[ { "task_name": "PMED", "problem_type": "PMED", "instruction": "Recently the city discussed which handful of public restrooms to put into service from several candidate points. The task is to pick that exact number of sites and assign each neighborhood to one, and only one, of them so that when all the walking distances are added up the total is as low as possible. The detailed list of neighborhoods, candidate sites, and distances is provided below.\n\nThere are 20 total locations; exactly 1 restrooms must be opened, and the locations are listed as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.\nWalking distance from 1 to 2 is 14.\nWalking distance from 1 to 3 is 46.\nWalking distance from 1 to 4 is 65.\nWalking distance from 1 to 5 is 54.\nWalking distance from 1 to 6 is 49.\nWalking distance from 1 to 7 is 31.\nWalking distance from 1 to 8 is 25.\nWalking distance from 1 to 9 is 51.\nWalking distance from 1 to 10 is 34.\nWalking distance from 1 to 11 is 76.\nWalking distance from 1 to 12 is 53.\nWalking distance from 1 to 13 is 63.\nWalking distance from 1 to 14 is 66.\nWalking distance from 1 to 15 is 47.\nWalking distance from 1 to 16 is 45.\nWalking distance from 1 to 17 is 21.\nWalking distance from 1 to 18 is 79.\nWalking distance from 1 to 19 is 51.\nWalking distance from 1 to 20 is 39.\nWalking distance from 2 to 1 is 14.\nWalking distance from 2 to 3 is 60.\nWalking distance from 2 to 4 is 53.\nWalking distance from 2 to 5 is 49.\nWalking distance from 2 to 6 is 53.\nWalking distance from 2 to 7 is 17.\nWalking distance from 2 to 8 is 39.\nWalking distance from 2 to 9 is 59.\nWalking distance from 2 to 10 is 20.\nWalking distance from 2 to 11 is 64.\nWalking distance from 2 to 12 is 64.\nWalking distance from 2 to 13 is 49.\nWalking distance from 2 to 14 is 62.\nWalking distance from 2 to 15 is 33.\nWalking distance from 2 to 16 is 56.\nWalking distance from 2 to 17 is 7.\nWalking distance from 2 to 18 is 65.\nWalking distance from 2 to 19 is 38.\nWalking distance from 2 to 20 is 48.\nWalking distance from 3 to 1 is 46.\nWalking distance from 3 to 2 is 60.\nWalking distance from 3 to 4 is 46.\nWalking distance from 3 to 5 is 75.\nWalking distance from 3 to 6 is 73.\nWalking distance from 3 to 7 is 56.\nWalking distance from 3 to 8 is 71.\nWalking distance from 3 to 9 is 75.\nWalking distance from 3 to 10 is 55.\nWalking distance from 3 to 11 is 88.\nWalking distance from 3 to 12 is 77.\nWalking distance from 3 to 13 is 79.\nWalking distance from 3 to 14 is 79.\nWalking distance from 3 to 15 is 61.\nWalking distance from 3 to 16 is 69.\nWalking distance from 3 to 17 is 63.\nWalking distance from 3 to 18 is 63.\nWalking distance from 3 to 19 is 69.\nWalking distance from 3 to 20 is 62.\nWalking distance from 4 to 1 is 65.\nWalking distance from 4 to 2 is 53.\nWalking distance from 4 to 3 is 46.\nWalking distance from 4 to 5 is 79.\nWalking distance from 4 to 6 is 52.\nWalking distance from 4 to 7 is 38.\nWalking distance from 4 to 8 is 54.\nWalking distance from 4 to 9 is 48.\nWalking distance from 4 to 10 is 57.\nWalking distance from 4 to 11 is 75.\nWalking distance from 4 to 12 is 64.\nWalking distance from 4 to 13 is 52.\nWalking distance from 4 to 14 is 42.\nWalking distance from 4 to 15 is 50.\nWalking distance from 4 to 16 is 56.\nWalking distance from 4 to 17 is 46.\nWalking distance from 4 to 18 is 88.\nWalking distance from 4 to 19 is 72.\nWalking distance from 4 to 20 is 51.\nWalking distance from 5 to 1 is 54.\nWalking distance from 5 to 2 is 49.\nWalking distance from 5 to 3 is 75.\nWalking distance from 5 to 4 is 79.\nWalking distance from 5 to 6 is 65.\nWalking distance from 5 to 7 is 64.\nWalking distance from 5 to 8 is 51.\nWalking distance from 5 to 9 is 50.\nWalking distance from 5 to 10 is 58.\nWalking distance from 5 to 11 is 79.\nWalking distance from 5 to 12 is 69.\nWalking distance from 5 to 13 is 58.\nWalking distance from 5 to 14 is 58.\nWalking distance from 5 to 15 is 62.\nWalking distance from 5 to 16 is 61.\nWalking distance from 5 to 17 is 54.\nWalking distance from 5 to 18 is 84.\nWalking distance from 5 to 19 is 60.\nWalking distance from 5 to 20 is 37.\nWalking distance from 6 to 1 is 49.\nWalking distance from 6 to 2 is 53.\nWalking distance from 6 to 3 is 73.\nWalking distance from 6 to 4 is 52.\nWalking distance from 6 to 5 is 65.\nWalking distance from 6 to 7 is 36.\nWalking distance from 6 to 8 is 52.\nWalking distance from 6 to 9 is 59.\nWalking distance from 6 to 10 is 63.\nWalking distance from 6 to 11 is 74.\nWalking distance from 6 to 12 is 12.\nWalking distance from 6 to 13 is 69.\nWalking distance from 6 to 14 is 74.\nWalking distance from 6 to 15 is 57.\nWalking distance from 6 to 16 is 4.\nWalking distance from 6 to 17 is 46.\nWalking distance from 6 to 18 is 89.\nWalking distance from 6 to 19 is 49.\nWalking distance from 6 to 20 is 66.\nWalking distance from 7 to 1 is 31.\nWalking distance from 7 to 2 is 17.\nWalking distance from 7 to 3 is 56.\nWalking distance from 7 to 4 is 38.\nWalking distance from 7 to 5 is 64.\nWalking distance from 7 to 6 is 36.\nWalking distance from 7 to 8 is 52.\nWalking distance from 7 to 9 is 61.\nWalking distance from 7 to 10 is 37.\nWalking distance from 7 to 11 is 57.\nWalking distance from 7 to 12 is 48.\nWalking distance from 7 to 13 is 58.\nWalking distance from 7 to 14 is 45.\nWalking distance from 7 to 15 is 27.\nWalking distance from 7 to 16 is 40.\nWalking distance from 7 to 17 is 10.\nWalking distance from 7 to 18 is 65.\nWalking distance from 7 to 19 is 40.\nWalking distance from 7 to 20 is 49.\nWalking distance from 8 to 1 is 25.\nWalking distance from 8 to 2 is 39.\nWalking distance from 8 to 3 is 71.\nWalking distance from 8 to 4 is 54.\nWalking distance from 8 to 5 is 51.\nWalking distance from 8 to 6 is 52.\nWalking distance from 8 to 7 is 52.\nWalking distance from 8 to 9 is 47.\nWalking distance from 8 to 10 is 59.\nWalking distance from 8 to 11 is 54.\nWalking distance from 8 to 12 is 64.\nWalking distance from 8 to 13 is 56.\nWalking distance from 8 to 14 is 41.\nWalking distance from 8 to 15 is 50.\nWalking distance from 8 to 16 is 56.\nWalking distance from 8 to 17 is 43.\nWalking distance from 8 to 18 is 81.\nWalking distance from 8 to 19 is 26.\nWalking distance from 8 to 20 is 14.\nWalking distance from 9 to 1 is 51.\nWalking distance from 9 to 2 is 59.\nWalking distance from 9 to 3 is 75.\nWalking distance from 9 to 4 is 48.\nWalking distance from 9 to 5 is 50.\nWalking distance from 9 to 6 is 59.\nWalking distance from 9 to 7 is 61.\nWalking distance from 9 to 8 is 47.\nWalking distance from 9 to 10 is 53.\nWalking distance from 9 to 11 is 68.\nWalking distance from 9 to 12 is 63.\nWalking distance from 9 to 13 is 48.\nWalking distance from 9 to 14 is 64.\nWalking distance from 9 to 15 is 64.\nWalking distance from 9 to 16 is 55.\nWalking distance from 9 to 17 is 52.\nWalking distance from 9 to 18 is 84.\nWalking distance from 9 to 19 is 35.\nWalking distance from 9 to 20 is 47.\nWalking distance from 10 to 1 is 34.\nWalking distance from 10 to 2 is 20.\nWalking distance from 10 to 3 is 55.\nWalking distance from 10 to 4 is 57.\nWalking distance from 10 to 5 is 58.\nWalking distance from 10 to 6 is 63.\nWalking distance from 10 to 7 is 37.\nWalking distance from 10 to 8 is 59.\nWalking distance from 10 to 9 is 53.\nWalking distance from 10 to 11 is 64.\nWalking distance from 10 to 12 is 67.\nWalking distance from 10 to 13 is 39.\nWalking distance from 10 to 14 is 62.\nWalking distance from 10 to 15 is 53.\nWalking distance from 10 to 16 is 59.\nWalking distance from 10 to 17 is 27.\nWalking distance from 10 to 18 is 64.\nWalking distance from 10 to 19 is 58.\nWalking distance from 10 to 20 is 51.\nWalking distance from 11 to 1 is 76.\nWalking distance from 11 to 2 is 64.\nWalking distance from 11 to 3 is 88.\nWalking distance from 11 to 4 is 75.\nWalking distance from 11 to 5 is 79.\nWalking distance from 11 to 6 is 74.\nWalking distance from 11 to 7 is 57.\nWalking distance from 11 to 8 is 54.\nWalking distance from 11 to 9 is 68.\nWalking distance from 11 to 10 is 64.\nWalking distance from 11 to 12 is 77.\nWalking distance from 11 to 13 is 74.\nWalking distance from 11 to 14 is 59.\nWalking distance from 11 to 15 is 74.\nWalking distance from 11 to 16 is 70.\nWalking distance from 11 to 17 is 67.\nWalking distance from 11 to 18 is 83.\nWalking distance from 11 to 19 is 80.\nWalking distance from 11 to 20 is 42.\nWalking distance from 12 to 1 is 53.\nWalking distance from 12 to 2 is 64.\nWalking distance from 12 to 3 is 77.\nWalking distance from 12 to 4 is 64.\nWalking distance from 12 to 5 is 69.\nWalking distance from 12 to 6 is 12.\nWalking distance from 12 to 7 is 48.\nWalking distance from 12 to 8 is 64.\nWalking distance from 12 to 9 is 63.\nWalking distance from 12 to 10 is 67.\nWalking distance from 12 to 11 is 77.\nWalking distance from 12 to 13 is 73.\nWalking distance from 12 to 14 is 84.\nWalking distance from 12 to 15 is 69.\nWalking distance from 12 to 16 is 8.\nWalking distance from 12 to 17 is 58.\nWalking distance from 12 to 18 is 93.\nWalking distance from 12 to 19 is 53.\nWalking distance from 12 to 20 is 75.\nWalking distance from 13 to 1 is 63.\nWalking distance from 13 to 2 is 49.\nWalking distance from 13 to 3 is 79.\nWalking distance from 13 to 4 is 52.\nWalking distance from 13 to 5 is 58.\nWalking distance from 13 to 6 is 69.\nWalking distance from 13 to 7 is 58.\nWalking distance from 13 to 8 is 56.\nWalking distance from 13 to 9 is 48.\nWalking distance from 13 to 10 is 39.\nWalking distance from 13 to 11 is 74.\nWalking distance from 13 to 12 is 73.\nWalking distance from 13 to 14 is 69.\nWalking distance from 13 to 15 is 54.\nWalking distance from 13 to 16 is 65.\nWalking distance from 13 to 17 is 48.\nWalking distance from 13 to 18 is 74.\nWalking distance from 13 to 19 is 49.\nWalking distance from 13 to 20 is 42.\nWalking distance from 14 to 1 is 66.\nWalking distance from 14 to 2 is 62.\nWalking distance from 14 to 3 is 79.\nWalking distance from 14 to 4 is 42.\nWalking distance from 14 to 5 is 58.\nWalking distance from 14 to 6 is 74.\nWalking distance from 14 to 7 is 45.\nWalking distance from 14 to 8 is 41.\nWalking distance from 14 to 9 is 64.\nWalking distance from 14 to 10 is 62.\nWalking distance from 14 to 11 is 59.\nWalking distance from 14 to 12 is 84.\nWalking distance from 14 to 13 is 69.\nWalking distance from 14 to 15 is 63.\nWalking distance from 14 to 16 is 76.\nWalking distance from 14 to 17 is 55.\nWalking distance from 14 to 18 is 96.\nWalking distance from 14 to 19 is 67.\nWalking distance from 14 to 20 is 27.\nWalking distance from 15 to 1 is 47.\nWalking distance from 15 to 2 is 33.\nWalking distance from 15 to 3 is 61.\nWalking distance from 15 to 4 is 50.\nWalking distance from 15 to 5 is 62.\nWalking distance from 15 to 6 is 57.\nWalking distance from 15 to 7 is 27.\nWalking distance from 15 to 8 is 50.\nWalking distance from 15 to 9 is 64.\nWalking distance from 15 to 10 is 53.\nWalking distance from 15 to 11 is 74.\nWalking distance from 15 to 12 is 69.\nWalking distance from 15 to 13 is 54.\nWalking distance from 15 to 14 is 63.\nWalking distance from 15 to 16 is 61.\nWalking distance from 15 to 17 is 35.\nWalking distance from 15 to 18 is 70.\nWalking distance from 15 to 19 is 57.\nWalking distance from 15 to 20 is 36.\nWalking distance from 16 to 1 is 45.\nWalking distance from 16 to 2 is 56.\nWalking distance from 16 to 3 is 69.\nWalking distance from 16 to 4 is 56.\nWalking distance from 16 to 5 is 61.\nWalking distance from 16 to 6 is 4.\nWalking distance from 16 to 7 is 40.\nWalking distance from 16 to 8 is 56.\nWalking distance from 16 to 9 is 55.\nWalking distance from 16 to 10 is 59.\nWalking distance from 16 to 11 is 70.\nWalking distance from 16 to 12 is 8.\nWalking distance from 16 to 13 is 65.\nWalking distance from 16 to 14 is 76.\nWalking distance from 16 to 15 is 61.\nWalking distance from 16 to 17 is 50.\nWalking distance from 16 to 18 is 85.\nWalking distance from 16 to 19 is 45.\nWalking distance from 16 to 20 is 67.\nWalking distance from 17 to 1 is 21.\nWalking distance from 17 to 2 is 7.\nWalking distance from 17 to 3 is 63.\nWalking distance from 17 to 4 is 46.\nWalking distance from 17 to 5 is 54.\nWalking distance from 17 to 6 is 46.\nWalking distance from 17 to 7 is 10.\nWalking distance from 17 to 8 is 43.\nWalking distance from 17 to 9 is 52.\nWalking distance from 17 to 10 is 27.\nWalking distance from 17 to 11 is 67.\nWalking distance from 17 to 12 is 58.\nWalking distance from 17 to 13 is 48.\nWalking distance from 17 to 14 is 55.\nWalking distance from 17 to 15 is 35.\nWalking distance from 17 to 16 is 50.\nWalking distance from 17 to 18 is 72.\nWalking distance from 17 to 19 is 31.\nWalking distance from 17 to 20 is 43.\nWalking distance from 18 to 1 is 79.\nWalking distance from 18 to 2 is 65.\nWalking distance from 18 to 3 is 63.\nWalking distance from 18 to 4 is 88.\nWalking distance from 18 to 5 is 84.\nWalking distance from 18 to 6 is 89.\nWalking distance from 18 to 7 is 65.\nWalking distance from 18 to 8 is 81.\nWalking distance from 18 to 9 is 84.\nWalking distance from 18 to 10 is 64.\nWalking distance from 18 to 11 is 83.\nWalking distance from 18 to 12 is 93.\nWalking distance from 18 to 13 is 74.\nWalking distance from 18 to 14 is 96.\nWalking distance from 18 to 15 is 70.\nWalking distance from 18 to 16 is 85.\nWalking distance from 18 to 17 is 72.\nWalking distance from 18 to 19 is 93.\nWalking distance from 18 to 20 is 85.\nWalking distance from 19 to 1 is 51.\nWalking distance from 19 to 2 is 38.\nWalking distance from 19 to 3 is 69.\nWalking distance from 19 to 4 is 72.\nWalking distance from 19 to 5 is 60.\nWalking distance from 19 to 6 is 49.\nWalking distance from 19 to 7 is 40.\nWalking distance from 19 to 8 is 26.\nWalking distance from 19 to 9 is 35.\nWalking distance from 19 to 10 is 58.\nWalking distance from 19 to 11 is 80.\nWalking distance from 19 to 12 is 53.\nWalking distance from 19 to 13 is 49.\nWalking distance from 19 to 14 is 67.\nWalking distance from 19 to 15 is 57.\nWalking distance from 19 to 16 is 45.\nWalking distance from 19 to 17 is 31.\nWalking distance from 19 to 18 is 93.\nWalking distance from 19 to 20 is 40.\nWalking distance from 20 to 1 is 39.\nWalking distance from 20 to 2 is 48.\nWalking distance from 20 to 3 is 62.\nWalking distance from 20 to 4 is 51.\nWalking distance from 20 to 5 is 37.\nWalking distance from 20 to 6 is 66.\nWalking distance from 20 to 7 is 49.\nWalking distance from 20 to 8 is 14.\nWalking distance from 20 to 9 is 47.\nWalking distance from 20 to 10 is 51.\nWalking distance from 20 to 11 is 42.\nWalking distance from 20 to 12 is 75.\nWalking distance from 20 to 13 is 42.\nWalking distance from 20 to 14 is 27.\nWalking distance from 20 to 15 is 36.\nWalking distance from 20 to 16 is 67.\nWalking distance from 20 to 17 is 43.\nWalking distance from 20 to 18 is 85.\nWalking distance from 20 to 19 is 40.\nThese distance records will be used to assign each neighborhood to an opened restroom so the total walking distance is minimized.\n\nWhen you send the final plan, please use this simple JSON layout so it's easy to check and compare:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis little sketch means: \"selected\" is the list of the sites we decide to open, and \"assignments\" lists, for each neighborhood in the same order as the input, which opened site that neighborhood will use. It's just the shape I need — a friendly form, not the actual answer yet.\n\nPlease make sure every identifier you put in there exactly matches the ones in the instance input — do not rename them or invent new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 14, 46, 65, 54, 49, 31, 25, 51, 34, 76, 53, 63, 66, 47, 45, 21, 79, 51, 39 ], [ 14, 0, 60, 53, 49, 53, 17, 39, 59, 20, 64, 64, 49, 62, 33, 56, 7, 65, 38, 48 ], [ 46, 60, 0, 46, 75, 73, 56, 71, 75, 55, 88, 77, 79, 79, 61, 69, 63, 63, 69, 62 ], [ 65, 53, 46, 0, 79, 52, 38, 54, 48, 57, 75, 64, 52, 42, 50, 56, 46, 88, 72, 51 ], [ 54, 49, 75, 79, 0, 65, 64, 51, 50, 58, 79, 69, 58, 58, 62, 61, 54, 84, 60, 37 ], [ 49, 53, 73, 52, 65, 0, 36, 52, 59, 63, 74, 12, 69, 74, 57, 4, 46, 89, 49, 66 ], [ 31, 17, 56, 38, 64, 36, 0, 52, 61, 37, 57, 48, 58, 45, 27, 40, 10, 65, 40, 49 ], [ 25, 39, 71, 54, 51, 52, 52, 0, 47, 59, 54, 64, 56, 41, 50, 56, 43, 81, 26, 14 ], [ 51, 59, 75, 48, 50, 59, 61, 47, 0, 53, 68, 63, 48, 64, 64, 55, 52, 84, 35, 47 ], [ 34, 20, 55, 57, 58, 63, 37, 59, 53, 0, 64, 67, 39, 62, 53, 59, 27, 64, 58, 51 ], [ 76, 64, 88, 75, 79, 74, 57, 54, 68, 64, 0, 77, 74, 59, 74, 70, 67, 83, 80, 42 ], [ 53, 64, 77, 64, 69, 12, 48, 64, 63, 67, 77, 0, 73, 84, 69, 8, 58, 93, 53, 75 ], [ 63, 49, 79, 52, 58, 69, 58, 56, 48, 39, 74, 73, 0, 69, 54, 65, 48, 74, 49, 42 ], [ 66, 62, 79, 42, 58, 74, 45, 41, 64, 62, 59, 84, 69, 0, 63, 76, 55, 96, 67, 27 ], [ 47, 33, 61, 50, 62, 57, 27, 50, 64, 53, 74, 69, 54, 63, 0, 61, 35, 70, 57, 36 ], [ 45, 56, 69, 56, 61, 4, 40, 56, 55, 59, 70, 8, 65, 76, 61, 0, 50, 85, 45, 67 ], [ 21, 7, 63, 46, 54, 46, 10, 43, 52, 27, 67, 58, 48, 55, 35, 50, 0, 72, 31, 43 ], [ 79, 65, 63, 88, 84, 89, 65, 81, 84, 64, 83, 93, 74, 96, 70, 85, 72, 0, 93, 85 ], [ 51, 38, 69, 72, 60, 49, 40, 26, 35, 58, 80, 53, 49, 67, 57, 45, 31, 93, 0, 40 ], [ 39, 48, 62, 51, 37, 66, 49, 14, 47, 51, 42, 75, 42, 27, 36, 67, 43, 85, 40, 0 ] ], "p": 1, "objective": 828.0 }, "solution": { "facilities": [ 16 ], "assignments": [ 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 ] }, "obj": 828.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 1, "sites": [ { "id": 1, "distances": { "1": 0, "2": 14, "3": 46, "4": 65, "5": 54, "6": 49, "7": 31, "8": 25, "9": 51, "10": 34, "11": 76, "12": 53, "13": 63, "14": 66, "15": 47, "16": 45, "17": 21, "18": 79, "19": 51, "20": 39 } }, { "id": 2, "distances": { "1": 14, "2": 0, "3": 60, "4": 53, "5": 49, "6": 53, "7": 17, "8": 39, "9": 59, "10": 20, "11": 64, "12": 64, "13": 49, "14": 62, "15": 33, "16": 56, "17": 7, "18": 65, "19": 38, "20": 48 } }, { "id": 3, "distances": { "1": 46, "2": 60, "3": 0, "4": 46, "5": 75, "6": 73, "7": 56, "8": 71, "9": 75, "10": 55, "11": 88, "12": 77, "13": 79, "14": 79, "15": 61, "16": 69, "17": 63, "18": 63, "19": 69, "20": 62 } }, { "id": 4, "distances": { "1": 65, "2": 53, "3": 46, "4": 0, "5": 79, "6": 52, "7": 38, "8": 54, "9": 48, "10": 57, "11": 75, "12": 64, "13": 52, "14": 42, "15": 50, "16": 56, "17": 46, "18": 88, "19": 72, "20": 51 } }, { "id": 5, "distances": { "1": 54, "2": 49, "3": 75, "4": 79, "5": 0, "6": 65, "7": 64, "8": 51, "9": 50, "10": 58, "11": 79, "12": 69, "13": 58, "14": 58, "15": 62, "16": 61, "17": 54, "18": 84, "19": 60, "20": 37 } }, { "id": 6, "distances": { "1": 49, "2": 53, "3": 73, "4": 52, "5": 65, "6": 0, "7": 36, "8": 52, "9": 59, "10": 63, "11": 74, "12": 12, "13": 69, "14": 74, "15": 57, "16": 4, "17": 46, "18": 89, "19": 49, "20": 66 } }, { "id": 7, "distances": { "1": 31, "2": 17, "3": 56, "4": 38, "5": 64, "6": 36, "7": 0, "8": 52, "9": 61, "10": 37, "11": 57, "12": 48, "13": 58, "14": 45, "15": 27, "16": 40, "17": 10, "18": 65, "19": 40, "20": 49 } }, { "id": 8, "distances": { "1": 25, "2": 39, "3": 71, "4": 54, "5": 51, "6": 52, "7": 52, "8": 0, "9": 47, "10": 59, "11": 54, "12": 64, "13": 56, "14": 41, "15": 50, "16": 56, "17": 43, "18": 81, "19": 26, "20": 14 } }, { "id": 9, "distances": { "1": 51, "2": 59, "3": 75, "4": 48, "5": 50, "6": 59, "7": 61, "8": 47, "9": 0, "10": 53, "11": 68, "12": 63, "13": 48, "14": 64, "15": 64, "16": 55, "17": 52, "18": 84, "19": 35, "20": 47 } }, { "id": 10, "distances": { "1": 34, "2": 20, "3": 55, "4": 57, "5": 58, "6": 63, "7": 37, "8": 59, "9": 53, "10": 0, "11": 64, "12": 67, "13": 39, "14": 62, "15": 53, "16": 59, "17": 27, "18": 64, "19": 58, "20": 51 } }, { "id": 11, "distances": { "1": 76, "2": 64, "3": 88, "4": 75, "5": 79, "6": 74, "7": 57, "8": 54, "9": 68, "10": 64, "11": 0, "12": 77, "13": 74, "14": 59, "15": 74, "16": 70, "17": 67, "18": 83, "19": 80, "20": 42 } }, { "id": 12, "distances": { "1": 53, "2": 64, "3": 77, "4": 64, "5": 69, "6": 12, "7": 48, "8": 64, "9": 63, "10": 67, "11": 77, "12": 0, "13": 73, "14": 84, "15": 69, "16": 8, "17": 58, "18": 93, "19": 53, "20": 75 } }, { "id": 13, "distances": { "1": 63, "2": 49, "3": 79, "4": 52, "5": 58, "6": 69, "7": 58, "8": 56, "9": 48, "10": 39, "11": 74, "12": 73, "13": 0, "14": 69, "15": 54, "16": 65, "17": 48, "18": 74, "19": 49, "20": 42 } }, { "id": 14, "distances": { "1": 66, "2": 62, "3": 79, "4": 42, "5": 58, "6": 74, "7": 45, "8": 41, "9": 64, "10": 62, "11": 59, "12": 84, "13": 69, "14": 0, "15": 63, "16": 76, "17": 55, "18": 96, "19": 67, "20": 27 } }, { "id": 15, "distances": { "1": 47, "2": 33, "3": 61, "4": 50, "5": 62, "6": 57, "7": 27, "8": 50, "9": 64, "10": 53, "11": 74, "12": 69, "13": 54, "14": 63, "15": 0, "16": 61, "17": 35, "18": 70, "19": 57, "20": 36 } }, { "id": 16, "distances": { "1": 45, "2": 56, "3": 69, "4": 56, "5": 61, "6": 4, "7": 40, "8": 56, "9": 55, "10": 59, "11": 70, "12": 8, "13": 65, "14": 76, "15": 61, "16": 0, "17": 50, "18": 85, "19": 45, "20": 67 } }, { "id": 17, "distances": { "1": 21, "2": 7, "3": 63, "4": 46, "5": 54, "6": 46, "7": 10, "8": 43, "9": 52, "10": 27, "11": 67, "12": 58, "13": 48, "14": 55, "15": 35, "16": 50, "17": 0, "18": 72, "19": 31, "20": 43 } }, { "id": 18, "distances": { "1": 79, "2": 65, "3": 63, "4": 88, "5": 84, "6": 89, "7": 65, "8": 81, "9": 84, "10": 64, "11": 83, "12": 93, "13": 74, "14": 96, "15": 70, "16": 85, "17": 72, "18": 0, "19": 93, "20": 85 } }, { "id": 19, "distances": { "1": 51, "2": 38, "3": 69, "4": 72, "5": 60, "6": 49, "7": 40, "8": 26, "9": 35, "10": 58, "11": 80, "12": 53, "13": 49, "14": 67, "15": 57, "16": 45, "17": 31, "18": 93, "19": 0, "20": 40 } }, { "id": 20, "distances": { "1": 39, "2": 48, "3": 62, "4": 51, "5": 37, "6": 66, "7": 49, "8": 14, "9": 47, "10": 51, "11": 42, "12": 75, "13": 42, "14": 27, "15": 36, "16": 67, "17": 43, "18": 85, "19": 40, "20": 0 } } ], "objective": 828.0 }, "solution_variant": { "selected": [ 17 ], "assignments": [ 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17 ] }, "context_index": 1, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "There’s a scheduling headache at the coffee chain: pick a certain number of sites to operate as cafés from a list of candidates, make sure every customer area is assigned to exactly one of those open spots, and prefer the arrangement that keeps the total travel for everyone smallest — that total is simply the sum of each area’s distance to whatever café serves it. The specific locations, pairwise distances, and how many cafés to open are given below.\n\n{\n \"total_candidate_sites\": 18,\n \"cafes_to_open\": 1,\n \"site_identifiers\": [\n \"A\",\n \"B\",\n \"C\",\n \"D\",\n \"E\",\n \"F\",\n \"G\",\n \"H\",\n \"I\",\n \"J\",\n \"K\",\n \"L\",\n \"M\",\n \"N\",\n \"O\",\n \"P\",\n \"Q\",\n \"R\"\n ],\n \"data\": [\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 43\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 46\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 51\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 31\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 31\n },\n {\n \"origin_area_id\": \"A\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 43\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 23\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 11\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 31\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 7\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 20\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 24\n },\n {\n \"origin_area_id\": \"B\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 16\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 43\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"C\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 43\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 35\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 54\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"D\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 23\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 35\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 12\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 35\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 24\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 17\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 16\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 10\n },\n {\n \"origin_area_id\": \"E\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 17\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 11\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 12\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 14\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 14\n },\n {\n \"origin_area_id\": \"F\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 5\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 15\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"G\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 46\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 35\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 15\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 48\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 50\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 47\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"H\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 48\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 56\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"I\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 51\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 31\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 54\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 50\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 56\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 43\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"J\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 7\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"K\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 20\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 20\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"L\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 23\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 28\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 24\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 22\n },\n {\n \"origin_area_id\": \"M\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 35\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 26\n },\n {\n \"origin_area_id\": \"N\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 17\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 47\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 43\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 41\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"O\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 31\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 25\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 39\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 40\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 16\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 14\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 36\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 30\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"P\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 19\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 31\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 24\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 10\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 14\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 21\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 33\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 29\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 22\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 26\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 18\n },\n {\n \"origin_area_id\": \"Q\",\n \"candidate_cafe_id\": \"R\",\n \"travel_distance\": 19\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"A\",\n \"travel_distance\": 32\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"B\",\n \"travel_distance\": 16\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"C\",\n \"travel_distance\": 37\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"D\",\n \"travel_distance\": 44\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"E\",\n \"travel_distance\": 17\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"F\",\n \"travel_distance\": 5\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"G\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"H\",\n \"travel_distance\": 38\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"I\",\n \"travel_distance\": 42\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"J\",\n \"travel_distance\": 45\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"K\",\n \"travel_distance\": 20\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"L\",\n \"travel_distance\": 23\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"M\",\n \"travel_distance\": 35\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"N\",\n \"travel_distance\": 27\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"O\",\n \"travel_distance\": 34\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"P\",\n \"travel_distance\": 19\n },\n {\n \"origin_area_id\": \"R\",\n \"candidate_cafe_id\": \"Q\",\n \"travel_distance\": 19\n }\n ]\n}\n\nOh, and when you send the final answer, please stick to this simple JSON layout so I can read it automatically:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis just sketches the shape I need: \"selected\" is the list of sites you decide to open, and \"assignments\" says, for each location in the original order, which open site serves it. It's just a template — not the final plan.\n\nAlso, please use the exact identifiers from the instance input — don't rename them or invent new ones. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 38, 43, 18, 29, 27, 41, 46, 37, 51, 36, 41, 45, 32, 36, 31, 31, 32 ], [ 38, 0, 37, 43, 23, 11, 25, 40, 45, 31, 7, 20, 28, 25, 39, 25, 24, 16 ], [ 43, 37, 0, 45, 29, 32, 33, 45, 40, 44, 36, 39, 29, 40, 45, 39, 21, 37 ], [ 18, 43, 45, 0, 35, 39, 36, 38, 44, 54, 38, 38, 44, 45, 44, 40, 29, 44 ], [ 29, 23, 29, 35, 0, 12, 27, 35, 28, 28, 30, 21, 24, 30, 17, 16, 10, 17 ], [ 27, 11, 32, 39, 12, 0, 29, 33, 38, 40, 18, 28, 30, 32, 29, 14, 14, 5 ], [ 41, 25, 33, 36, 27, 29, 0, 15, 44, 40, 30, 36, 37, 29, 42, 33, 21, 34 ], [ 46, 40, 45, 38, 35, 33, 15, 0, 48, 50, 34, 37, 40, 30, 47, 36, 33, 38 ], [ 37, 45, 40, 44, 28, 38, 44, 48, 0, 56, 38, 36, 41, 42, 45, 42, 33, 42 ], [ 51, 31, 44, 54, 28, 40, 40, 50, 56, 0, 38, 25, 40, 38, 43, 38, 29, 45 ], [ 36, 7, 36, 38, 30, 18, 30, 34, 38, 38, 0, 27, 21, 18, 37, 32, 29, 20 ], [ 41, 20, 39, 38, 21, 28, 36, 37, 36, 25, 27, 0, 40, 37, 38, 32, 18, 23 ], [ 45, 28, 29, 44, 24, 30, 37, 40, 41, 40, 21, 40, 0, 37, 41, 34, 22, 35 ], [ 32, 25, 40, 45, 30, 32, 29, 30, 42, 38, 18, 37, 37, 0, 29, 37, 26, 27 ], [ 36, 39, 45, 44, 17, 29, 42, 47, 45, 43, 37, 38, 41, 29, 0, 30, 27, 34 ], [ 31, 25, 39, 40, 16, 14, 33, 36, 42, 38, 32, 32, 34, 37, 30, 0, 18, 19 ], [ 31, 24, 21, 29, 10, 14, 21, 33, 33, 29, 29, 18, 22, 26, 27, 18, 0, 19 ], [ 32, 16, 37, 44, 17, 5, 34, 38, 42, 45, 20, 23, 35, 27, 34, 19, 19, 0 ] ], "p": 1, "objective": 404.0 }, "solution": { "facilities": [ 16 ], "assignments": [ 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 ] }, "obj": 404.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 1, "sites": [ { "id": "A", "distances": { "A": 0, "B": 38, "C": 43, "D": 18, "E": 29, "F": 27, "G": 41, "H": 46, "I": 37, "J": 51, "K": 36, "L": 41, "M": 45, "N": 32, "O": 36, "P": 31, "Q": 31, "R": 32 } }, { "id": "B", "distances": { "A": 38, "B": 0, "C": 37, "D": 43, "E": 23, "F": 11, "G": 25, "H": 40, "I": 45, "J": 31, "K": 7, "L": 20, "M": 28, "N": 25, "O": 39, "P": 25, "Q": 24, "R": 16 } }, { "id": "C", "distances": { "A": 43, "B": 37, "C": 0, "D": 45, "E": 29, "F": 32, "G": 33, "H": 45, "I": 40, "J": 44, "K": 36, "L": 39, "M": 29, "N": 40, "O": 45, "P": 39, "Q": 21, "R": 37 } }, { "id": "D", "distances": { "A": 18, "B": 43, "C": 45, "D": 0, "E": 35, "F": 39, "G": 36, "H": 38, "I": 44, "J": 54, "K": 38, "L": 38, "M": 44, "N": 45, "O": 44, "P": 40, "Q": 29, "R": 44 } }, { "id": "E", "distances": { "A": 29, "B": 23, "C": 29, "D": 35, "E": 0, "F": 12, "G": 27, "H": 35, "I": 28, "J": 28, "K": 30, "L": 21, "M": 24, "N": 30, "O": 17, "P": 16, "Q": 10, "R": 17 } }, { "id": "F", "distances": { "A": 27, "B": 11, "C": 32, "D": 39, "E": 12, "F": 0, "G": 29, "H": 33, "I": 38, "J": 40, "K": 18, "L": 28, "M": 30, "N": 32, "O": 29, "P": 14, "Q": 14, "R": 5 } }, { "id": "G", "distances": { "A": 41, "B": 25, "C": 33, "D": 36, "E": 27, "F": 29, "G": 0, "H": 15, "I": 44, "J": 40, "K": 30, "L": 36, "M": 37, "N": 29, "O": 42, "P": 33, "Q": 21, "R": 34 } }, { "id": "H", "distances": { "A": 46, "B": 40, "C": 45, "D": 38, "E": 35, "F": 33, "G": 15, "H": 0, "I": 48, "J": 50, "K": 34, "L": 37, "M": 40, "N": 30, "O": 47, "P": 36, "Q": 33, "R": 38 } }, { "id": "I", "distances": { "A": 37, "B": 45, "C": 40, "D": 44, "E": 28, "F": 38, "G": 44, "H": 48, "I": 0, "J": 56, "K": 38, "L": 36, "M": 41, "N": 42, "O": 45, "P": 42, "Q": 33, "R": 42 } }, { "id": "J", "distances": { "A": 51, "B": 31, "C": 44, "D": 54, "E": 28, "F": 40, "G": 40, "H": 50, "I": 56, "J": 0, "K": 38, "L": 25, "M": 40, "N": 38, "O": 43, "P": 38, "Q": 29, "R": 45 } }, { "id": "K", "distances": { "A": 36, "B": 7, "C": 36, "D": 38, "E": 30, "F": 18, "G": 30, "H": 34, "I": 38, "J": 38, "K": 0, "L": 27, "M": 21, "N": 18, "O": 37, "P": 32, "Q": 29, "R": 20 } }, { "id": "L", "distances": { "A": 41, "B": 20, "C": 39, "D": 38, "E": 21, "F": 28, "G": 36, "H": 37, "I": 36, "J": 25, "K": 27, "L": 0, "M": 40, "N": 37, "O": 38, "P": 32, "Q": 18, "R": 23 } }, { "id": "M", "distances": { "A": 45, "B": 28, "C": 29, "D": 44, "E": 24, "F": 30, "G": 37, "H": 40, "I": 41, "J": 40, "K": 21, "L": 40, "M": 0, "N": 37, "O": 41, "P": 34, "Q": 22, "R": 35 } }, { "id": "N", "distances": { "A": 32, "B": 25, "C": 40, "D": 45, "E": 30, "F": 32, "G": 29, "H": 30, "I": 42, "J": 38, "K": 18, "L": 37, "M": 37, "N": 0, "O": 29, "P": 37, "Q": 26, "R": 27 } }, { "id": "O", "distances": { "A": 36, "B": 39, "C": 45, "D": 44, "E": 17, "F": 29, "G": 42, "H": 47, "I": 45, "J": 43, "K": 37, "L": 38, "M": 41, "N": 29, "O": 0, "P": 30, "Q": 27, "R": 34 } }, { "id": "P", "distances": { "A": 31, "B": 25, "C": 39, "D": 40, "E": 16, "F": 14, "G": 33, "H": 36, "I": 42, "J": 38, "K": 32, "L": 32, "M": 34, "N": 37, "O": 30, "P": 0, "Q": 18, "R": 19 } }, { "id": "Q", "distances": { "A": 31, "B": 24, "C": 21, "D": 29, "E": 10, "F": 14, "G": 21, "H": 33, "I": 33, "J": 29, "K": 29, "L": 18, "M": 22, "N": 26, "O": 27, "P": 18, "Q": 0, "R": 19 } }, { "id": "R", "distances": { "A": 32, "B": 16, "C": 37, "D": 44, "E": 17, "F": 5, "G": 34, "H": 38, "I": 42, "J": 45, "K": 20, "L": 23, "M": 35, "N": 27, "O": 34, "P": 19, "Q": 19, "R": 0 } } ], "objective": 404.0 }, "solution_variant": { "selected": [ "Q" ], "assignments": [ "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q", "Q" ] }, "context_index": 2, "input_format": "json", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Recently the housing office talked about installing a set number of quiet pods and assigning every dorm block to one of them so students walk as little as possible. A plan is judged by the total distance students would travel — you get that by adding the distance from each dorm block to its assigned pod — and the aim is to make that sum as small as possible. No dorm block can be left out or split across multiple pods. The full data and distances are shown below.\n\n# total_candidate_locations=15\n# pods_to_install=3\n# location_ids=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\norigin_location_id,destination_location_id,walk_distance\n0,1,12\n0,2,55\n0,3,78\n0,4,67\n0,5,51\n0,6,44\n0,7,27\n0,8,53\n0,9,36\n0,10,66\n0,11,48\n0,12,35\n0,13,111\n0,14,59\n1,0,12\n1,2,66\n1,3,90\n1,4,79\n1,5,63\n1,6,56\n1,7,39\n1,8,58\n1,9,48\n1,10,65\n1,11,60\n1,12,47\n1,13,121\n1,14,71\n2,0,55\n2,1,66\n2,3,113\n2,4,95\n2,5,85\n2,6,67\n2,7,60\n2,8,44\n2,9,61\n2,10,63\n2,11,69\n2,12,74\n2,13,118\n2,14,87\n3,0,78\n3,1,90\n3,2,113\n3,4,125\n3,5,89\n3,6,107\n3,7,105\n3,8,107\n3,9,94\n3,10,114\n3,11,88\n3,12,83\n3,13,150\n3,14,77\n4,0,67\n4,1,79\n4,2,95\n4,3,125\n4,5,66\n4,6,79\n4,7,94\n4,8,96\n4,9,79\n4,10,96\n4,11,113\n4,12,87\n4,13,128\n4,14,101\n5,0,51\n5,1,63\n5,2,85\n5,3,89\n5,4,66\n5,6,68\n5,7,78\n5,8,70\n5,9,61\n5,10,30\n5,11,61\n5,12,48\n5,13,93\n5,14,64\n6,0,44\n6,1,56\n6,2,67\n6,3,107\n6,4,79\n6,5,68\n6,7,71\n6,8,67\n6,9,64\n6,10,98\n6,11,62\n6,12,77\n6,13,129\n6,14,68\n7,0,27\n7,1,39\n7,2,60\n7,3,105\n7,4,94\n7,5,78\n7,6,71\n7,8,52\n7,9,63\n7,10,84\n7,11,75\n7,12,62\n7,13,128\n7,14,61\n8,0,53\n8,1,58\n8,2,44\n8,3,107\n8,4,96\n8,5,70\n8,6,67\n8,7,52\n8,9,17\n8,10,74\n8,11,81\n8,12,47\n8,13,103\n8,14,75\n9,0,36\n9,1,48\n9,2,61\n9,3,94\n9,4,79\n9,5,61\n9,6,64\n9,7,63\n9,8,17\n9,10,89\n9,11,80\n9,12,64\n9,13,94\n9,14,66\n10,0,66\n10,1,65\n10,2,63\n10,3,114\n10,4,96\n10,5,30\n10,6,98\n10,7,84\n10,8,74\n10,9,89\n10,11,78\n10,12,65\n10,13,123\n10,14,94\n11,0,48\n11,1,60\n11,2,69\n11,3,88\n11,4,113\n11,5,61\n11,6,62\n11,7,75\n11,8,81\n11,9,80\n11,10,78\n11,12,34\n11,13,112\n11,14,65\n12,0,35\n12,1,47\n12,2,74\n12,3,83\n12,4,87\n12,5,48\n12,6,77\n12,7,62\n12,8,47\n12,9,64\n12,10,65\n12,11,34\n12,13,140\n12,14,65\n13,0,111\n13,1,121\n13,2,118\n13,3,150\n13,4,128\n13,5,93\n13,6,129\n13,7,128\n13,8,103\n13,9,94\n13,10,123\n13,11,112\n13,12,140\n13,14,98\n14,0,59\n14,1,71\n14,2,87\n14,3,77\n14,4,101\n14,5,64\n14,6,68\n14,7,61\n14,8,75\n14,9,66\n14,10,94\n14,11,65\n14,12,65\n14,13,98\n\nIf you want to hand me a plan, just stick to this simple JSON shape — nothing fancy, just a tidy way to show which pods are opened and which pod each dorm is assigned to.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty straightforward: \"selected\" lists the pod locations you choose to open, and \"assignments\" lists, for each dorm block (in the same order as the input), which opened pod that dorm would use. Think of it like filling out a short form—this block is just a sketch of the expected shape, not the actual final plan.\n\nPlease remember: use the exact identifiers from the instance input — do not rename or invent labels. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 12, 55, 78, 67, 51, 44, 27, 53, 36, 66, 48, 35, 111, 59 ], [ 12, 0, 66, 90, 79, 63, 56, 39, 58, 48, 65, 60, 47, 121, 71 ], [ 55, 66, 0, 113, 95, 85, 67, 60, 44, 61, 63, 69, 74, 118, 87 ], [ 78, 90, 113, 0, 125, 89, 107, 105, 107, 94, 114, 88, 83, 150, 77 ], [ 67, 79, 95, 125, 0, 66, 79, 94, 96, 79, 96, 113, 87, 128, 101 ], [ 51, 63, 85, 89, 66, 0, 68, 78, 70, 61, 30, 61, 48, 93, 64 ], [ 44, 56, 67, 107, 79, 68, 0, 71, 67, 64, 98, 62, 77, 129, 68 ], [ 27, 39, 60, 105, 94, 78, 71, 0, 52, 63, 84, 75, 62, 128, 61 ], [ 53, 58, 44, 107, 96, 70, 67, 52, 0, 17, 74, 81, 47, 103, 75 ], [ 36, 48, 61, 94, 79, 61, 64, 63, 17, 0, 89, 80, 64, 94, 66 ], [ 66, 65, 63, 114, 96, 30, 98, 84, 74, 89, 0, 78, 65, 123, 94 ], [ 48, 60, 69, 88, 113, 61, 62, 75, 81, 80, 78, 0, 34, 112, 65 ], [ 35, 47, 74, 83, 87, 48, 77, 62, 47, 64, 65, 34, 0, 140, 65 ], [ 111, 121, 118, 150, 128, 93, 129, 128, 103, 94, 123, 112, 140, 0, 98 ], [ 59, 71, 87, 77, 101, 64, 68, 61, 75, 66, 94, 65, 65, 98, 0 ] ], "p": 3, "objective": 543.0 }, "solution": { "facilities": [ 0, 5, 13 ], "assignments": [ 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 5, 0, 0, 13, 0 ] }, "obj": 543.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 15, "num_open": 3, "sites": [ { "id": 0, "distances": { "0": 0, "1": 12, "2": 55, "3": 78, "4": 67, "5": 51, "6": 44, "7": 27, "8": 53, "9": 36, "10": 66, "11": 48, "12": 35, "13": 111, "14": 59 } }, { "id": 1, "distances": { "0": 12, "1": 0, "2": 66, "3": 90, "4": 79, "5": 63, "6": 56, "7": 39, "8": 58, "9": 48, "10": 65, "11": 60, "12": 47, "13": 121, "14": 71 } }, { "id": 2, "distances": { "0": 55, "1": 66, "2": 0, "3": 113, "4": 95, "5": 85, "6": 67, "7": 60, "8": 44, "9": 61, "10": 63, "11": 69, "12": 74, "13": 118, "14": 87 } }, { "id": 3, "distances": { "0": 78, "1": 90, "2": 113, "3": 0, "4": 125, "5": 89, "6": 107, "7": 105, "8": 107, "9": 94, "10": 114, "11": 88, "12": 83, "13": 150, "14": 77 } }, { "id": 4, "distances": { "0": 67, "1": 79, "2": 95, "3": 125, "4": 0, "5": 66, "6": 79, "7": 94, "8": 96, "9": 79, "10": 96, "11": 113, "12": 87, "13": 128, "14": 101 } }, { "id": 5, "distances": { "0": 51, "1": 63, "2": 85, "3": 89, "4": 66, "5": 0, "6": 68, "7": 78, "8": 70, "9": 61, "10": 30, "11": 61, "12": 48, "13": 93, "14": 64 } }, { "id": 6, "distances": { "0": 44, "1": 56, "2": 67, "3": 107, "4": 79, "5": 68, "6": 0, "7": 71, "8": 67, "9": 64, "10": 98, "11": 62, "12": 77, "13": 129, "14": 68 } }, { "id": 7, "distances": { "0": 27, "1": 39, "2": 60, "3": 105, "4": 94, "5": 78, "6": 71, "7": 0, "8": 52, "9": 63, "10": 84, "11": 75, "12": 62, "13": 128, "14": 61 } }, { "id": 8, "distances": { "0": 53, "1": 58, "2": 44, "3": 107, "4": 96, "5": 70, "6": 67, "7": 52, "8": 0, "9": 17, "10": 74, "11": 81, "12": 47, "13": 103, "14": 75 } }, { "id": 9, "distances": { "0": 36, "1": 48, "2": 61, "3": 94, "4": 79, "5": 61, "6": 64, "7": 63, "8": 17, "9": 0, "10": 89, "11": 80, "12": 64, "13": 94, "14": 66 } }, { "id": 10, "distances": { "0": 66, "1": 65, "2": 63, "3": 114, "4": 96, "5": 30, "6": 98, "7": 84, "8": 74, "9": 89, "10": 0, "11": 78, "12": 65, "13": 123, "14": 94 } }, { "id": 11, "distances": { "0": 48, "1": 60, "2": 69, "3": 88, "4": 113, "5": 61, "6": 62, "7": 75, "8": 81, "9": 80, "10": 78, "11": 0, "12": 34, "13": 112, "14": 65 } }, { "id": 12, "distances": { "0": 35, "1": 47, "2": 74, "3": 83, "4": 87, "5": 48, "6": 77, "7": 62, "8": 47, "9": 64, "10": 65, "11": 34, "12": 0, "13": 140, "14": 65 } }, { "id": 13, "distances": { "0": 111, "1": 121, "2": 118, "3": 150, "4": 128, "5": 93, "6": 129, "7": 128, "8": 103, "9": 94, "10": 123, "11": 112, "12": 140, "13": 0, "14": 98 } }, { "id": 14, "distances": { "0": 59, "1": 71, "2": 87, "3": 77, "4": 101, "5": 64, "6": 68, "7": 61, "8": 75, "9": 66, "10": 94, "11": 65, "12": 65, "13": 98, "14": 0 } } ], "objective": 543.0 }, "solution_variant": { "selected": [ 0, 5, 13 ], "assignments": [ 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 5, 0, 0, 13, 0 ] }, "context_index": 3, "input_format": "csv", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "There's a logistics puzzle at work: from a bunch of possible locker locations pick a fixed number to actually open, and then attach every delivery address to one of those open lockers. One solution beats another if, when you sum up how far all couriers must travel from addresses to their assigned lockers, that grand total is lower. Every address must be assigned to exactly one open locker — no address left out and no address sent to two lockers. The specific candidate sites and distances are shown below.\n\n{\n \"total_locations\": 17,\n \"lockers_to_open\": 1,\n \"location_ids\": [\n 0,\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16\n ],\n \"data\": [\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 1,\n \"travel_distance\": 82\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 2,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 3,\n \"travel_distance\": 73\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 4,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 5,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 6,\n \"travel_distance\": 16\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 7,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 8,\n \"travel_distance\": 64\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 9,\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 10,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 11,\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 12,\n \"travel_distance\": 79\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 13,\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 14,\n \"travel_distance\": 101\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 15,\n \"travel_distance\": 81\n },\n {\n \"origin_location_id\": 0,\n \"destination_location_id\": 16,\n \"travel_distance\": 64\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 0,\n \"travel_distance\": 82\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 2,\n \"travel_distance\": 43\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 3,\n \"travel_distance\": 69\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 4,\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 5,\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 6,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 7,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 8,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 9,\n \"travel_distance\": 47\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 10,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 11,\n \"travel_distance\": 62\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 12,\n \"travel_distance\": 93\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 13,\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 14,\n \"travel_distance\": 92\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 15,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 1,\n \"destination_location_id\": 16,\n \"travel_distance\": 68\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 0,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 1,\n \"travel_distance\": 43\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 3,\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 4,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 5,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 6,\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 7,\n \"travel_distance\": 50\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 8,\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 9,\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 10,\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 11,\n \"travel_distance\": 47\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 12,\n \"travel_distance\": 76\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 13,\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 14,\n \"travel_distance\": 58\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 15,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 2,\n \"destination_location_id\": 16,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 0,\n \"travel_distance\": 73\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 1,\n \"travel_distance\": 69\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 2,\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 4,\n \"travel_distance\": 75\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 5,\n \"travel_distance\": 58\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 6,\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 7,\n \"travel_distance\": 62\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 8,\n \"travel_distance\": 67\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 9,\n \"travel_distance\": 38\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 10,\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 11,\n \"travel_distance\": 53\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 12,\n \"travel_distance\": 85\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 13,\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 14,\n \"travel_distance\": 94\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 15,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 3,\n \"destination_location_id\": 16,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 0,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 1,\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 2,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 3,\n \"travel_distance\": 75\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 5,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 6,\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 7,\n \"travel_distance\": 70\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 8,\n \"travel_distance\": 51\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 9,\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 10,\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 11,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 12,\n \"travel_distance\": 85\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 13,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 14,\n \"travel_distance\": 76\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 15,\n \"travel_distance\": 73\n },\n {\n \"origin_location_id\": 4,\n \"destination_location_id\": 16,\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 0,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 1,\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 2,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 3,\n \"travel_distance\": 58\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 4,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 6,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 7,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 8,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 9,\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 10,\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 11,\n \"travel_distance\": 51\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 12,\n \"travel_distance\": 72\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 13,\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 14,\n \"travel_distance\": 88\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 15,\n \"travel_distance\": 69\n },\n {\n \"origin_location_id\": 5,\n \"destination_location_id\": 16,\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 0,\n \"travel_distance\": 16\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 1,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 2,\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 3,\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 4,\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 5,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 7,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 8,\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 9,\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 10,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 11,\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 12,\n \"travel_distance\": 75\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 13,\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 14,\n \"travel_distance\": 93\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 15,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 6,\n \"destination_location_id\": 16,\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 0,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 1,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 2,\n \"travel_distance\": 50\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 3,\n \"travel_distance\": 62\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 4,\n \"travel_distance\": 70\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 5,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 6,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 8,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 9,\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 10,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 11,\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 12,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 13,\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 14,\n \"travel_distance\": 78\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 15,\n \"travel_distance\": 23\n },\n {\n \"origin_location_id\": 7,\n \"destination_location_id\": 16,\n \"travel_distance\": 68\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 0,\n \"travel_distance\": 64\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 1,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 2,\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 3,\n \"travel_distance\": 67\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 4,\n \"travel_distance\": 51\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 5,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 6,\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 7,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 9,\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 10,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 11,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 12,\n \"travel_distance\": 83\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 13,\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 14,\n \"travel_distance\": 80\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 15,\n \"travel_distance\": 69\n },\n {\n \"origin_location_id\": 8,\n \"destination_location_id\": 16,\n \"travel_distance\": 58\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 0,\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 1,\n \"travel_distance\": 47\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 2,\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 3,\n \"travel_distance\": 38\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 4,\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 5,\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 6,\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 7,\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 8,\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 10,\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 11,\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 12,\n \"travel_distance\": 67\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 13,\n \"travel_distance\": 7\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 14,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 15,\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": 9,\n \"destination_location_id\": 16,\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 0,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 1,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 2,\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 3,\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 4,\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 5,\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 6,\n \"travel_distance\": 57\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 7,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 8,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 9,\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 11,\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 12,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 13,\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 14,\n \"travel_distance\": 89\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 15,\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": 10,\n \"destination_location_id\": 16,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 0,\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 1,\n \"travel_distance\": 62\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 2,\n \"travel_distance\": 47\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 3,\n \"travel_distance\": 53\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 4,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 5,\n \"travel_distance\": 51\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 6,\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 7,\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 8,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 9,\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 10,\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 12,\n \"travel_distance\": 64\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 13,\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 14,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 15,\n \"travel_distance\": 63\n },\n {\n \"origin_location_id\": 11,\n \"destination_location_id\": 16,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 0,\n \"travel_distance\": 79\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 1,\n \"travel_distance\": 93\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 2,\n \"travel_distance\": 76\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 3,\n \"travel_distance\": 85\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 4,\n \"travel_distance\": 85\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 5,\n \"travel_distance\": 72\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 6,\n \"travel_distance\": 75\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 7,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 8,\n \"travel_distance\": 83\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 9,\n \"travel_distance\": 67\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 10,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 11,\n \"travel_distance\": 64\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 13,\n \"travel_distance\": 66\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 14,\n \"travel_distance\": 114\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 15,\n \"travel_distance\": 73\n },\n {\n \"origin_location_id\": 12,\n \"destination_location_id\": 16,\n \"travel_distance\": 85\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 0,\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 1,\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 2,\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 3,\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 4,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 5,\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 6,\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 7,\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 8,\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 9,\n \"travel_distance\": 7\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 10,\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 11,\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 12,\n \"travel_distance\": 66\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 14,\n \"travel_distance\": 70\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 15,\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": 13,\n \"destination_location_id\": 16,\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 0,\n \"travel_distance\": 101\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 1,\n \"travel_distance\": 92\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 2,\n \"travel_distance\": 58\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 3,\n \"travel_distance\": 94\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 4,\n \"travel_distance\": 76\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 5,\n \"travel_distance\": 88\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 6,\n \"travel_distance\": 93\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 7,\n \"travel_distance\": 78\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 8,\n \"travel_distance\": 80\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 9,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 10,\n \"travel_distance\": 89\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 11,\n \"travel_distance\": 77\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 12,\n \"travel_distance\": 114\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 13,\n \"travel_distance\": 70\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 15,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 14,\n \"destination_location_id\": 16,\n \"travel_distance\": 68\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 0,\n \"travel_distance\": 81\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 1,\n \"travel_distance\": 55\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 2,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 3,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 4,\n \"travel_distance\": 73\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 5,\n \"travel_distance\": 69\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 6,\n \"travel_distance\": 65\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 7,\n \"travel_distance\": 23\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 8,\n \"travel_distance\": 69\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 9,\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 10,\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 11,\n \"travel_distance\": 63\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 12,\n \"travel_distance\": 73\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 13,\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 14,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 15,\n \"destination_location_id\": 16,\n \"travel_distance\": 61\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 0,\n \"travel_distance\": 64\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 1,\n \"travel_distance\": 68\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 2,\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 3,\n \"travel_distance\": 71\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 4,\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 5,\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 6,\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 7,\n \"travel_distance\": 68\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 8,\n \"travel_distance\": 58\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 9,\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 10,\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 11,\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 12,\n \"travel_distance\": 85\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 13,\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 14,\n \"travel_distance\": 68\n },\n {\n \"origin_location_id\": 16,\n \"destination_location_id\": 15,\n \"travel_distance\": 61\n }\n ]\n}\n\nJust so we're on the same page, please reply using a little JSON sketch that shows which sites you open and, for every address, which open site it gets attached to. Something like this:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of sites you decide to open (use the same identifiers from the instance). \"assignments\" is parallel to the address list in the instance: for each address, put the identifier of the open site it's assigned to. This is just the shape I want — not the real answer yet.\n\nAlso please remember: use the exact identifiers as they appear in the input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 82, 56, 73, 61, 59, 16, 65, 64, 35, 61, 40, 79, 42, 101, 81, 64 ], [ 82, 0, 43, 69, 44, 60, 71, 61, 55, 47, 57, 62, 93, 46, 92, 55, 68 ], [ 56, 43, 0, 36, 55, 52, 40, 50, 44, 32, 42, 47, 76, 31, 58, 65, 56 ], [ 73, 69, 36, 0, 75, 58, 60, 62, 67, 38, 48, 53, 85, 37, 94, 71, 71 ], [ 61, 44, 55, 75, 0, 65, 45, 70, 51, 45, 27, 52, 85, 52, 76, 73, 34 ], [ 59, 60, 52, 58, 65, 0, 59, 57, 57, 28, 46, 51, 72, 27, 88, 69, 39 ], [ 16, 71, 40, 60, 45, 59, 0, 57, 60, 31, 57, 36, 75, 33, 93, 65, 48 ], [ 65, 61, 50, 62, 70, 57, 57, 0, 59, 30, 56, 49, 77, 34, 78, 23, 68 ], [ 64, 55, 44, 67, 51, 57, 60, 59, 0, 29, 55, 56, 83, 36, 80, 69, 58 ], [ 35, 47, 32, 38, 45, 28, 31, 30, 29, 0, 26, 31, 67, 7, 77, 49, 41 ], [ 61, 57, 42, 48, 27, 46, 57, 56, 55, 26, 0, 41, 77, 25, 89, 49, 59 ], [ 40, 62, 47, 53, 52, 51, 36, 49, 56, 31, 41, 0, 64, 30, 77, 63, 52 ], [ 79, 93, 76, 85, 85, 72, 75, 77, 83, 67, 77, 64, 0, 66, 114, 73, 85 ], [ 42, 46, 31, 37, 52, 27, 33, 34, 36, 7, 25, 30, 66, 0, 70, 48, 40 ], [ 101, 92, 58, 94, 76, 88, 93, 78, 80, 77, 89, 77, 114, 70, 0, 71, 68 ], [ 81, 55, 65, 71, 73, 69, 65, 23, 69, 49, 49, 63, 73, 48, 71, 0, 61 ], [ 64, 68, 56, 71, 34, 39, 48, 68, 58, 41, 59, 52, 85, 40, 68, 61, 0 ] ], "p": 1, "objective": 613.0 }, "solution": { "facilities": [ 9 ], "assignments": [ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 ] }, "obj": 613.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 1, "sites": [ { "id": 0, "distances": { "0": 0, "1": 82, "2": 56, "3": 73, "4": 61, "5": 59, "6": 16, "7": 65, "8": 64, "9": 35, "10": 61, "11": 40, "12": 79, "13": 42, "14": 101, "15": 81, "16": 64 } }, { "id": 1, "distances": { "0": 82, "1": 0, "2": 43, "3": 69, "4": 44, "5": 60, "6": 71, "7": 61, "8": 55, "9": 47, "10": 57, "11": 62, "12": 93, "13": 46, "14": 92, "15": 55, "16": 68 } }, { "id": 2, "distances": { "0": 56, "1": 43, "2": 0, "3": 36, "4": 55, "5": 52, "6": 40, "7": 50, "8": 44, "9": 32, "10": 42, "11": 47, "12": 76, "13": 31, "14": 58, "15": 65, "16": 56 } }, { "id": 3, "distances": { "0": 73, "1": 69, "2": 36, "3": 0, "4": 75, "5": 58, "6": 60, "7": 62, "8": 67, "9": 38, "10": 48, "11": 53, "12": 85, "13": 37, "14": 94, "15": 71, "16": 71 } }, { "id": 4, "distances": { "0": 61, "1": 44, "2": 55, "3": 75, "4": 0, "5": 65, "6": 45, "7": 70, "8": 51, "9": 45, "10": 27, "11": 52, "12": 85, "13": 52, "14": 76, "15": 73, "16": 34 } }, { "id": 5, "distances": { "0": 59, "1": 60, "2": 52, "3": 58, "4": 65, "5": 0, "6": 59, "7": 57, "8": 57, "9": 28, "10": 46, "11": 51, "12": 72, "13": 27, "14": 88, "15": 69, "16": 39 } }, { "id": 6, "distances": { "0": 16, "1": 71, "2": 40, "3": 60, "4": 45, "5": 59, "6": 0, "7": 57, "8": 60, "9": 31, "10": 57, "11": 36, "12": 75, "13": 33, "14": 93, "15": 65, "16": 48 } }, { "id": 7, "distances": { "0": 65, "1": 61, "2": 50, "3": 62, "4": 70, "5": 57, "6": 57, "7": 0, "8": 59, "9": 30, "10": 56, "11": 49, "12": 77, "13": 34, "14": 78, "15": 23, "16": 68 } }, { "id": 8, "distances": { "0": 64, "1": 55, "2": 44, "3": 67, "4": 51, "5": 57, "6": 60, "7": 59, "8": 0, "9": 29, "10": 55, "11": 56, "12": 83, "13": 36, "14": 80, "15": 69, "16": 58 } }, { "id": 9, "distances": { "0": 35, "1": 47, "2": 32, "3": 38, "4": 45, "5": 28, "6": 31, "7": 30, "8": 29, "9": 0, "10": 26, "11": 31, "12": 67, "13": 7, "14": 77, "15": 49, "16": 41 } }, { "id": 10, "distances": { "0": 61, "1": 57, "2": 42, "3": 48, "4": 27, "5": 46, "6": 57, "7": 56, "8": 55, "9": 26, "10": 0, "11": 41, "12": 77, "13": 25, "14": 89, "15": 49, "16": 59 } }, { "id": 11, "distances": { "0": 40, "1": 62, "2": 47, "3": 53, "4": 52, "5": 51, "6": 36, "7": 49, "8": 56, "9": 31, "10": 41, "11": 0, "12": 64, "13": 30, "14": 77, "15": 63, "16": 52 } }, { "id": 12, "distances": { "0": 79, "1": 93, "2": 76, "3": 85, "4": 85, "5": 72, "6": 75, "7": 77, "8": 83, "9": 67, "10": 77, "11": 64, "12": 0, "13": 66, "14": 114, "15": 73, "16": 85 } }, { "id": 13, "distances": { "0": 42, "1": 46, "2": 31, "3": 37, "4": 52, "5": 27, "6": 33, "7": 34, "8": 36, "9": 7, "10": 25, "11": 30, "12": 66, "13": 0, "14": 70, "15": 48, "16": 40 } }, { "id": 14, "distances": { "0": 101, "1": 92, "2": 58, "3": 94, "4": 76, "5": 88, "6": 93, "7": 78, "8": 80, "9": 77, "10": 89, "11": 77, "12": 114, "13": 70, "14": 0, "15": 71, "16": 68 } }, { "id": 15, "distances": { "0": 81, "1": 55, "2": 65, "3": 71, "4": 73, "5": 69, "6": 65, "7": 23, "8": 69, "9": 49, "10": 49, "11": 63, "12": 73, "13": 48, "14": 71, "15": 0, "16": 61 } }, { "id": 16, "distances": { "0": 64, "1": 68, "2": 56, "3": 71, "4": 34, "5": 39, "6": 48, "7": 68, "8": 58, "9": 41, "10": 59, "11": 52, "12": 85, "13": 40, "14": 68, "15": 61, "16": 0 } } ], "objective": 613.0 }, "solution_variant": { "selected": [ 9 ], "assignments": [ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 ] }, "context_index": 4, "input_format": "json", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Around here the food bank coordinator must decide which fixed number of proposed sites will become distribution hubs. Every client area gets assigned to exactly one of the opened hubs — nothing can be split or skipped — and choices are judged by total travel distance: sum the distances from each area to its assigned hub, and the smaller that total, the better the setup. The concrete list of potential sites and their distances appears below.\n\nThere are 20 proposed sites; the coordinator must open exactly 2 of them. Site identifiers in order: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.\nDistance from 0 to 1: 47.\nDistance from 0 to 2: 51.\nDistance from 0 to 3: 115.\nDistance from 0 to 4: 140.\nDistance from 0 to 5: 117.\nDistance from 0 to 6: 86.\nDistance from 0 to 7: 153.\nDistance from 0 to 8: 182.\nDistance from 0 to 9: 206.\nDistance from 0 to 10: 159.\nDistance from 0 to 11: 114.\nDistance from 0 to 12: 155.\nDistance from 0 to 13: 106.\nDistance from 0 to 14: 154.\nDistance from 0 to 15: 98.\nDistance from 0 to 16: 211.\nDistance from 0 to 17: 140.\nDistance from 0 to 18: 116.\nDistance from 0 to 19: 155.\nDistance from 1 to 0: 47.\nDistance from 1 to 2: 4.\nDistance from 1 to 3: 162.\nDistance from 1 to 4: 187.\nDistance from 1 to 5: 163.\nDistance from 1 to 6: 133.\nDistance from 1 to 7: 135.\nDistance from 1 to 8: 151.\nDistance from 1 to 9: 221.\nDistance from 1 to 10: 144.\nDistance from 1 to 11: 67.\nDistance from 1 to 12: 132.\nDistance from 1 to 13: 83.\nDistance from 1 to 14: 107.\nDistance from 1 to 15: 51.\nDistance from 1 to 16: 188.\nDistance from 1 to 17: 163.\nDistance from 1 to 18: 163.\nDistance from 1 to 19: 202.\nDistance from 2 to 0: 51.\nDistance from 2 to 1: 4.\nDistance from 2 to 3: 164.\nDistance from 2 to 4: 189.\nDistance from 2 to 5: 159.\nDistance from 2 to 6: 135.\nDistance from 2 to 7: 131.\nDistance from 2 to 8: 147.\nDistance from 2 to 9: 217.\nDistance from 2 to 10: 140.\nDistance from 2 to 11: 63.\nDistance from 2 to 12: 128.\nDistance from 2 to 13: 79.\nDistance from 2 to 14: 103.\nDistance from 2 to 15: 47.\nDistance from 2 to 16: 184.\nDistance from 2 to 17: 167.\nDistance from 2 to 18: 167.\nDistance from 2 to 19: 206.\nDistance from 3 to 0: 115.\nDistance from 3 to 1: 162.\nDistance from 3 to 2: 164.\nDistance from 3 to 4: 25.\nDistance from 3 to 5: 117.\nDistance from 3 to 6: 57.\nDistance from 3 to 7: 176.\nDistance from 3 to 8: 160.\nDistance from 3 to 9: 177.\nDistance from 3 to 10: 191.\nDistance from 3 to 11: 159.\nDistance from 3 to 12: 134.\nDistance from 3 to 13: 85.\nDistance from 3 to 14: 192.\nDistance from 3 to 15: 136.\nDistance from 3 to 16: 190.\nDistance from 3 to 17: 111.\nDistance from 3 to 18: 199.\nDistance from 3 to 19: 194.\nDistance from 4 to 0: 140.\nDistance from 4 to 1: 187.\nDistance from 4 to 2: 189.\nDistance from 4 to 3: 25.\nDistance from 4 to 5: 92.\nDistance from 4 to 6: 82.\nDistance from 4 to 7: 201.\nDistance from 4 to 8: 185.\nDistance from 4 to 9: 202.\nDistance from 4 to 10: 216.\nDistance from 4 to 11: 184.\nDistance from 4 to 12: 159.\nDistance from 4 to 13: 110.\nDistance from 4 to 14: 217.\nDistance from 4 to 15: 161.\nDistance from 4 to 16: 215.\nDistance from 4 to 17: 136.\nDistance from 4 to 18: 224.\nDistance from 4 to 19: 219.\nDistance from 5 to 0: 117.\nDistance from 5 to 1: 163.\nDistance from 5 to 2: 159.\nDistance from 5 to 3: 117.\nDistance from 5 to 4: 92.\nDistance from 5 to 6: 142.\nDistance from 5 to 7: 135.\nDistance from 5 to 8: 177.\nDistance from 5 to 9: 219.\nDistance from 5 to 10: 205.\nDistance from 5 to 11: 195.\nDistance from 5 to 12: 162.\nDistance from 5 to 13: 148.\nDistance from 5 to 14: 176.\nDistance from 5 to 15: 183.\nDistance from 5 to 16: 253.\nDistance from 5 to 17: 196.\nDistance from 5 to 18: 187.\nDistance from 5 to 19: 226.\nDistance from 6 to 0: 86.\nDistance from 6 to 1: 133.\nDistance from 6 to 2: 135.\nDistance from 6 to 3: 57.\nDistance from 6 to 4: 82.\nDistance from 6 to 5: 142.\nDistance from 6 to 7: 119.\nDistance from 6 to 8: 143.\nDistance from 6 to 9: 120.\nDistance from 6 to 10: 174.\nDistance from 6 to 11: 130.\nDistance from 6 to 12: 105.\nDistance from 6 to 13: 56.\nDistance from 6 to 14: 163.\nDistance from 6 to 15: 107.\nDistance from 6 to 16: 161.\nDistance from 6 to 17: 54.\nDistance from 6 to 18: 170.\nDistance from 6 to 19: 137.\nDistance from 7 to 0: 153.\nDistance from 7 to 1: 135.\nDistance from 7 to 2: 131.\nDistance from 7 to 3: 176.\nDistance from 7 to 4: 201.\nDistance from 7 to 5: 135.\nDistance from 7 to 6: 119.\nDistance from 7 to 8: 94.\nDistance from 7 to 9: 216.\nDistance from 7 to 10: 158.\nDistance from 7 to 11: 178.\nDistance from 7 to 12: 89.\nDistance from 7 to 13: 138.\nDistance from 7 to 14: 140.\nDistance from 7 to 15: 84.\nDistance from 7 to 16: 191.\nDistance from 7 to 17: 155.\nDistance from 7 to 18: 163.\nDistance from 7 to 19: 202.\nDistance from 8 to 0: 182.\nDistance from 8 to 1: 151.\nDistance from 8 to 2: 147.\nDistance from 8 to 3: 160.\nDistance from 8 to 4: 185.\nDistance from 8 to 5: 177.\nDistance from 8 to 6: 143.\nDistance from 8 to 7: 94.\nDistance from 8 to 9: 221.\nDistance from 8 to 10: 133.\nDistance from 8 to 11: 210.\nDistance from 8 to 12: 183.\nDistance from 8 to 13: 171.\nDistance from 8 to 14: 53.\nDistance from 8 to 15: 109.\nDistance from 8 to 16: 97.\nDistance from 8 to 17: 130.\nDistance from 8 to 18: 176.\nDistance from 8 to 19: 215.\nDistance from 9 to 0: 206.\nDistance from 9 to 1: 221.\nDistance from 9 to 2: 217.\nDistance from 9 to 3: 177.\nDistance from 9 to 4: 202.\nDistance from 9 to 5: 219.\nDistance from 9 to 6: 120.\nDistance from 9 to 7: 216.\nDistance from 9 to 8: 221.\nDistance from 9 to 10: 88.\nDistance from 9 to 11: 198.\nDistance from 9 to 12: 225.\nDistance from 9 to 13: 176.\nDistance from 9 to 14: 272.\nDistance from 9 to 15: 227.\nDistance from 9 to 16: 226.\nDistance from 9 to 17: 174.\nDistance from 9 to 18: 131.\nDistance from 9 to 19: 115.\nDistance from 10 to 0: 159.\nDistance from 10 to 1: 144.\nDistance from 10 to 2: 140.\nDistance from 10 to 3: 191.\nDistance from 10 to 4: 216.\nDistance from 10 to 5: 205.\nDistance from 10 to 6: 174.\nDistance from 10 to 7: 158.\nDistance from 10 to 8: 133.\nDistance from 10 to 9: 88.\nDistance from 10 to 11: 183.\nDistance from 10 to 12: 177.\nDistance from 10 to 13: 199.\nDistance from 10 to 14: 186.\nDistance from 10 to 15: 142.\nDistance from 10 to 16: 138.\nDistance from 10 to 17: 161.\nDistance from 10 to 18: 43.\nDistance from 10 to 19: 82.\nDistance from 11 to 0: 114.\nDistance from 11 to 1: 67.\nDistance from 11 to 2: 63.\nDistance from 11 to 3: 159.\nDistance from 11 to 4: 184.\nDistance from 11 to 5: 195.\nDistance from 11 to 6: 130.\nDistance from 11 to 7: 178.\nDistance from 11 to 8: 210.\nDistance from 11 to 9: 198.\nDistance from 11 to 10: 183.\nDistance from 11 to 12: 123.\nDistance from 11 to 13: 74.\nDistance from 11 to 14: 166.\nDistance from 11 to 15: 110.\nDistance from 11 to 16: 179.\nDistance from 11 to 17: 184.\nDistance from 11 to 18: 199.\nDistance from 11 to 19: 215.\nDistance from 12 to 0: 155.\nDistance from 12 to 1: 132.\nDistance from 12 to 2: 128.\nDistance from 12 to 3: 134.\nDistance from 12 to 4: 159.\nDistance from 12 to 5: 162.\nDistance from 12 to 6: 105.\nDistance from 12 to 7: 89.\nDistance from 12 to 8: 183.\nDistance from 12 to 9: 225.\nDistance from 12 to 10: 177.\nDistance from 12 to 11: 123.\nDistance from 12 to 13: 49.\nDistance from 12 to 14: 187.\nDistance from 12 to 15: 157.\nDistance from 12 to 16: 154.\nDistance from 12 to 17: 159.\nDistance from 12 to 18: 134.\nDistance from 12 to 19: 173.\nDistance from 13 to 0: 106.\nDistance from 13 to 1: 83.\nDistance from 13 to 2: 79.\nDistance from 13 to 3: 85.\nDistance from 13 to 4: 110.\nDistance from 13 to 5: 148.\nDistance from 13 to 6: 56.\nDistance from 13 to 7: 138.\nDistance from 13 to 8: 171.\nDistance from 13 to 9: 176.\nDistance from 13 to 10: 199.\nDistance from 13 to 11: 74.\nDistance from 13 to 12: 49.\nDistance from 13 to 14: 169.\nDistance from 13 to 15: 113.\nDistance from 13 to 16: 105.\nDistance from 13 to 17: 110.\nDistance from 13 to 18: 172.\nDistance from 13 to 19: 193.\nDistance from 14 to 0: 154.\nDistance from 14 to 1: 107.\nDistance from 14 to 2: 103.\nDistance from 14 to 3: 192.\nDistance from 14 to 4: 217.\nDistance from 14 to 5: 176.\nDistance from 14 to 6: 163.\nDistance from 14 to 7: 140.\nDistance from 14 to 8: 53.\nDistance from 14 to 9: 272.\nDistance from 14 to 10: 186.\nDistance from 14 to 11: 166.\nDistance from 14 to 12: 187.\nDistance from 14 to 13: 169.\nDistance from 14 to 15: 56.\nDistance from 14 to 16: 150.\nDistance from 14 to 17: 183.\nDistance from 14 to 18: 229.\nDistance from 14 to 19: 268.\nDistance from 15 to 0: 98.\nDistance from 15 to 1: 51.\nDistance from 15 to 2: 47.\nDistance from 15 to 3: 136.\nDistance from 15 to 4: 161.\nDistance from 15 to 5: 183.\nDistance from 15 to 6: 107.\nDistance from 15 to 7: 84.\nDistance from 15 to 8: 109.\nDistance from 15 to 9: 227.\nDistance from 15 to 10: 142.\nDistance from 15 to 11: 110.\nDistance from 15 to 12: 157.\nDistance from 15 to 13: 113.\nDistance from 15 to 14: 56.\nDistance from 15 to 16: 206.\nDistance from 15 to 17: 161.\nDistance from 15 to 18: 185.\nDistance from 15 to 19: 224.\nDistance from 16 to 0: 211.\nDistance from 16 to 1: 188.\nDistance from 16 to 2: 184.\nDistance from 16 to 3: 190.\nDistance from 16 to 4: 215.\nDistance from 16 to 5: 253.\nDistance from 16 to 6: 161.\nDistance from 16 to 7: 191.\nDistance from 16 to 8: 97.\nDistance from 16 to 9: 226.\nDistance from 16 to 10: 138.\nDistance from 16 to 11: 179.\nDistance from 16 to 12: 154.\nDistance from 16 to 13: 105.\nDistance from 16 to 14: 150.\nDistance from 16 to 15: 206.\nDistance from 16 to 17: 215.\nDistance from 16 to 18: 95.\nDistance from 16 to 19: 134.\nDistance from 17 to 0: 140.\nDistance from 17 to 1: 163.\nDistance from 17 to 2: 167.\nDistance from 17 to 3: 111.\nDistance from 17 to 4: 136.\nDistance from 17 to 5: 196.\nDistance from 17 to 6: 54.\nDistance from 17 to 7: 155.\nDistance from 17 to 8: 130.\nDistance from 17 to 9: 174.\nDistance from 17 to 10: 161.\nDistance from 17 to 11: 184.\nDistance from 17 to 12: 159.\nDistance from 17 to 13: 110.\nDistance from 17 to 14: 183.\nDistance from 17 to 15: 161.\nDistance from 17 to 16: 215.\nDistance from 17 to 18: 122.\nDistance from 17 to 19: 161.\nDistance from 18 to 0: 116.\nDistance from 18 to 1: 163.\nDistance from 18 to 2: 167.\nDistance from 18 to 3: 199.\nDistance from 18 to 4: 224.\nDistance from 18 to 5: 187.\nDistance from 18 to 6: 170.\nDistance from 18 to 7: 163.\nDistance from 18 to 8: 176.\nDistance from 18 to 9: 131.\nDistance from 18 to 10: 43.\nDistance from 18 to 11: 199.\nDistance from 18 to 12: 134.\nDistance from 18 to 13: 172.\nDistance from 18 to 14: 229.\nDistance from 18 to 15: 185.\nDistance from 18 to 16: 95.\nDistance from 18 to 17: 122.\nDistance from 18 to 19: 39.\nDistance from 19 to 0: 155.\nDistance from 19 to 1: 202.\nDistance from 19 to 2: 206.\nDistance from 19 to 3: 194.\nDistance from 19 to 4: 219.\nDistance from 19 to 5: 226.\nDistance from 19 to 6: 137.\nDistance from 19 to 7: 202.\nDistance from 19 to 8: 215.\nDistance from 19 to 9: 115.\nDistance from 19 to 10: 82.\nDistance from 19 to 11: 215.\nDistance from 19 to 12: 173.\nDistance from 19 to 13: 193.\nDistance from 19 to 14: 268.\nDistance from 19 to 15: 224.\nDistance from 19 to 16: 134.\nDistance from 19 to 17: 161.\nDistance from 19 to 18: 39.\nRecord each origin–destination distance on its own line as shown above.\n\nI'll just mention casually how I’d like the final reply packaged — a small JSON outline to make things easy to read and parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the proposed sites you decide to open (those are the hub locations). \"assignments\" is a list that picks, for each client area in the same order they appear in the instance, which opened site it gets assigned to. Think of it like filling out a simple form: pick the open hubs, then say which hub each area goes to.\n\nThis JSON is just a sketch of the shape I expect, not the actual solution values.\n\nPlease be careful to use the exact identifiers given in the instance input — do not rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 47, 51, 115, 140, 117, 86, 153, 182, 206, 159, 114, 155, 106, 154, 98, 211, 140, 116, 155 ], [ 47, 0, 4, 162, 187, 163, 133, 135, 151, 221, 144, 67, 132, 83, 107, 51, 188, 163, 163, 202 ], [ 51, 4, 0, 164, 189, 159, 135, 131, 147, 217, 140, 63, 128, 79, 103, 47, 184, 167, 167, 206 ], [ 115, 162, 164, 0, 25, 117, 57, 176, 160, 177, 191, 159, 134, 85, 192, 136, 190, 111, 199, 194 ], [ 140, 187, 189, 25, 0, 92, 82, 201, 185, 202, 216, 184, 159, 110, 217, 161, 215, 136, 224, 219 ], [ 117, 163, 159, 117, 92, 0, 142, 135, 177, 219, 205, 195, 162, 148, 176, 183, 253, 196, 187, 226 ], [ 86, 133, 135, 57, 82, 142, 0, 119, 143, 120, 174, 130, 105, 56, 163, 107, 161, 54, 170, 137 ], [ 153, 135, 131, 176, 201, 135, 119, 0, 94, 216, 158, 178, 89, 138, 140, 84, 191, 155, 163, 202 ], [ 182, 151, 147, 160, 185, 177, 143, 94, 0, 221, 133, 210, 183, 171, 53, 109, 97, 130, 176, 215 ], [ 206, 221, 217, 177, 202, 219, 120, 216, 221, 0, 88, 198, 225, 176, 272, 227, 226, 174, 131, 115 ], [ 159, 144, 140, 191, 216, 205, 174, 158, 133, 88, 0, 183, 177, 199, 186, 142, 138, 161, 43, 82 ], [ 114, 67, 63, 159, 184, 195, 130, 178, 210, 198, 183, 0, 123, 74, 166, 110, 179, 184, 199, 215 ], [ 155, 132, 128, 134, 159, 162, 105, 89, 183, 225, 177, 123, 0, 49, 187, 157, 154, 159, 134, 173 ], [ 106, 83, 79, 85, 110, 148, 56, 138, 171, 176, 199, 74, 49, 0, 169, 113, 105, 110, 172, 193 ], [ 154, 107, 103, 192, 217, 176, 163, 140, 53, 272, 186, 166, 187, 169, 0, 56, 150, 183, 229, 268 ], [ 98, 51, 47, 136, 161, 183, 107, 84, 109, 227, 142, 110, 157, 113, 56, 0, 206, 161, 185, 224 ], [ 211, 188, 184, 190, 215, 253, 161, 191, 97, 226, 138, 179, 154, 105, 150, 206, 0, 215, 95, 134 ], [ 140, 163, 167, 111, 136, 196, 54, 155, 130, 174, 161, 184, 159, 110, 183, 161, 215, 0, 122, 161 ], [ 116, 163, 167, 199, 224, 187, 170, 163, 176, 131, 43, 199, 134, 172, 229, 185, 95, 122, 0, 39 ], [ 155, 202, 206, 194, 219, 226, 137, 202, 215, 115, 82, 215, 173, 193, 268, 224, 134, 161, 39, 0 ] ], "p": 2, "objective": 1751.0 }, "solution": { "facilities": [ 2, 6 ], "assignments": [ 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 2, 2, 6, 6, 2, 6 ] }, "obj": 1751.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 2, "sites": [ { "id": 0, "distances": { "0": 0, "1": 47, "2": 51, "3": 115, "4": 140, "5": 117, "6": 86, "7": 153, "8": 182, "9": 206, "10": 159, "11": 114, "12": 155, "13": 106, "14": 154, "15": 98, "16": 211, "17": 140, "18": 116, "19": 155 } }, { "id": 1, "distances": { "0": 47, "1": 0, "2": 4, "3": 162, "4": 187, "5": 163, "6": 133, "7": 135, "8": 151, "9": 221, "10": 144, "11": 67, "12": 132, "13": 83, "14": 107, "15": 51, "16": 188, "17": 163, "18": 163, "19": 202 } }, { "id": 2, "distances": { "0": 51, "1": 4, "2": 0, "3": 164, "4": 189, "5": 159, "6": 135, "7": 131, "8": 147, "9": 217, "10": 140, "11": 63, "12": 128, "13": 79, "14": 103, "15": 47, "16": 184, "17": 167, "18": 167, "19": 206 } }, { "id": 3, "distances": { "0": 115, "1": 162, "2": 164, "3": 0, "4": 25, "5": 117, "6": 57, "7": 176, "8": 160, "9": 177, "10": 191, "11": 159, "12": 134, "13": 85, "14": 192, "15": 136, "16": 190, "17": 111, "18": 199, "19": 194 } }, { "id": 4, "distances": { "0": 140, "1": 187, "2": 189, "3": 25, "4": 0, "5": 92, "6": 82, "7": 201, "8": 185, "9": 202, "10": 216, "11": 184, "12": 159, "13": 110, "14": 217, "15": 161, "16": 215, "17": 136, "18": 224, "19": 219 } }, { "id": 5, "distances": { "0": 117, "1": 163, "2": 159, "3": 117, "4": 92, "5": 0, "6": 142, "7": 135, "8": 177, "9": 219, "10": 205, "11": 195, "12": 162, "13": 148, "14": 176, "15": 183, "16": 253, "17": 196, "18": 187, "19": 226 } }, { "id": 6, "distances": { "0": 86, "1": 133, "2": 135, "3": 57, "4": 82, "5": 142, "6": 0, "7": 119, "8": 143, "9": 120, "10": 174, "11": 130, "12": 105, "13": 56, "14": 163, "15": 107, "16": 161, "17": 54, "18": 170, "19": 137 } }, { "id": 7, "distances": { "0": 153, "1": 135, "2": 131, "3": 176, "4": 201, "5": 135, "6": 119, "7": 0, "8": 94, "9": 216, "10": 158, "11": 178, "12": 89, "13": 138, "14": 140, "15": 84, "16": 191, "17": 155, "18": 163, "19": 202 } }, { "id": 8, "distances": { "0": 182, "1": 151, "2": 147, "3": 160, "4": 185, "5": 177, "6": 143, "7": 94, "8": 0, "9": 221, "10": 133, "11": 210, "12": 183, "13": 171, "14": 53, "15": 109, "16": 97, "17": 130, "18": 176, "19": 215 } }, { "id": 9, "distances": { "0": 206, "1": 221, "2": 217, "3": 177, "4": 202, "5": 219, "6": 120, "7": 216, "8": 221, "9": 0, "10": 88, "11": 198, "12": 225, "13": 176, "14": 272, "15": 227, "16": 226, "17": 174, "18": 131, "19": 115 } }, { "id": 10, "distances": { "0": 159, "1": 144, "2": 140, "3": 191, "4": 216, "5": 205, "6": 174, "7": 158, "8": 133, "9": 88, "10": 0, "11": 183, "12": 177, "13": 199, "14": 186, "15": 142, "16": 138, "17": 161, "18": 43, "19": 82 } }, { "id": 11, "distances": { "0": 114, "1": 67, "2": 63, "3": 159, "4": 184, "5": 195, "6": 130, "7": 178, "8": 210, "9": 198, "10": 183, "11": 0, "12": 123, "13": 74, "14": 166, "15": 110, "16": 179, "17": 184, "18": 199, "19": 215 } }, { "id": 12, "distances": { "0": 155, "1": 132, "2": 128, "3": 134, "4": 159, "5": 162, "6": 105, "7": 89, "8": 183, "9": 225, "10": 177, "11": 123, "12": 0, "13": 49, "14": 187, "15": 157, "16": 154, "17": 159, "18": 134, "19": 173 } }, { "id": 13, "distances": { "0": 106, "1": 83, "2": 79, "3": 85, "4": 110, "5": 148, "6": 56, "7": 138, "8": 171, "9": 176, "10": 199, "11": 74, "12": 49, "13": 0, "14": 169, "15": 113, "16": 105, "17": 110, "18": 172, "19": 193 } }, { "id": 14, "distances": { "0": 154, "1": 107, "2": 103, "3": 192, "4": 217, "5": 176, "6": 163, "7": 140, "8": 53, "9": 272, "10": 186, "11": 166, "12": 187, "13": 169, "14": 0, "15": 56, "16": 150, "17": 183, "18": 229, "19": 268 } }, { "id": 15, "distances": { "0": 98, "1": 51, "2": 47, "3": 136, "4": 161, "5": 183, "6": 107, "7": 84, "8": 109, "9": 227, "10": 142, "11": 110, "12": 157, "13": 113, "14": 56, "15": 0, "16": 206, "17": 161, "18": 185, "19": 224 } }, { "id": 16, "distances": { "0": 211, "1": 188, "2": 184, "3": 190, "4": 215, "5": 253, "6": 161, "7": 191, "8": 97, "9": 226, "10": 138, "11": 179, "12": 154, "13": 105, "14": 150, "15": 206, "16": 0, "17": 215, "18": 95, "19": 134 } }, { "id": 17, "distances": { "0": 140, "1": 163, "2": 167, "3": 111, "4": 136, "5": 196, "6": 54, "7": 155, "8": 130, "9": 174, "10": 161, "11": 184, "12": 159, "13": 110, "14": 183, "15": 161, "16": 215, "17": 0, "18": 122, "19": 161 } }, { "id": 18, "distances": { "0": 116, "1": 163, "2": 167, "3": 199, "4": 224, "5": 187, "6": 170, "7": 163, "8": 176, "9": 131, "10": 43, "11": 199, "12": 134, "13": 172, "14": 229, "15": 185, "16": 95, "17": 122, "18": 0, "19": 39 } }, { "id": 19, "distances": { "0": 155, "1": 202, "2": 206, "3": 194, "4": 219, "5": 226, "6": 137, "7": 202, "8": 215, "9": 115, "10": 82, "11": 215, "12": 173, "13": 193, "14": 268, "15": 224, "16": 134, "17": 161, "18": 39, "19": 0 } } ], "objective": 1751.0 }, "solution_variant": { "selected": [ 2, 6 ], "assignments": [ 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 2, 2, 6, 6, 2, 6 ] }, "context_index": 5, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone in the planning office is trying to map out where to activate a fixed number of free Wi‑Fi hotspots from among possible sites. Once the chosen hotspots are up, each block has to be connected to exactly one of them — no block is left unassigned or tied to more than one hotspot. The better the plan, the less total distance users have to travel, which is measured by adding up each block’s distance to its assigned hotspot; the plan with the smallest sum is preferred. The concrete candidate locations, the distances between them, and the number of hotspots to turn on are shown below.