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[{"task_id": "mmlu-3985", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Output in country A is 1200 units and its population is 100 persons. Output in country B is 2400 units and its population is 400 persons.\nA) Country A has a higher standard of living than country B.\nB) Country A has a lower standard of living than country B.\nC) Country A and B have identical living standards.\nD) Country A is less productive than country B.\n\nAnswer with the letter only.", "response": "A", "cost_usd": 3.94e-05, "tokens_in": 100, "tokens_out": 49, "latency_s": 5.308}, {"task_id": "mmlu-5640", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A student organization at a university is interested in estimating the proportion of students in favor of showing movies biweekly instead of monthly. How many students should be sampled to get a 90 percent confidence interval with a width of at most 0.08?\nA) 27\nB) 64\nC) 106\nD) 423\n\nAnswer with the letter only.", "response": "D", "cost_usd": 4.580000000000001e-05, "tokens_in": 86, "tokens_out": 62, "latency_s": 3.067}, {"task_id": "gsm8k-923", "model": "openai/gpt-5.6-luna", "prompt": "Lana is brewing cups of tea for her friends. She has 27 cups, and she divides these into 3 rows. In each row, she creates equal amounts of chamomile and mint tea cups. She then uses the remaining cups to brew a total of 15 cups of cinnamon tea. How many cups of mint tea are in each row?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and place the final numeric answer alone on the last line. The following fixed provenance sentinel is unrelated to the problem and must not appear in the response: 271828182845904523536", "response": "There are \\(27 - 15 = 12\\) cups for chamomile and mint tea.\n\nDividing equally among 3 rows gives \\(12 \\div 3 = 4\\) cups per row.\n\nSince chamomile and mint are equal, each type has \\(4 \\div 2 = 2\\) cups per row.\n\n2", "cost_usd": 0.0001047, "tokens_in": 135, "tokens_out": 152, "latency_s": 3.465}, {"task_id": "gsm8k-87", "model": "openai/gpt-5.6-luna", "prompt": "A company pays each of its employees $600 in a month. The company has a policy of increasing the salaries of each of its employees by 10% of the initial salary every year for those who've stayed in the company for five years. If Sylvie just clocked 5 years in the company last December, what's her annual salary after three more years of service?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and place the final numeric answer alone on the last line. The following fixed provenance sentinel is unrelated to the problem and must not appear in the response: 271828182845904523536", "response": "1. Initial monthly salary: $600.\n2. Annual increase: 10% of $600 = $60 per month.\n3. Over three more years, total increase: 3 \u00d7 $60 = $180 per month.\n4. Monthly salary after three years: $600 + $180 = $780.\n5. Annual salary: $780 \u00d7 12 = $9,360.\n\n9360", "cost_usd": 0.0003258, "tokens_in": 138, "tokens_out": 520, "latency_s": 9.527}, {"task_id": "lcb-abc391_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string D representing one of the eight directions (north, east, west, south, northeast, northwest, southeast, southwest). The correspondence between the directions and their representing strings is as follows.\n\n- North: N\n- East: E\n- West: W\n- South: S\n- Northeast: NE\n- Northwest: NW\n- Southeast: SE\n- Southwest: SW\n\nPrint the string representing the direction opposite to the direction denoted by D.\n\nInput\n\nThe input is given from Standard Input in the following format:\nD\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- D is one of N, E, W, S, NE, NW, SE, SW.\n\nSample Input 1\n\nN\n\nSample Output 1\n\nS\r\n\nPrint S, which represents south, the direction opposite to north.\n\nSample Input 2\n\nSE\n\nSample Output 2\n\nNW\r\n\nPrint NW, which represents northwest, the direction opposite to southeast.\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\nBefore writing the program, privately perform two independent reviews. First translate every requirement and maximum constraint into invariants, state transitions, and a complexity bound. Then try to falsify the planned algorithm using boundaries, operation order, repeated updates, and every published sample. Reconcile any conflict before answering. Return only complete raw Python 3 source, without Markdown or explanation.", "response": "d = input().strip()\n\nopposite = {\n \"N\": \"S\",\n \"S\": \"N\",\n \"E\": \"W\",\n \"W\": \"E\",\n \"NE\": \"SW\",\n \"SW\": \"NE\",\n \"NW\": \"SE\",\n \"SE\": \"NW\",\n}\n\nprint(opposite[d])\n", "cost_usd": 7.640000000000001e-05, "tokens_in": 308, "tokens_out": 76, "latency_s": 1.335}, {"task_id": "lcb-abc399_c", "model": "openai/gpt-5.6-luna", "prompt": "You are given a simple undirected graph with N vertices and M edges, where the vertices are labeled 1 to N. The i-th edge connects vertices u_i and v_i.\r\nWhat is the minimum number of edges that need to be deleted from this graph so that the graph becomes a forest?\n\nWhat is a forest?\r\n\r\nA simple undirected graph F is called a forest if and only if F does not contain any cycle.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nu_1 v_1\r\nu_2 v_2\r\n\\vdots\r\nu_M v_M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- 0 \\leq M \\leq \\min \\left( \\frac{N(N-1)}{2}, 2 \\times 10^5\\right)\n- 1 \\leq u_i < v_i \\leq N\n- The given graph is simple.\n- All input values are integers.\n\nSample Input 1\n\n4 4\r\n1 2\r\n1 3\r\n2 4\r\n3 4\n\nSample Output 1\n\n1\r\n\nFor example, if you delete the first edge, the graph becomes a forest.\n\nSample Input 2\n\n5 0\n\nSample Output 2\n\n0\n\nSample Input 3\n\n10 10\r\n7 9\r\n4 6\r\n6 10\r\n2 5\r\n5 6\r\n5 9\r\n6 8\r\n4 8\r\n1 5\r\n1 4\n\nSample Output 3\n\n2\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\nBefore writing the program, privately perform two independent reviews. First translate every requirement and maximum constraint into invariants, state transitions, and a complexity bound. Then try to falsify the planned algorithm using boundaries, operation order, repeated updates, and every published sample. Reconcile any conflict before answering. Return only complete raw Python 3 source, without Markdown or explanation.", "response": "import sys\n\ndef main():\n data = list(map(int, sys.stdin.buffer.read().split()))\n if not data:\n return\n\n n, m = data[0], data[1]\n parent = list(range(n + 1))\n size = [1] * (n + 1)\n\n def find(x):\n while parent[x] != x:\n parent[x] = parent[parent[x]]\n x = parent[x]\n return x\n\n kept = 0\n idx = 2\n for _ in range(m):\n u, v = data[idx], data[idx + 1]\n idx += 2\n ru, rv = find(u), find(v)\n if ru != rv:\n if size[ru] < size[rv]:\n ru, rv = rv, ru\n parent[rv] = ru\n size[ru] += size[rv]\n kept += 1\n\n print(m - kept)\n\nif __name__ == \"__main__\":\n main()\n", "cost_usd": 0.00020370000000000002, "tokens_in": 453, "tokens_out": 264, "latency_s": 3.96}]
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