\leq j \\leq R_i, add an undirected edge with cost C_i between vertices N + i and j.\n\nDetermine if the graph is connected after all operations are completed. If it is connected, find the cost of a minimum spanning tree of the graph.\nA minimum spanning tree is a spanning tree with the smallest possible cost, and the cost of a spanning tree is the sum of the costs of the edges used in the spanning tree.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN Q\r\nL_1 R_1 C_1\r\nL_2 R_2 C_2\r\n\\vdots\r\nL_Q R_Q C_Q\n\nOutput\n\nIf the graph is connected, print the cost of a minimum spanning tree. Otherwise, print -1.\n\nConstraints\n\n\n- 1 \\leq N, Q \\leq 2 \\times 10^5\n- 1 \\leq L_i \\leq R_i \\leq N\n- 1 \\leq C_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n4 3\r\n1 2 2\r\n1 3 4\r\n2 4 5\n\nSample Output 1\n\n22\r\n\nThe following edges form a minimum spanning tree:\n\n- An edge with cost 2 connecting vertices 1 and 5\n- An edge with cost 2 connecting vertices 2 and 5\n- An edge with cost 4 connecting vertices 1 and 6\n- An edge with cost 4 connecting vertices 3 and 6\n- An edge with cost 5 connecting vertices 3 and 7\n- An edge with cost 5 connecting vertices 4 and 7\n\nSince 2 + 2 + 4 + 4 + 5 + 5 = 22, print 22.\n\nSample Input 2\n\n6 2\r\n1 2 10\r\n4 6 10\n\nSample Output 2\n\n-1\r\n\nThe graph is disconnected.\n\nSample Input 3\n\n200000 4\r\n1 200000 1000000000\r\n1 200000 998244353\r\n1 200000 999999999\r\n1 200000 999999999\n\nSample Output 3\n\n199651870599998",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Find the number, modulo 998244353, of permutations P=(P_1,P_2,\\cdots,P_N) of (1,2,\\cdots,N) that satisfy all of the following M conditions.\n\n- The i-th condition: The maximum among P_{L_i},P_{L_i+1},\\cdots,P_{R_i} is not P_{X_i}.\nHere, L_i, R_i, and X_i are integers given in the input.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nL_1 R_1 X_1\nL_2 R_2 X_2\n\\vdots\nL_M R_M X_M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 500\n- 1 \\leq M \\leq 10^5\n- 1 \\leq L_i \\leq X_i \\leq R_i \\leq N\n- All input values are integers.\n\nSample Input 1\n\n3 2\n1 3 2\n1 2 1\n\nSample Output 1\n\n1\n\nOnly one permutation, P=(1,2,3), satisfies the conditions.\n\nSample Input 2\n\n5 1\n1 1 1\n\nSample Output 2\n\n0\n\nSample Input 3\n\n10 5\n3 8 4\n3 10 4\n1 7 2\n1 8 3\n3 8 7\n\nSample Output 3\n\n1598400\n\nSample Input 4\n\n15 17\n2 11 9\n2 15 13\n1 14 2\n5 11 5\n3 15 11\n1 6 2\n4 15 12\n3 11 6\n9 13 10\n2 14 6\n10 15 11\n1 8 6\n6 14 8\n2 10 2\n6 12 6\n3 14 12\n2 6 2\n\nSample Output 4\n\n921467228",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given positive integers N, M, K, and a sequence of non-negative integers: A=(A_1,A_2,\\ldots,A_N).\nFor a non-empty non-negative integer sequence B=(B_1,B_2,\\ldots,B_{|B|}), we define its score as follows.\n\n- If the length of B is a multiple of M: (B_1 \\oplus B_2 \\oplus \\dots \\oplus B_{|B|})^K\n- Otherwise: 0\n\nHere, \\oplus represents the bitwise XOR.\nFind the sum, modulo 998244353, of the scores of the 2^N-1 non-empty subsequences of A.\nWhat is bitwise XOR? The bitwise XOR of non-negative integers A and B, denoted as A \\oplus B, is defined as follows: - In the binary representation of A \\oplus B, the digit at position 2^k (k \\geq 0) is 1 if exactly one of A and B has a 1 in that position in their binary representations, and 0 otherwise. For example, 3 \\oplus 5 = 6 (in binary: 011 \\oplus 101 = 110). In general, the XOR of k integers p_1, \\dots, p_k is defined as (\\cdots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\cdots \\oplus p_k), and it can be proved that this is independent of the order of p_1, \\dots, p_k.