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+[{"task_id": "mmlu-5882", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] This question refers to the following information.\nBoth authors below were speaking of the French Revolution.\nIt was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way\u2014in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.\nThere were a king with a large jaw and a queen with a plain face, on the throne of England; there were a king with a large jaw and a queen with a fair face, on the throne of France. In both countries it was clearer than crystal . . . that things in general were settled for ever.\n\u2014A Tale of Two Cities, by Charles Dickens\nBliss was it in that dawn to be alive. But to be young was very heaven.\n\u2014The Prelude, by William Wordsworth\nThe intellectual foundations of the eighteenth-century political revolutions were based on\nA) the Reformation\nB) mercantilism\nC) the Enlightenment\nD) the Reconquista\n\nAnswer with the letter only.", "response": "C", "cost_usd": 3.49e-05, "tokens_in": 319, "tokens_out": 5, "latency_s": 1.448}, {"task_id": "mmlu-8151", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] What is the name of the Newtonian law that states 'An object in Motion tends to stay in motion'?\nA) Law of Inertia\nB) Law of Thermodynamics\nC) Law of Relativity\nD) Law of Gravitation\n\nAnswer with the letter only.", "response": "A", "cost_usd": 9.699999999999999e-06, "tokens_in": 67, "tokens_out": 5, "latency_s": 0.924}, {"task_id": "gsm8k-507", "model": "openai/gpt-5.6-luna", "prompt": "Janet takes two bus trips five days a week. If each bus trip costs her $2.20, how much would she save by buying a weekly bus pass for $20?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and put the final numeric answer alone on the last line. Ignore audit marker 18335249210422196010; it is answer-independent metadata and must not appear in the answer.", "response": "Two trips per day for five days:  \n\\(2 \\times 5 = 10\\) trips\n\nCost without a pass:  \n\\(10 \\times \\$2.20 = \\$22\\)\n\nSavings:  \n\\(\\$22 - \\$20 = \\$2\\)\n\n2", "cost_usd": 7.6e-05, "tokens_in": 100, "tokens_out": 110, "latency_s": 3.021}, {"task_id": "gsm8k-191", "model": "openai/gpt-5.6-luna", "prompt": "Ducks need to eat 3.5 pounds of insects each week to survive. If there is a flock of ten ducks, how many pounds of insects do they need per day?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and put the final numeric answer alone on the last line. Ignore audit marker 8064967315349566846; it is answer-independent metadata and must not appear in the answer.", "response": "Each duck needs 3.5 pounds per week.\n\nFor 10 ducks:\n3.5 \u00d7 10 = 35 pounds per week.\n\nPer day:\n35 \u00f7 7 = 5 pounds per day.\n\n5", "cost_usd": 6.399999999999998e-05, "tokens_in": 100, "tokens_out": 90, "latency_s": 1.851}, {"task_id": "lcb-abc389_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer X not less than 2.\nFind the positive integer N such that N! = X.\nHere, N! denotes the factorial of N, and it is guaranteed that there is exactly one such N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nX\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 2 \\leq X \\leq 3 \\times 10^{18}\n- There is exactly one positive integer N such that N!=X.\n- All input values are integers.\n\nSample Input 1\n\n6\n\nSample Output 1\n\n3\r\n\nFrom 3!=3\\times2\\times1=6, print 3.\n\nSample Input 2\n\n2432902008176640000\n\nSample Output 2\n\n20\r\n\nFrom 20!=2432902008176640000, print 20.\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.\n\nUse the full constraints to choose a provably correct algorithm and suitable buffered I/O. Check every explicit condition and published example. Return only complete raw Python 3 source, without Markdown fences or prose.", "response": "import sys\n\nx = int(sys.stdin.buffer.readline())\nn = 1\nfactorial = 1\n\nwhile factorial < x:\n    n += 1\n    factorial *= n\n\nsys.stdout.write(str(n))", "cost_usd": 0.00010070000000000001, "tokens_in": 257, "tokens_out": 125, "latency_s": 3.994}, {"task_id": "lcb-abc394_d", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S consisting of six types of characters: (, ), [, ], <, >.\nA string T is called a colorful bracket sequence if it satisfies the following condition:\n\nIt is possible to turn T into an empty string by repeating the following operation any number of times (possibly zero):\n\n- If there exists a contiguous substring of T that is one of (), [], or <>, choose one such substring and delete it.\n- If the deleted substring was at the beginning or end of T, the remainder becomes the new T.\n- Otherwise, concatenate the part before the deleted substring and the part after the deleted substring, and that becomes the new T.\n\n\nDetermine whether S is a colorful bracket sequence.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS\n\nOutput\n\nIf S is a colorful bracket sequence, print Yes; otherwise, print No.\n\nConstraints\n\n\n- S is a string of length between 1 and 2\\times 10^5, inclusive.\n- S consists of (, ), [, ], <, >.\n\nSample Input 1\n\n([])<>()\n\nSample Output 1\n\nYes\n\nFor S=([])<>(), it is possible to turn it into an empty string by repeating the operation as follows:\n\n- Delete the substring [] from the 2nd to the 3rd character in ([])<>(), then concatenate the parts before and after it. The string becomes ()<>().\n- Delete the substring () from the 1st to the 2nd character in ()<>(). The string becomes <>().