\n\n# total_candidate_locations=18\n# hotspots_to_activate=2\n# location_ids=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17\norigin_location_id,destination_location_id,pairwise_travel_distance\n0,1,48\n0,2,67\n0,3,62\n0,4,61\n0,5,60\n0,6,51\n0,7,37\n0,8,14\n0,9,40\n0,10,48\n0,11,54\n0,12,56\n0,13,27\n0,14,34\n0,15,66\n0,16,48\n0,17,61\n1,0,48\n1,2,36\n1,3,45\n1,4,68\n1,5,45\n1,6,34\n1,7,33\n1,8,39\n1,9,8\n1,10,56\n1,11,44\n1,12,48\n1,13,30\n1,14,31\n1,15,51\n1,16,27\n1,17,40\n2,0,67\n2,1,36\n2,3,66\n2,4,72\n2,5,63\n2,6,54\n2,7,51\n2,8,61\n2,9,30\n2,10,49\n2,11,63\n2,12,60\n2,13,52\n2,14,42\n2,15,56\n2,16,63\n2,17,76\n3,0,62\n3,1,45\n3,2,66\n3,4,27\n3,5,57\n3,6,34\n3,7,62\n3,8,48\n3,9,47\n3,10,46\n3,11,59\n3,12,60\n3,13,53\n3,14,42\n3,15,26\n3,16,40\n3,17,53\n4,0,61\n4,1,68\n4,2,72\n4,3,27\n4,5,72\n4,6,56\n4,7,41\n4,8,64\n4,9,60\n4,10,58\n4,11,71\n4,12,63\n4,13,59\n4,14,40\n4,15,53\n4,16,67\n4,17,80\n5,0,60\n5,1,45\n5,2,63\n5,3,57\n5,4,72\n5,6,56\n5,7,47\n5,8,46\n5,9,39\n5,10,59\n5,11,68\n5,12,54\n5,13,41\n5,14,32\n5,15,64\n5,16,72\n5,17,85\n6,0,51\n6,1,34\n6,2,54\n6,3,34\n6,4,56\n6,5,56\n6,7,38\n6,8,37\n6,9,33\n6,10,34\n6,11,47\n6,12,47\n6,13,32\n6,14,24\n6,15,56\n6,16,29\n6,17,42\n7,0,37\n7,1,33\n7,2,51\n7,3,62\n7,4,41\n7,5,47\n7,6,38\n7,8,23\n7,9,27\n7,10,51\n7,11,45\n7,12,47\n7,13,18\n7,14,33\n7,15,59\n7,16,57\n7,17,70\n8,0,14\n8,1,39\n8,2,61\n8,3,48\n8,4,64\n8,5,46\n8,6,37\n8,7,23\n8,9,33\n8,10,42\n8,11,40\n8,12,42\n8,13,13\n8,14,48\n8,15,54\n8,16,34\n8,17,47\n9,0,40\n9,1,8\n9,2,30\n9,3,47\n9,4,60\n9,5,39\n9,6,33\n9,7,27\n9,8,33\n9,10,48\n9,11,38\n9,12,40\n9,13,24\n9,14,23\n9,15,43\n9,16,35\n9,17,48\n10,0,48\n10,1,56\n10,2,49\n10,3,46\n10,4,58\n10,5,59\n10,6,34\n10,7,51\n10,8,42\n10,9,48\n10,11,51\n10,12,27\n10,13,33\n10,14,34\n10,15,66\n10,16,51\n10,17,64\n11,0,54\n11,1,44\n11,2,63\n11,3,59\n11,4,71\n11,5,68\n11,6,47\n11,7,45\n11,8,40\n11,9,38\n11,10,51\n11,12,56\n11,13,27\n11,14,50\n11,15,62\n11,16,45\n11,17,58\n12,0,56\n12,1,48\n12,2,60\n12,3,60\n12,4,63\n12,5,54\n12,6,47\n12,7,47\n12,8,42\n12,9,40\n12,10,27\n12,11,56\n12,13,29\n12,14,23\n12,15,55\n12,16,65\n12,17,78\n13,0,27\n13,1,30\n13,2,52\n13,3,53\n13,4,59\n13,5,41\n13,6,32\n13,7,18\n13,8,13\n13,9,24\n13,10,33\n13,11,27\n13,12,29\n13,14,44\n13,15,59\n13,16,47\n13,17,60\n14,0,34\n14,1,31\n14,2,42\n14,3,42\n14,4,40\n14,5,32\n14,6,24\n14,7,33\n14,8,48\n14,9,23\n14,10,34\n14,11,50\n14,12,23\n14,13,44\n14,15,32\n14,16,53\n14,17,66\n15,0,66\n15,1,51\n15,2,56\n15,3,26\n15,4,53\n15,5,64\n15,6,56\n15,7,59\n15,8,54\n15,9,43\n15,10,66\n15,11,62\n15,12,55\n15,13,59\n15,14,32\n15,16,66\n15,17,79\n16,0,48\n16,1,27\n16,2,63\n16,3,40\n16,4,67\n16,5,72\n16,6,29\n16,7,57\n16,8,34\n16,9,35\n16,10,51\n16,11,45\n16,12,65\n16,13,47\n16,14,53\n16,15,66\n16,17,13\n17,0,61\n17,1,40\n17,2,76\n17,3,53\n17,4,80\n17,5,85\n17,6,42\n17,7,70\n17,8,47\n17,9,48\n17,10,64\n17,11,58\n17,12,78\n17,13,60\n17,14,66\n17,15,79\n17,16,13\n\nIf you like, you can just send back the plan in a tiny JSON snippet so it's easy to read and parse. Here's the shape I'd expect — nothing complicated, just which sites you turn on and which site each block connects to:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of hotspot sites you're switching on, and \"assignments\" as, for each block (in the same order the instance lists them), the selected site that block will use. Super informal: first array = which spots open, second array = where each block connects.\n\nThis JSON is only a sketch of the expected shape — not the actual answer.\n\nPlease use the exact identifiers from the instance input — no renaming and no new labels.\nFor example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 48, 67, 62, 61, 60, 51, 37, 14, 40, 48, 54, 56, 27, 34, 66, 48, 61 ], [ 48, 0, 36, 45, 68, 45, 34, 33, 39, 8, 56, 44, 48, 30, 31, 51, 27, 40 ], [ 67, 36, 0, 66, 72, 63, 54, 51, 61, 30, 49, 63, 60, 52, 42, 56, 63, 76 ], [ 62, 45, 66, 0, 27, 57, 34, 62, 48, 47, 46, 59, 60, 53, 42, 26, 40, 53 ], [ 61, 68, 72, 27, 0, 72, 56, 41, 64, 60, 58, 71, 63, 59, 40, 53, 67, 80 ], [ 60, 45, 63, 57, 72, 0, 56, 47, 46, 39, 59, 68, 54, 41, 32, 64, 72, 85 ], [ 51, 34, 54, 34, 56, 56, 0, 38, 37, 33, 34, 47, 47, 32, 24, 56, 29, 42 ], [ 37, 33, 51, 62, 41, 47, 38, 0, 23, 27, 51, 45, 47, 18, 33, 59, 57, 70 ], [ 14, 39, 61, 48, 64, 46, 37, 23, 0, 33, 42, 40, 42, 13, 48, 54, 34, 47 ], [ 40, 8, 30, 47, 60, 39, 33, 27, 33, 0, 48, 38, 40, 24, 23, 43, 35, 48 ], [ 48, 56, 49, 46, 58, 59, 34, 51, 42, 48, 0, 51, 27, 33, 34, 66, 51, 64 ], [ 54, 44, 63, 59, 71, 68, 47, 45, 40, 38, 51, 0, 56, 27, 50, 62, 45, 58 ], [ 56, 48, 60, 60, 63, 54, 47, 47, 42, 40, 27, 56, 0, 29, 23, 55, 65, 78 ], [ 27, 30, 52, 53, 59, 41, 32, 18, 13, 24, 33, 27, 29, 0, 44, 59, 47, 60 ], [ 34, 31, 42, 42, 40, 32, 24, 33, 48, 23, 34, 50, 23, 44, 0, 32, 53, 66 ], [ 66, 51, 56, 26, 53, 64, 56, 59, 54, 43, 66, 62, 55, 59, 32, 0, 66, 79 ], [ 48, 27, 63, 40, 67, 72, 29, 57, 34, 35, 51, 45, 65, 47, 53, 66, 0, 13 ], [ 61, 40, 76, 53, 80, 85, 42, 70, 47, 48, 64, 58, 78, 60, 66, 79, 13, 0 ] ], "p": 2, "objective": 494.0 }, "solution": { "facilities": [ 8, 14 ], "assignments": [ 8, 14, 14, 14, 14, 14, 14, 8, 8, 14, 14, 8, 14, 8, 14, 14, 8, 8 ] }, "obj": 494.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 2, "sites": [ { "id": 0, "distances": { "0": 0, "1": 48, "2": 67, "3": 62, "4": 61, "5": 60, "6": 51, "7": 37, "8": 14, "9": 40, "10": 48, "11": 54, "12": 56, "13": 27, "14": 34, "15": 66, "16": 48, "17": 61 } }, { "id": 1, "distances": { "0": 48, "1": 0, "2": 36, "3": 45, "4": 68, "5": 45, "6": 34, "7": 33, "8": 39, "9": 8, "10": 56, "11": 44, "12": 48, "13": 30, "14": 31, "15": 51, "16": 27, "17": 40 } }, { "id": 2, "distances": { "0": 67, "1": 36, "2": 0, "3": 66, "4": 72, "5": 63, "6": 54, "7": 51, "8": 61, "9": 30, "10": 49, "11": 63, "12": 60, "13": 52, "14": 42, "15": 56, "16": 63, "17": 76 } }, { "id": 3, "distances": { "0": 62, "1": 45, "2": 66, "3": 0, "4": 27, "5": 57, "6": 34, "7": 62, "8": 48, "9": 47, "10": 46, "11": 59, "12": 60, "13": 53, "14": 42, "15": 26, "16": 40, "17": 53 } }, { "id": 4, "distances": { "0": 61, "1": 68, "2": 72, "3": 27, "4": 0, "5": 72, "6": 56, "7": 41, "8": 64, "9": 60, "10": 58, "11": 71, "12": 63, "13": 59, "14": 40, "15": 53, "16": 67, "17": 80 } }, { "id": 5, "distances": { "0": 60, "1": 45, "2": 63, "3": 57, "4": 72, "5": 0, "6": 56, "7": 47, "8": 46, "9": 39, "10": 59, "11": 68, "12": 54, "13": 41, "14": 32, "15": 64, "16": 72, "17": 85 } }, { "id": 6, "distances": { "0": 51, "1": 34, "2": 54, "3": 34, "4": 56, "5": 56, "6": 0, "7": 38, "8": 37, "9": 33, "10": 34, "11": 47, "12": 47, "13": 32, "14": 24, "15": 56, "16": 29, "17": 42 } }, { "id": 7, "distances": { "0": 37, "1": 33, "2": 51, "3": 62, "4": 41, "5": 47, "6": 38, "7": 0, "8": 23, "9": 27, "10": 51, "11": 45, "12": 47, "13": 18, "14": 33, "15": 59, "16": 57, "17": 70 } }, { "id": 8, "distances": { "0": 14, "1": 39, "2": 61, "3": 48, "4": 64, "5": 46, "6": 37, "7": 23, "8": 0, "9": 33, "10": 42, "11": 40, "12": 42, "13": 13, "14": 48, "15": 54, "16": 34, "17": 47 } }, { "id": 9, "distances": { "0": 40, "1": 8, "2": 30, "3": 47, "4": 60, "5": 39, "6": 33, "7": 27, "8": 33, "9": 0, "10": 48, "11": 38, "12": 40, "13": 24, "14": 23, "15": 43, "16": 35, "17": 48 } }, { "id": 10, "distances": { "0": 48, "1": 56, "2": 49, "3": 46, "4": 58, "5": 59, "6": 34, "7": 51, "8": 42, "9": 48, "10": 0, "11": 51, "12": 27, "13": 33, "14": 34, "15": 66, "16": 51, "17": 64 } }, { "id": 11, "distances": { "0": 54, "1": 44, "2": 63, "3": 59, "4": 71, "5": 68, "6": 47, "7": 45, "8": 40, "9": 38, "10": 51, "11": 0, "12": 56, "13": 27, "14": 50, "15": 62, "16": 45, "17": 58 } }, { "id": 12, "distances": { "0": 56, "1": 48, "2": 60, "3": 60, "4": 63, "5": 54, "6": 47, "7": 47, "8": 42, "9": 40, "10": 27, "11": 56, "12": 0, "13": 29, "14": 23, "15": 55, "16": 65, "17": 78 } }, { "id": 13, "distances": { "0": 27, "1": 30, "2": 52, "3": 53, "4": 59, "5": 41, "6": 32, "7": 18, "8": 13, "9": 24, "10": 33, "11": 27, "12": 29, "13": 0, "14": 44, "15": 59, "16": 47, "17": 60 } }, { "id": 14, "distances": { "0": 34, "1": 31, "2": 42, "3": 42, "4": 40, "5": 32, "6": 24, "7": 33, "8": 48, "9": 23, "10": 34, "11": 50, "12": 23, "13": 44, "14": 0, "15": 32, "16": 53, "17": 66 } }, { "id": 15, "distances": { "0": 66, "1": 51, "2": 56, "3": 26, "4": 53, "5": 64, "6": 56, "7": 59, "8": 54, "9": 43, "10": 66, "11": 62, "12": 55, "13": 59, "14": 32, "15": 0, "16": 66, "17": 79 } }, { "id": 16, "distances": { "0": 48, "1": 27, "2": 63, "3": 40, "4": 67, "5": 72, "6": 29, "7": 57, "8": 34, "9": 35, "10": 51, "11": 45, "12": 65, "13": 47, "14": 53, "15": 66, "16": 0, "17": 13 } }, { "id": 17, "distances": { "0": 61, "1": 40, "2": 76, "3": 53, "4": 80, "5": 85, "6": 42, "7": 70, "8": 47, "9": 48, "10": 64, "11": 58, "12": 78, "13": 60, "14": 66, "15": 79, "16": 13, "17": 0 } } ], "objective": 494.0 }, "solution_variant": { "selected": [ 8, 14 ], "assignments": [ 8, 14, 14, 14, 14, 14, 14, 8, 8, 14, 14, 8, 14, 8, 14, 14, 8, 8 ] }, "context_index": 6, "input_format": "csv", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Many people on the team know we need to open only a handful of garages as charging sites and then assign each vehicle base to one of those sites. That means choosing a fixed number of depots, making sure every base goes to exactly one open depot (nothing left out, nothing doubled up), and measuring a plan by summing the drives from each base to its depot — the lower that sum, the better. The full set of garages, bases, and distance values is shown below.\n\nBelow are the 16 candidate garages and bases; we will open exactly 2 depots and the locations (in order) are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.\nDrive distance from 1 to 2 is 34.\nDrive distance from 1 to 3 is 33.\nDrive distance from 1 to 4 is 46.\nDrive distance from 1 to 5 is 35.\nDrive distance from 1 to 6 is 44.\nDrive distance from 1 to 7 is 31.\nDrive distance from 1 to 8 is 34.\nDrive distance from 1 to 9 is 28.\nDrive distance from 1 to 10 is 20.\nDrive distance from 1 to 11 is 28.\nDrive distance from 1 to 12 is 33.\nDrive distance from 1 to 13 is 34.\nDrive distance from 1 to 14 is 32.\nDrive distance from 1 to 15 is 29.\nDrive distance from 1 to 16 is 39.\nDrive distance from 2 to 1 is 34.\nDrive distance from 2 to 3 is 36.\nDrive distance from 2 to 4 is 46.\nDrive distance from 2 to 5 is 36.\nDrive distance from 2 to 6 is 44.\nDrive distance from 2 to 7 is 39.\nDrive distance from 2 to 8 is 36.\nDrive distance from 2 to 9 is 32.\nDrive distance from 2 to 10 is 37.\nDrive distance from 2 to 11 is 38.\nDrive distance from 2 to 12 is 42.\nDrive distance from 2 to 13 is 33.\nDrive distance from 2 to 14 is 36.\nDrive distance from 2 to 15 is 36.\nDrive distance from 2 to 16 is 40.\nDrive distance from 3 to 1 is 33.\nDrive distance from 3 to 2 is 36.\nDrive distance from 3 to 4 is 18.\nDrive distance from 3 to 5 is 13.\nDrive distance from 3 to 6 is 21.\nDrive distance from 3 to 7 is 14.\nDrive distance from 3 to 8 is 26.\nDrive distance from 3 to 9 is 26.\nDrive distance from 3 to 10 is 31.\nDrive distance from 3 to 11 is 18.\nDrive distance from 3 to 12 is 40.\nDrive distance from 3 to 13 is 28.\nDrive distance from 3 to 14 is 20.\nDrive distance from 3 to 15 is 14.\nDrive distance from 3 to 16 is 23.\nDrive distance from 4 to 1 is 46.\nDrive distance from 4 to 2 is 46.\nDrive distance from 4 to 3 is 18.\nDrive distance from 4 to 5 is 26.\nDrive distance from 4 to 6 is 24.\nDrive distance from 4 to 7 is 29.\nDrive distance from 4 to 8 is 34.\nDrive distance from 4 to 9 is 30.\nDrive distance from 4 to 10 is 46.\nDrive distance from 4 to 11 is 21.\nDrive distance from 4 to 12 is 48.\nDrive distance from 4 to 13 is 37.\nDrive distance from 4 to 14 is 28.\nDrive distance from 4 to 15 is 17.\nDrive distance from 4 to 16 is 27.\nDrive distance from 5 to 1 is 35.\nDrive distance from 5 to 2 is 36.\nDrive distance from 5 to 3 is 13.\nDrive distance from 5 to 4 is 26.\nDrive distance from 5 to 6 is 26.\nDrive distance from 5 to 7 is 10.\nDrive distance from 5 to 8 is 23.\nDrive distance from 5 to 9 is 33.\nDrive distance from 5 to 10 is 35.\nDrive distance from 5 to 11 is 22.\nDrive distance from 5 to 12 is 40.\nDrive distance from 5 to 13 is 31.\nDrive distance from 5 to 14 is 27.\nDrive distance from 5 to 15 is 19.\nDrive distance from 5 to 16 is 29.\nDrive distance from 6 to 1 is 44.\nDrive distance from 6 to 2 is 44.\nDrive distance from 6 to 3 is 21.\nDrive distance from 6 to 4 is 24.\nDrive distance from 6 to 5 is 26.\nDrive distance from 6 to 7 is 29.\nDrive distance from 6 to 8 is 34.\nDrive distance from 6 to 9 is 31.\nDrive distance from 6 to 10 is 46.\nDrive distance from 6 to 11 is 21.\nDrive distance from 6 to 12 is 48.\nDrive distance from 6 to 13 is 33.\nDrive distance from 6 to 14 is 28.\nDrive distance from 6 to 15 is 17.\nDrive distance from 6 to 16 is 27.\nDrive distance from 7 to 1 is 31.\nDrive distance from 7 to 2 is 39.\nDrive distance from 7 to 3 is 14.\nDrive distance from 7 to 4 is 29.\nDrive distance from 7 to 5 is 10.\nDrive distance from 7 to 6 is 29.\nDrive distance from 7 to 8 is 13.\nDrive distance from 7 to 9 is 25.\nDrive distance from 7 to 10 is 33.\nDrive distance from 7 to 11 is 12.\nDrive distance from 7 to 12 is 33.\nDrive distance from 7 to 13 is 24.\nDrive distance from 7 to 14 is 17.\nDrive distance from 7 to 15 is 14.\nDrive distance from 7 to 16 is 24.\nDrive distance from 8 to 1 is 34.\nDrive distance from 8 to 2 is 36.\nDrive distance from 8 to 3 is 26.\nDrive distance from 8 to 4 is 34.\nDrive distance from 8 to 5 is 23.\nDrive distance from 8 to 6 is 34.\nDrive distance from 8 to 7 is 13.\nDrive distance from 8 to 9 is 12.\nDrive distance from 8 to 10 is 29.\nDrive distance from 8 to 11 is 17.\nDrive distance from 8 to 12 is 36.\nDrive distance from 8 to 13 is 26.\nDrive distance from 8 to 14 is 22.\nDrive distance from 8 to 15 is 19.\nDrive distance from 8 to 16 is 25.\nDrive distance from 9 to 1 is 28.\nDrive distance from 9 to 2 is 32.\nDrive distance from 9 to 3 is 26.\nDrive distance from 9 to 4 is 30.\nDrive distance from 9 to 5 is 33.\nDrive distance from 9 to 6 is 31.\nDrive distance from 9 to 7 is 25.\nDrive distance from 9 to 8 is 12.\nDrive distance from 9 to 10 is 32.\nDrive distance from 9 to 11 is 21.\nDrive distance from 9 to 12 is 30.\nDrive distance from 9 to 13 is 22.\nDrive distance from 9 to 14 is 29.\nDrive distance from 9 to 15 is 18.\nDrive distance from 9 to 16 is 22.\nDrive distance from 10 to 1 is 20.\nDrive distance from 10 to 2 is 37.\nDrive distance from 10 to 3 is 31.\nDrive distance from 10 to 4 is 46.\nDrive distance from 10 to 5 is 35.\nDrive distance from 10 to 6 is 46.\nDrive distance from 10 to 7 is 33.\nDrive distance from 10 to 8 is 29.\nDrive distance from 10 to 9 is 32.\nDrive distance from 10 to 11 is 33.\nDrive distance from 10 to 12 is 40.\nDrive distance from 10 to 13 is 39.\nDrive distance from 10 to 14 is 32.\nDrive distance from 10 to 15 is 29.\nDrive distance from 10 to 16 is 38.\nDrive distance from 11 to 1 is 28.\nDrive distance from 11 to 2 is 38.\nDrive distance from 11 to 3 is 18.\nDrive distance from 11 to 4 is 21.\nDrive distance from 11 to 5 is 22.\nDrive distance from 11 to 6 is 21.\nDrive distance from 11 to 7 is 12.\nDrive distance from 11 to 8 is 17.\nDrive distance from 11 to 9 is 21.\nDrive distance from 11 to 10 is 33.\nDrive distance from 11 to 12 is 28.\nDrive distance from 11 to 13 is 24.\nDrive distance from 11 to 14 is 17.\nDrive distance from 11 to 15 is 14.\nDrive distance from 11 to 16 is 24.\nDrive distance from 12 to 1 is 33.\nDrive distance from 12 to 2 is 42.\nDrive distance from 12 to 3 is 40.\nDrive distance from 12 to 4 is 48.\nDrive distance from 12 to 5 is 40.\nDrive distance from 12 to 6 is 48.\nDrive distance from 12 to 7 is 33.\nDrive distance from 12 to 8 is 36.\nDrive distance from 12 to 9 is 30.\nDrive distance from 12 to 10 is 40.\nDrive distance from 12 to 11 is 28.\nDrive distance from 12 to 13 is 35.\nDrive distance from 12 to 14 is 40.\nDrive distance from 12 to 15 is 36.\nDrive distance from 12 to 16 is 46.\nDrive distance from 13 to 1 is 34.\nDrive distance from 13 to 2 is 33.\nDrive distance from 13 to 3 is 28.\nDrive distance from 13 to 4 is 37.\nDrive distance from 13 to 5 is 31.\nDrive distance from 13 to 6 is 33.\nDrive distance from 13 to 7 is 24.\nDrive distance from 13 to 8 is 26.\nDrive distance from 13 to 9 is 22.\nDrive distance from 13 to 10 is 39.\nDrive distance from 13 to 11 is 24.\nDrive distance from 13 to 12 is 35.\nDrive distance from 13 to 14 is 23.\nDrive distance from 13 to 15 is 20.\nDrive distance from 13 to 16 is 30.\nDrive distance from 14 to 1 is 32.\nDrive distance from 14 to 2 is 36.\nDrive distance from 14 to 3 is 20.\nDrive distance from 14 to 4 is 28.\nDrive distance from 14 to 5 is 27.\nDrive distance from 14 to 6 is 28.\nDrive distance from 14 to 7 is 17.\nDrive distance from 14 to 8 is 22.\nDrive distance from 14 to 9 is 29.\nDrive distance from 14 to 10 is 32.\nDrive distance from 14 to 11 is 17.\nDrive distance from 14 to 12 is 40.\nDrive distance from 14 to 13 is 23.\nDrive distance from 14 to 15 is 11.\nDrive distance from 14 to 16 is 21.\nDrive distance from 15 to 1 is 29.\nDrive distance from 15 to 2 is 36.\nDrive distance from 15 to 3 is 14.\nDrive distance from 15 to 4 is 17.\nDrive distance from 15 to 5 is 19.\nDrive distance from 15 to 6 is 17.\nDrive distance from 15 to 7 is 14.\nDrive distance from 15 to 8 is 19.\nDrive distance from 15 to 9 is 18.\nDrive distance from 15 to 10 is 29.\nDrive distance from 15 to 11 is 14.\nDrive distance from 15 to 12 is 36.\nDrive distance from 15 to 13 is 20.\nDrive distance from 15 to 14 is 11.\nDrive distance from 15 to 16 is 10.\nDrive distance from 16 to 1 is 39.\nDrive distance from 16 to 2 is 40.\nDrive distance from 16 to 3 is 23.\nDrive distance from 16 to 4 is 27.\nDrive distance from 16 to 5 is 29.\nDrive distance from 16 to 6 is 27.\nDrive distance from 16 to 7 is 24.\nDrive distance from 16 to 8 is 25.\nDrive distance from 16 to 9 is 22.\nDrive distance from 16 to 10 is 38.\nDrive distance from 16 to 11 is 24.\nDrive distance from 16 to 12 is 46.\nDrive distance from 16 to 13 is 30.\nDrive distance from 16 to 14 is 21.\nDrive distance from 16 to 15 is 10.\nUse these 16 locations and distances to evaluate plans that open 2 depots.\n\nAlso, when you reply with a candidate plan, please use this simple JSON shape so it's straightforward to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nQuick note on what that means in plain terms: \"selected\" is the list of garages (sites) you choose to open. \"assignments\" lists, in the same order as the vehicle bases are given in the instance, which opened site each base is assigned to. Think of it like a short form: pick the open sites, then say for each base which open site it uses.\n\nThis JSON is just the shape I need — not the filled-in answer. When you fill it in, be sure to use the exact identifiers from the instance input with no renaming or made-up labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 34, 33, 46, 35, 44, 31, 34, 28, 20, 28, 33, 34, 32, 29, 39 ], [ 34, 0, 36, 46, 36, 44, 39, 36, 32, 37, 38, 42, 33, 36, 36, 40 ], [ 33, 36, 0, 18, 13, 21, 14, 26, 26, 31, 18, 40, 28, 20, 14, 23 ], [ 46, 46, 18, 0, 26, 24, 29, 34, 30, 46, 21, 48, 37, 28, 17, 27 ], [ 35, 36, 13, 26, 0, 26, 10, 23, 33, 35, 22, 40, 31, 27, 19, 29 ], [ 44, 44, 21, 24, 26, 0, 29, 34, 31, 46, 21, 48, 33, 28, 17, 27 ], [ 31, 39, 14, 29, 10, 29, 0, 13, 25, 33, 12, 33, 24, 17, 14, 24 ], [ 34, 36, 26, 34, 23, 34, 13, 0, 12, 29, 17, 36, 26, 22, 19, 25 ], [ 28, 32, 26, 30, 33, 31, 25, 12, 0, 32, 21, 30, 22, 29, 18, 22 ], [ 20, 37, 31, 46, 35, 46, 33, 29, 32, 0, 33, 40, 39, 32, 29, 38 ], [ 28, 38, 18, 21, 22, 21, 12, 17, 21, 33, 0, 28, 24, 17, 14, 24 ], [ 33, 42, 40, 48, 40, 48, 33, 36, 30, 40, 28, 0, 35, 40, 36, 46 ], [ 34, 33, 28, 37, 31, 33, 24, 26, 22, 39, 24, 35, 0, 23, 20, 30 ], [ 32, 36, 20, 28, 27, 28, 17, 22, 29, 32, 17, 40, 23, 0, 11, 21 ], [ 29, 36, 14, 17, 19, 17, 14, 19, 18, 29, 14, 36, 20, 11, 0, 10 ], [ 39, 40, 23, 27, 29, 27, 24, 25, 22, 38, 24, 46, 30, 21, 10, 0 ] ], "p": 2, "objective": 260.0 }, "solution": { "facilities": [ 0, 14 ], "assignments": [ 0, 0, 14, 14, 14, 14, 14, 14, 14, 0, 14, 0, 14, 14, 14, 14 ] }, "obj": 260.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 2, "sites": [ { "id": 1, "distances": { "1": 0, "2": 34, "3": 33, "4": 46, "5": 35, "6": 44, "7": 31, "8": 34, "9": 28, "10": 20, "11": 28, "12": 33, "13": 34, "14": 32, "15": 29, "16": 39 } }, { "id": 2, "distances": { "1": 34, "2": 0, "3": 36, "4": 46, "5": 36, "6": 44, "7": 39, "8": 36, "9": 32, "10": 37, "11": 38, "12": 42, "13": 33, "14": 36, "15": 36, "16": 40 } }, { "id": 3, "distances": { "1": 33, "2": 36, "3": 0, "4": 18, "5": 13, "6": 21, "7": 14, "8": 26, "9": 26, "10": 31, "11": 18, "12": 40, "13": 28, "14": 20, "15": 14, "16": 23 } }, { "id": 4, "distances": { "1": 46, "2": 46, "3": 18, "4": 0, "5": 26, "6": 24, "7": 29, "8": 34, "9": 30, "10": 46, "11": 21, "12": 48, "13": 37, "14": 28, "15": 17, "16": 27 } }, { "id": 5, "distances": { "1": 35, "2": 36, "3": 13, "4": 26, "5": 0, "6": 26, "7": 10, "8": 23, "9": 33, "10": 35, "11": 22, "12": 40, "13": 31, "14": 27, "15": 19, "16": 29 } }, { "id": 6, "distances": { "1": 44, "2": 44, "3": 21, "4": 24, "5": 26, "6": 0, "7": 29, "8": 34, "9": 31, "10": 46, "11": 21, "12": 48, "13": 33, "14": 28, "15": 17, "16": 27 } }, { "id": 7, "distances": { "1": 31, "2": 39, "3": 14, "4": 29, "5": 10, "6": 29, "7": 0, "8": 13, "9": 25, "10": 33, "11": 12, "12": 33, "13": 24, "14": 17, "15": 14, "16": 24 } }, { "id": 8, "distances": { "1": 34, "2": 36, "3": 26, "4": 34, "5": 23, "6": 34, "7": 13, "8": 0, "9": 12, "10": 29, "11": 17, "12": 36, "13": 26, "14": 22, "15": 19, "16": 25 } }, { "id": 9, "distances": { "1": 28, "2": 32, "3": 26, "4": 30, "5": 33, "6": 31, "7": 25, "8": 12, "9": 0, "10": 32, "11": 21, "12": 30, "13": 22, "14": 29, "15": 18, "16": 22 } }, { "id": 10, "distances": { "1": 20, "2": 37, "3": 31, "4": 46, "5": 35, "6": 46, "7": 33, "8": 29, "9": 32, "10": 0, "11": 33, "12": 40, "13": 39, "14": 32, "15": 29, "16": 38 } }, { "id": 11, "distances": { "1": 28, "2": 38, "3": 18, "4": 21, "5": 22, "6": 21, "7": 12, "8": 17, "9": 21, "10": 33, "11": 0, "12": 28, "13": 24, "14": 17, "15": 14, "16": 24 } }, { "id": 12, "distances": { "1": 33, "2": 42, "3": 40, "4": 48, "5": 40, "6": 48, "7": 33, "8": 36, "9": 30, "10": 40, "11": 28, "12": 0, "13": 35, "14": 40, "15": 36, "16": 46 } }, { "id": 13, "distances": { "1": 34, "2": 33, "3": 28, "4": 37, "5": 31, "6": 33, "7": 24, "8": 26, "9": 22, "10": 39, "11": 24, "12": 35, "13": 0, "14": 23, "15": 20, "16": 30 } }, { "id": 14, "distances": { "1": 32, "2": 36, "3": 20, "4": 28, "5": 27, "6": 28, "7": 17, "8": 22, "9": 29, "10": 32, "11": 17, "12": 40, "13": 23, "14": 0, "15": 11, "16": 21 } }, { "id": 15, "distances": { "1": 29, "2": 36, "3": 14, "4": 17, "5": 19, "6": 17, "7": 14, "8": 19, "9": 18, "10": 29, "11": 14, "12": 36, "13": 20, "14": 11, "15": 0, "16": 10 } }, { "id": 16, "distances": { "1": 39, "2": 40, "3": 23, "4": 27, "5": 29, "6": 27, "7": 24, "8": 25, "9": 22, "10": 38, "11": 24, "12": 46, "13": 30, "14": 21, "15": 10, "16": 0 } } ], "objective": 260.0 }, "solution_variant": { "selected": [ 1, 15 ], "assignments": [ 1, 1, 15, 15, 15, 15, 15, 15, 15, 1, 15, 1, 15, 15, 15, 15 ] }, "context_index": 7, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Many people will be coming and the team must choose exactly a certain number of staffed info points from the proposed spots, then assign each campsite to one of those points. The better the choice, the less everyone walks — you figure that by summing each campsite’s distance to its assigned booth and preferring the layout with the smallest sum. No campsite can be skipped or linked to more than one booth. Concrete details are listed below.\n\nThere are 18 proposed spots; you must staff exactly 4 booths chosen from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.\nFrom site 0 to site 1: walking distance 20.\nFrom site 0 to site 2: walking distance 51.\nFrom site 0 to site 3: walking distance 65.\nFrom site 0 to site 4: walking distance 46.\nFrom site 0 to site 5: walking distance 47.\nFrom site 0 to site 6: walking distance 66.\nFrom site 0 to site 7: walking distance 73.\nFrom site 0 to site 8: walking distance 27.\nFrom site 0 to site 9: walking distance 84.\nFrom site 0 to site 10: walking distance 70.\nFrom site 0 to site 11: walking distance 49.\nFrom site 0 to site 12: walking distance 49.\nFrom site 0 to site 13: walking distance 56.\nFrom site 0 to site 14: walking distance 77.\nFrom site 0 to site 15: walking distance 55.\nFrom site 0 to site 16: walking distance 47.\nFrom site 0 to site 17: walking distance 44.\nFrom site 1 to site 0: walking distance 20.\nFrom site 1 to site 2: walking distance 60.\nFrom site 1 to site 3: walking distance 45.\nFrom site 1 to site 4: walking distance 26.\nFrom site 1 to site 5: walking distance 27.\nFrom site 1 to site 6: walking distance 52.\nFrom site 1 to site 7: walking distance 53.\nFrom site 1 to site 8: walking distance 47.\nFrom site 1 to site 9: walking distance 64.\nFrom site 1 to site 10: walking distance 50.\nFrom site 1 to site 11: walking distance 29.\nFrom site 1 to site 12: walking distance 29.\nFrom site 1 to site 13: walking distance 60.\nFrom site 1 to site 14: walking distance 69.\nFrom site 1 to site 15: walking distance 35.\nFrom site 1 to site 16: walking distance 27.\nFrom site 1 to site 17: walking distance 58.\nFrom site 2 to site 0: walking distance 51.\nFrom site 2 to site 1: walking distance 60.\nFrom site 2 to site 3: walking distance 70.\nFrom site 2 to site 4: walking distance 59.\nFrom site 2 to site 5: walking distance 33.\nFrom site 2 to site 6: walking distance 29.\nFrom site 2 to site 7: walking distance 51.\nFrom site 2 to site 8: walking distance 30.\nFrom site 2 to site 9: walking distance 69.\nFrom site 2 to site 10: walking distance 53.\nFrom site 2 to site 11: walking distance 50.\nFrom site 2 to site 12: walking distance 53.\nFrom site 2 to site 13: walking distance 58.\nFrom site 2 to site 14: walking distance 32.\nFrom site 2 to site 15: walking distance 52.\nFrom site 2 to site 16: walking distance 60.\nFrom site 2 to site 17: walking distance 31.\nFrom site 3 to site 0: walking distance 65.\nFrom site 3 to site 1: walking distance 45.\nFrom site 3 to site 2: walking distance 70.\nFrom site 3 to site 4: walking distance 39.\nFrom site 3 to site 5: walking distance 42.\nFrom site 3 to site 6: walking distance 44.\nFrom site 3 to site 7: walking distance 62.\nFrom site 3 to site 8: walking distance 51.\nFrom site 3 to site 9: walking distance 62.\nFrom site 3 to site 10: walking distance 37.\nFrom site 3 to site 11: walking distance 45.\nFrom site 3 to site 12: walking distance 42.\nFrom site 3 to site 13: walking distance 43.\nFrom site 3 to site 14: walking distance 57.\nFrom site 3 to site 15: walking distance 19.\nFrom site 3 to site 16: walking distance 41.\nFrom site 3 to site 17: walking distance 70.\nFrom site 4 to site 0: walking distance 46.\nFrom site 4 to site 1: walking distance 26.\nFrom site 4 to site 2: walking distance 59.\nFrom site 4 to site 3: walking distance 39.\nFrom site 4 to site 5: walking distance 40.\nFrom site 4 to site 6: walking distance 42.\nFrom site 4 to site 7: walking distance 49.\nFrom site 4 to site 8: walking distance 64.\nFrom site 4 to site 9: walking distance 49.\nFrom site 4 to site 10: walking distance 48.\nFrom site 4 to site 11: walking distance 34.\nFrom site 4 to site 12: walking distance 23.\nFrom site 4 to site 13: walking distance 49.\nFrom site 4 to site 14: walking distance 58.\nFrom site 4 to site 15: walking distance 23.\nFrom site 4 to site 16: walking distance 35.\nFrom site 4 to site 17: walking distance 64.\nFrom site 5 to site 0: walking distance 47.\nFrom site 5 to site 1: walking distance 27.\nFrom site 5 to site 2: walking distance 33.\nFrom site 5 to site 3: walking distance 42.\nFrom site 5 to site 4: walking distance 40.\nFrom site 5 to site 6: walking distance 27.\nFrom site 5 to site 7: walking distance 26.\nFrom site 5 to site 8: walking distance 51.\nFrom site 5 to site 9: walking distance 62.\nFrom site 5 to site 10: walking distance 51.\nFrom site 5 to site 11: walking distance 49.\nFrom site 5 to site 12: walking distance 50.\nFrom site 5 to site 13: walking distance 49.\nFrom site 5 to site 14: walking distance 56.\nFrom site 5 to site 15: walking distance 23.\nFrom site 5 to site 16: walking distance 45.\nFrom site 5 to site 17: walking distance 58.\nFrom site 6 to site 0: walking distance 66.\nFrom site 6 to site 1: walking distance 52.\nFrom site 6 to site 2: walking distance 29.\nFrom site 6 to site 3: walking distance 44.\nFrom site 6 to site 4: walking distance 42.\nFrom site 6 to site 5: walking distance 27.\nFrom site 6 to site 7: walking distance 53.\nFrom site 6 to site 8: walking distance 45.\nFrom site 6 to site 9: walking distance 55.\nFrom site 6 to site 10: walking distance 53.\nFrom site 6 to site 11: walking distance 51.\nFrom site 6 to site 12: walking distance 61.\nFrom site 6 to site 13: walking distance 45.\nFrom site 6 to site 14: walking distance 54.\nFrom site 6 to site 15: walking distance 25.\nFrom site 6 to site 16: walking distance 47.\nFrom site 6 to site 17: walking distance 46.\nFrom site 7 to site 0: walking distance 73.\nFrom site 7 to site 1: walking distance 53.\nFrom site 7 to site 2: walking distance 51.\nFrom site 7 to site 3: walking distance 62.\nFrom site 7 to site 4: walking distance 49.\nFrom site 7 to site 5: walking distance 26.\nFrom site 7 to site 6: walking distance 53.\nFrom site 7 to site 8: walking distance 71.\nFrom site 7 to site 9: walking distance 57.\nFrom site 7 to site 10: walking distance 61.\nFrom site 7 to site 11: walking distance 59.\nFrom site 7 to site 12: walking distance 26.\nFrom site 7 to site 13: walking distance 42.\nFrom site 7 to site 14: walking distance 58.\nFrom site 7 to site 15: walking distance 43.\nFrom site 7 to site 16: walking distance 64.\nFrom site 7 to site 17: walking distance 78.\nFrom site 8 to site 0: walking distance 27.\nFrom site 8 to site 1: walking distance 47.\nFrom site 8 to site 2: walking distance 30.\nFrom site 8 to site 3: walking distance 51.\nFrom site 8 to site 4: walking distance 64.\nFrom site 8 to site 5: walking distance 51.\nFrom site 8 to site 6: walking distance 45.\nFrom site 8 to site 7: walking distance 71.\nFrom site 8 to site 9: walking distance 74.\nFrom site 8 to site 10: walking distance 51.\nFrom site 8 to site 11: walking distance 42.\nFrom site 8 to site 12: walking distance 57.\nFrom site 8 to site 13: walking distance 45.\nFrom site 8 to site 14: walking distance 56.\nFrom site 8 to site 15: walking distance 54.\nFrom site 8 to site 16: walking distance 60.\nFrom site 8 to site 17: walking distance 23.\nFrom site 9 to site 0: walking distance 84.\nFrom site 9 to site 1: walking distance 64.\nFrom site 9 to site 2: walking distance 69.\nFrom site 9 to site 3: walking distance 62.\nFrom site 9 to site 4: walking distance 49.\nFrom site 9 to site 5: walking distance 62.\nFrom site 9 to site 6: walking distance 55.\nFrom site 9 to site 7: walking distance 57.\nFrom site 9 to site 8: walking distance 74.\nFrom site 9 to site 10: walking distance 56.\nFrom site 9 to site 11: walking distance 47.\nFrom site 9 to site 12: walking distance 59.\nFrom site 9 to site 13: walking distance 44.\nFrom site 9 to site 14: walking distance 65.\nFrom site 9 to site 15: walking distance 58.\nFrom site 9 to site 16: walking distance 73.\nFrom site 9 to site 17: walking distance 75.\nFrom site 10 to site 0: walking distance 70.\nFrom site 10 to site 1: walking distance 50.\nFrom site 10 to site 2: walking distance 53.\nFrom site 10 to site 3: walking distance 37.\nFrom site 10 to site 4: walking distance 48.\nFrom site 10 to site 5: walking distance 51.\nFrom site 10 to site 6: walking distance 53.\nFrom site 10 to site 7: walking distance 61.\nFrom site 10 to site 8: walking distance 51.\nFrom site 10 to site 9: walking distance 56.\nFrom site 10 to site 11: walking distance 42.\nFrom site 10 to site 12: walking distance 51.\nFrom site 10 to site 13: walking distance 21.\nFrom site 10 to site 14: walking distance 50.\nFrom site 10 to site 15: walking distance 34.\nFrom site 10 to site 16: walking distance 50.\nFrom site 10 to site 17: walking distance 52.\nFrom site 11 to site 0: walking distance 49.\nFrom site 11 to site 1: walking distance 29.\nFrom site 11 to site 2: walking distance 50.\nFrom site 11 to site 3: walking distance 45.\nFrom site 11 to site 4: walking distance 34.\nFrom site 11 to site 5: walking distance 49.\nFrom site 11 to site 6: walking distance 51.\nFrom site 11 to site 7: walking distance 59.\nFrom site 11 to site 8: walking distance 42.\nFrom site 11 to site 9: walking distance 47.\nFrom site 11 to site 10: walking distance 42.\nFrom site 11 to site 12: walking distance 40.\nFrom site 11 to site 13: walking distance 47.\nFrom site 11 to site 14: walking distance 56.\nFrom site 11 to site 15: walking distance 26.\nFrom site 11 to site 16: walking distance 38.\nFrom site 11 to site 17: walking distance 43.\nFrom site 12 to site 0: walking distance 49.\nFrom site 12 to site 1: walking distance 29.\nFrom site 12 to site 2: walking distance 53.\nFrom site 12 to site 3: walking distance 42.\nFrom site 12 to site 4: walking distance 23.\nFrom site 12 to site 5: walking distance 50.\nFrom site 12 to site 6: walking distance 61.\nFrom site 12 to site 7: walking distance 26.\nFrom site 12 to site 8: walking distance 57.\nFrom site 12 to site 9: walking distance 59.\nFrom site 12 to site 10: walking distance 51.\nFrom site 12 to site 11: walking distance 40.\nFrom site 12 to site 13: walking distance 56.\nFrom site 12 to site 14: walking distance 60.\nFrom site 12 to site 15: walking distance 46.\nFrom site 12 to site 16: walking distance 38.\nFrom site 12 to site 17: walking distance 67.\nFrom site 13 to site 0: walking distance 56.\nFrom site 13 to site 1: walking distance 60.\nFrom site 13 to site 2: walking distance 58.\nFrom site 13 to site 3: walking distance 43.\nFrom site 13 to site 4: walking distance 49.\nFrom site 13 to site 5: walking distance 49.\nFrom site 13 to site 6: walking distance 45.\nFrom site 13 to site 7: walking distance 42.\nFrom site 13 to site 8: walking distance 45.\nFrom site 13 to site 9: walking distance 44.\nFrom site 13 to site 10: walking distance 21.\nFrom site 13 to site 11: walking distance 47.\nFrom site 13 to site 12: walking distance 56.\nFrom site 13 to site 14: walking distance 54.\nFrom site 13 to site 15: walking distance 53.\nFrom site 13 to site 16: walking distance 69.\nFrom site 13 to site 17: walking distance 61.\nFrom site 14 to site 0: walking distance 77.\nFrom site 14 to site 1: walking distance 69.\nFrom site 14 to site 2: walking distance 32.\nFrom site 14 to site 3: walking distance 57.\nFrom site 14 to site 4: walking distance 58.\nFrom site 14 to site 5: walking distance 56.\nFrom site 14 to site 6: walking distance 54.\nFrom site 14 to site 7: walking distance 58.\nFrom site 14 to site 8: walking distance 56.\nFrom site 14 to site 9: walking distance 65.\nFrom site 14 to site 10: walking distance 50.\nFrom site 14 to site 11: walking distance 56.\nFrom site 14 to site 12: walking distance 60.\nFrom site 14 to site 13: walking distance 54.\nFrom site 14 to site 15: walking distance 62.\nFrom site 14 to site 16: walking distance 70.\nFrom site 14 to site 17: walking distance 63.\nFrom site 15 to site 0: walking distance 55.\nFrom site 15 to site 1: walking distance 35.\nFrom site 15 to site 2: walking distance 52.\nFrom site 15 to site 3: walking distance 19.\nFrom site 15 to site 4: walking distance 23.\nFrom site 15 to site 5: walking distance 23.\nFrom site 15 to site 6: walking distance 25.\nFrom site 15 to site 7: walking distance 43.\nFrom site 15 to site 8: walking distance 54.\nFrom site 15 to site 9: walking distance 58.\nFrom site 15 to site 10: walking distance 34.\nFrom site 15 to site 11: walking distance 26.\nFrom site 15 to site 12: walking distance 46.\nFrom site 15 to site 13: walking distance 53.\nFrom site 15 to site 14: walking distance 62.\nFrom site 15 to site 16: walking distance 22.\nFrom site 15 to site 17: walking distance 53.\nFrom site 16 to site 0: walking distance 47.\nFrom site 16 to site 1: walking distance 27.\nFrom site 16 to site 2: walking distance 60.\nFrom site 16 to site 3: walking distance 41.\nFrom site 16 to site 4: walking distance 35.\nFrom site 16 to site 5: walking distance 45.\nFrom site 16 to site 6: walking distance 47.\nFrom site 16 to site 7: walking distance 64.\nFrom site 16 to site 8: walking distance 60.\nFrom site 16 to site 9: walking distance 73.\nFrom site 16 to site 10: walking distance 50.\nFrom site 16 to site 11: walking distance 38.\nFrom site 16 to site 12: walking distance 38.\nFrom site 16 to site 13: walking distance 69.\nFrom site 16 to site 14: walking distance 70.\nFrom site 16 to site 15: walking distance 22.\nFrom site 16 to site 17: walking distance 67.\nFrom site 17 to site 0: walking distance 44.\nFrom site 17 to site 1: walking distance 58.\nFrom site 17 to site 2: walking distance 31.\nFrom site 17 to site 3: walking distance 70.\nFrom site 17 to site 4: walking distance 64.\nFrom site 17 to site 5: walking distance 58.\nFrom site 17 to site 6: walking distance 46.\nFrom site 17 to site 7: walking distance 78.\nFrom site 17 to site 8: walking distance 23.\nFrom site 17 to site 9: walking distance 75.\nFrom site 17 to site 10: walking distance 52.\nFrom site 17 to site 11: walking distance 43.\nFrom site 17 to site 12: walking distance 67.\nFrom site 17 to site 13: walking distance 61.\nFrom site 17 to site 14: walking distance 63.\nFrom site 17 to site 15: walking distance 53.\nFrom site 17 to site 16: walking distance 67.\nUse these distances to assign every campsite to one staffed booth so your chosen 4 booths minimize total walking.\n\nJust so we're on the same page, please return your answer in this little JSON shape — it's just a compact way to say which spots we open and where each campsite should go.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of staffed info points you decide to open, and \"assignments\" as, for each campsite in the original list (in that same order), the open site it gets sent to. This is only a sketch of the expected shape — not the real solution itself.\n\nOne important note: every identifier you put in here must exactly match the identifiers used in the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 20, 51, 65, 46, 47, 66, 73, 27, 84, 70, 49, 49, 56, 77, 55, 47, 44 ], [ 20, 0, 60, 45, 26, 27, 52, 53, 47, 64, 50, 29, 29, 60, 69, 35, 27, 58 ], [ 51, 60, 0, 70, 59, 33, 29, 51, 30, 69, 53, 50, 53, 58, 32, 52, 60, 31 ], [ 65, 45, 70, 0, 39, 42, 44, 62, 51, 62, 37, 45, 42, 43, 57, 19, 41, 70 ], [ 46, 26, 59, 39, 0, 40, 42, 49, 64, 49, 48, 34, 23, 49, 58, 23, 35, 64 ], [ 47, 27, 33, 42, 40, 0, 27, 26, 51, 62, 51, 49, 50, 49, 56, 23, 45, 58 ], [ 66, 52, 29, 44, 42, 27, 0, 53, 45, 55, 53, 51, 61, 45, 54, 25, 47, 46 ], [ 73, 53, 51, 62, 49, 26, 53, 0, 71, 57, 61, 59, 26, 42, 58, 43, 64, 78 ], [ 27, 47, 30, 51, 64, 51, 45, 71, 0, 74, 51, 42, 57, 45, 56, 54, 60, 23 ], [ 84, 64, 69, 62, 49, 62, 55, 57, 74, 0, 56, 47, 59, 44, 65, 58, 73, 75 ], [ 70, 50, 53, 37, 48, 51, 53, 61, 51, 56, 0, 42, 51, 21, 50, 34, 50, 52 ], [ 49, 29, 50, 45, 34, 49, 51, 59, 42, 47, 42, 0, 40, 47, 56, 26, 38, 43 ], [ 49, 29, 53, 42, 23, 50, 61, 26, 57, 59, 51, 40, 0, 56, 60, 46, 38, 67 ], [ 56, 60, 58, 43, 49, 49, 45, 42, 45, 44, 21, 47, 56, 0, 54, 53, 69, 61 ], [ 77, 69, 32, 57, 58, 56, 54, 58, 56, 65, 50, 56, 60, 54, 0, 62, 70, 63 ], [ 55, 35, 52, 19, 23, 23, 25, 43, 54, 58, 34, 26, 46, 53, 62, 0, 22, 53 ], [ 47, 27, 60, 41, 35, 45, 47, 64, 60, 73, 50, 38, 38, 69, 70, 22, 0, 67 ], [ 44, 58, 31, 70, 64, 58, 46, 78, 23, 75, 52, 43, 67, 61, 63, 53, 67, 0 ] ], "p": 4, "objective": 387.0 }, "solution": { "facilities": [ 1, 2, 13, 15 ], "assignments": [ 1, 1, 2, 15, 15, 15, 15, 13, 2, 13, 13, 15, 1, 13, 2, 15, 15, 2 ] }, "obj": 387.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 4, "sites": [ { "id": 0, "distances": { "0": 0, "1": 20, "2": 51, "3": 65, "4": 46, "5": 47, "6": 66, "7": 73, "8": 27, "9": 84, "10": 70, "11": 49, "12": 49, "13": 56, "14": 77, "15": 55, "16": 47, "17": 44 } }, { "id": 1, "distances": { "0": 20, "1": 0, "2": 60, "3": 45, "4": 26, "5": 27, "6": 52, "7": 53, "8": 47, "9": 64, "10": 50, "11": 29, "12": 29, "13": 60, "14": 69, "15": 35, "16": 27, "17": 58 } }, { "id": 2, "distances": { "0": 51, "1": 60, "2": 0, "3": 70, "4": 59, "5": 33, "6": 29, "7": 51, "8": 30, "9": 69, "10": 53, "11": 50, "12": 53, "13": 58, "14": 32, "15": 52, "16": 60, "17": 31 } }, { "id": 3, "distances": { "0": 65, "1": 45, "2": 70, "3": 0, "4": 39, "5": 42, "6": 44, "7": 62, "8": 51, "9": 62, "10": 37, "11": 45, "12": 42, "13": 43, "14": 57, "15": 19, "16": 41, "17": 70 } }, { "id": 4, "distances": { "0": 46, "1": 26, "2": 59, "3": 39, "4": 0, "5": 40, "6": 42, "7": 49, "8": 64, "9": 49, "10": 48, "11": 34, "12": 23, "13": 49, "14": 58, "15": 23, "16": 35, "17": 64 } }, { "id": 5, "distances": { "0": 47, "1": 27, "2": 33, "3": 42, "4": 40, "5": 0, "6": 27, "7": 26, "8": 51, "9": 62, "10": 51, "11": 49, "12": 50, "13": 49, "14": 56, "15": 23, "16": 45, "17": 58 } }, { "id": 6, "distances": { "0": 66, "1": 52, "2": 29, "3": 44, "4": 42, "5": 27, "6": 0, "7": 53, "8": 45, "9": 55, "10": 53, "11": 51, "12": 61, "13": 45, "14": 54, "15": 25, "16": 47, "17": 46 } }, { "id": 7, "distances": { "0": 73, "1": 53, "2": 51, "3": 62, "4": 49, "5": 26, "6": 53, "7": 0, "8": 71, "9": 57, "10": 61, "11": 59, "12": 26, "13": 42, "14": 58, "15": 43, "16": 64, "17": 78 } }, { "id": 8, "distances": { "0": 27, "1": 47, "2": 30, "3": 51, "4": 64, "5": 51, "6": 45, "7": 71, "8": 0, "9": 74, "10": 51, "11": 42, "12": 57, "13": 45, "14": 56, "15": 54, "16": 60, "17": 23 } }, { "id": 9, "distances": { "0": 84, "1": 64, "2": 69, "3": 62, "4": 49, "5": 62, "6": 55, "7": 57, "8": 74, "9": 0, "10": 56, "11": 47, "12": 59, "13": 44, "14": 65, "15": 58, "16": 73, "17": 75 } }, { "id": 10, "distances": { "0": 70, "1": 50, "2": 53, "3": 37, "4": 48, "5": 51, "6": 53, "7": 61, "8": 51, "9": 56, "10": 0, "11": 42, "12": 51, "13": 21, "14": 50, "15": 34, "16": 50, "17": 52 } }, { "id": 11, "distances": { "0": 49, "1": 29, "2": 50, "3": 45, "4": 34, "5": 49, "6": 51, "7": 59, "8": 42, "9": 47, "10": 42, "11": 0, "12": 40, "13": 47, "14": 56, "15": 26, "16": 38, "17": 43 } }, { "id": 12, "distances": { "0": 49, "1": 29, "2": 53, "3": 42, "4": 23, "5": 50, "6": 61, "7": 26, "8": 57, "9": 59, "10": 51, "11": 40, "12": 0, "13": 56, "14": 60, "15": 46, "16": 38, "17": 67 } }, { "id": 13, "distances": { "0": 56, "1": 60, "2": 58, "3": 43, "4": 49, "5": 49, "6": 45, "7": 42, "8": 45, "9": 44, "10": 21, "11": 47, "12": 56, "13": 0, "14": 54, "15": 53, "16": 69, "17": 61 } }, { "id": 14, "distances": { "0": 77, "1": 69, "2": 32, "3": 57, "4": 58, "5": 56, "6": 54, "7": 58, "8": 56, "9": 65, "10": 50, "11": 56, "12": 60, "13": 54, "14": 0, "15": 62, "16": 70, "17": 63 } }, { "id": 15, "distances": { "0": 55, "1": 35, "2": 52, "3": 19, "4": 23, "5": 23, "6": 25, "7": 43, "8": 54, "9": 58, "10": 34, "11": 26, "12": 46, "13": 53, "14": 62, "15": 0, "16": 22, "17": 53 } }, { "id": 16, "distances": { "0": 47, "1": 27, "2": 60, "3": 41, "4": 35, "5": 45, "6": 47, "7": 64, "8": 60, "9": 73, "10": 50, "11": 38, "12": 38, "13": 69, "14": 70, "15": 22, "16": 0, "17": 67 } }, { "id": 17, "distances": { "0": 44, "1": 58, "2": 31, "3": 70, "4": 64, "5": 58, "6": 46, "7": 78, "8": 23, "9": 75, "10": 52, "11": 43, "12": 67, "13": 61, "14": 63, "15": 53, "16": 67, "17": 0 } } ], "objective": 387.0 }, "solution_variant": { "selected": [ 1, 2, 13, 15 ], "assignments": [ 1, 1, 2, 15, 15, 15, 15, 13, 2, 13, 13, 15, 1, 13, 2, 15, 15, 2 ] }, "context_index": 8, "input_format": "nl", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Back when the planners drew the master plan they left a shortlist of possible dock sites and now must pick a limited number to actually build. Each residential cluster must be connected to one of the selected docks — one connection per cluster, no extras — and the goal is to keep residents’ trips short. Practically that means for any proposed set of docks you measure each cluster’s distance to its chosen dock, add up those distances, and prefer the arrangement with the smallest total. The detailed list of candidate sites, clusters, and distances is given below.\n\nIt contains 15 mapped locations, of which 3 docks must be opened; the location identifiers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.\nDistance between 0 and 1: 29.\nDistance between 0 and 2: 72.\nDistance between 0 and 3: 45.\nDistance between 0 and 4: 43.\nDistance between 0 and 5: 51.\nDistance between 0 and 6: 77.\nDistance between 0 and 7: 61.\nDistance between 0 and 8: 105.\nDistance between 0 and 9: 60.\nDistance between 0 and 10: 69.\nDistance between 0 and 11: 39.\nDistance between 0 and 12: 57.\nDistance between 0 and 13: 89.\nDistance between 0 and 14: 49.\nDistance between 1 and 0: 29.\nDistance between 1 and 2: 66.\nDistance between 1 and 3: 40.\nDistance between 1 and 4: 38.\nDistance between 1 and 5: 61.\nDistance between 1 and 6: 72.\nDistance between 1 and 7: 56.\nDistance between 1 and 8: 90.\nDistance between 1 and 9: 66.\nDistance between 1 and 10: 78.\nDistance between 1 and 11: 34.\nDistance between 1 and 12: 52.\nDistance between 1 and 13: 75.\nDistance between 1 and 14: 44.\nDistance between 2 and 0: 72.\nDistance between 2 and 1: 66.\nDistance between 2 and 3: 27.\nDistance between 2 and 4: 57.\nDistance between 2 and 5: 62.\nDistance between 2 and 6: 93.\nDistance between 2 and 7: 67.\nDistance between 2 and 8: 65.\nDistance between 2 and 9: 74.\nDistance between 2 and 10: 14.\nDistance between 2 and 11: 61.\nDistance between 2 and 12: 79.\nDistance between 2 and 13: 41.\nDistance between 2 and 14: 71.\nDistance between 3 and 0: 45.\nDistance between 3 and 1: 40.\nDistance between 3 and 2: 27.\nDistance between 3 and 4: 44.\nDistance between 3 and 5: 67.\nDistance between 3 and 6: 88.\nDistance between 3 and 7: 72.\nDistance between 3 and 8: 92.\nDistance between 3 and 9: 75.\nDistance between 3 and 10: 41.\nDistance between 3 and 11: 40.\nDistance between 3 and 12: 58.\nDistance between 3 and 13: 68.\nDistance between 3 and 14: 50.\nDistance between 4 and 0: 43.\nDistance between 4 and 1: 38.\nDistance between 4 and 2: 57.\nDistance between 4 and 3: 44.\nDistance between 4 and 5: 23.\nDistance between 4 and 6: 68.\nDistance between 4 and 7: 60.\nDistance between 4 and 8: 84.\nDistance between 4 and 9: 74.\nDistance between 4 and 10: 71.\nDistance between 4 and 11: 18.\nDistance between 4 and 12: 36.\nDistance between 4 and 13: 68.\nDistance between 4 and 14: 28.\nDistance between 5 and 0: 51.\nDistance between 5 and 1: 61.\nDistance between 5 and 2: 62.\nDistance between 5 and 3: 67.\nDistance between 5 and 4: 23.\nDistance between 5 and 6: 73.\nDistance between 5 and 7: 67.\nDistance between 5 and 8: 107.\nDistance between 5 and 9: 72.\nDistance between 5 and 10: 76.\nDistance between 5 and 11: 41.\nDistance between 5 and 12: 59.\nDistance between 5 and 13: 87.\nDistance between 5 and 14: 51.\nDistance between 6 and 0: 77.\nDistance between 6 and 1: 72.\nDistance between 6 and 2: 93.\nDistance between 6 and 3: 88.\nDistance between 6 and 4: 68.\nDistance between 6 and 5: 73.\nDistance between 6 and 7: 41.\nDistance between 6 and 8: 114.\nDistance between 6 and 9: 86.\nDistance between 6 and 10: 106.\nDistance between 6 and 11: 68.\nDistance between 6 and 12: 86.\nDistance between 6 and 13: 84.\nDistance between 6 and 14: 78.\nDistance between 7 and 0: 61.\nDistance between 7 and 1: 56.\nDistance between 7 and 2: 67.\nDistance between 7 and 3: 72.\nDistance between 7 and 4: 60.\nDistance between 7 and 5: 67.\nDistance between 7 and 6: 41.\nDistance between 7 and 8: 80.\nDistance between 7 and 9: 85.\nDistance between 7 and 10: 68.\nDistance between 7 and 11: 64.\nDistance between 7 and 12: 82.\nDistance between 7 and 13: 92.\nDistance between 7 and 14: 74.\nDistance between 8 and 0: 105.\nDistance between 8 and 1: 90.\nDistance between 8 and 2: 65.\nDistance between 8 and 3: 92.\nDistance between 8 and 4: 84.\nDistance between 8 and 5: 107.\nDistance between 8 and 6: 114.\nDistance between 8 and 7: 80.\nDistance between 8 and 9: 110.\nDistance between 8 and 10: 79.\nDistance between 8 and 11: 74.\nDistance between 8 and 12: 92.\nDistance between 8 and 13: 90.\nDistance between 8 and 14: 84.\nDistance between 9 and 0: 60.\nDistance between 9 and 1: 66.\nDistance between 9 and 2: 74.\nDistance between 9 and 3: 75.\nDistance between 9 and 4: 74.\nDistance between 9 and 5: 72.\nDistance between 9 and 6: 86.\nDistance between 9 and 7: 85.\nDistance between 9 and 8: 110.\nDistance between 9 and 10: 71.\nDistance between 9 and 11: 64.\nDistance between 9 and 12: 80.\nDistance between 9 and 13: 99.\nDistance between 9 and 14: 74.\nDistance between 10 and 0: 69.\nDistance between 10 and 1: 78.\nDistance between 10 and 2: 14.\nDistance between 10 and 3: 41.\nDistance between 10 and 4: 71.\nDistance between 10 and 5: 76.\nDistance between 10 and 6: 106.\nDistance between 10 and 7: 68.\nDistance between 10 and 8: 79.\nDistance between 10 and 9: 71.\nDistance between 10 and 11: 65.\nDistance between 10 and 12: 65.\nDistance between 10 and 13: 55.\nDistance between 10 and 14: 75.\nDistance between 11 and 0: 39.\nDistance between 11 and 1: 34.\nDistance between 11 and 2: 61.\nDistance between 11 and 3: 40.\nDistance between 11 and 4: 18.\nDistance between 11 and 5: 41.\nDistance between 11 and 6: 68.\nDistance between 11 and 7: 64.\nDistance between 11 and 8: 74.\nDistance between 11 and 9: 64.\nDistance between 11 and 10: 65.\nDistance between 11 and 12: 24.\nDistance between 11 and 13: 56.\nDistance between 11 and 14: 16.\nDistance between 12 and 0: 57.\nDistance between 12 and 1: 52.\nDistance between 12 and 2: 79.\nDistance between 12 and 3: 58.\nDistance between 12 and 4: 36.\nDistance between 12 and 5: 59.\nDistance between 12 and 6: 86.\nDistance between 12 and 7: 82.\nDistance between 12 and 8: 92.\nDistance between 12 and 9: 80.\nDistance between 12 and 10: 65.\nDistance between 12 and 11: 24.\nDistance between 12 and 13: 74.\nDistance between 12 and 14: 34.\nDistance between 13 and 0: 89.\nDistance between 13 and 1: 75.\nDistance between 13 and 2: 41.\nDistance between 13 and 3: 68.\nDistance between 13 and 4: 68.\nDistance between 13 and 5: 87.\nDistance between 13 and 6: 84.\nDistance between 13 and 7: 92.\nDistance between 13 and 8: 90.\nDistance between 13 and 9: 99.\nDistance between 13 and 10: 55.\nDistance between 13 and 11: 56.\nDistance between 13 and 12: 74.\nDistance between 13 and 14: 40.\nDistance between 14 and 0: 49.\nDistance between 14 and 1: 44.\nDistance between 14 and 2: 71.\nDistance between 14 and 3: 50.\nDistance between 14 and 4: 28.\nDistance between 14 and 5: 51.\nDistance between 14 and 6: 78.\nDistance between 14 and 7: 74.\nDistance between 14 and 8: 84.\nDistance between 14 and 9: 74.\nDistance between 14 and 10: 75.\nDistance between 14 and 11: 16.\nDistance between 14 and 12: 34.\nDistance between 14 and 13: 40.\nUse these records to assign each residential cluster to one open dock so the total travel distance is minimized.\n\nOh, and when you send the final answer, please follow this simple JSON layout so it's easy to check automatically:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of it like a little form: \"selected\" is the shortlist of docks you actually build, and \"assignments\" lists, for each residential cluster (in the same order as the instance input), which of those built docks it connects to. The placeholders are just showing the shape I expect — they aren't the real choices.\n\nPlease make sure to use the exact identifiers from the instance input (do not rename them or invent new ones).\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 29, 72, 45, 43, 51, 77, 61, 105, 60, 69, 39, 57, 89, 49 ], [ 29, 0, 66, 40, 38, 61, 72, 56, 90, 66, 78, 34, 52, 75, 44 ], [ 72, 66, 0, 27, 57, 62, 93, 67, 65, 74, 14, 61, 79, 41, 71 ], [ 45, 40, 27, 0, 44, 67, 88, 72, 92, 75, 41, 40, 58, 68, 50 ], [ 43, 38, 57, 44, 0, 23, 68, 60, 84, 74, 71, 18, 36, 68, 28 ], [ 51, 61, 62, 67, 23, 0, 73, 67, 107, 72, 76, 41, 59, 87, 51 ], [ 77, 72, 93, 88, 68, 73, 0, 41, 114, 86, 106, 68, 86, 84, 78 ], [ 61, 56, 67, 72, 60, 67, 41, 0, 80, 85, 68, 64, 82, 92, 74 ], [ 105, 90, 65, 92, 84, 107, 114, 80, 0, 110, 79, 74, 92, 90, 84 ], [ 60, 66, 74, 75, 74, 72, 86, 85, 110, 0, 71, 64, 80, 99, 74 ], [ 69, 78, 14, 41, 71, 76, 106, 68, 79, 71, 0, 65, 65, 55, 75 ], [ 39, 34, 61, 40, 18, 41, 68, 64, 74, 64, 65, 0, 24, 56, 16 ], [ 57, 52, 79, 58, 36, 59, 86, 82, 92, 80, 65, 24, 0, 74, 34 ], [ 89, 75, 41, 68, 68, 87, 84, 92, 90, 99, 55, 56, 74, 0, 40 ], [ 49, 44, 71, 50, 28, 51, 78, 74, 84, 74, 75, 16, 34, 40, 0 ] ], "p": 3, "objective": 424.0 }, "solution": { "facilities": [ 2, 7, 11 ], "assignments": [ 11, 11, 2, 2, 11, 11, 7, 7, 2, 11, 2, 11, 11, 2, 11 ] }, "obj": 424.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 15, "num_open": 3, "sites": [ { "id": 0, "distances": { "0": 0, "1": 29, "2": 72, "3": 45, "4": 43, "5": 51, "6": 77, "7": 61, "8": 105, "9": 60, "10": 69, "11": 39, "12": 57, "13": 89, "14": 49 } }, { "id": 1, "distances": { "0": 29, "1": 0, "2": 66, "3": 40, "4": 38, "5": 61, "6": 72, "7": 56, "8": 90, "9": 66, "10": 78, "11": 34, "12": 52, "13": 75, "14": 44 } }, { "id": 2, "distances": { "0": 72, "1": 66, "2": 0, "3": 27, "4": 57, "5": 62, "6": 93, "7": 67, "8": 65, "9": 74, "10": 14, "11": 61, "12": 79, "13": 41, "14": 71 } }, { "id": 3, "distances": { "0": 45, "1": 40, "2": 27, "3": 0, "4": 44, "5": 67, "6": 88, "7": 72, "8": 92, "9": 75, "10": 41, "11": 40, "12": 58, "13": 68, "14": 50 } }, { "id": 4, "distances": { "0": 43, "1": 38, "2": 57, "3": 44, "4": 0, "5": 23, "6": 68, "7": 60, "8": 84, "9": 74, "10": 71, "11": 18, "12": 36, "13": 68, "14": 28 } }, { "id": 5, "distances": { "0": 51, "1": 61, "2": 62, "3": 67, "4": 23, "5": 0, "6": 73, "7": 67, "8": 107, "9": 72, "10": 76, "11": 41, "12": 59, "13": 87, "14": 51 } }, { "id": 6, "distances": { "0": 77, "1": 72, "2": 93, "3": 88, "4": 68, "5": 73, "6": 0, "7": 41, "8": 114, "9": 86, "10": 106, "11": 68, "12": 86, "13": 84, "14": 78 } }, { "id": 7, "distances": { "0": 61, "1": 56, "2": 67, "3": 72, "4": 60, "5": 67, "6": 41, "7": 0, "8": 80, "9": 85, "10": 68, "11": 64, "12": 82, "13": 92, "14": 74 } }, { "id": 8, "distances": { "0": 105, "1": 90, "2": 65, "3": 92, "4": 84, "5": 107, "6": 114, "7": 80, "8": 0, "9": 110, "10": 79, "11": 74, "12": 92, "13": 90, "14": 84 } }, { "id": 9, "distances": { "0": 60, "1": 66, "2": 74, "3": 75, "4": 74, "5": 72, "6": 86, "7": 85, "8": 110, "9": 0, "10": 71, "11": 64, "12": 80, "13": 99, "14": 74 } }, { "id": 10, "distances": { "0": 69, "1": 78, "2": 14, "3": 41, "4": 71, "5": 76, "6": 106, "7": 68, "8": 79, "9": 71, "10": 0, "11": 65, "12": 65, "13": 55, "14": 75 } }, { "id": 11, "distances": { "0": 39, "1": 34, "2": 61, "3": 40, "4": 18, "5": 41, "6": 68, "7": 64, "8": 74, "9": 64, "10": 65, "11": 0, "12": 24, "13": 56, "14": 16 } }, { "id": 12, "distances": { "0": 57, "1": 52, "2": 79, "3": 58, "4": 36, "5": 59, "6": 86, "7": 82, "8": 92, "9": 80, "10": 65, "11": 24, "12": 0, "13": 74, "14": 34 } }, { "id": 13, "distances": { "0": 89, "1": 75, "2": 41, "3": 68, "4": 68, "5": 87, "6": 84, "7": 92, "8": 90, "9": 99, "10": 55, "11": 56, "12": 74, "13": 0, "14": 40 } }, { "id": 14, "distances": { "0": 49, "1": 44, "2": 71, "3": 50, "4": 28, "5": 51, "6": 78, "7": 74, "8": 84, "9": 74, "10": 75, "11": 16, "12": 34, "13": 40, "14": 0 } } ], "objective": 424.0 }, "solution_variant": { "selected": [ 2, 7, 11 ], "assignments": [ 11, 11, 2, 2, 11, 11, 7, 7, 2, 11, 2, 11, 11, 2, 11 ] }, "context_index": 9, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "We’re sorting out which mailboxes to keep on our routes, but there’s a limit on how many can stay open. From the candidate locations, a fixed number will be kept, and every delivery neighborhood must be linked to one of those kept boxes — one link per neighborhood, exactly. The goal is simple in everyday terms: make the total walking distance for everyone as low as possible by summing each neighborhood’s distance to its chosen mailbox and choosing the arrangement with the lowest sum. The specific mailbox options and distance details are listed below.\n\nThere are 18 candidate mailbox posts; we must keep 6 open, chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.\nFor delivery neighborhood 1, we measure a walking distance of 36 to mailbox 2.\nFor delivery neighborhood 1, we measure a walking distance of 36 to mailbox 3.\nFor delivery neighborhood 1, we measure a walking distance of 35 to mailbox 4.\nFor delivery neighborhood 1, we measure a walking distance of 27 to mailbox 5.\nFor delivery neighborhood 1, we measure a walking distance of 35 to mailbox 6.\nFor delivery neighborhood 1, we measure a walking distance of 39 to mailbox 7.\nFor delivery neighborhood 1, we measure a walking distance of 34 to mailbox 8.\nFor delivery neighborhood 1, we measure a walking distance of 34 to mailbox 9.\nFor delivery neighborhood 1, we measure a walking distance of 42 to mailbox 10.\nFor delivery neighborhood 1, we measure a walking distance of 39 to mailbox 11.\nFor delivery neighborhood 1, we measure a walking distance of 33 to mailbox 12.\nFor delivery neighborhood 1, we measure a walking distance of 34 to mailbox 13.\nFor delivery neighborhood 1, we measure a walking distance of 34 to mailbox 14.\nFor delivery neighborhood 1, we measure a walking distance of 22 to mailbox 15.\nFor delivery neighborhood 1, we measure a walking distance of 45 to mailbox 16.\nFor delivery neighborhood 1, we measure a walking distance of 55 to mailbox 17.\nFor delivery neighborhood 1, we measure a walking distance of 46 to mailbox 18.\nFor delivery neighborhood 2, we measure a walking distance of 36 to mailbox 1.\nFor delivery neighborhood 2, we measure a walking distance of 29 to mailbox 3.\nFor delivery neighborhood 2, we measure a walking distance of 23 to mailbox 4.\nFor delivery neighborhood 2, we measure a walking distance of 19 to mailbox 5.\nFor delivery neighborhood 2, we measure a walking distance of 16 to mailbox 6.\nFor delivery neighborhood 2, we measure a walking distance of 37 to mailbox 7.\nFor delivery neighborhood 2, we measure a walking distance of 18 to mailbox 8.\nFor delivery neighborhood 2, we measure a walking distance of 40 to mailbox 9.\nFor delivery neighborhood 2, we measure a walking distance of 28 to mailbox 10.\nFor delivery neighborhood 2, we measure a walking distance of 14 to mailbox 11.\nFor delivery neighborhood 2, we measure a walking distance of 15 to mailbox 12.\nFor delivery neighborhood 2, we measure a walking distance of 34 to mailbox 13.\nFor delivery neighborhood 2, we measure a walking distance of 27 to mailbox 14.\nFor delivery neighborhood 2, we measure a walking distance of 28 to mailbox 15.\nFor delivery neighborhood 2, we measure a walking distance of 36 to mailbox 16.\nFor delivery neighborhood 2, we measure a walking distance of 34 to mailbox 17.\nFor delivery neighborhood 2, we measure a walking distance of 40 to mailbox 18.\nFor delivery neighborhood 3, we measure a walking distance of 36 to mailbox 1.\nFor delivery neighborhood 3, we measure a walking distance of 29 to mailbox 2.\nFor delivery neighborhood 3, we measure a walking distance of 28 to mailbox 4.\nFor delivery neighborhood 3, we measure a walking distance of 22 to mailbox 5.\nFor delivery neighborhood 3, we measure a walking distance of 25 to mailbox 6.\nFor delivery neighborhood 3, we measure a walking distance of 43 to mailbox 7.\nFor delivery neighborhood 3, we measure a walking distance of 34 to mailbox 8.\nFor delivery neighborhood 3, we measure a walking distance of 37 to mailbox 9.\nFor delivery neighborhood 3, we measure a walking distance of 24 to mailbox 10.\nFor delivery neighborhood 3, we measure a walking distance of 29 to mailbox 11.\nFor delivery neighborhood 3, we measure a walking distance of 16 to mailbox 12.\nFor delivery neighborhood 3, we measure a walking distance of 39 to mailbox 13.\nFor delivery neighborhood 3, we measure a walking distance of 41 to mailbox 14.\nFor delivery neighborhood 3, we measure a walking distance of 22 to mailbox 15.\nFor delivery neighborhood 3, we measure a walking distance of 37 to mailbox 16.\nFor delivery neighborhood 3, we measure a walking distance of 52 to mailbox 17.\nFor delivery neighborhood 3, we measure a walking distance of 39 to mailbox 18.\nFor delivery neighborhood 4, we measure a walking distance of 35 to mailbox 1.\nFor delivery neighborhood 4, we measure a walking distance of 23 to mailbox 2.\nFor delivery neighborhood 4, we measure a walking distance of 28 to mailbox 3.\nFor delivery neighborhood 4, we measure a walking distance of 27 to mailbox 5.\nFor delivery neighborhood 4, we measure a walking distance of 24 to mailbox 6.\nFor delivery neighborhood 4, we measure a walking distance of 44 to mailbox 7.\nFor delivery neighborhood 4, we measure a walking distance of 32 to mailbox 8.\nFor delivery neighborhood 4, we measure a walking distance of 45 to mailbox 9.\nFor delivery neighborhood 4, we measure a walking distance of 34 to mailbox 10.\nFor delivery neighborhood 4, we measure a walking distance of 25 to mailbox 11.\nFor delivery neighborhood 4, we measure a walking distance of 12 to mailbox 12.\nFor delivery neighborhood 4, we measure a walking distance of 31 to mailbox 13.\nFor delivery neighborhood 4, we measure a walking distance of 44 to mailbox 14.\nFor delivery neighborhood 4, we measure a walking distance of 41 to mailbox 15.\nFor delivery neighborhood 4, we measure a walking distance of 23 to mailbox 16.\nFor delivery neighborhood 4, we measure a walking distance of 41 to mailbox 17.\nFor delivery neighborhood 4, we measure a walking distance of 42 to mailbox 18.\nFor delivery neighborhood 5, we measure a walking distance of 27 to mailbox 1.\nFor delivery neighborhood 5, we measure a walking distance of 19 to mailbox 2.\nFor delivery neighborhood 5, we measure a walking distance of 22 to mailbox 3.\nFor delivery neighborhood 5, we measure a walking distance of 27 to mailbox 4.\nFor delivery neighborhood 5, we measure a walking distance of 21 to mailbox 6.\nFor delivery neighborhood 5, we measure a walking distance of 23 to mailbox 7.\nFor delivery neighborhood 5, we measure a walking distance of 27 to mailbox 8.\nFor delivery neighborhood 5, we measure a walking distance of 36 to mailbox 9.\nFor delivery neighborhood 5, we measure a walking distance of 33 to mailbox 10.\nFor delivery neighborhood 5, we measure a walking distance of 25 to mailbox 11.\nFor delivery neighborhood 5, we measure a walking distance of 17 to mailbox 12.\nFor delivery neighborhood 5, we measure a walking distance of 39 to mailbox 13.\nFor delivery neighborhood 5, we measure a walking distance of 29 to mailbox 14.\nFor delivery neighborhood 5, we measure a walking distance of 20 to mailbox 15.\nFor delivery neighborhood 5, we measure a walking distance of 34 to mailbox 16.\nFor delivery neighborhood 5, we measure a walking distance of 47 to mailbox 17.\nFor delivery neighborhood 5, we measure a walking distance of 31 to mailbox 18.\nFor delivery neighborhood 6, we measure a walking distance of 35 to mailbox 1.\nFor delivery neighborhood 6, we measure a walking distance of 16 to mailbox 2.\nFor delivery neighborhood 6, we measure a walking distance of 25 to mailbox 3.\nFor delivery neighborhood 6, we measure a walking distance of 24 to mailbox 4.\nFor delivery neighborhood 6, we measure a walking distance of 21 to mailbox 5.\nFor delivery neighborhood 6, we measure a walking distance of 39 to mailbox 7.\nFor delivery neighborhood 6, we measure a walking distance of 22 to mailbox 8.\nFor delivery neighborhood 6, we measure a walking distance of 36 to mailbox 9.\nFor delivery neighborhood 6, we measure a walking distance of 28 to mailbox 10.\nFor delivery neighborhood 6, we measure a walking distance of 14 to mailbox 11.\nFor delivery neighborhood 6, we measure a walking distance of 15 to mailbox 12.\nFor delivery neighborhood 6, we measure a walking distance of 42 to mailbox 13.\nFor delivery neighborhood 6, we measure a walking distance of 37 to mailbox 14.\nFor delivery neighborhood 6, we measure a walking distance of 37 to mailbox 15.\nFor delivery neighborhood 6, we measure a walking distance of 35 to mailbox 16.\nFor delivery neighborhood 6, we measure a walking distance of 36 to mailbox 17.\nFor delivery neighborhood 6, we measure a walking distance of 34 to mailbox 18.\nFor delivery neighborhood 7, we measure a walking distance of 39 to mailbox 1.\nFor delivery neighborhood 7, we measure a walking distance of 37 to mailbox 2.\nFor delivery neighborhood 7, we measure a walking distance of 43 to mailbox 3.\nFor delivery neighborhood 7, we measure a walking distance of 44 to mailbox 4.\nFor delivery neighborhood 7, we measure a walking distance of 23 to mailbox 5.\nFor delivery neighborhood 7, we measure a walking distance of 39 to mailbox 6.\nFor delivery neighborhood 7, we measure a walking distance of 29 to mailbox 8.\nFor delivery neighborhood 7, we measure a walking distance of 48 to mailbox 9.\nFor delivery neighborhood 7, we measure a walking distance of 41 to mailbox 10.\nFor delivery neighborhood 7, we measure a walking distance of 44 to mailbox 11.\nFor delivery neighborhood 7, we measure a walking distance of 40 to mailbox 12.\nFor delivery neighborhood 7, we measure a walking distance of 49 to mailbox 13.\nFor delivery neighborhood 7, we measure a walking distance of 33 to mailbox 14.\nFor delivery neighborhood 7, we measure a walking distance of 32 to mailbox 15.\nFor delivery neighborhood 7, we measure a walking distance of 48 to mailbox 16.\nFor delivery neighborhood 7, we measure a walking distance of 65 to mailbox 17.\nFor delivery neighborhood 7, we measure a walking distance of 45 to mailbox 18.\nFor delivery neighborhood 8, we measure a walking distance of 34 to mailbox 1.\nFor delivery neighborhood 8, we measure a walking distance of 18 to mailbox 2.\nFor delivery neighborhood 8, we measure a walking distance of 34 to mailbox 3.\nFor delivery neighborhood 8, we measure a walking distance of 32 to mailbox 4.\nFor delivery neighborhood 8, we measure a walking distance of 27 to mailbox 5.\nFor delivery neighborhood 8, we measure a walking distance of 22 to mailbox 6.\nFor delivery neighborhood 8, we measure a walking distance of 29 to mailbox 7.\nFor delivery neighborhood 8, we measure a walking distance of 48 to mailbox 9.\nFor delivery neighborhood 8, we measure a walking distance of 32 to mailbox 10.\nFor delivery neighborhood 8, we measure a walking distance of 22 to mailbox 11.\nFor delivery neighborhood 8, we measure a walking distance of 23 to mailbox 12.\nFor delivery neighborhood 8, we measure a walking distance of 27 to mailbox 13.\nFor delivery neighborhood 8, we measure a walking distance of 35 to mailbox 14.\nFor delivery neighborhood 8, we measure a walking distance of 36 to mailbox 15.\nFor delivery neighborhood 8, we measure a walking distance of 36 to mailbox 16.\nFor delivery neighborhood 8, we measure a walking distance of 44 to mailbox 17.\nFor delivery neighborhood 8, we measure a walking distance of 35 to mailbox 18.\nFor delivery neighborhood 9, we measure a walking distance of 34 to mailbox 1.\nFor delivery neighborhood 9, we measure a walking distance of 40 to mailbox 2.\nFor delivery neighborhood 9, we measure a walking distance of 37 to mailbox 3.\nFor delivery neighborhood 9, we measure a walking distance of 45 to mailbox 4.\nFor delivery neighborhood 9, we measure a walking distance of 36 to mailbox 5.\nFor delivery neighborhood 9, we measure a walking distance of 36 to mailbox 6.\nFor delivery neighborhood 9, we measure a walking distance of 48 to mailbox 7.\nFor delivery neighborhood 9, we measure a walking distance of 48 to mailbox 8.\nFor delivery neighborhood 9, we measure a walking distance of 42 to mailbox 10.\nFor delivery neighborhood 9, we measure a walking distance of 46 to mailbox 11.\nFor delivery neighborhood 9, we measure a walking distance of 39 to mailbox 12.\nFor delivery neighborhood 9, we measure a walking distance of 42 to mailbox 13.\nFor delivery neighborhood 9, we measure a walking distance of 43 to mailbox 14.\nFor delivery neighborhood 9, we measure a walking distance of 24 to mailbox 15.\nFor delivery neighborhood 9, we measure a walking distance of 42 to mailbox 16.\nFor delivery neighborhood 9, we measure a walking distance of 60 to mailbox 17.\nFor delivery neighborhood 9, we measure a walking distance of 45 to mailbox 18.\nFor delivery neighborhood 10, we measure a walking distance of 42 to mailbox 1.\nFor delivery neighborhood 10, we measure a walking distance of 28 to mailbox 2.\nFor delivery neighborhood 10, we measure a walking distance of 24 to mailbox 3.\nFor delivery neighborhood 10, we measure a walking distance of 34 to mailbox 4.\nFor delivery neighborhood 10, we measure a walking distance of 33 to mailbox 5.\nFor delivery neighborhood 10, we measure a walking distance of 28 to mailbox 6.\nFor delivery neighborhood 10, we measure a walking distance of 41 to mailbox 7.\nFor delivery neighborhood 10, we measure a walking distance of 32 to mailbox 8.\nFor delivery neighborhood 10, we measure a walking distance of 42 to mailbox 9.\nFor delivery neighborhood 10, we measure a walking distance of 16 to mailbox 11.\nFor delivery neighborhood 10, we measure a walking distance of 27 to mailbox 12.\nFor delivery neighborhood 10, we measure a walking distance of 43 to mailbox 13.\nFor delivery neighborhood 10, we measure a walking distance of 36 to mailbox 14.\nFor delivery neighborhood 10, we measure a walking distance of 35 to mailbox 15.\nFor delivery neighborhood 10, we measure a walking distance of 38 to mailbox 16.\nFor delivery neighborhood 10, we measure a walking distance of 49 to mailbox 17.\nFor delivery neighborhood 10, we measure a walking distance of 22 to mailbox 18.\nFor delivery neighborhood 11, we measure a walking distance of 39 to mailbox 1.\nFor delivery neighborhood 11, we measure a walking distance of 14 to mailbox 2.\nFor delivery neighborhood 11, we measure a walking distance of 29 to mailbox 3.\nFor delivery neighborhood 11, we measure a walking distance of 25 to mailbox 4.\nFor delivery neighborhood 11, we measure a walking distance of 25 to mailbox 5.\nFor delivery neighborhood 11, we measure a walking distance of 14 to mailbox 6.\nFor delivery neighborhood 11, we measure a walking distance of 44 to mailbox 7.\nFor delivery neighborhood 11, we measure a walking distance of 22 to mailbox 8.\nFor delivery neighborhood 11, we measure a walking distance of 46 to mailbox 9.\nFor delivery neighborhood 11, we measure a walking distance of 16 to mailbox 10.\nFor delivery neighborhood 11, we measure a walking distance of 13 to mailbox 12.\nFor delivery neighborhood 11, we measure a walking distance of 40 to mailbox 13.\nFor delivery neighborhood 11, we measure a walking distance of 35 to mailbox 14.\nFor delivery neighborhood 11, we measure a walking distance of 36 to mailbox 15.\nFor delivery neighborhood 11, we measure a walking distance of 34 to mailbox 16.\nFor delivery neighborhood 11, we measure a walking distance of 42 to mailbox 17.\nFor delivery neighborhood 11, we measure a walking distance of 36 to mailbox 18.\nFor delivery neighborhood 12, we measure a walking distance of 33 to mailbox 1.\nFor delivery neighborhood 12, we measure a walking distance of 15 to mailbox 2.\nFor delivery neighborhood 12, we measure a walking distance of 16 to mailbox 3.\nFor delivery neighborhood 12, we measure a walking distance of 12 to mailbox 4.\nFor delivery neighborhood 12, we measure a walking distance of 17 to mailbox 5.\nFor delivery neighborhood 12, we measure a walking distance of 15 to mailbox 6.\nFor delivery neighborhood 12, we measure a walking distance of 40 to mailbox 7.\nFor delivery neighborhood 12, we measure a walking distance of 23 to mailbox 8.\nFor delivery neighborhood 12, we measure a walking distance of 39 to mailbox 9.\nFor delivery neighborhood 12, we measure a walking distance of 27 to mailbox 10.\nFor delivery neighborhood 12, we measure a walking distance of 13 to mailbox 11.\nFor delivery neighborhood 12, we measure a walking distance of 32 to mailbox 13.\nFor delivery neighborhood 12, we measure a walking distance of 36 to mailbox 14.\nFor delivery neighborhood 12, we measure a walking distance of 31 to mailbox 15.\nFor delivery neighborhood 12, we measure a walking distance of 21 to mailbox 16.\nFor delivery neighborhood 12, we measure a walking distance of 39 to mailbox 17.\nFor delivery neighborhood 12, we measure a walking distance of 30 to mailbox 18.\nFor delivery neighborhood 13, we measure a walking distance of 34 to mailbox 1.\nFor delivery neighborhood 13, we measure a walking distance of 34 to mailbox 2.\nFor delivery neighborhood 13, we measure a walking distance of 39 to mailbox 3.\nFor delivery neighborhood 13, we measure a walking distance of 31 to mailbox 4.\nFor delivery neighborhood 13, we measure a walking distance of 39 to mailbox 5.\nFor delivery neighborhood 13, we measure a walking distance of 42 to mailbox 6.\nFor delivery neighborhood 13, we measure a walking distance of 49 to mailbox 7.\nFor delivery neighborhood 13, we measure a walking distance of 27 to mailbox 8.\nFor delivery neighborhood 13, we measure a walking distance of 42 to mailbox 9.\nFor delivery neighborhood 13, we measure a walking distance of 43 to mailbox 10.\nFor delivery neighborhood 13, we measure a walking distance of 40 to mailbox 11.\nFor delivery neighborhood 13, we measure a walking distance of 32 to mailbox 12.\nFor delivery neighborhood 13, we measure a walking distance of 55 to mailbox 14.\nFor delivery neighborhood 13, we measure a walking distance of 36 to mailbox 15.\nFor delivery neighborhood 13, we measure a walking distance of 47 to mailbox 16.\nFor delivery neighborhood 13, we measure a walking distance of 62 to mailbox 17.\nFor delivery neighborhood 13, we measure a walking distance of 57 to mailbox 18.\nFor delivery neighborhood 14, we measure a walking distance of 34 to mailbox 1.\nFor delivery neighborhood 14, we measure a walking distance of 27 to mailbox 2.\nFor delivery neighborhood 14, we measure a walking distance of 41 to mailbox 3.\nFor delivery neighborhood 14, we measure a walking distance of 44 to mailbox 4.\nFor delivery neighborhood 14, we measure a walking distance of 29 to mailbox 5.\nFor delivery neighborhood 14, we measure a walking distance of 37 to mailbox 6.\nFor delivery neighborhood 14, we measure a walking distance of 33 to mailbox 7.\nFor delivery neighborhood 14, we measure a walking distance of 35 to mailbox 8.\nFor delivery neighborhood 14, we measure a walking distance of 43 to mailbox 9.\nFor delivery neighborhood 14, we measure a walking distance of 36 to mailbox 10.\nFor delivery neighborhood 14, we measure a walking distance of 35 to mailbox 11.\nFor delivery neighborhood 14, we measure a walking distance of 36 to mailbox 12.\nFor delivery neighborhood 14, we measure a walking distance of 55 to mailbox 13.\nFor delivery neighborhood 14, we measure a walking distance of 27 to mailbox 15.\nFor delivery neighborhood 14, we measure a walking distance of 47 to mailbox 16.\nFor delivery neighborhood 14, we measure a walking distance of 55 to mailbox 17.\nFor delivery neighborhood 14, we measure a walking distance of 40 to mailbox 18.\nFor delivery neighborhood 15, we measure a walking distance of 22 to mailbox 1.\nFor delivery neighborhood 15, we measure a walking distance of 28 to mailbox 2.\nFor delivery neighborhood 15, we measure a walking distance of 22 to mailbox 3.\nFor delivery neighborhood 15, we measure a walking distance of 41 to mailbox 4.\nFor delivery neighborhood 15, we measure a walking distance of 20 to mailbox 5.\nFor delivery neighborhood 15, we measure a walking distance of 37 to mailbox 6.\nFor delivery neighborhood 15, we measure a walking distance of 32 to mailbox 7.\nFor delivery neighborhood 15, we measure a walking distance of 36 to mailbox 8.\nFor delivery neighborhood 15, we measure a walking distance of 24 to mailbox 9.\nFor delivery neighborhood 15, we measure a walking distance of 35 to mailbox 10.\nFor delivery neighborhood 15, we measure a walking distance of 36 to mailbox 11.\nFor delivery neighborhood 15, we measure a walking distance of 31 to mailbox 12.\nFor delivery neighborhood 15, we measure a walking distance of 36 to mailbox 13.\nFor delivery neighborhood 15, we measure a walking distance of 27 to mailbox 14.\nFor delivery neighborhood 15, we measure a walking distance of 36 to mailbox 16.\nFor delivery neighborhood 15, we measure a walking distance of 54 to mailbox 17.\nFor delivery neighborhood 15, we measure a walking distance of 39 to mailbox 18.\nFor delivery neighborhood 16, we measure a walking distance of 45 to mailbox 1.\nFor delivery neighborhood 16, we measure a walking distance of 36 to mailbox 2.\nFor delivery neighborhood 16, we measure a walking distance of 37 to mailbox 3.\nFor delivery neighborhood 16, we measure a walking distance of 23 to mailbox 4.\nFor delivery neighborhood 16, we measure a walking distance of 34 to mailbox 5.\nFor delivery neighborhood 16, we measure a walking distance of 35 to mailbox 6.\nFor delivery neighborhood 16, we measure a walking distance of 48 to mailbox 7.\nFor delivery neighborhood 16, we measure a walking distance of 36 to mailbox 8.\nFor delivery neighborhood 16, we measure a walking distance of 42 to mailbox 9.\nFor delivery neighborhood 16, we measure a walking distance of 38 to mailbox 10.\nFor delivery neighborhood 16, we measure a walking distance of 34 to mailbox 11.\nFor delivery neighborhood 16, we measure a walking distance of 21 to mailbox 12.\nFor delivery neighborhood 16, we measure a walking distance of 47 to mailbox 13.\nFor delivery neighborhood 16, we measure a walking distance of 47 to mailbox 14.\nFor delivery neighborhood 16, we measure a walking distance of 36 to mailbox 15.\nFor delivery neighborhood 16, we measure a walking distance of 18 to mailbox 17.\nFor delivery neighborhood 16, we measure a walking distance of 41 to mailbox 18.\nFor delivery neighborhood 17, we measure a walking distance of 55 to mailbox 1.\nFor delivery neighborhood 17, we measure a walking distance of 34 to mailbox 2.\nFor delivery neighborhood 17, we measure a walking distance of 52 to mailbox 3.\nFor delivery neighborhood 17, we measure a walking distance of 41 to mailbox 4.\nFor delivery neighborhood 17, we measure a walking distance of 47 to mailbox 5.\nFor delivery neighborhood 17, we measure a walking distance of 36 to mailbox 6.\nFor delivery neighborhood 17, we measure a walking distance of 65 to mailbox 7.\nFor delivery neighborhood 17, we measure a walking distance of 44 to mailbox 8.\nFor delivery neighborhood 17, we measure a walking distance of 60 to mailbox 9.\nFor delivery neighborhood 17, we measure a walking distance of 49 to mailbox 10.\nFor delivery neighborhood 17, we measure a walking distance of 42 to mailbox 11.\nFor delivery neighborhood 17, we measure a walking distance of 39 to mailbox 12.\nFor delivery neighborhood 17, we measure a walking distance of 62 to mailbox 13.\nFor delivery neighborhood 17, we measure a walking distance of 55 to mailbox 14.\nFor delivery neighborhood 17, we measure a walking distance of 54 to mailbox 15.\nFor delivery neighborhood 17, we measure a walking distance of 18 to mailbox 16.\nFor delivery neighborhood 17, we measure a walking distance of 53 to mailbox 18.\nFor delivery neighborhood 18, we measure a walking distance of 46 to mailbox 1.\nFor delivery neighborhood 18, we measure a walking distance of 40 to mailbox 2.\nFor delivery neighborhood 18, we measure a walking distance of 39 to mailbox 3.\nFor delivery neighborhood 18, we measure a walking distance of 42 to mailbox 4.\nFor delivery neighborhood 18, we measure a walking distance of 31 to mailbox 5.\nFor delivery neighborhood 18, we measure a walking distance of 34 to mailbox 6.\nFor delivery neighborhood 18, we measure a walking distance of 45 to mailbox 7.\nFor delivery neighborhood 18, we measure a walking distance of 35 to mailbox 8.\nFor delivery neighborhood 18, we measure a walking distance of 45 to mailbox 9.\nFor delivery neighborhood 18, we measure a walking distance of 22 to mailbox 10.\nFor delivery neighborhood 18, we measure a walking distance of 36 to mailbox 11.\nFor delivery neighborhood 18, we measure a walking distance of 30 to mailbox 12.\nFor delivery neighborhood 18, we measure a walking distance of 57 to mailbox 13.\nFor delivery neighborhood 18, we measure a walking distance of 40 to mailbox 14.\nFor delivery neighborhood 18, we measure a walking distance of 39 to mailbox 15.\nFor delivery neighborhood 18, we measure a walking distance of 41 to mailbox 16.\nFor delivery neighborhood 18, we measure a walking distance of 53 to mailbox 17.\nWe’ll use these distances to choose which 6 of the 18 candidate posts to keep.\n\nAlso, when you send the result back, just use this simple JSON layout so it's easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of the mailboxes we decide to keep open. \"assignments\" is a list (in the same order as the input locations) that says which kept mailbox each neighborhood is linked to. It's just a sketch of the shape I expect — you'll fill in the actual identifiers from the instance.\n\nPlease use the exact identifiers from the input (do not rename them or invent new labels). \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 36, 36, 35, 27, 35, 39, 34, 34, 42, 39, 33, 34, 34, 22, 45, 55, 46 ], [ 36, 0, 29, 23, 19, 16, 37, 18, 40, 28, 14, 15, 34, 27, 28, 36, 34, 40 ], [ 36, 29, 0, 28, 22, 25, 43, 34, 37, 24, 29, 16, 39, 41, 22, 37, 52, 39 ], [ 35, 23, 28, 0, 27, 24, 44, 32, 45, 34, 25, 12, 31, 44, 41, 23, 41, 42 ], [ 27, 19, 22, 27, 0, 21, 23, 27, 36, 33, 25, 17, 39, 29, 20, 34, 47, 31 ], [ 35, 16, 25, 24, 21, 0, 39, 22, 36, 28, 14, 15, 42, 37, 37, 35, 36, 34 ], [ 39, 37, 43, 44, 23, 39, 0, 29, 48, 41, 44, 40, 49, 33, 32, 48, 65, 45 ], [ 34, 18, 34, 32, 27, 22, 29, 0, 48, 32, 22, 23, 27, 35, 36, 36, 44, 35 ], [ 34, 40, 37, 45, 36, 36, 48, 48, 0, 42, 46, 39, 42, 43, 24, 42, 60, 45 ], [ 42, 28, 24, 34, 33, 28, 41, 32, 42, 0, 16, 27, 43, 36, 35, 38, 49, 22 ], [ 39, 14, 29, 25, 25, 14, 44, 22, 46, 16, 0, 13, 40, 35, 36, 34, 42, 36 ], [ 33, 15, 16, 12, 17, 15, 40, 23, 39, 27, 13, 0, 32, 36, 31, 21, 39, 30 ], [ 34, 34, 39, 31, 39, 42, 49, 27, 42, 43, 40, 32, 0, 55, 36, 47, 62, 57 ], [ 34, 27, 41, 44, 29, 37, 33, 35, 43, 36, 35, 36, 55, 0, 27, 47, 55, 40 ], [ 22, 28, 22, 41, 20, 37, 32, 36, 24, 35, 36, 31, 36, 27, 0, 36, 54, 39 ], [ 45, 36, 37, 23, 34, 35, 48, 36, 42, 38, 34, 21, 47, 47, 36, 0, 18, 41 ], [ 55, 34, 52, 41, 47, 36, 65, 44, 60, 49, 42, 39, 62, 55, 54, 18, 0, 53 ], [ 46, 40, 39, 42, 31, 34, 45, 35, 45, 22, 36, 30, 57, 40, 39, 41, 53, 0 ] ], "p": 6, "objective": 224.0 }, "solution": { "facilities": [ 6, 9, 11, 12, 14, 15 ], "assignments": [ 14, 11, 11, 11, 11, 11, 6, 11, 14, 9, 11, 11, 12, 14, 14, 15, 15, 9 ] }, "obj": 224.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 6, "sites": [ { "id": 1, "distances": { "1": 0, "2": 36, "3": 36, "4": 35, "5": 27, "6": 35, "7": 39, "8": 34, "9": 34, "10": 42, "11": 39, "12": 33, "13": 34, "14": 34, "15": 22, "16": 45, "17": 55, "18": 46 } }, { "id": 2, "distances": { "1": 36, "2": 0, "3": 29, "4": 23, "5": 19, "6": 16, "7": 37, "8": 18, "9": 40, "10": 28, "11": 14, "12": 15, "13": 34, "14": 27, "15": 28, "16": 36, "17": 34, "18": 40 } }, { "id": 3, "distances": { "1": 36, "2": 29, "3": 0, "4": 28, "5": 22, "6": 25, "7": 43, "8": 34, "9": 37, "10": 24, "11": 29, "12": 16, "13": 39, "14": 41, "15": 22, "16": 37, "17": 52, "18": 39 } }, { "id": 4, "distances": { "1": 35, "2": 23, "3": 28, "4": 0, "5": 27, "6": 24, "7": 44, "8": 32, "9": 45, "10": 34, "11": 25, "12": 12, "13": 31, "14": 44, "15": 41, "16": 23, "17": 41, "18": 42 } }, { "id": 5, "distances": { "1": 27, "2": 19, "3": 22, "4": 27, "5": 0, "6": 21, "7": 23, "8": 27, "9": 36, "10": 33, "11": 25, "12": 17, "13": 39, "14": 29, "15": 20, "16": 34, "17": 47, "18": 31 } }, { "id": 6, "distances": { "1": 35, "2": 16, "3": 25, "4": 24, "5": 21, "6": 0, "7": 39, "8": 22, "9": 36, "10": 28, "11": 14, "12": 15, "13": 42, "14": 37, "15": 37, "16": 35, "17": 36, "18": 34 } }, { "id": 7, "distances": { "1": 39, "2": 37, "3": 43, "4": 44, "5": 23, "6": 39, "7": 0, "8": 29, "9": 48, "10": 41, "11": 44, "12": 40, "13": 49, "14": 33, "15": 32, "16": 48, "17": 65, "18": 45 } }, { "id": 8, "distances": { "1": 34, "2": 18, "3": 34, "4": 32, "5": 27, "6": 22, "7": 29, "8": 0, "9": 48, "10": 32, "11": 22, "12": 23, "13": 27, "14": 35, "15": 36, "16": 36, "17": 44, "18": 35 } }, { "id": 9, "distances": { "1": 34, "2": 40, "3": 37, "4": 45, "5": 36, "6": 36, "7": 48, "8": 48, "9": 0, "10": 42, "11": 46, "12": 39, "13": 42, "14": 43, "15": 24, "16": 42, "17": 60, "18": 45 } }, { "id": 10, "distances": { "1": 42, "2": 28, "3": 24, "4": 34, "5": 33, "6": 28, "7": 41, "8": 32, "9": 42, "10": 0, "11": 16, "12": 27, "13": 43, "14": 36, "15": 35, "16": 38, "17": 49, "18": 22 } }, { "id": 11, "distances": { "1": 39, "2": 14, "3": 29, "4": 25, "5": 25, "6": 14, "7": 44, "8": 22, "9": 46, "10": 16, "11": 0, "12": 13, "13": 40, "14": 35, "15": 36, "16": 34, "17": 42, "18": 36 } }, { "id": 12, "distances": { "1": 33, "2": 15, "3": 16, "4": 12, "5": 17, "6": 15, "7": 40, "8": 23, "9": 39, "10": 27, "11": 13, "12": 0, "13": 32, "14": 36, "15": 31, "16": 21, "17": 39, "18": 30 } }, { "id": 13, "distances": { "1": 34, "2": 34, "3": 39, "4": 31, "5": 39, "6": 42, "7": 49, "8": 27, "9": 42, "10": 43, "11": 40, "12": 32, "13": 0, "14": 55, "15": 36, "16": 47, "17": 62, "18": 57 } }, { "id": 14, "distances": { "1": 34, "2": 27, "3": 41, "4": 44, "5": 29, "6": 37, "7": 33, "8": 35, "9": 43, "10": 36, "11": 35, "12": 36, "13": 55, "14": 0, "15": 27, "16": 47, "17": 55, "18": 40 } }, { "id": 15, "distances": { "1": 22, "2": 28, "3": 22, "4": 41, "5": 20, "6": 37, "7": 32, "8": 36, "9": 24, "10": 35, "11": 36, "12": 31, "13": 36, "14": 27, "15": 0, "16": 36, "17": 54, "18": 39 } }, { "id": 16, "distances": { "1": 45, "2": 36, "3": 37, "4": 23, "5": 34, "6": 35, "7": 48, "8": 36, "9": 42, "10": 38, "11": 34, "12": 21, "13": 47, "14": 47, "15": 36, "16": 0, "17": 18, "18": 41 } }, { "id": 17, "distances": { "1": 55, "2": 34, "3": 52, "4": 41, "5": 47, "6": 36, "7": 65, "8": 44, "9": 60, "10": 49, "11": 42, "12": 39, "13": 62, "14": 55, "15": 54, "16": 18, "17": 0, "18": 53 } }, { "id": 18, "distances": { "1": 46, "2": 40, "3": 39, "4": 42, "5": 31, "6": 34, "7": 45, "8": 35, "9": 45, "10": 22, "11": 36, "12": 30, "13": 57, "14": 40, "15": 39, "16": 41, "17": 53, "18": 0 } } ], "objective": 224.0 }, "solution_variant": { "selected": [ 7, 10, 12, 13, 15, 16 ], "assignments": [ 15, 12, 12, 12, 12, 12, 7, 12, 15, 10, 12, 12, 13, 15, 15, 16, 16, 10 ] }, "context_index": 10, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Many people depend on the cooperative to pick a handful of collection yards from a list of candidates and then route each farm to one of those yards. The rule is strict: there’s a fixed number of yards to run, and each farm must be assigned to exactly one open yard — no splitting or omissions. A better routing is the one that makes the sum of all farm-to-yard trips as small as possible; just add up each farm’s distance to its assigned yard to see how good it is. The concrete data about farms and distances appears below.\n\nBelow are the 20 candidate yards (IDs: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T); the cooperative must open exactly 2 of them and assign every farm to one opened yard.\nDistance from A to B: 73.\nDistance from A to C: 106.\nDistance from A to D: 144.\nDistance from A to E: 196.\nDistance from A to F: 151.\nDistance from A to G: 51.\nDistance from A to H: 133.\nDistance from A to I: 56.\nDistance from A to J: 114.\nDistance from A to K: 129.\nDistance from A to L: 104.\nDistance from A to M: 41.\nDistance from A to N: 33.\nDistance from A to O: 53.\nDistance from A to P: 48.\nDistance from A to Q: 50.\nDistance from A to R: 121.\nDistance from A to S: 94.\nDistance from A to T: 31.\nDistance from B to A: 73.\nDistance from B to C: 108.\nDistance from B to D: 147.\nDistance from B to E: 199.\nDistance from B to F: 201.\nDistance from B to G: 110.\nDistance from B to H: 189.\nDistance from B to I: 129.\nDistance from B to J: 139.\nDistance from B to K: 152.\nDistance from B to L: 127.\nDistance from B to M: 54.\nDistance from B to N: 58.\nDistance from B to O: 126.\nDistance from B to P: 121.\nDistance from B to Q: 95.\nDistance from B to R: 181.\nDistance from B to S: 119.\nDistance from B to T: 56.\nDistance from C to A: 106.\nDistance from C to B: 108.\nDistance from C to D: 115.\nDistance from C to E: 167.\nDistance from C to F: 160.\nDistance from C to G: 134.\nDistance from C to H: 138.\nDistance from C to I: 162.\nDistance from C to J: 88.\nDistance from C to K: 116.\nDistance from C to L: 91.\nDistance from C to M: 99.\nDistance from C to N: 91.\nDistance from C to O: 159.\nDistance from C to P: 154.\nDistance from C to Q: 128.\nDistance from C to R: 204.\nDistance from C to S: 148.\nDistance from C to T: 89.\nDistance from D to A: 144.\nDistance from D to B: 147.\nDistance from D to C: 115.\nDistance from D to E: 52.\nDistance from D to F: 100.\nDistance from D to G: 117.\nDistance from D to H: 169.\nDistance from D to I: 195.\nDistance from D to J: 141.\nDistance from D to K: 179.\nDistance from D to L: 162.\nDistance from D to M: 141.\nDistance from D to N: 144.\nDistance from D to O: 197.\nDistance from D to P: 192.\nDistance from D to Q: 112.\nDistance from D to R: 183.\nDistance from D to S: 201.\nDistance from D to T: 142.