| [{"task_id": "mmlu-7868", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Which of these household pets should be vaccinated for parvovirus?\nA) hamster\nB) cat\nC) dog\nD) bird\n\nAnswer with the letter only.", "response": "C", "cost_usd": 7.5e-06, "tokens_in": 45, "tokens_out": 5, "latency_s": 1.47}, {"task_id": "mmlu-2479", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)\nT \u2228 U\nW \u00b7 T / U\nA) Valid\nB) Invalid. Counterexample when T and W are true and U is false\nC) Invalid. Counterexample when T is true and W and U are false\nD) Invalid. Counterexample when W is true and T and U are false\n\nAnswer with the letter only.", "response": "B", "cost_usd": 4.64e-05, "tokens_in": 134, "tokens_out": 55, "latency_s": 2.241}, {"task_id": "gsm8k-1290", "model": "openai/gpt-5.6-luna", "prompt": "A small sunflower has 3 dozen seeds and a large sunflower has 50% more seeds than a small sunflower. How many sunflower seeds are there altogether?\n\nReason step by step, then give the final answer as a single number.", "response": "A small sunflower has \\(3 \\times 12 = 36\\) seeds.\n\nA large sunflower has \\(50\\%\\) more: \\(36 + 18 = 54\\) seeds.\n\nAltogether: \\(36 + 54 = 90\\).\n\n90", "cost_usd": 7.069999999999998e-05, "tokens_in": 53, "tokens_out": 109, "latency_s": 2.55}, {"task_id": "gsm8k-106", "model": "openai/gpt-5.6-luna", "prompt": "John has 3 boxes. Each box is 5 inches by 6 inches by 4 inches. The walls are 1 inch thick. What is the total inner volume of all 3 boxes?\n\nReason step by step, then give the final answer as a single number.", "response": "1. Subtract 2 inches for the 1-inch-thick walls on each dimension:\n - Length: \\(5 - 2 = 3\\)\n - Width: \\(6 - 2 = 4\\)\n - Height: \\(4 - 2 = 2\\)\n\n2. Inner volume of one box:\n \\[\n 3 \\times 4 \\times 2 = 24\n \\]\n\n3. Inner volume of 3 boxes:\n \\[\n 24 \\times 3 = 72\n \\]\n\n72", "cost_usd": 0.0001271, "tokens_in": 65, "tokens_out": 201, "latency_s": 3.103}, {"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.", "response": "import sys\n\nx = int(sys.stdin.readline())\nfactorial = 1\nn = 1\n\nwhile factorial < x:\n n += 1\n factorial *= n\n\nprint(n)", "cost_usd": 4.8099999999999977e-05, "tokens_in": 217, "tokens_out": 44, "latency_s": 1.185}, {"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.", "response": "import sys\n\ndef solve():\n data = list(map(int, sys.stdin.buffer.read().split()))\n t = data[0]\n pos = 1\n out = []\n\n for _ in range(t):\n n = data[pos]\n pos += 1\n a = data[pos:pos + 2 * n]\n pos += 2 * n\n\n first = [-1] * (n + 1)\n bad = [False] * (n + 1)\n\n for i in range(2 * n - 1):\n if a[i] == a[i + 1]:\n bad[a[i]] = True\n elif a[i] != a[i + 1]:\n x, y = a[i], a[i + 1]\n if x > y:\n x, y = y, x\n key = (x, y)\n if key not in first:\n first[key] = i\n else:\n pass\n\n edges = {}\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 key = (x, y)\n if key in edges:\n mn, mx = edges[key]\n if i < mn:\n mn = i\n if i > mx:\n mx = i\n edges[key] = (mn, mx)\n else:\n edges[key] = (i, i)\n\n ans = 0\n for (x, y), (mn, mx) in edges.items():\n if not bad[x] and not bad[y] and mx - mn > 1:\n ans += 1\n\n out.append(str(ans))\n\n sys.stdout.write(\"\\n\".join(out))\n\nif __name__ == \"__main__\":\n solve()\n", "cost_usd": 0.001218, "tokens_in": 702, "tokens_out": 1913, "latency_s": 18.938}] |