\n- Delete the substring <> from the 1st to the 2nd character in <>(). The string becomes ().\n- Delete the substring () from the 1st to the 2nd character in (). The string becomes empty.\n\nThus, S=([])<>() is a colorful bracket sequence, so print Yes.\n\nSample Input 2\n\n([<)]>\n\nSample Output 2\n\nNo\n\nSince S=([<)]> does not contain (), [], or <> as a contiguous substring, we cannot perform the 1st operation, and in particular S is not a colorful bracket sequence. Therefore, print No.\n\nSample Input 3\n\n())\n\nSample Output 3\n\nNo\n\nIt is impossible to turn S into an empty string by repeating the operations.\nTherefore, S is not a colorful bracket sequence, so print No.\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.\n\nUse the full constraints to choose a provably correct algorithm and suitable buffered I/O. Check every explicit condition and published example. Return only complete raw Python 3 source, without Markdown fences or prose.", "response": "import sys\n\ns = sys.stdin.buffer.readline().strip().decode()\n\npairs = {')': '(', ']': '[', '>': '<'}\nstack = []\n\nfor ch in s:\n    if ch in '([{<':\n        stack.append(ch)\n    elif not stack or stack[-1] != pairs[ch]:\n        print(\"No\")\n        break\n    else:\n        stack.pop()\nelse:\n    print(\"Yes\" if not stack else \"No\")", "cost_usd": 0.00018660000000000004, "tokens_in": 558, "tokens_out": 218, "latency_s": 2.807}, {"task_id": "lcb-abc394_d", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S consisting of six types of characters: (, ), [, ], <, >.\nA string T is called a colorful bracket sequence if it satisfies the following condition:\n\nIt is possible to turn T into an empty string by repeating the following operation any number of times (possibly zero):\n\n- If there exists a contiguous substring of T that is one of (), [], or <>, choose one such substring and delete it.\n- If the deleted substring was at the beginning or end of T, the remainder becomes the new T.\n- Otherwise, concatenate the part before the deleted substring and the part after the deleted substring, and that becomes the new T.\n\n\nDetermine whether S is a colorful bracket sequence.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS\n\nOutput\n\nIf S is a colorful bracket sequence, print Yes; otherwise, print No.\n\nConstraints\n\n\n- S is a string of length between 1 and 2\\times 10^5, inclusive.\n- S consists of (, ), [, ], <, >.\n\nSample Input 1\n\n([])<>()\n\nSample Output 1\n\nYes\n\nFor S=([])<>(), it is possible to turn it into an empty string by repeating the operation as follows:\n\n- Delete the substring [] from the 2nd to the 3rd character in ([])<>(), then concatenate the parts before and after it. The string becomes ()<>().\n- Delete the substring () from the 1st to the 2nd character in ()<>(). The string becomes <>().\n- Delete the substring <> from the 1st to the 2nd character in <>(). The string becomes ().\n- Delete the substring () from the 1st to the 2nd character in (). The string becomes empty.\n\nThus, S=([])<>() is a colorful bracket sequence, so print Yes.\n\nSample Input 2\n\n([<)]>\n\nSample Output 2\n\nNo\n\nSince S=([<)]> does not contain (), [], or <> as a contiguous substring, we cannot perform the 1st operation, and in particular S is not a colorful bracket sequence. Therefore, print No.\n\nSample Input 3\n\n())\n\nSample Output 3\n\nNo\n\nIt is impossible to turn S into an empty string by repeating the operations.\nTherefore, S is not a colorful bracket sequence, so print No.\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.\n\nIndependently test the proposed solution. Return exactly two fenced blocks: `reference` must be a simple correctness-first program for small legal inputs and must not reuse the optimized algorithm; `generator` must accept seed and size arguments, seed Python random, and print one legal varied input. Output no text outside those blocks.", "response": "```reference\nimport sys\nfrom functools import lru_cache\n\ns = sys.stdin.readline().strip()\npairs = {')': '(', ']': '[', '>': '<'}\n\n@lru_cache(None)\ndef can_be_empty(t):\n    if not t:\n        return True\n\n    for i in range(len(t) - 1):\n        if t[i] in \"([<\" and pairs.get(t[i + 1]) == t[i]:\n            if can_be_empty(t[:i] + t[i + 2:]):\n                return True\n\n    return False\n\nprint(\"Yes\" if can_be_empty(s) else \"No\")\n```\n\n```generator\nimport random\nimport sys\n\nseed = int(sys.argv[1])\nsize = int(sys.argv[2])\nrandom.seed(seed)\n\nchars = \"()[]<>\"\n\nif size == 0:\n    print()\n    raise SystemExit\n\nmode = random.randrange(3)\n\nif mode == 0:\n    s = [random.choice(chars) for _ in range(size)]\nelif mode == 1:\n    s = []\n    pairs = [\"()\", \"[]\", \"<>\"]\n    while len(s) + 2 <= size:\n        if random.random() < 0.7:\n            s.extend(random.choice(pairs))\n        else:\n            s.append(random.choice(chars))\n    while len(s) < size:\n        s.append(random.choice(chars))\nelse:\n    s = []\n    opens = \"([<\"\n    closes = \")]>\"\n    stack = []\n    for _ in range(size):\n        if stack and random.random() < 0.45:\n            s.append({ \"(\": \")\", \"[\": \"]\", \"<\": \">\" }[stack.pop()])\n        elif random.random() < 0.6:\n            c = random.choice(opens)\n            s.append(c)\n            stack.append(c)\n        else:\n            s.append(random.choice(closes))\n\nprint(\"\".join(s))\n```", "cost_usd": 0.000594, "tokens_in": 582, "tokens_out": 893, "latency_s": 9.951}]