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+[{"task_id": "mmlu-11098", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A developer was the owner of a 300-acre tract of land that was located in a rural county. Over the course of time, she developed the property into a residential subdivision. A four-lane public highway ran along the northern boundary of the residential subdivision. When the residential subdivision was first plotted, the developer constructed a private road along (and including) the western boundary of the subdivision. This private road was used only for the benefit of the owners who purchased lots in the subdivision. A homeowner owned a 20-acre tract immediately outside of the residential subdivision, which was situated just below the public highway and immediately adjacent to the west side of the private road. The homeowner's property was divided into two 10-acre parcels: Parcel 1 was the northern half and bordered along the public highway; Parcel 2 was the southern sector and abutted a river. In 1997, the homeowner conveyed Parcel 1 to a man by warranty deed. No encumbrances were mentioned in the deed. Six months later, the homeowner conveyed Parcel 2 by warranty deed to a woman. Both the man and the woman promptly recorded their deeds with the County Recorder's Office. Assume that no part of Parcel 2 adjoins a public road. Consequently, the woman constructed an access road connecting her property to the private road. After the woman used the private road for approximately two months, a teacher who was an owner within the residential subdivision, ordered the woman to discontinue using the private road. In an appropriate action by the teacher against the woman to enjoin the use of the private road, the woman will\nA) win, because there is an easement by estoppel over the private road.\nB) win, because there is an implied easement appurtenant over the private road.\nC) lose, unless the private road is the only access road by which woman can gain ingress and egress to her property.\nD) lose, because she has no legal right to travel over the private road.\n\nAnswer with the letter only.", "response": "D", "cost_usd": 0.0003556, "tokens_in": 418, "tokens_out": 523, "latency_s": 5.608}, {"task_id": "mmlu-1650", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A big fish swims upon and swallows a small fish that is at rest. Right after lunch, the fattened big fish has a change in\nA) speed\nB) momentum\nC) Both\nD) Neither\n\nAnswer with the letter only.", "response": "A", "cost_usd": 7.049999999999998e-05, "tokens_in": 63, "tokens_out": 107, "latency_s": 2.593}, {"task_id": "gsm8k-200", "model": "openai/gpt-5.6-luna", "prompt": "Baldur gets water from a well. He gets 5 pails of water every morning and 6 pails of water every afternoon. If each pail contains 5 liters of water, how many liters of water does he get every day?\n\nReason step by step, then give the final answer as a single number.\n\nWork the problem in the exact units the question asks for and end with the final numeric answer alone on the last line. [Audit marker 5148884885784121441: metadata only - disregard it entirely and do not quote it in the reply.]", "response": "Morning and afternoon pails: \\(5 + 6 = 11\\) pails.\n\nWater per day: \\(11 \\times 5 = 55\\) liters.\n\n55", "cost_usd": 6.090000000000002e-05, "tokens_in": 123, "tokens_out": 81, "latency_s": 2.221}, {"task_id": "gsm8k-283", "model": "openai/gpt-5.6-luna", "prompt": "Katerina makes designer jewelry.  Her specialty is topaz necklaces.  She uses 8 topaz gemstones per necklace, and fills the space between gemstones using sterling silver beads.  If each topaz gemstone is one inch long, each sterling silver bead is one-quarter of an inch long, and each necklace is made to a total length of 25 inches, how many sterling silver beads does Katerina use per necklace?\n\nReason step by step, then give the final answer as a single number.