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M K\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N,K \\leq 2 \\times 10^5\n- 1 \\leq M \\leq 100\n- 0 \\leq A_i < 2^{20}\n- All input values are integers.\n\nSample Input 1\n\n3 2 2\r\n1 2 3\n\nSample Output 1\n\n14\r\n\nHere are the scores of the 2^3-1=7 non-empty subsequences of A.\n\n- (1): 0\n- (2): 0\n- (3): 0\n- (1,2): (1\\oplus2)^2=9\n- (1,3): (1\\oplus3)^2=4\n- (2,3): (2\\oplus3)^2=1\n- (1,2,3): 0\n\nTherefore, the sought sum is 0+0+0+9+4+1+0=14.\n\nSample Input 2\n\n10 5 3\r\n100 100 100 100 100 100 100 100 100 100\n\nSample Output 2\n\n252000000\n\nSample Input 3\n\n16 4 100\r\n7053 3876 3178 8422 7802 5998 2334 6757 6889 6637 7365 9495 7848 9026 7312 6558\n\nSample Output 3\n\n432440016",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.An election is being held with N candidates numbered 1, 2, \\ldots, N. There are K votes, some of which have been counted so far.\nUp until now, candidate i has received A_i votes.\nAfter all ballots are counted, candidate i (1 \\leq i \\leq N) will be elected if and only if the number of candidates who have received more votes than them is less than M. There may be multiple candidates elected.\nFor each candidate, find the minimum number of additional votes they need from the remaining ballots to guarantee their victory regardless of how the other candidates receive votes.\nFormally, solve the following problem for each i = 1,2,\\ldots,N.\nDetermine if there is a non-negative integer X not exceeding K - \\displaystyle{\\sum_{i=1}^{N}} A_i satisfying the following condition. If it exists, find the minimum possible such integer.\n\n- If candidate i receives X additional votes, then candidate i will always be elected.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M K\nA_1 A_2 \\ldots A_N\n\nOutput\n\nLet C_i be the minimum number of additional votes candidate i needs from the remaining ballots to guarantee their victory regardless of how other candidates receive votes. Print C_1, C_2, \\ldots, C_N separated by spaces.\nIf candidate i has already secured their victory, then let C_i = 0. If candidate i cannot secure their victory under any circumstances, then let C_i = -1.\n\nConstraints\n\n\n- 1 \\leq M \\leq N \\leq 2 \\times 10^5\n- 1 \\leq K \\leq 10^{12}\n- 0 \\leq A_i \\leq 10^{12}\n- \\displaystyle{\\sum_{i=1}^{N} A_i} \\leq K\n- All input values are integers.\n\nSample Input 1\n\n5 2 16\n3 1 4 1 5\n\nSample Output 1\n\n2 -1 1 -1 0\n\n14 votes have been counted so far, and 2 votes are left.\nThe C to output is (2, -1, 1, -1, 0). For example:\n\n- Candidate 1 can secure their victory by obtaining 2 more votes, while not by obtaining 1 more vote. Thus, C_1 = 2.\n- Candidate 2 can never (even if they obtain 2 more votes) secure their victory, so C_2 = -1.\n\nSample Input 2\n\n12 1 570\n81 62 17 5 5 86 15 7 79 26 6 28\n\nSample Output 2\n\n79 89 111 117 117 74 112 116 80 107 117 106",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a mysterious button.\r\nWhen you press this button, you receive one candy, unless less than C seconds have elapsed since you last received a candy.\nTakahashi decided to press this button N times.\r\nHe will press the button for the i-th time T_i seconds from now.