\nDistance from E to A: 196.\nDistance from E to B: 199.\nDistance from E to C: 167.\nDistance from E to D: 52.\nDistance from E to F: 48.\nDistance from E to G: 169.\nDistance from E to H: 220.\nDistance from E to I: 143.\nDistance from E to J: 120.\nDistance from E to K: 198.\nDistance from E to L: 173.\nDistance from E to M: 193.\nDistance from E to N: 195.\nDistance from E to O: 156.\nDistance from E to P: 151.\nDistance from E to Q: 164.\nDistance from E to R: 235.\nDistance from E to S: 162.\nDistance from E to T: 193.\nDistance from F to A: 151.\nDistance from F to B: 201.\nDistance from F to C: 160.\nDistance from F to D: 100.\nDistance from F to E: 48.\nDistance from F to G: 201.\nDistance from F to H: 172.\nDistance from F to I: 95.\nDistance from F to J: 72.\nDistance from F to K: 150.\nDistance from F to L: 125.\nDistance from F to M: 155.\nDistance from F to N: 147.\nDistance from F to O: 108.\nDistance from F to P: 103.\nDistance from F to Q: 178.\nDistance from F to R: 267.\nDistance from F to S: 114.\nDistance from F to T: 145.\nDistance from G to A: 51.\nDistance from G to B: 110.\nDistance from G to C: 134.\nDistance from G to D: 117.\nDistance from G to E: 169.\nDistance from G to F: 201.\nDistance from G to H: 184.\nDistance from G to I: 107.\nDistance from G to J: 142.\nDistance from G to K: 118.\nDistance from G to L: 93.\nDistance from G to M: 68.\nDistance from G to N: 60.\nDistance from G to O: 104.\nDistance from G to P: 99.\nDistance from G to Q: 23.\nDistance from G to R: 94.\nDistance from G to S: 131.\nDistance from G to T: 62.\nDistance from H to A: 133.\nDistance from H to B: 189.\nDistance from H to C: 138.\nDistance from H to D: 169.\nDistance from H to E: 220.\nDistance from H to F: 172.\nDistance from H to G: 184.\nDistance from H to I: 77.\nDistance from H to J: 146.\nDistance from H to K: 206.\nDistance from H to L: 181.\nDistance from H to M: 157.\nDistance from H to N: 149.\nDistance from H to O: 90.\nDistance from H to P: 85.\nDistance from H to Q: 175.\nDistance from H to R: 254.\nDistance from H to S: 206.\nDistance from H to T: 147.\nDistance from I to A: 56.\nDistance from I to B: 129.\nDistance from I to C: 162.\nDistance from I to D: 195.\nDistance from I to E: 143.\nDistance from I to F: 95.\nDistance from I to G: 107.\nDistance from I to H: 77.\nDistance from I to J: 136.\nDistance from I to K: 182.\nDistance from I to L: 160.\nDistance from I to M: 97.\nDistance from I to N: 89.\nDistance from I to O: 13.\nDistance from I to P: 8.\nDistance from I to Q: 98.\nDistance from I to R: 177.\nDistance from I to S: 150.\nDistance from I to T: 87.\nDistance from J to A: 114.\nDistance from J to B: 139.\nDistance from J to C: 88.\nDistance from J to D: 141.\nDistance from J to E: 120.\nDistance from J to F: 72.\nDistance from J to G: 142.\nDistance from J to H: 146.\nDistance from J to I: 136.\nDistance from J to K: 78.\nDistance from J to L: 53.\nDistance from J to M: 107.\nDistance from J to N: 99.\nDistance from J to O: 149.\nDistance from J to P: 144.\nDistance from J to Q: 136.\nDistance from J to R: 212.\nDistance from J to S: 156.\nDistance from J to T: 97.\nDistance from K to A: 129.\nDistance from K to B: 152.\nDistance from K to C: 116.\nDistance from K to D: 179.\nDistance from K to E: 198.\nDistance from K to F: 150.\nDistance from K to G: 118.\nDistance from K to H: 206.\nDistance from K to I: 182.\nDistance from K to J: 78.\nDistance from K to L: 25.\nDistance from K to M: 122.\nDistance from K to N: 114.\nDistance from K to O: 182.\nDistance from K to P: 177.\nDistance from K to Q: 114.\nDistance from K to R: 188.\nDistance from K to S: 171.\nDistance from K to T: 112.\nDistance from L to A: 104.\nDistance from L to B: 127.\nDistance from L to C: 91.\nDistance from L to D: 162.\nDistance from L to E: 173.\nDistance from L to F: 125.\nDistance from L to G: 93.\nDistance from L to H: 181.\nDistance from L to I: 160.\nDistance from L to J: 53.\nDistance from L to K: 25.\nDistance from L to M: 97.\nDistance from L to N: 89.\nDistance from L to O: 157.\nDistance from L to P: 152.\nDistance from L to Q: 92.\nDistance from L to R: 163.\nDistance from L to S: 146.\nDistance from L to T: 87.\nDistance from M to A: 41.\nDistance from M to B: 54.\nDistance from M to C: 99.\nDistance from M to D: 141.\nDistance from M to E: 193.\nDistance from M to F: 155.\nDistance from M to G: 68.\nDistance from M to H: 157.\nDistance from M to I: 97.\nDistance from M to J: 107.\nDistance from M to K: 122.\nDistance from M to L: 97.\nDistance from M to N: 8.\nDistance from M to O: 94.\nDistance from M to P: 89.\nDistance from M to Q: 45.\nDistance from M to R: 134.\nDistance from M to S: 87.\nDistance from M to T: 10.\nDistance from N to A: 33.\nDistance from N to B: 58.\nDistance from N to C: 91.\nDistance from N to D: 144.\nDistance from N to E: 195.\nDistance from N to F: 147.\nDistance from N to G: 60.\nDistance from N to H: 149.\nDistance from N to I: 89.\nDistance from N to J: 99.\nDistance from N to K: 114.\nDistance from N to L: 89.\nDistance from N to M: 8.\nDistance from N to O: 86.\nDistance from N to P: 81.\nDistance from N to Q: 37.\nDistance from N to R: 126.\nDistance from N to S: 79.\nDistance from N to T: 2.\nDistance from O to A: 53.\nDistance from O to B: 126.\nDistance from O to C: 159.\nDistance from O to D: 197.\nDistance from O to E: 156.\nDistance from O to F: 108.\nDistance from O to G: 104.\nDistance from O to H: 90.\nDistance from O to I: 13.\nDistance from O to J: 149.\nDistance from O to K: 182.\nDistance from O to L: 157.\nDistance from O to M: 94.\nDistance from O to N: 86.\nDistance from O to P: 5.\nDistance from O to Q: 103.\nDistance from O to R: 174.\nDistance from O to S: 147.\nDistance from O to T: 84.\nDistance from P to A: 48.\nDistance from P to B: 121.\nDistance from P to C: 154.\nDistance from P to D: 192.\nDistance from P to E: 151.\nDistance from P to F: 103.\nDistance from P to G: 99.\nDistance from P to H: 85.\nDistance from P to I: 8.\nDistance from P to J: 144.\nDistance from P to K: 177.\nDistance from P to L: 152.\nDistance from P to M: 89.\nDistance from P to N: 81.\nDistance from P to O: 5.\nDistance from P to Q: 98.\nDistance from P to R: 169.\nDistance from P to S: 142.\nDistance from P to T: 79.\nDistance from Q to A: 50.\nDistance from Q to B: 95.\nDistance from Q to C: 128.\nDistance from Q to D: 112.\nDistance from Q to E: 164.\nDistance from Q to F: 178.\nDistance from Q to G: 23.\nDistance from Q to H: 175.\nDistance from Q to I: 98.\nDistance from Q to J: 136.\nDistance from Q to K: 114.\nDistance from Q to L: 92.\nDistance from Q to M: 45.\nDistance from Q to N: 37.\nDistance from Q to O: 103.\nDistance from Q to P: 98.\nDistance from Q to R: 89.\nDistance from Q to S: 116.\nDistance from Q to T: 39.\nDistance from R to A: 121.\nDistance from R to B: 181.\nDistance from R to C: 204.\nDistance from R to D: 183.\nDistance from R to E: 235.\nDistance from R to F: 267.\nDistance from R to G: 94.\nDistance from R to H: 254.\nDistance from R to I: 177.\nDistance from R to J: 212.\nDistance from R to K: 188.\nDistance from R to L: 163.\nDistance from R to M: 134.\nDistance from R to N: 126.\nDistance from R to O: 174.\nDistance from R to P: 169.\nDistance from R to Q: 89.\nDistance from R to S: 198.\nDistance from R to T: 128.\nDistance from S to A: 94.\nDistance from S to B: 119.\nDistance from S to C: 148.\nDistance from S to D: 201.\nDistance from S to E: 162.\nDistance from S to F: 114.\nDistance from S to G: 131.\nDistance from S to H: 206.\nDistance from S to I: 150.\nDistance from S to J: 156.\nDistance from S to K: 171.\nDistance from S to L: 146.\nDistance from S to M: 87.\nDistance from S to N: 79.\nDistance from S to O: 147.\nDistance from S to P: 142.\nDistance from S to Q: 116.\nDistance from S to R: 198.\nDistance from S to T: 77.\nDistance from T to A: 31.\nDistance from T to B: 56.\nDistance from T to C: 89.\nDistance from T to D: 142.\nDistance from T to E: 193.\nDistance from T to F: 145.\nDistance from T to G: 62.\nDistance from T to H: 147.\nDistance from T to I: 87.\nDistance from T to J: 97.\nDistance from T to K: 112.\nDistance from T to L: 87.\nDistance from T to M: 10.\nDistance from T to N: 2.\nDistance from T to O: 84.\nDistance from T to P: 79.\nDistance from T to Q: 39.\nDistance from T to R: 128.\nDistance from T to S: 77.\nThese distances will be used to assign farms to the chosen yards so the cooperative can minimize the total travel distance.\n\nOh, and when you reply, please use this simple JSON layout so I can read the shortlist and the farm-to-yard assignments easily:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis is just a sketch of the shape I need:\n- \"selected\" is the list of yards you decide to open (those are the yard identifiers).\n- \"assignments\" lists, for each farm in the same order as the instance, which open yard it goes to (use the yard identifier you picked).\n\nPlease use the identifiers exactly as they appear in the instance input — no renaming and no new labels. For example:\n- plain numbers such as “1” or “23”\n- single capital letters like “A” or “B”\n- a capital letter followed by digits like “A1” or “X7”", "instance": { "distance_matrix": [ [ 0, 73, 106, 144, 196, 151, 51, 133, 56, 114, 129, 104, 41, 33, 53, 48, 50, 121, 94, 31 ], [ 73, 0, 108, 147, 199, 201, 110, 189, 129, 139, 152, 127, 54, 58, 126, 121, 95, 181, 119, 56 ], [ 106, 108, 0, 115, 167, 160, 134, 138, 162, 88, 116, 91, 99, 91, 159, 154, 128, 204, 148, 89 ], [ 144, 147, 115, 0, 52, 100, 117, 169, 195, 141, 179, 162, 141, 144, 197, 192, 112, 183, 201, 142 ], [ 196, 199, 167, 52, 0, 48, 169, 220, 143, 120, 198, 173, 193, 195, 156, 151, 164, 235, 162, 193 ], [ 151, 201, 160, 100, 48, 0, 201, 172, 95, 72, 150, 125, 155, 147, 108, 103, 178, 267, 114, 145 ], [ 51, 110, 134, 117, 169, 201, 0, 184, 107, 142, 118, 93, 68, 60, 104, 99, 23, 94, 131, 62 ], [ 133, 189, 138, 169, 220, 172, 184, 0, 77, 146, 206, 181, 157, 149, 90, 85, 175, 254, 206, 147 ], [ 56, 129, 162, 195, 143, 95, 107, 77, 0, 136, 182, 160, 97, 89, 13, 8, 98, 177, 150, 87 ], [ 114, 139, 88, 141, 120, 72, 142, 146, 136, 0, 78, 53, 107, 99, 149, 144, 136, 212, 156, 97 ], [ 129, 152, 116, 179, 198, 150, 118, 206, 182, 78, 0, 25, 122, 114, 182, 177, 114, 188, 171, 112 ], [ 104, 127, 91, 162, 173, 125, 93, 181, 160, 53, 25, 0, 97, 89, 157, 152, 92, 163, 146, 87 ], [ 41, 54, 99, 141, 193, 155, 68, 157, 97, 107, 122, 97, 0, 8, 94, 89, 45, 134, 87, 10 ], [ 33, 58, 91, 144, 195, 147, 60, 149, 89, 99, 114, 89, 8, 0, 86, 81, 37, 126, 79, 2 ], [ 53, 126, 159, 197, 156, 108, 104, 90, 13, 149, 182, 157, 94, 86, 0, 5, 103, 174, 147, 84 ], [ 48, 121, 154, 192, 151, 103, 99, 85, 8, 144, 177, 152, 89, 81, 5, 0, 98, 169, 142, 79 ], [ 50, 95, 128, 112, 164, 178, 23, 175, 98, 136, 114, 92, 45, 37, 103, 98, 0, 89, 116, 39 ], [ 121, 181, 204, 183, 235, 267, 94, 254, 177, 212, 188, 163, 134, 126, 174, 169, 89, 0, 198, 128 ], [ 94, 119, 148, 201, 162, 114, 131, 206, 150, 156, 171, 146, 87, 79, 147, 142, 116, 198, 0, 77 ], [ 31, 56, 89, 142, 193, 145, 62, 147, 87, 97, 112, 87, 10, 2, 84, 79, 39, 128, 77, 0 ] ], "p": 2, "objective": 1268.0 }, "solution": { "facilities": [ 8, 19 ], "assignments": [ 19, 19, 19, 19, 8, 8, 19, 8, 8, 19, 19, 19, 19, 19, 8, 8, 19, 19, 19, 19 ] }, "obj": 1268.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 2, "sites": [ { "id": "A", "distances": { "A": 0, "B": 73, "C": 106, "D": 144, "E": 196, "F": 151, "G": 51, "H": 133, "I": 56, "J": 114, "K": 129, "L": 104, "M": 41, "N": 33, "O": 53, "P": 48, "Q": 50, "R": 121, "S": 94, "T": 31 } }, { "id": "B", "distances": { "A": 73, "B": 0, "C": 108, "D": 147, "E": 199, "F": 201, "G": 110, "H": 189, "I": 129, "J": 139, "K": 152, "L": 127, "M": 54, "N": 58, "O": 126, "P": 121, "Q": 95, "R": 181, "S": 119, "T": 56 } }, { "id": "C", "distances": { "A": 106, "B": 108, "C": 0, "D": 115, "E": 167, "F": 160, "G": 134, "H": 138, "I": 162, "J": 88, "K": 116, "L": 91, "M": 99, "N": 91, "O": 159, "P": 154, "Q": 128, "R": 204, "S": 148, "T": 89 } }, { "id": "D", "distances": { "A": 144, "B": 147, "C": 115, "D": 0, "E": 52, "F": 100, "G": 117, "H": 169, "I": 195, "J": 141, "K": 179, "L": 162, "M": 141, "N": 144, "O": 197, "P": 192, "Q": 112, "R": 183, "S": 201, "T": 142 } }, { "id": "E", "distances": { "A": 196, "B": 199, "C": 167, "D": 52, "E": 0, "F": 48, "G": 169, "H": 220, "I": 143, "J": 120, "K": 198, "L": 173, "M": 193, "N": 195, "O": 156, "P": 151, "Q": 164, "R": 235, "S": 162, "T": 193 } }, { "id": "F", "distances": { "A": 151, "B": 201, "C": 160, "D": 100, "E": 48, "F": 0, "G": 201, "H": 172, "I": 95, "J": 72, "K": 150, "L": 125, "M": 155, "N": 147, "O": 108, "P": 103, "Q": 178, "R": 267, "S": 114, "T": 145 } }, { "id": "G", "distances": { "A": 51, "B": 110, "C": 134, "D": 117, "E": 169, "F": 201, "G": 0, "H": 184, "I": 107, "J": 142, "K": 118, "L": 93, "M": 68, "N": 60, "O": 104, "P": 99, "Q": 23, "R": 94, "S": 131, "T": 62 } }, { "id": "H", "distances": { "A": 133, "B": 189, "C": 138, "D": 169, "E": 220, "F": 172, "G": 184, "H": 0, "I": 77, "J": 146, "K": 206, "L": 181, "M": 157, "N": 149, "O": 90, "P": 85, "Q": 175, "R": 254, "S": 206, "T": 147 } }, { "id": "I", "distances": { "A": 56, "B": 129, "C": 162, "D": 195, "E": 143, "F": 95, "G": 107, "H": 77, "I": 0, "J": 136, "K": 182, "L": 160, "M": 97, "N": 89, "O": 13, "P": 8, "Q": 98, "R": 177, "S": 150, "T": 87 } }, { "id": "J", "distances": { "A": 114, "B": 139, "C": 88, "D": 141, "E": 120, "F": 72, "G": 142, "H": 146, "I": 136, "J": 0, "K": 78, "L": 53, "M": 107, "N": 99, "O": 149, "P": 144, "Q": 136, "R": 212, "S": 156, "T": 97 } }, { "id": "K", "distances": { "A": 129, "B": 152, "C": 116, "D": 179, "E": 198, "F": 150, "G": 118, "H": 206, "I": 182, "J": 78, "K": 0, "L": 25, "M": 122, "N": 114, "O": 182, "P": 177, "Q": 114, "R": 188, "S": 171, "T": 112 } }, { "id": "L", "distances": { "A": 104, "B": 127, "C": 91, "D": 162, "E": 173, "F": 125, "G": 93, "H": 181, "I": 160, "J": 53, "K": 25, "L": 0, "M": 97, "N": 89, "O": 157, "P": 152, "Q": 92, "R": 163, "S": 146, "T": 87 } }, { "id": "M", "distances": { "A": 41, "B": 54, "C": 99, "D": 141, "E": 193, "F": 155, "G": 68, "H": 157, "I": 97, "J": 107, "K": 122, "L": 97, "M": 0, "N": 8, "O": 94, "P": 89, "Q": 45, "R": 134, "S": 87, "T": 10 } }, { "id": "N", "distances": { "A": 33, "B": 58, "C": 91, "D": 144, "E": 195, "F": 147, "G": 60, "H": 149, "I": 89, "J": 99, "K": 114, "L": 89, "M": 8, "N": 0, "O": 86, "P": 81, "Q": 37, "R": 126, "S": 79, "T": 2 } }, { "id": "O", "distances": { "A": 53, "B": 126, "C": 159, "D": 197, "E": 156, "F": 108, "G": 104, "H": 90, "I": 13, "J": 149, "K": 182, "L": 157, "M": 94, "N": 86, "O": 0, "P": 5, "Q": 103, "R": 174, "S": 147, "T": 84 } }, { "id": "P", "distances": { "A": 48, "B": 121, "C": 154, "D": 192, "E": 151, "F": 103, "G": 99, "H": 85, "I": 8, "J": 144, "K": 177, "L": 152, "M": 89, "N": 81, "O": 5, "P": 0, "Q": 98, "R": 169, "S": 142, "T": 79 } }, { "id": "Q", "distances": { "A": 50, "B": 95, "C": 128, "D": 112, "E": 164, "F": 178, "G": 23, "H": 175, "I": 98, "J": 136, "K": 114, "L": 92, "M": 45, "N": 37, "O": 103, "P": 98, "Q": 0, "R": 89, "S": 116, "T": 39 } }, { "id": "R", "distances": { "A": 121, "B": 181, "C": 204, "D": 183, "E": 235, "F": 267, "G": 94, "H": 254, "I": 177, "J": 212, "K": 188, "L": 163, "M": 134, "N": 126, "O": 174, "P": 169, "Q": 89, "R": 0, "S": 198, "T": 128 } }, { "id": "S", "distances": { "A": 94, "B": 119, "C": 148, "D": 201, "E": 162, "F": 114, "G": 131, "H": 206, "I": 150, "J": 156, "K": 171, "L": 146, "M": 87, "N": 79, "O": 147, "P": 142, "Q": 116, "R": 198, "S": 0, "T": 77 } }, { "id": "T", "distances": { "A": 31, "B": 56, "C": 89, "D": 142, "E": 193, "F": 145, "G": 62, "H": 147, "I": 87, "J": 97, "K": 112, "L": 87, "M": 10, "N": 2, "O": 84, "P": 79, "Q": 39, "R": 128, "S": 77, "T": 0 } } ], "objective": 1268.0 }, "solution_variant": { "selected": [ "I", "T" ], "assignments": [ "T", "T", "T", "T", "I", "I", "T", "I", "I", "T", "T", "T", "T", "T", "I", "I", "T", "T", "T", "T" ] }, "context_index": 11, "input_format": "nl", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone in the ranger office needs to decide which clearings get staffed first-aid teams and then connect every trailhead to one staffed clearing so hikers aren’t wandering around. The rule of thumb is: compute how far people from each trailhead would have to go to reach their assigned station, sum those distances across all trailheads, and prefer the setup with the smallest total distance. Each trailhead gets one—and only one—assigned station; none can be left out or routed to multiple stations. The exact list of clearings, trailheads, and their pairwise distances appears below.\n\n{\n \"total_locations_count\": 16,\n \"num_first_aid_to_staff\": 1,\n \"location_ids\": [\n 0,\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15\n ],\n \"data\": [\n {\n \"from_location_id\": 0,\n \"to_location_id\": 1,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 2,\n \"travel_distance\": 61\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 3,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 4,\n \"travel_distance\": 56\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 5,\n \"travel_distance\": 43\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 6,\n \"travel_distance\": 24\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 7,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 8,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 9,\n \"travel_distance\": 52\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 10,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 11,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 12,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 13,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 14,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 0,\n \"to_location_id\": 15,\n \"travel_distance\": 21\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 0,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 2,\n \"travel_distance\": 49\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 3,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 4,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 5,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 6,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 7,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 8,\n \"travel_distance\": 27\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 9,\n \"travel_distance\": 45\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 10,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 11,\n \"travel_distance\": 7\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 12,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 13,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 14,\n \"travel_distance\": 15\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 15,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 0,\n \"travel_distance\": 61\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 1,\n \"travel_distance\": 49\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 3,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 4,\n \"travel_distance\": 73\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 5,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 6,\n \"travel_distance\": 56\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 7,\n \"travel_distance\": 63\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 8,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 9,\n \"travel_distance\": 67\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 10,\n \"travel_distance\": 65\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 11,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 12,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 13,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 14,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 15,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 0,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 1,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 2,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 4,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 5,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 6,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 7,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 8,\n \"travel_distance\": 19\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 9,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 10,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 11,\n \"travel_distance\": 24\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 12,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 13,\n \"travel_distance\": 46\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 14,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 15,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 0,\n \"travel_distance\": 56\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 1,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 2,\n \"travel_distance\": 73\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 3,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 5,\n \"travel_distance\": 54\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 6,\n \"travel_distance\": 62\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 7,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 8,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 9,\n \"travel_distance\": 69\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 10,\n \"travel_distance\": 50\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 11,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 12,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 13,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 14,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 15,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 0,\n \"travel_distance\": 43\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 1,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 2,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 3,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 4,\n \"travel_distance\": 54\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 6,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 7,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 8,\n \"travel_distance\": 18\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 9,\n \"travel_distance\": 62\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 10,\n \"travel_distance\": 55\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 11,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 12,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 13,\n \"travel_distance\": 52\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 14,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 15,\n \"travel_distance\": 51\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 0,\n \"travel_distance\": 24\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 1,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 2,\n \"travel_distance\": 56\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 3,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 4,\n \"travel_distance\": 62\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 5,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 7,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 8,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 9,\n \"travel_distance\": 63\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 10,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 11,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 12,\n \"travel_distance\": 43\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 13,\n \"travel_distance\": 55\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 14,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 15,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 0,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 1,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 2,\n \"travel_distance\": 63\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 3,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 4,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 5,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 6,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 8,\n \"travel_distance\": 46\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 9,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 10,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 11,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 12,\n \"travel_distance\": 37\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 13,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 14,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 15,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 0,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 1,\n \"travel_distance\": 27\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 2,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 3,\n \"travel_distance\": 19\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 4,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 5,\n \"travel_distance\": 18\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 6,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 7,\n \"travel_distance\": 46\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 9,\n \"travel_distance\": 53\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 10,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 11,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 12,\n \"travel_distance\": 30\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 13,\n \"travel_distance\": 52\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 14,\n \"travel_distance\": 16\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 15,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 0,\n \"travel_distance\": 52\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 1,\n \"travel_distance\": 45\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 2,\n \"travel_distance\": 67\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 3,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 4,\n \"travel_distance\": 69\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 5,\n \"travel_distance\": 62\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 6,\n \"travel_distance\": 63\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 7,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 8,\n \"travel_distance\": 53\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 10,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 11,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 12,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 13,\n \"travel_distance\": 66\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 14,\n \"travel_distance\": 55\n },\n {\n \"from_location_id\": 9,\n \"to_location_id\": 15,\n \"travel_distance\": 63\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 0,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 1,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 2,\n \"travel_distance\": 65\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 3,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 4,\n \"travel_distance\": 50\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 5,\n \"travel_distance\": 55\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 6,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 7,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 8,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 9,\n \"travel_distance\": 58\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 11,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 12,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 13,\n \"travel_distance\": 54\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 14,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 10,\n \"to_location_id\": 15,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 0,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 1,\n \"travel_distance\": 7\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 2,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 3,\n \"travel_distance\": 24\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 4,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 5,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 6,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 7,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 8,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 9,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 10,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 12,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 13,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 14,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 11,\n \"to_location_id\": 15,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 0,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 1,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 2,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 3,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 4,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 5,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 6,\n \"travel_distance\": 43\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 7,\n \"travel_distance\": 37\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 8,\n \"travel_distance\": 30\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 9,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 10,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 11,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 13,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 14,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 12,\n \"to_location_id\": 15,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 0,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 1,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 2,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 3,\n \"travel_distance\": 46\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 4,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 5,\n \"travel_distance\": 52\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 6,\n \"travel_distance\": 55\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 7,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 8,\n \"travel_distance\": 52\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 9,\n \"travel_distance\": 66\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 10,\n \"travel_distance\": 54\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 11,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 12,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 14,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 13,\n \"to_location_id\": 15,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 0,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 1,\n \"travel_distance\": 15\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 2,\n \"travel_distance\": 57\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 3,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 4,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 5,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 6,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 7,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 8,\n \"travel_distance\": 16\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 9,\n \"travel_distance\": 55\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 10,\n \"travel_distance\": 48\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 11,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 12,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 13,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 14,\n \"to_location_id\": 15,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 0,\n \"travel_distance\": 21\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 1,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 2,\n \"travel_distance\": 60\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 3,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 4,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 5,\n \"travel_distance\": 51\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 6,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 7,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 8,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 9,\n \"travel_distance\": 63\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 10,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 11,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 12,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 13,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 15,\n \"to_location_id\": 14,\n \"travel_distance\": 33\n }\n ]\n}\n\nOh, and when you send back the plan, just use this little JSON layout so it's easy to plug into the other tools:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of it like a simple form: \"selected\" is the list of clearings we decide to staff, and \"assignments\" is which staffed clearing each trailhead gets routed to (one entry per trailhead, in the same order as the trailheads are listed in the instance). This JSON is just a sketch of the shape I need — not your final answer — so fill in the actual identifiers from the instance when you reply.\n\nPlease be careful to use the exact identifiers given in the instance input — no renaming, no made-up labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 29, 61, 34, 56, 43, 24, 39, 31, 52, 42, 36, 29, 33, 32, 21 ], [ 29, 0, 49, 25, 36, 39, 36, 26, 27, 45, 33, 7, 22, 25, 15, 22 ], [ 61, 49, 0, 57, 73, 58, 56, 63, 60, 67, 65, 48, 60, 48, 57, 60 ], [ 34, 25, 57, 0, 47, 33, 41, 44, 19, 58, 47, 24, 35, 46, 31, 25 ], [ 56, 36, 73, 47, 0, 54, 62, 58, 42, 69, 50, 35, 57, 57, 48, 40 ], [ 43, 39, 58, 33, 54, 0, 38, 58, 18, 62, 55, 40, 39, 52, 28, 51 ], [ 24, 36, 56, 41, 62, 38, 0, 41, 26, 63, 44, 40, 43, 55, 36, 31 ], [ 39, 26, 63, 44, 58, 58, 41, 0, 46, 60, 40, 29, 37, 47, 41, 44 ], [ 31, 27, 60, 19, 42, 18, 26, 46, 0, 53, 44, 34, 30, 52, 16, 36 ], [ 52, 45, 67, 58, 69, 62, 63, 60, 53, 0, 58, 44, 25, 66, 55, 63 ], [ 42, 33, 65, 47, 50, 55, 44, 40, 44, 58, 0, 32, 33, 54, 48, 40 ], [ 36, 7, 48, 24, 35, 40, 40, 29, 34, 44, 32, 0, 29, 28, 22, 25 ], [ 29, 22, 60, 35, 57, 39, 43, 37, 30, 25, 33, 29, 0, 44, 32, 42 ], [ 33, 25, 48, 46, 57, 52, 55, 47, 52, 66, 54, 28, 44, 0, 40, 41 ], [ 32, 15, 57, 31, 48, 28, 36, 41, 16, 55, 48, 22, 32, 40, 0, 33 ], [ 21, 22, 60, 25, 40, 51, 31, 44, 36, 63, 40, 25, 42, 41, 33, 0 ] ], "p": 1, "objective": 436.0 }, "solution": { "facilities": [ 1 ], "assignments": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] }, "obj": 436.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 1, "sites": [ { "id": 0, "distances": { "0": 0, "1": 29, "2": 61, "3": 34, "4": 56, "5": 43, "6": 24, "7": 39, "8": 31, "9": 52, "10": 42, "11": 36, "12": 29, "13": 33, "14": 32, "15": 21 } }, { "id": 1, "distances": { "0": 29, "1": 0, "2": 49, "3": 25, "4": 36, "5": 39, "6": 36, "7": 26, "8": 27, "9": 45, "10": 33, "11": 7, "12": 22, "13": 25, "14": 15, "15": 22 } }, { "id": 2, "distances": { "0": 61, "1": 49, "2": 0, "3": 57, "4": 73, "5": 58, "6": 56, "7": 63, "8": 60, "9": 67, "10": 65, "11": 48, "12": 60, "13": 48, "14": 57, "15": 60 } }, { "id": 3, "distances": { "0": 34, "1": 25, "2": 57, "3": 0, "4": 47, "5": 33, "6": 41, "7": 44, "8": 19, "9": 58, "10": 47, "11": 24, "12": 35, "13": 46, "14": 31, "15": 25 } }, { "id": 4, "distances": { "0": 56, "1": 36, "2": 73, "3": 47, "4": 0, "5": 54, "6": 62, "7": 58, "8": 42, "9": 69, "10": 50, "11": 35, "12": 57, "13": 57, "14": 48, "15": 40 } }, { "id": 5, "distances": { "0": 43, "1": 39, "2": 58, "3": 33, "4": 54, "5": 0, "6": 38, "7": 58, "8": 18, "9": 62, "10": 55, "11": 40, "12": 39, "13": 52, "14": 28, "15": 51 } }, { "id": 6, "distances": { "0": 24, "1": 36, "2": 56, "3": 41, "4": 62, "5": 38, "6": 0, "7": 41, "8": 26, "9": 63, "10": 44, "11": 40, "12": 43, "13": 55, "14": 36, "15": 31 } }, { "id": 7, "distances": { "0": 39, "1": 26, "2": 63, "3": 44, "4": 58, "5": 58, "6": 41, "7": 0, "8": 46, "9": 60, "10": 40, "11": 29, "12": 37, "13": 47, "14": 41, "15": 44 } }, { "id": 8, "distances": { "0": 31, "1": 27, "2": 60, "3": 19, "4": 42, "5": 18, "6": 26, "7": 46, "8": 0, "9": 53, "10": 44, "11": 34, "12": 30, "13": 52, "14": 16, "15": 36 } }, { "id": 9, "distances": { "0": 52, "1": 45, "2": 67, "3": 58, "4": 69, "5": 62, "6": 63, "7": 60, "8": 53, "9": 0, "10": 58, "11": 44, "12": 25, "13": 66, "14": 55, "15": 63 } }, { "id": 10, "distances": { "0": 42, "1": 33, "2": 65, "3": 47, "4": 50, "5": 55, "6": 44, "7": 40, "8": 44, "9": 58, "10": 0, "11": 32, "12": 33, "13": 54, "14": 48, "15": 40 } }, { "id": 11, "distances": { "0": 36, "1": 7, "2": 48, "3": 24, "4": 35, "5": 40, "6": 40, "7": 29, "8": 34, "9": 44, "10": 32, "11": 0, "12": 29, "13": 28, "14": 22, "15": 25 } }, { "id": 12, "distances": { "0": 29, "1": 22, "2": 60, "3": 35, "4": 57, "5": 39, "6": 43, "7": 37, "8": 30, "9": 25, "10": 33, "11": 29, "12": 0, "13": 44, "14": 32, "15": 42 } }, { "id": 13, "distances": { "0": 33, "1": 25, "2": 48, "3": 46, "4": 57, "5": 52, "6": 55, "7": 47, "8": 52, "9": 66, "10": 54, "11": 28, "12": 44, "13": 0, "14": 40, "15": 41 } }, { "id": 14, "distances": { "0": 32, "1": 15, "2": 57, "3": 31, "4": 48, "5": 28, "6": 36, "7": 41, "8": 16, "9": 55, "10": 48, "11": 22, "12": 32, "13": 40, "14": 0, "15": 33 } }, { "id": 15, "distances": { "0": 21, "1": 22, "2": 60, "3": 25, "4": 40, "5": 51, "6": 31, "7": 44, "8": 36, "9": 63, "10": 40, "11": 25, "12": 42, "13": 41, "14": 33, "15": 0 } } ], "objective": 436.0 }, "solution_variant": { "selected": [ 1 ], "assignments": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] }, "context_index": 12, "input_format": "json", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I’m running the ride‑hail ops side and need to pick which driver rest stops to keep open from a list of possible spots. The plan is to choose a fixed number of those stops and then link every service zone to one of the open stops — one and only one, no zone left out or split between stops. The better choice is the one that makes the drivers travel the least overall, measured by adding up the distance from each zone to its assigned rest stop. Concrete details are shown below.\n\n{\n \"total_candidate_locations\": 17,\n \"stops_to_keep_open\": 1,\n \"location_ids\": [\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16,\n 17\n ],\n \"data\": [\n {\n \"source_location_id\": 1,\n \"target_location_id\": 2,\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 3,\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 4,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 5,\n \"travel_distance\": 16\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 6,\n \"travel_distance\": 33\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 7,\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 8,\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 9,\n \"travel_distance\": 16\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 10,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 11,\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 12,\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 13,\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 14,\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 15,\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 16,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 1,\n \"target_location_id\": 17,\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": 2,\n \"target_location_id\": 1,\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": 2,\n \"target_location_id\": 3,\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": 2,\n \"target_location_id\": 4,\n 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7,\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 8,\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 9,\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 10,\n \"travel_distance\": 52\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 11,\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 12,\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 13,\n \"travel_distance\": 37\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 14,\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 16,\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": 15,\n \"target_location_id\": 17,\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 1,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 2,\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 3,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 4,\n \"travel_distance\": 20\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 5,\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 6,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 7,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 8,\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 9,\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 10,\n \"travel_distance\": 41\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 11,\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 12,\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 13,\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 14,\n \"travel_distance\": 40\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 15,\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": 16,\n \"target_location_id\": 17,\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 1,\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 2,\n \"travel_distance\": 59\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 3,\n \"travel_distance\": 50\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 4,\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 5,\n \"travel_distance\": 44\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 6,\n \"travel_distance\": 50\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 7,\n \"travel_distance\": 25\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 8,\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 9,\n \"travel_distance\": 40\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 10,\n \"travel_distance\": 64\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 11,\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 12,\n \"travel_distance\": 56\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 13,\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 14,\n \"travel_distance\": 42\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 15,\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": 17,\n \"target_location_id\": 16,\n \"travel_distance\": 45\n }\n ]\n}\n\nI'll keep the answer in a tiny, predictable JSON shape so it's easy to plug into whatever you're using. Something like this:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the rest stops we choose to keep open. \"assignments\" is a list, in the same order as the input zones, saying which open stop each zone gets linked to. Super casual — think of it as filling out a form, not a report.\n\nThis JSON is just a sketch of the shape I need you to return, not the actual choices. And please use the exact identifiers from the instance input — don't rename them or invent new labels. \n\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 32, 30, 31, 16, 33, 34, 34, 16, 31, 38, 34, 48, 34, 26, 31, 53 ], [ 32, 0, 35, 19, 28, 35, 39, 40, 29, 44, 25, 38, 37, 30, 29, 39, 59 ], [ 30, 35, 0, 31, 39, 26, 44, 39, 26, 37, 25, 44, 50, 39, 41, 31, 50 ], [ 31, 19, 31, 0, 29, 31, 40, 30, 25, 42, 34, 25, 43, 34, 10, 20, 53 ], [ 16, 28, 39, 29, 0, 40, 25, 18, 30, 45, 42, 42, 41, 30, 39, 27, 44 ], [ 33, 35, 26, 31, 40, 0, 44, 39, 32, 47, 29, 50, 50, 39, 41, 31, 50 ], [ 34, 39, 44, 40, 25, 44, 0, 21, 28, 45, 33, 34, 42, 37, 48, 31, 25 ], [ 34, 40, 39, 30, 18, 39, 21, 0, 32, 43, 34, 33, 27, 16, 28, 26, 26 ], [ 16, 29, 26, 25, 30, 32, 28, 32, 0, 27, 34, 30, 42, 29, 35, 30, 40 ], [ 31, 44, 37, 42, 45, 47, 45, 43, 27, 0, 49, 45, 59, 45, 52, 41, 64 ], [ 38, 25, 25, 34, 42, 29, 33, 34, 34, 49, 0, 35, 49, 40, 43, 31, 53 ], [ 34, 38, 44, 25, 42, 50, 34, 33, 30, 45, 35, 0, 46, 43, 35, 35, 56 ], [ 48, 37, 50, 43, 41, 50, 42, 27, 42, 59, 49, 46, 0, 15, 37, 46, 53 ], [ 34, 30, 39, 34, 30, 39, 37, 16, 29, 45, 40, 43, 15, 0, 26, 40, 42 ], [ 26, 29, 41, 10, 39, 41, 48, 28, 35, 52, 43, 35, 37, 26, 0, 30, 43 ], [ 31, 39, 31, 20, 27, 31, 31, 26, 30, 41, 31, 35, 46, 40, 30, 0, 45 ], [ 53, 59, 50, 53, 44, 50, 25, 26, 40, 64, 53, 56, 53, 42, 43, 45, 0 ] ], "p": 1, "objective": 485.0 }, "solution": { "facilities": [ 8 ], "assignments": [ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 ] }, "obj": 485.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 1, "sites": [ { "id": 1, "distances": { "1": 0, "2": 32, "3": 30, "4": 31, "5": 16, "6": 33, "7": 34, "8": 34, "9": 16, "10": 31, "11": 38, "12": 34, "13": 48, "14": 34, "15": 26, "16": 31, "17": 53 } }, { "id": 2, "distances": { "1": 32, "2": 0, "3": 35, "4": 19, "5": 28, "6": 35, "7": 39, "8": 40, "9": 29, "10": 44, "11": 25, "12": 38, "13": 37, "14": 30, "15": 29, "16": 39, "17": 59 } }, { "id": 3, "distances": { "1": 30, "2": 35, "3": 0, "4": 31, "5": 39, "6": 26, "7": 44, "8": 39, "9": 26, "10": 37, "11": 25, "12": 44, "13": 50, "14": 39, "15": 41, "16": 31, "17": 50 } }, { "id": 4, "distances": { "1": 31, "2": 19, "3": 31, "4": 0, "5": 29, "6": 31, "7": 40, "8": 30, "9": 25, "10": 42, "11": 34, "12": 25, "13": 43, "14": 34, "15": 10, "16": 20, "17": 53 } }, { "id": 5, "distances": { "1": 16, "2": 28, "3": 39, "4": 29, "5": 0, "6": 40, "7": 25, "8": 18, "9": 30, "10": 45, "11": 42, "12": 42, "13": 41, "14": 30, "15": 39, "16": 27, "17": 44 } }, { "id": 6, "distances": { "1": 33, "2": 35, "3": 26, "4": 31, "5": 40, "6": 0, "7": 44, "8": 39, "9": 32, "10": 47, "11": 29, "12": 50, "13": 50, "14": 39, "15": 41, "16": 31, "17": 50 } }, { "id": 7, "distances": { "1": 34, "2": 39, "3": 44, "4": 40, "5": 25, "6": 44, "7": 0, "8": 21, "9": 28, "10": 45, "11": 33, "12": 34, "13": 42, "14": 37, "15": 48, "16": 31, "17": 25 } }, { "id": 8, "distances": { "1": 34, "2": 40, "3": 39, "4": 30, "5": 18, "6": 39, "7": 21, "8": 0, "9": 32, "10": 43, "11": 34, "12": 33, "13": 27, "14": 16, "15": 28, "16": 26, "17": 26 } }, { "id": 9, "distances": { "1": 16, "2": 29, "3": 26, "4": 25, "5": 30, "6": 32, "7": 28, "8": 32, "9": 0, "10": 27, "11": 34, "12": 30, "13": 42, "14": 29, "15": 35, "16": 30, "17": 40 } }, { "id": 10, "distances": { "1": 31, "2": 44, "3": 37, "4": 42, "5": 45, "6": 47, "7": 45, "8": 43, "9": 27, "10": 0, "11": 49, "12": 45, "13": 59, "14": 45, "15": 52, "16": 41, "17": 64 } }, { "id": 11, "distances": { "1": 38, "2": 25, "3": 25, "4": 34, "5": 42, "6": 29, "7": 33, "8": 34, "9": 34, "10": 49, "11": 0, "12": 35, "13": 49, "14": 40, "15": 43, "16": 31, "17": 53 } }, { "id": 12, "distances": { "1": 34, "2": 38, "3": 44, "4": 25, "5": 42, "6": 50, "7": 34, "8": 33, "9": 30, "10": 45, "11": 35, "12": 0, "13": 46, "14": 43, "15": 35, "16": 35, "17": 56 } }, { "id": 13, "distances": { "1": 48, "2": 37, "3": 50, "4": 43, "5": 41, "6": 50, "7": 42, "8": 27, "9": 42, "10": 59, "11": 49, "12": 46, "13": 0, "14": 15, "15": 37, "16": 46, "17": 53 } }, { "id": 14, "distances": { "1": 34, "2": 30, "3": 39, "4": 34, "5": 30, "6": 39, "7": 37, "8": 16, "9": 29, "10": 45, "11": 40, "12": 43, "13": 15, "14": 0, "15": 26, "16": 40, "17": 42 } }, { "id": 15, "distances": { "1": 26, "2": 29, "3": 41, "4": 10, "5": 39, "6": 41, "7": 48, "8": 28, "9": 35, "10": 52, "11": 43, "12": 35, "13": 37, "14": 26, "15": 0, "16": 30, "17": 43 } }, { "id": 16, "distances": { "1": 31, "2": 39, "3": 31, "4": 20, "5": 27, "6": 31, "7": 31, "8": 26, "9": 30, "10": 41, "11": 31, "12": 35, "13": 46, "14": 40, "15": 30, "16": 0, "17": 45 } }, { "id": 17, "distances": { "1": 53, "2": 59, "3": 50, "4": 53, "5": 44, "6": 50, "7": 25, "8": 26, "9": 40, "10": 64, "11": 53, "12": 56, "13": 53, "14": 42, "15": 43, "16": 45, "17": 0 } } ], "objective": 485.0 }, "solution_variant": { "selected": [ 9 ], "assignments": [ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 ] }, "context_index": 13, "input_format": "json", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I run the hospital’s community outreach, and now I have to pick a fixed number of pop‑up vaccination clinics to open in town at some of the community centers. Every neighborhood needs to be signed up with exactly one of those clinics — nobody gets left out or sent to two places — and the whole point is to make the total travel everyone has to do as small as possible. That means adding up the distance from each neighborhood to the clinic it’s assigned to, and choosing clinic sites so that that sum is as low as it can be. The specific list of candidate centers and the distances between neighborhoods and centers are shown below.\n\nThere are 16 locations in total; I must open 5 clinics and the listed location IDs are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.\nI note the travel distance from 1 to 2 is 46.\nI note the travel distance from 1 to 3 is 51.\nI note the travel distance from 1 to 4 is 38.\nI note the travel distance from 1 to 5 is 59.\nI note the travel distance from 1 to 6 is 30.\nI note the travel distance from 1 to 7 is 50.\nI note the travel distance from 1 to 8 is 54.\nI note the travel distance from 1 to 9 is 37.\nI note the travel distance from 1 to 10 is 25.\nI note the travel distance from 1 to 11 is 48.\nI note the travel distance from 1 to 12 is 33.\nI note the travel distance from 1 to 13 is 36.\nI note the travel distance from 1 to 14 is 49.\nI note the travel distance from 1 to 15 is 51.\nI note the travel distance from 1 to 16 is 16.\nI note the travel distance from 2 to 1 is 46.\nI note the travel distance from 2 to 3 is 27.\nI note the travel distance from 2 to 4 is 49.\nI note the travel distance from 2 to 5 is 41.\nI note the travel distance from 2 to 6 is 24.\nI note the travel distance from 2 to 7 is 43.\nI note the travel distance from 2 to 8 is 35.\nI note the travel distance from 2 to 9 is 60.\nI note the travel distance from 2 to 10 is 37.\nI note the travel distance from 2 to 11 is 39.\nI note the travel distance from 2 to 12 is 39.\nI note the travel distance from 2 to 13 is 40.\nI note the travel distance from 2 to 14 is 36.\nI note the travel distance from 2 to 15 is 39.\nI note the travel distance from 2 to 16 is 35.\nI note the travel distance from 3 to 1 is 51.\nI note the travel distance from 3 to 2 is 27.\nI note the travel distance from 3 to 4 is 56.\nI note the travel distance from 3 to 5 is 52.\nI note the travel distance from 3 to 6 is 31.\nI note the travel distance from 3 to 7 is 50.\nI note the travel distance from 3 to 8 is 42.\nI note the travel distance from 3 to 9 is 66.\nI note the travel distance from 3 to 10 is 42.\nI note the travel distance from 3 to 11 is 46.\nI note the travel distance from 3 to 12 is 46.\nI note the travel distance from 3 to 13 is 45.\nI note the travel distance from 3 to 14 is 47.\nI note the travel distance from 3 to 15 is 44.\nI note the travel distance from 3 to 16 is 42.\nI note the travel distance from 4 to 1 is 38.\nI note the travel distance from 4 to 2 is 49.\nI note the travel distance from 4 to 3 is 56.\nI note the travel distance from 4 to 5 is 64.\nI note the travel distance from 4 to 6 is 51.\nI note the travel distance from 4 to 7 is 70.\nI note the travel distance from 4 to 8 is 64.\nI note the travel distance from 4 to 9 is 75.\nI note the travel distance from 4 to 10 is 35.\nI note the travel distance from 4 to 11 is 52.\nI note the travel distance from 4 to 12 is 38.\nI note the travel distance from 4 to 13 is 47.\nI note the travel distance from 4 to 14 is 69.\nI note the travel distance from 4 to 15 is 57.\nI note the travel distance from 4 to 16 is 22.\nI note the travel distance from 5 to 1 is 59.\nI note the travel distance from 5 to 2 is 41.\nI note the travel distance from 5 to 3 is 52.\nI note the travel distance from 5 to 4 is 64.\nI note the travel distance from 5 to 6 is 58.\nI note the travel distance from 5 to 7 is 69.\nI note the travel distance from 5 to 8 is 51.\nI note the travel distance from 5 to 9 is 67.\nI note the travel distance from 5 to 10 is 59.\nI note the travel distance from 5 to 11 is 78.\nI note the travel distance from 5 to 12 is 53.\nI note the travel distance from 5 to 13 is 61.\nI note the travel distance from 5 to 14 is 68.\nI note the travel distance from 5 to 15 is 27.\nI note the travel distance from 5 to 16 is 50.\nI note the travel distance from 6 to 1 is 30.\nI note the travel distance from 6 to 2 is 24.\nI note the travel distance from 6 to 3 is 31.\nI note the travel distance from 6 to 4 is 51.\nI note the travel distance from 6 to 5 is 58.\nI note the travel distance from 6 to 7 is 47.\nI note the travel distance from 6 to 8 is 33.\nI note the travel distance from 6 to 9 is 44.\nI note the travel distance from 6 to 10 is 40.\nI note the travel distance from 6 to 11 is 40.\nI note the travel distance from 6 to 12 is 15.\nI note the travel distance from 6 to 13 is 39.\nI note the travel distance from 6 to 14 is 44.\nI note the travel distance from 6 to 15 is 59.\nI note the travel distance from 6 to 16 is 39.\nI note the travel distance from 7 to 1 is 50.\nI note the travel distance from 7 to 2 is 43.\nI note the travel distance from 7 to 3 is 50.\nI note the travel distance from 7 to 4 is 70.\nI note the travel distance from 7 to 5 is 69.\nI note the travel distance from 7 to 6 is 47.\nI note the travel distance from 7 to 8 is 58.\nI note the travel distance from 7 to 9 is 72.\nI note the travel distance from 7 to 10 is 41.\nI note the travel distance from 7 to 11 is 62.\nI note the travel distance from 7 to 12 is 51.\nI note the travel distance from 7 to 13 is 52.\nI note the travel distance from 7 to 14 is 63.\nI note the travel distance from 7 to 15 is 48.\nI note the travel distance from 7 to 16 is 48.\nI note the travel distance from 8 to 1 is 54.\nI note the travel distance from 8 to 2 is 35.\nI note the travel distance from 8 to 3 is 42.\nI note the travel distance from 8 to 4 is 64.\nI note the travel distance from 8 to 5 is 51.\nI note the travel distance from 8 to 6 is 33.\nI note the travel distance from 8 to 7 is 58.\nI note the travel distance from 8 to 9 is 68.\nI note the travel distance from 8 to 10 is 61.\nI note the travel distance from 8 to 11 is 54.\nI note the travel distance from 8 to 12 is 44.\nI note the travel distance from 8 to 13 is 48.\nI note the travel distance from 8 to 14 is 55.\nI note the travel distance from 8 to 15 is 54.\nI note the travel distance from 8 to 16 is 50.\nI note the travel distance from 9 to 1 is 37.\nI note the travel distance from 9 to 2 is 60.\nI note the travel distance from 9 to 3 is 66.\nI note the travel distance from 9 to 4 is 75.\nI note the travel distance from 9 to 5 is 67.\nI note the travel distance from 9 to 6 is 44.\nI note the travel distance from 9 to 7 is 72.\nI note the travel distance from 9 to 8 is 68.\nI note the travel distance from 9 to 10 is 53.\nI note the travel distance from 9 to 11 is 54.\nI note the travel distance from 9 to 12 is 39.\nI note the travel distance from 9 to 13 is 58.\nI note the travel distance from 9 to 14 is 71.\nI note the travel distance from 9 to 15 is 62.\nI note the travel distance from 9 to 16 is 53.\nI note the travel distance from 10 to 1 is 25.\nI note the travel distance from 10 to 2 is 37.\nI note the travel distance from 10 to 3 is 42.\nI note the travel distance from 10 to 4 is 35.\nI note the travel distance from 10 to 5 is 59.\nI note the travel distance from 10 to 6 is 40.\nI note the travel distance from 10 to 7 is 41.\nI note the travel distance from 10 to 8 is 61.\nI note the travel distance from 10 to 9 is 53.\nI note the travel distance from 10 to 11 is 51.\nI note the travel distance from 10 to 12 is 37.\nI note the travel distance from 10 to 13 is 27.\nI note the travel distance from 10 to 14 is 40.\nI note the travel distance from 10 to 15 is 42.\nI note the travel distance from 10 to 16 is 21.\nI note the travel distance from 11 to 1 is 48.\nI note the travel distance from 11 to 2 is 39.\nI note the travel distance from 11 to 3 is 46.\nI note the travel distance from 11 to 4 is 52.\nI note the travel distance from 11 to 5 is 78.\nI note the travel distance from 11 to 6 is 40.\nI note the travel distance from 11 to 7 is 62.\nI note the travel distance from 11 to 8 is 54.\nI note the travel distance from 11 to 9 is 54.\nI note the travel distance from 11 to 10 is 51.\nI note the travel distance from 11 to 12 is 27.\nI note the travel distance from 11 to 13 is 59.\nI note the travel distance from 11 to 14 is 59.\nI note the travel distance from 11 to 15 is 66.\nI note the travel distance from 11 to 16 is 38.\nI note the travel distance from 12 to 1 is 33.\nI note the travel distance from 12 to 2 is 39.\nI note the travel distance from 12 to 3 is 46.\nI note the travel distance from 12 to 4 is 38.\nI note the travel distance from 12 to 5 is 53.\nI note the travel distance from 12 to 6 is 15.\nI note the travel distance from 12 to 7 is 51.\nI note the travel distance from 12 to 8 is 44.\nI note the travel distance from 12 to 9 is 39.\nI note the travel distance from 12 to 10 is 37.\nI note the travel distance from 12 to 11 is 27.\nI note the travel distance from 12 to 13 is 34.\nI note the travel distance from 12 to 14 is 58.\nI note the travel distance from 12 to 15 is 47.\nI note the travel distance from 12 to 16 is 43.\nI note the travel distance from 13 to 1 is 36.\nI note the travel distance from 13 to 2 is 40.\nI note the travel distance from 13 to 3 is 45.\nI note the travel distance from 13 to 4 is 47.\nI note the travel distance from 13 to 5 is 61.\nI note the travel distance from 13 to 6 is 39.\nI note the travel distance from 13 to 7 is 52.\nI note the travel distance from 13 to 8 is 48.\nI note the travel distance from 13 to 9 is 58.\nI note the travel distance from 13 to 10 is 27.\nI note the travel distance from 13 to 11 is 59.\nI note the travel distance from 13 to 12 is 34.\nI note the travel distance from 13 to 14 is 38.\nI note the travel distance from 13 to 15 is 45.\nI note the travel distance from 13 to 16 is 34.\nI note the travel distance from 14 to 1 is 49.\nI note the travel distance from 14 to 2 is 36.\nI note the travel distance from 14 to 3 is 47.\nI note the travel distance from 14 to 4 is 69.\nI note the travel distance from 14 to 5 is 68.\nI note the travel distance from 14 to 6 is 44.\nI note the travel distance from 14 to 7 is 63.\nI note the travel distance from 14 to 8 is 55.\nI note the travel distance from 14 to 9 is 71.\nI note the travel distance from 14 to 10 is 40.\nI note the travel distance from 14 to 11 is 59.\nI note the travel distance from 14 to 12 is 58.\nI note the travel distance from 14 to 13 is 38.\nI note the travel distance from 14 to 15 is 57.\nI note the travel distance from 14 to 16 is 47.\nI note the travel distance from 15 to 1 is 51.\nI note the travel distance from 15 to 2 is 39.\nI note the travel distance from 15 to 3 is 44.\nI note the travel distance from 15 to 4 is 57.\nI note the travel distance from 15 to 5 is 27.\nI note the travel distance from 15 to 6 is 59.\nI note the travel distance from 15 to 7 is 48.\nI note the travel distance from 15 to 8 is 54.\nI note the travel distance from 15 to 9 is 62.\nI note the travel distance from 15 to 10 is 42.\nI note the travel distance from 15 to 11 is 66.\nI note the travel distance from 15 to 12 is 47.\nI note the travel distance from 15 to 13 is 45.\nI note the travel distance from 15 to 14 is 57.\nI note the travel distance from 15 to 16 is 43.\nI note the travel distance from 16 to 1 is 16.\nI note the travel distance from 16 to 2 is 35.\nI note the travel distance from 16 to 3 is 42.\nI note the travel distance from 16 to 4 is 22.\nI note the travel distance from 16 to 5 is 50.\nI note the travel distance from 16 to 6 is 39.\nI note the travel distance from 16 to 7 is 48.\nI note the travel distance from 16 to 8 is 50.\nI note the travel distance from 16 to 9 is 53.\nI note the travel distance from 16 to 10 is 21.\nI note the travel distance from 16 to 11 is 38.\nI note the travel distance from 16 to 12 is 43.\nI note the travel distance from 16 to 13 is 34.\nI note the travel distance from 16 to 14 is 47.\nI note the travel distance from 16 to 15 is 43.\nWith these distances, I'll choose 5 clinic sites from the 16 locations to minimize total travel.\n\nI'll put the actual choices and assignments into a simple JSON snippet so it's easy to read and reuse. It'll follow this shape:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where I'll list which community centers we decide to open as pop‑up clinics, and \"assignments\" is a matching list showing, for each neighborhood in the order they were given, which opened site it gets signed up with. This is just a sketch of the shape I will use — not the final answer.\n\nPlease make sure to use the exact identifiers from the instance input (don't rename them and don't invent new ones):\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 46, 51, 38, 59, 30, 50, 54, 37, 25, 48, 33, 36, 49, 51, 16 ], [ 46, 0, 27, 49, 41, 24, 43, 35, 60, 37, 39, 39, 40, 36, 39, 35 ], [ 51, 27, 0, 56, 52, 31, 50, 42, 66, 42, 46, 46, 45, 47, 44, 42 ], [ 38, 49, 56, 0, 64, 51, 70, 64, 75, 35, 52, 38, 47, 69, 57, 22 ], [ 59, 41, 52, 64, 0, 58, 69, 51, 67, 59, 78, 53, 61, 68, 27, 50 ], [ 30, 24, 31, 51, 58, 0, 47, 33, 44, 40, 40, 15, 39, 44, 59, 39 ], [ 50, 43, 50, 70, 69, 47, 0, 58, 72, 41, 62, 51, 52, 63, 48, 48 ], [ 54, 35, 42, 64, 51, 33, 58, 0, 68, 61, 54, 44, 48, 55, 54, 50 ], [ 37, 60, 66, 75, 67, 44, 72, 68, 0, 53, 54, 39, 58, 71, 62, 53 ], [ 25, 37, 42, 35, 59, 40, 41, 61, 53, 0, 51, 37, 27, 40, 42, 21 ], [ 48, 39, 46, 52, 78, 40, 62, 54, 54, 51, 0, 27, 59, 59, 66, 38 ], [ 33, 39, 46, 38, 53, 15, 51, 44, 39, 37, 27, 0, 34, 58, 47, 43 ], [ 36, 40, 45, 47, 61, 39, 52, 48, 58, 27, 59, 34, 0, 38, 45, 34 ], [ 49, 36, 47, 69, 68, 44, 63, 55, 71, 40, 59, 58, 38, 0, 57, 47 ], [ 51, 39, 44, 57, 27, 59, 48, 54, 62, 42, 66, 47, 45, 57, 0, 43 ], [ 16, 35, 42, 22, 50, 39, 48, 50, 53, 21, 38, 43, 34, 47, 43, 0 ] ], "p": 5, "objective": 299.0 }, "solution": { "facilities": [ 1, 6, 11, 14, 15 ], "assignments": [ 15, 1, 1, 15, 14, 11, 6, 1, 11, 15, 11, 11, 11, 1, 14, 15 ] }, "obj": 299.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 5, "sites": [ { "id": 1, "distances": { "1": 0, "2": 46, "3": 51, "4": 38, "5": 59, "6": 30, "7": 50, "8": 54, "9": 37, "10": 25, "11": 48, "12": 33, "13": 36, "14": 49, "15": 51, "16": 16 } }, { "id": 2, "distances": { "1": 46, "2": 0, "3": 27, "4": 49, "5": 41, "6": 24, "7": 43, "8": 35, "9": 60, "10": 37, "11": 39, "12": 39, "13": 40, "14": 36, "15": 39, "16": 35 } }, { "id": 3, "distances": { "1": 51, "2": 27, "3": 0, "4": 56, "5": 52, "6": 31, "7": 50, "8": 42, "9": 66, "10": 42, "11": 46, "12": 46, "13": 45, "14": 47, "15": 44, "16": 42 } }, { "id": 4, "distances": { "1": 38, "2": 49, "3": 56, "4": 0, "5": 64, "6": 51, "7": 70, "8": 64, "9": 75, "10": 35, "11": 52, "12": 38, "13": 47, "14": 69, "15": 57, "16": 22 } }, { "id": 5, "distances": { "1": 59, "2": 41, "3": 52, "4": 64, "5": 0, "6": 58, "7": 69, "8": 51, "9": 67, "10": 59, "11": 78, "12": 53, "13": 61, "14": 68, "15": 27, "16": 50 } }, { "id": 6, "distances": { "1": 30, "2": 24, "3": 31, "4": 51, "5": 58, "6": 0, "7": 47, "8": 33, "9": 44, "10": 40, "11": 40, "12": 15, "13": 39, "14": 44, "15": 59, "16": 39 } }, { "id": 7, "distances": { "1": 50, "2": 43, "3": 50, "4": 70, "5": 69, "6": 47, "7": 0, "8": 58, "9": 72, "10": 41, "11": 62, "12": 51, "13": 52, "14": 63, "15": 48, "16": 48 } }, { "id": 8, "distances": { "1": 54, "2": 35, "3": 42, "4": 64, "5": 51, "6": 33, "7": 58, "8": 0, "9": 68, "10": 61, "11": 54, "12": 44, "13": 48, "14": 55, "15": 54, "16": 50 } }, { "id": 9, "distances": { "1": 37, "2": 60, "3": 66, "4": 75, "5": 67, "6": 44, "7": 72, "8": 68, "9": 0, "10": 53, "11": 54, "12": 39, "13": 58, "14": 71, "15": 62, "16": 53 } }, { "id": 10, "distances": { "1": 25, "2": 37, "3": 42, "4": 35, "5": 59, "6": 40, "7": 41, "8": 61, "9": 53, "10": 0, "11": 51, "12": 37, "13": 27, "14": 40, "15": 42, "16": 21 } }, { "id": 11, "distances": { "1": 48, "2": 39, "3": 46, "4": 52, "5": 78, "6": 40, "7": 62, "8": 54, "9": 54, "10": 51, "11": 0, "12": 27, "13": 59, "14": 59, "15": 66, "16": 38 } }, { "id": 12, "distances": { "1": 33, "2": 39, "3": 46, "4": 38, "5": 53, "6": 15, "7": 51, "8": 44, "9": 39, "10": 37, "11": 27, "12": 0, "13": 34, "14": 58, "15": 47, "16": 43 } }, { "id": 13, "distances": { "1": 36, "2": 40, "3": 45, "4": 47, "5": 61, "6": 39, "7": 52, "8": 48, "9": 58, "10": 27, "11": 59, "12": 34, "13": 0, "14": 38, "15": 45, "16": 34 } }, { "id": 14, "distances": { "1": 49, "2": 36, "3": 47, "4": 69, "5": 68, "6": 44, "7": 63, "8": 55, "9": 71, "10": 40, "11": 59, "12": 58, "13": 38, "14": 0, "15": 57, "16": 47 } }, { "id": 15, "distances": { "1": 51, "2": 39, "3": 44, "4": 57, "5": 27, "6": 59, "7": 48, "8": 54, "9": 62, "10": 42, "11": 66, "12": 47, "13": 45, "14": 57, "15": 0, "16": 43 } }, { "id": 16, "distances": { "1": 16, "2": 35, "3": 42, "4": 22, "5": 50, "6": 39, "7": 48, "8": 50, "9": 53, "10": 21, "11": 38, "12": 43, "13": 34, "14": 47, "15": 43, "16": 0 } } ], "objective": 299.0 }, "solution_variant": { "selected": [ 2, 7, 12, 15, 16 ], "assignments": [ 16, 2, 2, 16, 15, 12, 7, 2, 12, 16, 12, 12, 12, 2, 15, 16 ] }, "context_index": 14, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "We’ve been handed a list of candidate spots for temporary library pop‑ups and have to choose only a set number to actually open. Then each residential block gets attached to one of the opened spots — only one — and the success of the plan is judged by the combined walking distance of everyone: sum up the distance from each block to its assigned pop‑up, and the lower that combined distance, the better. The concrete locations and distances follow below.\n\nThere are 16 locations listed in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and we must open exactly 3 pop-ups.\nFrom 1 to 2: walking distance 37.\nFrom 1 to 3: walking distance 58.\nFrom 1 to 4: walking distance 58.\nFrom 1 to 5: walking distance 74.\nFrom 1 to 6: walking distance 35.\nFrom 1 to 7: walking distance 63.\nFrom 1 to 8: walking distance 46.\nFrom 1 to 9: walking distance 65.\nFrom 1 to 10: walking distance 76.\nFrom 1 to 11: walking distance 53.\nFrom 1 to 12: walking distance 29.\nFrom 1 to 13: walking distance 50.\nFrom 1 to 14: walking distance 35.\nFrom 1 to 15: walking distance 44.\nFrom 1 to 16: walking distance 59.\nFrom 2 to 1: walking distance 37.\nFrom 2 to 3: walking distance 63.\nFrom 2 to 4: walking distance 62.\nFrom 2 to 5: walking distance 59.\nFrom 2 to 6: walking distance 35.\nFrom 2 to 7: walking distance 65.\nFrom 2 to 8: walking distance 60.\nFrom 2 to 9: walking distance 66.\nFrom 2 to 10: walking distance 85.\nFrom 2 to 11: walking distance 53.\nFrom 2 to 12: walking distance 62.\nFrom 2 to 13: walking distance 54.\nFrom 2 to 14: walking distance 54.\nFrom 2 to 15: walking distance 57.\nFrom 2 to 16: walking distance 36.\nFrom 3 to 1: walking distance 58.\nFrom 3 to 2: walking distance 63.\nFrom 3 to 4: walking distance 39.\nFrom 3 to 5: walking distance 68.\nFrom 3 to 6: walking distance 46.\nFrom 3 to 7: walking distance 53.\nFrom 3 to 8: walking distance 63.\nFrom 3 to 9: walking distance 63.\nFrom 3 to 10: walking distance 80.\nFrom 3 to 11: walking distance 36.\nFrom 3 to 12: walking distance 55.\nFrom 3 to 13: walking distance 33.\nFrom 3 to 14: walking distance 39.\nFrom 3 to 15: walking distance 68.\nFrom 3 to 16: walking distance 63.\nFrom 4 to 1: walking distance 58.\nFrom 4 to 2: walking distance 62.\nFrom 4 to 3: walking distance 39.\nFrom 4 to 5: walking distance 42.\nFrom 4 to 6: walking distance 53.\nFrom 4 to 7: walking distance 46.\nFrom 4 to 8: walking distance 65.\nFrom 4 to 9: walking distance 66.\nFrom 4 to 10: walking distance 75.\nFrom 4 to 11: walking distance 37.\nFrom 4 to 12: walking distance 55.\nFrom 4 to 13: walking distance 38.\nFrom 4 to 14: walking distance 56.\nFrom 4 to 15: walking distance 68.\nFrom 4 to 16: walking distance 55.\nFrom 5 to 1: walking distance 74.\nFrom 5 to 2: walking distance 59.\nFrom 5 to 3: walking distance 68.\nFrom 5 to 4: walking distance 42.\nFrom 5 to 6: walking distance 47.\nFrom 5 to 7: walking distance 48.\nFrom 5 to 8: walking distance 67.\nFrom 5 to 9: walking distance 75.\nFrom 5 to 10: walking distance 98.\nFrom 5 to 11: walking distance 65.\nFrom 5 to 12: walking distance 81.\nFrom 5 to 13: walking distance 71.\nFrom 5 to 14: walking distance 66.\nFrom 5 to 15: walking distance 77.\nFrom 5 to 16: walking distance 43.\nFrom 6 to 1: walking distance 35.\nFrom 6 to 2: walking distance 35.\nFrom 6 to 3: walking distance 46.\nFrom 6 to 4: walking distance 53.\nFrom 6 to 5: walking distance 47.\nFrom 6 to 7: walking distance 44.\nFrom 6 to 8: walking distance 63.\nFrom 6 to 9: walking distance 58.\nFrom 6 to 10: walking distance 71.\nFrom 6 to 11: walking distance 36.\nFrom 6 to 12: walking distance 58.\nFrom 6 to 13: walking distance 63.\nFrom 6 to 14: walking distance 33.\nFrom 6 to 15: walking distance 40.\nFrom 6 to 16: walking distance 34.\nFrom 7 to 1: walking distance 63.\nFrom 7 to 2: walking distance 65.\nFrom 7 to 3: walking distance 53.\nFrom 7 to 4: walking distance 46.\nFrom 7 to 5: walking distance 48.\nFrom 7 to 6: walking distance 44.\nFrom 7 to 8: walking distance 19.\nFrom 7 to 9: walking distance 76.\nFrom 7 to 10: walking distance 88.\nFrom 7 to 11: walking distance 49.\nFrom 7 to 12: walking distance 56.\nFrom 7 to 13: walking distance 56.\nFrom 7 to 14: walking distance 48.\nFrom 7 to 15: walking distance 42.\nFrom 7 to 16: walking distance 49.\nFrom 8 to 1: walking distance 46.\nFrom 8 to 2: walking distance 60.\nFrom 8 to 3: walking distance 63.\nFrom 8 to 4: walking distance 65.\nFrom 8 to 5: walking distance 67.\nFrom 8 to 6: walking distance 63.\nFrom 8 to 7: walking distance 19.\nFrom 8 to 9: walking distance 78.\nFrom 8 to 10: walking distance 90.\nFrom 8 to 11: walking distance 59.\nFrom 8 to 12: walking distance 39.\nFrom 8 to 13: walking distance 64.\nFrom 8 to 14: walking distance 49.\nFrom 8 to 15: walking distance 57.\nFrom 8 to 16: walking distance 61.\nFrom 9 to 1: walking distance 65.\nFrom 9 to 2: walking distance 66.\nFrom 9 to 3: walking distance 63.\nFrom 9 to 4: walking distance 66.\nFrom 9 to 5: walking distance 75.\nFrom 9 to 6: walking distance 58.\nFrom 9 to 7: walking distance 76.\nFrom 9 to 8: walking distance 78.\nFrom 9 to 10: walking distance 93.\nFrom 9 to 11: walking distance 63.\nFrom 9 to 12: walking distance 77.\nFrom 9 to 13: walking distance 60.\nFrom 9 to 14: walking distance 53.\nFrom 9 to 15: walking distance 36.\nFrom 9 to 16: walking distance 65.\nFrom 10 to 1: walking distance 76.\nFrom 10 to 2: walking distance 85.\nFrom 10 to 3: walking distance 80.\nFrom 10 to 4: walking distance 75.\nFrom 10 to 5: walking distance 98.\nFrom 10 to 6: walking distance 71.\nFrom 10 to 7: walking distance 88.\nFrom 10 to 8: walking distance 90.\nFrom 10 to 9: walking distance 93.\nFrom 10 to 11: walking distance 89.\nFrom 10 to 12: walking distance 73.\nFrom 10 to 13: walking distance 76.\nFrom 10 to 14: walking distance 57.\nFrom 10 to 15: walking distance 70.\nFrom 10 to 16: walking distance 97.\nFrom 11 to 1: walking distance 53.\nFrom 11 to 2: walking distance 53.\nFrom 11 to 3: walking distance 36.\nFrom 11 to 4: walking distance 37.\nFrom 11 to 5: walking distance 65.\nFrom 11 to 6: walking distance 36.\nFrom 11 to 7: walking distance 49.\nFrom 11 to 8: walking distance 59.\nFrom 11 to 9: walking distance 63.\nFrom 11 to 10: walking distance 89.\nFrom 11 to 12: walking distance 73.\nFrom 11 to 13: walking distance 55.\nFrom 11 to 14: walking distance 51.\nFrom 11 to 15: walking distance 47.\nFrom 11 to 16: walking distance 64.\nFrom 12 to 1: walking distance 29.\nFrom 12 to 2: walking distance 62.\nFrom 12 to 3: walking distance 55.\nFrom 12 to 4: walking distance 55.\nFrom 12 to 5: walking distance 81.\nFrom 12 to 6: walking distance 58.\nFrom 12 to 7: walking distance 56.\nFrom 12 to 8: walking distance 39.\nFrom 12 to 9: walking distance 77.\nFrom 12 to 10: walking distance 73.\nFrom 12 to 11: walking distance 73.\nFrom 12 to 13: walking distance 47.\nFrom 12 to 14: walking distance 32.\nFrom 12 to 15: walking distance 54.\nFrom 12 to 16: walking distance 69.\nFrom 13 to 1: walking distance 50.\nFrom 13 to 2: walking distance 54.\nFrom 13 to 3: walking distance 33.\nFrom 13 to 4: walking distance 38.\nFrom 13 to 5: walking distance 71.\nFrom 13 to 6: walking distance 63.\nFrom 13 to 7: walking distance 56.\nFrom 13 to 8: walking distance 64.\nFrom 13 to 9: walking distance 60.\nFrom 13 to 10: walking distance 76.\nFrom 13 to 11: walking distance 55.\nFrom 13 to 12: walking distance 47.\nFrom 13 to 14: walking distance 43.\nFrom 13 to 15: walking distance 62.\nFrom 13 to 16: walking distance 52.\nFrom 14 to 1: walking distance 35.\nFrom 14 to 2: walking distance 54.\nFrom 14 to 3: walking distance 39.\nFrom 14 to 4: walking distance 56.\nFrom 14 to 5: walking distance 66.\nFrom 14 to 6: walking distance 33.\nFrom 14 to 7: walking distance 48.\nFrom 14 to 8: walking distance 49.\nFrom 14 to 9: walking distance 53.\nFrom 14 to 10: walking distance 57.\nFrom 14 to 11: walking distance 51.\nFrom 14 to 12: walking distance 32.\nFrom 14 to 13: walking distance 43.\nFrom 14 to 15: walking distance 30.\nFrom 14 to 16: walking distance 57.\nFrom 15 to 1: walking distance 44.\nFrom 15 to 2: walking distance 57.\nFrom 15 to 3: walking distance 68.\nFrom 15 to 4: walking distance 68.\nFrom 15 to 5: walking distance 77.\nFrom 15 to 6: walking distance 40.\nFrom 15 to 7: walking distance 42.\nFrom 15 to 8: walking distance 57.\nFrom 15 to 9: walking distance 36.\nFrom 15 to 10: walking distance 70.\nFrom 15 to 11: walking distance 47.\nFrom 15 to 12: walking distance 54.\nFrom 15 to 13: walking distance 62.\nFrom 15 to 14: walking distance 30.\nFrom 15 to 16: walking distance 57.\nFrom 16 to 1: walking distance 59.\nFrom 16 to 2: walking distance 36.\nFrom 16 to 3: walking distance 63.\nFrom 16 to 4: walking distance 55.\nFrom 16 to 5: walking distance 43.\nFrom 16 to 6: walking distance 34.\nFrom 16 to 7: walking distance 49.\nFrom 16 to 8: walking distance 61.\nFrom 16 to 9: walking distance 65.\nFrom 16 to 10: walking distance 97.\nFrom 16 to 11: walking distance 64.\nFrom 16 to 12: walking distance 69.\nFrom 16 to 13: walking distance 52.\nFrom 16 to 14: walking distance 57.\nFrom 16 to 15: walking distance 57.\nWe'll use these distances to choose 3 pop-ups and assign each of the 16 locations so the total walking distance is minimized.\n\nAlso, when you send the actual selection back, please use this JSON layout so it's easy for me to read and parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n'selected' is where you list the pop‑up locations you choose to open, and 'assignments' lists, for each residential block in the same order as the input, which opened pop‑up it gets attached to. Think of it like a simple form: which sites are open, and which open site each block is assigned to.\n\nThis is just the sketch of the shape I expect — not the final answer.\n\nAll identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 37, 58, 58, 74, 35, 63, 46, 65, 76, 53, 29, 50, 35, 44, 59 ], [ 37, 0, 63, 62, 59, 35, 65, 60, 66, 85, 53, 62, 54, 54, 57, 36 ], [ 58, 63, 0, 39, 68, 46, 53, 63, 63, 80, 36, 55, 33, 39, 68, 63 ], [ 58, 62, 39, 0, 42, 53, 46, 65, 66, 75, 37, 55, 38, 56, 68, 55 ], [ 74, 59, 68, 42, 0, 47, 48, 67, 75, 98, 65, 81, 71, 66, 77, 43 ], [ 35, 35, 46, 53, 47, 0, 44, 63, 58, 71, 36, 58, 63, 33, 40, 34 ], [ 63, 65, 53, 46, 48, 44, 0, 19, 76, 88, 49, 56, 56, 48, 42, 49 ], [ 46, 60, 63, 65, 67, 63, 19, 0, 78, 90, 59, 39, 64, 49, 57, 61 ], [ 65, 66, 63, 66, 75, 58, 76, 78, 0, 93, 63, 77, 60, 53, 36, 65 ], [ 76, 85, 80, 75, 98, 71, 88, 90, 93, 0, 89, 73, 76, 57, 70, 97 ], [ 53, 53, 36, 37, 65, 36, 49, 59, 63, 89, 0, 73, 55, 51, 47, 64 ], [ 29, 62, 55, 55, 81, 58, 56, 39, 77, 73, 73, 0, 47, 32, 54, 69 ], [ 50, 54, 33, 38, 71, 63, 56, 64, 60, 76, 55, 47, 0, 43, 62, 52 ], [ 35, 54, 39, 56, 66, 33, 48, 49, 53, 57, 51, 32, 43, 0, 30, 57 ], [ 44, 57, 68, 68, 77, 40, 42, 57, 36, 70, 47, 54, 62, 30, 0, 57 ], [ 59, 36, 63, 55, 43, 34, 49, 61, 65, 97, 64, 69, 52, 57, 57, 0 ] ], "p": 3, "objective": 506.0 }, "solution": { "facilities": [ 5, 6, 13 ], "assignments": [ 13, 5, 13, 6, 5, 5, 6, 6, 13, 13, 5, 13, 13, 13, 13, 5 ] }, "obj": 506.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 3, "sites": [ { "id": 1, "distances": { "1": 0, "2": 37, "3": 58, "4": 58, "5": 74, "6": 35, "7": 63, "8": 46, "9": 65, "10": 76, "11": 53, "12": 29, "13": 50, "14": 35, "15": 44, "16": 59 } }, { "id": 2, "distances": { "1": 37, "2": 0, "3": 63, "4": 62, "5": 59, "6": 35, "7": 65, "8": 60, "9": 66, "10": 85, "11": 53, "12": 62, "13": 54, "14": 54, "15": 57, "16": 36 } }, { "id": 3, "distances": { "1": 58, "2": 63, "3": 0, "4": 39, "5": 68, "6": 46, "7": 53, "8": 63, "9": 63, "10": 80, "11": 36, "12": 55, "13": 33, "14": 39, "15": 68, "16": 63 } }, { "id": 4, "distances": { "1": 58, "2": 62, "3": 39, "4": 0, "5": 42, "6": 53, "7": 46, "8": 65, "9": 66, "10": 75, "11": 37, "12": 55, "13": 38, "14": 56, "15": 68, "16": 55 } }, { "id": 5, "distances": { "1": 74, "2": 59, "3": 68, "4": 42, "5": 0, "6": 47, "7": 48, "8": 67, "9": 75, "10": 98, "11": 65, "12": 81, "13": 71, "14": 66, "15": 77, "16": 43 } }, { "id": 6, "distances": { "1": 35, "2": 35, "3": 46, "4": 53, "5": 47, "6": 0, "7": 44, "8": 63, "9": 58, "10": 71, "11": 36, "12": 58, "13": 63, "14": 33, "15": 40, "16": 34 } }, { "id": 7, "distances": { "1": 63, "2": 65, "3": 53, "4": 46, "5": 48, "6": 44, "7": 0, "8": 19, "9": 76, "10": 88, "11": 49, "12": 56, "13": 56, "14": 48, "15": 42, "16": 49 } }, { "id": 8, "distances": { "1": 46, "2": 60, "3": 63, "4": 65, "5": 67, "6": 63, "7": 19, "8": 0, "9": 78, "10": 90, "11": 59, "12": 39, "13": 64, "14": 49, "15": 57, "16": 61 } }, { "id": 9, "distances": { "1": 65, "2": 66, "3": 63, "4": 66, "5": 75, "6": 58, "7": 76, "8": 78, "9": 0, "10": 93, "11": 63, "12": 77, "13": 60, "14": 53, "15": 36, "16": 65 } }, { "id": 10, "distances": { "1": 76, "2": 85, "3": 80, "4": 75, "5": 98, "6": 71, "7": 88, "8": 90, "9": 93, "10": 0, "11": 89, "12": 73, "13": 76, "14": 57, "15": 70, "16": 97 } }, { "id": 11, "distances": { "1": 53, "2": 53, "3": 36, "4": 37, "5": 65, "6": 36, "7": 49, "8": 59, "9": 63, "10": 89, "11": 0, "12": 73, "13": 55, "14": 51, "15": 47, "16": 64 } }, { "id": 12, "distances": { "1": 29, "2": 62, "3": 55, "4": 55, "5": 81, "6": 58, "7": 56, "8": 39, "9": 77, "10": 73, "11": 73, "12": 0, "13": 47, "14": 32, "15": 54, "16": 69 } }, { "id": 13, "distances": { "1": 50, "2": 54, "3": 33, "4": 38, "5": 71, "6": 63, "7": 56, "8": 64, "9": 60, "10": 76, "11": 55, "12": 47, "13": 0, "14": 43, "15": 62, "16": 52 } }, { "id": 14, "distances": { "1": 35, "2": 54, "3": 39, "4": 56, "5": 66, "6": 33, "7": 48, "8": 49, "9": 53, "10": 57, "11": 51, "12": 32, "13": 43, "14": 0, "15": 30, "16": 57 } }, { "id": 15, "distances": { "1": 44, "2": 57, "3": 68, "4": 68, "5": 77, "6": 40, "7": 42, "8": 57, "9": 36, "10": 70, "11": 47, "12": 54, "13": 62, "14": 30, "15": 0, "16": 57 } }, { "id": 16, "distances": { "1": 59, "2": 36, "3": 63, "4": 55, "5": 43, "6": 34, "7": 49, "8": 61, "9": 65, "10": 97, "11": 64, "12": 69, "13": 52, "14": 57, "15": 57, "16": 0 } } ], "objective": 506.0 }, "solution_variant": { "selected": [ 6, 7, 14 ], "assignments": [ 14, 6, 14, 7, 6, 6, 7, 7, 14, 14, 6, 14, 14, 14, 14, 6 ] }, "context_index": 15, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone at the waste reduction office has to decide which curbside candidates will get the new glass bins — but only a set number can be installed. Each neighborhood must go to one, and only one, installed bin; then the quality of any selection is judged by adding together all the distances people would travel from their area to their assigned bin — the lower that combined distance, the more efficient the placement. The exact spots and distance details appear below.\n\nThere are 16 locations in this instance, 5 glass bins may be installed, and the location identifiers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.\nSomeone at the office notes that 1 is 56 from 2.\nSomeone at the office notes that 1 is 46 from 3.\nSomeone at the office notes that 1 is 29 from 4.\nSomeone at the office notes that 1 is 28 from 5.\nSomeone at the office notes that 1 is 39 from 6.\nSomeone at the office notes that 1 is 30 from 7.\nSomeone at the office notes that 1 is 33 from 8.\nSomeone at the office notes that 1 is 64 from 9.\nSomeone at the office notes that 1 is 55 from 10.\nSomeone at the office notes that 1 is 59 from 11.\nSomeone at the office notes that 1 is 32 from 12.\nSomeone at the office notes that 1 is 10 from 13.\nSomeone at the office notes that 1 is 25 from 14.\nSomeone at the office notes that 1 is 16 from 15.\nSomeone at the office notes that 1 is 27 from 16.\nSomeone at the office notes that 2 is 56 from 1.\nSomeone at the office notes that 2 is 40 from 3.\nSomeone at the office notes that 2 is 57 from 4.\nSomeone at the office notes that 2 is 48 from 5.\nSomeone at the office notes that 2 is 61 from 6.\nSomeone at the office notes that 2 is 59 from 7.\nSomeone at the office notes that 2 is 54 from 8.\nSomeone at the office notes that 2 is 67 from 9.\nSomeone at the office notes that 2 is 48 from 10.\nSomeone at the office notes that 2 is 62 from 11.\nSomeone at the office notes that 2 is 68 from 12.\nSomeone at the office notes that 2 is 46 from 13.\nSomeone at the office notes that 2 is 52 from 14.\nSomeone at the office notes that 2 is 52 from 15.\nSomeone at the office notes that 2 is 60 from 16.\nSomeone at the office notes that 3 is 46 from 1.\nSomeone at the office notes that 3 is 40 from 2.\nSomeone at the office notes that 3 is 37 from 4.\nSomeone at the office notes that 3 is 54 from 5.\nSomeone at the office notes that 3 is 32 from 6.\nSomeone at the office notes that 3 is 19 from 7.\nSomeone at the office notes that 3 is 33 from 8.\nSomeone at the office notes that 3 is 27 from 9.\nSomeone at the office notes that 3 is 64 from 10.\nSomeone at the office notes that 3 is 54 from 11.\nSomeone at the office notes that 3 is 54 from 12.\nSomeone at the office notes that 3 is 38 from 13.\nSomeone at the office notes that 3 is 34 from 14.\nSomeone at the office notes that 3 is 44 from 15.\nSomeone at the office notes that 3 is 61 from 16.\nSomeone at the office notes that 4 is 29 from 1.\nSomeone at the office notes that 4 is 57 from 2.\nSomeone at the office notes that 4 is 37 from 3.\nSomeone at the office notes that 4 is 49 from 5.\nSomeone at the office notes that 4 is 24 from 6.\nSomeone at the office notes that 4 is 56 from 7.\nSomeone at the office notes that 4 is 32 from 8.\nSomeone at the office notes that 4 is 64 from 9.\nSomeone at the office notes that 4 is 68 from 10.\nSomeone at the office notes that 4 is 68 from 11.\nSomeone at the office notes that 4 is 37 from 12.\nSomeone at the office notes that 4 is 31 from 13.\nSomeone at the office notes that 4 is 36 from 14.\nSomeone at the office notes that 4 is 32 from 15.\nSomeone at the office notes that 4 is 56 from 16.\nSomeone at the office notes that 5 is 28 from 1.\nSomeone at the office notes that 5 is 48 from 2.\nSomeone at the office notes that 5 is 54 from 3.\nSomeone at the office notes that 5 is 49 from 4.\nSomeone at the office notes that 5 is 51 from 6.\nSomeone at the office notes that 5 is 46 from 7.\nSomeone at the office notes that 5 is 43 from 8.\nSomeone at the office notes that 5 is 69 from 9.\nSomeone at the office notes that 5 is 65 from 10.\nSomeone at the office notes that 5 is 69 from 11.\nSomeone at the office notes that 5 is 40 from 12.\nSomeone at the office notes that 5 is 18 from 13.\nSomeone at the office notes that 5 is 37 from 14.\nSomeone at the office notes that 5 is 24 from 15.\nSomeone at the office notes that 5 is 43 from 16.\nSomeone at the office notes that 6 is 39 from 1.\nSomeone at the office notes that 6 is 61 from 2.\nSomeone at the office notes that 6 is 32 from 3.\nSomeone at the office notes that 6 is 24 from 4.\nSomeone at the office notes that 6 is 51 from 5.\nSomeone at the office notes that 6 is 49 from 7.\nSomeone at the office notes that 6 is 34 from 8.\nSomeone at the office notes that 6 is 59 from 9.\nSomeone at the office notes that 6 is 66 from 10.\nSomeone at the office notes that 6 is 70 from 11.\nSomeone at the office notes that 6 is 55 from 12.\nSomeone at the office notes that 6 is 33 from 13.\nSomeone at the office notes that 6 is 14 from 14.\nSomeone at the office notes that 6 is 39 from 15.\nSomeone at the office notes that 6 is 54 from 16.\nSomeone at the office notes that 7 is 30 from 1.\nSomeone at the office notes that 7 is 59 from 2.\nSomeone at the office notes that 7 is 19 from 3.\nSomeone at the office notes that 7 is 56 from 4.\nSomeone at the office notes that 7 is 46 from 5.\nSomeone at the office notes that 7 is 49 from 6.\nSomeone at the office notes that 7 is 44 from 8.\nSomeone at the office notes that 7 is 43 from 9.\nSomeone at the office notes that 7 is 45 from 10.\nSomeone at the office notes that 7 is 59 from 11.\nSomeone at the office notes that 7 is 42 from 12.\nSomeone at the office notes that 7 is 28 from 13.\nSomeone at the office notes that 7 is 43 from 14.\nSomeone at the office notes that 7 is 34 from 15.\nSomeone at the office notes that 7 is 45 from 16.\nSomeone at the office notes that 8 is 33 from 1.\nSomeone at the office notes that 8 is 54 from 2.\nSomeone at the office notes that 8 is 33 from 3.\nSomeone at the office notes that 8 is 32 from 4.\nSomeone at the office notes that 8 is 43 from 5.\nSomeone at the office notes that 8 is 34 from 6.\nSomeone at the office notes that 8 is 44 from 7.\nSomeone at the office notes that 8 is 48 from 9.\nSomeone at the office notes that 8 is 54 from 10.\nSomeone at the office notes that 8 is 42 from 11.\nSomeone at the office notes that 8 is 41 from 12.\nSomeone at the office notes that 8 is 25 from 13.\nSomeone at the office notes that 8 is 44 from 14.\nSomeone at the office notes that 8 is 31 from 15.\nSomeone at the office notes that 8 is 48 from 16.\nSomeone at the office notes that 9 is 64 from 1.\nSomeone at the office notes that 9 is 67 from 2.\nSomeone at the office notes that 9 is 27 from 3.\nSomeone at the office notes that 9 is 64 from 4.\nSomeone at the office notes that 9 is 69 from 5.\nSomeone at the office notes that 9 is 59 from 6.\nSomeone at the office notes that 9 is 43 from 7.\nSomeone at the office notes that 9 is 48 from 8.\nSomeone at the office notes that 9 is 74 from 10.\nSomeone at the office notes that 9 is 68 from 11.\nSomeone at the office notes that 9 is 60 from 12.\nSomeone at the office notes that 9 is 54 from 13.\nSomeone at the office notes that 9 is 61 from 14.\nSomeone at the office notes that 9 is 49 from 15.\nSomeone at the office notes that 9 is 79 from 16.\nSomeone at the office notes that 10 is 55 from 1.\nSomeone at the office notes that 10 is 48 from 2.\nSomeone at the office notes that 10 is 64 from 3.\nSomeone at the office notes that 10 is 68 from 4.\nSomeone at the office notes that 10 is 65 from 5.\nSomeone at the office notes that 10 is 66 from 6.\nSomeone at the office notes that 10 is 45 from 7.\nSomeone at the office notes that 10 is 54 from 8.\nSomeone at the office notes that 10 is 74 from 9.\nSomeone at the office notes that 10 is 14 from 11.\nSomeone at the office notes that 10 is 54 from 12.\nSomeone at the office notes that 10 is 47 from 13.\nSomeone at the office notes that 10 is 52 from 14.\nSomeone at the office notes that 10 is 53 from 15.\nSomeone at the office notes that 10 is 70 from 16.\nSomeone at the office notes that 11 is 59 from 1.\nSomeone at the office notes that 11 is 62 from 2.\nSomeone at the office notes that 11 is 54 from 3.\nSomeone at the office notes that 11 is 68 from 4.\nSomeone at the office notes that 11 is 69 from 5.\nSomeone at the office notes that 11 is 70 from 6.\nSomeone at the office notes that 11 is 59 from 7.\nSomeone at the office notes that 11 is 42 from 8.\nSomeone at the office notes that 11 is 68 from 9.\nSomeone at the office notes that 11 is 14 from 10.\nSomeone at the office notes that 11 is 67 from 12.\nSomeone at the office notes that 11 is 53 from 13.\nSomeone at the office notes that 11 is 56 from 14.\nSomeone at the office notes that 11 is 56 from 15.\nSomeone at the office notes that 11 is 74 from 16.\nSomeone at the office notes that 12 is 32 from 1.\nSomeone at the office notes that 12 is 68 from 2.\nSomeone at the office notes that 12 is 54 from 3.\nSomeone at the office notes that 12 is 37 from 4.\nSomeone at the office notes that 12 is 40 from 5.\nSomeone at the office notes that 12 is 55 from 6.