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+[{"task_id": "mmlu-5567", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Consider a hypothesis test with H0 : \u03bc = 70 and Ha : \u03bc < 70. Which of the following choices of significance level and sample size results in the greatest power of the test when \u03bc = 65?\nA) \u03b1 = 0.05, n = 15\nB) \u03b1 = 0.01, n = 15\nC) \u03b1 = 0.05, n = 30\nD) \u03b1 = 0.01, n = 30\n\nAnswer with the letter only.", "response": "C", "cost_usd": 1.47e-05, "tokens_in": 117, "tokens_out": 5, "latency_s": 5.626}, {"task_id": "mmlu-11334", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A new gang member, hoping to impress the gang's leader, pointed a gun at a pedestrian and ordered her to give him her expensive watch, which she did. The gang member then tossed the watch to the gang leader, who was standing nearby. Although totally surprised by this act, the gang leader put the watch in his pocket. The pedestrian ran away. What crime did the gang leader commit?\nA) Accessory after the fact to robbery.\nB) Accomplice to robbery.\nC) Conspiracy to commit robbery.\nD) Receiving stolen property.\n\nAnswer with the letter only.", "response": "D", "cost_usd": 9.2e-05, "tokens_in": 128, "tokens_out": 132, "latency_s": 2.96}, {"task_id": "gsm8k-901", "model": "openai/gpt-5.6-luna", "prompt": "Calvin is making soup for his family for dinner. He has a pot with enough soup to fill four adult's bowls or eight child's bowls. He is an adult and will be eating with his adult wife and their two children. If everyone eats one bowl at a meal, how many times will each child be able to have a bowl of soup for lunch from the leftover soup?\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 8701559398887361747; it is answer-independent metadata and must not appear in the answer.", "response": "1. The pot holds 4 adult bowls, equivalent to 8 child bowls.\n2. Dinner uses 2 adult bowls for the adults and 2 child bowls for the children.\n3. This uses 3 adult-bowl equivalents, leaving 1 adult bowl equivalent.\n4. One adult bowl is enough for 2 child bowls, so each child can have one lunch bowl.\n\n1", "cost_usd": 0.0001315, "tokens_in": 139, "tokens_out": 196, "latency_s": 8.572}, {"task_id": "gsm8k-688", "model": "openai/gpt-5.6-luna", "prompt": "John is very tired. He decides to take a nap, but he wants to finish his homework first. If John has 20 minutes of math homework, 40 minutes of reading homework, and 20 minutes of history homework and 3 hours before he has to eat dinner, how many minutes does John have to nap?\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 16796323408686856612; it is answer-independent metadata and must not appear in the answer.", "response": "Math, reading, and history homework take:\n\n20 + 40 + 20 = 80 minutes\n\nThree hours is:\n\n3 \u00d7 60 = 180 minutes\n\nTime left for a nap:\n\n180 \u2212 80 = 100 minutes\n\n100", "cost_usd": 7.220000000000002e-05, "tokens_in": 128, "tokens_out": 99, "latency_s": 4.744}, {"task_id": "lcb-abc396_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer sequence of length N: A = (A_1,A_2,\\ldots,A_N).\nDetermine whether there is a place in A where the same element appears three or more times in a row.\nMore formally, determine whether there exists an integer i with 1 \\le i \\le N-2 such that A_i = A_{i+1} = A_{i+2}.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nIf there is a place in A where the same element appears three or more times in a row, print Yes. Otherwise, print No.\n\nConstraints\n\n\n- 3 \\le N \\le 100\n- 1 \\le A_i \\le 100\n- All input values are integers.\n\nSample Input 1\n\n5\r\n1 4 4 4 2\n\nSample Output 1\n\nYes\r\n\nWe have A=(1,4,4,4,2). There is a place where 4 appears three times in a row, so print Yes.\n\nSample Input 2\n\n6\r\n2 4 4 2 2 4\n\nSample Output 2\n\nNo\r\n\nWe have A=(2,4,4,2,2,4). There is no place where the same element appears three or more times in a row, so print No.\n\nSample Input 3\n\n8\r\n1 4 2 5 7 7 7 2\n\nSample Output 3\n\nYes\n\nSample Input 4\n\n10\r\n1 2 3 4 5 6 7 8 9 10\n\nSample Output 4\n\nNo\n\nSample Input 5\n\n13\r\n1 1 1 1 1 1 1 1 1 1 1 1 1\n\nSample Output 5\n\nYes\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\ndata = list(map(int, sys.stdin.buffer.read().split()))\nn = data[0]\na = data[1:1 + n]\n\nfor i in range(n - 2):\n    if a[i] == a[i + 1] == a[i + 2]:\n        print(\"Yes\")\n        break\nelse:\n    print(\"No\")", "cost_usd": 9.519999999999998e-05, "tokens_in": 478, "tokens_out": 79, "latency_s": 1.567}, {"task_id": "lcb-arc191_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S of length N and a string T of length M, both consisting of digits from 1 to 9.