\nHow many candies will he receive?\n\nInput\n\nThe input is given from Standard Input in the following format:\nN C\r\nT_1 T_2 \\dots T_N\n\nOutput\n\nPrint the number of candies that Takahashi will receive.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- 1 \\leq C \\leq 1000\n- 0 \\leq T_1 < T_2 < \\dots < T_N \\leq 1000\n- All input values are integers.\n\nSample Input 1\n\n6 5\r\n1 3 7 8 10 12\n\nSample Output 1\n\n3\r\n\nTakahashi will press the button six times.\n\n- 1st press (1 second from now): You always receive a candy when pressing the button for the first time.\n- 2nd press (3 seconds from now): 3 - 1 = 2 < C seconds have elapsed since he last received a candy, so he does not receive a candy.\n- 3rd press (7 seconds from now): 7 - 1 = 6 \\geq C seconds have elapsed since he last received a candy, so he receives a candy.\n- 4th press (8 seconds from now): 8 - 7 = 1 < C second has elapsed since he last received a candy, so he does not receive a candy.\n- 5th press (10 seconds from now): 10 - 7 = 3 < C seconds have elapsed since he last received a candy, so he does not receive a candy.\n- 6th press (12 seconds from now): 12 - 7 = 5 \\geq C seconds have elapsed since he last received a candy, so he receives a candy.\n\nTherefore, he receives three candies.\n\nSample Input 2\n\n3 2\r\n0 2 4\n\nSample Output 2\n\n3\n\nSample Input 3\n\n10 3\r\n0 3 4 6 9 12 15 17 19 20\n\nSample Output 3\n\n7",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of uppercase English letters.\nFind the number of integer triples (i, j, k) satisfying both of the following conditions:\n\n- 1 \\leq i < j < k \\leq |S|\n- The length-3 string formed by concatenating S_i, S_j, and S_k in this order is a palindrome.\n\nHere, |S| denotes the length of S, and S_x denotes the x-th character of S.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- S is a string of length between 1 and 2 \\times 10^5, inclusive, consisting of uppercase English letters.\n\nSample Input 1\n\nABCACC\n\nSample Output 1\n\n5\r\n\nThe triples satisfying the conditions are (i, j, k) = (1, 2, 4), (1, 3, 4), (3, 4, 5), (3, 4, 6), (3, 5, 6).\n\nSample Input 2\n\nOOOOOOOO\n\nSample Output 2\n\n56\n\nSample Input 3\n\nXYYXYYXYXXX\n\nSample Output 3\n\n75",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array points where points[i] = [x_i, y_i] represents the coordinates of a point on an infinite plane.\nYour task is to find the maximum area of a rectangle that:\n\nCan be formed using four of these points as its corners.\nDoes not contain any other point inside or on its border.\nHas its edges parallel to the axes.\n\nReturn the maximum area that you can obtain or -1 if no such rectangle is possible.\n \nExample 1:\n\nInput: points = [[1,1],[1,3],[3,1],[3,3]]\nOutput: 4\nExplanation:\n\nWe can make a rectangle with these 4 points as corners and there is no other point that lies inside or on the border. Hence, the maximum possible area would be 4.\n\nExample 2:\n\nInput: points = [[1,1],[1,3],[3,1],[3,3],[2,2]]\nOutput: -1\nExplanation:\n\nThere is only one rectangle possible is with points [1,1], [1,3], [3,1] and [3,3] but [2,2] will always lie inside it. Hence, returning -1.\n\nExample 3:\n\nInput: points = [[1,1],[1,3],[3,1],[3,3],[1,2],[3,2]]\nOutput: 2\nExplanation:\n\nThe maximum area rectangle is formed by the points [1,3], [1,2], [3,2], [3,3], which has an area of 2. Additionally, the points [1,1], [1,2], [3,1], [3,2] also form a valid rectangle with the same area.\n\n \nConstraints:\n\n1 <= points.length <= 10\npoints[i].length == 2\n0 <= x_i, y_i <= 100\nAll the given points are unique.",