\nSomeone at the office notes that 12 is 42 from 7.\nSomeone at the office notes that 12 is 41 from 8.\nSomeone at the office notes that 12 is 60 from 9.\nSomeone at the office notes that 12 is 54 from 10.\nSomeone at the office notes that 12 is 67 from 11.\nSomeone at the office notes that 12 is 22 from 13.\nSomeone at the office notes that 12 is 41 from 14.\nSomeone at the office notes that 12 is 23 from 15.\nSomeone at the office notes that 12 is 47 from 16.\nSomeone at the office notes that 13 is 10 from 1.\nSomeone at the office notes that 13 is 46 from 2.\nSomeone at the office notes that 13 is 38 from 3.\nSomeone at the office notes that 13 is 31 from 4.\nSomeone at the office notes that 13 is 18 from 5.\nSomeone at the office notes that 13 is 33 from 6.\nSomeone at the office notes that 13 is 28 from 7.\nSomeone at the office notes that 13 is 25 from 8.\nSomeone at the office notes that 13 is 54 from 9.\nSomeone at the office notes that 13 is 47 from 10.\nSomeone at the office notes that 13 is 53 from 11.\nSomeone at the office notes that 13 is 22 from 12.\nSomeone at the office notes that 13 is 19 from 14.\nSomeone at the office notes that 13 is 6 from 15.\nSomeone at the office notes that 13 is 25 from 16.\nSomeone at the office notes that 14 is 25 from 1.\nSomeone at the office notes that 14 is 52 from 2.\nSomeone at the office notes that 14 is 34 from 3.\nSomeone at the office notes that 14 is 36 from 4.\nSomeone at the office notes that 14 is 37 from 5.\nSomeone at the office notes that 14 is 14 from 6.\nSomeone at the office notes that 14 is 43 from 7.\nSomeone at the office notes that 14 is 44 from 8.\nSomeone at the office notes that 14 is 61 from 9.\nSomeone at the office notes that 14 is 52 from 10.\nSomeone at the office notes that 14 is 56 from 11.\nSomeone at the office notes that 14 is 41 from 12.\nSomeone at the office notes that 14 is 19 from 13.\nSomeone at the office notes that 14 is 25 from 15.\nSomeone at the office notes that 14 is 40 from 16.\nSomeone at the office notes that 15 is 16 from 1.\nSomeone at the office notes that 15 is 52 from 2.\nSomeone at the office notes that 15 is 44 from 3.\nSomeone at the office notes that 15 is 32 from 4.\nSomeone at the office notes that 15 is 24 from 5.\nSomeone at the office notes that 15 is 39 from 6.\nSomeone at the office notes that 15 is 34 from 7.\nSomeone at the office notes that 15 is 31 from 8.\nSomeone at the office notes that 15 is 49 from 9.\nSomeone at the office notes that 15 is 53 from 10.\nSomeone at the office notes that 15 is 56 from 11.\nSomeone at the office notes that 15 is 23 from 12.\nSomeone at the office notes that 15 is 6 from 13.\nSomeone at the office notes that 15 is 25 from 14.\nSomeone at the office notes that 15 is 31 from 16.\nSomeone at the office notes that 16 is 27 from 1.\nSomeone at the office notes that 16 is 60 from 2.\nSomeone at the office notes that 16 is 61 from 3.\nSomeone at the office notes that 16 is 56 from 4.\nSomeone at the office notes that 16 is 43 from 5.\nSomeone at the office notes that 16 is 54 from 6.\nSomeone at the office notes that 16 is 45 from 7.\nSomeone at the office notes that 16 is 48 from 8.\nSomeone at the office notes that 16 is 79 from 9.\nSomeone at the office notes that 16 is 70 from 10.\nSomeone at the office notes that 16 is 74 from 11.\nSomeone at the office notes that 16 is 47 from 12.\nSomeone at the office notes that 16 is 25 from 13.\nSomeone at the office notes that 16 is 40 from 14.\nSomeone at the office notes that 16 is 31 from 15.\nThese distances will be used by someone at the waste reduction office to assign each neighborhood and select 5 sites across the 16 locations to minimize total travel.\n\nYou can put the answer in a small JSON snippet like this so it's easy to parse and check — something casual and form-like:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nselected lists which curbside spots actually get bins installed. assignments lists, for each neighborhood (in the same order as the input), which opened spot that neighborhood will go to. Think of it like a simple form: picked sites up top, then a list saying where each area should drop off their glass.\n\nThis JSON is just a sketch of the shape I need back, not the final answer itself. Please make sure all identifiers you use match exactly what's in the instance input — do not rename them and do not invent new labels. \n\nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 56, 46, 29, 28, 39, 30, 33, 64, 55, 59, 32, 10, 25, 16, 27 ], [ 56, 0, 40, 57, 48, 61, 59, 54, 67, 48, 62, 68, 46, 52, 52, 60 ], [ 46, 40, 0, 37, 54, 32, 19, 33, 27, 64, 54, 54, 38, 34, 44, 61 ], [ 29, 57, 37, 0, 49, 24, 56, 32, 64, 68, 68, 37, 31, 36, 32, 56 ], [ 28, 48, 54, 49, 0, 51, 46, 43, 69, 65, 69, 40, 18, 37, 24, 43 ], [ 39, 61, 32, 24, 51, 0, 49, 34, 59, 66, 70, 55, 33, 14, 39, 54 ], [ 30, 59, 19, 56, 46, 49, 0, 44, 43, 45, 59, 42, 28, 43, 34, 45 ], [ 33, 54, 33, 32, 43, 34, 44, 0, 48, 54, 42, 41, 25, 44, 31, 48 ], [ 64, 67, 27, 64, 69, 59, 43, 48, 0, 74, 68, 60, 54, 61, 49, 79 ], [ 55, 48, 64, 68, 65, 66, 45, 54, 74, 0, 14, 54, 47, 52, 53, 70 ], [ 59, 62, 54, 68, 69, 70, 59, 42, 68, 14, 0, 67, 53, 56, 56, 74 ], [ 32, 68, 54, 37, 40, 55, 42, 41, 60, 54, 67, 0, 22, 41, 23, 47 ], [ 10, 46, 38, 31, 18, 33, 28, 25, 54, 47, 53, 22, 0, 19, 6, 25 ], [ 25, 52, 34, 36, 37, 14, 43, 44, 61, 52, 56, 41, 19, 0, 25, 40 ], [ 16, 52, 44, 32, 24, 39, 34, 31, 49, 53, 56, 23, 6, 25, 0, 31 ], [ 27, 60, 61, 56, 43, 54, 45, 48, 79, 70, 74, 47, 25, 40, 31, 0 ] ], "p": 5, "objective": 204.0 }, "solution": { "facilities": [ 1, 2, 5, 10, 12 ], "assignments": [ 12, 1, 2, 5, 12, 5, 2, 12, 2, 10, 10, 12, 12, 5, 12, 12 ] }, "obj": 204.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 5, "sites": [ { "id": 1, "distances": { "1": 0, "2": 56, "3": 46, "4": 29, "5": 28, "6": 39, "7": 30, "8": 33, "9": 64, "10": 55, "11": 59, "12": 32, "13": 10, "14": 25, "15": 16, "16": 27 } }, { "id": 2, "distances": { "1": 56, "2": 0, "3": 40, "4": 57, "5": 48, "6": 61, "7": 59, "8": 54, "9": 67, "10": 48, "11": 62, "12": 68, "13": 46, "14": 52, "15": 52, "16": 60 } }, { "id": 3, "distances": { "1": 46, "2": 40, "3": 0, "4": 37, "5": 54, "6": 32, "7": 19, "8": 33, "9": 27, "10": 64, "11": 54, "12": 54, "13": 38, "14": 34, "15": 44, "16": 61 } }, { "id": 4, "distances": { "1": 29, "2": 57, "3": 37, "4": 0, "5": 49, "6": 24, "7": 56, "8": 32, "9": 64, "10": 68, "11": 68, "12": 37, "13": 31, "14": 36, "15": 32, "16": 56 } }, { "id": 5, "distances": { "1": 28, "2": 48, "3": 54, "4": 49, "5": 0, "6": 51, "7": 46, "8": 43, "9": 69, "10": 65, "11": 69, "12": 40, "13": 18, "14": 37, "15": 24, "16": 43 } }, { "id": 6, "distances": { "1": 39, "2": 61, "3": 32, "4": 24, "5": 51, "6": 0, "7": 49, "8": 34, "9": 59, "10": 66, "11": 70, "12": 55, "13": 33, "14": 14, "15": 39, "16": 54 } }, { "id": 7, "distances": { "1": 30, "2": 59, "3": 19, "4": 56, "5": 46, "6": 49, "7": 0, "8": 44, "9": 43, "10": 45, "11": 59, "12": 42, "13": 28, "14": 43, "15": 34, "16": 45 } }, { "id": 8, "distances": { "1": 33, "2": 54, "3": 33, "4": 32, "5": 43, "6": 34, "7": 44, "8": 0, "9": 48, "10": 54, "11": 42, "12": 41, "13": 25, "14": 44, "15": 31, "16": 48 } }, { "id": 9, "distances": { "1": 64, "2": 67, "3": 27, "4": 64, "5": 69, "6": 59, "7": 43, "8": 48, "9": 0, "10": 74, "11": 68, "12": 60, "13": 54, "14": 61, "15": 49, "16": 79 } }, { "id": 10, "distances": { "1": 55, "2": 48, "3": 64, "4": 68, "5": 65, "6": 66, "7": 45, "8": 54, "9": 74, "10": 0, "11": 14, "12": 54, "13": 47, "14": 52, "15": 53, "16": 70 } }, { "id": 11, "distances": { "1": 59, "2": 62, "3": 54, "4": 68, "5": 69, "6": 70, "7": 59, "8": 42, "9": 68, "10": 14, "11": 0, "12": 67, "13": 53, "14": 56, "15": 56, "16": 74 } }, { "id": 12, "distances": { "1": 32, "2": 68, "3": 54, "4": 37, "5": 40, "6": 55, "7": 42, "8": 41, "9": 60, "10": 54, "11": 67, "12": 0, "13": 22, "14": 41, "15": 23, "16": 47 } }, { "id": 13, "distances": { "1": 10, "2": 46, "3": 38, "4": 31, "5": 18, "6": 33, "7": 28, "8": 25, "9": 54, "10": 47, "11": 53, "12": 22, "13": 0, "14": 19, "15": 6, "16": 25 } }, { "id": 14, "distances": { "1": 25, "2": 52, "3": 34, "4": 36, "5": 37, "6": 14, "7": 43, "8": 44, "9": 61, "10": 52, "11": 56, "12": 41, "13": 19, "14": 0, "15": 25, "16": 40 } }, { "id": 15, "distances": { "1": 16, "2": 52, "3": 44, "4": 32, "5": 24, "6": 39, "7": 34, "8": 31, "9": 49, "10": 53, "11": 56, "12": 23, "13": 6, "14": 25, "15": 0, "16": 31 } }, { "id": 16, "distances": { "1": 27, "2": 60, "3": 61, "4": 56, "5": 43, "6": 54, "7": 45, "8": 48, "9": 79, "10": 70, "11": 74, "12": 47, "13": 25, "14": 40, "15": 31, "16": 0 } } ], "objective": 204.0 }, "solution_variant": { "selected": [ 2, 3, 6, 11, 13 ], "assignments": [ 13, 2, 3, 6, 13, 6, 3, 13, 3, 11, 11, 13, 13, 6, 13, 13 ] }, "context_index": 16, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "We’re juggling limited maintenance crews and can only staff a set number of warming huts across the slopes. The job is to pick which ones to keep open and then assign each lift terminal to exactly one of those open huts — nothing can be skipped and no terminal gets two huts. To see which choice is best, we sum the distances from every terminal to its assigned hut and aim for the lowest possible total. The concrete details follow below.\n\nWe have 15 total locations, can keep 1 huts open, and the candidate sites (each a lift terminal) are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.\nWe record a travel distance of 44 from 0 to 1.\nWe record a travel distance of 30 from 0 to 2.\nWe record a travel distance of 28 from 0 to 3.\nWe record a travel distance of 33 from 0 to 4.\nWe record a travel distance of 51 from 0 to 5.\nWe record a travel distance of 35 from 0 to 6.\nWe record a travel distance of 31 from 0 to 7.\nWe record a travel distance of 30 from 0 to 8.\nWe record a travel distance of 31 from 0 to 9.\nWe record a travel distance of 31 from 0 to 10.\nWe record a travel distance of 25 from 0 to 11.\nWe record a travel distance of 30 from 0 to 12.\nWe record a travel distance of 23 from 0 to 13.\nWe record a travel distance of 30 from 0 to 14.\nWe record a travel distance of 44 from 1 to 0.\nWe record a travel distance of 35 from 1 to 2.\nWe record a travel distance of 28 from 1 to 3.\nWe record a travel distance of 18 from 1 to 4.\nWe record a travel distance of 52 from 1 to 5.\nWe record a travel distance of 35 from 1 to 6.\nWe record a travel distance of 23 from 1 to 7.\nWe record a travel distance of 48 from 1 to 8.\nWe record a travel distance of 40 from 1 to 9.\nWe record a travel distance of 39 from 1 to 10.\nWe record a travel distance of 33 from 1 to 11.\nWe record a travel distance of 43 from 1 to 12.\nWe record a travel distance of 24 from 1 to 13.\nWe record a travel distance of 38 from 1 to 14.\nWe record a travel distance of 30 from 2 to 0.\nWe record a travel distance of 35 from 2 to 1.\nWe record a travel distance of 25 from 2 to 3.\nWe record a travel distance of 25 from 2 to 4.\nWe record a travel distance of 21 from 2 to 5.\nWe record a travel distance of 35 from 2 to 6.\nWe record a travel distance of 14 from 2 to 7.\nWe record a travel distance of 43 from 2 to 8.\nWe record a travel distance of 33 from 2 to 9.\nWe record a travel distance of 34 from 2 to 10.\nWe record a travel distance of 23 from 2 to 11.\nWe record a travel distance of 39 from 2 to 12.\nWe record a travel distance of 25 from 2 to 13.\nWe record a travel distance of 22 from 2 to 14.\nWe record a travel distance of 28 from 3 to 0.\nWe record a travel distance of 28 from 3 to 1.\nWe record a travel distance of 25 from 3 to 2.\nWe record a travel distance of 18 from 3 to 4.\nWe record a travel distance of 37 from 3 to 5.\nWe record a travel distance of 29 from 3 to 6.\nWe record a travel distance of 20 from 3 to 7.\nWe record a travel distance of 43 from 3 to 8.\nWe record a travel distance of 24 from 3 to 9.\nWe record a travel distance of 27 from 3 to 10.\nWe record a travel distance of 12 from 3 to 11.\nWe record a travel distance of 30 from 3 to 12.\nWe record a travel distance of 26 from 3 to 13.\nWe record a travel distance of 24 from 3 to 14.\nWe record a travel distance of 33 from 4 to 0.\nWe record a travel distance of 18 from 4 to 1.\nWe record a travel distance of 25 from 4 to 2.\nWe record a travel distance of 18 from 4 to 3.\nWe record a travel distance of 42 from 4 to 5.\nWe record a travel distance of 29 from 4 to 6.\nWe record a travel distance of 13 from 4 to 7.\nWe record a travel distance of 30 from 4 to 8.\nWe record a travel distance of 32 from 4 to 9.\nWe record a travel distance of 31 from 4 to 10.\nWe record a travel distance of 23 from 4 to 11.\nWe record a travel distance of 33 from 4 to 12.\nWe record a travel distance of 26 from 4 to 13.\nWe record a travel distance of 26 from 4 to 14.\nWe record a travel distance of 51 from 5 to 0.\nWe record a travel distance of 52 from 5 to 1.\nWe record a travel distance of 21 from 5 to 2.\nWe record a travel distance of 37 from 5 to 3.\nWe record a travel distance of 42 from 5 to 4.\nWe record a travel distance of 55 from 5 to 6.\nWe record a travel distance of 35 from 5 to 7.\nWe record a travel distance of 64 from 5 to 8.\nWe record a travel distance of 54 from 5 to 9.\nWe record a travel distance of 55 from 5 to 10.\nWe record a travel distance of 43 from 5 to 11.\nWe record a travel distance of 57 from 5 to 12.\nWe record a travel distance of 46 from 5 to 13.\nWe record a travel distance of 39 from 5 to 14.\nWe record a travel distance of 35 from 6 to 0.\nWe record a travel distance of 35 from 6 to 1.\nWe record a travel distance of 35 from 6 to 2.\nWe record a travel distance of 29 from 6 to 3.\nWe record a travel distance of 29 from 6 to 4.\nWe record a travel distance of 55 from 6 to 5.\nWe record a travel distance of 24 from 6 to 7.\nWe record a travel distance of 59 from 6 to 8.\nWe record a travel distance of 43 from 6 to 9.\nWe record a travel distance of 44 from 6 to 10.\nWe record a travel distance of 35 from 6 to 11.\nWe record a travel distance of 39 from 6 to 12.\nWe record a travel distance of 36 from 6 to 13.\nWe record a travel distance of 35 from 6 to 14.\nWe record a travel distance of 31 from 7 to 0.\nWe record a travel distance of 23 from 7 to 1.\nWe record a travel distance of 14 from 7 to 2.\nWe record a travel distance of 20 from 7 to 3.\nWe record a travel distance of 13 from 7 to 4.\nWe record a travel distance of 35 from 7 to 5.\nWe record a travel distance of 24 from 7 to 6.\nWe record a travel distance of 43 from 7 to 8.\nWe record a travel distance of 19 from 7 to 9.\nWe record a travel distance of 20 from 7 to 10.\nWe record a travel distance of 20 from 7 to 11.\nWe record a travel distance of 29 from 7 to 12.\nWe record a travel distance of 19 from 7 to 13.\nWe record a travel distance of 23 from 7 to 14.\nWe record a travel distance of 30 from 8 to 0.\nWe record a travel distance of 48 from 8 to 1.\nWe record a travel distance of 43 from 8 to 2.\nWe record a travel distance of 43 from 8 to 3.\nWe record a travel distance of 30 from 8 to 4.\nWe record a travel distance of 64 from 8 to 5.\nWe record a travel distance of 59 from 8 to 6.\nWe record a travel distance of 43 from 8 to 7.\nWe record a travel distance of 55 from 8 to 9.\nWe record a travel distance of 39 from 8 to 10.\nWe record a travel distance of 44 from 8 to 11.\nWe record a travel distance of 57 from 8 to 12.\nWe record a travel distance of 47 from 8 to 13.\nWe record a travel distance of 43 from 8 to 14.\nWe record a travel distance of 31 from 9 to 0.\nWe record a travel distance of 40 from 9 to 1.\nWe record a travel distance of 33 from 9 to 2.\nWe record a travel distance of 24 from 9 to 3.\nWe record a travel distance of 32 from 9 to 4.\nWe record a travel distance of 54 from 9 to 5.\nWe record a travel distance of 43 from 9 to 6.\nWe record a travel distance of 19 from 9 to 7.\nWe record a travel distance of 55 from 9 to 8.\nWe record a travel distance of 37 from 9 to 10.\nWe record a travel distance of 19 from 9 to 11.\nWe record a travel distance of 31 from 9 to 12.\nWe record a travel distance of 32 from 9 to 13.\nWe record a travel distance of 34 from 9 to 14.\nWe record a travel distance of 31 from 10 to 0.\nWe record a travel distance of 39 from 10 to 1.\nWe record a travel distance of 34 from 10 to 2.\nWe record a travel distance of 27 from 10 to 3.\nWe record a travel distance of 31 from 10 to 4.\nWe record a travel distance of 55 from 10 to 5.\nWe record a travel distance of 44 from 10 to 6.\nWe record a travel distance of 20 from 10 to 7.\nWe record a travel distance of 39 from 10 to 8.\nWe record a travel distance of 37 from 10 to 9.\nWe record a travel distance of 33 from 10 to 11.\nWe record a travel distance of 31 from 10 to 12.\nWe record a travel distance of 27 from 10 to 13.\nWe record a travel distance of 28 from 10 to 14.\nWe record a travel distance of 25 from 11 to 0.\nWe record a travel distance of 33 from 11 to 1.\nWe record a travel distance of 23 from 11 to 2.\nWe record a travel distance of 12 from 11 to 3.\nWe record a travel distance of 23 from 11 to 4.\nWe record a travel distance of 43 from 11 to 5.\nWe record a travel distance of 35 from 11 to 6.\nWe record a travel distance of 20 from 11 to 7.\nWe record a travel distance of 44 from 11 to 8.\nWe record a travel distance of 19 from 11 to 9.\nWe record a travel distance of 33 from 11 to 10.\nWe record a travel distance of 34 from 11 to 12.\nWe record a travel distance of 26 from 11 to 13.\nWe record a travel distance of 23 from 11 to 14.\nWe record a travel distance of 30 from 12 to 0.\nWe record a travel distance of 43 from 12 to 1.\nWe record a travel distance of 39 from 12 to 2.\nWe record a travel distance of 30 from 12 to 3.\nWe record a travel distance of 33 from 12 to 4.\nWe record a travel distance of 57 from 12 to 5.\nWe record a travel distance of 39 from 12 to 6.\nWe record a travel distance of 29 from 12 to 7.\nWe record a travel distance of 57 from 12 to 8.\nWe record a travel distance of 31 from 12 to 9.\nWe record a travel distance of 31 from 12 to 10.\nWe record a travel distance of 34 from 12 to 11.\nWe record a travel distance of 34 from 12 to 13.\nWe record a travel distance of 44 from 12 to 14.\nWe record a travel distance of 23 from 13 to 0.\nWe record a travel distance of 24 from 13 to 1.\nWe record a travel distance of 25 from 13 to 2.\nWe record a travel distance of 26 from 13 to 3.\nWe record a travel distance of 26 from 13 to 4.\nWe record a travel distance of 46 from 13 to 5.\nWe record a travel distance of 36 from 13 to 6.\nWe record a travel distance of 19 from 13 to 7.\nWe record a travel distance of 47 from 13 to 8.\nWe record a travel distance of 32 from 13 to 9.\nWe record a travel distance of 27 from 13 to 10.\nWe record a travel distance of 26 from 13 to 11.\nWe record a travel distance of 34 from 13 to 12.\nWe record a travel distance of 30 from 13 to 14.\nWe record a travel distance of 30 from 14 to 0.\nWe record a travel distance of 38 from 14 to 1.\nWe record a travel distance of 22 from 14 to 2.\nWe record a travel distance of 24 from 14 to 3.\nWe record a travel distance of 26 from 14 to 4.\nWe record a travel distance of 39 from 14 to 5.\nWe record a travel distance of 35 from 14 to 6.\nWe record a travel distance of 23 from 14 to 7.\nWe record a travel distance of 43 from 14 to 8.\nWe record a travel distance of 34 from 14 to 9.\nWe record a travel distance of 28 from 14 to 10.\nWe record a travel distance of 23 from 14 to 11.\nWe record a travel distance of 44 from 14 to 12.\nWe record a travel distance of 30 from 14 to 13.\nWe’ll pick which 1 huts to staff among the 15 locations above to minimize the total travel distance.\n\nI'll keep the answer shape simple so you can plug values in easily — below is the expected JSON layout you should follow.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty straightforward: \"selected\" is the list of warming huts we choose to staff (the ones we leave open), and \"assignments\" lists, in the same order as the terminals in the instance, which open hut each terminal is assigned to. Think of it like a short form: pick your open huts, then for every terminal say which open hut serves it.\n\nThis JSON is just a sketch of the shape I need you to return — not the actual solution yet. Also, please use the exact identifiers from the instance input, no renaming and no new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 44, 30, 28, 33, 51, 35, 31, 30, 31, 31, 25, 30, 23, 30 ], [ 44, 0, 35, 28, 18, 52, 35, 23, 48, 40, 39, 33, 43, 24, 38 ], [ 30, 35, 0, 25, 25, 21, 35, 14, 43, 33, 34, 23, 39, 25, 22 ], [ 28, 28, 25, 0, 18, 37, 29, 20, 43, 24, 27, 12, 30, 26, 24 ], [ 33, 18, 25, 18, 0, 42, 29, 13, 30, 32, 31, 23, 33, 26, 26 ], [ 51, 52, 21, 37, 42, 0, 55, 35, 64, 54, 55, 43, 57, 46, 39 ], [ 35, 35, 35, 29, 29, 55, 0, 24, 59, 43, 44, 35, 39, 36, 35 ], [ 31, 23, 14, 20, 13, 35, 24, 0, 43, 19, 20, 20, 29, 19, 23 ], [ 30, 48, 43, 43, 30, 64, 59, 43, 0, 55, 39, 44, 57, 47, 43 ], [ 31, 40, 33, 24, 32, 54, 43, 19, 55, 0, 37, 19, 31, 32, 34 ], [ 31, 39, 34, 27, 31, 55, 44, 20, 39, 37, 0, 33, 31, 27, 28 ], [ 25, 33, 23, 12, 23, 43, 35, 20, 44, 19, 33, 0, 34, 26, 23 ], [ 30, 43, 39, 30, 33, 57, 39, 29, 57, 31, 31, 34, 0, 34, 44 ], [ 23, 24, 25, 26, 26, 46, 36, 19, 47, 32, 27, 26, 34, 0, 30 ], [ 30, 38, 22, 24, 26, 39, 35, 23, 43, 34, 28, 23, 44, 30, 0 ] ], "p": 1, "objective": 333.0 }, "solution": { "facilities": [ 7 ], "assignments": [ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 ] }, "obj": 333.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 15, "num_open": 1, "sites": [ { "id": 0, "distances": { "0": 0, "1": 44, "2": 30, "3": 28, "4": 33, "5": 51, "6": 35, "7": 31, "8": 30, "9": 31, "10": 31, "11": 25, "12": 30, "13": 23, "14": 30 } }, { "id": 1, "distances": { "0": 44, "1": 0, "2": 35, "3": 28, "4": 18, "5": 52, "6": 35, "7": 23, "8": 48, "9": 40, "10": 39, "11": 33, "12": 43, "13": 24, "14": 38 } }, { "id": 2, "distances": { "0": 30, "1": 35, "2": 0, "3": 25, "4": 25, "5": 21, "6": 35, "7": 14, "8": 43, "9": 33, "10": 34, "11": 23, "12": 39, "13": 25, "14": 22 } }, { "id": 3, "distances": { "0": 28, "1": 28, "2": 25, "3": 0, "4": 18, "5": 37, "6": 29, "7": 20, "8": 43, "9": 24, "10": 27, "11": 12, "12": 30, "13": 26, "14": 24 } }, { "id": 4, "distances": { "0": 33, "1": 18, "2": 25, "3": 18, "4": 0, "5": 42, "6": 29, "7": 13, "8": 30, "9": 32, "10": 31, "11": 23, "12": 33, "13": 26, "14": 26 } }, { "id": 5, "distances": { "0": 51, "1": 52, "2": 21, "3": 37, "4": 42, "5": 0, "6": 55, "7": 35, "8": 64, "9": 54, "10": 55, "11": 43, "12": 57, "13": 46, "14": 39 } }, { "id": 6, "distances": { "0": 35, "1": 35, "2": 35, "3": 29, "4": 29, "5": 55, "6": 0, "7": 24, "8": 59, "9": 43, "10": 44, "11": 35, "12": 39, "13": 36, "14": 35 } }, { "id": 7, "distances": { "0": 31, "1": 23, "2": 14, "3": 20, "4": 13, "5": 35, "6": 24, "7": 0, "8": 43, "9": 19, "10": 20, "11": 20, "12": 29, "13": 19, "14": 23 } }, { "id": 8, "distances": { "0": 30, "1": 48, "2": 43, "3": 43, "4": 30, "5": 64, "6": 59, "7": 43, "8": 0, "9": 55, "10": 39, "11": 44, "12": 57, "13": 47, "14": 43 } }, { "id": 9, "distances": { "0": 31, "1": 40, "2": 33, "3": 24, "4": 32, "5": 54, "6": 43, "7": 19, "8": 55, "9": 0, "10": 37, "11": 19, "12": 31, "13": 32, "14": 34 } }, { "id": 10, "distances": { "0": 31, "1": 39, "2": 34, "3": 27, "4": 31, "5": 55, "6": 44, "7": 20, "8": 39, "9": 37, "10": 0, "11": 33, "12": 31, "13": 27, "14": 28 } }, { "id": 11, "distances": { "0": 25, "1": 33, "2": 23, "3": 12, "4": 23, "5": 43, "6": 35, "7": 20, "8": 44, "9": 19, "10": 33, "11": 0, "12": 34, "13": 26, "14": 23 } }, { "id": 12, "distances": { "0": 30, "1": 43, "2": 39, "3": 30, "4": 33, "5": 57, "6": 39, "7": 29, "8": 57, "9": 31, "10": 31, "11": 34, "12": 0, "13": 34, "14": 44 } }, { "id": 13, "distances": { "0": 23, "1": 24, "2": 25, "3": 26, "4": 26, "5": 46, "6": 36, "7": 19, "8": 47, "9": 32, "10": 27, "11": 26, "12": 34, "13": 0, "14": 30 } }, { "id": 14, "distances": { "0": 30, "1": 38, "2": 22, "3": 24, "4": 26, "5": 39, "6": 35, "7": 23, "8": 43, "9": 34, "10": 28, "11": 23, "12": 44, "13": 30, "14": 0 } } ], "objective": 333.0 }, "solution_variant": { "selected": [ 7 ], "assignments": [ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 ] }, "context_index": 17, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I manage the gear and trucks for a construction company, and the puzzle this week is picking a set number of yards to turn into equipment depots. Once those depots are chosen, every job site has to be assigned to one—and only one—of the open depots. The idea is simple: look at the distance from each site to the depot it's tied to, add up all those hauling distances, and try to make that grand total as small as possible. The exact candidate yards, the distances between places, and how many depots we’re allowed to open are listed below.\n\n# num_locations=16\n# num_depots_to_open=3\n# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P\norigin_location_id,destination_location_id,haul_distance\nA,B,19\nA,C,24\nA,D,17\nA,E,27\nA,F,25\nA,G,30\nA,H,22\nA,I,31\nA,J,20\nA,K,23\nA,L,19\nA,M,17\nA,N,15\nA,O,26\nA,P,25\nB,A,19\nB,C,23\nB,D,23\nB,E,26\nB,F,17\nB,G,33\nB,H,29\nB,I,33\nB,J,13\nB,K,22\nB,L,26\nB,M,31\nB,N,29\nB,O,30\nB,P,24\nC,A,24\nC,B,23\nC,D,34\nC,E,14\nC,F,28\nC,G,33\nC,H,24\nC,I,38\nC,J,36\nC,K,11\nC,L,25\nC,M,37\nC,N,35\nC,O,23\nC,P,39\nD,A,17\nD,B,23\nD,C,34\nD,E,20\nD,F,30\nD,G,28\nD,H,27\nD,I,28\nD,J,13\nD,K,23\nD,L,16\nD,M,32\nD,N,30\nD,O,25\nD,P,37\nE,A,27\nE,B,26\nE,C,14\nE,D,20\nE,F,26\nE,G,28\nE,H,26\nE,I,27\nE,J,28\nE,K,25\nE,L,25\nE,M,30\nE,N,28\nE,O,20\nE,P,34\nF,A,25\nF,B,17\nF,C,28\nF,D,30\nF,E,26\nF,G,36\nF,H,25\nF,I,35\nF,J,28\nF,K,26\nF,L,30\nF,M,14\nF,N,12\nF,O,33\nF,P,41\nG,A,30\nG,B,33\nG,C,33\nG,D,28\nG,E,28\nG,F,36\nG,H,34\nG,I,40\nG,J,31\nG,K,42\nG,L,30\nG,M,38\nG,N,36\nG,O,41\nG,P,45\nH,A,22\nH,B,29\nH,C,24\nH,D,27\nH,E,26\nH,F,25\nH,G,34\nH,I,23\nH,J,27\nH,K,34\nH,L,23\nH,M,29\nH,N,27\nH,O,27\nH,P,34\nI,A,31\nI,B,33\nI,C,38\nI,D,28\nI,E,27\nI,F,35\nI,G,40\nI,H,23\nI,J,31\nI,K,42\nI,L,32\nI,M,33\nI,N,31\nI,O,33\nI,P,39\nJ,A,20\nJ,B,13\nJ,C,36\nJ,D,13\nJ,E,28\nJ,F,28\nJ,G,31\nJ,H,27\nJ,I,31\nJ,K,29\nJ,L,19\nJ,M,24\nJ,N,22\nJ,O,26\nJ,P,37\nK,A,23\nK,B,22\nK,C,11\nK,D,23\nK,E,25\nK,F,26\nK,G,42\nK,H,34\nK,I,42\nK,J,29\nK,L,28\nK,M,34\nK,N,32\nK,O,33\nK,P,28\nL,A,19\nL,B,26\nL,C,25\nL,D,16\nL,E,25\nL,F,30\nL,G,30\nL,H,23\nL,I,32\nL,J,19\nL,K,28\nL,M,28\nL,N,26\nL,O,20\nL,P,43\nM,A,17\nM,B,31\nM,C,37\nM,D,32\nM,E,30\nM,F,14\nM,G,38\nM,H,29\nM,I,33\nM,J,24\nM,K,34\nM,L,28\nM,N,2\nM,O,37\nM,P,42\nN,A,15\nN,B,29\nN,C,35\nN,D,30\nN,E,28\nN,F,12\nN,G,36\nN,H,27\nN,I,31\nN,J,22\nN,K,32\nN,L,26\nN,M,2\nN,O,35\nN,P,40\nO,A,26\nO,B,30\nO,C,23\nO,D,25\nO,E,20\nO,F,33\nO,G,41\nO,H,27\nO,I,33\nO,J,26\nO,K,33\nO,L,20\nO,M,37\nO,N,35\nO,P,41\nP,A,25\nP,B,24\nP,C,39\nP,D,37\nP,E,34\nP,F,41\nP,G,45\nP,H,34\nP,I,39\nP,J,37\nP,K,28\nP,L,43\nP,M,42\nP,N,40\nP,O,41\n\nI'll keep the answer format simple so you can plug it into whatever tool or checklist you're using — here's the little JSON sketch I'd like the final reply to follow.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list which yards you decide to open as depots. \"assignments\" is a parallel list that, for each candidate location in the same order as the input, names the open yard that location will use. Think of it like a short form: the first array says which yards are turned into depots, the second array ties every job site to one of those depots.\n\nThis JSON is just the shape I want the answer to take — a sketch, not the actual solution values.\n\nPlease remember: use the identifiers exactly as they appear in the instance input — do not rename them and do not invent any new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 19, 24, 17, 27, 25, 30, 22, 31, 20, 23, 19, 17, 15, 26, 25 ], [ 19, 0, 23, 23, 26, 17, 33, 29, 33, 13, 22, 26, 31, 29, 30, 24 ], [ 24, 23, 0, 34, 14, 28, 33, 24, 38, 36, 11, 25, 37, 35, 23, 39 ], [ 17, 23, 34, 0, 20, 30, 28, 27, 28, 13, 23, 16, 32, 30, 25, 37 ], [ 27, 26, 14, 20, 0, 26, 28, 26, 27, 28, 25, 25, 30, 28, 20, 34 ], [ 25, 17, 28, 30, 26, 0, 36, 25, 35, 28, 26, 30, 14, 12, 33, 41 ], [ 30, 33, 33, 28, 28, 36, 0, 34, 40, 31, 42, 30, 38, 36, 41, 45 ], [ 22, 29, 24, 27, 26, 25, 34, 0, 23, 27, 34, 23, 29, 27, 27, 34 ], [ 31, 33, 38, 28, 27, 35, 40, 23, 0, 31, 42, 32, 33, 31, 33, 39 ], [ 20, 13, 36, 13, 28, 28, 31, 27, 31, 0, 29, 19, 24, 22, 26, 37 ], [ 23, 22, 11, 23, 25, 26, 42, 34, 42, 29, 0, 28, 34, 32, 33, 28 ], [ 19, 26, 25, 16, 25, 30, 30, 23, 32, 19, 28, 0, 28, 26, 20, 43 ], [ 17, 31, 37, 32, 30, 14, 38, 29, 33, 24, 34, 28, 0, 2, 37, 42 ], [ 15, 29, 35, 30, 28, 12, 36, 27, 31, 22, 32, 26, 2, 0, 35, 40 ], [ 26, 30, 23, 25, 20, 33, 41, 27, 33, 26, 33, 20, 37, 35, 0, 41 ], [ 25, 24, 39, 37, 34, 41, 45, 34, 39, 37, 28, 43, 42, 40, 41, 0 ] ], "p": 3, "objective": 245.0 }, "solution": { "facilities": [ 0, 2, 13 ], "assignments": [ 0, 0, 2, 0, 2, 13, 0, 0, 0, 0, 2, 0, 13, 13, 2, 0 ] }, "obj": 245.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 3, "sites": [ { "id": "A", "distances": { "A": 0, "B": 19, "C": 24, "D": 17, "E": 27, "F": 25, "G": 30, "H": 22, "I": 31, "J": 20, "K": 23, "L": 19, "M": 17, "N": 15, "O": 26, "P": 25 } }, { "id": "B", "distances": { "A": 19, "B": 0, "C": 23, "D": 23, "E": 26, "F": 17, "G": 33, "H": 29, "I": 33, "J": 13, "K": 22, "L": 26, "M": 31, "N": 29, "O": 30, "P": 24 } }, { "id": "C", "distances": { "A": 24, "B": 23, "C": 0, "D": 34, "E": 14, "F": 28, "G": 33, "H": 24, "I": 38, "J": 36, "K": 11, "L": 25, "M": 37, "N": 35, "O": 23, "P": 39 } }, { "id": "D", "distances": { "A": 17, "B": 23, "C": 34, "D": 0, "E": 20, "F": 30, "G": 28, "H": 27, "I": 28, "J": 13, "K": 23, "L": 16, "M": 32, "N": 30, "O": 25, "P": 37 } }, { "id": "E", "distances": { "A": 27, "B": 26, "C": 14, "D": 20, "E": 0, "F": 26, "G": 28, "H": 26, "I": 27, "J": 28, "K": 25, "L": 25, "M": 30, "N": 28, "O": 20, "P": 34 } }, { "id": "F", "distances": { "A": 25, "B": 17, "C": 28, "D": 30, "E": 26, "F": 0, "G": 36, "H": 25, "I": 35, "J": 28, "K": 26, "L": 30, "M": 14, "N": 12, "O": 33, "P": 41 } }, { "id": "G", "distances": { "A": 30, "B": 33, "C": 33, "D": 28, "E": 28, "F": 36, "G": 0, "H": 34, "I": 40, "J": 31, "K": 42, "L": 30, "M": 38, "N": 36, "O": 41, "P": 45 } }, { "id": "H", "distances": { "A": 22, "B": 29, "C": 24, "D": 27, "E": 26, "F": 25, "G": 34, "H": 0, "I": 23, "J": 27, "K": 34, "L": 23, "M": 29, "N": 27, "O": 27, "P": 34 } }, { "id": "I", "distances": { "A": 31, "B": 33, "C": 38, "D": 28, "E": 27, "F": 35, "G": 40, "H": 23, "I": 0, "J": 31, "K": 42, "L": 32, "M": 33, "N": 31, "O": 33, "P": 39 } }, { "id": "J", "distances": { "A": 20, "B": 13, "C": 36, "D": 13, "E": 28, "F": 28, "G": 31, "H": 27, "I": 31, "J": 0, "K": 29, "L": 19, "M": 24, "N": 22, "O": 26, "P": 37 } }, { "id": "K", "distances": { "A": 23, "B": 22, "C": 11, "D": 23, "E": 25, "F": 26, "G": 42, "H": 34, "I": 42, "J": 29, "K": 0, "L": 28, "M": 34, "N": 32, "O": 33, "P": 28 } }, { "id": "L", "distances": { "A": 19, "B": 26, "C": 25, "D": 16, "E": 25, "F": 30, "G": 30, "H": 23, "I": 32, "J": 19, "K": 28, "L": 0, "M": 28, "N": 26, "O": 20, "P": 43 } }, { "id": "M", "distances": { "A": 17, "B": 31, "C": 37, "D": 32, "E": 30, "F": 14, "G": 38, "H": 29, "I": 33, "J": 24, "K": 34, "L": 28, "M": 0, "N": 2, "O": 37, "P": 42 } }, { "id": "N", "distances": { "A": 15, "B": 29, "C": 35, "D": 30, "E": 28, "F": 12, "G": 36, "H": 27, "I": 31, "J": 22, "K": 32, "L": 26, "M": 2, "N": 0, "O": 35, "P": 40 } }, { "id": "O", "distances": { "A": 26, "B": 30, "C": 23, "D": 25, "E": 20, "F": 33, "G": 41, "H": 27, "I": 33, "J": 26, "K": 33, "L": 20, "M": 37, "N": 35, "O": 0, "P": 41 } }, { "id": "P", "distances": { "A": 25, "B": 24, "C": 39, "D": 37, "E": 34, "F": 41, "G": 45, "H": 34, "I": 39, "J": 37, "K": 28, "L": 43, "M": 42, "N": 40, "O": 41, "P": 0 } } ], "objective": 245.0 }, "solution_variant": { "selected": [ "A", "C", "N" ], "assignments": [ "A", "A", "C", "A", "C", "N", "A", "A", "A", "A", "C", "A", "N", "N", "C", "A" ] }, "context_index": 18, "input_format": "csv", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Picture this: a map of neighborhoods and potential store windows, and a limit on how many pop‑ups can actually be opened. The task is to decide which storefronts to activate and which single open space each artist neighborhood will go to — every neighborhood must be assigned to exactly one chosen storefront, with no overlaps or gaps. The winning setup is the one that keeps visitors’ journeys short overall — for each neighborhood note the distance to its assigned pop‑up, add all those distances together, and choose the plan with the lowest sum. The detailed data appears below.\n\nBelow are 19 locations, 1 pop‑ups to open, and the location identifiers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.\n1 to 2: travel distance 41.\n1 to 3: travel distance 65.\n1 to 4: travel distance 45.\n1 to 5: travel distance 58.\n1 to 6: travel distance 46.\n1 to 7: travel distance 34.\n1 to 8: travel distance 35.\n1 to 9: travel distance 37.\n1 to 10: travel distance 33.\n1 to 11: travel distance 21.\n1 to 12: travel distance 43.\n1 to 13: travel distance 52.\n1 to 14: travel distance 38.\n1 to 15: travel distance 51.\n1 to 16: travel distance 23.\n1 to 17: travel distance 47.\n1 to 18: travel distance 51.\n1 to 19: travel distance 54.\n2 to 1: travel distance 41.\n2 to 3: travel distance 34.\n2 to 4: travel distance 38.\n2 to 5: travel distance 25.\n2 to 6: travel distance 40.\n2 to 7: travel distance 27.\n2 to 8: travel distance 20.\n2 to 9: travel distance 42.\n2 to 10: travel distance 23.\n2 to 11: travel distance 48.\n2 to 12: travel distance 37.\n2 to 13: travel distance 19.\n2 to 14: travel distance 21.\n2 to 15: travel distance 16.\n2 to 16: travel distance 47.\n2 to 17: travel distance 13.\n2 to 18: travel distance 40.\n2 to 19: travel distance 44.\n3 to 1: travel distance 65.\n3 to 2: travel distance 34.\n3 to 4: travel distance 62.\n3 to 5: travel distance 59.\n3 to 6: travel distance 63.\n3 to 7: travel distance 51.\n3 to 8: travel distance 47.\n3 to 9: travel distance 72.\n3 to 10: travel distance 57.\n3 to 11: travel distance 72.\n3 to 12: travel distance 52.\n3 to 13: travel distance 53.\n3 to 14: travel distance 55.\n3 to 15: travel distance 50.\n3 to 16: travel distance 45.\n3 to 17: travel distance 47.\n3 to 18: travel distance 68.\n3 to 19: travel distance 67.\n4 to 1: travel distance 45.\n4 to 2: travel distance 38.\n4 to 3: travel distance 62.\n4 to 5: travel distance 47.\n4 to 6: travel distance 55.\n4 to 7: travel distance 25.\n4 to 8: travel distance 32.\n4 to 9: travel distance 47.\n4 to 10: travel distance 44.\n4 to 11: travel distance 52.\n4 to 12: travel distance 35.\n4 to 13: travel distance 49.\n4 to 14: travel distance 40.\n4 to 15: travel distance 47.\n4 to 16: travel distance 59.\n4 to 17: travel distance 44.\n4 to 18: travel distance 48.\n4 to 19: travel distance 43.\n5 to 1: travel distance 58.\n5 to 2: travel distance 25.\n5 to 3: travel distance 59.\n5 to 4: travel distance 47.\n5 to 6: travel distance 28.\n5 to 7: travel distance 51.\n5 to 8: travel distance 45.\n5 to 9: travel distance 55.\n5 to 10: travel distance 48.\n5 to 11: travel distance 65.\n5 to 12: travel distance 60.\n5 to 13: travel distance 42.\n5 to 14: travel distance 34.\n5 to 15: travel distance 41.\n5 to 16: travel distance 47.\n5 to 17: travel distance 38.\n5 to 18: travel distance 56.\n5 to 19: travel distance 32.\n6 to 1: travel distance 46.\n6 to 2: travel distance 40.\n6 to 3: travel distance 63.\n6 to 4: travel distance 55.\n6 to 5: travel distance 28.\n6 to 7: travel distance 47.\n6 to 8: travel distance 41.\n6 to 9: travel distance 59.\n6 to 10: travel distance 47.\n6 to 11: travel distance 53.\n6 to 12: travel distance 56.\n6 to 13: travel distance 57.\n6 to 14: travel distance 42.\n6 to 15: travel distance 46.\n6 to 16: travel distance 55.\n6 to 17: travel distance 43.\n6 to 18: travel distance 61.\n6 to 19: travel distance 24.\n7 to 1: travel distance 34.\n7 to 2: travel distance 27.\n7 to 3: travel distance 51.\n7 to 4: travel distance 25.\n7 to 5: travel distance 51.\n7 to 6: travel distance 47.\n7 to 8: travel distance 21.\n7 to 9: travel distance 41.\n7 to 10: travel distance 37.\n7 to 11: travel distance 41.\n7 to 12: travel distance 38.\n7 to 13: travel distance 38.\n7 to 14: travel distance 29.\n7 to 15: travel distance 39.\n7 to 16: travel distance 48.\n7 to 17: travel distance 33.\n7 to 18: travel distance 37.\n7 to 19: travel distance 36.\n8 to 1: travel distance 35.\n8 to 2: travel distance 20.\n8 to 3: travel distance 47.\n8 to 4: travel distance 32.\n8 to 5: travel distance 45.\n8 to 6: travel distance 41.\n8 to 7: travel distance 21.\n8 to 9: travel distance 39.\n8 to 10: travel distance 37.\n8 to 11: travel distance 42.\n8 to 12: travel distance 23.\n8 to 13: travel distance 17.\n8 to 14: travel distance 18.\n8 to 15: travel distance 36.\n8 to 16: travel distance 37.\n8 to 17: travel distance 16.\n8 to 18: travel distance 34.\n8 to 19: travel distance 31.\n9 to 1: travel distance 37.\n9 to 2: travel distance 42.\n9 to 3: travel distance 72.\n9 to 4: travel distance 47.\n9 to 5: travel distance 55.\n9 to 6: travel distance 59.\n9 to 7: travel distance 41.\n9 to 8: travel distance 39.\n9 to 10: travel distance 21.\n9 to 11: travel distance 44.\n9 to 12: travel distance 44.\n9 to 13: travel distance 56.\n9 to 14: travel distance 21.\n9 to 15: travel distance 48.\n9 to 16: travel distance 60.\n9 to 17: travel distance 43.\n9 to 18: travel distance 30.\n9 to 19: travel distance 58.\n10 to 1: travel distance 33.\n10 to 2: travel distance 23.\n10 to 3: travel distance 57.\n10 to 4: travel distance 44.\n10 to 5: travel distance 48.\n10 to 6: travel distance 47.\n10 to 7: travel distance 37.\n10 to 8: travel distance 37.\n10 to 9: travel distance 21.\n10 to 11: travel distance 40.\n10 to 12: travel distance 40.\n10 to 13: travel distance 42.\n10 to 14: travel distance 30.\n10 to 15: travel distance 39.\n10 to 16: travel distance 56.\n10 to 17: travel distance 36.\n10 to 18: travel distance 39.\n10 to 19: travel distance 51.\n11 to 1: travel distance 21.\n11 to 2: travel distance 48.\n11 to 3: travel distance 72.\n11 to 4: travel distance 52.\n11 to 5: travel distance 65.\n11 to 6: travel distance 53.\n11 to 7: travel distance 41.\n11 to 8: travel distance 42.\n11 to 9: travel distance 44.\n11 to 10: travel distance 40.\n11 to 12: travel distance 50.\n11 to 13: travel distance 59.\n11 to 14: travel distance 50.\n11 to 15: travel distance 58.\n11 to 16: travel distance 44.\n11 to 17: travel distance 54.\n11 to 18: travel distance 58.\n11 to 19: travel distance 61.\n12 to 1: travel distance 43.\n12 to 2: travel distance 37.\n12 to 3: travel distance 52.\n12 to 4: travel distance 35.\n12 to 5: travel distance 60.\n12 to 6: travel distance 56.\n12 to 7: travel distance 38.\n12 to 8: travel distance 23.\n12 to 9: travel distance 44.\n12 to 10: travel distance 40.\n12 to 11: travel distance 50.\n12 to 13: travel distance 39.\n12 to 14: travel distance 35.\n12 to 15: travel distance 31.\n12 to 16: travel distance 54.\n12 to 17: travel distance 24.\n12 to 18: travel distance 51.\n12 to 19: travel distance 48.\n13 to 1: travel distance 52.\n13 to 2: travel distance 19.\n13 to 3: travel distance 53.\n13 to 4: travel distance 49.\n13 to 5: travel distance 42.\n13 to 6: travel distance 57.\n13 to 7: travel distance 38.\n13 to 8: travel distance 17.\n13 to 9: travel distance 56.\n13 to 10: travel distance 42.\n13 to 11: travel distance 59.\n13 to 12: travel distance 39.\n13 to 14: travel distance 35.\n13 to 15: travel distance 35.\n13 to 16: travel distance 54.\n13 to 17: travel distance 15.\n13 to 18: travel distance 51.\n13 to 19: travel distance 48.\n14 to 1: travel distance 38.\n14 to 2: travel distance 21.\n14 to 3: travel distance 55.\n14 to 4: travel distance 40.\n14 to 5: travel distance 34.\n14 to 6: travel distance 42.\n14 to 7: travel distance 29.\n14 to 8: travel distance 18.\n14 to 9: travel distance 21.\n14 to 10: travel distance 30.\n14 to 11: travel distance 50.\n14 to 12: travel distance 35.\n14 to 13: travel distance 35.\n14 to 15: travel distance 27.\n14 to 16: travel distance 45.\n14 to 17: travel distance 22.\n14 to 18: travel distance 39.\n14 to 19: travel distance 43.\n15 to 1: travel distance 51.\n15 to 2: travel distance 16.\n15 to 3: travel distance 50.\n15 to 4: travel distance 47.\n15 to 5: travel distance 41.\n15 to 6: travel distance 46.\n15 to 7: travel distance 39.\n15 to 8: travel distance 36.\n15 to 9: travel distance 48.\n15 to 10: travel distance 39.\n15 to 11: travel distance 58.\n15 to 12: travel distance 31.\n15 to 13: travel distance 35.\n15 to 14: travel distance 27.\n15 to 16: travel distance 62.\n15 to 17: travel distance 21.\n15 to 18: travel distance 50.\n15 to 19: travel distance 50.\n16 to 1: travel distance 23.\n16 to 2: travel distance 47.\n16 to 3: travel distance 45.\n16 to 4: travel distance 59.\n16 to 5: travel distance 47.\n16 to 6: travel distance 55.\n16 to 7: travel distance 48.\n16 to 8: travel distance 37.\n16 to 9: travel distance 60.\n16 to 10: travel distance 56.\n16 to 11: travel distance 44.\n16 to 12: travel distance 54.\n16 to 13: travel distance 54.\n16 to 14: travel distance 45.\n16 to 15: travel distance 62.\n16 to 17: travel distance 48.\n16 to 18: travel distance 61.\n16 to 19: travel distance 59.\n17 to 1: travel distance 47.\n17 to 2: travel distance 13.\n17 to 3: travel distance 47.\n17 to 4: travel distance 44.\n17 to 5: travel distance 38.\n17 to 6: travel distance 43.\n17 to 7: travel distance 33.\n17 to 8: travel distance 16.\n17 to 9: travel distance 43.\n17 to 10: travel distance 36.\n17 to 11: travel distance 54.\n17 to 12: travel distance 24.\n17 to 13: travel distance 15.\n17 to 14: travel distance 22.\n17 to 15: travel distance 21.\n17 to 16: travel distance 48.\n17 to 18: travel distance 46.\n17 to 19: travel distance 43.\n18 to 1: travel distance 51.\n18 to 2: travel distance 40.\n18 to 3: travel distance 68.\n18 to 4: travel distance 48.\n18 to 5: travel distance 56.\n18 to 6: travel distance 61.\n18 to 7: travel distance 37.\n18 to 8: travel distance 34.\n18 to 9: travel distance 30.\n18 to 10: travel distance 39.\n18 to 11: travel distance 58.\n18 to 12: travel distance 51.\n18 to 13: travel distance 51.\n18 to 14: travel distance 39.\n18 to 15: travel distance 50.\n18 to 16: travel distance 61.\n18 to 17: travel distance 46.\n18 to 19: travel distance 59.\n19 to 1: travel distance 54.\n19 to 2: travel distance 44.\n19 to 3: travel distance 67.\n19 to 4: travel distance 43.\n19 to 5: travel distance 32.\n19 to 6: travel distance 24.\n19 to 7: travel distance 36.\n19 to 8: travel distance 31.\n19 to 9: travel distance 58.\n19 to 10: travel distance 51.\n19 to 11: travel distance 61.\n19 to 12: travel distance 48.\n19 to 13: travel distance 48.\n19 to 14: travel distance 43.\n19 to 15: travel distance 50.\n19 to 16: travel distance 59.\n19 to 17: travel distance 43.\n19 to 18: travel distance 59.\nUse these distance records to evaluate total visitor travel when selecting 1 pop‑ups.\n\nYou can just return the plan using a tiny JSON snippet like this — nothing fancy, just that shape so it’s easy to read and check.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of storefronts you decide to open. \"assignments\" lists, for each neighborhood in the input (in the same order), which opened storefront that neighborhood will go to. Super casual: think of \"selected\" as the open pop‑ups and \"assignments\" as each neighborhood’s chosen window.\n\nThis JSON is just the shape I need — not the real answer itself. Please make sure you use the exact identifiers from the instance input with no renaming and no invented labels. Valid identifiers look like:\n- plain numbers such as “1” or “23”\n- single capital letters like “A” or “B”\n- a capital letter followed by digits like “A1” or “X7”", "instance": { "distance_matrix": [ [ 0, 41, 65, 45, 58, 46, 34, 35, 37, 33, 21, 43, 52, 38, 51, 23, 47, 51, 54 ], [ 41, 0, 34, 38, 25, 40, 27, 20, 42, 23, 48, 37, 19, 21, 16, 47, 13, 40, 44 ], [ 65, 34, 0, 62, 59, 63, 51, 47, 72, 57, 72, 52, 53, 55, 50, 45, 47, 68, 67 ], [ 45, 38, 62, 0, 47, 55, 25, 32, 47, 44, 52, 35, 49, 40, 47, 59, 44, 48, 43 ], [ 58, 25, 59, 47, 0, 28, 51, 45, 55, 48, 65, 60, 42, 34, 41, 47, 38, 56, 32 ], [ 46, 40, 63, 55, 28, 0, 47, 41, 59, 47, 53, 56, 57, 42, 46, 55, 43, 61, 24 ], [ 34, 27, 51, 25, 51, 47, 0, 21, 41, 37, 41, 38, 38, 29, 39, 48, 33, 37, 36 ], [ 35, 20, 47, 32, 45, 41, 21, 0, 39, 37, 42, 23, 17, 18, 36, 37, 16, 34, 31 ], [ 37, 42, 72, 47, 55, 59, 41, 39, 0, 21, 44, 44, 56, 21, 48, 60, 43, 30, 58 ], [ 33, 23, 57, 44, 48, 47, 37, 37, 21, 0, 40, 40, 42, 30, 39, 56, 36, 39, 51 ], [ 21, 48, 72, 52, 65, 53, 41, 42, 44, 40, 0, 50, 59, 50, 58, 44, 54, 58, 61 ], [ 43, 37, 52, 35, 60, 56, 38, 23, 44, 40, 50, 0, 39, 35, 31, 54, 24, 51, 48 ], [ 52, 19, 53, 49, 42, 57, 38, 17, 56, 42, 59, 39, 0, 35, 35, 54, 15, 51, 48 ], [ 38, 21, 55, 40, 34, 42, 29, 18, 21, 30, 50, 35, 35, 0, 27, 45, 22, 39, 43 ], [ 51, 16, 50, 47, 41, 46, 39, 36, 48, 39, 58, 31, 35, 27, 0, 62, 21, 50, 50 ], [ 23, 47, 45, 59, 47, 55, 48, 37, 60, 56, 44, 54, 54, 45, 62, 0, 48, 61, 59 ], [ 47, 13, 47, 44, 38, 43, 33, 16, 43, 36, 54, 24, 15, 22, 21, 48, 0, 46, 43 ], [ 51, 40, 68, 48, 56, 61, 37, 34, 30, 39, 58, 51, 51, 39, 50, 61, 46, 0, 59 ], [ 54, 44, 67, 43, 32, 24, 36, 31, 58, 51, 61, 48, 48, 43, 50, 59, 43, 59, 0 ] ], "p": 1, "objective": 571.0 }, "solution": { "facilities": [ 7 ], "assignments": [ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 ] }, "obj": 571.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 1, "sites": [ { "id": 1, "distances": { "1": 0, "2": 41, "3": 65, "4": 45, "5": 58, "6": 46, "7": 34, "8": 35, "9": 37, "10": 33, "11": 21, "12": 43, "13": 52, "14": 38, "15": 51, "16": 23, "17": 47, "18": 51, "19": 54 } }, { "id": 2, "distances": { "1": 41, "2": 0, "3": 34, "4": 38, "5": 25, "6": 40, "7": 27, "8": 20, "9": 42, "10": 23, "11": 48, "12": 37, "13": 19, "14": 21, "15": 16, "16": 47, "17": 13, "18": 40, "19": 44 } }, { "id": 3, "distances": { "1": 65, "2": 34, "3": 0, "4": 62, "5": 59, "6": 63, "7": 51, "8": 47, "9": 72, "10": 57, "11": 72, "12": 52, "13": 53, "14": 55, "15": 50, "16": 45, "17": 47, "18": 68, "19": 67 } }, { "id": 4, "distances": { "1": 45, "2": 38, "3": 62, "4": 0, "5": 47, "6": 55, "7": 25, "8": 32, "9": 47, "10": 44, "11": 52, "12": 35, "13": 49, "14": 40, "15": 47, "16": 59, "17": 44, "18": 48, "19": 43 } }, { "id": 5, "distances": { "1": 58, "2": 25, "3": 59, "4": 47, "5": 0, "6": 28, "7": 51, "8": 45, "9": 55, "10": 48, "11": 65, "12": 60, "13": 42, "14": 34, "15": 41, "16": 47, "17": 38, "18": 56, "19": 32 } }, { "id": 6, "distances": { "1": 46, "2": 40, "3": 63, "4": 55, "5": 28, "6": 0, "7": 47, "8": 41, "9": 59, "10": 47, "11": 53, "12": 56, "13": 57, "14": 42, "15": 46, "16": 55, "17": 43, "18": 61, "19": 24 } }, { "id": 7, "distances": { "1": 34, "2": 27, "3": 51, "4": 25, "5": 51, "6": 47, "7": 0, "8": 21, "9": 41, "10": 37, "11": 41, "12": 38, "13": 38, "14": 29, "15": 39, "16": 48, "17": 33, "18": 37, "19": 36 } }, { "id": 8, "distances": { "1": 35, "2": 20, "3": 47, "4": 32, "5": 45, "6": 41, "7": 21, "8": 0, "9": 39, "10": 37, "11": 42, "12": 23, "13": 17, "14": 18, "15": 36, "16": 37, "17": 16, "18": 34, "19": 31 } }, { "id": 9, "distances": { "1": 37, "2": 42, "3": 72, "4": 47, "5": 55, "6": 59, "7": 41, "8": 39, "9": 0, "10": 21, "11": 44, "12": 44, "13": 56, "14": 21, "15": 48, "16": 60, "17": 43, "18": 30, "19": 58 } }, { "id": 10, "distances": { "1": 33, "2": 23, "3": 57, "4": 44, "5": 48, "6": 47, "7": 37, "8": 37, "9": 21, "10": 0, "11": 40, "12": 40, "13": 42, "14": 30, "15": 39, "16": 56, "17": 36, "18": 39, "19": 51 } }, { "id": 11, "distances": { "1": 21, "2": 48, "3": 72, "4": 52, "5": 65, "6": 53, "7": 41, "8": 42, "9": 44, "10": 40, "11": 0, "12": 50, "13": 59, "14": 50, "15": 58, "16": 44, "17": 54, "18": 58, "19": 61 } }, { "id": 12, "distances": { "1": 43, "2": 37, "3": 52, "4": 35, "5": 60, "6": 56, "7": 38, "8": 23, "9": 44, "10": 40, "11": 50, "12": 0, "13": 39, "14": 35, "15": 31, "16": 54, "17": 24, "18": 51, "19": 48 } }, { "id": 13, "distances": { "1": 52, "2": 19, "3": 53, "4": 49, "5": 42, "6": 57, "7": 38, "8": 17, "9": 56, "10": 42, "11": 59, "12": 39, "13": 0, "14": 35, "15": 35, "16": 54, "17": 15, "18": 51, "19": 48 } }, { "id": 14, "distances": { "1": 38, "2": 21, "3": 55, "4": 40, "5": 34, "6": 42, "7": 29, "8": 18, "9": 21, "10": 30, "11": 50, "12": 35, "13": 35, "14": 0, "15": 27, "16": 45, "17": 22, "18": 39, "19": 43 } }, { "id": 15, "distances": { "1": 51, "2": 16, "3": 50, "4": 47, "5": 41, "6": 46, "7": 39, "8": 36, "9": 48, "10": 39, "11": 58, "12": 31, "13": 35, "14": 27, "15": 0, "16": 62, "17": 21, "18": 50, "19": 50 } }, { "id": 16, "distances": { "1": 23, "2": 47, "3": 45, "4": 59, "5": 47, "6": 55, "7": 48, "8": 37, "9": 60, "10": 56, "11": 44, "12": 54, "13": 54, "14": 45, "15": 62, "16": 0, "17": 48, "18": 61, "19": 59 } }, { "id": 17, "distances": { "1": 47, "2": 13, "3": 47, "4": 44, "5": 38, "6": 43, "7": 33, "8": 16, "9": 43, "10": 36, "11": 54, "12": 24, "13": 15, "14": 22, "15": 21, "16": 48, "17": 0, "18": 46, "19": 43 } }, { "id": 18, "distances": { "1": 51, "2": 40, "3": 68, "4": 48, "5": 56, "6": 61, "7": 37, "8": 34, "9": 30, "10": 39, "11": 58, "12": 51, "13": 51, "14": 39, "15": 50, "16": 61, "17": 46, "18": 0, "19": 59 } }, { "id": 19, "distances": { "1": 54, "2": 44, "3": 67, "4": 43, "5": 32, "6": 24, "7": 36, "8": 31, "9": 58, "10": 51, "11": 61, "12": 48, "13": 48, "14": 43, "15": 50, "16": 59, "17": 43, "18": 59, "19": 0 } } ], "objective": 571.0 }, "solution_variant": { "selected": [ 8 ], "assignments": [ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 ] }, "context_index": 19, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "We need to decide where to put a set number of health posts and which village goes to which post so folks don’t travel farther than necessary. Pick exactly the number of clinics allowed, and then give each village one—and only one—clinic to use; nothing is left unassigned and nothing is doubled up. What makes one arrangement better than another is simply the total distance everyone has to travel: compute it by summing each village’s trip to its assigned clinic, and aim for that sum to be as small as possible. The specific villages, possible locations, pairwise distances, and the allowed clinic count are listed below.\n\n{\n \"total_villages\": 15,\n \"clinics_to_open\": 2,\n \"village_ids\": [\n \"A\",\n \"B\",\n \"C\",\n \"D\",\n \"E\",\n \"F\",\n \"G\",\n \"H\",\n \"I\",\n \"J\",\n \"K\",\n \"L\",\n \"M\",\n \"N\",\n \"O\"\n ],\n \"data\": [\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"B\",\n \"travel_distance\": 105\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"C\",\n \"travel_distance\": 81\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"D\",\n \"travel_distance\": 120\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"E\",\n \"travel_distance\": 85\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"F\",\n \"travel_distance\": 109\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"G\",\n \"travel_distance\": 113\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"H\",\n \"travel_distance\": 92\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"I\",\n \"travel_distance\": 60\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"J\",\n \"travel_distance\": 46\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"K\",\n \"travel_distance\": 75\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"L\",\n \"travel_distance\": 70\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"M\",\n \"travel_distance\": 113\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"N\",\n \"travel_distance\": 91\n },\n {\n \"origin_village\": \"A\",\n \"destination_village\": \"O\",\n \"travel_distance\": 91\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"A\",\n \"travel_distance\": 105\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"C\",\n \"travel_distance\": 59\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"D\",\n \"travel_distance\": 66\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"E\",\n \"travel_distance\": 84\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"F\",\n \"travel_distance\": 104\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"G\",\n \"travel_distance\": 58\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"H\",\n \"travel_distance\": 99\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"I\",\n \"travel_distance\": 80\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"J\",\n \"travel_distance\": 68\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"K\",\n \"travel_distance\": 91\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"L\",\n \"travel_distance\": 109\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"M\",\n \"travel_distance\": 102\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"N\",\n \"travel_distance\": 100\n },\n {\n \"origin_village\": \"B\",\n \"destination_village\": \"O\",\n \"travel_distance\": 18\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"A\",\n \"travel_distance\": 81\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"B\",\n \"travel_distance\": 59\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"D\",\n \"travel_distance\": 103\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"E\",\n \"travel_distance\": 67\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"F\",\n \"travel_distance\": 82\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"G\",\n \"travel_distance\": 41\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"H\",\n \"travel_distance\": 92\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"I\",\n \"travel_distance\": 81\n },\n {\n \"origin_village\": \"C\",\n \"destination_village\": \"J\",\n 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\"destination_village\": \"B\",\n \"travel_distance\": 18\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"C\",\n \"travel_distance\": 77\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"D\",\n \"travel_distance\": 84\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"E\",\n \"travel_distance\": 92\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"F\",\n \"travel_distance\": 98\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"G\",\n \"travel_distance\": 76\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"H\",\n \"travel_distance\": 93\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"I\",\n \"travel_distance\": 72\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"J\",\n \"travel_distance\": 62\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"K\",\n \"travel_distance\": 97\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"L\",\n \"travel_distance\": 91\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"M\",\n \"travel_distance\": 112\n },\n {\n \"origin_village\": \"O\",\n \"destination_village\": \"N\",\n \"travel_distance\": 94\n }\n ]\n}\n\nOh, and to keep things tidy, please give your answer using this simple JSON layout so it's easy to read and use:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is just the list of clinics you choose to open. \"assignments\" is a list that says which clinic each village will use (in the same order the villages were listed). This is just a sketch of the shape I expect — not the actual solution.\n\nPlease make sure you use the exact identifiers from the instance input with no renaming and no new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”\".", "instance": { "distance_matrix": [ [ 0, 105, 81, 120, 85, 109, 113, 92, 60, 46, 75, 70, 113, 91, 91 ], [ 105, 0, 59, 66, 84, 104, 58, 99, 80, 68, 91, 109, 102, 100, 18 ], [ 81, 59, 0, 103, 67, 82, 41, 92, 81, 74, 102, 98, 94, 84, 77 ], [ 120, 66, 103, 0, 77, 135, 99, 85, 100, 86, 106, 70, 124, 106, 84 ], [ 85, 84, 67, 77, 0, 95, 66, 89, 93, 79, 80, 62, 119, 97, 92 ], [ 109, 104, 82, 135, 95, 0, 122, 136, 110, 96, 128, 87, 134, 115, 98 ], [ 113, 58, 41, 99, 66, 122, 0, 83, 80, 67, 110, 88, 93, 111, 76 ], [ 92, 99, 92, 85, 89, 136, 83, 0, 59, 46, 89, 83, 107, 87, 93 ], [ 60, 80, 81, 100, 93, 110, 80, 59, 0, 14, 77, 93, 80, 85, 72 ], [ 46, 68, 74, 86, 79, 96, 67, 46, 14, 0, 63, 79, 73, 71, 62 ], [ 75, 91, 102, 106, 80, 128, 110, 89, 77, 63, 0, 89, 108, 100, 97 ], [ 70, 109, 98, 70, 62, 87, 88, 83, 93, 79, 89, 0, 137, 111, 91 ], [ 113, 102, 94, 124, 119, 134, 93, 107, 80, 73, 108, 137, 0, 120, 112 ], [ 91, 100, 84, 106, 97, 115, 111, 87, 85, 71, 100, 111, 120, 0, 94 ], [ 91, 18, 77, 84, 92, 98, 76, 93, 72, 62, 97, 91, 112, 94, 0 ] ], "p": 2, "objective": 768.0 }, "solution": { "facilities": [ 1, 9 ], "assignments": [ 9, 1, 1, 1, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 1 ] }, "obj": 768.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 15, "num_open": 2, "sites": [ { "id": "A", "distances": { "A": 0, "B": 105, "C": 81, "D": 120, "E": 85, "F": 109, "G": 113, "H": 92, "I": 60, "J": 46, "K": 75, "L": 70, "M": 113, "N": 91, "O": 91 } }, { "id": "B", "distances": { "A": 105, "B": 0, "C": 59, "D": 66, "E": 84, "F": 104, "G": 58, "H": 99, "I": 80, "J": 68, "K": 91, "L": 109, "M": 102, "N": 100, "O": 18 } }, { "id": "C", "distances": { "A": 81, "B": 59, "C": 0, "D": 103, "E": 67, "F": 82, "G": 41, "H": 92, "I": 81, "J": 74, "K": 102, "L": 98, "M": 94, "N": 84, "O": 77 } }, { "id": "D", "distances": { "A": 120, "B": 66, "C": 103, "D": 0, "E": 77, "F": 135, "G": 99, "H": 85, "I": 100, "J": 86, "K": 106, "L": 70, "M": 124, "N": 106, "O": 84 } }, { "id": "E", "distances": { "A": 85, "B": 84, "C": 67, "D": 77, "E": 0, "F": 95, "G": 66, "H": 89, "I": 93, "J": 79, "K": 80, "L": 62, "M": 119, "N": 97, "O": 92 } }, { "id": "F", "distances": { "A": 109, "B": 104, "C": 82, "D": 135, "E": 95, "F": 0, "G": 122, "H": 136, "I": 110, "J": 96, "K": 128, "L": 87, "M": 134, "N": 115, "O": 98 } }, { "id": "G", "distances": { "A": 113, "B": 58, "C": 41, "D": 99, "E": 66, "F": 122, "G": 0, "H": 83, "I": 80, "J": 67, "K": 110, "L": 88, "M": 93, "N": 111, "O": 76 } }, { "id": "H", "distances": { "A": 92, "B": 99, "C": 92, "D": 85, "E": 89, "F": 136, "G": 83, "H": 0, "I": 59, "J": 46, "K": 89, "L": 83, "M": 107, "N": 87, "O": 93 } }, { "id": "I", "distances": { "A": 60, "B": 80, "C": 81, "D": 100, "E": 93, "F": 110, "G": 80, "H": 59, "I": 0, "J": 14, "K": 77, "L": 93, "M": 80, "N": 85, "O": 72 } }, { "id": "J", "distances": { "A": 46, "B": 68, "C": 74, "D": 86, "E": 79, "F": 96, "G": 67, "H": 46, "I": 14, "J": 0, "K": 63, "L": 79, "M": 73, "N": 71, "O": 62 } }, { "id": "K", "distances": { "A": 75, "B": 91, "C": 102, "D": 106, "E": 80, "F": 128, "G": 110, "H": 89, "I": 77, "J": 63, "K": 0, "L": 89, "M": 108, "N": 100, "O": 97 } }, { "id": "L", "distances": { "A": 70, "B": 109, "C": 98, "D": 70, "E": 62, "F": 87, "G": 88, "H": 83, "I": 93, "J": 79, "K": 89, "L": 0, "M": 137, "N": 111, "O": 91 } }, { "id": "M", "distances": { "A": 113, "B": 102, "C": 94, "D": 124, "E": 119, "F": 134, "G": 93, "H": 107, "I": 80, "J": 73, "K": 108, "L": 137, "M": 0, "N": 120, "O": 112 } }, { "id": "N", "distances": { "A": 91, "B": 100, "C": 84, "D": 106, "E": 97, "F": 115, "G": 111, "H": 87, "I": 85, "J": 71, "K": 100, "L": 111, "M": 120, "N": 0, "O": 94 } }, { "id": "O", "distances": { "A": 91, "B": 18, "C": 77, "D": 84, "E": 92, "F": 98, "G": 76, "H": 93, "I": 72, "J": 62, "K": 97, "L": 91, "M": 112, "N": 94, "O": 0 } } ], "objective": 768.0 }, "solution_variant": { "selected": [ "B", "J" ], "assignments": [ "J", "B", "B", "B", "J", "J", "B", "J", "J", "J", "J", "J", "J", "J", "B" ] }, "context_index": 20, "input_format": "json", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone in charge of the chain has to choose a limited set of stores to keep running and then assign each customer zone to a single one of those stores. Each zone gets one, and only one, assigned store — nothing gets skipped or duplicated. The way to measure success is to add together the distance from each zone to its chosen store; the smaller that grand total, the better the decision. See the detailed instance information below.\n\nThere are 20 candidate locations; 1 stores must be kept open, and every ID in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 denotes a location that must be assigned to exactly one open store.\nThe travel distance from origin location 1 to destination location 2 is 60.\nThe travel distance from origin location 1 to destination location 3 is 55.\nThe travel distance from origin location 1 to destination location 4 is 78.\nThe travel distance from origin location 1 to destination location 5 is 77.\nThe travel distance from origin location 1 to destination location 6 is 100.\nThe travel distance from origin location 1 to destination location 7 is 52.\nThe travel distance from origin location 1 to destination location 8 is 64.\nThe travel distance from origin location 1 to destination location 9 is 71.\nThe travel distance from origin location 1 to destination location 10 is 94.\nThe travel distance from origin location 1 to destination location 11 is 51.\nThe travel distance from origin location 1 to destination location 12 is 62.\nThe travel distance from origin location 1 to destination location 13 is 92.\nThe travel distance from origin location 1 to destination location 14 is 66.\nThe travel distance from origin location 1 to destination location 15 is 25.\nThe travel distance from origin location 1 to destination location 16 is 117.\nThe travel distance from origin location 1 to destination location 17 is 128.\nThe travel distance from origin location 1 to destination location 18 is 58.\nThe travel distance from origin location 1 to destination location 19 is 60.\nThe travel distance from origin location 1 to destination location 20 is 78.\nThe travel distance from origin location 2 to destination location 1 is 60.\nThe travel distance from origin location 2 to destination location 3 is 15.\nThe travel distance from origin location 2 to destination location 4 is 71.\nThe travel distance from origin location 2 to destination location 5 is 70.\nThe travel distance from origin location 2 to destination location 6 is 52.\nThe travel distance from origin location 2 to destination location 7 is 64.\nThe travel distance from origin location 2 to destination location 8 is 24.\nThe travel distance from origin location 2 to destination location 9 is 43.\nThe travel distance from origin location 2 to destination location 10 is 48.\nThe travel distance from origin location 2 to destination location 11 is 53.\nThe travel distance from origin location 2 to destination location 12 is 96.\nThe travel distance from origin location 2 to destination location 13 is 65.\nThe travel distance from origin location 2 to destination location 14 is 84.\nThe travel distance from origin location 2 to destination location 15 is 48.\nThe travel distance from origin location 2 to destination location 16 is 116.\nThe travel distance from origin location 2 to destination location 17 is 107.\nThe travel distance from origin location 2 to destination location 18 is 41.\nThe travel distance from origin location 2 to destination location 19 is 65.\nThe travel distance from origin location 2 to destination location 20 is 69.\nThe travel distance from origin location 3 to destination location 1 is 55.\nThe travel distance from origin location 3 to destination location 2 is 15.\nThe travel distance from origin location 3 to destination location 4 is 56.\nThe travel distance from origin location 3 to destination location 5 is 55.\nThe travel distance from origin location 3 to destination location 6 is 45.\nThe travel distance from origin location 3 to destination location 7 is 49.\nThe travel distance from origin location 3 to destination location 8 is 9.\nThe travel distance from origin location 3 to destination location 9 is 44.\nThe travel distance from origin location 3 to destination location 10 is 63.\nThe travel distance from origin location 3 to destination location 11 is 48.\nThe travel distance from origin location 3 to destination location 12 is 81.\nThe travel distance from origin location 3 to destination location 13 is 50.\nThe travel distance from origin location 3 to destination location 14 is 79.\nThe travel distance from origin location 3 to destination location 15 is 58.\nThe travel distance from origin location 3 to destination location 16 is 101.\nThe travel distance from origin location 3 to destination location 17 is 102.\nThe travel distance from origin location 3 to destination location 18 is 26.\nThe travel distance from origin location 3 to destination location 19 is 50.\nThe travel distance from origin location 3 to destination location 20 is 54.\nThe travel distance from origin location 4 to destination location 1 is 78.\nThe travel distance from origin location 4 to destination location 2 is 71.\nThe travel distance from origin location 4 to destination location 3 is 56.\nThe travel distance from origin location 4 to destination location 5 is 65.\nThe travel distance from origin location 4 to destination location 6 is 101.\nThe travel distance from origin location 4 to destination location 7 is 66.\nThe travel distance from origin location 4 to destination location 8 is 47.\nThe travel distance from origin location 4 to destination location 9 is 69.\nThe travel distance from origin location 4 to destination location 10 is 97.\nThe travel distance from origin location 4 to destination location 11 is 59.\nThe travel distance from origin location 4 to destination location 12 is 71.\nThe travel distance from origin location 4 to destination location 13 is 83.\nThe travel distance from origin location 4 to destination location 14 is 89.\nThe travel distance from origin location 4 to destination location 15 is 70.\nThe travel distance from origin location 4 to destination location 16 is 102.\nThe travel distance from origin location 4 to destination location 17 is 87.\nThe travel distance from origin location 4 to destination location 18 is 30.\nThe travel distance from origin location 4 to destination location 19 is 18.\nThe travel distance from origin location 4 to destination location 20 is 58.\nThe travel distance from origin location 5 to destination location 1 is 77.\nThe travel distance from origin location 5 to destination location 2 is 70.\nThe travel distance from origin location 5 to destination location 3 is 55.\nThe travel distance from origin location 5 to destination location 4 is 65.\nThe travel distance from origin location 5 to destination location 6 is 100.\nThe travel distance from origin location 5 to destination location 7 is 77.\nThe travel distance from origin location 5 to destination location 8 is 46.\nThe travel distance from origin location 5 to destination location 9 is 76.\nThe travel distance from origin location 5 to destination location 10 is 70.\nThe travel distance from origin location 5 to destination location 11 is 64.\nThe travel distance from origin location 5 to destination location 12 is 60.\nThe travel distance from origin location 5 to destination location 13 is 100.\nThe travel distance from origin location 5 to destination location 14 is 94.\nThe travel distance from origin location 5 to destination location 15 is 66.\nThe travel distance from origin location 5 to destination location 16 is 115.\nThe travel distance from origin location 5 to destination location 17 is 107.\nThe travel distance from origin location 5 to destination location 18 is 35.\nThe travel distance from origin location 5 to destination location 19 is 73.\nThe travel distance from origin location 5 to destination location 20 is 37.\nThe travel distance from origin location 6 to destination location 1 is 100.\nThe travel distance from origin location 6 to destination location 2 is 52.\nThe travel distance from origin location 6 to destination location 3 is 45.\nThe travel distance from origin location 6 to destination location 4 is 101.\nThe travel distance from origin location 6 to destination location 5 is 100.\nThe travel distance from origin location 6 to destination location 7 is 94.\nThe travel distance from origin location 6 to destination location 8 is 54.\nThe travel distance from origin location 6 to destination location 9 is 73.\nThe travel distance from origin location 6 to destination location 10 is 82.\nThe travel distance from origin location 6 to destination location 11 is 90.\nThe travel distance from origin location 6 to destination location 12 is 126.\nThe travel distance from origin location 6 to destination location 13 is 55.\nThe travel distance from origin location 6 to destination location 14 is 86.\nThe travel distance from origin location 6 to destination location 15 is 82.\nThe travel distance from origin location 6 to destination location 16 is 146.\nThe travel distance from origin location 6 to destination location 17 is 132.\nThe travel distance from origin location 6 to destination location 18 is 71.\nThe travel distance from origin location 6 to destination location 19 is 95.\nThe travel distance from origin location 6 to destination location 20 is 99.\nThe travel distance from origin location 7 to destination location 1 is 52.\nThe travel distance from origin location 7 to destination location 2 is 64.\nThe travel distance from origin location 7 to destination location 3 is 49.\nThe travel distance from origin location 7 to destination location 4 is 66.\nThe travel distance from origin location 7 to destination location 5 is 77.\nThe travel distance from origin location 7 to destination location 6 is 94.\nThe travel distance from origin location 7 to destination location 8 is 40.\nThe travel distance from origin location 7 to destination location 9 is 61.\nThe travel distance from origin location 7 to destination location 10 is 80.\nThe travel distance from origin location 7 to destination location 11 is 71.\nThe travel distance from origin location 7 to destination location 12 is 95.\nThe travel distance from origin location 7 to destination location 13 is 75.\nThe travel distance from origin location 7 to destination location 14 is 78.\nThe travel distance from origin location 7 to destination location 15 is 27.\nThe travel distance from origin location 7 to destination location 16 is 116.\nThe travel distance from origin location 7 to destination location 17 is 120.\nThe travel distance from origin location 7 to destination location 18 is 42.\nThe travel distance from origin location 7 to destination location 19 is 74.\nThe travel distance from origin location 7 to destination location 20 is 70.\nThe travel distance from origin location 8 to destination location 1 is 64.\nThe travel distance from origin location 8 to destination location 2 is 24.\nThe travel distance from origin location 8 to destination location 3 is 9.\nThe travel distance from origin location 8 to destination location 4 is 47.\nThe travel distance from origin location 8 to destination location 5 is 46.\nThe travel distance from origin location 8 to destination location 6 is 54.\nThe travel distance from origin location 8 to destination location 7 is 40.\nThe travel distance from origin location 8 to destination location 9 is 35.\nThe travel distance from origin location 8 to destination location 10 is 72.\nThe travel distance from origin location 8 to destination location 11 is 46.\nThe travel distance from origin location 8 to destination location 12 is 72.\nThe travel distance from origin location 8 to destination location 13 is 58.\nThe travel distance from origin location 8 to destination location 14 is 76.\nThe travel distance from origin location 8 to destination location 15 is 49.\nThe travel distance from origin location 8 to destination location 16 is 92.\nThe travel distance from origin location 8 to destination location 17 is 95.\nThe travel distance from origin location 8 to destination location 18 is 17.\nThe travel distance from origin location 8 to destination location 19 is 41.\nThe travel distance from origin location 8 to destination location 20 is 45.\nThe travel distance from origin location 9 to destination location 1 is 71.\nThe travel distance from origin location 9 to destination location 2 is 43.\nThe travel distance from origin location 9 to destination location 3 is 44.\nThe travel distance from origin location 9 to destination location 4 is 69.\nThe travel distance from origin location 9 to destination location 5 is 76.\nThe travel distance from origin location 9 to destination location 6 is 73.\nThe travel distance from origin location 9 to destination location 7 is 61.\nThe travel distance from origin location 9 to destination location 8 is 35.\nThe travel distance from origin location 9 to destination location 10 is 39.\nThe travel distance from origin location 9 to destination location 11 is 78.\nThe travel distance from origin location 9 to destination location 12 is 102.\nThe travel distance from origin location 9 to destination location 13 is 90.\nThe travel distance from origin location 9 to destination location 14 is 93.\nThe travel distance from origin location 9 to destination location 15 is 46.\nThe travel distance from origin location 9 to destination location 16 is 127.\nThe travel distance from origin location 9 to destination location 17 is 114.\nThe travel distance from origin location 9 to destination location 18 is 50.\nThe travel distance from origin location 9 to destination location 19 is 76.\nThe travel distance from origin location 9 to destination location 20 is 78.\nThe travel distance from origin location 10 to destination location 1 is 94.\nThe travel distance from origin location 10 to destination location 2 is 48.\nThe travel distance from origin location 10 to destination location 3 is 63.\nThe travel distance from origin location 10 to destination location 4 is 97.\nThe travel distance from origin location 10 to destination location 5 is 70.\nThe travel distance from origin location 10 to destination location 6 is 82.\nThe travel distance from origin location 10 to destination location 7 is 80.\nThe travel distance from origin location 10 to destination location 8 is 72.\nThe travel distance from origin location 10 to destination location 9 is 39.\nThe travel distance from origin location 10 to destination location 11 is 64.\nThe travel distance from origin location 10 to destination location 12 is 108.\nThe travel distance from origin location 10 to destination location 13 is 105.\nThe travel distance from origin location 10 to destination location 14 is 92.\nThe travel distance from origin location 10 to destination location 15 is 78.\nThe travel distance from origin location 10 to destination location 16 is 111.\nThe travel distance from origin location 10 to destination location 17 is 111.\nThe travel distance from origin location 10 to destination location 18 is 67.\nThe travel distance from origin location 10 to destination location 19 is 92.\nThe travel distance from origin location 10 to destination location 20 is 85.\nThe travel distance from origin location 11 to destination location 1 is 51.\nThe travel distance from origin location 11 to destination location 2 is 53.\nThe travel distance from origin location 11 to destination location 3 is 48.\nThe travel distance from origin location 11 to destination location 4 is 59.\nThe travel distance from origin location 11 to destination location 5 is 64.\nThe travel distance from origin location 11 to destination location 6 is 90.\nThe travel distance from origin location 11 to destination location 7 is 71.\nThe travel distance from origin location 11 to destination location 8 is 46.\nThe travel distance from origin location 11 to destination location 9 is 78.\nThe travel distance from origin location 11 to destination location 10 is 64.\nThe travel distance from origin location 11 to destination location 12 is 74.\nThe travel distance from origin location 11 to destination location 13 is 67.\nThe travel distance from origin location 11 to destination location 14 is 88.\nThe travel distance from origin location 11 to destination location 15 is 45.\nThe travel distance from origin location 11 to destination location 16 is 106.\nThe travel distance from origin location 11 to destination location 17 is 89.\nThe travel distance from origin location 11 to destination location 18 is 29.\nThe travel distance from origin location 11 to destination location 19 is 67.\nThe travel distance from origin location 11 to destination location 20 is 41.\nThe travel distance from origin location 12 to destination location 1 is 62.\nThe travel distance from origin location 12 to destination location 2 is 96.\nThe travel distance from origin location 12 to destination location 3 is 81.\nThe travel distance from origin location 12 to destination location 4 is 71.\nThe travel distance from origin location 12 to destination location 5 is 60.\nThe travel distance from origin location 12 to destination location 6 is 126.\nThe travel distance from origin location 12 to destination location 7 is 95.\nThe travel distance from origin location 12 to destination location 8 is 72.\nThe travel distance from origin location 12 to destination location 9 is 102.\nThe travel distance from origin location 12 to destination location 10 is 108.\nThe travel distance from origin location 12 to destination location 11 is 74.\nThe travel distance from origin location 12 to destination location 13 is 115.\nThe travel distance from origin location 12 to destination location 14 is 118.\nThe travel distance from origin location 12 to destination location 15 is 87.\nThe travel distance from origin location 12 to destination location 16 is 65.\nThe travel distance from origin location 12 to destination location 17 is 108.\nThe travel distance from origin location 12 to destination location 18 is 59.\nThe travel distance from origin location 12 to destination location 19 is 89.\nThe travel distance from origin location 12 to destination location 20 is 45.\nThe travel distance from origin location 13 to destination location 1 is 92.\nThe travel distance from origin location 13 to destination location 2 is 65.\nThe travel distance from origin location 13 to destination location 3 is 50.\nThe travel distance from origin location 13 to destination location 4 is 83.\nThe travel distance from origin location 13 to destination location 5 is 100.\nThe travel distance from origin location 13 to destination location 6 is 55.\nThe travel distance from origin location 13 to destination location 7 is 75.\nThe travel distance from origin location 13 to destination location 8 is 58.\nThe travel distance from origin location 13 to destination location 9 is 90.\nThe travel distance from origin location 13 to destination location 10 is 105.\nThe travel distance from origin location 13 to destination location 11 is 67.\nThe travel distance from origin location 13 to destination location 12 is 115.\nThe travel distance from origin location 13 to destination location 14 is 119.\nThe travel distance from origin location 13 to destination location 15 is 80.\nThe travel distance from origin location 13 to destination location 16 is 116.\nThe travel distance from origin location 13 to destination location 17 is 114.\nThe travel distance from origin location 13 to destination location 18 is 67.\nThe travel distance from origin location 13 to destination location 19 is 65.\nThe travel distance from origin location 13 to destination location 20 is 92.\nThe travel distance from origin location 14 to destination location 1 is 66.\nThe travel distance from origin location 14 to destination location 2 is 84.\nThe travel distance from origin location 14 to destination location 3 is 79.\nThe travel distance from origin location 14 to destination location 4 is 89.\nThe travel distance from origin location 14 to destination location 5 is 94.\nThe travel distance from origin location 14 to destination location 6 is 86.\nThe travel distance from origin location 14 to destination location 7 is 78.\nThe travel distance from origin location 14 to destination location 8 is 76.\nThe travel distance from origin location 14 to destination location 9 is 93.\nThe travel distance from origin location 14 to destination location 10 is 92.\nThe travel distance from origin location 14 to destination location 11 is 88.\nThe travel distance from origin location 14 to destination location 12 is 118.\nThe travel distance from origin location 14 to destination location 13 is 119.\nThe travel distance from origin location 14 to destination location 15 is 69.\nThe travel distance from origin location 14 to destination location 16 is 115.\nThe travel distance from origin location 14 to destination location 17 is 137.\nThe travel distance from origin location 14 to destination location 18 is 59.\nThe travel distance from origin location 14 to destination location 19 is 97.\nThe travel distance from origin location 14 to destination location 20 is 87.\nThe travel distance from origin location 15 to destination location 1 is 25.\nThe travel distance from origin location 15 to destination location 2 is 48.\nThe travel distance from origin location 15 to destination location 3 is 58.\nThe travel distance from origin location 15 to destination location 4 is 70.\nThe travel distance from origin location 15 to destination location 5 is 66.\nThe travel distance from origin location 15 to destination location 6 is 82.\nThe travel distance from origin location 15 to destination location 7 is 27.\nThe travel distance from origin location 15 to destination location 8 is 49.\nThe travel distance from origin location 15 to destination location 9 is 46.\nThe travel distance from origin location 15 to destination location 10 is 78.\nThe travel distance from origin location 15 to destination location 11 is 45.\nThe travel distance from origin location 15 to destination location 12 is 87.\nThe travel distance from origin location 15 to destination location 13 is 80.\nThe travel distance from origin location 15 to destination location 14 is 69.\nThe travel distance from origin location 15 to destination location 16 is 114.\nThe travel distance from origin location 15 to destination location 17 is 103.\nThe travel distance from origin location 15 to destination location 18 is 47.\nThe travel distance from origin location 15 to destination location 19 is 63.\nThe travel distance from origin location 15 to destination location 20 is 69.\nThe travel distance from origin location 16 to destination location 1 is 117.\nThe travel distance from origin location 16 to destination location 2 is 116.\nThe travel distance from origin location 16 to destination location 3 is 101.\nThe travel distance from origin location 16 to destination location 4 is 102.\nThe travel distance from origin location 16 to destination location 5 is 115.\nThe travel distance from origin location 16 to destination location 6 is 146.\nThe travel distance from origin location 16 to destination location 7 is 116.\nThe travel distance from origin location 16 to destination location 8 is 92.\nThe travel distance from origin location 16 to destination location 9 is 127.\nThe travel distance from origin location 16 to destination location 10 is 111.\nThe travel distance from origin location 16 to destination location 11 is 106.\nThe travel distance from origin location 16 to destination location 12 is 65.\nThe travel distance from origin location 16 to destination location 13 is 116.\nThe travel distance from origin location 16 to destination location 14 is 115.\nThe travel distance from origin location 16 to destination location 15 is 114.\nThe travel distance from origin location 16 to destination location 17 is 43.\nThe travel distance from origin location 16 to destination location 18 is 80.\nThe travel distance from origin location 16 to destination location 19 is 99.\nThe travel distance from origin location 16 to destination location 20 is 105.\nThe travel distance from origin location 17 to destination location 1 is 128.\nThe travel distance from origin location 17 to destination location 2 is 107.\nThe travel distance from origin location 17 to destination location 3 is 102.\nThe travel distance from origin location 17 to destination location 4 is 87.\nThe travel distance from origin location 17 to destination location 5 is 107.\nThe travel distance from origin location 17 to destination location 6 is 132.\nThe travel distance from origin location 17 to destination location 7 is 120.\nThe travel distance from origin location 17 to destination location 8 is 95.\nThe travel distance from origin location 17 to destination location 9 is 114.\nThe travel distance from origin location 17 to destination location 10 is 111.\nThe travel distance from origin location 17 to destination location 11 is 89.\nThe travel distance from origin location 17 to destination location 12 is 108.\nThe travel distance from origin location 17 to destination location 13 is 114.\nThe travel distance from origin location 17 to destination location 14 is 137.\nThe travel distance from origin location 17 to destination location 15 is 103.\nThe travel distance from origin location 17 to destination location 16 is 43.\nThe travel distance from origin location 17 to destination location 18 is 78.\nThe travel distance from origin location 17 to destination location 19 is 69.\nThe travel distance from origin location 17 to destination location 20 is 103.\nThe travel distance from origin location 18 to destination location 1 is 58.\nThe travel distance from origin location 18 to destination location 2 is 41.\nThe travel distance from origin location 18 to destination location 3 is 26.\nThe travel distance from origin location 18 to destination location 4 is 30.\nThe travel distance from origin location 18 to destination location 5 is 35.\nThe travel distance from origin location 18 to destination location 6 is 71.\nThe travel distance from origin location 18 to destination location 7 is 42.\nThe travel distance from origin location 18 to destination location 8 is 17.\nThe travel distance from origin location 18 to destination location 9 is 50.\nThe travel distance from origin location 18 to destination location 10 is 67.\nThe travel distance from origin location 18 to destination location 11 is 29.\nThe travel distance from origin location 18 to destination location 12 is 59.\nThe travel distance from origin location 18 to destination location 13 is 67.\nThe travel distance from origin location 18 to destination location 14 is 59.\nThe travel distance from origin location 18 to destination location 15 is 47.\nThe travel distance from origin location 18 to destination location 16 is 80.\nThe travel distance from origin location 18 to destination location 17 is 78.\nThe travel distance from origin location 18 to destination location 19 is 38.\nThe travel distance from origin location 18 to destination location 20 is 28.\nThe travel distance from origin location 19 to destination location 1 is 60.\nThe travel distance from origin location 19 to destination location 2 is 65.\nThe travel distance from origin location 19 to destination location 3 is 50.\nThe travel distance from origin location 19 to destination location 4 is 18.\nThe travel distance from origin location 19 to destination location 5 is 73.\nThe travel distance from origin location 19 to destination location 6 is 95.\nThe travel distance from origin location 19 to destination location 7 is 74.\nThe travel distance from origin location 19 to destination location 8 is 41.\nThe travel distance from origin location 19 to destination location 9 is 76.\nThe travel distance from origin location 19 to destination location 10 is 92.\nThe travel distance from origin location 19 to destination location 11 is 67.\nThe travel distance from origin location 19 to destination location 12 is 89.\nThe travel distance from origin location 19 to destination location 13 is 65.\nThe travel distance from origin location 19 to destination location 14 is 97.\nThe travel distance from origin location 19 to destination location 15 is 63.\nThe travel distance from origin location 19 to destination location 16 is 99.\nThe travel distance from origin location 19 to destination location 17 is 69.\nThe travel distance from origin location 19 to destination location 18 is 38.\nThe travel distance from origin location 19 to destination location 20 is 66.\nThe travel distance from origin location 20 to destination location 1 is 78.\nThe travel distance from origin location 20 to destination location 2 is 69.\nThe travel distance from origin location 20 to destination location 3 is 54.\nThe travel distance from origin location 20 to destination location 4 is 58.\nThe travel distance from origin location 20 to destination location 5 is 37.\nThe travel distance from origin location 20 to destination location 6 is 99.\nThe travel distance from origin location 20 to destination location 7 is 70.\nThe travel distance from origin location 20 to destination location 8 is 45.