\nYou will perform the following operation for k=1,2,\\ldots,M in order:\n\n- Choose an integer i such that 1 \\le i \\le N. Then, replace the i-th character of S with the k-th character of T.\n\nFind the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nS\nT\n\nOutput\n\nPrint the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nConstraints\n\n\n- 1 \\le N,M \\le 10^6\n- N and M are integers.\n- S is a string of length N consisting of digits from 1 through 9.\n- T is a string of length M consisting of digits from 1 through 9.\n\nSample Input 1\n\n3 3\n191\n325\n\nSample Output 1\n\n593\n\nThe following sequence of operations is optimal:\n\n- For k=1: Choose i=3. Then, S = 193.\n- For k=2: Choose i=1. Then, S = 293.\n- For k=3: Choose i=1. Then, S = 593.\n\nIn this case, the value of S interpreted as an integer is 593, which is the maximum.\n\nSample Input 2\n\n3 9\n191\n998244353\n\nSample Output 2\n\n993\n\nSample Input 3\n\n11 13\n31415926535\n2718281828459\n\nSample Output 3\n\n98888976555\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\ndef main():\n    data = sys.stdin.buffer.read().split()\n    n = int(data[0])\n    m = int(data[1])\n    s = data[2].decode()\n    t = data[3].decode()\n\n    positions = [[] for _ in range(10)]\n    for i, ch in enumerate(t):\n        positions[ord(ch) - 48].append(i)\n\n    selected = bytearray(m)\n    ans = list(s)\n\n    for i in range(n - 1):\n        current = ord(ans[i]) - 48\n        digit = 9\n        while digit > current and not positions[digit]:\n            digit -= 1\n        if digit > current:\n            idx = positions[digit].pop()\n            selected[idx] = 1\n            ans[i] = chr(48 + digit)\n\n    last_unselected = -1\n    for i in range(m - 1, -1, -1):\n        if not selected[i]:\n            last_unselected = i\n            break\n\n    if last_unselected != -1:\n        ans[-1] = t[last_unselected]\n\n    sys.stdout.write(''.join(ans))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.0019066, "tokens_in": 436, "tokens_out": 3105, "latency_s": 37.828}, {"task_id": "lcb-arc191_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S of length N and a string T of length M, both consisting of digits from 1 to 9.\nYou will perform the following operation for k=1,2,\\ldots,M in order:\n\n- Choose an integer i such that 1 \\le i \\le N. Then, replace the i-th character of S with the k-th character of T.\n\nFind the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nS\nT\n\nOutput\n\nPrint the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nConstraints\n\n\n- 1 \\le N,M \\le 10^6\n- N and M are integers.\n- S is a string of length N consisting of digits from 1 through 9.\n- T is a string of length M consisting of digits from 1 through 9.\n\nSample Input 1\n\n3 3\n191\n325\n\nSample Output 1\n\n593\n\nThe following sequence of operations is optimal:\n\n- For k=1: Choose i=3. Then, S = 193.\n- For k=2: Choose i=1. Then, S = 293.\n- For k=3: Choose i=1. Then, S = 593.\n\nIn this case, the value of S interpreted as an integer is 593, which is the maximum.\n\nSample Input 2\n\n3 9\n191\n998244353\n\nSample Output 2\n\n993\n\nSample Input 3\n\n11 13\n31415926535\n2718281828459\n\nSample Output 3\n\n98888976555\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\nA generated legal case disagrees with an independently derived small-case reference. Solve the original problem again from first principles; do not patch or special-case this case.\nInput:\n3 3\n191\n325\n\nPrevious output:\n592\nReference output:\n593\nReturn only complete raw Python 3 source.", "response": "import sys\n\ndef main():\n    input = sys.stdin.readline\n    N, M = map(int, input().split())\n    s = list(input().strip())\n    t = input().strip()\n\n    cnt = [0] * 10\n    for ch in t[:max(0, M - N + 1)]:\n        cnt[int(ch)] += 1\n\n    mandatory = int(t[-1])\n    selected = [False] * N\n    mandatory_used = False\n\n    for i, ch in enumerate(s):\n        cur = int(ch)\n        chosen = 0\n\n        for d in range(9, cur, -1):\n            if cnt[d]:\n                chosen = d\n                cnt[d] -= 1\n                break\n\n        if chosen:\n            s[i] = str(chosen)\n            selected[i] = True\n        elif not mandatory_used and mandatory > cur:\n            s[i] = str(mandatory)\n            selected[i] = True\n            mandatory_used = True\n\n    if not mandatory_used:\n        for i in range(N - 1, -1, -1):\n            if not selected[i]:\n                s[i] = str(mandatory)\n                mandatory_used = True\n                break\n\n    if not mandatory_used:\n        s[-1] = str(mandatory)\n\n    sys.stdout.write(\"\".join(s))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.0016501000000000003, "tokens_in": 457, "tokens_out": 2674, "latency_s": 35.679}]