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+[{"task_id": "mmlu-5870", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] This question refers to the following information.\nI walk alongside the column, ask what's going on.\nA soldier says simply: \"They call up more every day.\n\"Some of us were sent north to the Yellow River at age fifteen,\nAnd now at forty we're heading off to the garrisons in the west.\nOn our first tour, the village headman had to tie our bandannas for us.\nWhen we came back, our hair was white, but still there's more unrest.\nThe frontier garrisons run with blood, enough to fill an ocean,\nBut the Martial Emperor's territorial ambitions have yet to crest.\nIn the hundred districts east of the mountains, throughout the land of Han,\nThere must be ten thousand villages that brambles now infest.\nEven if wives are strong enough to handle a hoe and plow,\nThe crops grow every which way, the fields are all a mess.\nIt's hardest for the Shanxi men, with their reputations as fighters:\nThey're rounded up like dogs or chickens, every male impressed.\n\"But sir, though it's good of you to ask,\nComplaining isn't part of the soldier's task.\nWe can only shake our heads. Take this winter:\nThe Shanxi troops were never sent home.\nThe District Officers are demanding the land tax,\nBut where will it come from? You can't get blood from a stone!\nI honestly think it's bad luck to bear a son now,\nIt's better to have a daughter: at least she can marry\nAnd live with the neighbors next door.\nBut a son will end up lying on some distant prairie.\"\nDu Fu, \"Ballad of the Army Carts,\" ca. 750 C.E.\nBased on the poem and your knowledge of history, Tang relations with western nomadic peoples and frontier peoples relied on which of the following?\nA) Adroit diplomacy and establishment of client relationships with bordering nomads\nB) The ability of the Tang emperor to project military power on the frontier in order to impose his will\nC) The permanent settlement of Han Chinese in frontier zones\nD) The payment of tribute to nomadic rulers\n\nAnswer with the letter only.", "response": "B", "cost_usd": 0.0001927, "tokens_in": 439, "tokens_out": 248, "latency_s": 7.836}, {"task_id": "mmlu-9736", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Nussbaum claims that to many current ethical theorists, turning to an ethical approach based on the virtues is connected with a turn toward:\nA) rationalism.\nB) empiricism.\nC) relativism.\nD) absolutism.\n\nAnswer with the letter only.", "response": "C", "cost_usd": 6.82e-05, "tokens_in": 64, "tokens_out": 103, "latency_s": 1.527}, {"task_id": "gsm8k-673", "model": "openai/gpt-5.6-luna", "prompt": "Janey has 3 more than twice the number of books that Sally has. If Janey has 21 books, how many does Sally have?\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 4573006690188683072; it is answer-independent metadata and must not appear in the answer.", "response": "Let \\(S\\) be the number of books Sally has.\n\n\\(21 = 2S + 3\\)\n\nSubtract 3: \\(18 = 2S\\)\n\nDivide by 2: \\(S = 9\\)\n\n9", "cost_usd": 7.050000000000003e-05, "tokens_in": 93, "tokens_out": 102, "latency_s": 4.242}, {"task_id": "gsm8k-1301", "model": "openai/gpt-5.6-luna", "prompt": "Randy has 9 oatmeal cookies, 4 chocolate chip cookies, and 5 sugar cookies. He ate 3 cookies for an early day snack, one of each flavor. He ate 2 oatmeal cookies for lunch. He gives 2 sugar cookies to his friends. Then, he bakes 4 of each flavor for dinner. How many cookies does he have now?\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 14837366066297815403; it is answer-independent metadata and must not appear in the answer.", "response": "Start with:\n- 9 oatmeal cookies\n- 4 chocolate chip cookies\n- 5 sugar cookies\n\nAfter eating one of each: \\(8 + 3 + 4 = 15\\) cookies.\n\nAfter eating 2 oatmeal cookies: \\(6 + 3 + 4 = 13\\) cookies.\n\nAfter giving away 2 sugar cookies: \\(6 + 3 + 2 = 11\\) cookies.\n\nAfter baking 4 of each flavor: \\(11 + 12 = 23\\) cookies.\n\n23", "cost_usd": 0.0001273, "tokens_in": 139, "tokens_out": 189, "latency_s": 2.627}, {"task_id": "lcb-abc400_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given two positive integers N and M.\nLet X = \\displaystyle\\sum_{i = 0}^{M} N^i. If X \\leq 10^9, print the value of X. If X > 10^9, print inf.