\nThe travel distance from origin location 20 to destination location 9 is 78.\nThe travel distance from origin location 20 to destination location 10 is 85.\nThe travel distance from origin location 20 to destination location 11 is 41.\nThe travel distance from origin location 20 to destination location 12 is 45.\nThe travel distance from origin location 20 to destination location 13 is 92.\nThe travel distance from origin location 20 to destination location 14 is 87.\nThe travel distance from origin location 20 to destination location 15 is 69.\nThe travel distance from origin location 20 to destination location 16 is 105.\nThe travel distance from origin location 20 to destination location 17 is 103.\nThe travel distance from origin location 20 to destination location 18 is 28.\nThe travel distance from origin location 20 to destination location 19 is 66.\nThese travel distances will be summed across all locations to form the total distance the chain seeks to minimize.\n\nOh, and when you send the solution back, just stick to this simple JSON shape so it's easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of store locations you decide to keep open, and \"assignments\" as, for each customer zone (in the same order as the input), which opened store that zone is assigned to. Super casual — it's just a form to fill, not the real answer yet.\n\nPlease use the exact identifiers from the instance input when you fill those placeholders — don't invent new labels or rename them. \n\n\"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 60, 55, 78, 77, 100, 52, 64, 71, 94, 51, 62, 92, 66, 25, 117, 128, 58, 60, 78 ], [ 60, 0, 15, 71, 70, 52, 64, 24, 43, 48, 53, 96, 65, 84, 48, 116, 107, 41, 65, 69 ], [ 55, 15, 0, 56, 55, 45, 49, 9, 44, 63, 48, 81, 50, 79, 58, 101, 102, 26, 50, 54 ], [ 78, 71, 56, 0, 65, 101, 66, 47, 69, 97, 59, 71, 83, 89, 70, 102, 87, 30, 18, 58 ], [ 77, 70, 55, 65, 0, 100, 77, 46, 76, 70, 64, 60, 100, 94, 66, 115, 107, 35, 73, 37 ], [ 100, 52, 45, 101, 100, 0, 94, 54, 73, 82, 90, 126, 55, 86, 82, 146, 132, 71, 95, 99 ], [ 52, 64, 49, 66, 77, 94, 0, 40, 61, 80, 71, 95, 75, 78, 27, 116, 120, 42, 74, 70 ], [ 64, 24, 9, 47, 46, 54, 40, 0, 35, 72, 46, 72, 58, 76, 49, 92, 95, 17, 41, 45 ], [ 71, 43, 44, 69, 76, 73, 61, 35, 0, 39, 78, 102, 90, 93, 46, 127, 114, 50, 76, 78 ], [ 94, 48, 63, 97, 70, 82, 80, 72, 39, 0, 64, 108, 105, 92, 78, 111, 111, 67, 92, 85 ], [ 51, 53, 48, 59, 64, 90, 71, 46, 78, 64, 0, 74, 67, 88, 45, 106, 89, 29, 67, 41 ], [ 62, 96, 81, 71, 60, 126, 95, 72, 102, 108, 74, 0, 115, 118, 87, 65, 108, 59, 89, 45 ], [ 92, 65, 50, 83, 100, 55, 75, 58, 90, 105, 67, 115, 0, 119, 80, 116, 114, 67, 65, 92 ], [ 66, 84, 79, 89, 94, 86, 78, 76, 93, 92, 88, 118, 119, 0, 69, 115, 137, 59, 97, 87 ], [ 25, 48, 58, 70, 66, 82, 27, 49, 46, 78, 45, 87, 80, 69, 0, 114, 103, 47, 63, 69 ], [ 117, 116, 101, 102, 115, 146, 116, 92, 127, 111, 106, 65, 116, 115, 114, 0, 43, 80, 99, 105 ], [ 128, 107, 102, 87, 107, 132, 120, 95, 114, 111, 89, 108, 114, 137, 103, 43, 0, 78, 69, 103 ], [ 58, 41, 26, 30, 35, 71, 42, 17, 50, 67, 29, 59, 67, 59, 47, 80, 78, 0, 38, 28 ], [ 60, 65, 50, 18, 73, 95, 74, 41, 76, 92, 67, 89, 65, 97, 63, 99, 69, 38, 0, 66 ], [ 78, 69, 54, 58, 37, 99, 70, 45, 78, 85, 41, 45, 92, 87, 69, 105, 103, 28, 66, 0 ] ], "p": 1, "objective": 922.0 }, "solution": { "facilities": [ 17 ], "assignments": [ 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17 ] }, "obj": 922.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 1, "sites": [ { "id": 1, "distances": { "1": 0, "2": 60, "3": 55, "4": 78, "5": 77, "6": 100, "7": 52, "8": 64, "9": 71, "10": 94, "11": 51, "12": 62, "13": 92, "14": 66, "15": 25, "16": 117, "17": 128, "18": 58, "19": 60, "20": 78 } }, { "id": 2, "distances": { "1": 60, "2": 0, "3": 15, "4": 71, "5": 70, "6": 52, "7": 64, "8": 24, "9": 43, "10": 48, "11": 53, "12": 96, "13": 65, "14": 84, "15": 48, "16": 116, "17": 107, "18": 41, "19": 65, "20": 69 } }, { "id": 3, "distances": { "1": 55, "2": 15, "3": 0, "4": 56, "5": 55, "6": 45, "7": 49, "8": 9, "9": 44, "10": 63, "11": 48, "12": 81, "13": 50, "14": 79, "15": 58, "16": 101, "17": 102, "18": 26, "19": 50, "20": 54 } }, { "id": 4, "distances": { "1": 78, "2": 71, "3": 56, "4": 0, "5": 65, "6": 101, "7": 66, "8": 47, "9": 69, "10": 97, "11": 59, "12": 71, "13": 83, "14": 89, "15": 70, "16": 102, "17": 87, "18": 30, "19": 18, "20": 58 } }, { "id": 5, "distances": { "1": 77, "2": 70, "3": 55, "4": 65, "5": 0, "6": 100, "7": 77, "8": 46, "9": 76, "10": 70, "11": 64, "12": 60, "13": 100, "14": 94, "15": 66, "16": 115, "17": 107, "18": 35, "19": 73, "20": 37 } }, { "id": 6, "distances": { "1": 100, "2": 52, "3": 45, "4": 101, "5": 100, "6": 0, "7": 94, "8": 54, "9": 73, "10": 82, "11": 90, "12": 126, "13": 55, "14": 86, "15": 82, "16": 146, "17": 132, "18": 71, "19": 95, "20": 99 } }, { "id": 7, "distances": { "1": 52, "2": 64, "3": 49, "4": 66, "5": 77, "6": 94, "7": 0, "8": 40, "9": 61, "10": 80, "11": 71, "12": 95, "13": 75, "14": 78, "15": 27, "16": 116, "17": 120, "18": 42, "19": 74, "20": 70 } }, { "id": 8, "distances": { "1": 64, "2": 24, "3": 9, "4": 47, "5": 46, "6": 54, "7": 40, "8": 0, "9": 35, "10": 72, "11": 46, "12": 72, "13": 58, "14": 76, "15": 49, "16": 92, "17": 95, "18": 17, "19": 41, "20": 45 } }, { "id": 9, "distances": { "1": 71, "2": 43, "3": 44, "4": 69, "5": 76, "6": 73, "7": 61, "8": 35, "9": 0, "10": 39, "11": 78, "12": 102, "13": 90, "14": 93, "15": 46, "16": 127, "17": 114, "18": 50, "19": 76, "20": 78 } }, { "id": 10, "distances": { "1": 94, "2": 48, "3": 63, "4": 97, "5": 70, "6": 82, "7": 80, "8": 72, "9": 39, "10": 0, "11": 64, "12": 108, "13": 105, "14": 92, "15": 78, "16": 111, "17": 111, "18": 67, "19": 92, "20": 85 } }, { "id": 11, "distances": { "1": 51, "2": 53, "3": 48, "4": 59, "5": 64, "6": 90, "7": 71, "8": 46, "9": 78, "10": 64, "11": 0, "12": 74, "13": 67, "14": 88, "15": 45, "16": 106, "17": 89, "18": 29, "19": 67, "20": 41 } }, { "id": 12, "distances": { "1": 62, "2": 96, "3": 81, "4": 71, "5": 60, "6": 126, "7": 95, "8": 72, "9": 102, "10": 108, "11": 74, "12": 0, "13": 115, "14": 118, "15": 87, "16": 65, "17": 108, "18": 59, "19": 89, "20": 45 } }, { "id": 13, "distances": { "1": 92, "2": 65, "3": 50, "4": 83, "5": 100, "6": 55, "7": 75, "8": 58, "9": 90, "10": 105, "11": 67, "12": 115, "13": 0, "14": 119, "15": 80, "16": 116, "17": 114, "18": 67, "19": 65, "20": 92 } }, { "id": 14, "distances": { "1": 66, "2": 84, "3": 79, "4": 89, "5": 94, "6": 86, "7": 78, "8": 76, "9": 93, "10": 92, "11": 88, "12": 118, "13": 119, "14": 0, "15": 69, "16": 115, "17": 137, "18": 59, "19": 97, "20": 87 } }, { "id": 15, "distances": { "1": 25, "2": 48, "3": 58, "4": 70, "5": 66, "6": 82, "7": 27, "8": 49, "9": 46, "10": 78, "11": 45, "12": 87, "13": 80, "14": 69, "15": 0, "16": 114, "17": 103, "18": 47, "19": 63, "20": 69 } }, { "id": 16, "distances": { "1": 117, "2": 116, "3": 101, "4": 102, "5": 115, "6": 146, "7": 116, "8": 92, "9": 127, "10": 111, "11": 106, "12": 65, "13": 116, "14": 115, "15": 114, "16": 0, "17": 43, "18": 80, "19": 99, "20": 105 } }, { "id": 17, "distances": { "1": 128, "2": 107, "3": 102, "4": 87, "5": 107, "6": 132, "7": 120, "8": 95, "9": 114, "10": 111, "11": 89, "12": 108, "13": 114, "14": 137, "15": 103, "16": 43, "17": 0, "18": 78, "19": 69, "20": 103 } }, { "id": 18, "distances": { "1": 58, "2": 41, "3": 26, "4": 30, "5": 35, "6": 71, "7": 42, "8": 17, "9": 50, "10": 67, "11": 29, "12": 59, "13": 67, "14": 59, "15": 47, "16": 80, "17": 78, "18": 0, "19": 38, "20": 28 } }, { "id": 19, "distances": { "1": 60, "2": 65, "3": 50, "4": 18, "5": 73, "6": 95, "7": 74, "8": 41, "9": 76, "10": 92, "11": 67, "12": 89, "13": 65, "14": 97, "15": 63, "16": 99, "17": 69, "18": 38, "19": 0, "20": 66 } }, { "id": 20, "distances": { "1": 78, "2": 69, "3": 54, "4": 58, "5": 37, "6": 99, "7": 70, "8": 45, "9": 78, "10": 85, "11": 41, "12": 45, "13": 92, "14": 87, "15": 69, "16": 105, "17": 103, "18": 28, "19": 66, "20": 0 } } ], "objective": 922.0 }, "solution_variant": { "selected": [ 18 ], "assignments": [ 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18 ] }, "context_index": 21, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I was handling the school bus plan for a neighborhood: pick a fixed number of pickup spots from a bunch of possible corners, then tell every home which stop they should use. The trick is to make those choices so kids travel as little as possible overall — add up the distance from each house to its assigned stop, and the plan with the smallest total distance wins. Nobody can be skipped or sent to two different stops: each address gets exactly one assigned pickup. The exact list of addresses, candidate stops, and distances are shown below.\n\n# total_candidate_locations=18\n# pickup_points_to_open=6\n# location_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18\nsource_location_id,destination_location_id,walking_distance\n1,2,49\n1,3,27\n1,4,36\n1,5,28\n1,6,42\n1,7,39\n1,8,34\n1,9,29\n1,10,51\n1,11,30\n1,12,31\n1,13,41\n1,14,26\n1,15,37\n1,16,47\n1,17,20\n1,18,37\n2,1,49\n2,3,46\n2,4,42\n2,5,53\n2,6,49\n2,7,54\n2,8,45\n2,9,50\n2,10,58\n2,11,53\n2,12,37\n2,13,54\n2,14,43\n2,15,50\n2,16,64\n2,17,40\n2,18,50\n3,1,27\n3,2,46\n3,4,23\n3,5,29\n3,6,27\n3,7,36\n3,8,21\n3,9,18\n3,10,30\n3,11,25\n3,12,18\n3,13,28\n3,14,16\n3,15,30\n3,16,34\n3,17,27\n3,18,16\n4,1,36\n4,2,42\n4,3,23\n4,5,42\n4,6,36\n4,7,24\n4,8,37\n4,9,32\n4,10,43\n4,11,41\n4,12,7\n4,13,44\n4,14,23\n4,15,40\n4,16,41\n4,17,16\n4,18,26\n5,1,28\n5,2,53\n5,3,29\n5,4,42\n5,6,44\n5,7,39\n5,8,22\n5,9,32\n5,10,53\n5,11,37\n5,12,42\n5,13,37\n5,14,26\n5,15,47\n5,16,43\n5,17,38\n5,18,40\n6,1,42\n6,2,49\n6,3,27\n6,4,36\n6,5,44\n6,7,42\n6,8,36\n6,9,39\n6,10,42\n6,11,39\n6,12,31\n6,13,43\n6,14,32\n6,15,45\n6,16,49\n6,17,34\n6,18,43\n7,1,39\n7,2,54\n7,3,36\n7,4,24\n7,5,39\n7,6,42\n7,8,17\n7,9,34\n7,10,60\n7,11,49\n7,12,31\n7,13,46\n7,14,31\n7,15,54\n7,16,52\n7,17,40\n7,18,41\n8,1,34\n8,2,45\n8,3,21\n8,4,37\n8,5,22\n8,6,36\n8,7,17\n8,9,33\n8,10,45\n8,11,32\n8,12,32\n8,13,29\n8,14,18\n8,15,39\n8,16,35\n8,17,34\n8,18,32\n9,1,29\n9,2,50\n9,3,18\n9,4,32\n9,5,32\n9,6,39\n9,7,34\n9,8,33\n9,10,42\n9,11,33\n9,12,25\n9,13,40\n9,14,17\n9,15,28\n9,16,42\n9,17,36\n9,18,31\n10,1,51\n10,2,58\n10,3,30\n10,4,43\n10,5,53\n10,6,42\n10,7,60\n10,8,45\n10,9,42\n10,11,42\n10,12,42\n10,13,52\n10,14,37\n10,15,54\n10,16,58\n10,17,37\n10,18,40\n11,1,30\n11,2,53\n11,3,25\n11,4,41\n11,5,37\n11,6,39\n11,7,49\n11,8,32\n11,9,33\n11,10,42\n11,12,36\n11,13,39\n11,14,28\n11,15,43\n11,16,38\n11,17,35\n11,18,35\n12,1,31\n12,2,37\n12,3,18\n12,4,7\n12,5,42\n12,6,31\n12,7,31\n12,8,32\n12,9,25\n12,10,42\n12,11,36\n12,13,46\n12,14,26\n12,15,41\n12,16,48\n12,17,11\n12,18,26\n13,1,41\n13,2,54\n13,3,28\n13,4,44\n13,5,37\n13,6,43\n13,7,46\n13,8,29\n13,9,40\n13,10,52\n13,11,39\n13,12,46\n13,14,25\n13,15,46\n13,16,40\n13,17,49\n13,18,39\n14,1,26\n14,2,43\n14,3,16\n14,4,23\n14,5,26\n14,6,32\n14,7,31\n14,8,18\n14,9,17\n14,10,37\n14,11,28\n14,12,26\n14,13,25\n14,15,32\n14,16,31\n14,17,25\n14,18,14\n15,1,37\n15,2,50\n15,3,30\n15,4,40\n15,5,47\n15,6,45\n15,7,54\n15,8,39\n15,9,28\n15,10,54\n15,11,43\n15,12,41\n15,13,46\n15,14,32\n15,16,51\n15,17,43\n15,18,42\n16,1,47\n16,2,64\n16,3,34\n16,4,41\n16,5,43\n16,6,49\n16,7,52\n16,8,35\n16,9,42\n16,10,58\n16,11,38\n16,12,48\n16,13,40\n16,14,31\n16,15,51\n16,17,45\n16,18,43\n17,1,20\n17,2,40\n17,3,27\n17,4,16\n17,5,38\n17,6,34\n17,7,40\n17,8,34\n17,9,36\n17,10,37\n17,11,35\n17,12,11\n17,13,49\n17,14,25\n17,15,43\n17,16,45\n17,18,35\n18,1,37\n18,2,50\n18,3,16\n18,4,26\n18,5,40\n18,6,43\n18,7,41\n18,8,32\n18,9,31\n18,10,40\n18,11,35\n18,12,26\n18,13,39\n18,14,14\n18,15,42\n18,16,43\n18,17,35\n\nIf you want to send the plan back in a machine-friendly way, a little JSON sketch like this is handy:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of corners we actually open as pickup stops. \"assignments\" is one entry per home (in the same order as the instance), showing which opened stop that home should use. Super informal: think of \"selected\" as the chosen stops and \"assignments\" as the form you'd fill out to say which stop each house goes to.\n\nThis JSON is just a sketch of the shape I expect, not the actual answer.\n\nPlease use the exact identifiers from the instance input — no renaming and no new labels. \nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 49, 27, 36, 28, 42, 39, 34, 29, 51, 30, 31, 41, 26, 37, 47, 20, 37 ], [ 49, 0, 46, 42, 53, 49, 54, 45, 50, 58, 53, 37, 54, 43, 50, 64, 40, 50 ], [ 27, 46, 0, 23, 29, 27, 36, 21, 18, 30, 25, 18, 28, 16, 30, 34, 27, 16 ], [ 36, 42, 23, 0, 42, 36, 24, 37, 32, 43, 41, 7, 44, 23, 40, 41, 16, 26 ], [ 28, 53, 29, 42, 0, 44, 39, 22, 32, 53, 37, 42, 37, 26, 47, 43, 38, 40 ], [ 42, 49, 27, 36, 44, 0, 42, 36, 39, 42, 39, 31, 43, 32, 45, 49, 34, 43 ], [ 39, 54, 36, 24, 39, 42, 0, 17, 34, 60, 49, 31, 46, 31, 54, 52, 40, 41 ], [ 34, 45, 21, 37, 22, 36, 17, 0, 33, 45, 32, 32, 29, 18, 39, 35, 34, 32 ], [ 29, 50, 18, 32, 32, 39, 34, 33, 0, 42, 33, 25, 40, 17, 28, 42, 36, 31 ], [ 51, 58, 30, 43, 53, 42, 60, 45, 42, 0, 42, 42, 52, 37, 54, 58, 37, 40 ], [ 30, 53, 25, 41, 37, 39, 49, 32, 33, 42, 0, 36, 39, 28, 43, 38, 35, 35 ], [ 31, 37, 18, 7, 42, 31, 31, 32, 25, 42, 36, 0, 46, 26, 41, 48, 11, 26 ], [ 41, 54, 28, 44, 37, 43, 46, 29, 40, 52, 39, 46, 0, 25, 46, 40, 49, 39 ], [ 26, 43, 16, 23, 26, 32, 31, 18, 17, 37, 28, 26, 25, 0, 32, 31, 25, 14 ], [ 37, 50, 30, 40, 47, 45, 54, 39, 28, 54, 43, 41, 46, 32, 0, 51, 43, 42 ], [ 47, 64, 34, 41, 43, 49, 52, 35, 42, 58, 38, 48, 40, 31, 51, 0, 45, 43 ], [ 20, 40, 27, 16, 38, 34, 40, 34, 36, 37, 35, 11, 49, 25, 43, 45, 0, 35 ], [ 37, 50, 16, 26, 40, 43, 41, 32, 31, 40, 35, 26, 39, 14, 42, 43, 35, 0 ] ], "p": 6, "objective": 244.0 }, "solution": { "facilities": [ 1, 2, 7, 9, 11, 15 ], "assignments": [ 2, 1, 2, 11, 7, 2, 7, 7, 2, 9, 2, 11, 2, 2, 2, 15, 11, 2 ] }, "obj": 244.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 6, "sites": [ { "id": 1, "distances": { "1": 0, "2": 49, "3": 27, "4": 36, "5": 28, "6": 42, "7": 39, "8": 34, "9": 29, "10": 51, "11": 30, "12": 31, "13": 41, "14": 26, "15": 37, "16": 47, "17": 20, "18": 37 } }, { "id": 2, "distances": { "1": 49, "2": 0, "3": 46, "4": 42, "5": 53, "6": 49, "7": 54, "8": 45, "9": 50, "10": 58, "11": 53, "12": 37, "13": 54, "14": 43, "15": 50, "16": 64, "17": 40, "18": 50 } }, { "id": 3, "distances": { "1": 27, "2": 46, "3": 0, "4": 23, "5": 29, "6": 27, "7": 36, "8": 21, "9": 18, "10": 30, "11": 25, "12": 18, "13": 28, "14": 16, "15": 30, "16": 34, "17": 27, "18": 16 } }, { "id": 4, "distances": { "1": 36, "2": 42, "3": 23, "4": 0, "5": 42, "6": 36, "7": 24, "8": 37, "9": 32, "10": 43, "11": 41, "12": 7, "13": 44, "14": 23, "15": 40, "16": 41, "17": 16, "18": 26 } }, { "id": 5, "distances": { "1": 28, "2": 53, "3": 29, "4": 42, "5": 0, "6": 44, "7": 39, "8": 22, "9": 32, "10": 53, "11": 37, "12": 42, "13": 37, "14": 26, "15": 47, "16": 43, "17": 38, "18": 40 } }, { "id": 6, "distances": { "1": 42, "2": 49, "3": 27, "4": 36, "5": 44, "6": 0, "7": 42, "8": 36, "9": 39, "10": 42, "11": 39, "12": 31, "13": 43, "14": 32, "15": 45, "16": 49, "17": 34, "18": 43 } }, { "id": 7, "distances": { "1": 39, "2": 54, "3": 36, "4": 24, "5": 39, "6": 42, "7": 0, "8": 17, "9": 34, "10": 60, "11": 49, "12": 31, "13": 46, "14": 31, "15": 54, "16": 52, "17": 40, "18": 41 } }, { "id": 8, "distances": { "1": 34, "2": 45, "3": 21, "4": 37, "5": 22, "6": 36, "7": 17, "8": 0, "9": 33, "10": 45, "11": 32, "12": 32, "13": 29, "14": 18, "15": 39, "16": 35, "17": 34, "18": 32 } }, { "id": 9, "distances": { "1": 29, "2": 50, "3": 18, "4": 32, "5": 32, "6": 39, "7": 34, "8": 33, "9": 0, "10": 42, "11": 33, "12": 25, "13": 40, "14": 17, "15": 28, "16": 42, "17": 36, "18": 31 } }, { "id": 10, "distances": { "1": 51, "2": 58, "3": 30, "4": 43, "5": 53, "6": 42, "7": 60, "8": 45, "9": 42, "10": 0, "11": 42, "12": 42, "13": 52, "14": 37, "15": 54, "16": 58, "17": 37, "18": 40 } }, { "id": 11, "distances": { "1": 30, "2": 53, "3": 25, "4": 41, "5": 37, "6": 39, "7": 49, "8": 32, "9": 33, "10": 42, "11": 0, "12": 36, "13": 39, "14": 28, "15": 43, "16": 38, "17": 35, "18": 35 } }, { "id": 12, "distances": { "1": 31, "2": 37, "3": 18, "4": 7, "5": 42, "6": 31, "7": 31, "8": 32, "9": 25, "10": 42, "11": 36, "12": 0, "13": 46, "14": 26, "15": 41, "16": 48, "17": 11, "18": 26 } }, { "id": 13, "distances": { "1": 41, "2": 54, "3": 28, "4": 44, "5": 37, "6": 43, "7": 46, "8": 29, "9": 40, "10": 52, "11": 39, "12": 46, "13": 0, "14": 25, "15": 46, "16": 40, "17": 49, "18": 39 } }, { "id": 14, "distances": { "1": 26, "2": 43, "3": 16, "4": 23, "5": 26, "6": 32, "7": 31, "8": 18, "9": 17, "10": 37, "11": 28, "12": 26, "13": 25, "14": 0, "15": 32, "16": 31, "17": 25, "18": 14 } }, { "id": 15, "distances": { "1": 37, "2": 50, "3": 30, "4": 40, "5": 47, "6": 45, "7": 54, "8": 39, "9": 28, "10": 54, "11": 43, "12": 41, "13": 46, "14": 32, "15": 0, "16": 51, "17": 43, "18": 42 } }, { "id": 16, "distances": { "1": 47, "2": 64, "3": 34, "4": 41, "5": 43, "6": 49, "7": 52, "8": 35, "9": 42, "10": 58, "11": 38, "12": 48, "13": 40, "14": 31, "15": 51, "16": 0, "17": 45, "18": 43 } }, { "id": 17, "distances": { "1": 20, "2": 40, "3": 27, "4": 16, "5": 38, "6": 34, "7": 40, "8": 34, "9": 36, "10": 37, "11": 35, "12": 11, "13": 49, "14": 25, "15": 43, "16": 45, "17": 0, "18": 35 } }, { "id": 18, "distances": { "1": 37, "2": 50, "3": 16, "4": 26, "5": 40, "6": 43, "7": 41, "8": 32, "9": 31, "10": 40, "11": 35, "12": 26, "13": 39, "14": 14, "15": 42, "16": 43, "17": 35, "18": 0 } } ], "objective": 244.0 }, "solution_variant": { "selected": [ 2, 3, 8, 10, 12, 16 ], "assignments": [ 3, 2, 3, 12, 8, 3, 8, 8, 3, 10, 3, 12, 3, 3, 3, 16, 12, 3 ] }, "context_index": 22, "input_format": "csv", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "There’s a small puzzle in the library budget: pick a set number of branches to run and then attach every neighborhood to one of those branches. Every neighborhood has to belong to exactly one branch, and the winning setup is the one that keeps the total travel distance for everyone as low as possible. Practically, you measure that by summing the distance from each neighborhood to its assigned branch — smaller totals mean a better fit. The concrete locations and distances are laid out below.\n\nThere are 17 neighborhoods listed; you must open exactly 2 branches, chosen from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.\nFrom 0 to 1, the travel distance is 68.\nFrom 0 to 2, the travel distance is 193.\nFrom 0 to 3, the travel distance is 140.\nFrom 0 to 4, the travel distance is 143.\nFrom 0 to 5, the travel distance is 170.\nFrom 0 to 6, the travel distance is 73.\nFrom 0 to 7, the travel distance is 205.\nFrom 0 to 8, the travel distance is 134.\nFrom 0 to 9, the travel distance is 197.\nFrom 0 to 10, the travel distance is 119.\nFrom 0 to 11, the travel distance is 132.\nFrom 0 to 12, the travel distance is 232.\nFrom 0 to 13, the travel distance is 190.\nFrom 0 to 14, the travel distance is 182.\nFrom 0 to 15, the travel distance is 86.\nFrom 0 to 16, the travel distance is 182.\nFrom 1 to 0, the travel distance is 68.\nFrom 1 to 2, the travel distance is 184.\nFrom 1 to 3, the travel distance is 131.\nFrom 1 to 4, the travel distance is 134.\nFrom 1 to 5, the travel distance is 128.\nFrom 1 to 6, the travel distance is 5.\nFrom 1 to 7, the travel distance is 181.\nFrom 1 to 8, the travel distance is 110.\nFrom 1 to 9, the travel distance is 173.\nFrom 1 to 10, the travel distance is 149.\nFrom 1 to 11, the travel distance is 157.\nFrom 1 to 12, the travel distance is 205.\nFrom 1 to 13, the travel distance is 122.\nFrom 1 to 14, the travel distance is 169.\nFrom 1 to 15, the travel distance is 62.\nFrom 1 to 16, the travel distance is 114.\nFrom 2 to 0, the travel distance is 193.\nFrom 2 to 1, the travel distance is 184.\nFrom 2 to 3, the travel distance is 53.\nFrom 2 to 4, the travel distance is 50.\nFrom 2 to 5, the travel distance is 141.\nFrom 2 to 6, the travel distance is 189.\nFrom 2 to 7, the travel distance is 179.\nFrom 2 to 8, the travel distance is 194.\nFrom 2 to 9, the travel distance is 257.\nFrom 2 to 10, the travel distance is 178.\nFrom 2 to 11, the travel distance is 115.\nFrom 2 to 12, the travel distance is 156.\nFrom 2 to 13, the travel distance is 240.\nFrom 2 to 14, the travel distance is 165.\nFrom 2 to 15, the travel distance is 146.\nFrom 2 to 16, the travel distance is 98.\nFrom 3 to 0, the travel distance is 140.\nFrom 3 to 1, the travel distance is 131.\nFrom 3 to 2, the travel distance is 53.\nFrom 3 to 4, the travel distance is 3.\nFrom 3 to 5, the travel distance is 88.\nFrom 3 to 6, the travel distance is 136.\nFrom 3 to 7, the travel distance is 196.\nFrom 3 to 8, the travel distance is 141.\nFrom 3 to 9, the travel distance is 204.\nFrom 3 to 10, the travel distance is 125.\nFrom 3 to 11, the travel distance is 62.\nFrom 3 to 12, the travel distance is 162.\nFrom 3 to 13, the travel distance is 201.\nFrom 3 to 14, the travel distance is 112.\nFrom 3 to 15, the travel distance is 93.\nFrom 3 to 16, the travel distance is 108.\nFrom 4 to 0, the travel distance is 143.\nFrom 4 to 1, the travel distance is 134.\nFrom 4 to 2, the travel distance is 50.\nFrom 4 to 3, the travel distance is 3.\nFrom 4 to 5, the travel distance is 91.\nFrom 4 to 6, the travel distance is 139.\nFrom 4 to 7, the travel distance is 199.\nFrom 4 to 8, the travel distance is 144.\nFrom 4 to 9, the travel distance is 207.\nFrom 4 to 10, the travel distance is 128.\nFrom 4 to 11, the travel distance is 65.\nFrom 4 to 12, the travel distance is 165.\nFrom 4 to 13, the travel distance is 204.\nFrom 4 to 14, the travel distance is 115.\nFrom 4 to 15, the travel distance is 96.\nFrom 4 to 16, the travel distance is 111.\nFrom 5 to 0, the travel distance is 170.\nFrom 5 to 1, the travel distance is 128.\nFrom 5 to 2, the travel distance is 141.\nFrom 5 to 3, the travel distance is 88.\nFrom 5 to 4, the travel distance is 91.\nFrom 5 to 6, the travel distance is 123.\nFrom 5 to 7, the travel distance is 162.\nFrom 5 to 8, the travel distance is 132.\nFrom 5 to 9, the travel distance is 153.\nFrom 5 to 10, the travel distance is 76.\nFrom 5 to 11, the travel distance is 40.\nFrom 5 to 12, the travel distance is 158.\nFrom 5 to 13, the travel distance is 118.\nFrom 5 to 14, the travel distance is 41.\nFrom 5 to 15, the travel distance is 84.\nFrom 5 to 16, the travel distance is 124.\nFrom 6 to 0, the travel distance is 73.\nFrom 6 to 1, the travel distance is 5.\nFrom 6 to 2, the travel distance is 189.\nFrom 6 to 3, the travel distance is 136.\nFrom 6 to 4, the travel distance is 139.\nFrom 6 to 5, the travel distance is 123.\nFrom 6 to 7, the travel distance is 186.\nFrom 6 to 8, the travel distance is 115.\nFrom 6 to 9, the travel distance is 168.\nFrom 6 to 10, the travel distance is 154.\nFrom 6 to 11, the travel distance is 162.\nFrom 6 to 12, the travel distance is 210.\nFrom 6 to 13, the travel distance is 127.\nFrom 6 to 14, the travel distance is 164.\nFrom 6 to 15, the travel distance is 67.\nFrom 6 to 16, the travel distance is 109.\nFrom 7 to 0, the travel distance is 205.\nFrom 7 to 1, the travel distance is 181.\nFrom 7 to 2, the travel distance is 179.\nFrom 7 to 3, the travel distance is 196.\nFrom 7 to 4, the travel distance is 199.\nFrom 7 to 5, the travel distance is 162.\nFrom 7 to 6, the travel distance is 186.\nFrom 7 to 8, the travel distance is 71.\nFrom 7 to 9, the travel distance is 208.\nFrom 7 to 10, the travel distance is 152.\nFrom 7 to 11, the travel distance is 198.\nFrom 7 to 12, the travel distance is 185.\nFrom 7 to 13, the travel distance is 173.\nFrom 7 to 14, the travel distance is 199.\nFrom 7 to 15, the travel distance is 119.\nFrom 7 to 16, the travel distance is 215.\nFrom 8 to 0, the travel distance is 134.\nFrom 8 to 1, the travel distance is 110.\nFrom 8 to 2, the travel distance is 194.\nFrom 8 to 3, the travel distance is 141.\nFrom 8 to 4, the travel distance is 144.\nFrom 8 to 5, the travel distance is 132.\nFrom 8 to 6, the travel distance is 115.\nFrom 8 to 7, the travel distance is 71.\nFrom 8 to 9, the travel distance is 137.\nFrom 8 to 10, the travel distance is 86.\nFrom 8 to 11, the travel distance is 143.\nFrom 8 to 12, the travel distance is 197.\nFrom 8 to 13, the travel distance is 165.\nFrom 8 to 14, the travel distance is 169.\nFrom 8 to 15, the travel distance is 48.\nFrom 8 to 16, the travel distance is 162.\nFrom 9 to 0, the travel distance is 197.\nFrom 9 to 1, the travel distance is 173.\nFrom 9 to 2, the travel distance is 257.\nFrom 9 to 3, the travel distance is 204.\nFrom 9 to 4, the travel distance is 207.\nFrom 9 to 5, the travel distance is 153.\nFrom 9 to 6, the travel distance is 168.\nFrom 9 to 7, the travel distance is 208.\nFrom 9 to 8, the travel distance is 137.\nFrom 9 to 10, the travel distance is 190.\nFrom 9 to 11, the travel distance is 193.\nFrom 9 to 12, the travel distance is 260.\nFrom 9 to 13, the travel distance is 204.\nFrom 9 to 14, the travel distance is 194.\nFrom 9 to 15, the travel distance is 111.\nFrom 9 to 16, the travel distance is 225.\nFrom 10 to 0, the travel distance is 119.\nFrom 10 to 1, the travel distance is 149.\nFrom 10 to 2, the travel distance is 178.\nFrom 10 to 3, the travel distance is 125.\nFrom 10 to 4, the travel distance is 128.\nFrom 10 to 5, the travel distance is 76.\nFrom 10 to 6, the travel distance is 154.\nFrom 10 to 7, the travel distance is 152.\nFrom 10 to 8, the travel distance is 86.\nFrom 10 to 9, the travel distance is 190.\nFrom 10 to 11, the travel distance is 116.\nFrom 10 to 12, the travel distance is 217.\nFrom 10 to 13, the travel distance is 133.\nFrom 10 to 14, the travel distance is 117.\nFrom 10 to 15, the travel distance is 87.\nFrom 10 to 16, the travel distance is 94.\nFrom 11 to 0, the travel distance is 132.\nFrom 11 to 1, the travel distance is 157.\nFrom 11 to 2, the travel distance is 115.\nFrom 11 to 3, the travel distance is 62.\nFrom 11 to 4, the travel distance is 65.\nFrom 11 to 5, the travel distance is 40.\nFrom 11 to 6, the travel distance is 162.\nFrom 11 to 7, the travel distance is 198.\nFrom 11 to 8, the travel distance is 143.\nFrom 11 to 9, the travel distance is 193.\nFrom 11 to 10, the travel distance is 116.\nFrom 11 to 12, the travel distance is 154.\nFrom 11 to 13, the travel distance is 139.\nFrom 11 to 14, the travel distance is 50.\nFrom 11 to 15, the travel distance is 95.\nFrom 11 to 16, the travel distance is 106.\nFrom 12 to 0, the travel distance is 232.\nFrom 12 to 1, the travel distance is 205.\nFrom 12 to 2, the travel distance is 156.\nFrom 12 to 3, the travel distance is 162.\nFrom 12 to 4, the travel distance is 165.\nFrom 12 to 5, the travel distance is 158.\nFrom 12 to 6, the travel distance is 210.\nFrom 12 to 7, the travel distance is 185.\nFrom 12 to 8, the travel distance is 197.\nFrom 12 to 9, the travel distance is 260.\nFrom 12 to 10, the travel distance is 217.\nFrom 12 to 11, the travel distance is 154.\nFrom 12 to 13, the travel distance is 206.\nFrom 12 to 14, the travel distance is 117.\nFrom 12 to 15, the travel distance is 149.\nFrom 12 to 16, the travel distance is 206.\nFrom 13 to 0, the travel distance is 190.\nFrom 13 to 1, the travel distance is 122.\nFrom 13 to 2, the travel distance is 240.\nFrom 13 to 3, the travel distance is 201.\nFrom 13 to 4, the travel distance is 204.\nFrom 13 to 5, the travel distance is 118.\nFrom 13 to 6, the travel distance is 127.\nFrom 13 to 7, the travel distance is 173.\nFrom 13 to 8, the travel distance is 165.\nFrom 13 to 9, the travel distance is 204.\nFrom 13 to 10, the travel distance is 133.\nFrom 13 to 11, the travel distance is 139.\nFrom 13 to 12, the travel distance is 206.\nFrom 13 to 14, the travel distance is 89.\nFrom 13 to 15, the travel distance is 136.\nFrom 13 to 16, the travel distance is 156.\nFrom 14 to 0, the travel distance is 182.\nFrom 14 to 1, the travel distance is 169.\nFrom 14 to 2, the travel distance is 165.\nFrom 14 to 3, the travel distance is 112.\nFrom 14 to 4, the travel distance is 115.\nFrom 14 to 5, the travel distance is 41.\nFrom 14 to 6, the travel distance is 164.\nFrom 14 to 7, the travel distance is 199.\nFrom 14 to 8, the travel distance is 169.\nFrom 14 to 9, the travel distance is 194.\nFrom 14 to 10, the travel distance is 117.\nFrom 14 to 11, the travel distance is 50.\nFrom 14 to 12, the travel distance is 117.\nFrom 14 to 13, the travel distance is 89.\nFrom 14 to 15, the travel distance is 121.\nFrom 14 to 16, the travel distance is 156.\nFrom 15 to 0, the travel distance is 86.\nFrom 15 to 1, the travel distance is 62.\nFrom 15 to 2, the travel distance is 146.\nFrom 15 to 3, the travel distance is 93.\nFrom 15 to 4, the travel distance is 96.\nFrom 15 to 5, the travel distance is 84.\nFrom 15 to 6, the travel distance is 67.\nFrom 15 to 7, the travel distance is 119.\nFrom 15 to 8, the travel distance is 48.\nFrom 15 to 9, the travel distance is 111.\nFrom 15 to 10, the travel distance is 87.\nFrom 15 to 11, the travel distance is 95.\nFrom 15 to 12, the travel distance is 149.\nFrom 15 to 13, the travel distance is 136.\nFrom 15 to 14, the travel distance is 121.\nFrom 15 to 16, the travel distance is 114.\nFrom 16 to 0, the travel distance is 182.\nFrom 16 to 1, the travel distance is 114.\nFrom 16 to 2, the travel distance is 98.\nFrom 16 to 3, the travel distance is 108.\nFrom 16 to 4, the travel distance is 111.\nFrom 16 to 5, the travel distance is 124.\nFrom 16 to 6, the travel distance is 109.\nFrom 16 to 7, the travel distance is 215.\nFrom 16 to 8, the travel distance is 162.\nFrom 16 to 9, the travel distance is 225.\nFrom 16 to 10, the travel distance is 94.\nFrom 16 to 11, the travel distance is 106.\nFrom 16 to 12, the travel distance is 206.\nFrom 16 to 13, the travel distance is 156.\nFrom 16 to 14, the travel distance is 156.\nFrom 16 to 15, the travel distance is 114.\nAssign each of the 17 neighborhoods to one of the 2 opened branches so the summed travel distances are as small as possible.\n\nAlso, please send the answer using this simple JSON layout so I can read it easily:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is just the list of branches you decide to keep open (the branch IDs). \"assignments\" is a parallel list that says, for each neighborhood in the instance (in the same order), which open branch that neighborhood is attached to. Think of it like filling out a short form: which branches are run, and then for every neighborhood which branch it goes to.\n\nThis JSON is only a sketch of the expected shape — don't treat the placeholders as the real solution. Make sure you use the exact identifiers from the instance input with no renaming or invented labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 68, 193, 140, 143, 170, 73, 205, 134, 197, 119, 132, 232, 190, 182, 86, 182 ], [ 68, 0, 184, 131, 134, 128, 5, 181, 110, 173, 149, 157, 205, 122, 169, 62, 114 ], [ 193, 184, 0, 53, 50, 141, 189, 179, 194, 257, 178, 115, 156, 240, 165, 146, 98 ], [ 140, 131, 53, 0, 3, 88, 136, 196, 141, 204, 125, 62, 162, 201, 112, 93, 108 ], [ 143, 134, 50, 3, 0, 91, 139, 199, 144, 207, 128, 65, 165, 204, 115, 96, 111 ], [ 170, 128, 141, 88, 91, 0, 123, 162, 132, 153, 76, 40, 158, 118, 41, 84, 124 ], [ 73, 5, 189, 136, 139, 123, 0, 186, 115, 168, 154, 162, 210, 127, 164, 67, 109 ], [ 205, 181, 179, 196, 199, 162, 186, 0, 71, 208, 152, 198, 185, 173, 199, 119, 215 ], [ 134, 110, 194, 141, 144, 132, 115, 71, 0, 137, 86, 143, 197, 165, 169, 48, 162 ], [ 197, 173, 257, 204, 207, 153, 168, 208, 137, 0, 190, 193, 260, 204, 194, 111, 225 ], [ 119, 149, 178, 125, 128, 76, 154, 152, 86, 190, 0, 116, 217, 133, 117, 87, 94 ], [ 132, 157, 115, 62, 65, 40, 162, 198, 143, 193, 116, 0, 154, 139, 50, 95, 106 ], [ 232, 205, 156, 162, 165, 158, 210, 185, 197, 260, 217, 154, 0, 206, 117, 149, 206 ], [ 190, 122, 240, 201, 204, 118, 127, 173, 165, 204, 133, 139, 206, 0, 89, 136, 156 ], [ 182, 169, 165, 112, 115, 41, 164, 199, 169, 194, 117, 50, 117, 89, 0, 121, 156 ], [ 86, 62, 146, 93, 96, 84, 67, 119, 48, 111, 87, 95, 149, 136, 121, 0, 114 ], [ 182, 114, 98, 108, 111, 124, 109, 215, 162, 225, 94, 106, 206, 156, 156, 114, 0 ] ], "p": 2, "objective": 1287.0 }, "solution": { "facilities": [ 3, 15 ], "assignments": [ 15, 15, 3, 3, 3, 15, 15, 15, 15, 15, 15, 3, 15, 15, 3, 15, 3 ] }, "obj": 1287.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 2, "sites": [ { "id": 0, "distances": { "0": 0, "1": 68, "2": 193, "3": 140, "4": 143, "5": 170, "6": 73, "7": 205, "8": 134, "9": 197, "10": 119, "11": 132, "12": 232, "13": 190, "14": 182, "15": 86, "16": 182 } }, { "id": 1, "distances": { "0": 68, "1": 0, "2": 184, "3": 131, "4": 134, "5": 128, "6": 5, "7": 181, "8": 110, "9": 173, "10": 149, "11": 157, "12": 205, "13": 122, "14": 169, "15": 62, "16": 114 } }, { "id": 2, "distances": { "0": 193, "1": 184, "2": 0, "3": 53, "4": 50, "5": 141, "6": 189, "7": 179, "8": 194, "9": 257, "10": 178, "11": 115, "12": 156, "13": 240, "14": 165, "15": 146, "16": 98 } }, { "id": 3, "distances": { "0": 140, "1": 131, "2": 53, "3": 0, "4": 3, "5": 88, "6": 136, "7": 196, "8": 141, "9": 204, "10": 125, "11": 62, "12": 162, "13": 201, "14": 112, "15": 93, "16": 108 } }, { "id": 4, "distances": { "0": 143, "1": 134, "2": 50, "3": 3, "4": 0, "5": 91, "6": 139, "7": 199, "8": 144, "9": 207, "10": 128, "11": 65, "12": 165, "13": 204, "14": 115, "15": 96, "16": 111 } }, { "id": 5, "distances": { "0": 170, "1": 128, "2": 141, "3": 88, "4": 91, "5": 0, "6": 123, "7": 162, "8": 132, "9": 153, "10": 76, "11": 40, "12": 158, "13": 118, "14": 41, "15": 84, "16": 124 } }, { "id": 6, "distances": { "0": 73, "1": 5, "2": 189, "3": 136, "4": 139, "5": 123, "6": 0, "7": 186, "8": 115, "9": 168, "10": 154, "11": 162, "12": 210, "13": 127, "14": 164, "15": 67, "16": 109 } }, { "id": 7, "distances": { "0": 205, "1": 181, "2": 179, "3": 196, "4": 199, "5": 162, "6": 186, "7": 0, "8": 71, "9": 208, "10": 152, "11": 198, "12": 185, "13": 173, "14": 199, "15": 119, "16": 215 } }, { "id": 8, "distances": { "0": 134, "1": 110, "2": 194, "3": 141, "4": 144, "5": 132, "6": 115, "7": 71, "8": 0, "9": 137, "10": 86, "11": 143, "12": 197, "13": 165, "14": 169, "15": 48, "16": 162 } }, { "id": 9, "distances": { "0": 197, "1": 173, "2": 257, "3": 204, "4": 207, "5": 153, "6": 168, "7": 208, "8": 137, "9": 0, "10": 190, "11": 193, "12": 260, "13": 204, "14": 194, "15": 111, "16": 225 } }, { "id": 10, "distances": { "0": 119, "1": 149, "2": 178, "3": 125, "4": 128, "5": 76, "6": 154, "7": 152, "8": 86, "9": 190, "10": 0, "11": 116, "12": 217, "13": 133, "14": 117, "15": 87, "16": 94 } }, { "id": 11, "distances": { "0": 132, "1": 157, "2": 115, "3": 62, "4": 65, "5": 40, "6": 162, "7": 198, "8": 143, "9": 193, "10": 116, "11": 0, "12": 154, "13": 139, "14": 50, "15": 95, "16": 106 } }, { "id": 12, "distances": { "0": 232, "1": 205, "2": 156, "3": 162, "4": 165, "5": 158, "6": 210, "7": 185, "8": 197, "9": 260, "10": 217, "11": 154, "12": 0, "13": 206, "14": 117, "15": 149, "16": 206 } }, { "id": 13, "distances": { "0": 190, "1": 122, "2": 240, "3": 201, "4": 204, "5": 118, "6": 127, "7": 173, "8": 165, "9": 204, "10": 133, "11": 139, "12": 206, "13": 0, "14": 89, "15": 136, "16": 156 } }, { "id": 14, "distances": { "0": 182, "1": 169, "2": 165, "3": 112, "4": 115, "5": 41, "6": 164, "7": 199, "8": 169, "9": 194, "10": 117, "11": 50, "12": 117, "13": 89, "14": 0, "15": 121, "16": 156 } }, { "id": 15, "distances": { "0": 86, "1": 62, "2": 146, "3": 93, "4": 96, "5": 84, "6": 67, "7": 119, "8": 48, "9": 111, "10": 87, "11": 95, "12": 149, "13": 136, "14": 121, "15": 0, "16": 114 } }, { "id": 16, "distances": { "0": 182, "1": 114, "2": 98, "3": 108, "4": 111, "5": 124, "6": 109, "7": 215, "8": 162, "9": 225, "10": 94, "11": 106, "12": 206, "13": 156, "14": 156, "15": 114, "16": 0 } } ], "objective": 1287.0 }, "solution_variant": { "selected": [ 3, 15 ], "assignments": [ 15, 15, 3, 3, 3, 15, 15, 15, 15, 15, 15, 3, 15, 15, 3, 15, 3 ] }, "context_index": 23, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "There's a plan to place a limited number of dropoff kiosks and organize the neighborhood so every street segment feeds into one of those kiosks. The decision is simply which locations to open, and success is judged by how small the total hauling distance becomes — calculated by adding together the distance from each street segment to the kiosk it uses. Every street segment must be routed to exactly one open kiosk, with none skipped or doubled up. The detailed list of candidate sites and distances is shown below.\n\nIt lists 16 candidate locations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and specifies the fixed number 5 of kiosks to open.\nOrigin 1 → destination 2, haul distance 39.\nOrigin 1 → destination 3, haul distance 27.\nOrigin 1 → destination 4, haul distance 34.\nOrigin 1 → destination 5, haul distance 23.\nOrigin 1 → destination 6, haul distance 30.\nOrigin 1 → destination 7, haul distance 22.\nOrigin 1 → destination 8, haul distance 34.\nOrigin 1 → destination 9, haul distance 32.\nOrigin 1 → destination 10, haul distance 12.\nOrigin 1 → destination 11, haul distance 36.\nOrigin 1 → destination 12, haul distance 30.\nOrigin 1 → destination 13, haul distance 24.\nOrigin 1 → destination 14, haul distance 24.\nOrigin 1 → destination 15, haul distance 27.\nOrigin 1 → destination 16, haul distance 31.\nOrigin 2 → destination 1, haul distance 39.\nOrigin 2 → destination 3, haul distance 55.\nOrigin 2 → destination 4, haul distance 54.\nOrigin 2 → destination 5, haul distance 54.\nOrigin 2 → destination 6, haul distance 52.\nOrigin 2 → destination 7, haul distance 42.\nOrigin 2 → destination 8, haul distance 45.\nOrigin 2 → destination 9, haul distance 34.\nOrigin 2 → destination 10, haul distance 48.\nOrigin 2 → destination 11, haul distance 47.\nOrigin 2 → destination 12, haul distance 36.\nOrigin 2 → destination 13, haul distance 47.\nOrigin 2 → destination 14, haul distance 32.\nOrigin 2 → destination 15, haul distance 26.\nOrigin 2 → destination 16, haul distance 59.\nOrigin 3 → destination 1, haul distance 27.\nOrigin 3 → destination 2, haul distance 55.\nOrigin 3 → destination 4, haul distance 41.\nOrigin 3 → destination 5, haul distance 38.\nOrigin 3 → destination 6, haul distance 44.\nOrigin 3 → destination 7, haul distance 35.\nOrigin 3 → destination 8, haul distance 34.\nOrigin 3 → destination 9, haul distance 50.\nOrigin 3 → destination 10, haul distance 38.\nOrigin 3 → destination 11, haul distance 43.\nOrigin 3 → destination 12, haul distance 33.\nOrigin 3 → destination 13, haul distance 35.\nOrigin 3 → destination 14, haul distance 44.\nOrigin 3 → destination 15, haul distance 32.\nOrigin 3 → destination 16, haul distance 25.\nOrigin 4 → destination 1, haul distance 34.\nOrigin 4 → destination 2, haul distance 54.\nOrigin 4 → destination 3, haul distance 41.\nOrigin 4 → destination 5, haul distance 40.\nOrigin 4 → destination 6, haul distance 20.\nOrigin 4 → destination 7, haul distance 34.\nOrigin 4 → destination 8, haul distance 34.\nOrigin 4 → destination 9, haul distance 28.\nOrigin 4 → destination 10, haul distance 22.\nOrigin 4 → destination 11, haul distance 46.\nOrigin 4 → destination 12, haul distance 32.\nOrigin 4 → destination 13, haul distance 16.\nOrigin 4 → destination 14, haul distance 39.\nOrigin 4 → destination 15, haul distance 37.\nOrigin 4 → destination 16, haul distance 39.\nOrigin 5 → destination 1, haul distance 23.\nOrigin 5 → destination 2, haul distance 54.\nOrigin 5 → destination 3, haul distance 38.\nOrigin 5 → destination 4, haul distance 40.\nOrigin 5 → destination 6, haul distance 36.\nOrigin 5 → destination 7, haul distance 27.\nOrigin 5 → destination 8, haul distance 41.\nOrigin 5 → destination 9, haul distance 37.\nOrigin 5 → destination 10, haul distance 29.\nOrigin 5 → destination 11, haul distance 41.\nOrigin 5 → destination 12, haul distance 29.\nOrigin 5 → destination 13, haul distance 27.\nOrigin 5 → destination 14, haul distance 42.\nOrigin 5 → destination 15, haul distance 39.\nOrigin 5 → destination 16, haul distance 47.\nOrigin 6 → destination 1, haul distance 30.\nOrigin 6 → destination 2, haul distance 52.\nOrigin 6 → destination 3, haul distance 44.\nOrigin 6 → destination 4, haul distance 20.\nOrigin 6 → destination 5, haul distance 36.\nOrigin 6 → destination 7, haul distance 25.\nOrigin 6 → destination 8, haul distance 40.\nOrigin 6 → destination 9, haul distance 37.\nOrigin 6 → destination 10, haul distance 24.\nOrigin 6 → destination 11, haul distance 39.\nOrigin 6 → destination 12, haul distance 31.\nOrigin 6 → destination 13, haul distance 22.\nOrigin 6 → destination 14, haul distance 36.\nOrigin 6 → destination 15, haul distance 41.\nOrigin 6 → destination 16, haul distance 46.\nOrigin 7 → destination 1, haul distance 22.\nOrigin 7 → destination 2, haul distance 42.\nOrigin 7 → destination 3, haul distance 35.\nOrigin 7 → destination 4, haul distance 34.\nOrigin 7 → destination 5, haul distance 27.\nOrigin 7 → destination 6, haul distance 25.\nOrigin 7 → destination 8, haul distance 33.\nOrigin 7 → destination 9, haul distance 34.\nOrigin 7 → destination 10, haul distance 14.\nOrigin 7 → destination 11, haul distance 28.\nOrigin 7 → destination 12, haul distance 33.\nOrigin 7 → destination 13, haul distance 19.\nOrigin 7 → destination 14, haul distance 43.\nOrigin 7 → destination 15, haul distance 34.\nOrigin 7 → destination 16, haul distance 26.\nOrigin 8 → destination 1, haul distance 34.\nOrigin 8 → destination 2, haul distance 45.\nOrigin 8 → destination 3, haul distance 34.\nOrigin 8 → destination 4, haul distance 34.\nOrigin 8 → destination 5, haul distance 41.\nOrigin 8 → destination 6, haul distance 40.\nOrigin 8 → destination 7, haul distance 33.\nOrigin 8 → destination 9, haul distance 34.\nOrigin 8 → destination 10, haul distance 37.\nOrigin 8 → destination 11, haul distance 39.\nOrigin 8 → destination 12, haul distance 28.\nOrigin 8 → destination 13, haul distance 18.\nOrigin 8 → destination 14, haul distance 42.\nOrigin 8 → destination 15, haul distance 36.\nOrigin 8 → destination 16, haul distance 41.\nOrigin 9 → destination 1, haul distance 32.\nOrigin 9 → destination 2, haul distance 34.\nOrigin 9 → destination 3, haul distance 50.\nOrigin 9 → destination 4, haul distance 28.\nOrigin 9 → destination 5, haul distance 37.\nOrigin 9 → destination 6, haul distance 37.\nOrigin 9 → destination 7, haul distance 34.\nOrigin 9 → destination 8, haul distance 34.\nOrigin 9 → destination 10, haul distance 40.\nOrigin 9 → destination 11, haul distance 45.\nOrigin 9 → destination 12, haul distance 29.\nOrigin 9 → destination 13, haul distance 34.\nOrigin 9 → destination 14, haul distance 42.\nOrigin 9 → destination 15, haul distance 39.\nOrigin 9 → destination 16, haul distance 36.\nOrigin 10 → destination 1, haul distance 12.\nOrigin 10 → destination 2, haul distance 48.\nOrigin 10 → destination 3, haul distance 38.\nOrigin 10 → destination 4, haul distance 22.\nOrigin 10 → destination 5, haul distance 29.\nOrigin 10 → destination 6, haul distance 24.\nOrigin 10 → destination 7, haul distance 14.\nOrigin 10 → destination 8, haul distance 37.\nOrigin 10 → destination 9, haul distance 40.\nOrigin 10 → destination 11, haul distance 36.\nOrigin 10 → destination 12, haul distance 37.\nOrigin 10 → destination 13, haul distance 23.\nOrigin 10 → destination 14, haul distance 36.\nOrigin 10 → destination 15, haul distance 39.\nOrigin 10 → destination 16, haul distance 40.\nOrigin 11 → destination 1, haul distance 36.\nOrigin 11 → destination 2, haul distance 47.\nOrigin 11 → destination 3, haul distance 43.\nOrigin 11 → destination 4, haul distance 46.\nOrigin 11 → destination 5, haul distance 41.\nOrigin 11 → destination 6, haul distance 39.\nOrigin 11 → destination 7, haul distance 28.\nOrigin 11 → destination 8, haul distance 39.\nOrigin 11 → destination 9, haul distance 45.\nOrigin 11 → destination 10, haul distance 36.\nOrigin 11 → destination 12, haul distance 37.\nOrigin 11 → destination 13, haul distance 37.\nOrigin 11 → destination 14, haul distance 39.\nOrigin 11 → destination 15, haul distance 41.\nOrigin 11 → destination 16, haul distance 40.\nOrigin 12 → destination 1, haul distance 30.\nOrigin 12 → destination 2, haul distance 36.\nOrigin 12 → destination 3, haul distance 33.\nOrigin 12 → destination 4, haul distance 32.\nOrigin 12 → destination 5, haul distance 29.\nOrigin 12 → destination 6, haul distance 31.\nOrigin 12 → destination 7, haul distance 33.\nOrigin 12 → destination 8, haul distance 28.\nOrigin 12 → destination 9, haul distance 29.\nOrigin 12 → destination 10, haul distance 37.\nOrigin 12 → destination 11, haul distance 37.\nOrigin 12 → destination 13, haul distance 28.\nOrigin 12 → destination 14, haul distance 37.\nOrigin 12 → destination 15, haul distance 32.\nOrigin 12 → destination 16, haul distance 36.\nOrigin 13 → destination 1, haul distance 24.\nOrigin 13 → destination 2, haul distance 47.\nOrigin 13 → destination 3, haul distance 35.\nOrigin 13 → destination 4, haul distance 16.\nOrigin 13 → destination 5, haul distance 27.\nOrigin 13 → destination 6, haul distance 22.\nOrigin 13 → destination 7, haul distance 19.\nOrigin 13 → destination 8, haul distance 18.\nOrigin 13 → destination 9, haul distance 34.\nOrigin 13 → destination 10, haul distance 23.\nOrigin 13 → destination 11, haul distance 37.\nOrigin 13 → destination 12, haul distance 28.\nOrigin 13 → destination 14, haul distance 24.\nOrigin 13 → destination 15, haul distance 21.\nOrigin 13 → destination 16, haul distance 34.\nOrigin 14 → destination 1, haul distance 24.\nOrigin 14 → destination 2, haul distance 32.\nOrigin 14 → destination 3, haul distance 44.\nOrigin 14 → destination 4, haul distance 39.\nOrigin 14 → destination 5, haul distance 42.\nOrigin 14 → destination 6, haul distance 36.\nOrigin 14 → destination 7, haul distance 43.\nOrigin 14 → destination 8, haul distance 42.\nOrigin 14 → destination 9, haul distance 42.\nOrigin 14 → destination 10, haul distance 36.\nOrigin 14 → destination 11, haul distance 39.\nOrigin 14 → destination 12, haul distance 37.\nOrigin 14 → destination 13, haul distance 24.\nOrigin 14 → destination 15, haul distance 43.\nOrigin 14 → destination 16, haul distance 48.\nOrigin 15 → destination 1, haul distance 27.\nOrigin 15 → destination 2, haul distance 26.\nOrigin 15 → destination 3, haul distance 32.\nOrigin 15 → destination 4, haul distance 37.\nOrigin 15 → destination 5, haul distance 39.\nOrigin 15 → destination 6, haul distance 41.\nOrigin 15 → destination 7, haul distance 34.\nOrigin 15 → destination 8, haul distance 36.\nOrigin 15 → destination 9, haul distance 39.\nOrigin 15 → destination 10, haul distance 39.\nOrigin 15 → destination 11, haul distance 41.\nOrigin 15 → destination 12, haul distance 32.\nOrigin 15 → destination 13, haul distance 21.\nOrigin 15 → destination 14, haul distance 43.\nOrigin 15 → destination 16, haul distance 42.\nOrigin 16 → destination 1, haul distance 31.\nOrigin 16 → destination 2, haul distance 59.\nOrigin 16 → destination 3, haul distance 25.\nOrigin 16 → destination 4, haul distance 39.\nOrigin 16 → destination 5, haul distance 47.\nOrigin 16 → destination 6, haul distance 46.\nOrigin 16 → destination 7, haul distance 26.\nOrigin 16 → destination 8, haul distance 41.\nOrigin 16 → destination 9, haul distance 36.\nOrigin 16 → destination 10, haul distance 40.\nOrigin 16 → destination 11, haul distance 40.\nOrigin 16 → destination 12, haul distance 36.\nOrigin 16 → destination 13, haul distance 34.\nOrigin 16 → destination 14, haul distance 48.\nOrigin 16 → destination 15, haul distance 42.\nTreat each record below as the hauling cost for assigning that origin to that destination; use these 16 locations and the 5 kiosk limit to evaluate total hauling distance.\n\nOh, and when you send the answer back, just put it in this simple JSON shape so I can read it automatically — nothing fancy, just a small object with which sites you opened and where every street segment goes:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis is just a sketch of the shape I need: \"selected\" is the list of kiosk sites you decide to open, and \"assignments\" lists, for every street segment (in the same order as they appear in the instance), which opened site it uses. Keep it light and exact — that JSON is the form, not the final content.\n\nPlease make sure all identifiers you put in those lists are used exactly as they appear in the instance input — no renaming, no made-up labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 39, 27, 34, 23, 30, 22, 34, 32, 12, 36, 30, 24, 24, 27, 31 ], [ 39, 0, 55, 54, 54, 52, 42, 45, 34, 48, 47, 36, 47, 32, 26, 59 ], [ 27, 55, 0, 41, 38, 44, 35, 34, 50, 38, 43, 33, 35, 44, 32, 25 ], [ 34, 54, 41, 0, 40, 20, 34, 34, 28, 22, 46, 32, 16, 39, 37, 39 ], [ 23, 54, 38, 40, 0, 36, 27, 41, 37, 29, 41, 29, 27, 42, 39, 47 ], [ 30, 52, 44, 20, 36, 0, 25, 40, 37, 24, 39, 31, 22, 36, 41, 46 ], [ 22, 42, 35, 34, 27, 25, 0, 33, 34, 14, 28, 33, 19, 43, 34, 26 ], [ 34, 45, 34, 34, 41, 40, 33, 0, 34, 37, 39, 28, 18, 42, 36, 41 ], [ 32, 34, 50, 28, 37, 37, 34, 34, 0, 40, 45, 29, 34, 42, 39, 36 ], [ 12, 48, 38, 22, 29, 24, 14, 37, 40, 0, 36, 37, 23, 36, 39, 40 ], [ 36, 47, 43, 46, 41, 39, 28, 39, 45, 36, 0, 37, 37, 39, 41, 40 ], [ 30, 36, 33, 32, 29, 31, 33, 28, 29, 37, 37, 0, 28, 37, 32, 36 ], [ 24, 47, 35, 16, 27, 22, 19, 18, 34, 23, 37, 28, 0, 24, 21, 34 ], [ 24, 32, 44, 39, 42, 36, 43, 42, 42, 36, 39, 37, 24, 0, 43, 48 ], [ 27, 26, 32, 37, 39, 41, 34, 36, 39, 39, 41, 32, 21, 43, 0, 42 ], [ 31, 59, 25, 39, 47, 46, 26, 41, 36, 40, 40, 36, 34, 48, 42, 0 ] ], "p": 5, "objective": 240.0 }, "solution": { "facilities": [ 0, 1, 2, 10, 12 ], "assignments": [ 0, 1, 2, 12, 0, 12, 12, 12, 0, 0, 10, 12, 12, 12, 12, 2 ] }, "obj": 240.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 5, "sites": [ { "id": 1, "distances": { "1": 0, "2": 39, "3": 27, "4": 34, "5": 23, "6": 30, "7": 22, "8": 34, "9": 32, "10": 12, "11": 36, "12": 30, "13": 24, "14": 24, "15": 27, "16": 31 } }, { "id": 2, "distances": { "1": 39, "2": 0, "3": 55, "4": 54, "5": 54, "6": 52, "7": 42, "8": 45, "9": 34, "10": 48, "11": 47, "12": 36, "13": 47, "14": 32, "15": 26, "16": 59 } }, { "id": 3, "distances": { "1": 27, "2": 55, "3": 0, "4": 41, "5": 38, "6": 44, "7": 35, "8": 34, "9": 50, "10": 38, "11": 43, "12": 33, "13": 35, "14": 44, "15": 32, "16": 25 } }, { "id": 4, "distances": { "1": 34, "2": 54, "3": 41, "4": 0, "5": 40, "6": 20, "7": 34, "8": 34, "9": 28, "10": 22, "11": 46, "12": 32, "13": 16, "14": 39, "15": 37, "16": 39 } }, { "id": 5, "distances": { "1": 23, "2": 54, "3": 38, "4": 40, "5": 0, "6": 36, "7": 27, "8": 41, "9": 37, "10": 29, "11": 41, "12": 29, "13": 27, "14": 42, "15": 39, "16": 47 } }, { "id": 6, "distances": { "1": 30, "2": 52, "3": 44, "4": 20, "5": 36, "6": 0, "7": 25, "8": 40, "9": 37, "10": 24, "11": 39, "12": 31, "13": 22, "14": 36, "15": 41, "16": 46 } }, { "id": 7, "distances": { "1": 22, "2": 42, "3": 35, "4": 34, "5": 27, "6": 25, "7": 0, "8": 33, "9": 34, "10": 14, "11": 28, "12": 33, "13": 19, "14": 43, "15": 34, "16": 26 } }, { "id": 8, "distances": { "1": 34, "2": 45, "3": 34, "4": 34, "5": 41, "6": 40, "7": 33, "8": 0, "9": 34, "10": 37, "11": 39, "12": 28, "13": 18, "14": 42, "15": 36, "16": 41 } }, { "id": 9, "distances": { "1": 32, "2": 34, "3": 50, "4": 28, "5": 37, "6": 37, "7": 34, "8": 34, "9": 0, "10": 40, "11": 45, "12": 29, "13": 34, "14": 42, "15": 39, "16": 36 } }, { "id": 10, "distances": { "1": 12, "2": 48, "3": 38, "4": 22, "5": 29, "6": 24, "7": 14, "8": 37, "9": 40, "10": 0, "11": 36, "12": 37, "13": 23, "14": 36, "15": 39, "16": 40 } }, { "id": 11, "distances": { "1": 36, "2": 47, "3": 43, "4": 46, "5": 41, "6": 39, "7": 28, "8": 39, "9": 45, "10": 36, "11": 0, "12": 37, "13": 37, "14": 39, "15": 41, "16": 40 } }, { "id": 12, "distances": { "1": 30, "2": 36, "3": 33, "4": 32, "5": 29, "6": 31, "7": 33, "8": 28, "9": 29, "10": 37, "11": 37, "12": 0, "13": 28, "14": 37, "15": 32, "16": 36 } }, { "id": 13, "distances": { "1": 24, "2": 47, "3": 35, "4": 16, "5": 27, "6": 22, "7": 19, "8": 18, "9": 34, "10": 23, "11": 37, "12": 28, "13": 0, "14": 24, "15": 21, "16": 34 } }, { "id": 14, "distances": { "1": 24, "2": 32, "3": 44, "4": 39, "5": 42, "6": 36, "7": 43, "8": 42, "9": 42, "10": 36, "11": 39, "12": 37, "13": 24, "14": 0, "15": 43, "16": 48 } }, { "id": 15, "distances": { "1": 27, "2": 26, "3": 32, "4": 37, "5": 39, "6": 41, "7": 34, "8": 36, "9": 39, "10": 39, "11": 41, "12": 32, "13": 21, "14": 43, "15": 0, "16": 42 } }, { "id": 16, "distances": { "1": 31, "2": 59, "3": 25, "4": 39, "5": 47, "6": 46, "7": 26, "8": 41, "9": 36, "10": 40, "11": 40, "12": 36, "13": 34, "14": 48, "15": 42, "16": 0 } } ], "objective": 240.0 }, "solution_variant": { "selected": [ 1, 2, 3, 11, 13 ], "assignments": [ 1, 2, 3, 13, 1, 13, 13, 13, 1, 1, 11, 13, 13, 13, 13, 3 ] }, "context_index": 24, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone in charge of campus housing needs to pick a limited number of service locations and then assign each dorm to exactly one of those locations, with the goal that the total distance students travel for services — obtained by totaling each dorm’s trip to its center — is as low as possible. It’s important that no dorm is left unassigned or assigned to more than one center. The specific instance details are shown below.\n\nThere are 15 candidate dormitories, 3 service centers to open, and the dormitory identifiers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.\nDormitory 0 is 32 away from candidate center 1.\nDormitory 0 is 36 away from candidate center 2.\nDormitory 0 is 29 away from candidate center 3.\nDormitory 0 is 36 away from candidate center 4.\nDormitory 0 is 48 away from candidate center 5.\nDormitory 0 is 35 away from candidate center 6.\nDormitory 0 is 37 away from candidate center 7.\nDormitory 0 is 33 away from candidate center 8.\nDormitory 0 is 45 away from candidate center 9.\nDormitory 0 is 26 away from candidate center 10.\nDormitory 0 is 48 away from candidate center 11.\nDormitory 0 is 30 away from candidate center 12.\nDormitory 0 is 36 away from candidate center 13.\nDormitory 0 is 32 away from candidate center 14.\nDormitory 1 is 32 away from candidate center 0.\nDormitory 1 is 40 away from candidate center 2.\nDormitory 1 is 29 away from candidate center 3.\nDormitory 1 is 32 away from candidate center 4.\nDormitory 1 is 42 away from candidate center 5.\nDormitory 1 is 40 away from candidate center 6.\nDormitory 1 is 40 away from candidate center 7.\nDormitory 1 is 27 away from candidate center 8.\nDormitory 1 is 45 away from candidate center 9.\nDormitory 1 is 26 away from candidate center 10.\nDormitory 1 is 38 away from candidate center 11.\nDormitory 1 is 36 away from candidate center 12.\nDormitory 1 is 36 away from candidate center 13.\nDormitory 1 is 43 away from candidate center 14.\nDormitory 2 is 36 away from candidate center 0.\nDormitory 2 is 40 away from candidate center 1.\nDormitory 2 is 41 away from candidate center 3.\nDormitory 2 is 32 away from candidate center 4.\nDormitory 2 is 55 away from candidate center 5.\nDormitory 2 is 42 away from candidate center 6.\nDormitory 2 is 42 away from candidate center 7.\nDormitory 2 is 27 away from candidate center 8.\nDormitory 2 is 52 away from candidate center 9.\nDormitory 2 is 35 away from candidate center 10.\nDormitory 2 is 53 away from candidate center 11.\nDormitory 2 is 35 away from candidate center 12.\nDormitory 2 is 45 away from candidate center 13.\nDormitory 2 is 37 away from candidate center 14.\nDormitory 3 is 29 away from candidate center 0.\nDormitory 3 is 29 away from candidate center 1.\nDormitory 3 is 41 away from candidate center 2.\nDormitory 3 is 21 away from candidate center 4.\nDormitory 3 is 49 away from candidate center 5.\nDormitory 3 is 37 away from candidate center 6.\nDormitory 3 is 35 away from candidate center 7.\nDormitory 3 is 15 away from candidate center 8.\nDormitory 3 is 43 away from candidate center 9.\nDormitory 3 is 26 away from candidate center 10.\nDormitory 3 is 37 away from candidate center 11.\nDormitory 3 is 19 away from candidate center 12.\nDormitory 3 is 33 away from candidate center 13.\nDormitory 3 is 35 away from candidate center 14.\nDormitory 4 is 36 away from candidate center 0.\nDormitory 4 is 32 away from candidate center 1.\nDormitory 4 is 32 away from candidate center 2.\nDormitory 4 is 21 away from candidate center 3.\nDormitory 4 is 54 away from candidate center 5.\nDormitory 4 is 34 away from candidate center 6.\nDormitory 4 is 36 away from candidate center 7.\nDormitory 4 is 26 away from candidate center 8.\nDormitory 4 is 48 away from candidate center 9.\nDormitory 4 is 29 away from candidate center 10.\nDormitory 4 is 47 away from candidate center 11.\nDormitory 4 is 31 away from candidate center 12.\nDormitory 4 is 34 away from candidate center 13.\nDormitory 4 is 39 away from candidate center 14.\nDormitory 5 is 48 away from candidate center 0.\nDormitory 5 is 42 away from candidate center 1.\nDormitory 5 is 55 away from candidate center 2.\nDormitory 5 is 49 away from candidate center 3.\nDormitory 5 is 54 away from candidate center 4.\nDormitory 5 is 62 away from candidate center 6.\nDormitory 5 is 53 away from candidate center 7.\nDormitory 5 is 42 away from candidate center 8.\nDormitory 5 is 61 away from candidate center 9.\nDormitory 5 is 42 away from candidate center 10.\nDormitory 5 is 69 away from candidate center 11.\nDormitory 5 is 59 away from candidate center 12.\nDormitory 5 is 55 away from candidate center 13.\nDormitory 5 is 58 away from candidate center 14.\nDormitory 6 is 35 away from candidate center 0.\nDormitory 6 is 40 away from candidate center 1.\nDormitory 6 is 42 away from candidate center 2.\nDormitory 6 is 37 away from candidate center 3.\nDormitory 6 is 34 away from candidate center 4.\nDormitory 6 is 62 away from candidate center 5.\nDormitory 6 is 38 away from candidate center 7.\nDormitory 6 is 30 away from candidate center 8.\nDormitory 6 is 48 away from candidate center 9.\nDormitory 6 is 40 away from candidate center 10.\nDormitory 6 is 52 away from candidate center 11.\nDormitory 6 is 44 away from candidate center 12.\nDormitory 6 is 47 away from candidate center 13.\nDormitory 6 is 45 away from candidate center 14.\nDormitory 7 is 37 away from candidate center 0.\nDormitory 7 is 40 away from candidate center 1.\nDormitory 7 is 42 away from candidate center 2.\nDormitory 7 is 35 away from candidate center 3.\nDormitory 7 is 36 away from candidate center 4.\nDormitory 7 is 53 away from candidate center 5.\nDormitory 7 is 38 away from candidate center 6.\nDormitory 7 is 28 away from candidate center 8.\nDormitory 7 is 49 away from candidate center 9.\nDormitory 7 is 28 away from candidate center 10.\nDormitory 7 is 50 away from candidate center 11.\nDormitory 7 is 35 away from candidate center 12.\nDormitory 7 is 36 away from candidate center 13.\nDormitory 7 is 26 away from candidate center 14.\nDormitory 8 is 33 away from candidate center 0.\nDormitory 8 is 27 away from candidate center 1.\nDormitory 8 is 27 away from candidate center 2.\nDormitory 8 is 15 away from candidate center 3.\nDormitory 8 is 26 away from candidate center 4.\nDormitory 8 is 42 away from candidate center 5.\nDormitory 8 is 30 away from candidate center 6.\nDormitory 8 is 28 away from candidate center 7.\nDormitory 8 is 36 away from candidate center 9.\nDormitory 8 is 11 away from candidate center 10.\nDormitory 8 is 43 away from candidate center 11.\nDormitory 8 is 32 away from candidate center 12.\nDormitory 8 is 35 away from candidate center 13.\nDormitory 8 is 20 away from candidate center 14.\nDormitory 9 is 45 away from candidate center 0.\nDormitory 9 is 45 away from candidate center 1.\nDormitory 9 is 52 away from candidate center 2.\nDormitory 9 is 43 away from candidate center 3.\nDormitory 9 is 48 away from candidate center 4.\nDormitory 9 is 61 away from candidate center 5.\nDormitory 9 is 48 away from candidate center 6.\nDormitory 9 is 49 away from candidate center 7.\nDormitory 9 is 36 away from candidate center 8.\nDormitory 9 is 33 away from candidate center 10.\nDormitory 9 is 55 away from candidate center 11.\nDormitory 9 is 40 away from candidate center 12.\nDormitory 9 is 49 away from candidate center 13.\nDormitory 9 is 47 away from candidate center 14.\nDormitory 10 is 26 away from candidate center 0.\nDormitory 10 is 26 away from candidate center 1.\nDormitory 10 is 35 away from candidate center 2.\nDormitory 10 is 26 away from candidate center 3.\nDormitory 10 is 29 away from candidate center 4.\nDormitory 10 is 42 away from candidate center 5.\nDormitory 10 is 40 away from candidate center 6.\nDormitory 10 is 28 away from candidate center 7.\nDormitory 10 is 11 away from candidate center 8.\nDormitory 10 is 33 away from candidate center 9.\nDormitory 10 is 39 away from candidate center 11.\nDormitory 10 is 32 away from candidate center 12.\nDormitory 10 is 30 away from candidate center 13.\nDormitory 10 is 27 away from candidate center 14.\nDormitory 11 is 48 away from candidate center 0.\nDormitory 11 is 38 away from candidate center 1.\nDormitory 11 is 53 away from candidate center 2.\nDormitory 11 is 37 away from candidate center 3.\nDormitory 11 is 47 away from candidate center 4.\nDormitory 11 is 69 away from candidate center 5.\nDormitory 11 is 52 away from candidate center 6.\nDormitory 11 is 50 away from candidate center 7.\nDormitory 11 is 43 away from candidate center 8.\nDormitory 11 is 55 away from candidate center 9.\nDormitory 11 is 39 away from candidate center 10.\nDormitory 11 is 52 away from candidate center 12.\nDormitory 11 is 52 away from candidate center 13.\nDormitory 11 is 54 away from candidate center 14.\nDormitory 12 is 30 away from candidate center 0.\nDormitory 12 is 36 away from candidate center 1.\nDormitory 12 is 35 away from candidate center 2.\nDormitory 12 is 19 away from candidate center 3.\nDormitory 12 is 31 away from candidate center 4.\nDormitory 12 is 59 away from candidate center 5.\nDormitory 12 is 44 away from candidate center 6.\nDormitory 12 is 35 away from candidate center 7.\nDormitory 12 is 32 away from candidate center 8.\nDormitory 12 is 40 away from candidate center 9.\nDormitory 12 is 32 away from candidate center 10.\nDormitory 12 is 52 away from candidate center 11.\nDormitory 12 is 37 away from candidate center 13.\nDormitory 12 is 46 away from candidate center 14.\nDormitory 13 is 36 away from candidate center 0.\nDormitory 13 is 36 away from candidate center 1.\nDormitory 13 is 45 away from candidate center 2.\nDormitory 13 is 33 away from candidate center 3.\nDormitory 13 is 34 away from candidate center 4.\nDormitory 13 is 55 away from candidate center 5.\nDormitory 13 is 47 away from candidate center 6.\nDormitory 13 is 36 away from candidate center 7.\nDormitory 13 is 35 away from candidate center 8.\nDormitory 13 is 49 away from candidate center 9.\nDormitory 13 is 30 away from candidate center 10.\nDormitory 13 is 52 away from candidate center 11.\nDormitory 13 is 37 away from candidate center 12.\nDormitory 13 is 36 away from candidate center 14.\nDormitory 14 is 32 away from candidate center 0.\nDormitory 14 is 43 away from candidate center 1.\nDormitory 14 is 37 away from candidate center 2.\nDormitory 14 is 35 away from candidate center 3.\nDormitory 14 is 39 away from candidate center 4.\nDormitory 14 is 58 away from candidate center 5.\nDormitory 14 is 45 away from candidate center 6.\nDormitory 14 is 26 away from candidate center 7.\nDormitory 14 is 20 away from candidate center 8.\nDormitory 14 is 47 away from candidate center 9.\nDormitory 14 is 27 away from candidate center 10.\nDormitory 14 is 54 away from candidate center 11.\nDormitory 14 is 46 away from candidate center 12.\nDormitory 14 is 36 away from candidate center 13.\nNo dormitory may be left unassigned or assigned to more than one center; assignments should minimize the total travel distance.\n\nOh, and when you send the answer back, keep it in this simple JSON shape so I can read it automatically:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nJust to explain, real quick: \"selected\" is where you list the locations you decide to open, and \"assignments\" lists, for each dorm (in the same order as the input), which open location that dorm is assigned to. Think of it like filling out a short form — which centers are open, and which center each dorm goes to. This block is just a sketch of the shape I need, not the actual solution.\n\nPlease use the exact identifiers from the instance input — don’t rename them or make up new labels. Valid identifiers look like:\n- plain numbers such as “1” or “23”\n- single capital letters like “A” or “B”\n- a capital letter followed by digits like “A1” or “X7”", "instance": { "distance_matrix": [ [ 0, 32, 36, 29, 36, 48, 35, 37, 33, 45, 26, 48, 30, 36, 32 ], [ 32, 0, 40, 29, 32, 42, 40, 40, 27, 45, 26, 38, 36, 36, 43 ], [ 36, 40, 0, 41, 32, 55, 42, 42, 27, 52, 35, 53, 35, 45, 37 ], [ 29, 29, 41, 0, 21, 49, 37, 35, 15, 43, 26, 37, 19, 33, 35 ], [ 36, 32, 32, 21, 0, 54, 34, 36, 26, 48, 29, 47, 31, 34, 39 ], [ 48, 42, 55, 49, 54, 0, 62, 53, 42, 61, 42, 69, 59, 55, 58 ], [ 35, 40, 42, 37, 34, 62, 0, 38, 30, 48, 40, 52, 44, 47, 45 ], [ 37, 40, 42, 35, 36, 53, 38, 0, 28, 49, 28, 50, 35, 36, 26 ], [ 33, 27, 27, 15, 26, 42, 30, 28, 0, 36, 11, 43, 32, 35, 20 ], [ 45, 45, 52, 43, 48, 61, 48, 49, 36, 0, 33, 55, 40, 49, 47 ], [ 26, 26, 35, 26, 29, 42, 40, 28, 11, 33, 0, 39, 32, 30, 27 ], [ 48, 38, 53, 37, 47, 69, 52, 50, 43, 55, 39, 0, 52, 52, 54 ], [ 30, 36, 35, 19, 31, 59, 44, 35, 32, 40, 32, 52, 0, 37, 46 ], [ 36, 36, 45, 33, 34, 55, 47, 36, 35, 49, 30, 52, 37, 0, 36 ], [ 32, 43, 37, 35, 39, 58, 45, 26, 20, 47, 27, 54, 46, 36, 0 ] ], "p": 3, "objective": 318.0 }, "solution": { "facilities": [ 3, 5, 8 ], "assignments": [ 3, 8, 8, 3, 3, 5, 8, 8, 8, 8, 8, 3, 3, 3, 8 ] }, "obj": 318.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 15, "num_open": 3, "sites": [ { "id": 0, "distances": { "0": 0, "1": 32, "2": 36, "3": 29, "4": 36, "5": 48, "6": 35, "7": 37, "8": 33, "9": 45, "10": 26, "11": 48, "12": 30, "13": 36, "14": 32 } }, { "id": 1, "distances": { "0": 32, "1": 0, "2": 40, "3": 29, "4": 32, "5": 42, "6": 40, "7": 40, "8": 27, "9": 45, "10": 26, "11": 38, "12": 36, "13": 36, "14": 43 } }, { "id": 2, "distances": { "0": 36, "1": 40, "2": 0, "3": 41, "4": 32, "5": 55, "6": 42, "7": 42, "8": 27, "9": 52, "10": 35, "11": 53, "12": 35, "13": 45, "14": 37 } }, { "id": 3, "distances": { "0": 29, "1": 29, "2": 41, "3": 0, "4": 21, "5": 49, "6": 37, "7": 35, "8": 15, "9": 43, "10": 26, "11": 37, "12": 19, "13": 33, "14": 35 } }, { "id": 4, "distances": { "0": 36, "1": 32, "2": 32, "3": 21, "4": 0, "5": 54, "6": 34, "7": 36, "8": 26, "9": 48, "10": 29, "11": 47, "12": 31, "13": 34, "14": 39 } }, { "id": 5, "distances": { "0": 48, "1": 42, "2": 55, "3": 49, "4": 54, "5": 0, "6": 62, "7": 53, "8": 42, "9": 61, "10": 42, "11": 69, "12": 59, "13": 55, "14": 58 } }, { "id": 6, "distances": { "0": 35, "1": 40, "2": 42, "3": 37, "4": 34, "5": 62, "6": 0, "7": 38, "8": 30, "9": 48, "10": 40, "11": 52, "12": 44, "13": 47, "14": 45 } }, { "id": 7, "distances": { "0": 37, "1": 40, "2": 42, "3": 35, "4": 36, "5": 53, "6": 38, "7": 0, "8": 28, "9": 49, "10": 28, "11": 50, "12": 35, "13": 36, "14": 26 } }, { "id": 8, "distances": { "0": 33, "1": 27, "2": 27, "3": 15, "4": 26, "5": 42, "6": 30, "7": 28, "8": 0, "9": 36, "10": 11, "11": 43, "12": 32, "13": 35, "14": 20 } }, { "id": 9, "distances": { "0": 45, "1": 45, "2": 52, "3": 43, "4": 48, "5": 61, "6": 48, "7": 49, "8": 36, "9": 0, "10": 33, "11": 55, "12": 40, "13": 49, "14": 47 } }, { "id": 10, "distances": { "0": 26, "1": 26, "2": 35, "3": 26, "4": 29, "5": 42, "6": 40, "7": 28, "8": 11, "9": 33, "10": 0, "11": 39, "12": 32, "13": 30, "14": 27 } }, { "id": 11, "distances": { "0": 48, "1": 38, "2": 53, "3": 37, "4": 47, "5": 69, "6": 52, "7": 50, "8": 43, "9": 55, "10": 39, "11": 0, "12": 52, "13": 52, "14": 54 } }, { "id": 12, "distances": { "0": 30, "1": 36, "2": 35, "3": 19, "4": 31, "5": 59, "6": 44, "7": 35, "8": 32, "9": 40, "10": 32, "11": 52, "12": 0, "13": 37, "14": 46 } }, { "id": 13, "distances": { "0": 36, "1": 36, "2": 45, "3": 33, "4": 34, "5": 55, "6": 47, "7": 36, "8": 35, "9": 49, "10": 30, "11": 52, "12": 37, "13": 0, "14": 36 } }, { "id": 14, "distances": { "0": 32, "1": 43, "2": 37, "3": 35, "4": 39, "5": 58, "6": 45, "7": 26, "8": 20, "9": 47, "10": 27, "11": 54, "12": 46, "13": 36, "14": 0 } } ], "objective": 318.0 }, "solution_variant": { "selected": [ 3, 5, 8 ], "assignments": [ 3, 8, 8, 3, 3, 5, 8, 8, 8, 8, 8, 3, 3, 3, 8 ] }, "context_index": 25, "input_format": "nl", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I run the small team that plans pickup points for a courier company, and the job is to pick a fixed number of hubs from a list of candidate spots and then link every delivery sector to one of those hubs. The idea is to keep the total driving as low as possible: for each sector, take the distance to the hub it's assigned to, add all those distances up, and the better plan is the one with the smallest total. Every sector has to be assigned to exactly one hub — no sector can be left out or be tied to two hubs. The exact list of candidate locations, sectors, and the distances between them are shown below.\n\nThere are 17 locations in total; I must open 6 hubs, and the location identifiers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.\nI record the travel distance from 1 to 2 as 61.\nI record the travel distance from 1 to 3 as 41.\nI record the travel distance from 1 to 4 as 61.\nI record the travel distance from 1 to 5 as 64.\nI record the travel distance from 1 to 6 as 46.\nI record the travel distance from 1 to 7 as 58.\nI record the travel distance from 1 to 8 as 8.\nI record the travel distance from 1 to 9 as 80.\nI record the travel distance from 1 to 10 as 62.\nI record the travel distance from 1 to 11 as 73.\nI record the travel distance from 1 to 12 as 82.\nI record the travel distance from 1 to 13 as 97.\nI record the travel distance from 1 to 14 as 6.\nI record the travel distance from 1 to 15 as 82.\nI record the travel distance from 1 to 16 as 42.\nI record the travel distance from 1 to 17 as 40.\nI record the travel distance from 2 to 1 as 61.\nI record the travel distance from 2 to 3 as 53.\nI record the travel distance from 2 to 4 as 23.\nI record the travel distance from 2 to 5 as 64.\nI record the travel distance from 2 to 6 as 53.\nI record the travel distance from 2 to 7 as 57.\nI record the travel distance from 2 to 8 as 61.\nI record the travel distance from 2 to 9 as 65.\nI record the travel distance from 2 to 10 as 26.\nI record the travel distance from 2 to 11 as 44.\nI record the travel distance from 2 to 12 as 74.\nI record the travel distance from 2 to 13 as 83.\nI record the travel distance from 2 to 14 as 59.\nI record the travel distance from 2 to 15 as 51.\nI record the travel distance from 2 to 16 as 55.\nI record the travel distance from 2 to 17 as 58.\nI record the travel distance from 3 to 1 as 41.\nI record the travel distance from 3 to 2 as 53.\nI record the travel distance from 3 to 4 as 30.\nI record the travel distance from 3 to 5 as 50.\nI record the travel distance from 3 to 6 as 56.\nI record the travel distance from 3 to 7 as 17.\nI record the travel distance from 3 to 8 as 33.\nI record the travel distance from 3 to 9 as 39.\nI record the travel distance from 3 to 10 as 40.\nI record the travel distance from 3 to 11 as 56.\nI record the travel distance from 3 to 12 as 88.\nI record the travel distance from 3 to 13 as 81.\nI record the travel distance from 3 to 14 as 39.\nI record the travel distance from 3 to 15 as 84.\nI record the travel distance from 3 to 16 as 60.\nI record the travel distance from 3 to 17 as 56.\nI record the travel distance from 4 to 1 as 61.\nI record the travel distance from 4 to 2 as 23.\nI record the travel distance from 4 to 3 as 30.\nI record the travel distance from 4 to 5 as 57.\nI record the travel distance from 4 to 6 as 45.\nI record the travel distance from 4 to 7 as 39.\nI record the travel distance from 4 to 8 as 53.\nI record the travel distance from 4 to 9 as 58.\nI record the travel distance from 4 to 10 as 29.\nI record the travel distance from 4 to 11 as 47.\nI record the travel distance from 4 to 12 as 75.\nI record the travel distance from 4 to 13 as 88.\nI record the travel distance from 4 to 14 as 59.\nI record the travel distance from 4 to 15 as 54.\nI record the travel distance from 4 to 16 as 47.\nI record the travel distance from 4 to 17 as 77.\nI record the travel distance from 5 to 1 as 64.\nI record the travel distance from 5 to 2 as 64.\nI record the travel distance from 5 to 3 as 50.\nI record the travel distance from 5 to 4 as 57.\nI record the travel distance from 5 to 6 as 48.\nI record the travel distance from 5 to 7 as 59.\nI record the travel distance from 5 to 8 as 56.\nI record the travel distance from 5 to 9 as 67.\nI record the travel distance from 5 to 10 as 41.\nI record the travel distance from 5 to 11 as 62.\nI record the travel distance from 5 to 12 as 78.\nI record the travel distance from 5 to 13 as 90.\nI record the travel distance from 5 to 14 as 62.\nI record the travel distance from 5 to 15 as 80.\nI record the travel distance from 5 to 16 as 50.\nI record the travel distance from 5 to 17 as 62.\nI record the travel distance from 6 to 1 as 46.\nI record the travel distance from 6 to 2 as 53.\nI record the travel distance from 6 to 3 as 56.\nI record the travel distance from 6 to 4 as 45.\nI record the travel distance from 6 to 5 as 48.\nI record the travel distance from 6 to 7 as 52.\nI record the travel distance from 6 to 8 as 38.\nI record the travel distance from 6 to 9 as 67.\nI record the travel distance from 6 to 10 as 51.\nI record the travel distance from 6 to 11 as 27.\nI record the travel distance from 6 to 12 as 66.\nI record the travel distance from 6 to 13 as 81.\nI record the travel distance from 6 to 14 as 44.\nI record the travel distance from 6 to 15 as 66.\nI record the travel distance from 6 to 16 as 32.\nI record the travel distance from 6 to 17 as 56.\nI record the travel distance from 7 to 1 as 58.\nI record the travel distance from 7 to 2 as 57.\nI record the travel distance from 7 to 3 as 17.\nI record the travel distance from 7 to 4 as 39.\nI record the travel distance from 7 to 5 as 59.\nI record the travel distance from 7 to 6 as 52.\nI record the travel distance from 7 to 8 as 50.\nI record the travel distance from 7 to 9 as 48.\nI record the travel distance from 7 to 10 as 49.\nI record the travel distance from 7 to 11 as 65.\nI record the travel distance from 7 to 12 as 88.\nI record the travel distance from 7 to 13 as 90.\nI record the travel distance from 7 to 14 as 56.\nI record the travel distance from 7 to 15 as 88.\nI record the travel distance from 7 to 16 as 54.\nI record the travel distance from 7 to 17 as 65.\nI record the travel distance from 8 to 1 as 8.\nI record the travel distance from 8 to 2 as 61.\nI record the travel distance from 8 to 3 as 33.\nI record the travel distance from 8 to 4 as 53.\nI record the travel distance from 8 to 5 as 56.\nI record the travel distance from 8 to 6 as 38.\nI record the travel distance from 8 to 7 as 50.\nI record the travel distance from 8 to 9 as 72.\nI record the travel distance from 8 to 10 as 59.\nI record the travel distance from 8 to 11 as 65.\nI record the travel distance from 8 to 12 as 74.\nI record the travel distance from 8 to 13 as 89.\nI record the travel distance from 8 to 14 as 6.\nI record the travel distance from 8 to 15 as 74.\nI record the travel distance from 8 to 16 as 34.\nI record the travel distance from 8 to 17 as 40.\nI record the travel distance from 9 to 1 as 80.\nI record the travel distance from 9 to 2 as 65.\nI record the travel distance from 9 to 3 as 39.\nI record the travel distance from 9 to 4 as 58.\nI record the travel distance from 9 to 5 as 67.\nI record the travel distance from 9 to 6 as 67.\nI record the travel distance from 9 to 7 as 48.\nI record the travel distance from 9 to 8 as 72.\nI record the travel distance from 9 to 10 as 45.\nI record the travel distance from 9 to 11 as 61.\nI record the travel distance from 9 to 12 as 101.\nI record the travel distance from 9 to 13 as 85.\nI record the travel distance from 9 to 14 as 78.\nI record the travel distance from 9 to 15 as 89.\nI record the travel distance from 9 to 16 as 73.\nI record the travel distance from 9 to 17 as 67.\nI record the travel distance from 10 to 1 as 62.\nI record the travel distance from 10 to 2 as 26.\nI record the travel distance from 10 to 3 as 40.\nI record the travel distance from 10 to 4 as 29.\nI record the travel distance from 10 to 5 as 41.\nI record the travel distance from 10 to 6 as 51.\nI record the travel distance from 10 to 7 as 49.\nI record the travel distance from 10 to 8 as 59.\nI record the travel distance from 10 to 9 as 45.\nI record the travel distance from 10 to 11 as 40.\nI record the travel distance from 10 to 12 as 70.\nI record the travel distance from 10 to 13 as 92.\nI record the travel distance from 10 to 14 as 59.\nI record the travel distance from 10 to 15 as 47.\nI record the travel distance from 10 to 16 as 53.\nI record the travel distance from 10 to 17 as 67.\nI record the travel distance from 11 to 1 as 73.\nI record the travel distance from 11 to 2 as 44.\nI record the travel distance from 11 to 3 as 56.\nI record the travel distance from 11 to 4 as 47.\nI record the travel distance from 11 to 5 as 62.\nI record the travel distance from 11 to 6 as 27.\nI record the travel distance from 11 to 7 as 65.\nI record the travel distance from 11 to 8 as 65.\nI record the travel distance from 11 to 9 as 61.\nI record the travel distance from 11 to 10 as 40.\nI record the travel distance from 11 to 12 as 81.\nI record the travel distance from 11 to 13 as 54.\nI record the travel distance from 11 to 14 as 71.\nI record the travel distance from 11 to 15 as 65.\nI record the travel distance from 11 to 16 as 59.\nI record the travel distance from 11 to 17 as 66.\nI record the travel distance from 12 to 1 as 82.\nI record the travel distance from 12 to 2 as 74.\nI record the travel distance from 12 to 3 as 88.\nI record the travel distance from 12 to 4 as 75.\nI record the travel distance from 12 to 5 as 78.\nI record the travel distance from 12 to 6 as 66.\nI record the travel distance from 12 to 7 as 88.\nI record the travel distance from 12 to 8 as 74.\nI record the travel distance from 12 to 9 as 101.\nI record the travel distance from 12 to 10 as 70.\nI record the travel distance from 12 to 11 as 81.\nI record the travel distance from 12 to 13 as 122.\nI record the travel distance from 12 to 14 as 80.\nI record the travel distance from 12 to 15 as 77.\nI record the travel distance from 12 to 16 as 68.\nI record the travel distance from 12 to 17 as 72.\nI record the travel distance from 13 to 1 as 97.\nI record the travel distance from 13 to 2 as 83.\nI record the travel distance from 13 to 3 as 81.\nI record the travel distance from 13 to 4 as 88.\nI record the travel distance from 13 to 5 as 90.\nI record the travel distance from 13 to 6 as 81.\nI record the travel distance from 13 to 7 as 90.\nI record the travel distance from 13 to 8 as 89.\nI record the travel distance from 13 to 9 as 85.\nI record the travel distance from 13 to 10 as 92.\nI record the travel distance from 13 to 11 as 54.\nI record the travel distance from 13 to 12 as 122.\nI record the travel distance from 13 to 14 as 92.\nI record the travel distance from 13 to 15 as 114.\nI record the travel distance from 13 to 16 as 92.\nI record the travel distance from 13 to 17 as 81.\nI record the travel distance from 14 to 1 as 6.\nI record the travel distance from 14 to 2 as 59.\nI record the travel distance from 14 to 3 as 39.\nI record the travel distance from 14 to 4 as 59.\nI record the travel distance from 14 to 5 as 62.\nI record the travel distance from 14 to 6 as 44.\nI record the travel distance from 14 to 7 as 56.\nI record the travel distance from 14 to 8 as 6.\nI record the travel distance from 14 to 9 as 78.\nI record the travel distance from 14 to 10 as 59.\nI record the travel distance from 14 to 11 as 71.\nI record the travel distance from 14 to 12 as 80.\nI record the travel distance from 14 to 13 as 92.\nI record the travel distance from 14 to 15 as 80.\nI record the travel distance from 14 to 16 as 40.\nI record the travel distance from 14 to 17 as 38.\nI record the travel distance from 15 to 1 as 82.\nI record the travel distance from 15 to 2 as 51.\nI record the travel distance from 15 to 3 as 84.\nI record the travel distance from 15 to 4 as 54.\nI record the travel distance from 15 to 5 as 80.\nI record the travel distance from 15 to 6 as 66.\nI record the travel distance from 15 to 7 as 88.\nI record the travel distance from 15 to 8 as 74.\nI record the travel distance from 15 to 9 as 89.\nI record the travel distance from 15 to 10 as 47.\nI record the travel distance from 15 to 11 as 65.\nI record the travel distance from 15 to 12 as 77.\nI record the travel distance from 15 to 13 as 114.\nI record the travel distance from 15 to 14 as 80.\nI record the travel distance from 15 to 16 as 68.\nI record the travel distance from 15 to 17 as 96.\nI record the travel distance from 16 to 1 as 42.\nI record the travel distance from 16 to 2 as 55.\nI record the travel distance from 16 to 3 as 60.\nI record the travel distance from 16 to 4 as 47.\nI record the travel distance from 16 to 5 as 50.\nI record the travel distance from 16 to 6 as 32.\nI record the travel distance from 16 to 7 as 54.\nI record the travel distance from 16 to 8 as 34.\nI record the travel distance from 16 to 9 as 73.\nI record the travel distance from 16 to 10 as 53.\nI record the travel distance from 16 to 11 as 59.\nI record the travel distance from 16 to 12 as 68.\nI record the travel distance from 16 to 13 as 92.\nI record the travel distance from 16 to 14 as 40.\nI record the travel distance from 16 to 15 as 68.\nI record the travel distance from 16 to 17 as 74.\nI record the travel distance from 17 to 1 as 40.\nI record the travel distance from 17 to 2 as 58.\nI record the travel distance from 17 to 3 as 56.\nI record the travel distance from 17 to 4 as 77.\nI record the travel distance from 17 to 5 as 62.\nI record the travel distance from 17 to 6 as 56.\nI record the travel distance from 17 to 7 as 65.\nI record the travel distance from 17 to 8 as 40.\nI record the travel distance from 17 to 9 as 67.\nI record the travel distance from 17 to 10 as 67.\nI record the travel distance from 17 to 11 as 66.\nI record the travel distance from 17 to 12 as 72.\nI record the travel distance from 17 to 13 as 81.\nI record the travel distance from 17 to 14 as 38.\nI record the travel distance from 17 to 15 as 96.\nI record the travel distance from 17 to 16 as 74.\nI'll use these distances to pick 6 hubs and assign every sector so total driving is minimized.\n\nAlso, when you send back a plan, please use this simple JSON layout so I can parse it easily — nothing fancy, just the shape below.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is just the list of hubs you choose to open. \"assignments\" is a list that, in the same order as the sectors in the input, says which opened hub each sector is linked to. Think of it like filling out a form: pick which spots are open, then for each sector write the open spot it's assigned to.\n\nThis JSON is only a sketch of the expected shape — not the actual answer. Also, all identifiers must be used exactly as they appear in the instance input — do not rename them or invent new labels.\n\n- Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 61, 41, 61, 64, 46, 58, 8, 80, 62, 73, 82, 97, 6, 82, 42, 40 ], [ 61, 0, 53, 23, 64, 53, 57, 61, 65, 26, 44, 74, 83, 59, 51, 55, 58 ], [ 41, 53, 0, 30, 50, 56, 17, 33, 39, 40, 56, 88, 81, 39, 84, 60, 56 ], [ 61, 23, 30, 0, 57, 45, 39, 53, 58, 29, 47, 75, 88, 59, 54, 47, 77 ], [ 64, 64, 50, 57, 0, 48, 59, 56, 67, 41, 62, 78, 90, 62, 80, 50, 62 ], [ 46, 53, 56, 45, 48, 0, 52, 38, 67, 51, 27, 66, 81, 44, 66, 32, 56 ], [ 58, 57, 17, 39, 59, 52, 0, 50, 48, 49, 65, 88, 90, 56, 88, 54, 65 ], [ 8, 61, 33, 53, 56, 38, 50, 0, 72, 59, 65, 74, 89, 6, 74, 34, 40 ], [ 80, 65, 39, 58, 67, 67, 48, 72, 0, 45, 61, 101, 85, 78, 89, 73, 67 ], [ 62, 26, 40, 29, 41, 51, 49, 59, 45, 0, 40, 70, 92, 59, 47, 53, 67 ], [ 73, 44, 56, 47, 62, 27, 65, 65, 61, 40, 0, 81, 54, 71, 65, 59, 66 ], [ 82, 74, 88, 75, 78, 66, 88, 74, 101, 70, 81, 0, 122, 80, 77, 68, 72 ], [ 97, 83, 81, 88, 90, 81, 90, 89, 85, 92, 54, 122, 0, 92, 114, 92, 81 ], [ 6, 59, 39, 59, 62, 44, 56, 6, 78, 59, 71, 80, 92, 0, 80, 40, 38 ], [ 82, 51, 84, 54, 80, 66, 88, 74, 89, 47, 65, 77, 114, 80, 0, 68, 96 ], [ 42, 55, 60, 47, 50, 32, 54, 34, 73, 53, 59, 68, 92, 40, 68, 0, 74 ], [ 40, 58, 56, 77, 62, 56, 65, 40, 67, 67, 66, 72, 81, 38, 96, 74, 0 ] ], "p": 6, "objective": 308.0 }, "solution": { "facilities": [ 2, 5, 9, 11, 12, 13 ], "assignments": [ 13, 9, 2, 9, 9, 5, 2, 13, 2, 9, 5, 11, 12, 13, 9, 5, 13 ] }, "obj": 308.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 6, "sites": [ { "id": 1, "distances": { "1": 0, "2": 61, "3": 41, "4": 61, "5": 64, "6": 46, "7": 58, "8": 8, "9": 80, "10": 62, "11": 73, "12": 82, "13": 97, "14": 6, "15": 82, "16": 42, "17": 40 } }, { "id": 2, "distances": { "1": 61, "2": 0, "3": 53, "4": 23, "5": 64, "6": 53, "7": 57, "8": 61, "9": 65, "10": 26, "11": 44, "12": 74, "13": 83, "14": 59, "15": 51, "16": 55, "17": 58 } }, { "id": 3, "distances": { "1": 41, "2": 53, "3": 0, "4": 30, "5": 50, "6": 56, "7": 17, "8": 33, "9": 39, "10": 40, "11": 56, "12": 88, "13": 81, "14": 39, "15": 84, "16": 60, "17": 56 } }, { "id": 4, "distances": { "1": 61, "2": 23, "3": 30, "4": 0, "5": 57, "6": 45, "7": 39, "8": 53, "9": 58, "10": 29, "11": 47, "12": 75, "13": 88, "14": 59, "15": 54, "16": 47, "17": 77 } }, { "id": 5, "distances": { "1": 64, "2": 64, "3": 50, "4": 57, "5": 0, "6": 48, "7": 59, "8": 56, "9": 67, "10": 41, "11": 62, "12": 78, "13": 90, "14": 62, "15": 80, "16": 50, "17": 62 } }, { "id": 6, "distances": { "1": 46, "2": 53, "3": 56, "4": 45, "5": 48, "6": 0, "7": 52, "8": 38, "9": 67, "10": 51, "11": 27, "12": 66, "13": 81, "14": 44, "15": 66, "16": 32, "17": 56 } }, { "id": 7, "distances": { "1": 58, "2": 57, "3": 17, "4": 39, "5": 59, "6": 52, "7": 0, "8": 50, "9": 48, "10": 49, "11": 65, "12": 88, "13": 90, "14": 56, "15": 88, "16": 54, "17": 65 } }, { "id": 8, "distances": { "1": 8, "2": 61, "3": 33, "4": 53, "5": 56, "6": 38, "7": 50, "8": 0, "9": 72, "10": 59, "11": 65, "12": 74, "13": 89, "14": 6, "15": 74, "16": 34, "17": 40 } }, { "id": 9, "distances": { "1": 80, "2": 65, "3": 39, "4": 58, "5": 67, "6": 67, "7": 48, "8": 72, "9": 0, "10": 45, "11": 61, "12": 101, "13": 85, "14": 78, "15": 89, "16": 73, "17": 67 } }, { "id": 10, "distances": { "1": 62, "2": 26, "3": 40, "4": 29, "5": 41, "6": 51, "7": 49, "8": 59, "9": 45, "10": 0, "11": 40, "12": 70, "13": 92, "14": 59, "15": 47, "16": 53, "17": 67 } }, { "id": 11, "distances": { "1": 73, "2": 44, "3": 56, "4": 47, "5": 62, "6": 27, "7": 65, "8": 65, "9": 61, "10": 40, "11": 0, "12": 81, "13": 54, "14": 71, "15": 65, "16": 59, "17": 66 } }, { "id": 12, "distances": { "1": 82, "2": 74, "3": 88, "4": 75, "5": 78, "6": 66, "7": 88, "8": 74, "9": 101, "10": 70, "11": 81, "12": 0, "13": 122, "14": 80, "15": 77, "16": 68, "17": 72 } }, { "id": 13, "distances": { "1": 97, "2": 83, "3": 81, "4": 88, "5": 90, "6": 81, "7": 90, "8": 89, "9": 85, "10": 92, "11": 54, "12": 122, "13": 0, "14": 92, "15": 114, "16": 92, "17": 81 } }, { "id": 14, "distances": { "1": 6, "2": 59, "3": 39, "4": 59, "5": 62, "6": 44, "7": 56, "8": 6, "9": 78, "10": 59, "11": 71, "12": 80, "13": 92, "14": 0, "15": 80, "16": 40, "17": 38 } }, { "id": 15, "distances": { "1": 82, "2": 51, "3": 84, "4": 54, "5": 80, "6": 66, "7": 88, "8": 74, "9": 89, "10": 47, "11": 65, "12": 77, "13": 114, "14": 80, "15": 0, "16": 68, "17": 96 } }, { "id": 16, "distances": { "1": 42, "2": 55, "3": 60, "4": 47, "5": 50, "6": 32, "7": 54, "8": 34, "9": 73, "10": 53, "11": 59, "12": 68, "13": 92, "14": 40, "15": 68, "16": 0, "17": 74 } }, { "id": 17, "distances": { "1": 40, "2": 58, "3": 56, "4": 77, "5": 62, "6": 56, "7": 65, "8": 40, "9": 67, "10": 67, "11": 66, "12": 72, "13": 81, "14": 38, "15": 96, "16": 74, "17": 0 } } ], "objective": 308.0 }, "solution_variant": { "selected": [ 3, 6, 10, 12, 13, 14 ], "assignments": [ 14, 10, 3, 10, 10, 6, 3, 14, 3, 10, 6, 12, 13, 14, 10, 6, 14 ] }, "context_index": 26, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I run the little farmer’s market and need to pick a fixed number of support tents to set up around the stalls. Each vendor has to be linked to one—and only one—of those tents, and the better setup is the one where, if you add up how far every vendor has to walk to their assigned tent, that total is as small as possible. No vendor can be left without a tent or assigned to two tents. The concrete list of stall spots and the distances between them will be shown below.