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|
[
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two positive integers n and k. There are n children numbered from 0 to n - 1 standing in a queue in order from left to right.\nInitially, child 0 holds a ball and the direction of passing the ball is towards the right direction. After each second, the child holding the ball passes it to the child next to them. Once the ball reaches either end of the line, i.e. child 0 or child n - 1, the direction of passing is reversed.\nReturn the number of the child who receives the ball after k seconds.\n \nExample 1:\n\nInput: n = 3, k = 5\nOutput: 1\nExplanation:\n\n\n\nTime elapsed\nChildren\n\n\n0\n[0, 1, 2]\n\n\n1\n[0, 1, 2]\n\n\n2\n[0, 1, 2]\n\n\n3\n[0, 1, 2]\n\n\n4\n[0, 1, 2]\n\n\n5\n[0, 1, 2]\n\n\n\n\nExample 2:\n\nInput: n = 5, k = 6\nOutput: 2\nExplanation:\n\n\n\nTime elapsed\nChildren\n\n\n0\n[0, 1, 2, 3, 4]\n\n\n1\n[0, 1, 2, 3, 4]\n\n\n2\n[0, 1, 2, 3, 4]\n\n\n3\n[0, 1, 2, 3, 4]\n\n\n4\n[0, 1, 2, 3, 4]\n\n\n5\n[0, 1, 2, 3, 4]\n\n\n6\n[0, 1, 2, 3, 4]\n\n\n\n\nExample 3:\n\nInput: n = 4, k = 2\nOutput: 2\nExplanation:\n\n\n\nTime elapsed\nChildren\n\n\n0\n[0, 1, 2, 3]\n\n\n1\n[0, 1, 2, 3]\n\n\n2\n[0, 1, 2, 3]\n\n\n\n\n \nConstraints:\n\n2 <= n <= 50\n1 <= k <= 50",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
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| 0 | 56 |
LiveCodeBenchV5
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{
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cells numbered from 1 to N in a row. Initially, M cells contain stones, and cell X_i contains A_i stones (1 \\leq i \\leq M).\nYou can perform the following operation any number of times (possibly zero):\n\n- If cell i (1 \\leq i \\leq N-1) contains a stone, move one stone from cell i to cell i+1.\n\nFind the minimum number of operations required to reach a state where each of the N cells contains exactly one stone. If it is impossible, print -1.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nX_1 X_2 \\ldots X_M\r\nA_1 A_2 \\ldots A_M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^{9}\n- 1 \\leq M \\leq 2 \\times 10^{5}\n- M \\leq N\n- 1 \\leq X_i \\leq N (1 \\leq i \\leq M)\n- X_i \\neq X_j (1 \\leq i < j \\leq M)\n- 1 \\leq A_i \\leq 2 \\times 10^{9} (1 \\leq i \\leq M)\n- All input values are integers.\n\nSample Input 1\n\n5 2\r\n1 4\r\n3 2\n\nSample Output 1\n\n4\r\n\nYou can reach a state where each of the five cells contains exactly one stone with four operations as follows:\n\n- Move one stone from cell 1 to cell 2.\n- Move one stone from cell 2 to cell 3.\n- Move one stone from cell 4 to cell 5.\n- Move one stone from cell 1 to cell 2.\n\nIt is impossible to achieve the goal in three or fewer operations. Therefore, print 4.\n\nSample Input 2\n\n10 3\r\n1 4 8\r\n4 2 4\n\nSample Output 2\n\n-1\r\n\nNo matter how you perform the operations, you cannot reach a state where all ten cells contain exactly one stone. Therefore, print -1.",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
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| 2 | 239 |
LiveCodeBenchV5
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{
"expected_answer": "",
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"reference_solution": ""
}
|
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.