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\n\nOutput\n\nPrint the value of X or inf as specified by the problem statement.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^9\n- 1 \\leq M \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n7 3\n\nSample Output 1\n\n400\r\n\nX = 1 + 7 + 49 + 343 = 400. Since 400 \\leq 10^9, print 400.\n\nSample Input 2\n\n1000000 2\n\nSample Output 2\n\ninf\r\n\nX = 1000001000001 > 10^9, so print inf.\n\nSample Input 3\n\n999999999 1\n\nSample Output 3\n\n1000000000\n\nSample Input 4\n\n998244353 99\n\nSample Output 4\n\ninf\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\nN, M = map(int, sys.stdin.buffer.read().split())\n\nlimit = 10**9\ntotal = 0\npower = 1\n\nfor _ in range(M + 1):\n    total += power\n    if total > limit:\n        print(\"inf\")\n        break\n    power *= N\nelse:\n    print(total)\n", "cost_usd": 0.00017679999999999996, "tokens_in": 328, "tokens_out": 240, "latency_s": 3.558}, {"task_id": "lcb-abc399_d", "model": "openai/gpt-5.6-luna", "prompt": "N couples are seated in a line.\nCount the number of pairs of couples such that neither couple was originally sitting next to each other, and both couples can end up sitting next to each other by swapping seats among those four people.\n\nThere is a sequence A = (A_1, A_2, \\dots, A_{2N}) of length 2N. Each of the integers 1, 2, \\dots, N appears exactly twice in A.\nFind the number of integer pairs (a, b) satisfying 1 \\leq a < b \\leq N and all of the following conditions:\n\n- The two occurrences of a in A are not adjacent.\n- The two occurrences of b in A are not adjacent.\n- By performing the following operation one or more times in any order, it is possible to reach a state where the two occurrences of a in A are adjacent and the two occurrences of b in A are also adjacent.\n- Choose an integer pair (i, j) (1 \\leq i \\leq 2N, 1 \\leq j \\leq 2N) such that A_i = a and A_j = b, and swap A_i with A_j.\n\n\n\nYou are given T test cases; solve each of them.\n\nInput\n\nThe input is given from Standard Input in the following format, where \\mathrm{case}_i denotes the i-th test case:\nT\n\\mathrm{case}_1\n\\mathrm{case}_2\n\\vdots\n\\mathrm{case}_T\n\nEach test case is given in the following format:\nN\nA_1 A_2 \\dots A_{2N}\n\nOutput\n\nPrint T lines. The i-th line should contain the answer for the i-th test case.\n\nConstraints\n\n\n- 1 \\leq T \\leq 2 \\times 10^5\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq A_i \\leq N\n- Each of 1, 2, \\dots, N appears exactly twice in A.\n- The sum of N over all test cases is at most 2 \\times 10^5.\n- All input values are integers.\n\nSample Input 1\n\n3\n3\n1 2 3 3 1 2\n4\n1 1 2 2 3 3 4 4\n5\n1 2 3 4 5 1 2 3 4 5\n\nSample Output 1\n\n1\n0\n4\n\nConsider the first test case.\n(a, b) = (1, 2) satisfies the conditions in the problem statement, for the following reasons:\n\n- The two occurrences of 1 in A are not adjacent.\n- The two occurrences of 2 in A are not adjacent.\n- By performing the operation where (i, j) = (1, 6) and swapping A_1 with A_6, you can reach a state where the two occurrences of 1 are adjacent and the two occurrences of 2 are also adjacent.\n\n(1, 2) is the only pair (a, b) that satisfies the conditions.\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 solve():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    t = data[0]\n    idx = 1\n    out = []\n\n    for _ in range(t):\n        n = data[idx]\n        idx += 1\n        a = data[idx:idx + 2 * n]\n        idx += 2 * n\n\n        bad = [False] * (n + 1)\n        for i in range(2 * n - 1):\n            if a[i] == a[i + 1]:\n                bad[a[i]] = True\n\n        first_edge = {}\n        ans = 0\n\n        for i in range(2 * n - 1):\n            x, y = a[i], a[i + 1]\n            if x == y:\n                continue\n            if x > y:\n                x, y = y, x\n\n            key = (x, y)\n            prev = first_edge.get(key)\n\n            if prev is None:\n                first_edge[key] = i\n            elif prev >= 0 and i - prev >= 2:\n                if not bad[x] and not bad[y]:\n                    ans += 1\n                first_edge[key] = -1\n\n        out.append(str(ans))\n\n    sys.stdout.write(\"\\n\".join(out))\n\nif __name__ == \"__main__\":\n    solve()\n", "cost_usd": 0.0012424, "tokens_in": 742, "tokens_out": 1947, "latency_s": 21.544}]