\n\n{\n \"num_stalls\": 19,\n \"num_tents_to_open\": 4,\n \"stall_ids\": [\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16,\n 17,\n 18,\n 19\n ],\n \"data\": [\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 2,\n \"walking_distance\": 38\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 3,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 4,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 5,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 6,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 7,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 8,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 9,\n \"walking_distance\": 25\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 10,\n \"walking_distance\": 34\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 11,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 12,\n \"walking_distance\": 27\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 13,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 14,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 15,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 16,\n \"walking_distance\": 48\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 17,\n \"walking_distance\": 40\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 18,\n \"walking_distance\": 22\n },\n {\n \"source_stall_id\": 1,\n \"target_stall_id\": 19,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 1,\n \"walking_distance\": 38\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 3,\n \"walking_distance\": 26\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 4,\n \"walking_distance\": 34\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 5,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 6,\n \"walking_distance\": 15\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 7,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 8,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 9,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 10,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 11,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 12,\n \"walking_distance\": 27\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 13,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 14,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 15,\n \"walking_distance\": 18\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 16,\n \"walking_distance\": 45\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 17,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 18,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 2,\n \"target_stall_id\": 19,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 1,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 2,\n \"walking_distance\": 26\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 4,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 5,\n \"walking_distance\": 24\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 6,\n \"walking_distance\": 19\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 7,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 8,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 9,\n \"walking_distance\": 21\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 10,\n \"walking_distance\": 27\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 11,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 12,\n \"walking_distance\": 29\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 13,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 14,\n \"walking_distance\": 38\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 15,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 16,\n \"walking_distance\": 49\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 17,\n \"walking_distance\": 40\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 18,\n \"walking_distance\": 29\n },\n {\n \"source_stall_id\": 3,\n \"target_stall_id\": 19,\n \"walking_distance\": 20\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 1,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 2,\n \"walking_distance\": 34\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 3,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 5,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 6,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 7,\n \"walking_distance\": 25\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 8,\n \"walking_distance\": 29\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 9,\n \"walking_distance\": 25\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 10,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 11,\n \"walking_distance\": 26\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 12,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 13,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 14,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 15,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 16,\n \"walking_distance\": 50\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 17,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 18,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 4,\n \"target_stall_id\": 19,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 1,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 2,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 3,\n \"walking_distance\": 24\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 4,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 6,\n \"walking_distance\": 21\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 7,\n \"walking_distance\": 28\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 8,\n \"walking_distance\": 18\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 9,\n \"walking_distance\": 26\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 10,\n \"walking_distance\": 26\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 11,\n \"walking_distance\": 27\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 12,\n \"walking_distance\": 24\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 13,\n \"walking_distance\": 26\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 14,\n \"walking_distance\": 39\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 15,\n \"walking_distance\": 27\n },\n {\n \"source_stall_id\": 5,\n \"target_stall_id\": 16,\n 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\"target_stall_id\": 3,\n \"walking_distance\": 29\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 4,\n \"walking_distance\": 30\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 5,\n \"walking_distance\": 20\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 6,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 7,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 8,\n \"walking_distance\": 24\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 9,\n \"walking_distance\": 14\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 10,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 11,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 12,\n \"walking_distance\": 19\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 13,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 14,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 15,\n \"walking_distance\": 18\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 16,\n \"walking_distance\": 46\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 17,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 18,\n \"target_stall_id\": 19,\n \"walking_distance\": 24\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 1,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 2,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 3,\n \"walking_distance\": 20\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 4,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 5,\n \"walking_distance\": 29\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 6,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 7,\n \"walking_distance\": 31\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 8,\n \"walking_distance\": 25\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 9,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 10,\n \"walking_distance\": 22\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 11,\n \"walking_distance\": 32\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 12,\n \"walking_distance\": 15\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 13,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 14,\n \"walking_distance\": 37\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 15,\n \"walking_distance\": 22\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 16,\n \"walking_distance\": 36\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 17,\n \"walking_distance\": 33\n },\n {\n \"source_stall_id\": 19,\n \"target_stall_id\": 18,\n \"walking_distance\": 24\n }\n ]\n}\n\nOh, and when you send the answer back, please stick to this JSON layout so it's easy to read and parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list which tent spots you'll actually set up. \"assignments\" is a one-to-one list (in the same order as the stall spots in the instance) saying which tent each vendor is linked to. Super informal sketch — this is the shape I need, not the final picks.\n\nQuick reminder: use the exact identifiers from the instance input — do not rename them or invent new ones. Valid identifiers look like:\n- plain numbers such as \"1\" or \"23\"\n- single capital letters like \"A\" or \"B\"\n- a capital letter followed by digits like \"A1\" or \"X7\"", "instance": { "distance_matrix": [ [ 0, 38, 28, 30, 28, 31, 32, 32, 25, 34, 31, 27, 36, 33, 36, 48, 40, 22, 32 ], [ 38, 0, 26, 34, 32, 15, 32, 28, 31, 36, 31, 27, 36, 36, 18, 45, 37, 30, 32 ], [ 28, 26, 0, 37, 24, 19, 36, 31, 21, 27, 37, 29, 31, 38, 32, 49, 40, 29, 20 ], [ 30, 34, 37, 0, 30, 37, 25, 29, 25, 33, 26, 30, 37, 37, 28, 50, 37, 30, 32 ], [ 28, 32, 24, 30, 0, 21, 28, 18, 26, 26, 27, 24, 26, 39, 27, 40, 43, 20, 29 ], [ 31, 15, 19, 37, 21, 0, 34, 29, 34, 29, 35, 33, 37, 27, 33, 51, 31, 31, 33 ], [ 32, 32, 36, 25, 28, 34, 0, 36, 31, 30, 1, 32, 43, 40, 36, 38, 36, 32, 31 ], [ 32, 28, 31, 29, 18, 29, 36, 0, 26, 34, 35, 19, 22, 38, 30, 30, 28, 24, 25 ], [ 25, 31, 21, 25, 26, 34, 31, 26, 0, 27, 32, 21, 37, 35, 21, 44, 32, 14, 32 ], [ 34, 36, 27, 33, 26, 29, 30, 34, 27, 0, 31, 30, 41, 38, 34, 44, 34, 33, 22 ], [ 31, 31, 37, 26, 27, 35, 1, 35, 32, 31, 0, 33, 43, 41, 37, 39, 37, 33, 32 ], [ 27, 27, 29, 30, 24, 33, 32, 19, 21, 30, 33, 0, 28, 34, 20, 31, 29, 19, 15 ], [ 36, 36, 31, 37, 26, 37, 43, 22, 37, 41, 43, 28, 0, 43, 38, 46, 47, 32, 33 ], [ 33, 36, 38, 37, 39, 27, 40, 38, 35, 38, 41, 34, 43, 0, 41, 53, 42, 31, 37 ], [ 36, 18, 32, 28, 27, 33, 36, 30, 21, 34, 37, 20, 38, 41, 0, 34, 35, 18, 22 ], [ 48, 45, 49, 50, 40, 51, 38, 30, 44, 44, 39, 31, 46, 53, 34, 0, 46, 46, 36 ], [ 40, 37, 40, 37, 43, 31, 36, 28, 32, 34, 37, 29, 47, 42, 35, 46, 0, 31, 33 ], [ 22, 30, 29, 30, 20, 31, 32, 24, 14, 33, 33, 19, 32, 31, 18, 46, 31, 0, 24 ], [ 32, 32, 20, 32, 29, 33, 31, 25, 32, 22, 32, 15, 33, 37, 22, 36, 33, 24, 0 ] ], "p": 4, "objective": 311.0 }, "solution": { "facilities": [ 5, 6, 7, 17 ], "assignments": [ 17, 5, 5, 6, 7, 5, 6, 7, 17, 5, 6, 7, 7, 5, 17, 7, 7, 17, 17 ] }, "obj": 311.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 4, "sites": [ { "id": 1, "distances": { "1": 0, "2": 38, "3": 28, "4": 30, "5": 28, "6": 31, "7": 32, "8": 32, "9": 25, "10": 34, "11": 31, "12": 27, "13": 36, "14": 33, "15": 36, "16": 48, "17": 40, "18": 22, "19": 32 } }, { "id": 2, "distances": { "1": 38, "2": 0, "3": 26, "4": 34, "5": 32, "6": 15, "7": 32, "8": 28, "9": 31, "10": 36, "11": 31, "12": 27, "13": 36, "14": 36, "15": 18, "16": 45, "17": 37, "18": 30, "19": 32 } }, { "id": 3, "distances": { "1": 28, "2": 26, "3": 0, "4": 37, "5": 24, "6": 19, "7": 36, "8": 31, "9": 21, "10": 27, "11": 37, "12": 29, "13": 31, "14": 38, "15": 32, "16": 49, "17": 40, "18": 29, "19": 20 } }, { "id": 4, "distances": { "1": 30, "2": 34, "3": 37, "4": 0, "5": 30, "6": 37, "7": 25, "8": 29, "9": 25, "10": 33, "11": 26, "12": 30, "13": 37, "14": 37, "15": 28, "16": 50, "17": 37, "18": 30, "19": 32 } }, { "id": 5, "distances": { "1": 28, "2": 32, "3": 24, "4": 30, "5": 0, "6": 21, "7": 28, "8": 18, "9": 26, "10": 26, "11": 27, "12": 24, "13": 26, "14": 39, "15": 27, "16": 40, "17": 43, "18": 20, "19": 29 } }, { "id": 6, "distances": { "1": 31, "2": 15, "3": 19, "4": 37, "5": 21, "6": 0, "7": 34, "8": 29, "9": 34, "10": 29, "11": 35, "12": 33, "13": 37, "14": 27, "15": 33, "16": 51, "17": 31, "18": 31, "19": 33 } }, { "id": 7, "distances": { "1": 32, "2": 32, "3": 36, "4": 25, "5": 28, "6": 34, "7": 0, "8": 36, "9": 31, "10": 30, "11": 1, "12": 32, "13": 43, "14": 40, "15": 36, "16": 38, "17": 36, "18": 32, "19": 31 } }, { "id": 8, "distances": { "1": 32, "2": 28, "3": 31, "4": 29, "5": 18, "6": 29, "7": 36, "8": 0, "9": 26, "10": 34, "11": 35, "12": 19, "13": 22, "14": 38, "15": 30, "16": 30, "17": 28, "18": 24, "19": 25 } }, { "id": 9, "distances": { "1": 25, "2": 31, "3": 21, "4": 25, "5": 26, "6": 34, "7": 31, "8": 26, "9": 0, "10": 27, "11": 32, "12": 21, "13": 37, "14": 35, "15": 21, "16": 44, "17": 32, "18": 14, "19": 32 } }, { "id": 10, "distances": { "1": 34, "2": 36, "3": 27, "4": 33, "5": 26, "6": 29, "7": 30, "8": 34, "9": 27, "10": 0, "11": 31, "12": 30, "13": 41, "14": 38, "15": 34, "16": 44, "17": 34, "18": 33, "19": 22 } }, { "id": 11, "distances": { "1": 31, "2": 31, "3": 37, "4": 26, "5": 27, "6": 35, "7": 1, "8": 35, "9": 32, "10": 31, "11": 0, "12": 33, "13": 43, "14": 41, "15": 37, "16": 39, "17": 37, "18": 33, "19": 32 } }, { "id": 12, "distances": { "1": 27, "2": 27, "3": 29, "4": 30, "5": 24, "6": 33, "7": 32, "8": 19, "9": 21, "10": 30, "11": 33, "12": 0, "13": 28, "14": 34, "15": 20, "16": 31, "17": 29, "18": 19, "19": 15 } }, { "id": 13, "distances": { "1": 36, "2": 36, "3": 31, "4": 37, "5": 26, "6": 37, "7": 43, "8": 22, "9": 37, "10": 41, "11": 43, "12": 28, "13": 0, "14": 43, "15": 38, "16": 46, "17": 47, "18": 32, "19": 33 } }, { "id": 14, "distances": { "1": 33, "2": 36, "3": 38, "4": 37, "5": 39, "6": 27, "7": 40, "8": 38, "9": 35, "10": 38, "11": 41, "12": 34, "13": 43, "14": 0, "15": 41, "16": 53, "17": 42, "18": 31, "19": 37 } }, { "id": 15, "distances": { "1": 36, "2": 18, "3": 32, "4": 28, "5": 27, "6": 33, "7": 36, "8": 30, "9": 21, "10": 34, "11": 37, "12": 20, "13": 38, "14": 41, "15": 0, "16": 34, "17": 35, "18": 18, "19": 22 } }, { "id": 16, "distances": { "1": 48, "2": 45, "3": 49, "4": 50, "5": 40, "6": 51, "7": 38, "8": 30, "9": 44, "10": 44, "11": 39, "12": 31, "13": 46, "14": 53, "15": 34, "16": 0, "17": 46, "18": 46, "19": 36 } }, { "id": 17, "distances": { "1": 40, "2": 37, "3": 40, "4": 37, "5": 43, "6": 31, "7": 36, "8": 28, "9": 32, "10": 34, "11": 37, "12": 29, "13": 47, "14": 42, "15": 35, "16": 46, "17": 0, "18": 31, "19": 33 } }, { "id": 18, "distances": { "1": 22, "2": 30, "3": 29, "4": 30, "5": 20, "6": 31, "7": 32, "8": 24, "9": 14, "10": 33, "11": 33, "12": 19, "13": 32, "14": 31, "15": 18, "16": 46, "17": 31, "18": 0, "19": 24 } }, { "id": 19, "distances": { "1": 32, "2": 32, "3": 20, "4": 32, "5": 29, "6": 33, "7": 31, "8": 25, "9": 32, "10": 22, "11": 32, "12": 15, "13": 33, "14": 37, "15": 22, "16": 36, "17": 33, "18": 24, "19": 0 } } ], "objective": 311.0 }, "solution_variant": { "selected": [ 6, 7, 8, 18 ], "assignments": [ 18, 6, 6, 7, 8, 6, 7, 8, 18, 6, 7, 8, 8, 6, 18, 8, 8, 18, 18 ] }, "context_index": 27, "input_format": "json", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Many people are waiting for supplies, so the plan is to pick a set number of distribution centers and link each neighborhood to one center for pickups. Nothing can be left unassigned and no neighborhood should be assigned to more than one center, and the aim is to minimize how far people in total must go. You judge each plan by summing up the distance from every neighborhood to its chosen center — the smallest sum means the least overall travel. The precise neighborhood list, candidate centers, and distances are shown below.\n\n{\n \"total_candidate_locations\": 20,\n \"centers_to_open\": 7,\n \"location_identifiers\": [\n \"A\",\n \"B\",\n \"C\",\n \"D\",\n \"E\",\n \"F\",\n \"G\",\n \"H\",\n \"I\",\n \"J\",\n \"K\",\n \"L\",\n \"M\",\n \"N\",\n \"O\",\n \"P\",\n \"Q\",\n \"R\",\n \"S\",\n \"T\"\n ],\n \"data\": [\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 17\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 24\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 47\n },\n {\n \"origin_location_id\": \"A\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 16\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 22\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 38\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 50\n },\n {\n \"origin_location_id\": \"B\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 22\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 15\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 24\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 54\n },\n {\n \"origin_location_id\": \"C\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 16\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 24\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 18\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"D\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 25\n },\n {\n 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\"destination_location_id\": \"B\",\n \"travel_distance\": 38\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"N\",\n \"destination_location_id\": \"K\",\n 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\"origin_location_id\": \"O\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 19\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 4\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": \"O\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 27\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 15\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 3\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 24\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 24\n },\n {\n \"origin_location_id\": \"P\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 25\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 36\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 29\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": \"Q\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 28\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 33\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 26\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 45\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 37\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 63\n },\n {\n \"origin_location_id\": \"R\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 47\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 50\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 54\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 49\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 54\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 50\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 21\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 60\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 52\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 59\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 50\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 48\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 46\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 24\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 63\n },\n {\n \"origin_location_id\": \"S\",\n \"destination_location_id\": \"T\",\n \"travel_distance\": 56\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"A\",\n \"travel_distance\": 31\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"B\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"C\",\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"D\",\n \"travel_distance\": 38\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"E\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"F\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"G\",\n \"travel_distance\": 40\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"H\",\n \"travel_distance\": 41\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"I\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"J\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"K\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"L\",\n \"travel_distance\": 44\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"M\",\n \"travel_distance\": 32\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"N\",\n \"travel_distance\": 30\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"O\",\n \"travel_distance\": 34\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"P\",\n \"travel_distance\": 39\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"Q\",\n \"travel_distance\": 35\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"R\",\n \"travel_distance\": 42\n },\n {\n \"origin_location_id\": \"T\",\n \"destination_location_id\": \"S\",\n \"travel_distance\": 56\n }\n ]\n}\n\nAlso, when you send back the plan, just stick to a simple JSON shape so it's easy to parse and check. Something like this is perfect:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of locations you'll open as distribution points. \"assignments\" is a list that, in the same order as the neighborhoods in the instance, says which opened location each neighborhood is assigned to. Think of the JSON as a quick form: which sites are active, and for every neighborhood which active site it should go to. It's just a sketch of the shape I need, not your final answer.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or invent new ones. \n- Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 28, 25, 30, 32, 28, 30, 28, 17, 31, 24, 31, 35, 32, 31, 27, 32, 35, 47, 31 ], [ 28, 0, 25, 16, 34, 22, 27, 29, 36, 27, 30, 46, 32, 38, 27, 31, 33, 26, 50, 35 ], [ 25, 25, 0, 39, 22, 35, 15, 33, 32, 30, 24, 42, 31, 37, 30, 34, 37, 28, 54, 44 ], [ 30, 16, 39, 0, 31, 35, 24, 18, 35, 29, 37, 40, 40, 39, 25, 15, 37, 32, 39, 38 ], [ 32, 34, 22, 31, 0, 31, 7, 28, 24, 31, 29, 44, 40, 41, 27, 31, 35, 40, 49, 35 ], [ 28, 22, 35, 35, 31, 0, 37, 33, 43, 38, 16, 49, 36, 35, 39, 30, 39, 37, 54, 34 ], [ 30, 27, 15, 24, 7, 37, 0, 29, 17, 29, 36, 37, 33, 36, 29, 31, 34, 33, 50, 40 ], [ 28, 29, 33, 18, 28, 33, 29, 0, 39, 21, 35, 41, 32, 27, 25, 3, 35, 45, 21, 41 ], [ 17, 36, 32, 35, 24, 43, 17, 39, 0, 19, 41, 35, 38, 41, 19, 36, 35, 31, 60, 39 ], [ 31, 27, 30, 29, 31, 38, 29, 21, 19, 0, 32, 31, 29, 35, 4, 24, 25, 26, 42, 34 ], [ 24, 30, 24, 37, 29, 16, 36, 35, 41, 32, 0, 47, 34, 33, 36, 32, 37, 45, 52, 32 ], [ 31, 46, 42, 40, 44, 49, 37, 41, 35, 31, 47, 0, 38, 14, 27, 44, 42, 40, 59, 44 ], [ 35, 32, 31, 40, 40, 36, 33, 32, 38, 29, 34, 38, 0, 27, 29, 35, 37, 33, 50, 32 ], [ 32, 38, 37, 39, 41, 35, 36, 27, 41, 35, 33, 14, 27, 0, 35, 30, 36, 42, 48, 30 ], [ 31, 27, 30, 25, 27, 39, 29, 25, 19, 4, 36, 27, 29, 35, 0, 28, 29, 26, 46, 34 ], [ 27, 31, 34, 15, 31, 30, 31, 3, 36, 24, 32, 44, 35, 30, 28, 0, 32, 45, 24, 39 ], [ 32, 33, 37, 37, 35, 39, 34, 35, 35, 25, 37, 42, 37, 36, 29, 32, 0, 37, 56, 35 ], [ 35, 26, 28, 32, 40, 37, 33, 45, 31, 26, 45, 40, 33, 42, 26, 45, 37, 0, 63, 42 ], [ 47, 50, 54, 39, 49, 54, 50, 21, 60, 42, 52, 59, 50, 48, 46, 24, 56, 63, 0, 56 ], [ 31, 35, 44, 38, 35, 34, 40, 41, 39, 34, 32, 44, 32, 30, 34, 39, 35, 42, 56, 0 ] ], "p": 7, "objective": 215.0 }, "solution": { "facilities": [ 5, 6, 9, 11, 12, 15, 19 ], "assignments": [ 15, 5, 6, 15, 6, 5, 6, 15, 6, 9, 5, 11, 12, 11, 9, 15, 9, 9, 15, 19 ] }, "obj": 215.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 7, "sites": [ { "id": "A", "distances": { "A": 0, "B": 28, "C": 25, "D": 30, "E": 32, "F": 28, "G": 30, "H": 28, "I": 17, "J": 31, "K": 24, "L": 31, "M": 35, "N": 32, "O": 31, "P": 27, "Q": 32, "R": 35, "S": 47, "T": 31 } }, { "id": "B", "distances": { "A": 28, "B": 0, "C": 25, "D": 16, "E": 34, "F": 22, "G": 27, "H": 29, "I": 36, "J": 27, "K": 30, "L": 46, "M": 32, "N": 38, "O": 27, "P": 31, "Q": 33, "R": 26, "S": 50, "T": 35 } }, { "id": "C", "distances": { "A": 25, "B": 25, "C": 0, "D": 39, "E": 22, "F": 35, "G": 15, "H": 33, "I": 32, "J": 30, "K": 24, "L": 42, "M": 31, "N": 37, "O": 30, "P": 34, "Q": 37, "R": 28, "S": 54, "T": 44 } }, { "id": "D", "distances": { "A": 30, "B": 16, "C": 39, "D": 0, "E": 31, "F": 35, "G": 24, "H": 18, "I": 35, "J": 29, "K": 37, "L": 40, "M": 40, "N": 39, "O": 25, "P": 15, "Q": 37, "R": 32, "S": 39, "T": 38 } }, { "id": "E", "distances": { "A": 32, "B": 34, "C": 22, "D": 31, "E": 0, "F": 31, "G": 7, "H": 28, "I": 24, "J": 31, "K": 29, "L": 44, "M": 40, "N": 41, "O": 27, "P": 31, "Q": 35, "R": 40, "S": 49, "T": 35 } }, { "id": "F", "distances": { "A": 28, "B": 22, "C": 35, "D": 35, "E": 31, "F": 0, "G": 37, "H": 33, "I": 43, "J": 38, "K": 16, "L": 49, "M": 36, "N": 35, "O": 39, "P": 30, "Q": 39, "R": 37, "S": 54, "T": 34 } }, { "id": "G", "distances": { "A": 30, "B": 27, "C": 15, "D": 24, "E": 7, "F": 37, "G": 0, "H": 29, "I": 17, "J": 29, "K": 36, "L": 37, "M": 33, "N": 36, "O": 29, "P": 31, "Q": 34, "R": 33, "S": 50, "T": 40 } }, { "id": "H", "distances": { "A": 28, "B": 29, "C": 33, "D": 18, "E": 28, "F": 33, "G": 29, "H": 0, "I": 39, "J": 21, "K": 35, "L": 41, "M": 32, "N": 27, "O": 25, "P": 3, "Q": 35, "R": 45, "S": 21, "T": 41 } }, { "id": "I", "distances": { "A": 17, "B": 36, "C": 32, "D": 35, "E": 24, "F": 43, "G": 17, "H": 39, "I": 0, "J": 19, "K": 41, "L": 35, "M": 38, "N": 41, "O": 19, "P": 36, "Q": 35, "R": 31, "S": 60, "T": 39 } }, { "id": "J", "distances": { "A": 31, "B": 27, "C": 30, "D": 29, "E": 31, "F": 38, "G": 29, "H": 21, "I": 19, "J": 0, "K": 32, "L": 31, "M": 29, "N": 35, "O": 4, "P": 24, "Q": 25, "R": 26, "S": 42, "T": 34 } }, { "id": "K", "distances": { "A": 24, "B": 30, "C": 24, "D": 37, "E": 29, "F": 16, "G": 36, "H": 35, "I": 41, "J": 32, "K": 0, "L": 47, "M": 34, "N": 33, "O": 36, "P": 32, "Q": 37, "R": 45, "S": 52, "T": 32 } }, { "id": "L", "distances": { "A": 31, "B": 46, "C": 42, "D": 40, "E": 44, "F": 49, "G": 37, "H": 41, "I": 35, "J": 31, "K": 47, "L": 0, "M": 38, "N": 14, "O": 27, "P": 44, "Q": 42, "R": 40, "S": 59, "T": 44 } }, { "id": "M", "distances": { "A": 35, "B": 32, "C": 31, "D": 40, "E": 40, "F": 36, "G": 33, "H": 32, "I": 38, "J": 29, "K": 34, "L": 38, "M": 0, "N": 27, "O": 29, "P": 35, "Q": 37, "R": 33, "S": 50, "T": 32 } }, { "id": "N", "distances": { "A": 32, "B": 38, "C": 37, "D": 39, "E": 41, "F": 35, "G": 36, "H": 27, "I": 41, "J": 35, "K": 33, "L": 14, "M": 27, "N": 0, "O": 35, "P": 30, "Q": 36, "R": 42, "S": 48, "T": 30 } }, { "id": "O", "distances": { "A": 31, "B": 27, "C": 30, "D": 25, "E": 27, "F": 39, "G": 29, "H": 25, "I": 19, "J": 4, "K": 36, "L": 27, "M": 29, "N": 35, "O": 0, "P": 28, "Q": 29, "R": 26, "S": 46, "T": 34 } }, { "id": "P", "distances": { "A": 27, "B": 31, "C": 34, "D": 15, "E": 31, "F": 30, "G": 31, "H": 3, "I": 36, "J": 24, "K": 32, "L": 44, "M": 35, "N": 30, "O": 28, "P": 0, "Q": 32, "R": 45, "S": 24, "T": 39 } }, { "id": "Q", "distances": { "A": 32, "B": 33, "C": 37, "D": 37, "E": 35, "F": 39, "G": 34, "H": 35, "I": 35, "J": 25, "K": 37, "L": 42, "M": 37, "N": 36, "O": 29, "P": 32, "Q": 0, "R": 37, "S": 56, "T": 35 } }, { "id": "R", "distances": { "A": 35, "B": 26, "C": 28, "D": 32, "E": 40, "F": 37, "G": 33, "H": 45, "I": 31, "J": 26, "K": 45, "L": 40, "M": 33, "N": 42, "O": 26, "P": 45, "Q": 37, "R": 0, "S": 63, "T": 42 } }, { "id": "S", "distances": { "A": 47, "B": 50, "C": 54, "D": 39, "E": 49, "F": 54, "G": 50, "H": 21, "I": 60, "J": 42, "K": 52, "L": 59, "M": 50, "N": 48, "O": 46, "P": 24, "Q": 56, "R": 63, "S": 0, "T": 56 } }, { "id": "T", "distances": { "A": 31, "B": 35, "C": 44, "D": 38, "E": 35, "F": 34, "G": 40, "H": 41, "I": 39, "J": 34, "K": 32, "L": 44, "M": 32, "N": 30, "O": 34, "P": 39, "Q": 35, "R": 42, "S": 56, "T": 0 } } ], "objective": 215.0 }, "solution_variant": { "selected": [ "F", "G", "J", "L", "M", "P", "T" ], "assignments": [ "P", "F", "G", "P", "G", "F", "G", "P", "G", "J", "F", "L", "M", "L", "J", "P", "J", "J", "P", "T" ] }, "context_index": 28, "input_format": "json", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Picture this: a few satellite offices need to be opened, and the task is picking which candidate sites to activate and then pairing every team location with one of those open sites. Every team must be assigned to a single opened office — no team unassigned and no double assignments. Judging plans is easy in practice: add up each location’s distance to its assigned office and prefer the arrangement with the smaller total commute. The detailed locations and the distances between them are shown below.\n\nThere are 19 candidate locations; open exactly 4 satellite offices, and the location identifiers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.\nAssign team location 1 to candidate office 2 with commute distance 38.\nAssign team location 1 to candidate office 3 with commute distance 33.\nAssign team location 1 to candidate office 4 with commute distance 38.\nAssign team location 1 to candidate office 5 with commute distance 42.\nAssign team location 1 to candidate office 6 with commute distance 42.\nAssign team location 1 to candidate office 7 with commute distance 35.\nAssign team location 1 to candidate office 8 with commute distance 40.\nAssign team location 1 to candidate office 9 with commute distance 31.\nAssign team location 1 to candidate office 10 with commute distance 25.\nAssign team location 1 to candidate office 11 with commute distance 45.\nAssign team location 1 to candidate office 12 with commute distance 36.\nAssign team location 1 to candidate office 13 with commute distance 42.\nAssign team location 1 to candidate office 14 with commute distance 51.\nAssign team location 1 to candidate office 15 with commute distance 17.\nAssign team location 1 to candidate office 16 with commute distance 33.\nAssign team location 1 to candidate office 17 with commute distance 37.\nAssign team location 1 to candidate office 18 with commute distance 35.\nAssign team location 1 to candidate office 19 with commute distance 30.\nAssign team location 2 to candidate office 1 with commute distance 38.\nAssign team location 2 to candidate office 3 with commute distance 38.\nAssign team location 2 to candidate office 4 with commute distance 38.\nAssign team location 2 to candidate office 5 with commute distance 35.\nAssign team location 2 to candidate office 6 with commute distance 33.\nAssign team location 2 to candidate office 7 with commute distance 38.\nAssign team location 2 to candidate office 8 with commute distance 39.\nAssign team location 2 to candidate office 9 with commute distance 33.\nAssign team location 2 to candidate office 10 with commute distance 38.\nAssign team location 2 to candidate office 11 with commute distance 37.\nAssign team location 2 to candidate office 12 with commute distance 33.\nAssign team location 2 to candidate office 13 with commute distance 31.\nAssign team location 2 to candidate office 14 with commute distance 50.\nAssign team location 2 to candidate office 15 with commute distance 32.\nAssign team location 2 to candidate office 16 with commute distance 30.\nAssign team location 2 to candidate office 17 with commute distance 38.\nAssign team location 2 to candidate office 18 with commute distance 30.\nAssign team location 2 to candidate office 19 with commute distance 29.\nAssign team location 3 to candidate office 1 with commute distance 33.\nAssign team location 3 to candidate office 2 with commute distance 38.\nAssign team location 3 to candidate office 4 with commute distance 8.\nAssign team location 3 to candidate office 5 with commute distance 33.\nAssign team location 3 to candidate office 6 with commute distance 44.\nAssign team location 3 to candidate office 7 with commute distance 21.\nAssign team location 3 to candidate office 8 with commute distance 38.\nAssign team location 3 to candidate office 9 with commute distance 22.\nAssign team location 3 to candidate office 10 with commute distance 28.\nAssign team location 3 to candidate office 11 with commute distance 36.\nAssign team location 3 to candidate office 12 with commute distance 33.\nAssign team location 3 to candidate office 13 with commute distance 35.\nAssign team location 3 to candidate office 14 with commute distance 43.\nAssign team location 3 to candidate office 15 with commute distance 18.\nAssign team location 3 to candidate office 16 with commute distance 28.\nAssign team location 3 to candidate office 17 with commute distance 37.\nAssign team location 3 to candidate office 18 with commute distance 25.\nAssign team location 3 to candidate office 19 with commute distance 23.\nAssign team location 4 to candidate office 1 with commute distance 38.\nAssign team location 4 to candidate office 2 with commute distance 38.\nAssign team location 4 to candidate office 3 with commute distance 8.\nAssign team location 4 to candidate office 5 with commute distance 31.\nAssign team location 4 to candidate office 6 with commute distance 40.\nAssign team location 4 to candidate office 7 with commute distance 29.\nAssign team location 4 to candidate office 8 with commute distance 33.\nAssign team location 4 to candidate office 9 with commute distance 21.\nAssign team location 4 to candidate office 10 with commute distance 33.\nAssign team location 4 to candidate office 11 with commute distance 33.\nAssign team location 4 to candidate office 12 with commute distance 29.\nAssign team location 4 to candidate office 13 with commute distance 27.\nAssign team location 4 to candidate office 14 with commute distance 35.\nAssign team location 4 to candidate office 15 with commute distance 21.\nAssign team location 4 to candidate office 16 with commute distance 30.\nAssign team location 4 to candidate office 17 with commute distance 39.\nAssign team location 4 to candidate office 18 with commute distance 33.\nAssign team location 4 to candidate office 19 with commute distance 23.\nAssign team location 5 to candidate office 1 with commute distance 42.\nAssign team location 5 to candidate office 2 with commute distance 35.\nAssign team location 5 to candidate office 3 with commute distance 33.\nAssign team location 5 to candidate office 4 with commute distance 31.\nAssign team location 5 to candidate office 6 with commute distance 38.\nAssign team location 5 to candidate office 7 with commute distance 17.\nAssign team location 5 to candidate office 8 with commute distance 34.\nAssign team location 5 to candidate office 9 with commute distance 34.\nAssign team location 5 to candidate office 10 with commute distance 39.\nAssign team location 5 to candidate office 11 with commute distance 43.\nAssign team location 5 to candidate office 12 with commute distance 37.\nAssign team location 5 to candidate office 13 with commute distance 22.\nAssign team location 5 to candidate office 14 with commute distance 33.\nAssign team location 5 to candidate office 15 with commute distance 27.\nAssign team location 5 to candidate office 16 with commute distance 11.\nAssign team location 5 to candidate office 17 with commute distance 14.\nAssign team location 5 to candidate office 18 with commute distance 28.\nAssign team location 5 to candidate office 19 with commute distance 29.\nAssign team location 6 to candidate office 1 with commute distance 42.\nAssign team location 6 to candidate office 2 with commute distance 33.\nAssign team location 6 to candidate office 3 with commute distance 44.\nAssign team location 6 to candidate office 4 with commute distance 40.\nAssign team location 6 to candidate office 5 with commute distance 38.\nAssign team location 6 to candidate office 7 with commute distance 33.\nAssign team location 6 to candidate office 8 with commute distance 50.\nAssign team location 6 to candidate office 9 with commute distance 40.\nAssign team location 6 to candidate office 10 with commute distance 43.\nAssign team location 6 to candidate office 11 with commute distance 42.\nAssign team location 6 to candidate office 12 with commute distance 41.\nAssign team location 6 to candidate office 13 with commute distance 48.\nAssign team location 6 to candidate office 14 with commute distance 56.\nAssign team location 6 to candidate office 15 with commute distance 31.\nAssign team location 6 to candidate office 16 with commute distance 39.\nAssign team location 6 to candidate office 17 with commute distance 46.\nAssign team location 6 to candidate office 18 with commute distance 38.\nAssign team location 6 to candidate office 19 with commute distance 34.\nAssign team location 7 to candidate office 1 with commute distance 35.\nAssign team location 7 to candidate office 2 with commute distance 38.\nAssign team location 7 to candidate office 3 with commute distance 21.\nAssign team location 7 to candidate office 4 with commute distance 29.\nAssign team location 7 to candidate office 5 with commute distance 17.\nAssign team location 7 to candidate office 6 with commute distance 33.\nAssign team location 7 to candidate office 8 with commute distance 29.\nAssign team location 7 to candidate office 9 with commute distance 17.\nAssign team location 7 to candidate office 10 with commute distance 35.\nAssign team location 7 to candidate office 11 with commute distance 32.\nAssign team location 7 to candidate office 12 with commute distance 33.\nAssign team location 7 to candidate office 13 with commute distance 30.\nAssign team location 7 to candidate office 14 with commute distance 49.\nAssign team location 7 to candidate office 15 with commute distance 27.\nAssign team location 7 to candidate office 16 with commute distance 25.\nAssign team location 7 to candidate office 17 with commute distance 28.\nAssign team location 7 to candidate office 18 with commute distance 27.\nAssign team location 7 to candidate office 19 with commute distance 12.\nAssign team location 8 to candidate office 1 with commute distance 40.\nAssign team location 8 to candidate office 2 with commute distance 39.\nAssign team location 8 to candidate office 3 with commute distance 38.\nAssign team location 8 to candidate office 4 with commute distance 33.\nAssign team location 8 to candidate office 5 with commute distance 34.\nAssign team location 8 to candidate office 6 with commute distance 50.\nAssign team location 8 to candidate office 7 with commute distance 29.\nAssign team location 8 to candidate office 9 with commute distance 31.\nAssign team location 8 to candidate office 10 with commute distance 43.\nAssign team location 8 to candidate office 11 with commute distance 44.\nAssign team location 8 to candidate office 12 with commute distance 33.\nAssign team location 8 to candidate office 13 with commute distance 34.\nAssign team location 8 to candidate office 14 with commute distance 51.\nAssign team location 8 to candidate office 15 with commute distance 34.\nAssign team location 8 to candidate office 16 with commute distance 33.\nAssign team location 8 to candidate office 17 with commute distance 29.\nAssign team location 8 to candidate office 18 with commute distance 27.\nAssign team location 8 to candidate office 19 with commute distance 30.\nAssign team location 9 to candidate office 1 with commute distance 31.\nAssign team location 9 to candidate office 2 with commute distance 33.\nAssign team location 9 to candidate office 3 with commute distance 22.\nAssign team location 9 to candidate office 4 with commute distance 21.\nAssign team location 9 to candidate office 5 with commute distance 34.\nAssign team location 9 to candidate office 6 with commute distance 40.\nAssign team location 9 to candidate office 7 with commute distance 17.\nAssign team location 9 to candidate office 8 with commute distance 31.\nAssign team location 9 to candidate office 10 with commute distance 33.\nAssign team location 9 to candidate office 11 with commute distance 31.\nAssign team location 9 to candidate office 12 with commute distance 29.\nAssign team location 9 to candidate office 13 with commute distance 25.\nAssign team location 9 to candidate office 14 with commute distance 40.\nAssign team location 9 to candidate office 15 with commute distance 21.\nAssign team location 9 to candidate office 16 with commute distance 29.\nAssign team location 9 to candidate office 17 with commute distance 33.\nAssign team location 9 to candidate office 18 with commute distance 31.\nAssign team location 9 to candidate office 19 with commute distance 22.\nAssign team location 10 to candidate office 1 with commute distance 25.\nAssign team location 10 to candidate office 2 with commute distance 38.\nAssign team location 10 to candidate office 3 with commute distance 28.\nAssign team location 10 to candidate office 4 with commute distance 33.\nAssign team location 10 to candidate office 5 with commute distance 39.\nAssign team location 10 to candidate office 6 with commute distance 43.\nAssign team location 10 to candidate office 7 with commute distance 35.\nAssign team location 10 to candidate office 8 with commute distance 43.\nAssign team location 10 to candidate office 9 with commute distance 33.\nAssign team location 10 to candidate office 11 with commute distance 30.\nAssign team location 10 to candidate office 12 with commute distance 31.\nAssign team location 10 to candidate office 13 with commute distance 40.\nAssign team location 10 to candidate office 14 with commute distance 46.\nAssign team location 10 to candidate office 15 with commute distance 12.\nAssign team location 10 to candidate office 16 with commute distance 28.\nAssign team location 10 to candidate office 17 with commute distance 32.\nAssign team location 10 to candidate office 18 with commute distance 30.\nAssign team location 10 to candidate office 19 with commute distance 32.\nAssign team location 11 to candidate office 1 with commute distance 45.\nAssign team location 11 to candidate office 2 with commute distance 37.\nAssign team location 11 to candidate office 3 with commute distance 36.\nAssign team location 11 to candidate office 4 with commute distance 33.\nAssign team location 11 to candidate office 5 with commute distance 43.\nAssign team location 11 to candidate office 6 with commute distance 42.\nAssign team location 11 to candidate office 7 with commute distance 32.\nAssign team location 11 to candidate office 8 with commute distance 44.\nAssign team location 11 to candidate office 9 with commute distance 31.\nAssign team location 11 to candidate office 10 with commute distance 30.\nAssign team location 11 to candidate office 12 with commute distance 32.\nAssign team location 11 to candidate office 13 with commute distance 26.\nAssign team location 11 to candidate office 14 with commute distance 50.\nAssign team location 11 to candidate office 15 with commute distance 32.\nAssign team location 11 to candidate office 16 with commute distance 42.\nAssign team location 11 to candidate office 17 with commute distance 45.\nAssign team location 11 to candidate office 18 with commute distance 29.\nAssign team location 11 to candidate office 19 with commute distance 22.\nAssign team location 12 to candidate office 1 with commute distance 36.\nAssign team location 12 to candidate office 2 with commute distance 33.\nAssign team location 12 to candidate office 3 with commute distance 33.\nAssign team location 12 to candidate office 4 with commute distance 29.\nAssign team location 12 to candidate office 5 with commute distance 37.\nAssign team location 12 to candidate office 6 with commute distance 41.\nAssign team location 12 to candidate office 7 with commute distance 33.\nAssign team location 12 to candidate office 8 with commute distance 33.\nAssign team location 12 to candidate office 9 with commute distance 29.\nAssign team location 12 to candidate office 10 with commute distance 31.\nAssign team location 12 to candidate office 11 with commute distance 32.\nAssign team location 12 to candidate office 13 with commute distance 20.\nAssign team location 12 to candidate office 14 with commute distance 41.\nAssign team location 12 to candidate office 15 with commute distance 23.\nAssign team location 12 to candidate office 16 with commute distance 26.\nAssign team location 12 to candidate office 17 with commute distance 31.\nAssign team location 12 to candidate office 18 with commute distance 23.\nAssign team location 12 to candidate office 19 with commute distance 25.\nAssign team location 13 to candidate office 1 with commute distance 42.\nAssign team location 13 to candidate office 2 with commute distance 31.\nAssign team location 13 to candidate office 3 with commute distance 35.\nAssign team location 13 to candidate office 4 with commute distance 27.\nAssign team location 13 to candidate office 5 with commute distance 22.\nAssign team location 13 to candidate office 6 with commute distance 48.\nAssign team location 13 to candidate office 7 with commute distance 30.\nAssign team location 13 to candidate office 8 with commute distance 34.\nAssign team location 13 to candidate office 9 with commute distance 25.\nAssign team location 13 to candidate office 10 with commute distance 40.\nAssign team location 13 to candidate office 11 with commute distance 26.\nAssign team location 13 to candidate office 12 with commute distance 20.\nAssign team location 13 to candidate office 14 with commute distance 44.\nAssign team location 13 to candidate office 15 with commute distance 28.\nAssign team location 13 to candidate office 16 with commute distance 17.\nAssign team location 13 to candidate office 17 with commute distance 33.\nAssign team location 13 to candidate office 18 with commute distance 24.\nAssign team location 13 to candidate office 19 with commute distance 25.\nAssign team location 14 to candidate office 1 with commute distance 51.\nAssign team location 14 to candidate office 2 with commute distance 50.\nAssign team location 14 to candidate office 3 with commute distance 43.\nAssign team location 14 to candidate office 4 with commute distance 35.\nAssign team location 14 to candidate office 5 with commute distance 33.\nAssign team location 14 to candidate office 6 with commute distance 56.\nAssign team location 14 to candidate office 7 with commute distance 49.\nAssign team location 14 to candidate office 8 with commute distance 51.\nAssign team location 14 to candidate office 9 with commute distance 40.\nAssign team location 14 to candidate office 10 with commute distance 46.\nAssign team location 14 to candidate office 11 with commute distance 50.\nAssign team location 14 to candidate office 12 with commute distance 41.\nAssign team location 14 to candidate office 13 with commute distance 44.\nAssign team location 14 to candidate office 15 with commute distance 38.\nAssign team location 14 to candidate office 16 with commute distance 44.\nAssign team location 14 to candidate office 17 with commute distance 46.\nAssign team location 14 to candidate office 18 with commute distance 32.\nAssign team location 14 to candidate office 19 with commute distance 40.\nAssign team location 15 to candidate office 1 with commute distance 17.\nAssign team location 15 to candidate office 2 with commute distance 32.\nAssign team location 15 to candidate office 3 with commute distance 18.\nAssign team location 15 to candidate office 4 with commute distance 21.\nAssign team location 15 to candidate office 5 with commute distance 27.\nAssign team location 15 to candidate office 6 with commute distance 31.\nAssign team location 15 to candidate office 7 with commute distance 27.\nAssign team location 15 to candidate office 8 with commute distance 34.\nAssign team location 15 to candidate office 9 with commute distance 21.\nAssign team location 15 to candidate office 10 with commute distance 12.\nAssign team location 15 to candidate office 11 with commute distance 32.\nAssign team location 15 to candidate office 12 with commute distance 23.\nAssign team location 15 to candidate office 13 with commute distance 28.\nAssign team location 15 to candidate office 14 with commute distance 38.\nAssign team location 15 to candidate office 16 with commute distance 16.\nAssign team location 15 to candidate office 17 with commute distance 24.\nAssign team location 15 to candidate office 18 with commute distance 22.\nAssign team location 15 to candidate office 19 with commute distance 24.\nAssign team location 16 to candidate office 1 with commute distance 33.\nAssign team location 16 to candidate office 2 with commute distance 30.\nAssign team location 16 to candidate office 3 with commute distance 28.\nAssign team location 16 to candidate office 4 with commute distance 30.\nAssign team location 16 to candidate office 5 with commute distance 11.\nAssign team location 16 to candidate office 6 with commute distance 39.\nAssign team location 16 to candidate office 7 with commute distance 25.\nAssign team location 16 to candidate office 8 with commute distance 33.\nAssign team location 16 to candidate office 9 with commute distance 29.\nAssign team location 16 to candidate office 10 with commute distance 28.\nAssign team location 16 to candidate office 11 with commute distance 42.\nAssign team location 16 to candidate office 12 with commute distance 26.\nAssign team location 16 to candidate office 13 with commute distance 17.\nAssign team location 16 to candidate office 14 with commute distance 44.\nAssign team location 16 to candidate office 15 with commute distance 16.\nAssign team location 16 to candidate office 17 with commute distance 25.\nAssign team location 16 to candidate office 18 with commute distance 33.\nAssign team location 16 to candidate office 19 with commute distance 26.\nAssign team location 17 to candidate office 1 with commute distance 37.\nAssign team location 17 to candidate office 2 with commute distance 38.\nAssign team location 17 to candidate office 3 with commute distance 37.\nAssign team location 17 to candidate office 4 with commute distance 39.\nAssign team location 17 to candidate office 5 with commute distance 14.\nAssign team location 17 to candidate office 6 with commute distance 46.\nAssign team location 17 to candidate office 7 with commute distance 28.\nAssign team location 17 to candidate office 8 with commute distance 29.\nAssign team location 17 to candidate office 9 with commute distance 33.\nAssign team location 17 to candidate office 10 with commute distance 32.\nAssign team location 17 to candidate office 11 with commute distance 45.\nAssign team location 17 to candidate office 12 with commute distance 31.\nAssign team location 17 to candidate office 13 with commute distance 33.\nAssign team location 17 to candidate office 14 with commute distance 46.\nAssign team location 17 to candidate office 15 with commute distance 24.\nAssign team location 17 to candidate office 16 with commute distance 25.\nAssign team location 17 to candidate office 18 with commute distance 30.\nAssign team location 17 to candidate office 19 with commute distance 29.\nAssign team location 18 to candidate office 1 with commute distance 35.\nAssign team location 18 to candidate office 2 with commute distance 30.\nAssign team location 18 to candidate office 3 with commute distance 25.\nAssign team location 18 to candidate office 4 with commute distance 33.\nAssign team location 18 to candidate office 5 with commute distance 28.\nAssign team location 18 to candidate office 6 with commute distance 38.\nAssign team location 18 to candidate office 7 with commute distance 27.\nAssign team location 18 to candidate office 8 with commute distance 27.\nAssign team location 18 to candidate office 9 with commute distance 31.\nAssign team location 18 to candidate office 10 with commute distance 30.\nAssign team location 18 to candidate office 11 with commute distance 29.\nAssign team location 18 to candidate office 12 with commute distance 23.\nAssign team location 18 to candidate office 13 with commute distance 24.\nAssign team location 18 to candidate office 14 with commute distance 32.\nAssign team location 18 to candidate office 15 with commute distance 22.\nAssign team location 18 to candidate office 16 with commute distance 33.\nAssign team location 18 to candidate office 17 with commute distance 30.\nAssign team location 18 to candidate office 19 with commute distance 17.\nAssign team location 19 to candidate office 1 with commute distance 30.\nAssign team location 19 to candidate office 2 with commute distance 29.\nAssign team location 19 to candidate office 3 with commute distance 23.\nAssign team location 19 to candidate office 4 with commute distance 23.\nAssign team location 19 to candidate office 5 with commute distance 29.\nAssign team location 19 to candidate office 6 with commute distance 34.\nAssign team location 19 to candidate office 7 with commute distance 12.\nAssign team location 19 to candidate office 8 with commute distance 30.\nAssign team location 19 to candidate office 9 with commute distance 22.\nAssign team location 19 to candidate office 10 with commute distance 32.\nAssign team location 19 to candidate office 11 with commute distance 22.\nAssign team location 19 to candidate office 12 with commute distance 25.\nAssign team location 19 to candidate office 13 with commute distance 25.\nAssign team location 19 to candidate office 14 with commute distance 40.\nAssign team location 19 to candidate office 15 with commute distance 24.\nAssign team location 19 to candidate office 16 with commute distance 26.\nAssign team location 19 to candidate office 17 with commute distance 29.\nAssign team location 19 to candidate office 18 with commute distance 17.\nChoose the 4 sites and assign every team to one opened office so the total commute (sum of all values) is minimized.\n\nAnd if it helps, just send the final plan in this little JSON shape so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of it like a simple form: \"selected\" is the list of candidate sites you decide to open, and \"assignments\" lists, for each original location (in the same order as the instance input), which opened site that location is paired with. This JSON is just a sketch of the shape I expect, not the actual answer.\n\nPlease use the exact identifiers from the instance input — don't rename them or invent new labels. \nFor example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 38, 33, 38, 42, 42, 35, 40, 31, 25, 45, 36, 42, 51, 17, 33, 37, 35, 30 ], [ 38, 0, 38, 38, 35, 33, 38, 39, 33, 38, 37, 33, 31, 50, 32, 30, 38, 30, 29 ], [ 33, 38, 0, 8, 33, 44, 21, 38, 22, 28, 36, 33, 35, 43, 18, 28, 37, 25, 23 ], [ 38, 38, 8, 0, 31, 40, 29, 33, 21, 33, 33, 29, 27, 35, 21, 30, 39, 33, 23 ], [ 42, 35, 33, 31, 0, 38, 17, 34, 34, 39, 43, 37, 22, 33, 27, 11, 14, 28, 29 ], [ 42, 33, 44, 40, 38, 0, 33, 50, 40, 43, 42, 41, 48, 56, 31, 39, 46, 38, 34 ], [ 35, 38, 21, 29, 17, 33, 0, 29, 17, 35, 32, 33, 30, 49, 27, 25, 28, 27, 12 ], [ 40, 39, 38, 33, 34, 50, 29, 0, 31, 43, 44, 33, 34, 51, 34, 33, 29, 27, 30 ], [ 31, 33, 22, 21, 34, 40, 17, 31, 0, 33, 31, 29, 25, 40, 21, 29, 33, 31, 22 ], [ 25, 38, 28, 33, 39, 43, 35, 43, 33, 0, 30, 31, 40, 46, 12, 28, 32, 30, 32 ], [ 45, 37, 36, 33, 43, 42, 32, 44, 31, 30, 0, 32, 26, 50, 32, 42, 45, 29, 22 ], [ 36, 33, 33, 29, 37, 41, 33, 33, 29, 31, 32, 0, 20, 41, 23, 26, 31, 23, 25 ], [ 42, 31, 35, 27, 22, 48, 30, 34, 25, 40, 26, 20, 0, 44, 28, 17, 33, 24, 25 ], [ 51, 50, 43, 35, 33, 56, 49, 51, 40, 46, 50, 41, 44, 0, 38, 44, 46, 32, 40 ], [ 17, 32, 18, 21, 27, 31, 27, 34, 21, 12, 32, 23, 28, 38, 0, 16, 24, 22, 24 ], [ 33, 30, 28, 30, 11, 39, 25, 33, 29, 28, 42, 26, 17, 44, 16, 0, 25, 33, 26 ], [ 37, 38, 37, 39, 14, 46, 28, 29, 33, 32, 45, 31, 33, 46, 24, 25, 0, 30, 29 ], [ 35, 30, 25, 33, 28, 38, 27, 27, 31, 30, 29, 23, 24, 32, 22, 33, 30, 0, 17 ], [ 30, 29, 23, 23, 29, 34, 12, 30, 22, 32, 22, 25, 25, 40, 24, 26, 29, 17, 0 ] ], "p": 4, "objective": 300.0 }, "solution": { "facilities": [ 4, 13, 14, 18 ], "assignments": [ 14, 18, 14, 14, 4, 14, 18, 18, 14, 14, 18, 14, 4, 13, 14, 4, 4, 18, 18 ] }, "obj": 300.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 4, "sites": [ { "id": 1, "distances": { "1": 0, "2": 38, "3": 33, "4": 38, "5": 42, "6": 42, "7": 35, "8": 40, "9": 31, "10": 25, "11": 45, "12": 36, "13": 42, "14": 51, "15": 17, "16": 33, "17": 37, "18": 35, "19": 30 } }, { "id": 2, "distances": { "1": 38, "2": 0, "3": 38, "4": 38, "5": 35, "6": 33, "7": 38, "8": 39, "9": 33, "10": 38, "11": 37, "12": 33, "13": 31, "14": 50, "15": 32, "16": 30, "17": 38, "18": 30, "19": 29 } }, { "id": 3, "distances": { "1": 33, "2": 38, "3": 0, "4": 8, "5": 33, "6": 44, "7": 21, "8": 38, "9": 22, "10": 28, "11": 36, "12": 33, "13": 35, "14": 43, "15": 18, "16": 28, "17": 37, "18": 25, "19": 23 } }, { "id": 4, "distances": { "1": 38, "2": 38, "3": 8, "4": 0, "5": 31, "6": 40, "7": 29, "8": 33, "9": 21, "10": 33, "11": 33, "12": 29, "13": 27, "14": 35, "15": 21, "16": 30, "17": 39, "18": 33, "19": 23 } }, { "id": 5, "distances": { "1": 42, "2": 35, "3": 33, "4": 31, "5": 0, "6": 38, "7": 17, "8": 34, "9": 34, "10": 39, "11": 43, "12": 37, "13": 22, "14": 33, "15": 27, "16": 11, "17": 14, "18": 28, "19": 29 } }, { "id": 6, "distances": { "1": 42, "2": 33, "3": 44, "4": 40, "5": 38, "6": 0, "7": 33, "8": 50, "9": 40, "10": 43, "11": 42, "12": 41, "13": 48, "14": 56, "15": 31, "16": 39, "17": 46, "18": 38, "19": 34 } }, { "id": 7, "distances": { "1": 35, "2": 38, "3": 21, "4": 29, "5": 17, "6": 33, "7": 0, "8": 29, "9": 17, "10": 35, "11": 32, "12": 33, "13": 30, "14": 49, "15": 27, "16": 25, "17": 28, "18": 27, "19": 12 } }, { "id": 8, "distances": { "1": 40, "2": 39, "3": 38, "4": 33, "5": 34, "6": 50, "7": 29, "8": 0, "9": 31, "10": 43, "11": 44, "12": 33, "13": 34, "14": 51, "15": 34, "16": 33, "17": 29, "18": 27, "19": 30 } }, { "id": 9, "distances": { "1": 31, "2": 33, "3": 22, "4": 21, "5": 34, "6": 40, "7": 17, "8": 31, "9": 0, "10": 33, "11": 31, "12": 29, "13": 25, "14": 40, "15": 21, "16": 29, "17": 33, "18": 31, "19": 22 } }, { "id": 10, "distances": { "1": 25, "2": 38, "3": 28, "4": 33, "5": 39, "6": 43, "7": 35, "8": 43, "9": 33, "10": 0, "11": 30, "12": 31, "13": 40, "14": 46, "15": 12, "16": 28, "17": 32, "18": 30, "19": 32 } }, { "id": 11, "distances": { "1": 45, "2": 37, "3": 36, "4": 33, "5": 43, "6": 42, "7": 32, "8": 44, "9": 31, "10": 30, "11": 0, "12": 32, "13": 26, "14": 50, "15": 32, "16": 42, "17": 45, "18": 29, "19": 22 } }, { "id": 12, "distances": { "1": 36, "2": 33, "3": 33, "4": 29, "5": 37, "6": 41, "7": 33, "8": 33, "9": 29, "10": 31, "11": 32, "12": 0, "13": 20, "14": 41, "15": 23, "16": 26, "17": 31, "18": 23, "19": 25 } }, { "id": 13, "distances": { "1": 42, "2": 31, "3": 35, "4": 27, "5": 22, "6": 48, "7": 30, "8": 34, "9": 25, "10": 40, "11": 26, "12": 20, "13": 0, "14": 44, "15": 28, "16": 17, "17": 33, "18": 24, "19": 25 } }, { "id": 14, "distances": { "1": 51, "2": 50, "3": 43, "4": 35, "5": 33, "6": 56, "7": 49, "8": 51, "9": 40, "10": 46, "11": 50, "12": 41, "13": 44, "14": 0, "15": 38, "16": 44, "17": 46, "18": 32, "19": 40 } }, { "id": 15, "distances": { "1": 17, "2": 32, "3": 18, "4": 21, "5": 27, "6": 31, "7": 27, "8": 34, "9": 21, "10": 12, "11": 32, "12": 23, "13": 28, "14": 38, "15": 0, "16": 16, "17": 24, "18": 22, "19": 24 } }, { "id": 16, "distances": { "1": 33, "2": 30, "3": 28, "4": 30, "5": 11, "6": 39, "7": 25, "8": 33, "9": 29, "10": 28, "11": 42, "12": 26, "13": 17, "14": 44, "15": 16, "16": 0, "17": 25, "18": 33, "19": 26 } }, { "id": 17, "distances": { "1": 37, "2": 38, "3": 37, "4": 39, "5": 14, "6": 46, "7": 28, "8": 29, "9": 33, "10": 32, "11": 45, "12": 31, "13": 33, "14": 46, "15": 24, "16": 25, "17": 0, "18": 30, "19": 29 } }, { "id": 18, "distances": { "1": 35, "2": 30, "3": 25, "4": 33, "5": 28, "6": 38, "7": 27, "8": 27, "9": 31, "10": 30, "11": 29, "12": 23, "13": 24, "14": 32, "15": 22, "16": 33, "17": 30, "18": 0, "19": 17 } }, { "id": 19, "distances": { "1": 30, "2": 29, "3": 23, "4": 23, "5": 29, "6": 34, "7": 12, "8": 30, "9": 22, "10": 32, "11": 22, "12": 25, "13": 25, "14": 40, "15": 24, "16": 26, "17": 29, "18": 17, "19": 0 } } ], "objective": 300.0 }, "solution_variant": { "selected": [ 5, 14, 15, 19 ], "assignments": [ 15, 19, 15, 15, 5, 15, 19, 19, 15, 15, 19, 15, 5, 14, 15, 5, 5, 19, 19 ] }, "context_index": 29, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "There’s a mobile library route to work out: decide which limited number of stops the van will use, and make sure every community cluster gets assigned to exactly one of those stops so nobody’s missed or doubled up. The measure of success is total visitor travel — add up each cluster’s distance to its chosen stop, and the plan with the lowest total is best. The specific candidate locations and distances are listed below.\n\n# total_locations=16\n# num_stops_to_schedule=2\n# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P\nfrom_location_id,to_location_id,travel_distance\nA,B,51\nA,C,39\nA,D,45\nA,E,31\nA,F,53\nA,G,45\nA,H,38\nA,I,49\nA,J,32\nA,K,35\nA,L,37\nA,M,50\nA,N,28\nA,O,53\nA,P,67\nB,A,51\nB,C,27\nB,D,62\nB,E,53\nB,F,62\nB,G,61\nB,H,22\nB,I,46\nB,J,52\nB,K,53\nB,L,52\nB,M,44\nB,N,48\nB,O,54\nB,P,84\nC,A,39\nC,B,27\nC,D,37\nC,E,30\nC,F,44\nC,G,38\nC,H,31\nC,I,37\nC,J,25\nC,K,26\nC,L,37\nC,M,17\nC,N,21\nC,O,45\nC,P,60\nD,A,45\nD,B,62\nD,C,37\nD,E,47\nD,F,54\nD,G,48\nD,H,41\nD,I,37\nD,J,29\nD,K,36\nD,L,37\nD,M,51\nD,N,37\nD,O,49\nD,P,56\nE,A,31\nE,B,53\nE,C,30\nE,D,47\nE,F,41\nE,G,66\nE,H,32\nE,I,49\nE,J,33\nE,K,56\nE,L,32\nE,M,47\nE,N,29\nE,O,35\nE,P,68\nF,A,53\nF,B,62\nF,C,44\nF,D,54\nF,E,41\nF,G,48\nF,H,60\nF,I,42\nF,J,25\nF,K,57\nF,L,53\nF,M,47\nF,N,31\nF,O,55\nF,P,58\nG,A,45\nG,B,61\nG,C,38\nG,D,48\nG,E,66\nG,F,48\nG,H,41\nG,I,50\nG,J,35\nG,K,52\nG,L,61\nG,M,55\nG,N,43\nG,O,67\nG,P,68\nH,A,38\nH,B,22\nH,C,31\nH,D,41\nH,E,32\nH,F,60\nH,G,41\nH,I,46\nH,J,37\nH,K,45\nH,L,46\nH,M,48\nH,N,45\nH,O,58\nH,P,68\nI,A,49\nI,B,46\nI,C,37\nI,D,37\nI,E,49\nI,F,42\nI,G,50\nI,H,46\nI,J,37\nI,K,15\nI,L,37\nI,M,54\nI,N,45\nI,O,39\nI,P,70\nJ,A,32\nJ,B,52\nJ,C,25\nJ,D,29\nJ,E,33\nJ,F,25\nJ,G,35\nJ,H,37\nJ,I,37\nJ,K,51\nJ,L,31\nJ,M,22\nJ,N,8\nJ,O,42\nJ,P,35\nK,A,35\nK,B,53\nK,C,26\nK,D,36\nK,E,56\nK,F,57\nK,G,52\nK,H,45\nK,I,15\nK,J,51\nK,L,45\nK,M,43\nK,N,44\nK,O,54\nK,P,72\nL,A,37\nL,B,52\nL,C,37\nL,D,37\nL,E,32\nL,F,53\nL,G,61\nL,H,46\nL,I,37\nL,J,31\nL,K,45\nL,M,53\nL,N,39\nL,O,32\nL,P,64\nM,A,50\nM,B,44\nM,C,17\nM,D,51\nM,E,47\nM,F,47\nM,G,55\nM,H,48\nM,I,54\nM,J,22\nM,K,43\nM,L,53\nM,N,26\nM,O,62\nM,P,57\nN,A,28\nN,B,48\nN,C,21\nN,D,37\nN,E,29\nN,F,31\nN,G,43\nN,H,45\nN,I,45\nN,J,8\nN,K,44\nN,L,39\nN,M,26\nN,O,47\nN,P,43\nO,A,53\nO,B,54\nO,C,45\nO,D,49\nO,E,35\nO,F,55\nO,G,67\nO,H,58\nO,I,39\nO,J,42\nO,K,54\nO,L,32\nO,M,62\nO,N,47\nO,P,75\nP,A,67\nP,B,84\nP,C,60\nP,D,56\nP,E,68\nP,F,58\nP,G,68\nP,H,68\nP,I,70\nP,J,35\nP,K,72\nP,L,64\nP,M,57\nP,N,43\nP,O,75\n\nWhen you send the final plan, just drop it in this simple JSON shape so everything stays tidy and easy to read:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the stops the mobile library will actually use, and \"assignments\" says, for each community cluster in the order they were given, which of those opened stops they should go to. Think of the JSON as a quick form to fill out — it's just the shape I need, not the final filled-in plan.\n\nPlease make sure you use the exact identifiers from the instance input — don't rename them or invent new ones. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 51, 39, 45, 31, 53, 45, 38, 49, 32, 35, 37, 50, 28, 53, 67 ], [ 51, 0, 27, 62, 53, 62, 61, 22, 46, 52, 53, 52, 44, 48, 54, 84 ], [ 39, 27, 0, 37, 30, 44, 38, 31, 37, 25, 26, 37, 17, 21, 45, 60 ], [ 45, 62, 37, 0, 47, 54, 48, 41, 37, 29, 36, 37, 51, 37, 49, 56 ], [ 31, 53, 30, 47, 0, 41, 66, 32, 49, 33, 56, 32, 47, 29, 35, 68 ], [ 53, 62, 44, 54, 41, 0, 48, 60, 42, 25, 57, 53, 47, 31, 55, 58 ], [ 45, 61, 38, 48, 66, 48, 0, 41, 50, 35, 52, 61, 55, 43, 67, 68 ], [ 38, 22, 31, 41, 32, 60, 41, 0, 46, 37, 45, 46, 48, 45, 58, 68 ], [ 49, 46, 37, 37, 49, 42, 50, 46, 0, 37, 15, 37, 54, 45, 39, 70 ], [ 32, 52, 25, 29, 33, 25, 35, 37, 37, 0, 51, 31, 22, 8, 42, 35 ], [ 35, 53, 26, 36, 56, 57, 52, 45, 15, 51, 0, 45, 43, 44, 54, 72 ], [ 37, 52, 37, 37, 32, 53, 61, 46, 37, 31, 45, 0, 53, 39, 32, 64 ], [ 50, 44, 17, 51, 47, 47, 55, 48, 54, 22, 43, 53, 0, 26, 62, 57 ], [ 28, 48, 21, 37, 29, 31, 43, 45, 45, 8, 44, 39, 26, 0, 47, 43 ], [ 53, 54, 45, 49, 35, 55, 67, 58, 39, 42, 54, 32, 62, 47, 0, 75 ], [ 67, 84, 60, 56, 68, 58, 68, 68, 70, 35, 72, 64, 57, 43, 75, 0 ] ], "p": 2, "objective": 405.0 }, "solution": { "facilities": [ 2, 9 ], "assignments": [ 9, 2, 2, 9, 2, 9, 9, 2, 2, 9, 2, 9, 2, 9, 9, 9 ] }, "obj": 405.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 2, "sites": [ { "id": "A", "distances": { "A": 0, "B": 51, "C": 39, "D": 45, "E": 31, "F": 53, "G": 45, "H": 38, "I": 49, "J": 32, "K": 35, "L": 37, "M": 50, "N": 28, "O": 53, "P": 67 } }, { "id": "B", "distances": { "A": 51, "B": 0, "C": 27, "D": 62, "E": 53, "F": 62, "G": 61, "H": 22, "I": 46, "J": 52, "K": 53, "L": 52, "M": 44, "N": 48, "O": 54, "P": 84 } }, { "id": "C", "distances": { "A": 39, "B": 27, "C": 0, "D": 37, "E": 30, "F": 44, "G": 38, "H": 31, "I": 37, "J": 25, "K": 26, "L": 37, "M": 17, "N": 21, "O": 45, "P": 60 } }, { "id": "D", "distances": { "A": 45, "B": 62, "C": 37, "D": 0, "E": 47, "F": 54, "G": 48, "H": 41, "I": 37, "J": 29, "K": 36, "L": 37, "M": 51, "N": 37, "O": 49, "P": 56 } }, { "id": "E", "distances": { "A": 31, "B": 53, "C": 30, "D": 47, "E": 0, "F": 41, "G": 66, "H": 32, "I": 49, "J": 33, "K": 56, "L": 32, "M": 47, "N": 29, "O": 35, "P": 68 } }, { "id": "F", "distances": { "A": 53, "B": 62, "C": 44, "D": 54, "E": 41, "F": 0, "G": 48, "H": 60, "I": 42, "J": 25, "K": 57, "L": 53, "M": 47, "N": 31, "O": 55, "P": 58 } }, { "id": "G", "distances": { "A": 45, "B": 61, "C": 38, "D": 48, "E": 66, "F": 48, "G": 0, "H": 41, "I": 50, "J": 35, "K": 52, "L": 61, "M": 55, "N": 43, "O": 67, "P": 68 } }, { "id": "H", "distances": { "A": 38, "B": 22, "C": 31, "D": 41, "E": 32, "F": 60, "G": 41, "H": 0, "I": 46, "J": 37, "K": 45, "L": 46, "M": 48, "N": 45, "O": 58, "P": 68 } }, { "id": "I", "distances": { "A": 49, "B": 46, "C": 37, "D": 37, "E": 49, "F": 42, "G": 50, "H": 46, "I": 0, "J": 37, "K": 15, "L": 37, "M": 54, "N": 45, "O": 39, "P": 70 } }, { "id": "J", "distances": { "A": 32, "B": 52, "C": 25, "D": 29, "E": 33, "F": 25, "G": 35, "H": 37, "I": 37, "J": 0, "K": 51, "L": 31, "M": 22, "N": 8, "O": 42, "P": 35 } }, { "id": "K", "distances": { "A": 35, "B": 53, "C": 26, "D": 36, "E": 56, "F": 57, "G": 52, "H": 45, "I": 15, "J": 51, "K": 0, "L": 45, "M": 43, "N": 44, "O": 54, "P": 72 } }, { "id": "L", "distances": { "A": 37, "B": 52, "C": 37, "D": 37, "E": 32, "F": 53, "G": 61, "H": 46, "I": 37, "J": 31, "K": 45, "L": 0, "M": 53, "N": 39, "O": 32, "P": 64 } }, { "id": "M", "distances": { "A": 50, "B": 44, "C": 17, "D": 51, "E": 47, "F": 47, "G": 55, "H": 48, "I": 54, "J": 22, "K": 43, "L": 53, "M": 0, "N": 26, "O": 62, "P": 57 } }, { "id": "N", "distances": { "A": 28, "B": 48, "C": 21, "D": 37, "E": 29, "F": 31, "G": 43, "H": 45, "I": 45, "J": 8, "K": 44, "L": 39, "M": 26, "N": 0, "O": 47, "P": 43 } }, { "id": "O", "distances": { "A": 53, "B": 54, "C": 45, "D": 49, "E": 35, "F": 55, "G": 67, "H": 58, "I": 39, "J": 42, "K": 54, "L": 32, "M": 62, "N": 47, "O": 0, "P": 75 } }, { "id": "P", "distances": { "A": 67, "B": 84, "C": 60, "D": 56, "E": 68, "F": 58, "G": 68, "H": 68, "I": 70, "J": 35, "K": 72, "L": 64, "M": 57, "N": 43, "O": 75, "P": 0 } } ], "objective": 405.0 }, "solution_variant": { "selected": [ "C", "J" ], "assignments": [ "J", "C", "C", "J", "C", "J", "J", "C", "C", "J", "C", "J", "C", "J", "J", "J" ] }, "context_index": 30, "input_format": "csv", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Recently the district decided to consolidate after-school offerings to a fixed number of campuses, so the superintendent has to pick which schools keep their centers and which ones will go to those centers. Each school must be assigned to a single open center, and every school must be covered. The aim is to cut down the total miles traveled across the whole district — simply add up the distance from each school to its assigned center, and the smaller that total is, the better. The exact school list and pairwise travel distances appear below.\n\n{\n \"num_schools\": 18,\n \"num_centers_to_open\": 1,\n \"school_ids\": [\n 0,\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16,\n 17\n ],\n \"data\": [\n {\n \"from_school_id\": 0,\n \"to_school_id\": 1,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 2,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 3,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 4,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 5,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 6,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 7,\n \"travel_distance\": 46\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 8,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 9,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 10,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 11,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 12,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 13,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 14,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 15,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 16,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 0,\n \"to_school_id\": 17,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 0,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 2,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 3,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 4,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 5,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 6,\n \"travel_distance\": 19\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 7,\n \"travel_distance\": 15\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 8,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 9,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 10,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 11,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 12,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 13,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 14,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 15,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 16,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 1,\n \"to_school_id\": 17,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 0,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 1,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 3,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 4,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 5,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 6,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 7,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 8,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 9,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 10,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 11,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 12,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 13,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 14,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 15,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 16,\n \"travel_distance\": 14\n },\n {\n \"from_school_id\": 2,\n \"to_school_id\": 17,\n \"travel_distance\": 18\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 0,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 1,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 2,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 4,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 5,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 6,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 7,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 8,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 9,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 10,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 11,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 12,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 13,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 14,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 15,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 16,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 3,\n \"to_school_id\": 17,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 0,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 1,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 2,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 3,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 5,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 6,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 7,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 8,\n \"travel_distance\": 17\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 9,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 10,\n \"travel_distance\": 13\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 11,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 12,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 13,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 14,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 15,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 16,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 4,\n \"to_school_id\": 17,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 0,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 1,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 2,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 3,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 4,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 6,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 7,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 8,\n \"travel_distance\": 22\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 9,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 10,\n \"travel_distance\": 24\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 11,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 12,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 13,\n \"travel_distance\": 24\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 14,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 15,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 16,\n \"travel_distance\": 8\n },\n {\n \"from_school_id\": 5,\n \"to_school_id\": 17,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 0,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 1,\n \"travel_distance\": 19\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 2,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 3,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 4,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 5,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 7,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 8,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 9,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 10,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 11,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 12,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 13,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 14,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 15,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 16,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 6,\n \"to_school_id\": 17,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 0,\n \"travel_distance\": 46\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 1,\n \"travel_distance\": 15\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 2,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 3,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 4,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 5,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 6,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 8,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 9,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 10,\n \"travel_distance\": 15\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 11,\n \"travel_distance\": 42\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 12,\n \"travel_distance\": 39\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 13,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 14,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 15,\n \"travel_distance\": 19\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 16,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 7,\n \"to_school_id\": 17,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 0,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 1,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 2,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 3,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 4,\n \"travel_distance\": 17\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 5,\n \"travel_distance\": 22\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 6,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 7,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 9,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 10,\n \"travel_distance\": 24\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 11,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 12,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 13,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 14,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 15,\n \"travel_distance\": 19\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 16,\n \"travel_distance\": 22\n },\n {\n \"from_school_id\": 8,\n \"to_school_id\": 17,\n \"travel_distance\": 17\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 0,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 1,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 2,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 3,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 4,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 5,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 6,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 7,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 8,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 10,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 11,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 12,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 13,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 14,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 15,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 16,\n \"travel_distance\": 17\n },\n {\n \"from_school_id\": 9,\n \"to_school_id\": 17,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 0,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 1,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 2,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 3,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 4,\n \"travel_distance\": 13\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 5,\n \"travel_distance\": 24\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 6,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 7,\n \"travel_distance\": 15\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 8,\n \"travel_distance\": 24\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 9,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 11,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 12,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 13,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 14,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 15,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 16,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 10,\n \"to_school_id\": 17,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 0,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 1,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 2,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 3,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 4,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 5,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 6,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 7,\n \"travel_distance\": 42\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 8,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 9,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 10,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 12,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 13,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 14,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 15,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 16,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 11,\n \"to_school_id\": 17,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 0,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 1,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 2,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 3,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 4,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 5,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 6,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 7,\n \"travel_distance\": 39\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 8,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 9,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 10,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 11,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 13,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 14,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 15,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 16,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 12,\n \"to_school_id\": 17,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 0,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 1,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 2,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 3,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 4,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 5,\n \"travel_distance\": 24\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 6,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 7,\n \"travel_distance\": 35\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 8,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 9,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 10,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 11,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 12,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 14,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 15,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 16,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 13,\n \"to_school_id\": 17,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 0,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 1,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 2,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 3,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 4,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 5,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 6,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 7,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 8,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 9,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 10,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 11,\n \"travel_distance\": 40\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 12,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 13,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 15,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 16,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 14,\n \"to_school_id\": 17,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 0,\n \"travel_distance\": 28\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 1,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 2,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 3,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 4,\n \"travel_distance\": 36\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 5,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 6,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 7,\n \"travel_distance\": 19\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 8,\n \"travel_distance\": 19\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 9,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 10,\n \"travel_distance\": 29\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 11,\n \"travel_distance\": 37\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 12,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 13,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 14,\n \"travel_distance\": 32\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 16,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 15,\n \"to_school_id\": 17,\n \"travel_distance\": 22\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 0,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 1,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 2,\n \"travel_distance\": 14\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 3,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 4,\n \"travel_distance\": 23\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 5,\n \"travel_distance\": 8\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 6,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 7,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 8,\n \"travel_distance\": 22\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 9,\n \"travel_distance\": 17\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 10,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 11,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 12,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 13,\n \"travel_distance\": 16\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 14,\n \"travel_distance\": 21\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 15,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 16,\n \"to_school_id\": 17,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 0,\n \"travel_distance\": 20\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 1,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 2,\n \"travel_distance\": 18\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 3,\n \"travel_distance\": 30\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 4,\n \"travel_distance\": 26\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 5,\n \"travel_distance\": 27\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 6,\n \"travel_distance\": 31\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 7,\n \"travel_distance\": 41\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 8,\n \"travel_distance\": 17\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 9,\n \"travel_distance\": 34\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 10,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 11,\n \"travel_distance\": 38\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 12,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 13,\n \"travel_distance\": 33\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 14,\n \"travel_distance\": 25\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 15,\n \"travel_distance\": 22\n },\n {\n \"from_school_id\": 17,\n \"to_school_id\": 16,\n \"travel_distance\": 26\n }\n ]\n}\n\nI'll put the output in a simple JSON shape so it's easy to follow. It will look like this:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nA quick, casual note on what those bits mean in our school story: \"selected\" is the list of schools that stay open as after-school centers, and \"assignments\" says, for each school (in the same order as the input), which open school it's assigned to. Think of \"selected\" like the checkboxes you tick, and \"assignments\" like the answers that point each school to its center.\n\nThis JSON is just a sketch of the expected shape, not the actual solution.