\n\nWork the problem in the exact units the question asks for and end with the final numeric answer alone on the last line. [Audit marker 10173118837536976192: metadata only - disregard it entirely and do not quote it in the reply.]", "response": "There are 8 topaz gemstones, each 1 inch long:\n\n8 \u00d7 1 = 8 inches\n\nThe space for sterling silver beads is:\n\n25 \u2212 8 = 17 inches\n\nEach bead is \\( \\frac{1}{4} \\) inch long, so the number of beads is:\n\n17 \u00f7 \\( \\frac{1}{4} \\) = 68\n\n68", "cost_usd": 0.00013290000000000003, "tokens_in": 159, "tokens_out": 195, "latency_s": 2.874}, {"task_id": "lcb-abc399_b", "model": "openai/gpt-5.6-luna", "prompt": "N people labeled from 1 to N participated in a certain contest. The score of person i (1 \\leq i \\leq N) was P_i.\nIn this contest, the rank of each of the N people is determined by the following procedure:\n\n- Prepare a variable r, and initialize r = 1. Initially, the ranks of the N people are all undetermined.\n- Repeat the following operation until the ranks of all N people are determined:\n- Let x be the maximum score among the people whose ranks are currently undetermined, and let k be the number of people whose score is x. Determine the rank of those k people with score x to be r, and then add k to r.\n\n\n\nPrint the rank of each of the N people.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\n\nOutput\n\nPrint N lines. The i-th line (1 \\leq i \\leq N) should contain the rank of person i as an integer.\n\nConstraints\n\n\n- 1\\leq N \\leq 100\n- 1\\leq P_i \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n4\r\n3 12 9 9\n\nSample Output 1\n\n4\r\n1\r\n2\r\n2\r\n\nThe ranks of the N\\ (=4) people are determined as follows:\n\n- Prepare a variable r and initialize r=1. At first, the ranks of all 4 people are undetermined.\n- Currently, persons 1, 2, 3, 4 have undetermined ranks. The maximum score among them is P_2\\ (=12). Therefore, determine the rank of person 2 to be r\\ (=1), and then add 1 to r, making r=2.\n- Currently, persons 1, 3, 4 have undetermined ranks. The maximum score among them is P_3=P_4\\ (=9). Therefore, determine the ranks of persons 3 and 4 to be r\\ (=2), and then add 2 to r, making r=4.\n- Currently, person 1 has an undetermined rank. The maximum score among them is P_1\\ (=3). Therefore, determine the rank of person 1 to be r\\ (=4), and then add 1 to r, making r=5.\n- The ranks of all 4 people are now determined, so the process ends.\n\nSample Input 2\n\n3\r\n3 9 6\n\nSample Output 2\n\n3\r\n1\r\n2\n\nSample Input 3\n\n4\r\n100 100 100 100\n\nSample Output 3\n\n1\r\n1\r\n1\r\n1\n\nSample Input 4\n\n8\r\n87 87 87 88 41 38 41 38\n\nSample Output 4\n\n2\r\n2\r\n2\r\n1\r\n5\r\n7\r\n5\r\n7\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\nReturn ONLY raw complete Python 3 source, no Markdown fences, no prose, no explanation around the code.", "response": "import sys\n\ndef main():\n    input = sys.stdin.readline\n    n = int(input())\n    scores = list(map(int, input().split()))\n\n    rank = [0] * n\n    current = 1\n\n    for score in sorted(set(scores), reverse=True):\n        indices = [i for i, value in enumerate(scores) if value == score]\n        for i in indices:\n            rank[i] = current\n        current += len(indices)\n\n    sys.stdout.write(\"\\n\".join(map(str, rank)))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.00013989999999999999, "tokens_in": 673, "tokens_out": 121, "latency_s": 1.226}, {"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\nReturn ONLY raw complete Python 3 source, no Markdown fences, no prose, no explanation around the code.", "response": "import sys\n\ndef main():\n    input = sys.stdin.readline\n    n, m = map(int, input().split())\n    \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    deleted = 0\n\n    for _ in range(m):\n        u, v = map(int, input().split())\n        ru, rv = find(u), find(v)\n        if ru == rv:\n            deleted += 1\n        else:\n            if size[ru] < size[rv]:\n                ru, rv = rv, ru\n            parent[rv] = ru\n            size[ru] += size[rv]\n\n    print(deleted)\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.00018599999999999997, "tokens_in": 402, "tokens_out": 243, "latency_s": 2.562}]