\n\n- Please use the identifiers exactly as they appear in the instance input — do not rename or invent new labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "distance_matrix": [ [ 0, 31, 34, 32, 41, 29, 38, 46, 31, 32, 37, 38, 35, 23, 33, 28, 21, 20 ], [ 31, 0, 29, 29, 26, 23, 19, 15, 26, 25, 16, 36, 32, 27, 32, 32, 20, 34 ], [ 34, 29, 0, 21, 25, 20, 32, 38, 16, 30, 30, 27, 29, 28, 28, 30, 14, 18 ], [ 32, 29, 21, 0, 31, 27, 28, 34, 32, 32, 35, 38, 29, 25, 23, 34, 27, 30 ], [ 41, 26, 25, 31, 0, 21, 33, 25, 17, 35, 13, 41, 27, 33, 34, 36, 23, 26 ], [ 29, 23, 20, 27, 21, 0, 30, 27, 22, 25, 24, 31, 27, 24, 25, 23, 8, 27 ], [ 38, 19, 32, 28, 33, 30, 0, 34, 37, 30, 27, 40, 38, 31, 33, 30, 30, 31 ], [ 46, 15, 38, 34, 25, 27, 34, 0, 36, 40, 15, 42, 39, 35, 40, 19, 26, 41 ], [ 31, 26, 16, 32, 17, 22, 37, 36, 0, 27, 24, 33, 32, 29, 29, 19, 22, 17 ], [ 32, 25, 30, 32, 35, 25, 30, 40, 27, 0, 31, 40, 38, 33, 33, 33, 17, 34 ], [ 37, 16, 30, 35, 13, 24, 27, 15, 24, 31, 0, 41, 34, 20, 37, 29, 16, 33 ], [ 38, 36, 27, 38, 41, 31, 40, 42, 33, 40, 41, 0, 36, 31, 40, 37, 25, 38 ], [ 35, 32, 29, 29, 27, 27, 38, 39, 32, 38, 34, 36, 0, 26, 34, 20, 26, 33 ], [ 23, 27, 28, 25, 33, 24, 31, 35, 29, 33, 20, 31, 26, 0, 30, 27, 16, 33 ], [ 33, 32, 28, 23, 34, 25, 33, 40, 29, 33, 37, 40, 34, 30, 0, 32, 21, 25 ], [ 28, 32, 30, 34, 36, 23, 30, 19, 19, 33, 29, 37, 20, 27, 32, 0, 25, 22 ], [ 21, 20, 14, 27, 23, 8, 30, 26, 22, 17, 16, 25, 26, 16, 21, 25, 0, 26 ], [ 20, 34, 18, 30, 26, 27, 31, 41, 17, 34, 33, 38, 33, 33, 25, 22, 26, 0 ] ], "p": 1, "objective": 363.0 }, "solution": { "facilities": [ 16 ], "assignments": [ 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 ] }, "obj": 363.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 1, "sites": [ { "id": 0, "distances": { "0": 0, "1": 31, "2": 34, "3": 32, "4": 41, "5": 29, "6": 38, "7": 46, "8": 31, "9": 32, "10": 37, "11": 38, "12": 35, "13": 23, "14": 33, "15": 28, "16": 21, "17": 20 } }, { "id": 1, "distances": { "0": 31, "1": 0, "2": 29, "3": 29, "4": 26, "5": 23, "6": 19, "7": 15, "8": 26, "9": 25, "10": 16, "11": 36, "12": 32, "13": 27, "14": 32, "15": 32, "16": 20, "17": 34 } }, { "id": 2, "distances": { "0": 34, "1": 29, "2": 0, "3": 21, "4": 25, "5": 20, "6": 32, "7": 38, "8": 16, "9": 30, "10": 30, "11": 27, "12": 29, "13": 28, "14": 28, "15": 30, "16": 14, "17": 18 } }, { "id": 3, "distances": { "0": 32, "1": 29, "2": 21, "3": 0, "4": 31, "5": 27, "6": 28, "7": 34, "8": 32, "9": 32, "10": 35, "11": 38, "12": 29, "13": 25, "14": 23, "15": 34, "16": 27, "17": 30 } }, { "id": 4, "distances": { "0": 41, "1": 26, "2": 25, "3": 31, "4": 0, "5": 21, "6": 33, "7": 25, "8": 17, "9": 35, "10": 13, "11": 41, "12": 27, "13": 33, "14": 34, "15": 36, "16": 23, "17": 26 } }, { "id": 5, "distances": { "0": 29, "1": 23, "2": 20, "3": 27, "4": 21, "5": 0, "6": 30, "7": 27, "8": 22, "9": 25, "10": 24, "11": 31, "12": 27, "13": 24, "14": 25, "15": 23, "16": 8, "17": 27 } }, { "id": 6, "distances": { "0": 38, "1": 19, "2": 32, "3": 28, "4": 33, "5": 30, "6": 0, "7": 34, "8": 37, "9": 30, "10": 27, "11": 40, "12": 38, "13": 31, "14": 33, "15": 30, "16": 30, "17": 31 } }, { "id": 7, "distances": { "0": 46, "1": 15, "2": 38, "3": 34, "4": 25, "5": 27, "6": 34, "7": 0, "8": 36, "9": 40, "10": 15, "11": 42, "12": 39, "13": 35, "14": 40, "15": 19, "16": 26, "17": 41 } }, { "id": 8, "distances": { "0": 31, "1": 26, "2": 16, "3": 32, "4": 17, "5": 22, "6": 37, "7": 36, "8": 0, "9": 27, "10": 24, "11": 33, "12": 32, "13": 29, "14": 29, "15": 19, "16": 22, "17": 17 } }, { "id": 9, "distances": { "0": 32, "1": 25, "2": 30, "3": 32, "4": 35, "5": 25, "6": 30, "7": 40, "8": 27, "9": 0, "10": 31, "11": 40, "12": 38, "13": 33, "14": 33, "15": 33, "16": 17, "17": 34 } }, { "id": 10, "distances": { "0": 37, "1": 16, "2": 30, "3": 35, "4": 13, "5": 24, "6": 27, "7": 15, "8": 24, "9": 31, "10": 0, "11": 41, "12": 34, "13": 20, "14": 37, "15": 29, "16": 16, "17": 33 } }, { "id": 11, "distances": { "0": 38, "1": 36, "2": 27, "3": 38, "4": 41, "5": 31, "6": 40, "7": 42, "8": 33, "9": 40, "10": 41, "11": 0, "12": 36, "13": 31, "14": 40, "15": 37, "16": 25, "17": 38 } }, { "id": 12, "distances": { "0": 35, "1": 32, "2": 29, "3": 29, "4": 27, "5": 27, "6": 38, "7": 39, "8": 32, "9": 38, "10": 34, "11": 36, "12": 0, "13": 26, "14": 34, "15": 20, "16": 26, "17": 33 } }, { "id": 13, "distances": { "0": 23, "1": 27, "2": 28, "3": 25, "4": 33, "5": 24, "6": 31, "7": 35, "8": 29, "9": 33, "10": 20, "11": 31, "12": 26, "13": 0, "14": 30, "15": 27, "16": 16, "17": 33 } }, { "id": 14, "distances": { "0": 33, "1": 32, "2": 28, "3": 23, "4": 34, "5": 25, "6": 33, "7": 40, "8": 29, "9": 33, "10": 37, "11": 40, "12": 34, "13": 30, "14": 0, "15": 32, "16": 21, "17": 25 } }, { "id": 15, "distances": { "0": 28, "1": 32, "2": 30, "3": 34, "4": 36, "5": 23, "6": 30, "7": 19, "8": 19, "9": 33, "10": 29, "11": 37, "12": 20, "13": 27, "14": 32, "15": 0, "16": 25, "17": 22 } }, { "id": 16, "distances": { "0": 21, "1": 20, "2": 14, "3": 27, "4": 23, "5": 8, "6": 30, "7": 26, "8": 22, "9": 17, "10": 16, "11": 25, "12": 26, "13": 16, "14": 21, "15": 25, "16": 0, "17": 26 } }, { "id": 17, "distances": { "0": 20, "1": 34, "2": 18, "3": 30, "4": 26, "5": 27, "6": 31, "7": 41, "8": 17, "9": 34, "10": 33, "11": 38, "12": 33, "13": 33, "14": 25, "15": 22, "16": 26, "17": 0 } } ], "objective": 363.0 }, "solution_variant": { "selected": [ 16 ], "assignments": [ 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 ] }, "context_index": 31, "input_format": "json", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I used to sketch coverage maps: there’s a handful of candidate towers and a bunch of sites that need service, and someone has to pick a fixed number of those towers to switch on. The idea is simple — every site is tied to just one of the towers that get turned on, and nothing gets left out or hooked to two towers at once. The \"best\" choice is the one that keeps the total travel distance as small as possible — add up each site’s distance to its assigned active tower, and that sum should be as low as it can be. The specific list of sites, candidate towers and the distances between them are shown below.\n\n# total_candidate_sites=17\n# towers_to_activate=3\n# site_identifiers=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q\nfrom_site_id,to_site_id,distance_between_sites\nA,B,53\nA,C,41\nA,D,55\nA,E,53\nA,F,68\nA,G,49\nA,H,48\nA,I,47\nA,J,86\nA,K,66\nA,L,43\nA,M,57\nA,N,54\nA,O,54\nA,P,69\nA,Q,49\nB,A,53\nB,C,45\nB,D,24\nB,E,45\nB,F,55\nB,G,45\nB,H,44\nB,I,46\nB,J,64\nB,K,47\nB,L,31\nB,M,61\nB,N,25\nB,O,45\nB,P,37\nB,Q,33\nC,A,41\nC,B,45\nC,D,35\nC,E,12\nC,F,27\nC,G,36\nC,H,7\nC,I,41\nC,J,67\nC,K,63\nC,L,49\nC,M,55\nC,N,30\nC,O,25\nC,P,36\nC,Q,22\nD,A,55\nD,B,24\nD,C,35\nD,E,25\nD,F,40\nD,G,27\nD,H,36\nD,I,26\nD,J,48\nD,K,42\nD,L,21\nD,M,42\nD,N,15\nD,O,40\nD,P,32\nD,Q,13\nE,A,53\nE,B,45\nE,C,12\nE,D,25\nE,F,17\nE,G,26\nE,H,13\nE,I,31\nE,J,59\nE,K,53\nE,L,39\nE,M,54\nE,N,20\nE,O,31\nE,P,35\nE,Q,12\nF,A,68\nF,B,55\nF,C,27\nF,D,40\nF,E,17\nF,G,41\nF,H,28\nF,I,46\nF,J,74\nF,K,55\nF,L,40\nF,M,69\nF,N,35\nF,O,46\nF,P,50\nF,Q,27\nG,A,49\nG,B,45\nG,C,36\nG,D,27\nG,E,26\nG,F,41\nG,H,37\nG,I,33\nG,J,61\nG,K,39\nG,L,21\nG,M,63\nG,N,22\nG,O,41\nG,P,37\nG,Q,14\nH,A,48\nH,B,44\nH,C,7\nH,D,36\nH,E,13\nH,F,28\nH,G,37\nH,I,42\nH,J,60\nH,K,64\nH,L,47\nH,M,62\nH,N,31\nH,O,18\nH,P,43\nH,Q,23\nI,A,47\nI,B,46\nI,C,41\nI,D,26\nI,E,31\nI,F,46\nI,G,33\nI,H,42\nI,J,60\nI,K,54\nI,L,35\nI,M,53\nI,N,21\nI,O,38\nI,P,42\nI,Q,19\nJ,A,86\nJ,B,64\nJ,C,67\nJ,D,48\nJ,E,59\nJ,F,74\nJ,G,61\nJ,H,60\nJ,I,60\nJ,K,62\nJ,L,60\nJ,M,79\nJ,N,49\nJ,O,69\nJ,P,66\nJ,Q,47\nK,A,66\nK,B,47\nK,C,63\nK,D,42\nK,E,53\nK,F,55\nK,G,39\nK,H,64\nK,I,54\nK,J,62\nK,L,52\nK,M,69\nK,N,43\nK,O,60\nK,P,54\nK,Q,41\nL,A,43\nL,B,31\nL,C,49\nL,D,21\nL,E,39\nL,F,40\nL,G,21\nL,H,47\nL,I,35\nL,J,60\nL,K,52\nL,M,48\nL,N,30\nL,O,41\nL,P,39\nL,Q,27\nM,A,57\nM,B,61\nM,C,55\nM,D,42\nM,E,54\nM,F,69\nM,G,63\nM,H,62\nM,I,53\nM,J,79\nM,K,69\nM,L,48\nM,N,57\nM,O,53\nM,P,71\nM,Q,55\nN,A,54\nN,B,25\nN,C,30\nN,D,15\nN,E,20\nN,F,35\nN,G,22\nN,H,31\nN,I,21\nN,J,49\nN,K,43\nN,L,30\nN,M,57\nN,O,36\nN,P,31\nN,Q,8\nO,A,54\nO,B,45\nO,C,25\nO,D,40\nO,E,31\nO,F,46\nO,G,41\nO,H,18\nO,I,38\nO,J,69\nO,K,60\nO,L,41\nO,M,53\nO,N,36\nO,P,38\nO,Q,28\nP,A,69\nP,B,37\nP,C,36\nP,D,32\nP,E,35\nP,F,50\nP,G,37\nP,H,43\nP,I,42\nP,J,66\nP,K,54\nP,L,39\nP,M,71\nP,N,31\nP,O,38\nP,Q,23\nQ,A,49\nQ,B,33\nQ,C,22\nQ,D,13\nQ,E,12\nQ,F,27\nQ,G,14\nQ,H,23\nQ,I,19\nQ,J,47\nQ,K,41\nQ,L,27\nQ,M,55\nQ,N,8\nQ,O,28\nQ,P,23\n\nAlso, when you send the solution back, just stick to this simple JSON shape — nothing fancy, just the fields shown below.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nIt's just a friendly form: \"selected\" is the list of sites you choose to turn on, and \"assignments\" lists, for every site in the instance (in the same order they were given), which opened site it's hooked up to. Think of it like filling out a short form rather than a complex file.\n\nThis JSON is only a sketch of the expected shape — not the actual answer. Important: use the exact identifiers from the instance input (no renaming, no new labels). For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 53, 41, 55, 53, 68, 49, 48, 47, 86, 66, 43, 57, 54, 54, 69, 49 ], [ 53, 0, 45, 24, 45, 55, 45, 44, 46, 64, 47, 31, 61, 25, 45, 37, 33 ], [ 41, 45, 0, 35, 12, 27, 36, 7, 41, 67, 63, 49, 55, 30, 25, 36, 22 ], [ 55, 24, 35, 0, 25, 40, 27, 36, 26, 48, 42, 21, 42, 15, 40, 32, 13 ], [ 53, 45, 12, 25, 0, 17, 26, 13, 31, 59, 53, 39, 54, 20, 31, 35, 12 ], [ 68, 55, 27, 40, 17, 0, 41, 28, 46, 74, 55, 40, 69, 35, 46, 50, 27 ], [ 49, 45, 36, 27, 26, 41, 0, 37, 33, 61, 39, 21, 63, 22, 41, 37, 14 ], [ 48, 44, 7, 36, 13, 28, 37, 0, 42, 60, 64, 47, 62, 31, 18, 43, 23 ], [ 47, 46, 41, 26, 31, 46, 33, 42, 0, 60, 54, 35, 53, 21, 38, 42, 19 ], [ 86, 64, 67, 48, 59, 74, 61, 60, 60, 0, 62, 60, 79, 49, 69, 66, 47 ], [ 66, 47, 63, 42, 53, 55, 39, 64, 54, 62, 0, 52, 69, 43, 60, 54, 41 ], [ 43, 31, 49, 21, 39, 40, 21, 47, 35, 60, 52, 0, 48, 30, 41, 39, 27 ], [ 57, 61, 55, 42, 54, 69, 63, 62, 53, 79, 69, 48, 0, 57, 53, 71, 55 ], [ 54, 25, 30, 15, 20, 35, 22, 31, 21, 49, 43, 30, 57, 0, 36, 31, 8 ], [ 54, 45, 25, 40, 31, 46, 41, 18, 38, 69, 60, 41, 53, 36, 0, 38, 28 ], [ 69, 37, 36, 32, 35, 50, 37, 43, 42, 66, 54, 39, 71, 31, 38, 0, 23 ], [ 49, 33, 22, 13, 12, 27, 14, 23, 19, 47, 41, 27, 55, 8, 28, 23, 0 ] ], "p": 3, "objective": 337.0 }, "solution": { "facilities": [ 2, 12, 16 ], "assignments": [ 2, 16, 2, 16, 16, 2, 16, 2, 16, 16, 16, 16, 12, 16, 2, 16, 16 ] }, "obj": 337.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 3, "sites": [ { "id": "A", "distances": { "A": 0, "B": 53, "C": 41, "D": 55, "E": 53, "F": 68, "G": 49, "H": 48, "I": 47, "J": 86, "K": 66, "L": 43, "M": 57, "N": 54, "O": 54, "P": 69, "Q": 49 } }, { "id": "B", "distances": { "A": 53, "B": 0, "C": 45, "D": 24, "E": 45, "F": 55, "G": 45, "H": 44, "I": 46, "J": 64, "K": 47, "L": 31, "M": 61, "N": 25, "O": 45, "P": 37, "Q": 33 } }, { "id": "C", "distances": { "A": 41, "B": 45, "C": 0, "D": 35, "E": 12, "F": 27, "G": 36, "H": 7, "I": 41, "J": 67, "K": 63, "L": 49, "M": 55, "N": 30, "O": 25, "P": 36, "Q": 22 } }, { "id": "D", "distances": { "A": 55, "B": 24, "C": 35, "D": 0, "E": 25, "F": 40, "G": 27, "H": 36, "I": 26, "J": 48, "K": 42, "L": 21, "M": 42, "N": 15, "O": 40, "P": 32, "Q": 13 } }, { "id": "E", "distances": { "A": 53, "B": 45, "C": 12, "D": 25, "E": 0, "F": 17, "G": 26, "H": 13, "I": 31, "J": 59, "K": 53, "L": 39, "M": 54, "N": 20, "O": 31, "P": 35, "Q": 12 } }, { "id": "F", "distances": { "A": 68, "B": 55, "C": 27, "D": 40, "E": 17, "F": 0, "G": 41, "H": 28, "I": 46, "J": 74, "K": 55, "L": 40, "M": 69, "N": 35, "O": 46, "P": 50, "Q": 27 } }, { "id": "G", "distances": { "A": 49, "B": 45, "C": 36, "D": 27, "E": 26, "F": 41, "G": 0, "H": 37, "I": 33, "J": 61, "K": 39, "L": 21, "M": 63, "N": 22, "O": 41, "P": 37, "Q": 14 } }, { "id": "H", "distances": { "A": 48, "B": 44, "C": 7, "D": 36, "E": 13, "F": 28, "G": 37, "H": 0, "I": 42, "J": 60, "K": 64, "L": 47, "M": 62, "N": 31, "O": 18, "P": 43, "Q": 23 } }, { "id": "I", "distances": { "A": 47, "B": 46, "C": 41, "D": 26, "E": 31, "F": 46, "G": 33, "H": 42, "I": 0, "J": 60, "K": 54, "L": 35, "M": 53, "N": 21, "O": 38, "P": 42, "Q": 19 } }, { "id": "J", "distances": { "A": 86, "B": 64, "C": 67, "D": 48, "E": 59, "F": 74, "G": 61, "H": 60, "I": 60, "J": 0, "K": 62, "L": 60, "M": 79, "N": 49, "O": 69, "P": 66, "Q": 47 } }, { "id": "K", "distances": { "A": 66, "B": 47, "C": 63, "D": 42, "E": 53, "F": 55, "G": 39, "H": 64, "I": 54, "J": 62, "K": 0, "L": 52, "M": 69, "N": 43, "O": 60, "P": 54, "Q": 41 } }, { "id": "L", "distances": { "A": 43, "B": 31, "C": 49, "D": 21, "E": 39, "F": 40, "G": 21, "H": 47, "I": 35, "J": 60, "K": 52, "L": 0, "M": 48, "N": 30, "O": 41, "P": 39, "Q": 27 } }, { "id": "M", "distances": { "A": 57, "B": 61, "C": 55, "D": 42, "E": 54, "F": 69, "G": 63, "H": 62, "I": 53, "J": 79, "K": 69, "L": 48, "M": 0, "N": 57, "O": 53, "P": 71, "Q": 55 } }, { "id": "N", "distances": { "A": 54, "B": 25, "C": 30, "D": 15, "E": 20, "F": 35, "G": 22, "H": 31, "I": 21, "J": 49, "K": 43, "L": 30, "M": 57, "N": 0, "O": 36, "P": 31, "Q": 8 } }, { "id": "O", "distances": { "A": 54, "B": 45, "C": 25, "D": 40, "E": 31, "F": 46, "G": 41, "H": 18, "I": 38, "J": 69, "K": 60, "L": 41, "M": 53, "N": 36, "O": 0, "P": 38, "Q": 28 } }, { "id": "P", "distances": { "A": 69, "B": 37, "C": 36, "D": 32, "E": 35, "F": 50, "G": 37, "H": 43, "I": 42, "J": 66, "K": 54, "L": 39, "M": 71, "N": 31, "O": 38, "P": 0, "Q": 23 } }, { "id": "Q", "distances": { "A": 49, "B": 33, "C": 22, "D": 13, "E": 12, "F": 27, "G": 14, "H": 23, "I": 19, "J": 47, "K": 41, "L": 27, "M": 55, "N": 8, "O": 28, "P": 23, "Q": 0 } } ], "objective": 337.0 }, "solution_variant": { "selected": [ "C", "M", "Q" ], "assignments": [ "C", "Q", "C", "Q", "Q", "C", "Q", "C", "Q", "Q", "Q", "Q", "M", "Q", "C", "Q", "Q" ] }, "context_index": 32, "input_format": "csv", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone managing maintenance for a bike-share needs to choose a predetermined number of hub locations and connect every station to exactly one hub — no station can be skipped or split between hubs. Since the travel distance between every pair of stations is available, each possible plan can be scored by adding up the distance from each station to its chosen hub, and the plan with the lowest total travel is preferred. The concrete details will be shown below.\n\n# total_stations=18\n# num_hubs_to_open=6\n# station_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R\nfrom_station_id,to_station_id,travel_distance\nA,B,96\nA,C,62\nA,D,64\nA,E,57\nA,F,85\nA,G,67\nA,H,57\nA,I,84\nA,J,80\nA,K,98\nA,L,69\nA,M,67\nA,N,53\nA,O,38\nA,P,71\nA,Q,83\nA,R,97\nB,A,96\nB,C,80\nB,D,71\nB,E,48\nB,F,114\nB,G,98\nB,H,75\nB,I,34\nB,J,91\nB,K,48\nB,L,72\nB,M,51\nB,N,86\nB,O,118\nB,P,113\nB,Q,112\nB,R,107\nC,A,62\nC,B,80\nC,D,49\nC,E,59\nC,F,69\nC,G,42\nC,H,44\nC,I,80\nC,J,59\nC,K,78\nC,L,41\nC,M,29\nC,N,58\nC,O,76\nC,P,80\nC,Q,67\nC,R,36\nD,A,64\nD,B,71\nD,C,49\nD,E,50\nD,F,57\nD,G,67\nD,H,59\nD,I,88\nD,J,76\nD,K,100\nD,L,36\nD,M,20\nD,N,25\nD,O,47\nD,P,65\nD,Q,55\nD,R,80\nE,A,57\nE,B,48\nE,C,59\nE,D,50\nE,F,75\nE,G,77\nE,H,69\nE,I,82\nE,J,52\nE,K,96\nE,L,37\nE,M,30\nE,N,54\nE,O,95\nE,P,84\nE,Q,73\nE,R,88\nF,A,85\nF,B,114\nF,C,69\nF,D,57\nF,E,75\nF,G,91\nF,H,92\nF,I,109\nF,J,90\nF,K,126\nF,L,64\nF,M,67\nF,N,46\nF,O,103\nF,P,103\nF,Q,2\nF,R,72\nG,A,67\nG,B,98\nG,C,42\nG,D,67\nG,E,77\nG,F,91\nG,H,74\nG,I,109\nG,J,81\nG,K,102\nG,L,71\nG,M,47\nG,N,78\nG,O,94\nG,P,99\nG,Q,89\nG,R,74\nH,A,57\nH,B,75\nH,C,44\nH,D,59\nH,E,69\nH,F,92\nH,G,74\nH,I,108\nH,J,78\nH,K,41\nH,L,49\nH,M,39\nH,N,59\nH,O,90\nH,P,57\nH,Q,94\nH,R,64\nI,A,84\nI,B,34\nI,C,80\nI,D,88\nI,E,82\nI,F,109\nI,G,109\nI,H,108\nI,J,104\nI,K,82\nI,L,86\nI,M,85\nI,N,77\nI,O,122\nI,P,127\nI,Q,107\nI,R,100\nJ,A,80\nJ,B,91\nJ,C,59\nJ,D,76\nJ,E,52\nJ,F,90\nJ,G,81\nJ,H,78\nJ,I,104\nJ,K,116\nJ,L,50\nJ,M,68\nJ,N,70\nJ,O,85\nJ,P,89\nJ,Q,88\nJ,R,79\nK,A,98\nK,B,48\nK,C,78\nK,D,100\nK,E,96\nK,F,126\nK,G,102\nK,H,41\nK,I,82\nK,J,116\nK,L,74\nK,M,80\nK,N,100\nK,O,131\nK,P,98\nK,Q,124\nK,R,98\nL,A,69\nL,B,72\nL,C,41\nL,D,36\nL,E,37\nL,F,64\nL,G,71\nL,H,49\nL,I,86\nL,J,50\nL,K,74\nL,M,46\nL,N,51\nL,O,79\nL,P,49\nL,Q,62\nL,R,61\nM,A,67\nM,B,51\nM,C,29\nM,D,20\nM,E,30\nM,F,67\nM,G,47\nM,H,39\nM,I,85\nM,J,68\nM,K,80\nM,L,46\nM,N,35\nM,O,67\nM,P,75\nM,Q,65\nM,R,65\nN,A,53\nN,B,86\nN,C,58\nN,D,25\nN,E,54\nN,F,46\nN,G,78\nN,H,59\nN,I,77\nN,J,70\nN,K,100\nN,L,51\nN,M,35\nN,O,72\nN,P,80\nN,Q,44\nN,R,83\nO,A,38\nO,B,118\nO,C,76\nO,D,47\nO,E,95\nO,F,103\nO,G,94\nO,H,90\nO,I,122\nO,J,85\nO,K,131\nO,L,79\nO,M,67\nO,N,72\nO,P,33\nO,Q,102\nO,R,112\nP,A,71\nP,B,113\nP,C,80\nP,D,65\nP,E,84\nP,F,103\nP,G,99\nP,H,57\nP,I,127\nP,J,89\nP,K,98\nP,L,49\nP,M,75\nP,N,80\nP,O,33\nP,Q,101\nP,R,100\nQ,A,83\nQ,B,112\nQ,C,67\nQ,D,55\nQ,E,73\nQ,F,2\nQ,G,89\nQ,H,94\nQ,I,107\nQ,J,88\nQ,K,124\nQ,L,62\nQ,M,65\nQ,N,44\nQ,O,102\nQ,P,101\nQ,R,70\nR,A,97\nR,B,107\nR,C,36\nR,D,80\nR,E,88\nR,F,72\nR,G,74\nR,H,64\nR,I,100\nR,J,79\nR,K,98\nR,L,61\nR,M,65\nR,N,83\nR,O,112\nR,P,100\nR,Q,70\n\nAlso, when you send the plan back, please follow this loose JSON shape so it's easy to read and check. Something like:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nQuick note on what those fields mean in plain language: \"selected\" is the list of stations you decide to open as hubs, and \"assignments\" lists, for every station in the network, which opened hub it gets connected to (one entry per station). This is just a sketch of the shape I need — not the final answer.\n\nAlso, please use the exact station identifiers from the instance input — do not rename them or invent new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 96, 62, 64, 57, 85, 67, 57, 84, 80, 98, 69, 67, 53, 38, 71, 83, 97 ], [ 96, 0, 80, 71, 48, 114, 98, 75, 34, 91, 48, 72, 51, 86, 118, 113, 112, 107 ], [ 62, 80, 0, 49, 59, 69, 42, 44, 80, 59, 78, 41, 29, 58, 76, 80, 67, 36 ], [ 64, 71, 49, 0, 50, 57, 67, 59, 88, 76, 100, 36, 20, 25, 47, 65, 55, 80 ], [ 57, 48, 59, 50, 0, 75, 77, 69, 82, 52, 96, 37, 30, 54, 95, 84, 73, 88 ], [ 85, 114, 69, 57, 75, 0, 91, 92, 109, 90, 126, 64, 67, 46, 103, 103, 2, 72 ], [ 67, 98, 42, 67, 77, 91, 0, 74, 109, 81, 102, 71, 47, 78, 94, 99, 89, 74 ], [ 57, 75, 44, 59, 69, 92, 74, 0, 108, 78, 41, 49, 39, 59, 90, 57, 94, 64 ], [ 84, 34, 80, 88, 82, 109, 109, 108, 0, 104, 82, 86, 85, 77, 122, 127, 107, 100 ], [ 80, 91, 59, 76, 52, 90, 81, 78, 104, 0, 116, 50, 68, 70, 85, 89, 88, 79 ], [ 98, 48, 78, 100, 96, 126, 102, 41, 82, 116, 0, 74, 80, 100, 131, 98, 124, 98 ], [ 69, 72, 41, 36, 37, 64, 71, 49, 86, 50, 74, 0, 46, 51, 79, 49, 62, 61 ], [ 67, 51, 29, 20, 30, 67, 47, 39, 85, 68, 80, 46, 0, 35, 67, 75, 65, 65 ], [ 53, 86, 58, 25, 54, 46, 78, 59, 77, 70, 100, 51, 35, 0, 72, 80, 44, 83 ], [ 38, 118, 76, 47, 95, 103, 94, 90, 122, 85, 131, 79, 67, 72, 0, 33, 102, 112 ], [ 71, 113, 80, 65, 84, 103, 99, 57, 127, 89, 98, 49, 75, 80, 33, 0, 101, 100 ], [ 83, 112, 67, 55, 73, 2, 89, 94, 107, 88, 124, 62, 65, 44, 102, 101, 0, 70 ], [ 97, 107, 36, 80, 88, 72, 74, 64, 100, 79, 98, 61, 65, 83, 112, 100, 70, 0 ] ], "p": 6, "objective": 398.0 }, "solution": { "facilities": [ 1, 2, 5, 9, 12, 14 ], "assignments": [ 14, 1, 2, 12, 12, 5, 2, 12, 1, 9, 1, 2, 12, 12, 14, 14, 5, 2 ] }, "obj": 398.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 6, "sites": [ { "id": "A", "distances": { "A": 0, "B": 96, "C": 62, "D": 64, "E": 57, "F": 85, "G": 67, "H": 57, "I": 84, "J": 80, "K": 98, "L": 69, "M": 67, "N": 53, "O": 38, "P": 71, "Q": 83, "R": 97 } }, { "id": "B", "distances": { "A": 96, "B": 0, "C": 80, "D": 71, "E": 48, "F": 114, "G": 98, "H": 75, "I": 34, "J": 91, "K": 48, "L": 72, "M": 51, "N": 86, "O": 118, "P": 113, "Q": 112, "R": 107 } }, { "id": "C", "distances": { "A": 62, "B": 80, "C": 0, "D": 49, "E": 59, "F": 69, "G": 42, "H": 44, "I": 80, "J": 59, "K": 78, "L": 41, "M": 29, "N": 58, "O": 76, "P": 80, "Q": 67, "R": 36 } }, { "id": "D", "distances": { "A": 64, "B": 71, "C": 49, "D": 0, "E": 50, "F": 57, "G": 67, "H": 59, "I": 88, "J": 76, "K": 100, "L": 36, "M": 20, "N": 25, "O": 47, "P": 65, "Q": 55, "R": 80 } }, { "id": "E", "distances": { "A": 57, "B": 48, "C": 59, "D": 50, "E": 0, "F": 75, "G": 77, "H": 69, "I": 82, "J": 52, "K": 96, "L": 37, "M": 30, "N": 54, "O": 95, "P": 84, "Q": 73, "R": 88 } }, { "id": "F", "distances": { "A": 85, "B": 114, "C": 69, "D": 57, "E": 75, "F": 0, "G": 91, "H": 92, "I": 109, "J": 90, "K": 126, "L": 64, "M": 67, "N": 46, "O": 103, "P": 103, "Q": 2, "R": 72 } }, { "id": "G", "distances": { "A": 67, "B": 98, "C": 42, "D": 67, "E": 77, "F": 91, "G": 0, "H": 74, "I": 109, "J": 81, "K": 102, "L": 71, "M": 47, "N": 78, "O": 94, "P": 99, "Q": 89, "R": 74 } }, { "id": "H", "distances": { "A": 57, "B": 75, "C": 44, "D": 59, "E": 69, "F": 92, "G": 74, "H": 0, "I": 108, "J": 78, "K": 41, "L": 49, "M": 39, "N": 59, "O": 90, "P": 57, "Q": 94, "R": 64 } }, { "id": "I", "distances": { "A": 84, "B": 34, "C": 80, "D": 88, "E": 82, "F": 109, "G": 109, "H": 108, "I": 0, "J": 104, "K": 82, "L": 86, "M": 85, "N": 77, "O": 122, "P": 127, "Q": 107, "R": 100 } }, { "id": "J", "distances": { "A": 80, "B": 91, "C": 59, "D": 76, "E": 52, "F": 90, "G": 81, "H": 78, "I": 104, "J": 0, "K": 116, "L": 50, "M": 68, "N": 70, "O": 85, "P": 89, "Q": 88, "R": 79 } }, { "id": "K", "distances": { "A": 98, "B": 48, "C": 78, "D": 100, "E": 96, "F": 126, "G": 102, "H": 41, "I": 82, "J": 116, "K": 0, "L": 74, "M": 80, "N": 100, "O": 131, "P": 98, "Q": 124, "R": 98 } }, { "id": "L", "distances": { "A": 69, "B": 72, "C": 41, "D": 36, "E": 37, "F": 64, "G": 71, "H": 49, "I": 86, "J": 50, "K": 74, "L": 0, "M": 46, "N": 51, "O": 79, "P": 49, "Q": 62, "R": 61 } }, { "id": "M", "distances": { "A": 67, "B": 51, "C": 29, "D": 20, "E": 30, "F": 67, "G": 47, "H": 39, "I": 85, "J": 68, "K": 80, "L": 46, "M": 0, "N": 35, "O": 67, "P": 75, "Q": 65, "R": 65 } }, { "id": "N", "distances": { "A": 53, "B": 86, "C": 58, "D": 25, "E": 54, "F": 46, "G": 78, "H": 59, "I": 77, "J": 70, "K": 100, "L": 51, "M": 35, "N": 0, "O": 72, "P": 80, "Q": 44, "R": 83 } }, { "id": "O", "distances": { "A": 38, "B": 118, "C": 76, "D": 47, "E": 95, "F": 103, "G": 94, "H": 90, "I": 122, "J": 85, "K": 131, "L": 79, "M": 67, "N": 72, "O": 0, "P": 33, "Q": 102, "R": 112 } }, { "id": "P", "distances": { "A": 71, "B": 113, "C": 80, "D": 65, "E": 84, "F": 103, "G": 99, "H": 57, "I": 127, "J": 89, "K": 98, "L": 49, "M": 75, "N": 80, "O": 33, "P": 0, "Q": 101, "R": 100 } }, { "id": "Q", "distances": { "A": 83, "B": 112, "C": 67, "D": 55, "E": 73, "F": 2, "G": 89, "H": 94, "I": 107, "J": 88, "K": 124, "L": 62, "M": 65, "N": 44, "O": 102, "P": 101, "Q": 0, "R": 70 } }, { "id": "R", "distances": { "A": 97, "B": 107, "C": 36, "D": 80, "E": 88, "F": 72, "G": 74, "H": 64, "I": 100, "J": 79, "K": 98, "L": 61, "M": 65, "N": 83, "O": 112, "P": 100, "Q": 70, "R": 0 } } ], "objective": 398.0 }, "solution_variant": { "selected": [ "B", "C", "F", "J", "M", "O" ], "assignments": [ "O", "B", "C", "M", "M", "F", "C", "M", "B", "J", "B", "C", "M", "M", "O", "O", "F", "C" ] }, "context_index": 33, "input_format": "csv", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Out in the suburbs the energy team mapped every parking lot and the drive between any two of them, then had to choose exactly a handful of lots to host charging stations and link every lot to one chosen station. The better the choice, the less everyone drives overall — you measure that by summing each parking lot’s distance to its assigned hub and looking for the smallest total. Every lot must be assigned once and only once, and the pairwise distances are provided; the concrete details follow below.\n\n{\n \"total_parking_lots\": 19,\n \"hubs_to_open\": 6,\n \"parking_lot_ids\": [\n 0,\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16,\n 17,\n 18\n ],\n \"data\": [\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 195\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 132\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 198\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 162\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 76\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 172\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 152\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 143\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 174\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 159\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 177\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 162\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 177\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 115\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 207\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 206\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 155\n },\n {\n \"origin_lot_id\": 0,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 118\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 195\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 122\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 165\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 122\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 150\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 155\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 117\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 108\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 120\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 72\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 115\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 89\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 173\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 111\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 186\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 186\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 103\n },\n {\n \"origin_lot_id\": 1,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 89\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 132\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 122\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 173\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 104\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 56\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 87\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 48\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 39\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 97\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 91\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 118\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 71\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 79\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 17\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 134\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 103\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 54\n },\n {\n \"origin_lot_id\": 2,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 77\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 198\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 165\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 173\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 134\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 147\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 122\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 161\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 170\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 138\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 93\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 177\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 136\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 101\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 156\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 153\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 170\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 196\n },\n {\n \"origin_lot_id\": 3,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 106\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 162\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 122\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 104\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 134\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 86\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 108\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 105\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 96\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 114\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 95\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 80\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 33\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 102\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 93\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 143\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 130\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 130\n },\n {\n \"origin_lot_id\": 4,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 92\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 76\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 150\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 56\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 147\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 86\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 115\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 76\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 67\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 125\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 108\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 139\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 92\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 101\n },\n {\n \"origin_lot_id\": 5,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 39\n 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\"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 165\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 144\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 97\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 69\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 91\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 185\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 84\n },\n {\n \"origin_lot_id\": 16,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 180\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 155\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 103\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 54\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 196\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 130\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 79\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 113\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 74\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 65\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 123\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 117\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 144\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 97\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 104\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 43\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 160\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 84\n },\n {\n \"origin_lot_id\": 17,\n \"destination_lot_id\": 18,\n \"drive_distance_between_lots\": 131\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 0,\n \"drive_distance_between_lots\": 118\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 1,\n \"drive_distance_between_lots\": 89\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 2,\n \"drive_distance_between_lots\": 77\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 3,\n \"drive_distance_between_lots\": 106\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 4,\n \"drive_distance_between_lots\": 92\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 5,\n \"drive_distance_between_lots\": 105\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 6,\n \"drive_distance_between_lots\": 80\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 7,\n \"drive_distance_between_lots\": 119\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 8,\n \"drive_distance_between_lots\": 116\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 9,\n \"drive_distance_between_lots\": 112\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 10,\n \"drive_distance_between_lots\": 67\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 11,\n \"drive_distance_between_lots\": 71\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 12,\n \"drive_distance_between_lots\": 110\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 13,\n \"drive_distance_between_lots\": 156\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 14,\n \"drive_distance_between_lots\": 94\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 15,\n \"drive_distance_between_lots\": 115\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 16,\n \"drive_distance_between_lots\": 180\n },\n {\n \"origin_lot_id\": 18,\n \"destination_lot_id\": 17,\n \"drive_distance_between_lots\": 131\n }\n ]\n}\n\nIf you send back a reply, keep it in this little JSON shape so it's easy to read and plug in:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis just sketches the form: \"selected\" lists the parking lots you'll open as charging hubs, and \"assignments\" lists, for each lot in the same order as the input, which opened lot it gets tied to. It's just the shape I expect, not the real answer.\n\nPlease use the identifiers from the instance exactly as given — don't rename them or invent new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 195, 132, 198, 162, 76, 172, 152, 143, 174, 159, 177, 162, 177, 115, 207, 206, 155, 118 ], [ 195, 0, 122, 165, 122, 150, 155, 117, 108, 120, 72, 115, 89, 173, 111, 186, 186, 103, 89 ], [ 132, 122, 0, 173, 104, 56, 87, 48, 39, 97, 91, 118, 71, 79, 17, 134, 103, 54, 77 ], [ 198, 165, 173, 0, 134, 147, 122, 161, 170, 138, 93, 177, 136, 101, 156, 153, 170, 196, 106 ], [ 162, 122, 104, 134, 0, 86, 108, 105, 96, 114, 95, 80, 33, 102, 93, 143, 130, 130, 92 ], [ 76, 150, 56, 147, 86, 0, 115, 76, 67, 125, 108, 139, 92, 101, 39, 156, 130, 79, 105 ], [ 172, 155, 87, 122, 108, 115, 0, 39, 48, 89, 83, 151, 107, 120, 76, 61, 149, 113, 80 ], [ 152, 117, 48, 161, 105, 76, 39, 0, 9, 50, 81, 119, 72, 99, 37, 100, 128, 74, 119 ], [ 143, 108, 39, 170, 96, 67, 48, 9, 0, 58, 90, 110, 63, 90, 28, 109, 119, 65, 116 ], [ 174, 120, 97, 138, 114, 125, 89, 50, 58, 0, 99, 141, 94, 148, 86, 150, 177, 123, 112 ], [ 159, 72, 91, 93, 95, 108, 83, 81, 90, 99, 0, 130, 97, 136, 74, 114, 165, 117, 67 ], [ 177, 115, 118, 177, 80, 139, 151, 119, 110, 141, 130, 0, 47, 147, 107, 186, 144, 144, 71 ], [ 162, 89, 71, 136, 33, 92, 107, 72, 63, 94, 97, 47, 0, 100, 60, 143, 97, 97, 110 ], [ 177, 173, 79, 101, 102, 101, 120, 99, 90, 148, 136, 147, 100, 0, 62, 156, 69, 104, 156 ], [ 115, 111, 17, 156, 93, 39, 76, 37, 28, 86, 74, 107, 60, 62, 0, 117, 91, 43, 94 ], [ 207, 186, 134, 153, 143, 156, 61, 100, 109, 150, 114, 186, 143, 156, 117, 0, 185, 160, 115 ], [ 206, 186, 103, 170, 130, 130, 149, 128, 119, 177, 165, 144, 97, 69, 91, 185, 0, 84, 180 ], [ 155, 103, 54, 196, 130, 79, 113, 74, 65, 123, 117, 144, 97, 104, 43, 160, 84, 0, 131 ], [ 118, 89, 77, 106, 92, 105, 80, 119, 116, 112, 67, 71, 110, 156, 94, 115, 180, 131, 0 ] ], "p": 6, "objective": 662.0 }, "solution": { "facilities": [ 0, 7, 10, 12, 14, 15 ], "assignments": [ 0, 10, 14, 10, 12, 14, 7, 7, 7, 7, 10, 12, 12, 14, 14, 15, 14, 14, 10 ] }, "obj": 662.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 6, "sites": [ { "id": 0, "distances": { "0": 0, "1": 195, "2": 132, "3": 198, "4": 162, "5": 76, "6": 172, "7": 152, "8": 143, "9": 174, "10": 159, "11": 177, "12": 162, "13": 177, "14": 115, "15": 207, "16": 206, "17": 155, "18": 118 } }, { "id": 1, "distances": { "0": 195, "1": 0, "2": 122, "3": 165, "4": 122, "5": 150, "6": 155, "7": 117, "8": 108, "9": 120, "10": 72, "11": 115, "12": 89, "13": 173, "14": 111, "15": 186, "16": 186, "17": 103, "18": 89 } }, { "id": 2, "distances": { "0": 132, "1": 122, "2": 0, "3": 173, "4": 104, "5": 56, "6": 87, "7": 48, "8": 39, "9": 97, "10": 91, "11": 118, "12": 71, "13": 79, "14": 17, "15": 134, "16": 103, "17": 54, "18": 77 } }, { "id": 3, "distances": { "0": 198, "1": 165, "2": 173, "3": 0, "4": 134, "5": 147, "6": 122, "7": 161, "8": 170, "9": 138, "10": 93, "11": 177, "12": 136, "13": 101, "14": 156, "15": 153, "16": 170, "17": 196, "18": 106 } }, { "id": 4, "distances": { "0": 162, "1": 122, "2": 104, "3": 134, "4": 0, "5": 86, "6": 108, "7": 105, "8": 96, "9": 114, "10": 95, "11": 80, "12": 33, "13": 102, "14": 93, "15": 143, "16": 130, "17": 130, "18": 92 } }, { "id": 5, "distances": { "0": 76, "1": 150, "2": 56, "3": 147, "4": 86, "5": 0, "6": 115, "7": 76, "8": 67, "9": 125, "10": 108, "11": 139, "12": 92, "13": 101, "14": 39, "15": 156, "16": 130, "17": 79, "18": 105 } }, { "id": 6, "distances": { "0": 172, "1": 155, "2": 87, "3": 122, "4": 108, "5": 115, "6": 0, "7": 39, "8": 48, "9": 89, "10": 83, "11": 151, "12": 107, "13": 120, "14": 76, "15": 61, "16": 149, "17": 113, "18": 80 } }, { "id": 7, "distances": { "0": 152, "1": 117, "2": 48, "3": 161, "4": 105, "5": 76, "6": 39, "7": 0, "8": 9, "9": 50, "10": 81, "11": 119, "12": 72, "13": 99, "14": 37, "15": 100, "16": 128, "17": 74, "18": 119 } }, { "id": 8, "distances": { "0": 143, "1": 108, "2": 39, "3": 170, "4": 96, "5": 67, "6": 48, "7": 9, "8": 0, "9": 58, "10": 90, "11": 110, "12": 63, "13": 90, "14": 28, "15": 109, "16": 119, "17": 65, "18": 116 } }, { "id": 9, "distances": { "0": 174, "1": 120, "2": 97, "3": 138, "4": 114, "5": 125, "6": 89, "7": 50, "8": 58, "9": 0, "10": 99, "11": 141, "12": 94, "13": 148, "14": 86, "15": 150, "16": 177, "17": 123, "18": 112 } }, { "id": 10, "distances": { "0": 159, "1": 72, "2": 91, "3": 93, "4": 95, "5": 108, "6": 83, "7": 81, "8": 90, "9": 99, "10": 0, "11": 130, "12": 97, "13": 136, "14": 74, "15": 114, "16": 165, "17": 117, "18": 67 } }, { "id": 11, "distances": { "0": 177, "1": 115, "2": 118, "3": 177, "4": 80, "5": 139, "6": 151, "7": 119, "8": 110, "9": 141, "10": 130, "11": 0, "12": 47, "13": 147, "14": 107, "15": 186, "16": 144, "17": 144, "18": 71 } }, { "id": 12, "distances": { "0": 162, "1": 89, "2": 71, "3": 136, "4": 33, "5": 92, "6": 107, "7": 72, "8": 63, "9": 94, "10": 97, "11": 47, "12": 0, "13": 100, "14": 60, "15": 143, "16": 97, "17": 97, "18": 110 } }, { "id": 13, "distances": { "0": 177, "1": 173, "2": 79, "3": 101, "4": 102, "5": 101, "6": 120, "7": 99, "8": 90, "9": 148, "10": 136, "11": 147, "12": 100, "13": 0, "14": 62, "15": 156, "16": 69, "17": 104, "18": 156 } }, { "id": 14, "distances": { "0": 115, "1": 111, "2": 17, "3": 156, "4": 93, "5": 39, "6": 76, "7": 37, "8": 28, "9": 86, "10": 74, "11": 107, "12": 60, "13": 62, "14": 0, "15": 117, "16": 91, "17": 43, "18": 94 } }, { "id": 15, "distances": { "0": 207, "1": 186, "2": 134, "3": 153, "4": 143, "5": 156, "6": 61, "7": 100, "8": 109, "9": 150, "10": 114, "11": 186, "12": 143, "13": 156, "14": 117, "15": 0, "16": 185, "17": 160, "18": 115 } }, { "id": 16, "distances": { "0": 206, "1": 186, "2": 103, "3": 170, "4": 130, "5": 130, "6": 149, "7": 128, "8": 119, "9": 177, "10": 165, "11": 144, "12": 97, "13": 69, "14": 91, "15": 185, "16": 0, "17": 84, "18": 180 } }, { "id": 17, "distances": { "0": 155, "1": 103, "2": 54, "3": 196, "4": 130, "5": 79, "6": 113, "7": 74, "8": 65, "9": 123, "10": 117, "11": 144, "12": 97, "13": 104, "14": 43, "15": 160, "16": 84, "17": 0, "18": 131 } }, { "id": 18, "distances": { "0": 118, "1": 89, "2": 77, "3": 106, "4": 92, "5": 105, "6": 80, "7": 119, "8": 116, "9": 112, "10": 67, "11": 71, "12": 110, "13": 156, "14": 94, "15": 115, "16": 180, "17": 131, "18": 0 } } ], "objective": 662.0 }, "solution_variant": { "selected": [ 0, 7, 10, 12, 14, 15 ], "assignments": [ 0, 10, 14, 10, 12, 14, 7, 7, 7, 7, 10, 12, 12, 14, 14, 15, 14, 14, 10 ] }, "context_index": 34, "input_format": "json", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Recently the sanitation director sketched out a plan: operate a fixed number of depots, then attach every pickup zone to a single open depot so service is complete and never duplicated. The scorecard was total distance driven — simply sum the distance from each zone to its assigned depot — and the goal was to make that total as low as possible. The exact distances and candidate sites follow below.\n\n# total_pickup_zones_and_candidates=19\n# depots_to_open=4\n# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S\norigin_zone_id,candidate_depot_id,travel_distance\nA,B,38\nA,C,47\nA,D,38\nA,E,39\nA,F,40\nA,G,29\nA,H,39\nA,I,46\nA,J,33\nA,K,36\nA,L,53\nA,M,35\nA,N,39\nA,O,38\nA,P,43\nA,Q,40\nA,R,50\nA,S,47\nB,A,38\nB,C,40\nB,D,27\nB,E,21\nB,F,16\nB,G,31\nB,H,32\nB,I,40\nB,J,25\nB,K,25\nB,L,29\nB,M,25\nB,N,38\nB,O,29\nB,P,34\nB,Q,25\nB,R,35\nB,S,35\nC,A,47\nC,B,40\nC,D,37\nC,E,31\nC,F,36\nC,G,23\nC,H,40\nC,I,35\nC,J,36\nC,K,19\nC,L,40\nC,M,33\nC,N,51\nC,O,39\nC,P,44\nC,Q,36\nC,R,43\nC,S,40\nD,A,38\nD,B,27\nD,C,37\nD,E,26\nD,F,23\nD,G,34\nD,H,30\nD,I,46\nD,J,36\nD,K,30\nD,L,37\nD,M,34\nD,N,36\nD,O,29\nD,P,7\nD,Q,38\nD,R,42\nD,S,30\nE,A,39\nE,B,21\nE,C,31\nE,D,26\nE,F,24\nE,G,30\nE,H,23\nE,I,38\nE,J,20\nE,K,24\nE,L,31\nE,M,28\nE,N,34\nE,O,28\nE,P,22\nE,Q,27\nE,R,26\nE,S,33\nF,A,40\nF,B,16\nF,C,36\nF,D,23\nF,E,24\nF,G,17\nF,H,19\nF,I,39\nF,J,25\nF,K,35\nF,L,39\nF,M,31\nF,N,40\nF,O,30\nF,P,30\nF,Q,28\nF,R,32\nF,S,19\nG,A,29\nG,B,31\nG,C,23\nG,D,34\nG,E,30\nG,F,17\nG,H,26\nG,I,39\nG,J,29\nG,K,22\nG,L,35\nG,M,20\nG,N,28\nG,O,32\nG,P,29\nG,Q,26\nG,R,39\nG,S,26\nH,A,39\nH,B,32\nH,C,40\nH,D,30\nH,E,23\nH,F,19\nH,G,26\nH,I,39\nH,J,28\nH,K,35\nH,L,38\nH,M,36\nH,N,39\nH,O,25\nH,P,23\nH,Q,27\nH,R,31\nH,S,28\nI,A,46\nI,B,40\nI,C,35\nI,D,46\nI,E,38\nI,F,39\nI,G,39\nI,H,39\nI,J,20\nI,K,34\nI,L,35\nI,M,30\nI,N,39\nI,O,33\nI,P,40\nI,Q,33\nI,R,51\nI,S,40\nJ,A,33\nJ,B,25\nJ,C,36\nJ,D,36\nJ,E,20\nJ,F,25\nJ,G,29\nJ,H,28\nJ,I,20\nJ,K,35\nJ,L,37\nJ,M,29\nJ,N,26\nJ,O,23\nJ,P,35\nJ,Q,13\nJ,R,32\nJ,S,36\nK,A,36\nK,B,25\nK,C,19\nK,D,30\nK,E,24\nK,F,35\nK,G,22\nK,H,35\nK,I,34\nK,J,35\nK,L,39\nK,M,26\nK,N,41\nK,O,30\nK,P,36\nK,Q,28\nK,R,41\nK,S,31\nL,A,53\nL,B,29\nL,C,40\nL,D,37\nL,E,31\nL,F,39\nL,G,35\nL,H,38\nL,I,35\nL,J,37\nL,K,39\nL,M,43\nL,N,50\nL,O,28\nL,P,35\nL,Q,34\nL,R,41\nL,S,46\nM,A,35\nM,B,25\nM,C,33\nM,D,34\nM,E,28\nM,F,31\nM,G,20\nM,H,36\nM,I,30\nM,J,29\nM,K,26\nM,L,43\nM,N,44\nM,O,29\nM,P,31\nM,Q,29\nM,R,47\nM,S,12\nN,A,39\nN,B,38\nN,C,51\nN,D,36\nN,E,34\nN,F,40\nN,G,28\nN,H,39\nN,I,39\nN,J,26\nN,K,41\nN,L,50\nN,M,44\nN,O,38\nN,P,40\nN,Q,33\nN,R,50\nN,S,42\nO,A,38\nO,B,29\nO,C,39\nO,D,29\nO,E,28\nO,F,30\nO,G,32\nO,H,25\nO,I,33\nO,J,23\nO,K,30\nO,L,28\nO,M,29\nO,N,38\nO,P,36\nO,Q,13\nO,R,36\nO,S,23\nP,A,43\nP,B,34\nP,C,44\nP,D,7\nP,E,22\nP,F,30\nP,G,29\nP,H,23\nP,I,40\nP,J,35\nP,K,36\nP,L,35\nP,M,31\nP,N,40\nP,O,36\nP,Q,31\nP,R,47\nP,S,33\nQ,A,40\nQ,B,25\nQ,C,36\nQ,D,38\nQ,E,27\nQ,F,28\nQ,G,26\nQ,H,27\nQ,I,33\nQ,J,13\nQ,K,28\nQ,L,34\nQ,M,29\nQ,N,33\nQ,O,13\nQ,P,31\nQ,R,38\nQ,S,36\nR,A,50\nR,B,35\nR,C,43\nR,D,42\nR,E,26\nR,F,32\nR,G,39\nR,H,31\nR,I,51\nR,J,32\nR,K,41\nR,L,41\nR,M,47\nR,N,50\nR,O,36\nR,P,47\nR,Q,38\nR,S,35\nS,A,47\nS,B,35\nS,C,40\nS,D,30\nS,E,33\nS,F,19\nS,G,26\nS,H,28\nS,I,40\nS,J,36\nS,K,31\nS,L,46\nS,M,12\nS,N,42\nS,O,23\nS,P,33\nS,Q,36\nS,R,35\n\nIf you want to give the solution back, just use this simple JSON shape so I can read it easily — nothing fancy, just a quick form to say which depots you open and which depot each pickup zone belongs to:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the depot IDs you decide to open. \"assignments\" is a list (in the same order as the pickup zones in the instance) saying which opened depot each zone is attached to. Think of it like filling out a form: picked depots in one box, and then one line per zone pointing to its depot.\n\nThis JSON is just a sketch of the shape I expect, not the actual answer — fill in the real IDs from the instance when you submit.\n\nPlease use the identifiers exactly as they appear in the instance input — do not rename them or invent new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 38, 47, 38, 39, 40, 29, 39, 46, 33, 36, 53, 35, 39, 38, 43, 40, 50, 47 ], [ 38, 0, 40, 27, 21, 16, 31, 32, 40, 25, 25, 29, 25, 38, 29, 34, 25, 35, 35 ], [ 47, 40, 0, 37, 31, 36, 23, 40, 35, 36, 19, 40, 33, 51, 39, 44, 36, 43, 40 ], [ 38, 27, 37, 0, 26, 23, 34, 30, 46, 36, 30, 37, 34, 36, 29, 7, 38, 42, 30 ], [ 39, 21, 31, 26, 0, 24, 30, 23, 38, 20, 24, 31, 28, 34, 28, 22, 27, 26, 33 ], [ 40, 16, 36, 23, 24, 0, 17, 19, 39, 25, 35, 39, 31, 40, 30, 30, 28, 32, 19 ], [ 29, 31, 23, 34, 30, 17, 0, 26, 39, 29, 22, 35, 20, 28, 32, 29, 26, 39, 26 ], [ 39, 32, 40, 30, 23, 19, 26, 0, 39, 28, 35, 38, 36, 39, 25, 23, 27, 31, 28 ], [ 46, 40, 35, 46, 38, 39, 39, 39, 0, 20, 34, 35, 30, 39, 33, 40, 33, 51, 40 ], [ 33, 25, 36, 36, 20, 25, 29, 28, 20, 0, 35, 37, 29, 26, 23, 35, 13, 32, 36 ], [ 36, 25, 19, 30, 24, 35, 22, 35, 34, 35, 0, 39, 26, 41, 30, 36, 28, 41, 31 ], [ 53, 29, 40, 37, 31, 39, 35, 38, 35, 37, 39, 0, 43, 50, 28, 35, 34, 41, 46 ], [ 35, 25, 33, 34, 28, 31, 20, 36, 30, 29, 26, 43, 0, 44, 29, 31, 29, 47, 12 ], [ 39, 38, 51, 36, 34, 40, 28, 39, 39, 26, 41, 50, 44, 0, 38, 40, 33, 50, 42 ], [ 38, 29, 39, 29, 28, 30, 32, 25, 33, 23, 30, 28, 29, 38, 0, 36, 13, 36, 23 ], [ 43, 34, 44, 7, 22, 30, 29, 23, 40, 35, 36, 35, 31, 40, 36, 0, 31, 47, 33 ], [ 40, 25, 36, 38, 27, 28, 26, 27, 33, 13, 28, 34, 29, 33, 13, 31, 0, 38, 36 ], [ 50, 35, 43, 42, 26, 32, 39, 31, 51, 32, 41, 41, 47, 50, 36, 47, 38, 0, 35 ], [ 47, 35, 40, 30, 33, 19, 26, 28, 40, 36, 31, 46, 12, 42, 23, 33, 36, 35, 0 ] ], "p": 4, "objective": 324.0 }, "solution": { "facilities": [ 5, 6, 9, 15 ], "assignments": [ 6, 5, 6, 15, 9, 5, 6, 5, 9, 9, 6, 6, 6, 9, 9, 15, 9, 5, 5 ] }, "obj": 324.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 4, "sites": [ { "id": "A", "distances": { "A": 0, "B": 38, "C": 47, "D": 38, "E": 39, "F": 40, "G": 29, "H": 39, "I": 46, "J": 33, "K": 36, "L": 53, "M": 35, "N": 39, "O": 38, "P": 43, "Q": 40, "R": 50, "S": 47 } }, { "id": "B", "distances": { "A": 38, "B": 0, "C": 40, "D": 27, "E": 21, "F": 16, "G": 31, "H": 32, "I": 40, "J": 25, "K": 25, "L": 29, "M": 25, "N": 38, "O": 29, "P": 34, "Q": 25, "R": 35, "S": 35 } }, { "id": "C", "distances": { "A": 47, "B": 40, "C": 0, "D": 37, "E": 31, "F": 36, "G": 23, "H": 40, "I": 35, "J": 36, "K": 19, "L": 40, "M": 33, "N": 51, "O": 39, "P": 44, "Q": 36, "R": 43, "S": 40 } }, { "id": "D", "distances": { "A": 38, "B": 27, "C": 37, "D": 0, "E": 26, "F": 23, "G": 34, "H": 30, "I": 46, "J": 36, "K": 30, "L": 37, "M": 34, "N": 36, "O": 29, "P": 7, "Q": 38, "R": 42, "S": 30 } }, { "id": "E", "distances": { "A": 39, "B": 21, "C": 31, "D": 26, "E": 0, "F": 24, "G": 30, "H": 23, "I": 38, "J": 20, "K": 24, "L": 31, "M": 28, "N": 34, "O": 28, "P": 22, "Q": 27, "R": 26, "S": 33 } }, { "id": "F", "distances": { "A": 40, "B": 16, "C": 36, "D": 23, "E": 24, "F": 0, "G": 17, "H": 19, "I": 39, "J": 25, "K": 35, "L": 39, "M": 31, "N": 40, "O": 30, "P": 30, "Q": 28, "R": 32, "S": 19 } }, { "id": "G", "distances": { "A": 29, "B": 31, "C": 23, "D": 34, "E": 30, "F": 17, "G": 0, "H": 26, "I": 39, "J": 29, "K": 22, "L": 35, "M": 20, "N": 28, "O": 32, "P": 29, "Q": 26, "R": 39, "S": 26 } }, { "id": "H", "distances": { "A": 39, "B": 32, "C": 40, "D": 30, "E": 23, "F": 19, "G": 26, "H": 0, "I": 39, "J": 28, "K": 35, "L": 38, "M": 36, "N": 39, "O": 25, "P": 23, "Q": 27, "R": 31, "S": 28 } }, { "id": "I", "distances": { "A": 46, "B": 40, "C": 35, "D": 46, "E": 38, "F": 39, "G": 39, "H": 39, "I": 0, "J": 20, "K": 34, "L": 35, "M": 30, "N": 39, "O": 33, "P": 40, "Q": 33, "R": 51, "S": 40 } }, { "id": "J", "distances": { "A": 33, "B": 25, "C": 36, "D": 36, "E": 20, "F": 25, "G": 29, "H": 28, "I": 20, "J": 0, "K": 35, "L": 37, "M": 29, "N": 26, "O": 23, "P": 35, "Q": 13, "R": 32, "S": 36 } }, { "id": "K", "distances": { "A": 36, "B": 25, "C": 19, "D": 30, "E": 24, "F": 35, "G": 22, "H": 35, "I": 34, "J": 35, "K": 0, "L": 39, "M": 26, "N": 41, "O": 30, "P": 36, "Q": 28, "R": 41, "S": 31 } }, { "id": "L", "distances": { "A": 53, "B": 29, "C": 40, "D": 37, "E": 31, "F": 39, "G": 35, "H": 38, "I": 35, "J": 37, "K": 39, "L": 0, "M": 43, "N": 50, "O": 28, "P": 35, "Q": 34, "R": 41, "S": 46 } }, { "id": "M", "distances": { "A": 35, "B": 25, "C": 33, "D": 34, "E": 28, "F": 31, "G": 20, "H": 36, "I": 30, "J": 29, "K": 26, "L": 43, "M": 0, "N": 44, "O": 29, "P": 31, "Q": 29, "R": 47, "S": 12 } }, { "id": "N", "distances": { "A": 39, "B": 38, "C": 51, "D": 36, "E": 34, "F": 40, "G": 28, "H": 39, "I": 39, "J": 26, "K": 41, "L": 50, "M": 44, "N": 0, "O": 38, "P": 40, "Q": 33, "R": 50, "S": 42 } }, { "id": "O", "distances": { "A": 38, "B": 29, "C": 39, "D": 29, "E": 28, "F": 30, "G": 32, "H": 25, "I": 33, "J": 23, "K": 30, "L": 28, "M": 29, "N": 38, "O": 0, "P": 36, "Q": 13, "R": 36, "S": 23 } }, { "id": "P", "distances": { "A": 43, "B": 34, "C": 44, "D": 7, "E": 22, "F": 30, "G": 29, "H": 23, "I": 40, "J": 35, "K": 36, "L": 35, "M": 31, "N": 40, "O": 36, "P": 0, "Q": 31, "R": 47, "S": 33 } }, { "id": "Q", "distances": { "A": 40, "B": 25, "C": 36, "D": 38, "E": 27, "F": 28, "G": 26, "H": 27, "I": 33, "J": 13, "K": 28, "L": 34, "M": 29, "N": 33, "O": 13, "P": 31, "Q": 0, "R": 38, "S": 36 } }, { "id": "R", "distances": { "A": 50, "B": 35, "C": 43, "D": 42, "E": 26, "F": 32, "G": 39, "H": 31, "I": 51, "J": 32, "K": 41, "L": 41, "M": 47, "N": 50, "O": 36, "P": 47, "Q": 38, "R": 0, "S": 35 } }, { "id": "S", "distances": { "A": 47, "B": 35, "C": 40, "D": 30, "E": 33, "F": 19, "G": 26, "H": 28, "I": 40, "J": 36, "K": 31, "L": 46, "M": 12, "N": 42, "O": 23, "P": 33, "Q": 36, "R": 35, "S": 0 } } ], "objective": 324.0 }, "solution_variant": { "selected": [ "F", "G", "J", "P" ], "assignments": [ "G", "F", "G", "P", "J", "F", "G", "F", "J", "J", "G", "G", "G", "J", "J", "P", "J", "F", "F" ] }, "context_index": 35, "input_format": "csv", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Many neighborhoods depend on a nearby ATM, so the operations group must pick a fixed number of candidate sites to actually host machines. After those sites are picked, every neighborhood must be assigned to one and only one of them — nothing left out and no double assignments. The best setup is the one that keeps overall customer travel as low as possible: add up the distances from each neighborhood to its assigned ATM, and look for the smallest total. The exact list of sites and pairwise distances appears below.\n\nThere are 15 candidate neighborhoods, exactly 5 of which must be opened as ATMs, and the location identifiers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.\nTravel distance from 0 to 1 is 34.\nTravel distance from 0 to 2 is 59.\nTravel distance from 0 to 3 is 45.\nTravel distance from 0 to 4 is 52.\nTravel distance from 0 to 5 is 39.\nTravel distance from 0 to 6 is 45.\nTravel distance from 0 to 7 is 39.\nTravel distance from 0 to 8 is 34.\nTravel distance from 0 to 9 is 46.\nTravel distance from 0 to 10 is 47.\nTravel distance from 0 to 11 is 43.\nTravel distance from 0 to 12 is 33.\nTravel distance from 0 to 13 is 42.\nTravel distance from 0 to 14 is 25.\nTravel distance from 1 to 0 is 34.\nTravel distance from 1 to 2 is 46.\nTravel distance from 1 to 3 is 35.\nTravel distance from 1 to 4 is 37.\nTravel distance from 1 to 5 is 33.\nTravel distance from 1 to 6 is 21.\nTravel distance from 1 to 7 is 30.\nTravel distance from 1 to 8 is 36.\nTravel distance from 1 to 9 is 37.\nTravel distance from 1 to 10 is 37.\nTravel distance from 1 to 11 is 26.\nTravel distance from 1 to 12 is 39.\nTravel distance from 1 to 13 is 14.\nTravel distance from 1 to 14 is 35.\nTravel distance from 2 to 0 is 59.\nTravel distance from 2 to 1 is 46.\nTravel distance from 2 to 3 is 29.\nTravel distance from 2 to 4 is 46.\nTravel distance from 2 to 5 is 42.\nTravel distance from 2 to 6 is 49.\nTravel distance from 2 to 7 is 37.\nTravel distance from 2 to 8 is 45.\nTravel distance from 2 to 9 is 46.\nTravel distance from 2 to 10 is 50.\nTravel distance from 2 to 11 is 37.\nTravel distance from 2 to 12 is 31.\nTravel distance from 2 to 13 is 45.\nTravel distance from 2 to 14 is 40.\nTravel distance from 3 to 0 is 45.\nTravel distance from 3 to 1 is 35.\nTravel distance from 3 to 2 is 29.\nTravel distance from 3 to 4 is 42.\nTravel distance from 3 to 5 is 38.\nTravel distance from 3 to 6 is 44.\nTravel distance from 3 to 7 is 35.\nTravel distance from 3 to 8 is 38.\nTravel distance from 3 to 9 is 40.\nTravel distance from 3 to 10 is 41.\nTravel distance from 3 to 11 is 39.\nTravel distance from 3 to 12 is 17.\nTravel distance from 3 to 13 is 31.\nTravel distance from 3 to 14 is 32.\nTravel distance from 4 to 0 is 52.\nTravel distance from 4 to 1 is 37.\nTravel distance from 4 to 2 is 46.\nTravel distance from 4 to 3 is 42.\nTravel distance from 4 to 5 is 42.\nTravel distance from 4 to 6 is 41.\nTravel distance from 4 to 7 is 23.\nTravel distance from 4 to 8 is 40.\nTravel distance from 4 to 9 is 30.\nTravel distance from 4 to 10 is 29.\nTravel distance from 4 to 11 is 39.\nTravel distance from 4 to 12 is 25.\nTravel distance from 4 to 13 is 42.\nTravel distance from 4 to 14 is 31.\nTravel distance from 5 to 0 is 39.\nTravel distance from 5 to 1 is 33.\nTravel distance from 5 to 2 is 42.\nTravel distance from 5 to 3 is 38.\nTravel distance from 5 to 4 is 42.\nTravel distance from 5 to 6 is 30.\nTravel distance from 5 to 7 is 35.\nTravel distance from 5 to 8 is 35.\nTravel distance from 5 to 9 is 22.\nTravel distance from 5 to 10 is 37.\nTravel distance from 5 to 11 is 36.\nTravel distance from 5 to 12 is 27.\nTravel distance from 5 to 13 is 28.\nTravel distance from 5 to 14 is 26.\nTravel distance from 6 to 0 is 45.\nTravel distance from 6 to 1 is 21.\nTravel distance from 6 to 2 is 49.\nTravel distance from 6 to 3 is 44.\nTravel distance from 6 to 4 is 41.\nTravel distance from 6 to 5 is 30.\nTravel distance from 6 to 7 is 34.\nTravel distance from 6 to 8 is 30.\nTravel distance from 6 to 9 is 34.\nTravel distance from 6 to 10 is 35.\nTravel distance from 6 to 11 is 32.\nTravel distance from 6 to 12 is 38.\nTravel distance from 6 to 13 is 29.\nTravel distance from 6 to 14 is 32.\nTravel distance from 7 to 0 is 39.\nTravel distance from 7 to 1 is 30.\nTravel distance from 7 to 2 is 37.\nTravel distance from 7 to 3 is 35.\nTravel distance from 7 to 4 is 23.\nTravel distance from 7 to 5 is 35.\nTravel distance from 7 to 6 is 34.\nTravel distance from 7 to 8 is 26.\nTravel distance from 7 to 9 is 36.\nTravel distance from 7 to 10 is 29.\nTravel distance from 7 to 11 is 30.\nTravel distance from 7 to 12 is 19.\nTravel distance from 7 to 13 is 26.\nTravel distance from 7 to 14 is 26.\nTravel distance from 8 to 0 is 34.\nTravel distance from 8 to 1 is 36.\nTravel distance from 8 to 2 is 45.\nTravel distance from 8 to 3 is 38.\nTravel distance from 8 to 4 is 40.\nTravel distance from 8 to 5 is 35.\nTravel distance from 8 to 6 is 30.\nTravel distance from 8 to 7 is 26.\nTravel distance from 8 to 9 is 40.\nTravel distance from 8 to 10 is 23.\nTravel distance from 8 to 11 is 40.\nTravel distance from 8 to 12 is 32.\nTravel distance from 8 to 13 is 34.\nTravel distance from 8 to 14 is 31.\nTravel distance from 9 to 0 is 46.\nTravel distance from 9 to 1 is 37.\nTravel distance from 9 to 2 is 46.\nTravel distance from 9 to 3 is 40.\nTravel distance from 9 to 4 is 30.\nTravel distance from 9 to 5 is 22.\nTravel distance from 9 to 6 is 34.\nTravel distance from 9 to 7 is 36.\nTravel distance from 9 to 8 is 40.\nTravel distance from 9 to 10 is 33.\nTravel distance from 9 to 11 is 33.\nTravel distance from 9 to 12 is 33.\nTravel distance from 9 to 13 is 35.\nTravel distance from 9 to 14 is 35.\nTravel distance from 10 to 0 is 47.\nTravel distance from 10 to 1 is 37.\nTravel distance from 10 to 2 is 50.\nTravel distance from 10 to 3 is 41.\nTravel distance from 10 to 4 is 29.\nTravel distance from 10 to 5 is 37.\nTravel distance from 10 to 6 is 35.\nTravel distance from 10 to 7 is 29.\nTravel distance from 10 to 8 is 23.\nTravel distance from 10 to 9 is 33.\nTravel distance from 10 to 11 is 33.\nTravel distance from 10 to 12 is 24.\nTravel distance from 10 to 13 is 36.\nTravel distance from 10 to 14 is 22.\nTravel distance from 11 to 0 is 43.\nTravel distance from 11 to 1 is 26.\nTravel distance from 11 to 2 is 37.\nTravel distance from 11 to 3 is 39.\nTravel distance from 11 to 4 is 39.\nTravel distance from 11 to 5 is 36.\nTravel distance from 11 to 6 is 32.\nTravel distance from 11 to 7 is 30.\nTravel distance from 11 to 8 is 40.\nTravel distance from 11 to 9 is 33.\nTravel distance from 11 to 10 is 33.\nTravel distance from 11 to 12 is 22.\nTravel distance from 11 to 13 is 22.\nTravel distance from 11 to 14 is 31.\nTravel distance from 12 to 0 is 33.\nTravel distance from 12 to 1 is 39.\nTravel distance from 12 to 2 is 31.\nTravel distance from 12 to 3 is 17.\nTravel distance from 12 to 4 is 25.\nTravel distance from 12 to 5 is 27.\nTravel distance from 12 to 6 is 38.\nTravel distance from 12 to 7 is 19.\nTravel distance from 12 to 8 is 32.\nTravel distance from 12 to 9 is 33.\nTravel distance from 12 to 10 is 24.\nTravel distance from 12 to 11 is 22.\nTravel distance from 12 to 13 is 28.\nTravel distance from 12 to 14 is 26.\nTravel distance from 13 to 0 is 42.\nTravel distance from 13 to 1 is 14.\nTravel distance from 13 to 2 is 45.\nTravel distance from 13 to 3 is 31.\nTravel distance from 13 to 4 is 42.\nTravel distance from 13 to 5 is 28.\nTravel distance from 13 to 6 is 29.\nTravel distance from 13 to 7 is 26.\nTravel distance from 13 to 8 is 34.\nTravel distance from 13 to 9 is 35.\nTravel distance from 13 to 10 is 36.\nTravel distance from 13 to 11 is 22.\nTravel distance from 13 to 12 is 28.\nTravel distance from 13 to 14 is 29.\nTravel distance from 14 to 0 is 25.\nTravel distance from 14 to 1 is 35.\nTravel distance from 14 to 2 is 40.\nTravel distance from 14 to 3 is 32.\nTravel distance from 14 to 4 is 31.\nTravel distance from 14 to 5 is 26.\nTravel distance from 14 to 6 is 32.\nTravel distance from 14 to 7 is 26.\nTravel distance from 14 to 8 is 31.\nTravel distance from 14 to 9 is 35.\nTravel distance from 14 to 10 is 22.\nTravel distance from 14 to 11 is 31.\nTravel distance from 14 to 12 is 26.\nTravel distance from 14 to 13 is 29.\nUse these pairwise distances to compute total travel when assigning each of the 15 neighborhoods to one of the 5 opened ATMs and select the setup with the smallest total travel.\n\nAlso, when you hand in the final picks and which neighborhood goes to which ATM, please stick to this simple JSON layout so it's easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of sites you're opening, and \"assignments\" as, for each neighborhood in the instance (in the same order the neighborhoods were listed), which opened site it uses. Super informal: selected = the ATMs you turn on, assignments = which ATM each neighborhood walks to.\n\nThis JSON is just a sketch of the expected shape — not the actual answer.\n\nPlease use the exact identifiers from the instance input when filling this in — don't rename or invent labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 34, 59, 45, 52, 39, 45, 39, 34, 46, 47, 43, 33, 42, 25 ], [ 34, 0, 46, 35, 37, 33, 21, 30, 36, 37, 37, 26, 39, 14, 35 ], [ 59, 46, 0, 29, 46, 42, 49, 37, 45, 46, 50, 37, 31, 45, 40 ], [ 45, 35, 29, 0, 42, 38, 44, 35, 38, 40, 41, 39, 17, 31, 32 ], [ 52, 37, 46, 42, 0, 42, 41, 23, 40, 30, 29, 39, 25, 42, 31 ], [ 39, 33, 42, 38, 42, 0, 30, 35, 35, 22, 37, 36, 27, 28, 26 ], [ 45, 21, 49, 44, 41, 30, 0, 34, 30, 34, 35, 32, 38, 29, 32 ], [ 39, 30, 37, 35, 23, 35, 34, 0, 26, 36, 29, 30, 19, 26, 26 ], [ 34, 36, 45, 38, 40, 35, 30, 26, 0, 40, 23, 40, 32, 34, 31 ], [ 46, 37, 46, 40, 30, 22, 34, 36, 40, 0, 33, 33, 33, 35, 35 ], [ 47, 37, 50, 41, 29, 37, 35, 29, 23, 33, 0, 33, 24, 36, 22 ], [ 43, 26, 37, 39, 39, 36, 32, 30, 40, 33, 33, 0, 22, 22, 31 ], [ 33, 39, 31, 17, 25, 27, 38, 19, 32, 33, 24, 22, 0, 28, 26 ], [ 42, 14, 45, 31, 42, 28, 29, 26, 34, 35, 36, 22, 28, 0, 29 ], [ 25, 35, 40, 32, 31, 26, 32, 26, 31, 35, 22, 31, 26, 29, 0 ] ], "p": 5, "objective": 216.0 }, "solution": { "facilities": [ 0, 1, 5, 10, 12 ], "assignments": [ 0, 1, 12, 12, 12, 5, 1, 12, 10, 5, 10, 12, 12, 1, 10 ] }, "obj": 216.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 15, "num_open": 5, "sites": [ { "id": 0, "distances": { "0": 0, "1": 34, "2": 59, "3": 45, "4": 52, "5": 39, "6": 45, "7": 39, "8": 34, "9": 46, "10": 47, "11": 43, "12": 33, "13": 42, "14": 25 } }, { "id": 1, "distances": { "0": 34, "1": 0, "2": 46, "3": 35, "4": 37, "5": 33, "6": 21, "7": 30, "8": 36, "9": 37, "10": 37, "11": 26, "12": 39, "13": 14, "14": 35 } }, { "id": 2, "distances": { "0": 59, "1": 46, "2": 0, "3": 29, "4": 46, "5": 42, "6": 49, "7": 37, "8": 45, "9": 46, "10": 50, "11": 37, "12": 31, "13": 45, "14": 40 } }, { "id": 3, "distances": { "0": 45, "1": 35, "2": 29, "3": 0, "4": 42, "5": 38, "6": 44, "7": 35, "8": 38, "9": 40, "10": 41, "11": 39, "12": 17, "13": 31, "14": 32 } }, { "id": 4, "distances": { "0": 52, "1": 37, "2": 46, "3": 42, "4": 0, "5": 42, "6": 41, "7": 23, "8": 40, "9": 30, "10": 29, "11": 39, "12": 25, "13": 42, "14": 31 } }, { "id": 5, "distances": { "0": 39, "1": 33, "2": 42, "3": 38, "4": 42, "5": 0, "6": 30, "7": 35, "8": 35, "9": 22, "10": 37, "11": 36, "12": 27, "13": 28, "14": 26 } }, { "id": 6, "distances": { "0": 45, "1": 21, "2": 49, "3": 44, "4": 41, "5": 30, "6": 0, "7": 34, "8": 30, "9": 34, "10": 35, "11": 32, "12": 38, "13": 29, "14": 32 } }, { "id": 7, "distances": { "0": 39, "1": 30, "2": 37, "3": 35, "4": 23, "5": 35, "6": 34, "7": 0, "8": 26, "9": 36, "10": 29, "11": 30, "12": 19, "13": 26, "14": 26 } }, { "id": 8, "distances": { "0": 34, "1": 36, "2": 45, "3": 38, "4": 40, "5": 35, "6": 30, "7": 26, "8": 0, "9": 40, "10": 23, "11": 40, "12": 32, "13": 34, "14": 31 } }, { "id": 9, "distances": { "0": 46, "1": 37, "2": 46, "3": 40, "4": 30, "5": 22, "6": 34, "7": 36, "8": 40, "9": 0, "10": 33, "11": 33, "12": 33, "13": 35, "14": 35 } }, { "id": 10, "distances": { "0": 47, "1": 37, "2": 50, "3": 41, "4": 29, "5": 37, "6": 35, "7": 29, "8": 23, "9": 33, "10": 0, "11": 33, "12": 24, "13": 36, "14": 22 } }, { "id": 11, "distances": { "0": 43, "1": 26, "2": 37, "3": 39, "4": 39, "5": 36, "6": 32, "7": 30, "8": 40, "9": 33, "10": 33, "11": 0, "12": 22, "13": 22, "14": 31 } }, { "id": 12, "distances": { "0": 33, "1": 39, "2": 31, "3": 17, "4": 25, "5": 27, "6": 38, "7": 19, "8": 32, "9": 33, "10": 24, "11": 22, "12": 0, "13": 28, "14": 26 } }, { "id": 13, "distances": { "0": 42, "1": 14, "2": 45, "3": 31, "4": 42, "5": 28, "6": 29, "7": 26, "8": 34, "9": 35, "10": 36, "11": 22, "12": 28, "13": 0, "14": 29 } }, { "id": 14, "distances": { "0": 25, "1": 35, "2": 40, "3": 32, "4": 31, "5": 26, "6": 32, "7": 26, "8": 31, "9": 35, "10": 22, "11": 31, "12": 26, "13": 29, "14": 0 } } ], "objective": 216.0 }, "solution_variant": { "selected": [ 0, 1, 5, 10, 12 ], "assignments": [ 0, 1, 12, 12, 12, 5, 1, 12, 10, 5, 10, 12, 12, 1, 10 ] }, "context_index": 36, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "At the rental shop the crew needs to choose a specific number of trailheads to keep gear at, and then assign each trailhead to one of those stocked spots so nothing is left unassigned or assigned twice. To judge different choices, total the travel distance from each trailhead to the stocked pickup it’s linked with — the plan with the lowest total distance makes the most sense for customers. The detailed list of trailheads and the distances between every pair appear below.\n\n# num_trailheads=19\n# num_stocked_pickup_sites=6\n# trailhead_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19\nfrom_trailhead,to_trailhead,travel_distance\n1,2,44\n1,3,59\n1,4,65\n1,5,17\n1,6,49\n1,7,51\n1,8,16\n1,9,12\n1,10,21\n1,11,43\n1,12,55\n1,13,49\n1,14,65\n1,15,48\n1,16,49\n1,17,45\n1,18,43\n1,19,33\n2,1,44\n2,3,37\n2,4,67\n2,5,37\n2,6,51\n2,7,71\n2,8,42\n2,9,32\n2,10,40\n2,11,61\n2,12,45\n2,13,60\n2,14,73\n2,15,55\n2,16,26\n2,17,35\n2,18,33\n2,19,23\n3,1,59\n3,2,37\n3,4,46\n3,5,44\n3,6,62\n3,7,65\n3,8,54\n3,9,47\n3,10,44\n3,11,49\n3,12,47\n3,13,60\n3,14,92\n3,15,55\n3,16,50\n3,17,53\n3,18,45\n3,19,54\n4,1,65\n4,2,67\n4,3,46\n4,5,50\n4,6,16\n4,7,84\n4,8,61\n4,9,53\n4,10,54\n4,11,49\n4,12,61\n4,13,49\n4,14,85\n4,15,63\n4,16,64\n4,17,54\n4,18,63\n4,19,56\n5,1,17\n5,2,37\n5,3,44\n5,4,50\n5,6,34\n5,7,34\n5,8,15\n5,9,5\n5,10,26\n5,11,43\n5,12,48\n5,13,41\n5,14,71\n5,15,31\n5,16,34\n5,17,38\n5,18,34\n5,19,26\n6,1,49\n6,2,51\n6,3,62\n6,4,16\n6,5,34\n6,7,68\n6,8,47\n6,9,37\n6,10,58\n6,11,60\n6,12,45\n6,13,33\n6,14,74\n6,15,58\n6,16,66\n6,17,46\n6,18,49\n6,19,40\n7,1,51\n7,2,71\n7,3,65\n7,4,84\n7,5,34\n7,6,68\n7,8,49\n7,9,39\n7,10,60\n7,11,77\n7,12,78\n7,13,73\n7,14,77\n7,15,63\n7,16,68\n7,17,69\n7,18,66\n7,19,60\n8,1,16\n8,2,42\n8,3,54\n8,4,61\n8,5,15\n8,6,47\n8,7,49\n8,9,10\n8,10,25\n8,11,47\n8,12,51\n8,13,33\n8,14,76\n8,15,44\n8,16,47\n8,17,43\n8,18,30\n8,19,31\n9,1,12\n9,2,32\n9,3,47\n9,4,53\n9,5,5\n9,6,37\n9,7,39\n9,8,10\n9,10,21\n9,11,43\n9,12,43\n9,13,43\n9,14,71\n9,15,36\n9,16,37\n9,17,33\n9,18,31\n9,19,21\n10,1,21\n10,2,40\n10,3,44\n10,4,54\n10,5,26\n10,6,58\n10,7,60\n10,8,25\n10,9,21\n10,11,22\n10,12,56\n10,13,44\n10,14,75\n10,15,34\n10,16,52\n10,17,54\n10,18,52\n10,19,37\n11,1,43\n11,2,61\n11,3,49\n11,4,49\n11,5,43\n11,6,60\n11,7,77\n11,8,47\n11,9,43\n11,10,22\n11,12,63\n11,13,56\n11,14,85\n11,15,44\n11,16,47\n11,17,62\n11,18,60\n11,19,47\n12,1,55\n12,2,45\n12,3,47\n12,4,61\n12,5,48\n12,6,45\n12,7,78\n12,8,51\n12,9,43\n12,10,56\n12,11,63\n12,13,48\n12,14,84\n12,15,53\n12,16,71\n12,17,30\n12,18,44\n12,19,34\n13,1,49\n13,2,60\n13,3,60\n13,4,49\n13,5,41\n13,6,33\n13,7,73\n13,8,33\n13,9,43\n13,10,44\n13,11,56\n13,12,48\n13,14,82\n13,15,42\n13,16,75\n13,17,55\n13,18,46\n13,19,56\n14,1,65\n14,2,73\n14,3,92\n14,4,85\n14,5,71\n14,6,74\n14,7,77\n14,8,76\n14,9,71\n14,10,75\n14,11,85\n14,12,84\n14,13,82\n14,15,72\n14,16,98\n14,17,74\n14,18,72\n14,19,62\n15,1,48\n15,2,55\n15,3,55\n15,4,63\n15,5,31\n15,6,58\n15,7,63\n15,8,44\n15,9,36\n15,10,34\n15,11,44\n15,12,53\n15,13,42\n15,14,72\n15,16,61\n15,17,36\n15,18,48\n15,19,44\n16,1,49\n16,2,26\n16,3,50\n16,4,64\n16,5,34\n16,6,66\n16,7,68\n16,8,47\n16,9,37\n16,10,52\n16,11,47\n16,12,71\n16,13,75\n16,14,98\n16,15,61\n16,17,59\n16,18,54\n16,19,49\n17,1,45\n17,2,35\n17,3,53\n17,4,54\n17,5,38\n17,6,46\n17,7,69\n17,8,43\n17,9,33\n17,10,54\n17,11,62\n17,12,30\n17,13,55\n17,14,74\n17,15,36\n17,16,59\n17,18,34\n17,19,24\n18,1,43\n18,2,33\n18,3,45\n18,4,63\n18,5,34\n18,6,49\n18,7,66\n18,8,30\n18,9,31\n18,10,52\n18,11,60\n18,12,44\n18,13,46\n18,14,72\n18,15,48\n18,16,54\n18,17,34\n18,19,22\n19,1,33\n19,2,23\n19,3,54\n19,4,56\n19,5,26\n19,6,40\n19,7,60\n19,8,31\n19,9,21\n19,10,37\n19,11,47\n19,12,34\n19,13,56\n19,14,62\n19,15,44\n19,16,49\n19,17,24\n19,18,22\n\nIf you want the answer in a neat, machine-friendly way, just follow this little JSON shape when you reply:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the trailheads we'll keep stocked (the pickup spots). \"assignments\" says, for each trailhead in the instance, which stocked pickup it's linked to. Super casual: think of \"selected\" as the handful of spots we actually stock, and \"assignments\" mapping every trailhead to one of those stocked spots.\n\nThis is just a sketch of the shape I expect, not the final plan.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 44, 59, 65, 17, 49, 51, 16, 12, 21, 43, 55, 49, 65, 48, 49, 45, 43, 33 ], [ 44, 0, 37, 67, 37, 51, 71, 42, 32, 40, 61, 45, 60, 73, 55, 26, 35, 33, 23 ], [ 59, 37, 0, 46, 44, 62, 65, 54, 47, 44, 49, 47, 60, 92, 55, 50, 53, 45, 54 ], [ 65, 67, 46, 0, 50, 16, 84, 61, 53, 54, 49, 61, 49, 85, 63, 64, 54, 63, 56 ], [ 17, 37, 44, 50, 0, 34, 34, 15, 5, 26, 43, 48, 41, 71, 31, 34, 38, 34, 26 ], [ 49, 51, 62, 16, 34, 0, 68, 47, 37, 58, 60, 45, 33, 74, 58, 66, 46, 49, 40 ], [ 51, 71, 65, 84, 34, 68, 0, 49, 39, 60, 77, 78, 73, 77, 63, 68, 69, 66, 60 ], [ 16, 42, 54, 61, 15, 47, 49, 0, 10, 25, 47, 51, 33, 76, 44, 47, 43, 30, 31 ], [ 12, 32, 47, 53, 5, 37, 39, 10, 0, 21, 43, 43, 43, 71, 36, 37, 33, 31, 21 ], [ 21, 40, 44, 54, 26, 58, 60, 25, 21, 0, 22, 56, 44, 75, 34, 52, 54, 52, 37 ], [ 43, 61, 49, 49, 43, 60, 77, 47, 43, 22, 0, 63, 56, 85, 44, 47, 62, 60, 47 ], [ 55, 45, 47, 61, 48, 45, 78, 51, 43, 56, 63, 0, 48, 84, 53, 71, 30, 44, 34 ], [ 49, 60, 60, 49, 41, 33, 73, 33, 43, 44, 56, 48, 0, 82, 42, 75, 55, 46, 56 ], [ 65, 73, 92, 85, 71, 74, 77, 76, 71, 75, 85, 84, 82, 0, 72, 98, 74, 72, 62 ], [ 48, 55, 55, 63, 31, 58, 63, 44, 36, 34, 44, 53, 42, 72, 0, 61, 36, 48, 44 ], [ 49, 26, 50, 64, 34, 66, 68, 47, 37, 52, 47, 71, 75, 98, 61, 0, 59, 54, 49 ], [ 45, 35, 53, 54, 38, 46, 69, 43, 33, 54, 62, 30, 55, 74, 36, 59, 0, 34, 24 ], [ 43, 33, 45, 63, 34, 49, 66, 30, 31, 52, 60, 44, 46, 72, 48, 54, 34, 0, 22 ], [ 33, 23, 54, 56, 26, 40, 60, 31, 21, 37, 47, 34, 56, 62, 44, 49, 24, 22, 0 ] ], "p": 6, "objective": 310.0 }, "solution": { "facilities": [ 2, 4, 5, 9, 13, 18 ], "assignments": [ 4, 18, 2, 5, 4, 5, 4, 4, 4, 9, 9, 18, 5, 13, 4, 4, 18, 18, 18 ] }, "obj": 310.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 6, "sites": [ { "id": 1, "distances": { "1": 0, "2": 44, "3": 59, "4": 65, "5": 17, "6": 49, "7": 51, "8": 16, "9": 12, "10": 21, "11": 43, "12": 55, "13": 49, "14": 65, "15": 48, "16": 49, "17": 45, "18": 43, "19": 33 } }, { "id": 2, "distances": { "1": 44, "2": 0, "3": 37, "4": 67, "5": 37, "6": 51, "7": 71, "8": 42, "9": 32, "10": 40, "11": 61, "12": 45, "13": 60, "14": 73, "15": 55, "16": 26, "17": 35, "18": 33, "19": 23 } }, { "id": 3, "distances": { "1": 59, "2": 37, "3": 0, "4": 46, "5": 44, "6": 62, "7": 65, "8": 54, "9": 47, "10": 44, "11": 49, "12": 47, "13": 60, "14": 92, "15": 55, "16": 50, "17": 53, "18": 45, "19": 54 } }, { "id": 4, "distances": { "1": 65, "2": 67, "3": 46, "4": 0, "5": 50, "6": 16, "7": 84, "8": 61, "9": 53, "10": 54, "11": 49, "12": 61, "13": 49, "14": 85, "15": 63, "16": 64, "17": 54, "18": 63, "19": 56 } }, { "id": 5, "distances": { "1": 17, "2": 37, "3": 44, "4": 50, "5": 0, "6": 34, "7": 34, "8": 15, "9": 5, "10": 26, "11": 43, "12": 48, "13": 41, "14": 71, "15": 31, "16": 34, "17": 38, "18": 34, "19": 26 } }, { "id": 6, "distances": { "1": 49, "2": 51, "3": 62, "4": 16, "5": 34, "6": 0, "7": 68, "8": 47, "9": 37, "10": 58, "11": 60, "12": 45, "13": 33, "14": 74, "15": 58, "16": 66, "17": 46, "18": 49, "19": 40 } }, { "id": 7, "distances": { "1": 51, "2": 71, "3": 65, "4": 84, "5": 34, "6": 68, "7": 0, "8": 49, "9": 39, "10": 60, "11": 77, "12": 78, "13": 73, "14": 77, "15": 63, "16": 68, "17": 69, "18": 66, "19": 60 } }, { "id": 8, "distances": { "1": 16, "2": 42, "3": 54, "4": 61, "5": 15, "6": 47, "7": 49, "8": 0, "9": 10, "10": 25, "11": 47, "12": 51, "13": 33, "14": 76, "15": 44, "16": 47, "17": 43, "18": 30, "19": 31 } }, { "id": 9, "distances": { "1": 12, "2": 32, "3": 47, "4": 53, "5": 5, "6": 37, "7": 39, "8": 10, "9": 0, "10": 21, "11": 43, "12": 43, "13": 43, "14": 71, "15": 36, "16": 37, "17": 33, "18": 31, "19": 21 } }, { "id": 10, "distances": { "1": 21, "2": 40, "3": 44, "4": 54, "5": 26, "6": 58, "7": 60, "8": 25, "9": 21, "10": 0, "11": 22, "12": 56, "13": 44, "14": 75, "15": 34, "16": 52, "17": 54, "18": 52, "19": 37 } }, { "id": 11, "distances": { "1": 43, "2": 61, "3": 49, "4": 49, "5": 43, "6": 60, "7": 77, "8": 47, "9": 43, "10": 22, "11": 0, "12": 63, "13": 56, "14": 85, "15": 44, "16": 47, "17": 62, "18": 60, "19": 47 } }, { "id": 12, "distances": { "1": 55, "2": 45, "3": 47, "4": 61, "5": 48, "6": 45, "7": 78, "8": 51, "9": 43, "10": 56, "11": 63, "12": 0, "13": 48, "14": 84, "15": 53, "16": 71, "17": 30, "18": 44, "19": 34 } }, { "id": 13, "distances": { "1": 49, "2": 60, "3": 60, "4": 49, "5": 41, "6": 33, "7": 73, "8": 33, "9": 43, "10": 44, "11": 56, "12": 48, "13": 0, "14": 82, "15": 42, "16": 75, "17": 55, "18": 46, "19": 56 } }, { "id": 14, "distances": { "1": 65, "2": 73, "3": 92, "4": 85, "5": 71, "6": 74, "7": 77, "8": 76, "9": 71, "10": 75, "11": 85, "12": 84, "13": 82, "14": 0, "15": 72, "16": 98, "17": 74, "18": 72, "19": 62 } }, { "id": 15, "distances": { "1": 48, "2": 55, "3": 55, "4": 63, "5": 31, "6": 58, "7": 63, "8": 44, "9": 36, "10": 34, "11": 44, "12": 53, "13": 42, "14": 72, "15": 0, "16": 61, "17": 36, "18": 48, "19": 44 } }, { "id": 16, "distances": { "1": 49, "2": 26, "3": 50, "4": 64, "5": 34, "6": 66, "7": 68, "8": 47, "9": 37, "10": 52, "11": 47, "12": 71, "13": 75, "14": 98, "15": 61, "16": 0, "17": 59, "18": 54, "19": 49 } }, { "id": 17, "distances": { "1": 45, "2": 35, "3": 53, "4": 54, "5": 38, "6": 46, "7": 69, "8": 43, "9": 33, "10": 54, "11": 62, "12": 30, "13": 55, "14": 74, "15": 36, "16": 59, "17": 0, "18": 34, "19": 24 } }, { "id": 18, "distances": { "1": 43, "2": 33, "3": 45, "4": 63, "5": 34, "6": 49, "7": 66, "8": 30, "9": 31, "10": 52, "11": 60, "12": 44, "13": 46, "14": 72, "15": 48, "16": 54, "17": 34, "18": 0, "19": 22 } }, { "id": 19, "distances": { "1": 33, "2": 23, "3": 54, "4": 56, "5": 26, "6": 40, "7": 60, "8": 31, "9": 21, "10": 37, "11": 47, "12": 34, "13": 56, "14": 62, "15": 44, "16": 49, "17": 24, "18": 22, "19": 0 } } ], "objective": 310.0 }, "solution_variant": { "selected": [ 3, 5, 6, 10, 14, 19 ], "assignments": [ 5, 19, 3, 6, 5, 6, 5, 5, 5, 10, 10, 19, 6, 14, 5, 5, 19, 19, 19 ] }, "context_index": 37, "input_format": "csv", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "In the neighborhood coordination meeting, the challenge was to pick a fixed number of truck parking locations and then attach every block to one of those live locations, using the known distances between blocks. The aim is to keep customer travel as low as possible — tally the distance from each block to its chosen parking location, add them all up, and the plan with the lowest total is preferred. Every single block must be assigned to exactly one open location; no block can be skipped or assigned to more than one. The specific blocks, candidate spots, and distances are shown below.\n\n# total_blocks=19\n# num_parking_locations_to_open=6\n# block_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S\nsource_block_id,target_block_id,travel_distance_between_blocks\nA,B,155\nA,C,224\nA,D,101\nA,E,116\nA,F,154\nA,G,77\nA,H,43\nA,I,88\nA,J,118\nA,K,123\nA,L,107\nA,M,70\nA,N,103\nA,O,117\nA,P,134\nA,Q,149\nA,R,191\nA,S,115\nB,A,155\nB,C,184\nB,D,69\nB,E,54\nB,F,92\nB,G,95\nB,H,114\nB,I,143\nB,J,137\nB,K,132\nB,L,133\nB,M,85\nB,N,105\nB,O,38\nB,P,154\nB,Q,117\nB,R,194\nB,S,198\nC,A,224\nC,B,184\nC,D,155\nC,E,170\nC,F,208\nC,G,212\nC,H,181\nC,I,145\nC,J,115\nC,K,120\nC,L,146\nC,M,200\nC,N,182\nC,O,153\nC,P,213\nC,Q,184\nC,R,264\nC,S,188\nD,A,101\nD,B,69\nD,C,155\nD,E,15\nD,F,53\nD,G,89\nD,H,58\nD,I,103\nD,J,106\nD,K,110\nD,L,69\nD,M,131\nD,N,131\nD,O,84\nD,P,85\nD,Q,48\nD,R,174\nD,S,129\nE,A,116\nE,B,54\nE,C,170\nE,D,15\nE,F,38\nE,G,74\nE,H,73\nE,I,118\nE,J,121\nE,K,125\nE,L,84\nE,M,139\nE,N,146\nE,O,92\nE,P,100\nE,Q,63\nE,R,189\nE,S,144\nF,A,154\nF,B,92\nF,C,208\nF,D,53\nF,E,38\nF,G,112\nF,H,111\nF,I,145\nF,J,159\nF,K,163\nF,L,110\nF,M,177\nF,N,129\nF,O,130\nF,P,138\nF,Q,101\nF,R,227\nF,S,182\nG,A,77\nG,B,95\nG,C,212\nG,D,89\nG,E,74\nG,F,112\nG,H,34\nG,I,79\nG,J,109\nG,K,114\nG,L,98\nG,M,106\nG,N,119\nG,O,59\nG,P,125\nG,Q,137\nG,R,178\nG,S,170\nH,A,43\nH,B,114\nH,C,181\nH,D,58\nH,E,73\nH,F,111\nH,G,34\nH,I,45\nH,J,75\nH,K,80\nH,L,64\nH,M,103\nH,N,85\nH,O,78\nH,P,91\nH,Q,106\nH,R,212\nH,S,136\nI,A,88\nI,B,143\nI,C,145\nI,D,103\nI,E,118\nI,F,145\nI,G,79\nI,H,45\nI,J,30\nI,K,35\nI,L,93\nI,M,148\nI,N,126\nI,O,107\nI,P,68\nI,Q,105\nI,R,245\nI,S,169\nJ,A,118\nJ,B,137\nJ,C,115\nJ,D,106\nJ,E,121\nJ,F,159\nJ,G,109\nJ,H,75\nJ,I,30\nJ,K,5\nJ,L,97\nJ,M,146\nJ,N,110\nJ,O,99\nJ,P,98\nJ,Q,135\nJ,R,215\nJ,S,139\nK,A,123\nK,B,132\nK,C,120\nK,D,110\nK,E,125\nK,F,163\nK,G,114\nK,H,80\nK,I,35\nK,J,5\nK,L,102\nK,M,141\nK,N,105\nK,O,94\nK,P,103\nK,Q,139\nK,R,220\nK,S,144\nL,A,107\nL,B,133\nL,C,146\nL,D,69\nL,E,84\nL,F,110\nL,G,98\nL,H,64\nL,I,93\nL,J,97\nL,K,102\nL,M,142\nL,N,116\nL,O,95\nL,P,141\nL,Q,104\nL,R,195\nL,S,144\nM,A,70\nM,B,85\nM,C,200\nM,D,131\nM,E,139\nM,F,177\nM,G,106\nM,H,103\nM,I,148\nM,J,146\nM,K,141\nM,L,142\nM,N,80\nM,O,47\nM,P,194\nM,Q,160\nM,R,203\nM,S,175\nN,A,103\nN,B,105\nN,C,182\nN,D,131\nN,E,146\nN,F,129\nN,G,119\nN,H,85\nN,I,126\nN,J,110\nN,K,105\nN,L,116\nN,M,80\nN,O,67\nN,P,172\nN,Q,154\nN,R,223\nN,S,182\nO,A,117\nO,B,38\nO,C,153\nO,D,84\nO,E,92\nO,F,130\nO,G,59\nO,H,78\nO,I,107\nO,J,99\nO,K,94\nO,L,95\nO,M,47\nO,N,67\nO,P,150\nO,Q,113\nO,R,156\nO,S,166\nP,A,134\nP,B,154\nP,C,213\nP,D,85\nP,E,100\nP,F,138\nP,G,125\nP,H,91\nP,I,68\nP,J,98\nP,K,103\nP,L,141\nP,M,194\nP,N,172\nP,O,150\nP,Q,37\nP,R,182\nP,S,118\nQ,A,149\nQ,B,117\nQ,C,184\nQ,D,48\nQ,E,63\nQ,F,101\nQ,G,137\nQ,H,106\nQ,I,105\nQ,J,135\nQ,K,139\nQ,L,104\nQ,M,160\nQ,N,154\nQ,O,113\nQ,P,37\nQ,R,145\nQ,S,81\nR,A,191\nR,B,194\nR,C,264\nR,D,174\nR,E,189\nR,F,227\nR,G,178\nR,H,212\nR,I,245\nR,J,215\nR,K,220\nR,L,195\nR,M,203\nR,N,223\nR,O,156\nR,P,182\nR,Q,145\nR,S,76\nS,A,115\nS,B,198\nS,C,188\nS,D,129\nS,E,144\nS,F,182\nS,G,170\nS,H,136\nS,I,169\nS,J,139\nS,K,144\nS,L,144\nS,M,175\nS,N,182\nS,O,166\nS,P,118\nS,Q,81\nS,R,76\n\nAlso, when you send back the plan, just use a small JSON snippet like this so it's easy to read and machine-friendly:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of it like a simple form: \"selected\" is the list of parking spots you decide to open, and \"assignments\" lists, for each block in the same order as the input, which open spot that block is attached to. This is just a sketch of the shape I want — not the final plan itself.\n\nPlease make sure to use the exact identifiers from the instance input for every spot and block — don’t rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 155, 224, 101, 116, 154, 77, 43, 88, 118, 123, 107, 70, 103, 117, 134, 149, 191, 115 ], [ 155, 0, 184, 69, 54, 92, 95, 114, 143, 137, 132, 133, 85, 105, 38, 154, 117, 194, 198 ], [ 224, 184, 0, 155, 170, 208, 212, 181, 145, 115, 120, 146, 200, 182, 153, 213, 184, 264, 188 ], [ 101, 69, 155, 0, 15, 53, 89, 58, 103, 106, 110, 69, 131, 131, 84, 85, 48, 174, 129 ], [ 116, 54, 170, 15, 0, 38, 74, 73, 118, 121, 125, 84, 139, 146, 92, 100, 63, 189, 144 ], [ 154, 92, 208, 53, 38, 0, 112, 111, 145, 159, 163, 110, 177, 129, 130, 138, 101, 227, 182 ], [ 77, 95, 212, 89, 74, 112, 0, 34, 79, 109, 114, 98, 106, 119, 59, 125, 137, 178, 170 ], [ 43, 114, 181, 58, 73, 111, 34, 0, 45, 75, 80, 64, 103, 85, 78, 91, 106, 212, 136 ], [ 88, 143, 145, 103, 118, 145, 79, 45, 0, 30, 35, 93, 148, 126, 107, 68, 105, 245, 169 ], [ 118, 137, 115, 106, 121, 159, 109, 75, 30, 0, 5, 97, 146, 110, 99, 98, 135, 215, 139 ], [ 123, 132, 120, 110, 125, 163, 114, 80, 35, 5, 0, 102, 141, 105, 94, 103, 139, 220, 144 ], [ 107, 133, 146, 69, 84, 110, 98, 64, 93, 97, 102, 0, 142, 116, 95, 141, 104, 195, 144 ], [ 70, 85, 200, 131, 139, 177, 106, 103, 148, 146, 141, 142, 0, 80, 47, 194, 160, 203, 175 ], [ 103, 105, 182, 131, 146, 129, 119, 85, 126, 110, 105, 116, 80, 0, 67, 172, 154, 223, 182 ], [ 117, 38, 153, 84, 92, 130, 59, 78, 107, 99, 94, 95, 47, 67, 0, 150, 113, 156, 166 ], [ 134, 154, 213, 85, 100, 138, 125, 91, 68, 98, 103, 141, 194, 172, 150, 0, 37, 182, 118 ], [ 149, 117, 184, 48, 63, 101, 137, 106, 105, 135, 139, 104, 160, 154, 113, 37, 0, 145, 81 ], [ 191, 194, 264, 174, 189, 227, 178, 212, 245, 215, 220, 195, 203, 223, 156, 182, 145, 0, 76 ], [ 115, 198, 188, 129, 144, 182, 170, 136, 169, 139, 144, 144, 175, 182, 166, 118, 81, 76, 0 ] ], "p": 6, "objective": 605.0 }, "solution": { "facilities": [ 2, 3, 7, 9, 14, 18 ], "assignments": [ 7, 14, 2, 3, 3, 3, 7, 7, 9, 9, 9, 7, 14, 14, 14, 3, 3, 18, 18 ] }, "obj": 605.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 6, "sites": [ { "id": "A", "distances": { "A": 0, "B": 155, "C": 224, "D": 101, "E": 116, "F": 154, "G": 77, "H": 43, "I": 88, "J": 118, "K": 123, "L": 107, "M": 70, "N": 103, "O": 117, "P": 134, "Q": 149, "R": 191, "S": 115 } }, { "id": "B", "distances": { "A": 155, "B": 0, "C": 184, "D": 69, "E": 54, "F": 92, "G": 95, "H": 114, "I": 143, "J": 137, "K": 132, "L": 133, "M": 85, "N": 105, "O": 38, "P": 154, "Q": 117, "R": 194, "S": 198 } }, { "id": "C", "distances": { "A": 224, "B": 184, "C": 0, "D": 155, "E": 170, "F": 208, "G": 212, "H": 181, "I": 145, "J": 115, "K": 120, "L": 146, "M": 200, "N": 182, "O": 153, "P": 213, "Q": 184, "R": 264, "S": 188 } }, { "id": "D", "distances": { "A": 101, "B": 69, "C": 155, "D": 0, "E": 15, "F": 53, "G": 89, "H": 58, "I": 103, "J": 106, "K": 110, "L": 69, "M": 131, "N": 131, "O": 84, "P": 85, "Q": 48, "R": 174, "S": 129 } }, { "id": "E", "distances": { "A": 116, "B": 54, "C": 170, "D": 15, "E": 0, "F": 38, "G": 74, "H": 73, "I": 118, "J": 121, "K": 125, "L": 84, "M": 139, "N": 146, "O": 92, "P": 100, "Q": 63, "R": 189, "S": 144 } }, { "id": "F", "distances": { "A": 154, "B": 92, "C": 208, "D": 53, "E": 38, "F": 0, "G": 112, "H": 111, "I": 145, "J": 159, "K": 163, "L": 110, "M": 177, "N": 129, "O": 130, "P": 138, "Q": 101, "R": 227, "S": 182 } }, { "id": "G", "distances": { "A": 77, "B": 95, "C": 212, "D": 89, "E": 74, "F": 112, "G": 0, "H": 34, "I": 79, "J": 109, "K": 114, "L": 98, "M": 106, "N": 119, "O": 59, "P": 125, "Q": 137, "R": 178, "S": 170 } }, { "id": "H", "distances": { "A": 43, "B": 114, "C": 181, "D": 58, "E": 73, "F": 111, "G": 34, "H": 0, "I": 45, "J": 75, "K": 80, "L": 64, "M": 103, "N": 85, "O": 78, "P": 91, "Q": 106, "R": 212, "S": 136 } }, { "id": "I", "distances": { "A": 88, "B": 143, "C": 145, "D": 103, "E": 118, "F": 145, "G": 79, "H": 45, "I": 0, "J": 30, "K": 35, "L": 93, "M": 148, "N": 126, "O": 107, "P": 68, "Q": 105, "R": 245, "S": 169 } }, { "id": "J", "distances": { "A": 118, "B": 137, "C": 115, "D": 106, "E": 121, "F": 159, "G": 109, "H": 75, "I": 30, "J": 0, "K": 5, "L": 97, "M": 146, "N": 110, "O": 99, "P": 98, "Q": 135, "R": 215, "S": 139 } }, { "id": "K", "distances": { "A": 123, "B": 132, "C": 120, "D": 110, "E": 125, "F": 163, "G": 114, "H": 80, "I": 35, "J": 5, "K": 0, "L": 102, "M": 141, "N": 105, "O": 94, "P": 103, "Q": 139, "R": 220, "S": 144 } }, { "id": "L", "distances": { "A": 107, "B": 133, "C": 146, "D": 69, "E": 84, "F": 110, "G": 98, "H": 64, "I": 93, "J": 97, "K": 102, "L": 0, "M": 142, "N": 116, "O": 95, "P": 141, "Q": 104, "R": 195, "S": 144 } }, { "id": "M", "distances": { "A": 70, "B": 85, "C": 200, "D": 131, "E": 139, "F": 177, "G": 106, "H": 103, "I": 148, "J": 146, "K": 141, "L": 142, "M": 0, "N": 80, "O": 47, "P": 194, "Q": 160, "R": 203, "S": 175 } }, { "id": "N", "distances": { "A": 103, "B": 105, "C": 182, "D": 131, "E": 146, "F": 129, "G": 119, "H": 85, "I": 126, "J": 110, "K": 105, "L": 116, "M": 80, "N": 0, "O": 67, "P": 172, "Q": 154, "R": 223, "S": 182 } }, { "id": "O", "distances": { "A": 117, "B": 38, "C": 153, "D": 84, "E": 92, "F": 130, "G": 59, "H": 78, "I": 107, "J": 99, "K": 94, "L": 95, "M": 47, "N": 67, "O": 0, "P": 150, "Q": 113, "R": 156, "S": 166 } }, { "id": "P", "distances": { "A": 134, "B": 154, "C": 213, "D": 85, "E": 100, "F": 138, "G": 125, "H": 91, "I": 68, "J": 98, "K": 103, "L": 141, "M": 194, "N": 172, "O": 150, "P": 0, "Q": 37, "R": 182, "S": 118 } }, { "id": "Q", "distances": { "A": 149, "B": 117, "C": 184, "D": 48, "E": 63, "F": 101, "G": 137, "H": 106, "I": 105, "J": 135, "K": 139, "L": 104, "M": 160, "N": 154, "O": 113, "P": 37, "Q": 0, "R": 145, "S": 81 } }, { "id": "R", "distances": { "A": 191, "B": 194, "C": 264, "D": 174, "E": 189, "F": 227, "G": 178, "H": 212, "I": 245, "J": 215, "K": 220, "L": 195, "M": 203, "N": 223, "O": 156, "P": 182, "Q": 145, "R": 0, "S": 76 } }, { "id": "S", "distances": { "A": 115, "B": 198, "C": 188, "D": 129, "E": 144, "F": 182, "G": 170, "H": 136, "I": 169, "J": 139, "K": 144, "L": 144, "M": 175, "N": 182, "O": 166, "P": 118, "Q": 81, "R": 76, "S": 0 } } ], "objective": 605.0 }, "solution_variant": { "selected": [ "C", "D", "H", "J", "O", "S" ], "assignments": [ "H", "O", "C", "D", "D", "D", "H", "H", "J", "J", "J", "H", "O", "O", "O", "D", "D", "S", "S" ] }, "context_index": 38, "input_format": "csv", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "In our town the blood-drive planners need to select a set number of staging hubs and then attach each outreach location to one hub only, so there are no duplicates or misses. We have the travel distance for every pair of locations, so the sensible choice is the one that minimizes overall travel — calculate that by adding up each location’s distance to its assigned hub, and choose the arrangement with the lowest total. Specific candidate sites and pairwise distances are listed below.\n\n{\n \"total_candidate_locations\": 16,\n \"num_staging_sites\": 1,\n \"location_identifiers\": [\n \"A\",\n \"B\",\n \"C\",\n \"D\",\n \"E\",\n \"F\",\n \"G\",\n \"H\",\n \"I\",\n \"J\",\n \"K\",\n \"L\",\n \"M\",\n \"N\",\n \"O\",\n \"P\"\n ],\n \"data\": [\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 52\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 59\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 47\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 44\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 60\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": \"A\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 52\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 40\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 33\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 18\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"B\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 25\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 56\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"C\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 59\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 56\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 51\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 42\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 13\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 66\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 57\n },\n {\n \"source_location_id\": \"D\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 37\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 51\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 41\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 22\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 17\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 15\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"E\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 22\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 47\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 40\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 41\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 42\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 33\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": \"F\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 33\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 50\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 50\n },\n {\n \"source_location_id\": \"G\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 44\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 18\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 42\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 22\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 42\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 25\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 23\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": \"H\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 13\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 60\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"I\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 17\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 25\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 2\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 41\n },\n {\n \"source_location_id\": \"J\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 36\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 15\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 23\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 2\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 47\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"K\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 16\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"L\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 21\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 60\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 66\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 50\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 60\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 47\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 54\n },\n {\n \"source_location_id\": \"M\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 45\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 29\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 33\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 31\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 16\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 49\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"N\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 18\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 53\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 57\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 46\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 50\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 43\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 48\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 41\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 39\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 34\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 54\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"O\",\n \"target_location_id\": \"P\",\n \"travel_distance\": 35\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"A\",\n \"travel_distance\": 27\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"B\",\n \"travel_distance\": 25\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"C\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"D\",\n \"travel_distance\": 37\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"E\",\n \"travel_distance\": 22\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"F\",\n \"travel_distance\": 26\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"G\",\n \"travel_distance\": 32\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"H\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"I\",\n \"travel_distance\": 24\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"J\",\n \"travel_distance\": 28\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"K\",\n \"travel_distance\": 30\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"L\",\n \"travel_distance\": 21\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"M\",\n \"travel_distance\": 38\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"N\",\n \"travel_distance\": 18\n },\n {\n \"source_location_id\": \"P\",\n \"target_location_id\": \"O\",\n \"travel_distance\": 35\n }\n ]\n}\n\nIf you'd like, you can just return the choices in a little JSON snippet like this—show which sites we open and which open site each outreach location is attached to.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the staging hubs we decide to open. \"assignments\" is a list, in the same order as the outreach locations appear in the input, saying which opened hub each location is attached to. Think of it like a simple form: a list of open sites and then, for each outreach point, the open site it's signed up with.\n\nThis JSON is just a sketch of the expected shape, not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or introduce new labels.\n\nValid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "distance_matrix": [ [ 0, 52, 53, 59, 39, 47, 34, 44, 49, 43, 45, 48, 60, 45, 53, 27 ], [ 52, 0, 35, 43, 29, 40, 33, 18, 38, 36, 34, 29, 39, 29, 39, 25 ], [ 53, 35, 0, 56, 24, 35, 36, 27, 49, 31, 29, 27, 48, 30, 30, 32 ], [ 59, 43, 56, 0, 51, 48, 38, 42, 13, 38, 36, 46, 66, 30, 57, 37 ], [ 39, 29, 24, 51, 0, 41, 35, 22, 45, 17, 15, 31, 49, 31, 38, 22 ], [ 47, 40, 35, 48, 41, 0, 32, 42, 36, 24, 26, 30, 53, 33, 46, 26 ], [ 34, 33, 36, 38, 35, 32, 0, 34, 31, 31, 32, 34, 50, 28, 50, 32 ], [ 44, 18, 27, 42, 22, 42, 34, 0, 46, 25, 23, 39, 34, 26, 43, 24 ], [ 49, 38, 49, 13, 45, 36, 31, 46, 0, 32, 34, 38, 60, 31, 48, 24 ], [ 43, 36, 31, 38, 17, 24, 31, 25, 32, 0, 2, 26, 49, 27, 41, 28 ], [ 45, 34, 29, 36, 15, 26, 32, 23, 34, 2, 0, 28, 47, 28, 39, 30 ], [ 48, 29, 27, 46, 31, 30, 34, 39, 38, 26, 28, 0, 49, 16, 34, 21 ], [ 60, 39, 48, 66, 49, 53, 50, 34, 60, 49, 47, 49, 0, 49, 54, 38 ], [ 45, 29, 30, 30, 31, 33, 28, 26, 31, 27, 28, 16, 49, 0, 27, 18 ], [ 53, 39, 30, 57, 38, 46, 50, 43, 48, 41, 39, 34, 54, 27, 0, 35 ], [ 27, 25, 32, 37, 22, 26, 32, 24, 24, 28, 30, 21, 38, 18, 35, 0 ] ], "p": 1, "objective": 419.0 }, "solution": { "facilities": [ 15 ], "assignments": [ 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15 ] }, "obj": 419.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 1, "sites": [ { "id": "A", "distances": { "A": 0, "B": 52, "C": 53, "D": 59, "E": 39, "F": 47, "G": 34, "H": 44, "I": 49, "J": 43, "K": 45, "L": 48, "M": 60, "N": 45, "O": 53, "P": 27 } }, { "id": "B", "distances": { "A": 52, "B": 0, "C": 35, "D": 43, "E": 29, "F": 40, "G": 33, "H": 18, "I": 38, "J": 36, "K": 34, "L": 29, "M": 39, "N": 29, "O": 39, "P": 25 } }, { "id": "C", "distances": { "A": 53, "B": 35, "C": 0, "D": 56, "E": 24, "F": 35, "G": 36, "H": 27, "I": 49, "J": 31, "K": 29, "L": 27, "M": 48, "N": 30, "O": 30, "P": 32 } }, { "id": "D", "distances": { "A": 59, "B": 43, "C": 56, "D": 0, "E": 51, "F": 48, "G": 38, "H": 42, "I": 13, "J": 38, "K": 36, "L": 46, "M": 66, "N": 30, "O": 57, "P": 37 } }, { "id": "E", "distances": { "A": 39, "B": 29, "C": 24, "D": 51, "E": 0, "F": 41, "G": 35, "H": 22, "I": 45, "J": 17, "K": 15, "L": 31, "M": 49, "N": 31, "O": 38, "P": 22 } }, { "id": "F", "distances": { "A": 47, "B": 40, "C": 35, "D": 48, "E": 41, "F": 0, "G": 32, "H": 42, "I": 36, "J": 24, "K": 26, "L": 30, "M": 53, "N": 33, "O": 46, "P": 26 } }, { "id": "G", "distances": { "A": 34, "B": 33, "C": 36, "D": 38, "E": 35, "F": 32, "G": 0, "H": 34, "I": 31, "J": 31, "K": 32, "L": 34, "M": 50, "N": 28, "O": 50, "P": 32 } }, { "id": "H", "distances": { "A": 44, "B": 18, "C": 27, "D": 42, "E": 22, "F": 42, "G": 34, "H": 0, "I": 46, "J": 25, "K": 23, "L": 39, "M": 34, "N": 26, "O": 43, "P": 24 } }, { "id": "I", "distances": { "A": 49, "B": 38, "C": 49, "D": 13, "E": 45, "F": 36, "G": 31, "H": 46, "I": 0, "J": 32, "K": 34, "L": 38, "M": 60, "N": 31, "O": 48, "P": 24 } }, { "id": "J", "distances": { "A": 43, "B": 36, "C": 31, "D": 38, "E": 17, "F": 24, "G": 31, "H": 25, "I": 32, "J": 0, "K": 2, "L": 26, "M": 49, "N": 27, "O": 41, "P": 28 } }, { "id": "K", "distances": { "A": 45, "B": 34, "C": 29, "D": 36, "E": 15, "F": 26, "G": 32, "H": 23, "I": 34, "J": 2, "K": 0, "L": 28, "M": 47, "N": 28, "O": 39, "P": 30 } }, { "id": "L", "distances": { "A": 48, "B": 29, "C": 27, "D": 46, "E": 31, "F": 30, "G": 34, "H": 39, "I": 38, "J": 26, "K": 28, "L": 0, "M": 49, "N": 16, "O": 34, "P": 21 } }, { "id": "M", "distances": { "A": 60, "B": 39, "C": 48, "D": 66, "E": 49, "F": 53, "G": 50, "H": 34, "I": 60, "J": 49, "K": 47, "L": 49, "M": 0, "N": 49, "O": 54, "P": 38 } }, { "id": "N", "distances": { "A": 45, "B": 29, "C": 30, "D": 30, "E": 31, "F": 33, "G": 28, "H": 26, "I": 31, "J": 27, "K": 28, "L": 16, "M": 49, "N": 0, "O": 27, "P": 18 } }, { "id": "O", "distances": { "A": 53, "B": 39, "C": 30, "D": 57, "E": 38, "F": 46, "G": 50, "H": 43, "I": 48, "J": 41, "K": 39, "L": 34, "M": 54, "N": 27, "O": 0, "P": 35 } }, { "id": "P", "distances": { "A": 27, "B": 25, "C": 32, "D": 37, "E": 22, "F": 26, "G": 32, "H": 24, "I": 24, "J": 28, "K": 30, "L": 21, "M": 38, "N": 18, "O": 35, "P": 0 } } ], "objective": 419.0 }, "solution_variant": { "selected": [ "P" ], "assignments": [ "P", "P", "P", "P", "P", "P", "P", "P", "P", "P", "P", "P", "P", "P", "P", "P" ] }, "context_index": 39, "input_format": "json", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Someone on the garden committee needs to decide which fixed number of tool-shed locations to open and then connect each garden plot to exactly one of those open sheds. The goal is to minimize the combined walking distance — you calculate that by adding the distance from every plot to its assigned shed, and the lower the total the better. It’s important that every plot is assigned to one shed only, and the full details of plots, candidate locations, and pairwise distances will be shown below.\n\nThere are 19 candidate locations, exactly 1 sheds must be opened, and the location identifiers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.\nFrom 0 to 1, the walking distance is 51.\nFrom 0 to 2, the walking distance is 33.\nFrom 0 to 3, the walking distance is 36.\nFrom 0 to 4, the walking distance is 45.\nFrom 0 to 5, the walking distance is 41.\nFrom 0 to 6, the walking distance is 58.\nFrom 0 to 7, the walking distance is 33.\nFrom 0 to 8, the walking distance is 27.\nFrom 0 to 9, the walking distance is 38.\nFrom 0 to 10, the walking distance is 11.\nFrom 0 to 11, the walking distance is 25.\nFrom 0 to 12, the walking distance is 33.\nFrom 0 to 13, the walking distance is 43.\nFrom 0 to 14, the walking distance is 32.\nFrom 0 to 15, the walking distance is 47.\nFrom 0 to 16, the walking distance is 48.\nFrom 0 to 17, the walking distance is 37.\nFrom 0 to 18, the walking distance is 32.\nFrom 1 to 0, the walking distance is 51.\nFrom 1 to 2, the walking distance is 50.\nFrom 1 to 3, the walking distance is 41.\nFrom 1 to 4, the walking distance is 58.\nFrom 1 to 5, the walking distance is 53.\nFrom 1 to 6, the walking distance is 54.\nFrom 1 to 7, the walking distance is 37.\nFrom 1 to 8, the walking distance is 44.\nFrom 1 to 9, the walking distance is 55.\nFrom 1 to 10, the walking distance is 48.\nFrom 1 to 11, the walking distance is 46.\nFrom 1 to 12, the walking distance is 36.\nFrom 1 to 13, the walking distance is 61.\nFrom 1 to 14, the walking distance is 69.\nFrom 1 to 15, the walking distance is 73.\nFrom 1 to 16, the walking distance is 61.\nFrom 1 to 17, the walking distance is 56.\nFrom 1 to 18, the walking distance is 56.\nFrom 2 to 0, the walking distance is 33.\nFrom 2 to 1, the walking distance is 50.\nFrom 2 to 3, the walking distance is 21.\nFrom 2 to 4, the walking distance is 48.\nFrom 2 to 5, the walking distance is 24.\nFrom 2 to 6, the walking distance is 62.\nFrom 2 to 7, the walking distance is 33.\nFrom 2 to 8, the walking distance is 40.\nFrom 2 to 9, the walking distance is 42.\nFrom 2 to 10, the walking distance is 28.\nFrom 2 to 11, the walking distance is 8.\nFrom 2 to 12, the walking distance is 31.\nFrom 2 to 13, the walking distance is 34.\nFrom 2 to 14, the walking distance is 38.\nFrom 2 to 15, the walking distance is 38.\nFrom 2 to 16, the walking distance is 43.\nFrom 2 to 17, the walking distance is 32.\nFrom 2 to 18, the walking distance is 27.\nFrom 3 to 0, the walking distance is 36.\nFrom 3 to 1, the walking distance is 41.\nFrom 3 to 2, the walking distance is 21.\nFrom 3 to 4, the walking distance is 46.\nFrom 3 to 5, the walking distance is 12.\nFrom 3 to 6, the walking distance is 67.\nFrom 3 to 7, the walking distance is 42.\nFrom 3 to 8, the walking distance is 47.\nFrom 3 to 9, the walking distance is 21.\nFrom 3 to 10, the walking distance is 33.\nFrom 3 to 11, the walking distance is 17.\nFrom 3 to 12, the walking distance is 23.\nFrom 3 to 13, the walking distance is 43.\nFrom 3 to 14, the walking distance is 42.\nFrom 3 to 15, the walking distance is 41.\nFrom 3 to 16, the walking distance is 52.\nFrom 3 to 17, the walking distance is 38.\nFrom 3 to 18, the walking distance is 41.\nFrom 4 to 0, the walking distance is 45.\nFrom 4 to 1, the walking distance is 58.\nFrom 4 to 2, the walking distance is 48.\nFrom 4 to 3, the walking distance is 46.\nFrom 4 to 5, the walking distance is 49.\nFrom 4 to 6, the walking distance is 73.\nFrom 4 to 7, the walking distance is 56.\nFrom 4 to 8, the walking distance is 59.\nFrom 4 to 9, the walking distance is 49.\nFrom 4 to 10, the walking distance is 43.\nFrom 4 to 11, the walking distance is 55.\nFrom 4 to 12, the walking distance is 31.\nFrom 4 to 13, the walking distance is 45.\nFrom 4 to 14, the walking distance is 47.\nFrom 4 to 15, the walking distance is 55.\nFrom 4 to 16, the walking distance is 48.\nFrom 4 to 17, the walking distance is 28.\nFrom 4 to 18, the walking distance is 37.\nFrom 5 to 0, the walking distance is 41.\nFrom 5 to 1, the walking distance is 53.\nFrom 5 to 2, the walking distance is 24.\nFrom 5 to 3, the walking distance is 12.\nFrom 5 to 4, the walking distance is 49.\nFrom 5 to 6, the walking distance is 73.\nFrom 5 to 7, the walking distance is 45.\nFrom 5 to 8, the walking distance is 39.\nFrom 5 to 9, the walking distance is 33.\nFrom 5 to 10, the walking distance is 36.\nFrom 5 to 11, the walking distance is 16.\nFrom 5 to 12, the walking distance is 32.\nFrom 5 to 13, the walking distance is 46.\nFrom 5 to 14, the walking distance is 39.\nFrom 5 to 15, the walking distance is 49.\nFrom 5 to 16, the walking distance is 55.\nFrom 5 to 17, the walking distance is 44.\nFrom 5 to 18, the walking distance is 38.\nFrom 6 to 0, the walking distance is 58.\nFrom 6 to 1, the walking distance is 54.\nFrom 6 to 2, the walking distance is 62.\nFrom 6 to 3, the walking distance is 67.\nFrom 6 to 4, the walking distance is 73.\nFrom 6 to 5, the walking distance is 73.\nFrom 6 to 7, the walking distance is 39.\nFrom 6 to 8, the walking distance is 46.\nFrom 6 to 9, the walking distance is 46.\nFrom 6 to 10, the walking distance is 47.\nFrom 6 to 11, the walking distance is 57.\nFrom 6 to 12, the walking distance is 57.\nFrom 6 to 13, the walking distance is 60.\nFrom 6 to 14, the walking distance is 64.\nFrom 6 to 15, the walking distance is 59.\nFrom 6 to 16, the walking distance is 62.\nFrom 6 to 17, the walking distance is 55.\nFrom 6 to 18, the walking distance is 58.\nFrom 7 to 0, the walking distance is 33.\nFrom 7 to 1, the walking distance is 37.\nFrom 7 to 2, the walking distance is 33.\nFrom 7 to 3, the walking distance is 42.\nFrom 7 to 4, the walking distance is 56.\nFrom 7 to 5, the walking distance is 45.\nFrom 7 to 6, the walking distance is 39.\nFrom 7 to 8, the walking distance is 7.\nFrom 7 to 9, the walking distance is 39.\nFrom 7 to 10, the walking distance is 22.\nFrom 7 to 11, the walking distance is 29.\nFrom 7 to 12, the walking distance is 39.\nFrom 7 to 13, the walking distance is 54.\nFrom 7 to 14, the walking distance is 48.\nFrom 7 to 15, the walking distance is 58.\nFrom 7 to 16, the walking distance is 34.\nFrom 7 to 17, the walking distance is 38.\nFrom 7 to 18, the walking distance is 44.\nFrom 8 to 0, the walking distance is 27.\nFrom 8 to 1, the walking distance is 44.\nFrom 8 to 2, the walking distance is 40.\nFrom 8 to 3, the walking distance is 47.\nFrom 8 to 4, the walking distance is 59.\nFrom 8 to 5, the walking distance is 39.\nFrom 8 to 6, the walking distance is 46.\nFrom 8 to 7, the walking distance is 7.\nFrom 8 to 9, the walking distance is 40.\nFrom 8 to 10, the walking distance is 16.\nFrom 8 to 11, the walking distance is 35.\nFrom 8 to 12, the walking distance is 42.\nFrom 8 to 13, the walking distance is 59.\nFrom 8 to 14, the walking distance is 42.\nFrom 8 to 15, the walking distance is 52.\nFrom 8 to 16, the walking distance is 27.\nFrom 8 to 17, the walking distance is 42.\nFrom 8 to 18, the walking distance is 49.\nFrom 9 to 0, the walking distance is 38.\nFrom 9 to 1, the walking distance is 55.\nFrom 9 to 2, the walking distance is 42.\nFrom 9 to 3, the walking distance is 21.\nFrom 9 to 4, the walking distance is 49.\nFrom 9 to 5, the walking distance is 33.\nFrom 9 to 6, the walking distance is 46.\nFrom 9 to 7, the walking distance is 39.\nFrom 9 to 8, the walking distance is 40.\nFrom 9 to 10, the walking distance is 27.\nFrom 9 to 11, the walking distance is 35.\nFrom 9 to 12, the walking distance is 33.\nFrom 9 to 13, the walking distance is 38.\nFrom 9 to 14, the walking distance is 42.\nFrom 9 to 15, the walking distance is 37.\nFrom 9 to 16, the walking distance is 39.\nFrom 9 to 17, the walking distance is 33.\nFrom 9 to 18, the walking distance is 20.\nFrom 10 to 0, the walking distance is 11.\nFrom 10 to 1, the walking distance is 48.\nFrom 10 to 2, the walking distance is 28.\nFrom 10 to 3, the walking distance is 33.\nFrom 10 to 4, the walking distance is 43.\nFrom 10 to 5, the walking distance is 36.\nFrom 10 to 6, the walking distance is 47.\nFrom 10 to 7, the walking distance is 22.\nFrom 10 to 8, the walking distance is 16.\nFrom 10 to 9, the walking distance is 27.\nFrom 10 to 11, the walking distance is 20.\nFrom 10 to 12, the walking distance is 30.\nFrom 10 to 13, the walking distance is 43.\nFrom 10 to 14, the walking distance is 38.\nFrom 10 to 15, the walking distance is 36.\nFrom 10 to 16, the walking distance is 41.\nFrom 10 to 17, the walking distance is 26.\nFrom 10 to 18, the walking distance is 34.\nFrom 11 to 0, the walking distance is 25.\nFrom 11 to 1, the walking distance is 46.\nFrom 11 to 2, the walking distance is 8.\nFrom 11 to 3, the walking distance is 17.\nFrom 11 to 4, the walking distance is 55.\nFrom 11 to 5, the walking distance is 16.\nFrom 11 to 6, the walking distance is 57.\nFrom 11 to 7, the walking distance is 29.\nFrom 11 to 8, the walking distance is 35.\nFrom 11 to 9, the walking distance is 35.\nFrom 11 to 10, the walking distance is 20.\nFrom 11 to 12, the walking distance is 37.\nFrom 11 to 13, the walking distance is 30.\nFrom 11 to 14, the walking distance is 35.\nFrom 11 to 15, the walking distance is 34.\nFrom 11 to 16, the walking distance is 39.\nFrom 11 to 17, the walking distance is 28.\nFrom 11 to 18, the walking distance is 35.\nFrom 12 to 0, the walking distance is 33.\nFrom 12 to 1, the walking distance is 36.\nFrom 12 to 2, the walking distance is 31.\nFrom 12 to 3, the walking distance is 23.\nFrom 12 to 4, the walking distance is 31.\nFrom 12 to 5, the walking distance is 32.\nFrom 12 to 6, the walking distance is 57.\nFrom 12 to 7, the walking distance is 39.\nFrom 12 to 8, the walking distance is 42.\nFrom 12 to 9, the walking distance is 33.\nFrom 12 to 10, the walking distance is 30.\nFrom 12 to 11, the walking distance is 37.\nFrom 12 to 13, the walking distance is 43.\nFrom 12 to 14, the walking distance is 51.\nFrom 12 to 15, the walking distance is 50.\nFrom 12 to 16, the walking distance is 41.\nFrom 12 to 17, the walking distance is 30.\nFrom 12 to 18, the walking distance is 20.\nFrom 13 to 0, the walking distance is 43.\nFrom 13 to 1, the walking distance is 61.\nFrom 13 to 2, the walking distance is 34.\nFrom 13 to 3, the walking distance is 43.\nFrom 13 to 4, the walking distance is 45.\nFrom 13 to 5, the walking distance is 46.\nFrom 13 to 6, the walking distance is 60.\nFrom 13 to 7, the walking distance is 54.\nFrom 13 to 8, the walking distance is 59.\nFrom 13 to 9, the walking distance is 38.\nFrom 13 to 10, the walking distance is 43.\nFrom 13 to 11, the walking distance is 30.\nFrom 13 to 12, the walking distance is 43.\nFrom 13 to 14, the walking distance is 44.\nFrom 13 to 15, the walking distance is 29.\nFrom 13 to 16, the walking distance is 38.\nFrom 13 to 17, the walking distance is 17.\nFrom 13 to 18, the walking distance is 44.\nFrom 14 to 0, the walking distance is 32.\nFrom 14 to 1, the walking distance is 69.\nFrom 14 to 2, the walking distance is 38.\nFrom 14 to 3, the walking distance is 42.\nFrom 14 to 4, the walking distance is 47.\nFrom 14 to 5, the walking distance is 39.\nFrom 14 to 6, the walking distance is 64.\nFrom 14 to 7, the walking distance is 48.\nFrom 14 to 8, the walking distance is 42.\nFrom 14 to 9, the walking distance is 42.\nFrom 14 to 10, the walking distance is 38.\nFrom 14 to 11, the walking distance is 35.\nFrom 14 to 12, the walking distance is 51.\nFrom 14 to 13, the walking distance is 44.\nFrom 14 to 15, the walking distance is 43.\nFrom 14 to 16, the walking distance is 55.\nFrom 14 to 17, the walking distance is 37.\nFrom 14 to 18, the walking distance is 55.\nFrom 15 to 0, the walking distance is 47.\nFrom 15 to 1, the walking distance is 73.\nFrom 15 to 2, the walking distance is 38.\nFrom 15 to 3, the walking distance is 41.\nFrom 15 to 4, the walking distance is 55.\nFrom 15 to 5, the walking distance is 49.\nFrom 15 to 6, the walking distance is 59.\nFrom 15 to 7, the walking distance is 58.\nFrom 15 to 8, the walking distance is 52.\nFrom 15 to 9, the walking distance is 37.\nFrom 15 to 10, the walking distance is 36.\nFrom 15 to 11, the walking distance is 34.\nFrom 15 to 12, the walking distance is 50.\nFrom 15 to 13, the walking distance is 29.\nFrom 15 to 14, the walking distance is 43.\nFrom 15 to 16, the walking distance is 56.\nFrom 15 to 17, the walking distance is 31.\nFrom 15 to 18, the walking distance is 51.\nFrom 16 to 0, the walking distance is 48.\nFrom 16 to 1, the walking distance is 61.\nFrom 16 to 2, the walking distance is 43.\nFrom 16 to 3, the walking distance is 52.\nFrom 16 to 4, the walking distance is 48.\nFrom 16 to 5, the walking distance is 55.\nFrom 16 to 6, the walking distance is 62.\nFrom 16 to 7, the walking distance is 34.\nFrom 16 to 8, the walking distance is 27.\nFrom 16 to 9, the walking distance is 39.\nFrom 16 to 10, the walking distance is 41.\nFrom 16 to 11, the walking distance is 39.\nFrom 16 to 12, the walking distance is 41.\nFrom 16 to 13, the walking distance is 38.\nFrom 16 to 14, the walking distance is 55.\nFrom 16 to 15, the walking distance is 56.\nFrom 16 to 17, the walking distance is 45.\nFrom 16 to 18, the walking distance is 52.\nFrom 17 to 0, the walking distance is 37.\nFrom 17 to 1, the walking distance is 56.\nFrom 17 to 2, the walking distance is 32.\nFrom 17 to 3, the walking distance is 38.\nFrom 17 to 4, the walking distance is 28.\nFrom 17 to 5, the walking distance is 44.\nFrom 17 to 6, the walking distance is 55.\nFrom 17 to 7, the walking distance is 38.\nFrom 17 to 8, the walking distance is 42.\nFrom 17 to 9, the walking distance is 33.\nFrom 17 to 10, the walking distance is 26.\nFrom 17 to 11, the walking distance is 28.\nFrom 17 to 12, the walking distance is 30.\nFrom 17 to 13, the walking distance is 17.\nFrom 17 to 14, the walking distance is 37.\nFrom 17 to 15, the walking distance is 31.\nFrom 17 to 16, the walking distance is 45.\nFrom 17 to 18, the walking distance is 31.\nFrom 18 to 0, the walking distance is 32.\nFrom 18 to 1, the walking distance is 56.\nFrom 18 to 2, the walking distance is 27.\nFrom 18 to 3, the walking distance is 41.\nFrom 18 to 4, the walking distance is 37.\nFrom 18 to 5, the walking distance is 38.\nFrom 18 to 6, the walking distance is 58.\nFrom 18 to 7, the walking distance is 44.\nFrom 18 to 8, the walking distance is 49.\nFrom 18 to 9, the walking distance is 20.\nFrom 18 to 10, the walking distance is 34.\nFrom 18 to 11, the walking distance is 35.\nFrom 18 to 12, the walking distance is 20.\nFrom 18 to 13, the walking distance is 44.\nFrom 18 to 14, the walking distance is 55.\nFrom 18 to 15, the walking distance is 51.\nFrom 18 to 16, the walking distance is 52.\nFrom 18 to 17, the walking distance is 31.\nAssign each plot to exactly one of the 1 opened sheds so the summed walking distance is minimized.\n\nIf you want to send the result back, just use this simple JSON layout so I can read it easily:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nHere \"selected\" is where you list the shed locations you decide to open, and \"assignments\" lists, in the same order as the plots appear in the instance, which opened shed each plot is assigned to. Think of it like a short form: which sheds are open, and who goes to which shed.\n\nThis is just a sketch of the shape I expect, not the actual answer — fill the placeholders with the real IDs from the instance.\n\nAll identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 51, 33, 36, 45, 41, 58, 33, 27, 38, 11, 25, 33, 43, 32, 47, 48, 37, 32 ], [ 51, 0, 50, 41, 58, 53, 54, 37, 44, 55, 48, 46, 36, 61, 69, 73, 61, 56, 56 ], [ 33, 50, 0, 21, 48, 24, 62, 33, 40, 42, 28, 8, 31, 34, 38, 38, 43, 32, 27 ], [ 36, 41, 21, 0, 46, 12, 67, 42, 47, 21, 33, 17, 23, 43, 42, 41, 52, 38, 41 ], [ 45, 58, 48, 46, 0, 49, 73, 56, 59, 49, 43, 55, 31, 45, 47, 55, 48, 28, 37 ], [ 41, 53, 24, 12, 49, 0, 73, 45, 39, 33, 36, 16, 32, 46, 39, 49, 55, 44, 38 ], [ 58, 54, 62, 67, 73, 73, 0, 39, 46, 46, 47, 57, 57, 60, 64, 59, 62, 55, 58 ], [ 33, 37, 33, 42, 56, 45, 39, 0, 7, 39, 22, 29, 39, 54, 48, 58, 34, 38, 44 ], [ 27, 44, 40, 47, 59, 39, 46, 7, 0, 40, 16, 35, 42, 59, 42, 52, 27, 42, 49 ], [ 38, 55, 42, 21, 49, 33, 46, 39, 40, 0, 27, 35, 33, 38, 42, 37, 39, 33, 20 ], [ 11, 48, 28, 33, 43, 36, 47, 22, 16, 27, 0, 20, 30, 43, 38, 36, 41, 26, 34 ], [ 25, 46, 8, 17, 55, 16, 57, 29, 35, 35, 20, 0, 37, 30, 35, 34, 39, 28, 35 ], [ 33, 36, 31, 23, 31, 32, 57, 39, 42, 33, 30, 37, 0, 43, 51, 50, 41, 30, 20 ], [ 43, 61, 34, 43, 45, 46, 60, 54, 59, 38, 43, 30, 43, 0, 44, 29, 38, 17, 44 ], [ 32, 69, 38, 42, 47, 39, 64, 48, 42, 42, 38, 35, 51, 44, 0, 43, 55, 37, 55 ], [ 47, 73, 38, 41, 55, 49, 59, 58, 52, 37, 36, 34, 50, 29, 43, 0, 56, 31, 51 ], [ 48, 61, 43, 52, 48, 55, 62, 34, 27, 39, 41, 39, 41, 38, 55, 56, 0, 45, 52 ], [ 37, 56, 32, 38, 28, 44, 55, 38, 42, 33, 26, 28, 30, 17, 37, 31, 45, 0, 31 ], [ 32, 56, 27, 41, 37, 38, 58, 44, 49, 20, 34, 35, 20, 44, 55, 51, 52, 31, 0 ] ], "p": 1, "objective": 579.0 }, "solution": { "facilities": [ 10 ], "assignments": [ 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 ] }, "obj": 579.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 19, "num_open": 1, "sites": [ { "id": 0, "distances": { "0": 0, "1": 51, "2": 33, "3": 36, "4": 45, "5": 41, "6": 58, "7": 33, "8": 27, "9": 38, "10": 11, "11": 25, "12": 33, "13": 43, "14": 32, "15": 47, "16": 48, "17": 37, "18": 32 } }, { "id": 1, "distances": { "0": 51, "1": 0, "2": 50, "3": 41, "4": 58, "5": 53, "6": 54, "7": 37, "8": 44, "9": 55, "10": 48, "11": 46, "12": 36, "13": 61, "14": 69, "15": 73, "16": 61, "17": 56, "18": 56 } }, { "id": 2, "distances": { "0": 33, "1": 50, "2": 0, "3": 21, "4": 48, "5": 24, "6": 62, "7": 33, "8": 40, "9": 42, "10": 28, "11": 8, "12": 31, "13": 34, "14": 38, "15": 38, "16": 43, "17": 32, "18": 27 } }, { "id": 3, "distances": { "0": 36, "1": 41, "2": 21, "3": 0, "4": 46, "5": 12, "6": 67, "7": 42, "8": 47, "9": 21, "10": 33, "11": 17, "12": 23, "13": 43, "14": 42, "15": 41, "16": 52, "17": 38, "18": 41 } }, { "id": 4, "distances": { "0": 45, "1": 58, "2": 48, "3": 46, "4": 0, "5": 49, "6": 73, "7": 56, "8": 59, "9": 49, "10": 43, "11": 55, "12": 31, "13": 45, "14": 47, "15": 55, "16": 48, "17": 28, "18": 37 } }, { "id": 5, "distances": { "0": 41, "1": 53, "2": 24, "3": 12, "4": 49, "5": 0, "6": 73, "7": 45, "8": 39, "9": 33, "10": 36, "11": 16, "12": 32, "13": 46, "14": 39, "15": 49, "16": 55, "17": 44, "18": 38 } }, { "id": 6, "distances": { "0": 58, "1": 54, "2": 62, "3": 67, "4": 73, "5": 73, "6": 0, "7": 39, "8": 46, "9": 46, "10": 47, "11": 57, "12": 57, "13": 60, "14": 64, "15": 59, "16": 62, "17": 55, "18": 58 } }, { "id": 7, "distances": { "0": 33, "1": 37, "2": 33, "3": 42, "4": 56, "5": 45, "6": 39, "7": 0, "8": 7, "9": 39, "10": 22, "11": 29, "12": 39, "13": 54, "14": 48, "15": 58, "16": 34, "17": 38, "18": 44 } }, { "id": 8, "distances": { "0": 27, "1": 44, "2": 40, "3": 47, "4": 59, "5": 39, "6": 46, "7": 7, "8": 0, "9": 40, "10": 16, "11": 35, "12": 42, "13": 59, "14": 42, "15": 52, "16": 27, "17": 42, "18": 49 } }, { "id": 9, "distances": { "0": 38, "1": 55, "2": 42, "3": 21, "4": 49, "5": 33, "6": 46, "7": 39, "8": 40, "9": 0, "10": 27, "11": 35, "12": 33, "13": 38, "14": 42, "15": 37, "16": 39, "17": 33, "18": 20 } }, { "id": 10, "distances": { "0": 11, "1": 48, "2": 28, "3": 33, "4": 43, "5": 36, "6": 47, "7": 22, "8": 16, "9": 27, "10": 0, "11": 20, "12": 30, "13": 43, "14": 38, "15": 36, "16": 41, "17": 26, "18": 34 } }, { "id": 11, "distances": { "0": 25, "1": 46, "2": 8, "3": 17, "4": 55, "5": 16, "6": 57, "7": 29, "8": 35, "9": 35, "10": 20, "11": 0, "12": 37, "13": 30, "14": 35, "15": 34, "16": 39, "17": 28, "18": 35 } }, { "id": 12, "distances": { "0": 33, "1": 36, "2": 31, "3": 23, "4": 31, "5": 32, "6": 57, "7": 39, "8": 42, "9": 33, "10": 30, "11": 37, "12": 0, "13": 43, "14": 51, "15": 50, "16": 41, "17": 30, "18": 20 } }, { "id": 13, "distances": { "0": 43, "1": 61, "2": 34, "3": 43, "4": 45, "5": 46, "6": 60, "7": 54, "8": 59, "9": 38, "10": 43, "11": 30, "12": 43, "13": 0, "14": 44, "15": 29, "16": 38, "17": 17, "18": 44 } }, { "id": 14, "distances": { "0": 32, "1": 69, "2": 38, "3": 42, "4": 47, "5": 39, "6": 64, "7": 48, "8": 42, "9": 42, "10": 38, "11": 35, "12": 51, "13": 44, "14": 0, "15": 43, "16": 55, "17": 37, "18": 55 } }, { "id": 15, "distances": { "0": 47, "1": 73, "2": 38, "3": 41, "4": 55, "5": 49, "6": 59, "7": 58, "8": 52, "9": 37, "10": 36, "11": 34, "12": 50, "13": 29, "14": 43, "15": 0, "16": 56, "17": 31, "18": 51 } }, { "id": 16, "distances": { "0": 48, "1": 61, "2": 43, "3": 52, "4": 48, "5": 55, "6": 62, "7": 34, "8": 27, "9": 39, "10": 41, "11": 39, "12": 41, "13": 38, "14": 55, "15": 56, "16": 0, "17": 45, "18": 52 } }, { "id": 17, "distances": { "0": 37, "1": 56, "2": 32, "3": 38, "4": 28, "5": 44, "6": 55, "7": 38, "8": 42, "9": 33, "10": 26, "11": 28, "12": 30, "13": 17, "14": 37, "15": 31, "16": 45, "17": 0, "18": 31 } }, { "id": 18, "distances": { "0": 32, "1": 56, "2": 27, "3": 41, "4": 37, "5": 38, "6": 58, "7": 44, "8": 49, "9": 20, "10": 34, "11": 35, "12": 20, "13": 44, "14": 55, "15": 51, "16": 52, "17": 31, "18": 0 } } ], "objective": 579.0 }, "solution_variant": { "selected": [ 10 ], "assignments": [ 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 ] }, "context_index": 40, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Many people are helping coordinate mobile food stops, and the trick is selecting a preset number of stops from a list of possibilities. Once those stops are set, every block must be matched to exactly one stop, and the quality of the choice is measured by adding up each block’s distance to its assigned stop — the smaller that grand total, the more efficient the plan. The exact list of locations and distances is given below.\n\nThere are 17 candidate locations; the coordinator must open exactly 6 stops chosen from A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q.\nFrom A to B, the travel distance is 142.\nFrom A to C, the travel distance is 193.\nFrom A to D, the travel distance is 132.\nFrom A to E, the travel distance is 133.\nFrom A to F, the travel distance is 83.\nFrom A to G, the travel distance is 116.\nFrom A to H, the travel distance is 153.\nFrom A to I, the travel distance is 59.\nFrom A to J, the travel distance is 70.\nFrom A to K, the travel distance is 98.\nFrom A to L, the travel distance is 106.\nFrom A to M, the travel distance is 103.\nFrom A to N, the travel distance is 154.\nFrom A to O, the travel distance is 131.\nFrom A to P, the travel distance is 11.\nFrom A to Q, the travel distance is 120.\nFrom B to A, the travel distance is 142.\nFrom B to C, the travel distance is 201.\nFrom B to D, the travel distance is 172.\nFrom B to E, the travel distance is 108.\nFrom B to F, the travel distance is 59.\nFrom B to G, the travel distance is 136.\nFrom B to H, the travel distance is 129.\nFrom B to I, the travel distance is 161.\nFrom B to J, the travel distance is 179.\nFrom B to K, the travel distance is 138.\nFrom B to L, the travel distance is 143.\nFrom B to M, the travel distance is 119.\nFrom B to N, the travel distance is 146.\nFrom B to O, the travel distance is 61.\nFrom B to P, the travel distance is 131.\nFrom B to Q, the travel distance is 147.\nFrom C to A, the travel distance is 193.\nFrom C to B, the travel distance is 201.\nFrom C to D, the travel distance is 231.\nFrom C to E, the travel distance is 189.\nFrom C to F, the travel distance is 182.\nFrom C to G, the travel distance is 143.\nFrom C to H, the travel distance is 199.\nFrom C to I, the travel distance is 147.\nFrom C to J, the travel distance is 132.\nFrom C to K, the travel distance is 106.\nFrom C to L, the travel distance is 96.\nFrom C to M, the travel distance is 126.\nFrom C to N, the travel distance is 63.\nFrom C to O, the travel distance is 142.\nFrom C to P, the travel distance is 182.\nFrom C to Q, the travel distance is 160.\nFrom D to A, the travel distance is 132.\nFrom D to B, the travel distance is 172.\nFrom D to C, the travel distance is 231.\nFrom D to E, the travel distance is 71.\nFrom D to F, the travel distance is 113.\nFrom D to G, the travel distance is 135.\nFrom D to H, the travel distance is 183.\nFrom D to I, the travel distance is 97.\nFrom D to J, the travel distance is 184.\nFrom D to K, the travel distance is 128.\nFrom D to L, the travel distance is 148.\nFrom D to M, the travel distance is 149.\nFrom D to N, the travel distance is 177.\nFrom D to O, the travel distance is 120.\nFrom D to P, the travel distance is 121.\nFrom D to Q, the travel distance is 182.\nFrom E to A, the travel distance is 133.\nFrom E to B, the travel distance is 108.\nFrom E to C, the travel distance is 189.\nFrom E to D, the travel distance is 71.\nFrom E to F, the travel distance is 114.\nFrom E to G, the travel distance is 124.\nFrom E to H, the travel distance is 124.\nFrom E to I, the travel distance is 98.\nFrom E to J, the travel distance is 159.\nFrom E to K, the travel distance is 129.\nFrom E to L, the travel distance is 123.\nFrom E to M, the travel distance is 107.\nFrom E to N, the travel distance is 134.\nFrom E to O, the travel distance is 49.\nFrom E to P, the travel distance is 122.\nFrom E to Q, the travel distance is 135.\nFrom F to A, the travel distance is 83.\nFrom F to B, the travel distance is 59.\nFrom F to C, the travel distance is 182.\nFrom F to D, the travel distance is 113.\nFrom F to E, the travel distance is 114.\nFrom F to G, the travel distance is 113.\nFrom F to H, the travel distance is 70.\nFrom F to I, the travel distance is 102.\nFrom F to J, the travel distance is 143.\nFrom F to K, the travel distance is 79.\nFrom F to L, the travel distance is 113.\nFrom F to M, the travel distance is 100.\nFrom F to N, the travel distance is 151.\nFrom F to O, the travel distance is 81.\nFrom F to P, the travel distance is 72.\nFrom F to Q, the travel distance is 133.\nFrom G to A, the travel distance is 116.\nFrom G to B, the travel distance is 136.\nFrom G to C, the travel distance is 143.\nFrom G to D, the travel distance is 135.\nFrom G to E, the travel distance is 124.\nFrom G to F, the travel distance is 113.\nFrom G to H, the travel distance is 134.\nFrom G to I, the travel distance is 151.\nFrom G to J, the travel distance is 139.\nFrom G to K, the travel distance is 113.\nFrom G to L, the travel distance is 103.\nFrom G to M, the travel distance is 17.\nFrom G to N, the travel distance is 88.\nFrom G to O, the travel distance is 77.\nFrom G to P, the travel distance is 105.\nFrom G to Q, the travel distance is 95.\nFrom H to A, the travel distance is 153.\nFrom H to B, the travel distance is 129.\nFrom H to C, the travel distance is 199.\nFrom H to D, the travel distance is 183.\nFrom H to E, the travel distance is 124.\nFrom H to F, the travel distance is 70.\nFrom H to G, the travel distance is 134.\nFrom H to I, the travel distance is 172.\nFrom H to J, the travel distance is 177.\nFrom H to K, the travel distance is 149.\nFrom H to L, the travel distance is 141.\nFrom H to M, the travel distance is 117.\nFrom H to N, the travel distance is 144.\nFrom H to O, the travel distance is 77.\nFrom H to P, the travel distance is 142.\nFrom H to Q, the travel distance is 145.\nFrom I to A, the travel distance is 59.\nFrom I to B, the travel distance is 161.\nFrom I to C, the travel distance is 147.\nFrom I to D, the travel distance is 97.\nFrom I to E, the travel distance is 98.\nFrom I to F, the travel distance is 102.\nFrom I to G, the travel distance is 151.\nFrom I to H, the travel distance is 172.\nFrom I to J, the travel distance is 87.\nFrom I to K, the travel distance is 85.\nFrom I to L, the travel distance is 51.\nFrom I to M, the travel distance is 138.\nFrom I to N, the travel distance is 143.\nFrom I to O, the travel distance is 123.\nFrom I to P, the travel distance is 60.\nFrom I to Q, the travel distance is 87.\nFrom J to A, the travel distance is 70.\nFrom J to B, the travel distance is 179.\nFrom J to C, the travel distance is 132.\nFrom J to D, the travel distance is 184.\nFrom J to E, the travel distance is 159.\nFrom J to F, the travel distance is 143.\nFrom J to G, the travel distance is 139.\nFrom J to H, the travel distance is 177.\nFrom J to I, the travel distance is 87.\nFrom J to K, the travel distance is 70.\nFrom J to L, the travel distance is 36.\nFrom J to M, the travel distance is 129.\nFrom J to N, the travel distance is 128.\nFrom J to O, the travel distance is 120.\nFrom J to P, the travel distance is 71.\nFrom J to Q, the travel distance is 157.\nFrom K to A, the travel distance is 98.\nFrom K to B, the travel distance is 138.\nFrom K to C, the travel distance is 106.\nFrom K to D, the travel distance is 128.\nFrom K to E, the travel distance is 129.\nFrom K to F, the travel distance is 79.\nFrom K to G, the travel distance is 113.\nFrom K to H, the travel distance is 149.\nFrom K to I, the travel distance is 85.\nFrom K to J, the travel distance is 70.\nFrom K to L, the travel distance is 34.\nFrom K to M, the travel distance is 105.\nFrom K to N, the travel distance is 104.\nFrom K to O, the travel distance is 96.\nFrom K to P, the travel distance is 87.\nFrom K to Q, the travel distance is 133.\nFrom L to A, the travel distance is 106.\nFrom L to B, the travel distance is 143.\nFrom L to C, the travel distance is 96.\nFrom L to D, the travel distance is 148.\nFrom L to E, the travel distance is 123.\nFrom L to F, the travel distance is 113.\nFrom L to G, the travel distance is 103.\nFrom L to H, the travel distance is 141.\nFrom L to I, the travel distance is 51.\nFrom L to J, the travel distance is 36.\nFrom L to K, the travel distance is 34.\nFrom L to M, the travel distance is 93.\nFrom L to N, the travel distance is 92.\nFrom L to O, the travel distance is 84.\nFrom L to P, the travel distance is 107.\nFrom L to Q, the travel distance is 121.\nFrom M to A, the travel distance is 103.\nFrom M to B, the travel distance is 119.\nFrom M to C, the travel distance is 126.\nFrom M to D, the travel distance is 149.\nFrom M to E, the travel distance is 107.\nFrom M to F, the travel distance is 100.\nFrom M to G, the travel distance is 17.\nFrom M to H, the travel distance is 117.\nFrom M to I, the travel distance is 138.\nFrom M to J, the travel distance is 129.\nFrom M to K, the travel distance is 105.\nFrom M to L, the travel distance is 93.\nFrom M to N, the travel distance is 71.\nFrom M to O, the travel distance is 60.\nFrom M to P, the travel distance is 92.\nFrom M to Q, the travel distance is 78.\nFrom N to A, the travel distance is 154.\nFrom N to B, the travel distance is 146.\nFrom N to C, the travel distance is 63.\nFrom N to D, the travel distance is 177.\nFrom N to E, the travel distance is 134.\nFrom N to F, the travel distance is 151.\nFrom N to G, the travel distance is 88.\nFrom N to H, the travel distance is 144.\nFrom N to I, the travel distance is 143.\nFrom N to J, the travel distance is 128.\nFrom N to K, the travel distance is 104.\nFrom N to L, the travel distance is 92.\nFrom N to M, the travel distance is 71.\nFrom N to O, the travel distance is 87.\nFrom N to P, the travel distance is 143.\nFrom N to Q, the travel distance is 105.\nFrom O to A, the travel distance is 131.\nFrom O to B, the travel distance is 61.\nFrom O to C, the travel distance is 142.\nFrom O to D, the travel distance is 120.\nFrom O to E, the travel distance is 49.\nFrom O to F, the travel distance is 81.\nFrom O to G, the travel distance is 77.\nFrom O to H, the travel distance is 77.\nFrom O to I, the travel distance is 123.\nFrom O to J, the travel distance is 120.\nFrom O to K, the travel distance is 96.\nFrom O to L, the travel distance is 84.\nFrom O to M, the travel distance is 60.\nFrom O to N, the travel distance is 87.\nFrom O to P, the travel distance is 120.\nFrom O to Q, the travel distance is 88.\nFrom P to A, the travel distance is 11.\nFrom P to B, the travel distance is 131.\nFrom P to C, the travel distance is 182.\nFrom P to D, the travel distance is 121.\nFrom P to E, the travel distance is 122.\nFrom P to F, the travel distance is 72.\nFrom P to G, the travel distance is 105.\nFrom P to H, the travel distance is 142.\nFrom P to I, the travel distance is 60.\nFrom P to J, the travel distance is 71.\nFrom P to K, the travel distance is 87.\nFrom P to L, the travel distance is 107.\nFrom P to M, the travel distance is 92.\nFrom P to N, the travel distance is 143.\nFrom P to O, the travel distance is 120.\nFrom P to Q, the travel distance is 109.\nFrom Q to A, the travel distance is 120.\nFrom Q to B, the travel distance is 147.\nFrom Q to C, the travel distance is 160.\nFrom Q to D, the travel distance is 182.\nFrom Q to E, the travel distance is 135.\nFrom Q to F, the travel distance is 133.\nFrom Q to G, the travel distance is 95.\nFrom Q to H, the travel distance is 145.\nFrom Q to I, the travel distance is 87.\nFrom Q to J, the travel distance is 157.\nFrom Q to K, the travel distance is 133.\nFrom Q to L, the travel distance is 121.\nFrom Q to M, the travel distance is 78.\nFrom Q to N, the travel distance is 105.\nFrom Q to O, the travel distance is 88.\nFrom Q to P, the travel distance is 109.\nThese distances are used to sum each block’s distance to its assigned stop and compare total costs for different choices of 6 stops among the 17 candidates.\n\nAlso, please structure your reply using this little JSON sketch so it's easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list which stops you decide to open (one placeholder per chosen stop). \"assignments\" is a matching list that, for each block in the original order, gives the open stop that block is assigned to. Think of it like filling out a simple form: which stops are open, and which open stop each block goes to.\n\nThis is just the shape I need—not the real answer. Make sure to use the exact identifiers from the instance input when you fill this in — do not rename them or invent new labels.\n\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 142, 193, 132, 133, 83, 116, 153, 59, 70, 98, 106, 103, 154, 131, 11, 120 ], [ 142, 0, 201, 172, 108, 59, 136, 129, 161, 179, 138, 143, 119, 146, 61, 131, 147 ], [ 193, 201, 0, 231, 189, 182, 143, 199, 147, 132, 106, 96, 126, 63, 142, 182, 160 ], [ 132, 172, 231, 0, 71, 113, 135, 183, 97, 184, 128, 148, 149, 177, 120, 121, 182 ], [ 133, 108, 189, 71, 0, 114, 124, 124, 98, 159, 129, 123, 107, 134, 49, 122, 135 ], [ 83, 59, 182, 113, 114, 0, 113, 70, 102, 143, 79, 113, 100, 151, 81, 72, 133 ], [ 116, 136, 143, 135, 124, 113, 0, 134, 151, 139, 113, 103, 17, 88, 77, 105, 95 ], [ 153, 129, 199, 183, 124, 70, 134, 0, 172, 177, 149, 141, 117, 144, 77, 142, 145 ], [ 59, 161, 147, 97, 98, 102, 151, 172, 0, 87, 85, 51, 138, 143, 123, 60, 87 ], [ 70, 179, 132, 184, 159, 143, 139, 177, 87, 0, 70, 36, 129, 128, 120, 71, 157 ], [ 98, 138, 106, 128, 129, 79, 113, 149, 85, 70, 0, 34, 105, 104, 96, 87, 133 ], [ 106, 143, 96, 148, 123, 113, 103, 141, 51, 36, 34, 0, 93, 92, 84, 107, 121 ], [ 103, 119, 126, 149, 107, 100, 17, 117, 138, 129, 105, 93, 0, 71, 60, 92, 78 ], [ 154, 146, 63, 177, 134, 151, 88, 144, 143, 128, 104, 92, 71, 0, 87, 143, 105 ], [ 131, 61, 142, 120, 49, 81, 77, 77, 123, 120, 96, 84, 60, 87, 0, 120, 88 ], [ 11, 131, 182, 121, 122, 72, 105, 142, 60, 71, 87, 107, 92, 143, 120, 0, 109 ], [ 120, 147, 160, 182, 135, 133, 95, 145, 87, 157, 133, 121, 78, 105, 88, 109, 0 ] ], "p": 6, "objective": 539.0 }, "solution": { "facilities": [ 0, 4, 5, 11, 12, 13 ], "assignments": [ 0, 5, 13, 4, 4, 5, 12, 5, 11, 11, 11, 11, 12, 13, 4, 0, 12 ] }, "obj": 539.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 6, "sites": [ { "id": "A", "distances": { "A": 0, "B": 142, "C": 193, "D": 132, "E": 133, "F": 83, "G": 116, "H": 153, "I": 59, "J": 70, "K": 98, "L": 106, "M": 103, "N": 154, "O": 131, "P": 11, "Q": 120 } }, { "id": "B", "distances": { "A": 142, "B": 0, "C": 201, "D": 172, "E": 108, "F": 59, "G": 136, "H": 129, "I": 161, "J": 179, "K": 138, "L": 143, "M": 119, "N": 146, "O": 61, "P": 131, "Q": 147 } }, { "id": "C", "distances": { "A": 193, "B": 201, "C": 0, "D": 231, "E": 189, "F": 182, "G": 143, "H": 199, "I": 147, "J": 132, "K": 106, "L": 96, "M": 126, "N": 63, "O": 142, "P": 182, "Q": 160 } }, { "id": "D", "distances": { "A": 132, "B": 172, "C": 231, "D": 0, "E": 71, "F": 113, "G": 135, "H": 183, "I": 97, "J": 184, "K": 128, "L": 148, "M": 149, "N": 177, "O": 120, "P": 121, "Q": 182 } }, { "id": "E", "distances": { "A": 133, "B": 108, "C": 189, "D": 71, "E": 0, "F": 114, "G": 124, "H": 124, "I": 98, "J": 159, "K": 129, "L": 123, "M": 107, "N": 134, "O": 49, "P": 122, "Q": 135 } }, { "id": "F", "distances": { "A": 83, "B": 59, "C": 182, "D": 113, "E": 114, "F": 0, "G": 113, "H": 70, "I": 102, "J": 143, "K": 79, "L": 113, "M": 100, "N": 151, "O": 81, "P": 72, "Q": 133 } }, { "id": "G", "distances": { "A": 116, "B": 136, "C": 143, "D": 135, "E": 124, "F": 113, "G": 0, "H": 134, "I": 151, "J": 139, "K": 113, "L": 103, "M": 17, "N": 88, "O": 77, "P": 105, "Q": 95 } }, { "id": "H", "distances": { "A": 153, "B": 129, "C": 199, "D": 183, "E": 124, "F": 70, "G": 134, "H": 0, "I": 172, "J": 177, "K": 149, "L": 141, "M": 117, "N": 144, "O": 77, "P": 142, "Q": 145 } }, { "id": "I", "distances": { "A": 59, "B": 161, "C": 147, "D": 97, "E": 98, "F": 102, "G": 151, "H": 172, "I": 0, "J": 87, "K": 85, "L": 51, "M": 138, "N": 143, "O": 123, "P": 60, "Q": 87 } }, { "id": "J", "distances": { "A": 70, "B": 179, "C": 132, "D": 184, "E": 159, "F": 143, "G": 139, "H": 177, "I": 87, "J": 0, "K": 70, "L": 36, "M": 129, "N": 128, "O": 120, "P": 71, "Q": 157 } }, { "id": "K", "distances": { "A": 98, "B": 138, "C": 106, "D": 128, "E": 129, "F": 79, "G": 113, "H": 149, "I": 85, "J": 70, "K": 0, "L": 34, "M": 105, "N": 104, "O": 96, "P": 87, "Q": 133 } }, { "id": "L", "distances": { "A": 106, "B": 143, "C": 96, "D": 148, "E": 123, "F": 113, "G": 103, "H": 141, "I": 51, "J": 36, "K": 34, "L": 0, "M": 93, "N": 92, "O": 84, "P": 107, "Q": 121 } }, { "id": "M", "distances": { "A": 103, "B": 119, "C": 126, "D": 149, "E": 107, "F": 100, "G": 17, "H": 117, "I": 138, "J": 129, "K": 105, "L": 93, "M": 0, "N": 71, "O": 60, "P": 92, "Q": 78 } }, { "id": "N", "distances": { "A": 154, "B": 146, "C": 63, "D": 177, "E": 134, "F": 151, "G": 88, "H": 144, "I": 143, "J": 128, "K": 104, "L": 92, "M": 71, "N": 0, "O": 87, "P": 143, "Q": 105 } }, { "id": "O", "distances": { "A": 131, "B": 61, "C": 142, "D": 120, "E": 49, "F": 81, "G": 77, "H": 77, "I": 123, "J": 120, "K": 96, "L": 84, "M": 60, "N": 87, "O": 0, "P": 120, "Q": 88 } }, { "id": "P", "distances": { "A": 11, "B": 131, "C": 182, "D": 121, "E": 122, "F": 72, "G": 105, "H": 142, "I": 60, "J": 71, "K": 87, "L": 107, "M": 92, "N": 143, "O": 120, "P": 0, "Q": 109 } }, { "id": "Q", "distances": { "A": 120, "B": 147, "C": 160, "D": 182, "E": 135, "F": 133, "G": 95, "H": 145, "I": 87, "J": 157, "K": 133, "L": 121, "M": 78, "N": 105, "O": 88, "P": 109, "Q": 0 } } ], "objective": 539.0 }, "solution_variant": { "selected": [ "A", "E", "F", "L", "M", "N" ], "assignments": [ "A", "F", "N", "E", "E", "F", "M", "F", "L", "L", "L", "L", "M", "N", "E", "A", "M" ] }, "context_index": 41, "input_format": "nl", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "A local clinic is planning to open a handful of satellite vaccine spots and needs to make two decisions: which fixed number of candidate locations to use, and which single chosen site each residential area will go to (no area left out, and none sent to more than one place). The practical test is to add up each area’s travel distance to its assigned site; the setup with the lowest total travel wins. See the exact locations and distances below.\n\nThere are 20 distinct locations, the clinic must open exactly 2 sites, and the location IDs are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.\nFrom location 1 to candidate site 2, the travel distance is 81.\nFrom location 1 to candidate site 3, the travel distance is 207.\nFrom location 1 to candidate site 4, the travel distance is 184.\nFrom location 1 to candidate site 5, the travel distance is 178.\nFrom location 1 to candidate site 6, the travel distance is 123.\nFrom location 1 to candidate site 7, the travel distance is 55.\nFrom location 1 to candidate site 8, the travel distance is 123.\nFrom location 1 to candidate site 9, the travel distance is 135.\nFrom location 1 to candidate site 10, the travel distance is 166.\nFrom location 1 to candidate site 11, the travel distance is 119.\nFrom location 1 to candidate site 12, the travel distance is 135.\nFrom location 1 to candidate site 13, the travel distance is 183.\nFrom location 1 to candidate site 14, the travel distance is 116.\nFrom location 1 to candidate site 15, the travel distance is 72.\nFrom location 1 to candidate site 16, the travel distance is 132.\nFrom location 1 to candidate site 17, the travel distance is 166.\nFrom location 1 to candidate site 18, the travel distance is 151.\nFrom location 1 to candidate site 19, the travel distance is 161.\nFrom location 1 to candidate site 20, the travel distance is 123.\nFrom location 2 to candidate site 1, the travel distance is 81.\nFrom location 2 to candidate site 3, the travel distance is 128.\nFrom location 2 to candidate site 4, the travel distance is 107.\nFrom location 2 to candidate site 5, the travel distance is 159.\nFrom location 2 to candidate site 6, the travel distance is 95.\nFrom location 2 to candidate site 7, the travel distance is 26.\nFrom location 2 to candidate site 8, the travel distance is 100.\nFrom location 2 to candidate site 9, the travel distance is 59.\nFrom location 2 to candidate site 10, the travel distance is 174.\nFrom location 2 to candidate site 11, the travel distance is 90.\nFrom location 2 to candidate site 12, the travel distance is 91.\nFrom location 2 to candidate site 13, the travel distance is 187.\nFrom location 2 to candidate site 14, the travel distance is 120.\nFrom location 2 to candidate site 15, the travel distance is 132.\nFrom location 2 to candidate site 16, the travel distance is 151.\nFrom location 2 to candidate site 17, the travel distance is 170.\nFrom location 2 to candidate site 18, the travel distance is 83.\nFrom location 2 to candidate site 19, the travel distance is 146.\nFrom location 2 to candidate site 20, the travel distance is 47.\nFrom location 3 to candidate site 1, the travel distance is 207.\nFrom location 3 to candidate site 2, the travel distance is 128.\nFrom location 3 to candidate site 4, the travel distance is 149.\nFrom location 3 to candidate site 5, the travel distance is 155.\nFrom location 3 to candidate site 6, the travel distance is 216.\nFrom location 3 to candidate site 7, the travel distance is 152.\nFrom location 3 to candidate site 8, the travel distance is 143.\nFrom location 3 to candidate site 9, the travel distance is 185.\nFrom location 3 to candidate site 10, the travel distance is 216.\nFrom location 3 to candidate site 11, the travel distance is 208.\nFrom location 3 to candidate site 12, the travel distance is 163.\nFrom location 3 to candidate site 13, the travel distance is 244.\nFrom location 3 to candidate site 14, the travel distance is 155.\nFrom location 3 to candidate site 15, the travel distance is 215.\nFrom location 3 to candidate site 16, the travel distance is 221.\nFrom location 3 to candidate site 17, the travel distance is 236.\nFrom location 3 to candidate site 18, the travel distance is 79.\nFrom location 3 to candidate site 19, the travel distance is 142.\nFrom location 3 to candidate site 20, the travel distance is 173.\nFrom location 4 to candidate site 1, the travel distance is 184.\nFrom location 4 to candidate site 2, the travel distance is 107.\nFrom location 4 to candidate site 3, the travel distance is 149.\nFrom location 4 to candidate site 5, the travel distance is 180.\nFrom location 4 to candidate site 6, the travel distance is 117.\nFrom location 4 to candidate site 7, the travel distance is 131.\nFrom location 4 to candidate site 8, the travel distance is 84.\nFrom location 4 to candidate site 9, the travel distance is 104.\nFrom location 4 to candidate site 10, the travel distance is 97.\nFrom location 4 to candidate site 11, the travel distance is 148.\nFrom location 4 to candidate site 12, the travel distance is 139.\nFrom location 4 to candidate site 13, the travel distance is 203.\nFrom location 4 to candidate site 14, the travel distance is 145.\nFrom location 4 to candidate site 15, the travel distance is 157.\nFrom location 4 to candidate site 16, the travel distance is 196.\nFrom location 4 to candidate site 17, the travel distance is 195.\nFrom location 4 to candidate site 18, the travel distance is 104.\nFrom location 4 to candidate site 19, the travel distance is 167.\nFrom location 4 to candidate site 20, the travel distance is 116.\nFrom location 5 to candidate site 1, the travel distance is 178.\nFrom location 5 to candidate site 2, the travel distance is 159.\nFrom location 5 to candidate site 3, the travel distance is 155.\nFrom location 5 to candidate site 4, the travel distance is 180.\nFrom location 5 to candidate site 6, the travel distance is 89.\nFrom location 5 to candidate site 7, the travel distance is 183.\nFrom location 5 to candidate site 8, the travel distance is 174.\nFrom location 5 to candidate site 9, the travel distance is 134.\nFrom location 5 to candidate site 10, the travel distance is 200.\nFrom location 5 to candidate site 11, the travel distance is 191.\nFrom location 5 to candidate site 12, the travel distance is 146.\nFrom location 5 to candidate site 13, the travel distance is 233.\nFrom location 5 to candidate site 14, the travel distance is 166.\nFrom location 5 to candidate site 15, the travel distance is 106.\nFrom location 5 to candidate site 16, the travel distance is 182.\nFrom location 5 to candidate site 17, the travel distance is 216.\nFrom location 5 to candidate site 18, the travel distance is 98.\nFrom location 5 to candidate site 19, the travel distance is 161.\nFrom location 5 to candidate site 20, the travel distance is 146.\nFrom location 6 to candidate site 1, the travel distance is 123.\nFrom location 6 to candidate site 2, the travel distance is 95.\nFrom location 6 to candidate site 3, the travel distance is 216.\nFrom location 6 to candidate site 4, the travel distance is 117.\nFrom location 6 to candidate site 5, the travel distance is 89.\nFrom location 6 to candidate site 7, the travel distance is 119.\nFrom location 6 to candidate site 8, the travel distance is 121.\nFrom location 6 to candidate site 9, the travel distance is 45.\nFrom location 6 to candidate site 10, the travel distance is 145.\nFrom location 6 to candidate site 11, the travel distance is 115.\nFrom location 6 to candidate site 12, the travel distance is 171.\nFrom location 6 to candidate site 13, the travel distance is 178.\nFrom location 6 to candidate site 14, the travel distance is 111.\nFrom location 6 to candidate site 15, the travel distance is 51.\nFrom location 6 to candidate site 16, the travel distance is 127.\nFrom location 6 to candidate site 17, the travel distance is 161.\nFrom location 6 to candidate site 18, the travel distance is 155.\nFrom location 6 to candidate site 19, the travel distance is 156.\nFrom location 6 to candidate site 20, the travel distance is 57.\nFrom location 7 to candidate site 1, the travel distance is 55.\nFrom location 7 to candidate site 2, the travel distance is 26.\nFrom location 7 to candidate site 3, the travel distance is 152.\nFrom location 7 to candidate site 4, the travel distance is 131.\nFrom location 7 to candidate site 5, the travel distance is 183.\nFrom location 7 to candidate site 6, the travel distance is 119.\nFrom location 7 to candidate site 8, the travel distance is 124.\nFrom location 7 to candidate site 9, the travel distance is 80.\nFrom location 7 to candidate site 10, the travel distance is 198.\nFrom location 7 to candidate site 11, the travel distance is 64.\nFrom location 7 to candidate site 12, the travel distance is 117.\nFrom location 7 to candidate site 13, the travel distance is 213.\nFrom location 7 to candidate site 14, the travel distance is 146.\nFrom location 7 to candidate site 15, the travel distance is 127.\nFrom location 7 to candidate site 16, the travel distance is 172.\nFrom location 7 to candidate site 17, the travel distance is 196.\nFrom location 7 to candidate site 18, the travel distance is 107.\nFrom location 7 to candidate site 19, the travel distance is 170.\nFrom location 7 to candidate site 20, the travel distance is 68.\nFrom location 8 to candidate site 1, the travel distance is 123.\nFrom location 8 to candidate site 2, the travel distance is 100.\nFrom location 8 to candidate site 3, the travel distance is 143.\nFrom location 8 to candidate site 4, the travel distance is 84.\nFrom location 8 to candidate site 5, the travel distance is 174.\nFrom location 8 to candidate site 6, the travel distance is 121.\nFrom location 8 to candidate site 7, the travel distance is 124.\nFrom location 8 to candidate site 9, the travel distance is 108.\nFrom location 8 to candidate site 10, the travel distance is 147.\nFrom location 8 to candidate site 11, the travel distance is 109.\nFrom location 8 to candidate site 12, the travel distance is 148.\nFrom location 8 to candidate site 13, the travel distance is 195.\nFrom location 8 to candidate site 14, the travel distance is 128.\nFrom location 8 to candidate site 15, the travel distance is 140.\nFrom location 8 to candidate site 16, the travel distance is 200.\nFrom location 8 to candidate site 17, the travel distance is 178.\nFrom location 8 to candidate site 18, the travel distance is 82.\nFrom location 8 to candidate site 19, the travel distance is 145.\nFrom location 8 to candidate site 20, the travel distance is 120.\nFrom location 9 to candidate site 1, the travel distance is 135.\nFrom location 9 to candidate site 2, the travel distance is 59.\nFrom location 9 to candidate site 3, the travel distance is 185.\nFrom location 9 to candidate site 4, the travel distance is 104.\nFrom location 9 to candidate site 5, the travel distance is 134.\nFrom location 9 to candidate site 6, the travel distance is 45.\nFrom location 9 to candidate site 7, the travel distance is 80.\nFrom location 9 to candidate site 8, the travel distance is 108.\nFrom location 9 to candidate site 10, the travel distance is 147.\nFrom location 9 to candidate site 11, the travel distance is 70.\nFrom location 9 to candidate site 12, the travel distance is 150.\nFrom location 9 to candidate site 13, the travel distance is 219.\nFrom location 9 to candidate site 14, the travel distance is 124.\nFrom location 9 to candidate site 15, the travel distance is 96.\nFrom location 9 to candidate site 16, the travel distance is 92.\nFrom location 9 to candidate site 17, the travel distance is 206.\nFrom location 9 to candidate site 18, the travel distance is 110.\nFrom location 9 to candidate site 19, the travel distance is 111.\nFrom location 9 to candidate site 20, the travel distance is 12.\nFrom location 10 to candidate site 1, the travel distance is 166.\nFrom location 10 to candidate site 2, the travel distance is 174.\nFrom location 10 to candidate site 3, the travel distance is 216.\nFrom location 10 to candidate site 4, the travel distance is 97.\nFrom location 10 to candidate site 5, the travel distance is 200.\nFrom location 10 to candidate site 6, the travel distance is 145.\nFrom location 10 to candidate site 7, the travel distance is 198.\nFrom location 10 to candidate site 8, the travel distance is 147.\nFrom location 10 to candidate site 9, the travel distance is 147.\nFrom location 10 to candidate site 11, the travel distance is 134.\nFrom location 10 to candidate site 12, the travel distance is 136.\nFrom location 10 to candidate site 13, the travel distance is 221.\nFrom location 10 to candidate site 14, the travel distance is 154.\nFrom location 10 to candidate site 15, the travel distance is 94.\nFrom location 10 to candidate site 16, the travel distance is 170.\nFrom location 10 to candidate site 17, the travel distance is 204.\nFrom location 10 to candidate site 18, the travel distance is 171.\nFrom location 10 to candidate site 19, the travel distance is 183.\nFrom location 10 to candidate site 20, the travel distance is 135.\nFrom location 11 to candidate site 1, the travel distance is 119.\nFrom location 11 to candidate site 2, the travel distance is 90.\nFrom location 11 to candidate site 3, the travel distance is 208.\nFrom location 11 to candidate site 4, the travel distance is 148.\nFrom location 11 to candidate site 5, the travel distance is 191.\nFrom location 11 to candidate site 6, the travel distance is 115.\nFrom location 11 to candidate site 7, the travel distance is 64.\nFrom location 11 to candidate site 8, the travel distance is 109.\nFrom location 11 to candidate site 9, the travel distance is 70.\nFrom location 11 to candidate site 10, the travel distance is 134.\nFrom location 11 to candidate site 12, the travel distance is 93.\nFrom location 11 to candidate site 13, the travel distance is 173.\nFrom location 11 to candidate site 14, the travel distance is 134.\nFrom location 11 to candidate site 15, the travel distance is 90.\nFrom location 11 to candidate site 16, the travel distance is 150.\nFrom location 11 to candidate site 17, the travel distance is 184.\nFrom location 11 to candidate site 18, the travel distance is 151.\nFrom location 11 to candidate site 19, the travel distance is 181.\nFrom location 11 to candidate site 20, the travel distance is 58.\nFrom location 12 to candidate site 1, the travel distance is 135.\nFrom location 12 to candidate site 2, the travel distance is 91.\nFrom location 12 to candidate site 3, the travel distance is 163.\nFrom location 12 to candidate site 4, the travel distance is 139.\nFrom location 12 to candidate site 5, the travel distance is 146.\nFrom location 12 to candidate site 6, the travel distance is 171.\nFrom location 12 to candidate site 7, the travel distance is 117.\nFrom location 12 to candidate site 8, the travel distance is 148.\nFrom location 12 to candidate site 9, the travel distance is 150.\nFrom location 12 to candidate site 10, the travel distance is 136.\nFrom location 12 to candidate site 11, the travel distance is 93.\nFrom location 12 to candidate site 13, the travel distance is 136.\nFrom location 12 to candidate site 14, the travel distance is 108.\nFrom location 12 to candidate site 15, the travel distance is 120.\nFrom location 12 to candidate site 16, the travel distance is 180.\nFrom location 12 to candidate site 17, the travel distance is 95.\nFrom location 12 to candidate site 18, the travel distance is 106.\nFrom location 12 to candidate site 19, the travel distance is 137.\nFrom location 12 to candidate site 20, the travel distance is 138.\nFrom location 13 to candidate site 1, the travel distance is 183.\nFrom location 13 to candidate site 2, the travel distance is 187.\nFrom location 13 to candidate site 3, the travel distance is 244.\nFrom location 13 to candidate site 4, the travel distance is 203.\nFrom location 13 to candidate site 5, the travel distance is 233.\nFrom location 13 to candidate site 6, the travel distance is 178.\nFrom location 13 to candidate site 7, the travel distance is 213.\nFrom location 13 to candidate site 8, the travel distance is 195.\nFrom location 13 to candidate site 9, the travel distance is 219.\nFrom location 13 to candidate site 10, the travel distance is 221.\nFrom location 13 to candidate site 11, the travel distance is 173.\nFrom location 13 to candidate site 12, the travel distance is 136.\nFrom location 13 to candidate site 14, the travel distance is 103.\nFrom location 13 to candidate site 15, the travel distance is 127.\nFrom location 13 to candidate site 16, the travel distance is 187.\nFrom location 13 to candidate site 17, the travel distance is 155.\nFrom location 13 to candidate site 18, the travel distance is 179.\nFrom location 13 to candidate site 19, the travel distance is 180.\nFrom location 13 to candidate site 20, the travel distance is 207.\nFrom location 14 to candidate site 1, the travel distance is 116.\nFrom location 14 to candidate site 2, the travel distance is 120.\nFrom location 14 to candidate site 3, the travel distance is 155.\nFrom location 14 to candidate site 4, the travel distance is 145.\nFrom location 14 to candidate site 5, the travel distance is 166.\nFrom location 14 to candidate site 6, the travel distance is 111.\nFrom location 14 to candidate site 7, the travel distance is 146.\nFrom location 14 to candidate site 8, the travel distance is 128.\nFrom location 14 to candidate site 9, the travel distance is 124.\nFrom location 14 to candidate site 10, the travel distance is 154.\nFrom location 14 to candidate site 11, the travel distance is 134.\nFrom location 14 to candidate site 12, the travel distance is 108.\nFrom location 14 to candidate site 13, the travel distance is 103.\nFrom location 14 to candidate site 15, the travel distance is 60.\nFrom location 14 to candidate site 16, the travel distance is 120.\nFrom location 14 to candidate site 17, the travel distance is 88.\nFrom location 14 to candidate site 18, the travel distance is 76.\nFrom location 14 to candidate site 19, the travel distance is 77.\nFrom location 14 to candidate site 20, the travel distance is 136.\nFrom location 15 to candidate site 1, the travel distance is 72.\nFrom location 15 to candidate site 2, the travel distance is 132.\nFrom location 15 to candidate site 3, the travel distance is 215.\nFrom location 15 to candidate site 4, the travel distance is 157.\nFrom location 15 to candidate site 5, the travel distance is 106.\nFrom location 15 to candidate site 6, the travel distance is 51.\nFrom location 15 to candidate site 7, the travel distance is 127.\nFrom location 15 to candidate site 8, the travel distance is 140.\nFrom location 15 to candidate site 9, the travel distance is 96.\nFrom location 15 to candidate site 10, the travel distance is 94.\nFrom location 15 to candidate site 11, the travel distance is 90.\nFrom location 15 to candidate site 12, the travel distance is 120.\nFrom location 15 to candidate site 13, the travel distance is 127.\nFrom location 15 to candidate site 14, the travel distance is 60.\nFrom location 15 to candidate site 16, the travel distance is 76.\nFrom location 15 to candidate site 17, the travel distance is 110.\nFrom location 15 to candidate site 18, the travel distance is 136.\nFrom location 15 to candidate site 19, the travel distance is 137.\nFrom location 15 to candidate site 20, the travel distance is 105.\nFrom location 16 to candidate site 1, the travel distance is 132.\nFrom location 16 to candidate site 2, the travel distance is 151.\nFrom location 16 to candidate site 3, the travel distance is 221.\nFrom location 16 to candidate site 4, the travel distance is 196.\nFrom location 16 to candidate site 5, the travel distance is 182.\nFrom location 16 to candidate site 6, the travel distance is 127.\nFrom location 16 to candidate site 7, the travel distance is 172.\nFrom location 16 to candidate site 8, the travel distance is 200.\nFrom location 16 to candidate site 9, the travel distance is 92.\nFrom location 16 to candidate site 10, the travel distance is 170.\nFrom location 16 to candidate site 11, the travel distance is 150.\nFrom location 16 to candidate site 12, the travel distance is 180.\nFrom location 16 to candidate site 13, the travel distance is 187.\nFrom location 16 to candidate site 14, the travel distance is 120.\nFrom location 16 to candidate site 15, the travel distance is 76.\nFrom location 16 to candidate site 17, the travel distance is 170.\nFrom location 16 to candidate site 18, the travel distance is 142.\nFrom location 16 to candidate site 19, the travel distance is 143.\nFrom location 16 to candidate site 20, the travel distance is 104.\nFrom location 17 to candidate site 1, the travel distance is 166.\nFrom location 17 to candidate site 2, the travel distance is 170.\nFrom location 17 to candidate site 3, the travel distance is 236.\nFrom location 17 to candidate site 4, the travel distance is 195.\nFrom location 17 to candidate site 5, the travel distance is 216.\nFrom location 17 to candidate site 6, the travel distance is 161.\nFrom location 17 to candidate site 7, the travel distance is 196.\nFrom location 17 to candidate site 8, the travel distance is 178.\nFrom location 17 to candidate site 9, the travel distance is 206.\nFrom location 17 to candidate site 10, the travel distance is 204.\nFrom location 17 to candidate site 11, the travel distance is 184.\nFrom location 17 to candidate site 12, the travel distance is 95.\nFrom location 17 to candidate site 13, the travel distance is 155.\nFrom location 17 to candidate site 14, the travel distance is 88.\nFrom location 17 to candidate site 15, the travel distance is 110.\nFrom location 17 to candidate site 16, the travel distance is 170.\nFrom location 17 to candidate site 18, the travel distance is 164.\nFrom location 17 to candidate site 19, the travel distance is 165.\nFrom location 17 to candidate site 20, the travel distance is 199.\nFrom location 18 to candidate site 1, the travel distance is 151.\nFrom location 18 to candidate site 2, the travel distance is 83.\nFrom location 18 to candidate site 3, the travel distance is 79.\nFrom location 18 to candidate site 4, the travel distance is 104.\nFrom location 18 to candidate site 5, the travel distance is 98.\nFrom location 18 to candidate site 6, the travel distance is 155.\nFrom location 18 to candidate site 7, the travel distance is 107.\nFrom location 18 to candidate site 8, the travel distance is 82.\nFrom location 18 to candidate site 9, the travel distance is 110.\nFrom location 18 to candidate site 10, the travel distance is 171.\nFrom location 18 to candidate site 11, the travel distance is 151.\nFrom location 18 to candidate site 12, the travel distance is 106.\nFrom location 18 to candidate site 13, the travel distance is 179.\nFrom location 18 to candidate site 14, the travel distance is 76.\nFrom location 18 to candidate site 15, the travel distance is 136.\nFrom location 18 to candidate site 16, the travel distance is 142.\nFrom location 18 to candidate site 17, the travel distance is 164.\nFrom location 18 to candidate site 19, the travel distance is 63.\nFrom location 18 to candidate site 20, the travel distance is 122.\nFrom location 19 to candidate site 1, the travel distance is 161.\nFrom location 19 to candidate site 2, the travel distance is 146.\nFrom location 19 to candidate site 3, the travel distance is 142.\nFrom location 19 to candidate site 4, the travel distance is 167.\nFrom location 19 to candidate site 5, the travel distance is 161.\nFrom location 19 to candidate site 6, the travel distance is 156.\nFrom location 19 to candidate site 7, the travel distance is 170.\nFrom location 19 to candidate site 8, the travel distance is 145.\nFrom location 19 to candidate site 9, the travel distance is 111.\nFrom location 19 to candidate site 10, the travel distance is 183.\nFrom location 19 to candidate site 11, the travel distance is 181.\nFrom location 19 to candidate site 12, the travel distance is 137.\nFrom location 19 to candidate site 13, the travel distance is 180.\nFrom location 19 to candidate site 14, the travel distance is 77.\nFrom location 19 to candidate site 15, the travel distance is 137.\nFrom location 19 to candidate site 16, the travel distance is 143.\nFrom location 19 to candidate site 17, the travel distance is 165.\nFrom location 19 to candidate site 18, the travel distance is 63.\nFrom location 19 to candidate site 20, the travel distance is 123.\nFrom location 20 to candidate site 1, the travel distance is 123.\nFrom location 20 to candidate site 2, the travel distance is 47.\nFrom location 20 to candidate site 3, the travel distance is 173.\nFrom location 20 to candidate site 4, the travel distance is 116.\nFrom location 20 to candidate site 5, the travel distance is 146.\nFrom location 20 to candidate site 6, the travel distance is 57.\nFrom location 20 to candidate site 7, the travel distance is 68.\nFrom location 20 to candidate site 8, the travel distance is 120.\nFrom location 20 to candidate site 9, the travel distance is 12.\nFrom location 20 to candidate site 10, the travel distance is 135.\nFrom location 20 to candidate site 11, the travel distance is 58.\nFrom location 20 to candidate site 12, the travel distance is 138.\nFrom location 20 to candidate site 13, the travel distance is 207.\nFrom location 20 to candidate site 14, the travel distance is 136.\nFrom location 20 to candidate site 15, the travel distance is 105.\nFrom location 20 to candidate site 16, the travel distance is 104.\nFrom location 20 to candidate site 17, the travel distance is 199.\nFrom location 20 to candidate site 18, the travel distance is 122.\nFrom location 20 to candidate site 19, the travel distance is 123.\nEvaluate assignments for opening 2 sites by summing each area's listed travel distances; the lowest total wins.\n\nTo keep things simple, here's the shape your answer should follow — just a quick JSON sketch of what I expect you to fill in.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list which candidate locations you'll open as vaccine spots. \"assignments\" is a one-to-one list (in the same order as the input areas) saying which opened site each area goes to. This JSON is just a template for the shape I want — not the real solution.\n\nAll identifiers in your actual answer must match the instance input exactly — do not rename them or invent new labels. \nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 81, 207, 184, 178, 123, 55, 123, 135, 166, 119, 135, 183, 116, 72, 132, 166, 151, 161, 123 ], [ 81, 0, 128, 107, 159, 95, 26, 100, 59, 174, 90, 91, 187, 120, 132, 151, 170, 83, 146, 47 ], [ 207, 128, 0, 149, 155, 216, 152, 143, 185, 216, 208, 163, 244, 155, 215, 221, 236, 79, 142, 173 ], [ 184, 107, 149, 0, 180, 117, 131, 84, 104, 97, 148, 139, 203, 145, 157, 196, 195, 104, 167, 116 ], [ 178, 159, 155, 180, 0, 89, 183, 174, 134, 200, 191, 146, 233, 166, 106, 182, 216, 98, 161, 146 ], [ 123, 95, 216, 117, 89, 0, 119, 121, 45, 145, 115, 171, 178, 111, 51, 127, 161, 155, 156, 57 ], [ 55, 26, 152, 131, 183, 119, 0, 124, 80, 198, 64, 117, 213, 146, 127, 172, 196, 107, 170, 68 ], [ 123, 100, 143, 84, 174, 121, 124, 0, 108, 147, 109, 148, 195, 128, 140, 200, 178, 82, 145, 120 ], [ 135, 59, 185, 104, 134, 45, 80, 108, 0, 147, 70, 150, 219, 124, 96, 92, 206, 110, 111, 12 ], [ 166, 174, 216, 97, 200, 145, 198, 147, 147, 0, 134, 136, 221, 154, 94, 170, 204, 171, 183, 135 ], [ 119, 90, 208, 148, 191, 115, 64, 109, 70, 134, 0, 93, 173, 134, 90, 150, 184, 151, 181, 58 ], [ 135, 91, 163, 139, 146, 171, 117, 148, 150, 136, 93, 0, 136, 108, 120, 180, 95, 106, 137, 138 ], [ 183, 187, 244, 203, 233, 178, 213, 195, 219, 221, 173, 136, 0, 103, 127, 187, 155, 179, 180, 207 ], [ 116, 120, 155, 145, 166, 111, 146, 128, 124, 154, 134, 108, 103, 0, 60, 120, 88, 76, 77, 136 ], [ 72, 132, 215, 157, 106, 51, 127, 140, 96, 94, 90, 120, 127, 60, 0, 76, 110, 136, 137, 105 ], [ 132, 151, 221, 196, 182, 127, 172, 200, 92, 170, 150, 180, 187, 120, 76, 0, 170, 142, 143, 104 ], [ 166, 170, 236, 195, 216, 161, 196, 178, 206, 204, 184, 95, 155, 88, 110, 170, 0, 164, 165, 199 ], [ 151, 83, 79, 104, 98, 155, 107, 82, 110, 171, 151, 106, 179, 76, 136, 142, 164, 0, 63, 122 ], [ 161, 146, 142, 167, 161, 156, 170, 145, 111, 183, 181, 137, 180, 77, 137, 143, 165, 63, 0, 123 ], [ 123, 47, 173, 116, 146, 57, 68, 120, 12, 135, 58, 138, 207, 136, 105, 104, 199, 122, 123, 0 ] ], "p": 2, "objective": 1564.0 }, "solution": { "facilities": [ 1, 14 ], "assignments": [ 14, 1, 1, 1, 14, 14, 1, 1, 1, 14, 1, 1, 14, 14, 14, 14, 14, 1, 14, 1 ] }, "obj": 1564.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 2, "sites": [ { "id": 1, "distances": { "1": 0, "2": 81, "3": 207, "4": 184, "5": 178, "6": 123, "7": 55, "8": 123, "9": 135, "10": 166, "11": 119, "12": 135, "13": 183, "14": 116, "15": 72, "16": 132, "17": 166, "18": 151, "19": 161, "20": 123 } }, { "id": 2, "distances": { "1": 81, "2": 0, "3": 128, "4": 107, "5": 159, "6": 95, "7": 26, "8": 100, "9": 59, "10": 174, "11": 90, "12": 91, "13": 187, "14": 120, "15": 132, "16": 151, "17": 170, "18": 83, "19": 146, "20": 47 } }, { "id": 3, "distances": { "1": 207, "2": 128, "3": 0, "4": 149, "5": 155, "6": 216, "7": 152, "8": 143, "9": 185, "10": 216, "11": 208, "12": 163, "13": 244, "14": 155, "15": 215, "16": 221, "17": 236, "18": 79, "19": 142, "20": 173 } }, { "id": 4, "distances": { "1": 184, "2": 107, "3": 149, "4": 0, "5": 180, "6": 117, "7": 131, "8": 84, "9": 104, "10": 97, "11": 148, "12": 139, "13": 203, "14": 145, "15": 157, "16": 196, "17": 195, "18": 104, "19": 167, "20": 116 } }, { "id": 5, "distances": { "1": 178, "2": 159, "3": 155, "4": 180, "5": 0, "6": 89, "7": 183, "8": 174, "9": 134, "10": 200, "11": 191, "12": 146, "13": 233, "14": 166, "15": 106, "16": 182, "17": 216, "18": 98, "19": 161, "20": 146 } }, { "id": 6, "distances": { "1": 123, "2": 95, "3": 216, "4": 117, "5": 89, "6": 0, "7": 119, "8": 121, "9": 45, "10": 145, "11": 115, "12": 171, "13": 178, "14": 111, "15": 51, "16": 127, "17": 161, "18": 155, "19": 156, "20": 57 } }, { "id": 7, "distances": { "1": 55, "2": 26, "3": 152, "4": 131, "5": 183, "6": 119, "7": 0, "8": 124, "9": 80, "10": 198, "11": 64, "12": 117, "13": 213, "14": 146, "15": 127, "16": 172, "17": 196, "18": 107, "19": 170, "20": 68 } }, { "id": 8, "distances": { "1": 123, "2": 100, "3": 143, "4": 84, "5": 174, "6": 121, "7": 124, "8": 0, "9": 108, "10": 147, "11": 109, "12": 148, "13": 195, "14": 128, "15": 140, "16": 200, "17": 178, "18": 82, "19": 145, "20": 120 } }, { "id": 9, "distances": { "1": 135, "2": 59, "3": 185, "4": 104, "5": 134, "6": 45, "7": 80, "8": 108, "9": 0, "10": 147, "11": 70, "12": 150, "13": 219, "14": 124, "15": 96, "16": 92, "17": 206, "18": 110, "19": 111, "20": 12 } }, { "id": 10, "distances": { "1": 166, "2": 174, "3": 216, "4": 97, "5": 200, "6": 145, "7": 198, "8": 147, "9": 147, "10": 0, "11": 134, "12": 136, "13": 221, "14": 154, "15": 94, "16": 170, "17": 204, "18": 171, "19": 183, "20": 135 } }, { "id": 11, "distances": { "1": 119, "2": 90, "3": 208, "4": 148, "5": 191, "6": 115, "7": 64, "8": 109, "9": 70, "10": 134, "11": 0, "12": 93, "13": 173, "14": 134, "15": 90, "16": 150, "17": 184, "18": 151, "19": 181, "20": 58 } }, { "id": 12, "distances": { "1": 135, "2": 91, "3": 163, "4": 139, "5": 146, "6": 171, "7": 117, "8": 148, "9": 150, "10": 136, "11": 93, "12": 0, "13": 136, "14": 108, "15": 120, "16": 180, "17": 95, "18": 106, "19": 137, "20": 138 } }, { "id": 13, "distances": { "1": 183, "2": 187, "3": 244, "4": 203, "5": 233, "6": 178, "7": 213, "8": 195, "9": 219, "10": 221, "11": 173, "12": 136, "13": 0, "14": 103, "15": 127, "16": 187, "17": 155, "18": 179, "19": 180, "20": 207 } }, { "id": 14, "distances": { "1": 116, "2": 120, "3": 155, "4": 145, "5": 166, "6": 111, "7": 146, "8": 128, "9": 124, "10": 154, "11": 134, "12": 108, "13": 103, "14": 0, "15": 60, "16": 120, "17": 88, "18": 76, "19": 77, "20": 136 } }, { "id": 15, "distances": { "1": 72, "2": 132, "3": 215, "4": 157, "5": 106, "6": 51, "7": 127, "8": 140, "9": 96, "10": 94, "11": 90, "12": 120, "13": 127, "14": 60, "15": 0, "16": 76, "17": 110, "18": 136, "19": 137, "20": 105 } }, { "id": 16, "distances": { "1": 132, "2": 151, "3": 221, "4": 196, "5": 182, "6": 127, "7": 172, "8": 200, "9": 92, "10": 170, "11": 150, "12": 180, "13": 187, "14": 120, "15": 76, "16": 0, "17": 170, "18": 142, "19": 143, "20": 104 } }, { "id": 17, "distances": { "1": 166, "2": 170, "3": 236, "4": 195, "5": 216, "6": 161, "7": 196, "8": 178, "9": 206, "10": 204, "11": 184, "12": 95, "13": 155, "14": 88, "15": 110, "16": 170, "17": 0, "18": 164, "19": 165, "20": 199 } }, { "id": 18, "distances": { "1": 151, "2": 83, "3": 79, "4": 104, "5": 98, "6": 155, "7": 107, "8": 82, "9": 110, "10": 171, "11": 151, "12": 106, "13": 179, "14": 76, "15": 136, "16": 142, "17": 164, "18": 0, "19": 63, "20": 122 } }, { "id": 19, "distances": { "1": 161, "2": 146, "3": 142, "4": 167, "5": 161, "6": 156, "7": 170, "8": 145, "9": 111, "10": 183, "11": 181, "12": 137, "13": 180, "14": 77, "15": 137, "16": 143, "17": 165, "18": 63, "19": 0, "20": 123 } }, { "id": 20, "distances": { "1": 123, "2": 47, "3": 173, "4": 116, "5": 146, "6": 57, "7": 68, "8": 120, "9": 12, "10": 135, "11": 58, "12": 138, "13": 207, "14": 136, "15": 105, "16": 104, "17": 199, "18": 122, "19": 123, "20": 0 } } ], "objective": 1564.0 }, "solution_variant": { "selected": [ 2, 15 ], "assignments": [ 15, 2, 2, 2, 15, 15, 2, 2, 2, 15, 2, 2, 15, 15, 15, 15, 15, 2, 15, 2 ] }, "context_index": 42, "input_format": "nl", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "A friend on the facilities crew explained they have to pick a limited number of locations for bike repair stands and assign every campus building to one of the opened stands so students’ walks are reasonable. The job is to select those exact-number spots out of the candidates and make sure each building is matched to only one kiosk, then judge the choices by summing the walking distance for every building-to-kiosk pair — smaller sums mean fewer people walking far. The concrete details will be shown below.\n\nThere are 17 candidate kiosk spots, they must pick exactly 2 to open, and the location IDs are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q.\nFrom location A to candidate kiosk B, the walking distance is 174.\nFrom location A to candidate kiosk C, the walking distance is 156.\nFrom location A to candidate kiosk D, the walking distance is 211.\nFrom location A to candidate kiosk E, the walking distance is 116.\nFrom location A to candidate kiosk F, the walking distance is 199.\nFrom location A to candidate kiosk G, the walking distance is 182.\nFrom location A to candidate kiosk H, the walking distance is 155.\nFrom location A to candidate kiosk I, the walking distance is 211.\nFrom location A to candidate kiosk J, the walking distance is 123.\nFrom location A to candidate kiosk K, the walking distance is 168.\nFrom location A to candidate kiosk L, the walking distance is 202.\nFrom location A to candidate kiosk M, the walking distance is 152.\nFrom location A to candidate kiosk N, the walking distance is 204.\nFrom location A to candidate kiosk O, the walking distance is 176.\nFrom location A to candidate kiosk P, the walking distance is 146.\nFrom location A to candidate kiosk Q, the walking distance is 171.\nFrom location B to candidate kiosk A, the walking distance is 174.\nFrom location B to candidate kiosk C, the walking distance is 23.\nFrom location B to candidate kiosk D, the walking distance is 37.\nFrom location B to candidate kiosk E, the walking distance is 134.\nFrom location B to candidate kiosk F, the walking distance is 118.\nFrom location B to candidate kiosk G, the walking distance is 20.\nFrom location B to candidate kiosk H, the walking distance is 154.\nFrom location B to candidate kiosk I, the walking distance is 139.\nFrom location B to candidate kiosk J, the walking distance is 61.\nFrom location B to candidate kiosk K, the walking distance is 111.\nFrom location B to candidate kiosk L, the walking distance is 145.\nFrom location B to candidate kiosk M, the walking distance is 80.\nFrom location B to candidate kiosk N, the walking distance is 93.\nFrom location B to candidate kiosk O, the walking distance is 127.\nFrom location B to candidate kiosk P, the walking distance is 111.\nFrom location B to candidate kiosk Q, the walking distance is 171.\nFrom location C to candidate kiosk A, the walking distance is 156.\nFrom location C to candidate kiosk B, the walking distance is 23.\nFrom location C to candidate kiosk D, the walking distance is 60.\nFrom location C to candidate kiosk E, the walking distance is 116.\nFrom location C to candidate kiosk F, the walking distance is 102.\nFrom location C to candidate kiosk G, the walking distance is 43.\nFrom location C to candidate kiosk H, the walking distance is 131.\nFrom location C to candidate kiosk I, the walking distance is 123.\nFrom location C to candidate kiosk J, the walking distance is 38.\nFrom location C to candidate kiosk K, the walking distance is 134.\nFrom location C to candidate kiosk L, the walking distance is 167.\nFrom location C to candidate kiosk M, the walking distance is 103.\nFrom location C to candidate kiosk N, the walking distance is 109.\nFrom location C to candidate kiosk O, the walking distance is 104.\nFrom location C to candidate kiosk P, the walking distance is 88.\nFrom location C to candidate kiosk Q, the walking distance is 171.\nFrom location D to candidate kiosk A, the walking distance is 211.\nFrom location D to candidate kiosk B, the walking distance is 37.\nFrom location D to candidate kiosk C, the walking distance is 60.\nFrom location D to candidate kiosk E, the walking distance is 117.\nFrom location D to candidate kiosk F, the walking distance is 155.\nFrom location D to candidate kiosk G, the walking distance is 57.\nFrom location D to candidate kiosk H, the walking distance is 191.\nFrom location D to candidate kiosk I, the walking distance is 176.\nFrom location D to candidate kiosk J, the walking distance is 98.\nFrom location D to candidate kiosk K, the walking distance is 148.\nFrom location D to candidate kiosk L, the walking distance is 182.\nFrom location D to candidate kiosk M, the walking distance is 117.\nFrom location D to candidate kiosk N, the walking distance is 130.\nFrom location D to candidate kiosk O, the walking distance is 164.\nFrom location D to candidate kiosk P, the walking distance is 148.\nFrom location D to candidate kiosk Q, the walking distance is 208.\nFrom location E to candidate kiosk A, the walking distance is 116.\nFrom location E to candidate kiosk B, the walking distance is 134.\nFrom location E to candidate kiosk C, the walking distance is 116.\nFrom location E to candidate kiosk D, the walking distance is 117.\nFrom location E to candidate kiosk F, the walking distance is 134.\nFrom location E to candidate kiosk G, the walking distance is 142.\nFrom location E to candidate kiosk H, the walking distance is 157.\nFrom location E to candidate kiosk I, the walking distance is 135.\nFrom location E to candidate kiosk J, the walking distance is 152.\nFrom location E to candidate kiosk K, the walking distance is 175.\nFrom location E to candidate kiosk L, the walking distance is 197.\nFrom location E to candidate kiosk M, the walking distance is 180.\nFrom location E to candidate kiosk N, the walking distance is 193.\nFrom location E to candidate kiosk O, the walking distance is 136.\nFrom location E to candidate kiosk P, the walking distance is 120.\nFrom location E to candidate kiosk Q, the walking distance is 196.\nFrom location F to candidate kiosk A, the walking distance is 199.\nFrom location F to candidate kiosk B, the walking distance is 118.\nFrom location F to candidate kiosk C, the walking distance is 102.\nFrom location F to candidate kiosk D, the walking distance is 155.\nFrom location F to candidate kiosk E, the walking distance is 134.\nFrom location F to candidate kiosk G, the walking distance is 98.\nFrom location F to candidate kiosk H, the walking distance is 77.\nFrom location F to candidate kiosk I, the walking distance is 21.\nFrom location F to candidate kiosk J, the walking distance is 122.\nFrom location F to candidate kiosk K, the walking distance is 126.\nFrom location F to candidate kiosk L, the walking distance is 136.\nFrom location F to candidate kiosk M, the walking distance is 175.\nFrom location F to candidate kiosk N, the walking distance is 115.\nFrom location F to candidate kiosk O, the walking distance is 107.\nFrom location F to candidate kiosk P, the walking distance is 76.\nFrom location F to candidate kiosk Q, the walking distance is 159.\nFrom location G to candidate kiosk A, the walking distance is 182.\nFrom location G to candidate kiosk B, the walking distance is 20.\nFrom location G to candidate kiosk C, the walking distance is 43.\nFrom location G to candidate kiosk D, the walking distance is 57.\nFrom location G to candidate kiosk E, the walking distance is 142.\nFrom location G to candidate kiosk F, the walking distance is 98.\nFrom location G to candidate kiosk H, the walking distance is 174.\nFrom location G to candidate kiosk I, the walking distance is 119.\nFrom location G to candidate kiosk J, the walking distance is 81.\nFrom location G to candidate kiosk K, the walking distance is 119.\nFrom location G to candidate kiosk L, the walking distance is 153.\nFrom location G to candidate kiosk M, the walking distance is 88.\nFrom location G to candidate kiosk N, the walking distance is 73.\nFrom location G to candidate kiosk O, the walking distance is 147.\nFrom location G to candidate kiosk P, the walking distance is 131.\nFrom location G to candidate kiosk Q, the walking distance is 179.\nFrom location H to candidate kiosk A, the walking distance is 155.\nFrom location H to candidate kiosk B, the walking distance is 154.\nFrom location H to candidate kiosk C, the walking distance is 131.\nFrom location H to candidate kiosk D, the walking distance is 191.\nFrom location H to candidate kiosk E, the walking distance is 157.\nFrom location H to candidate kiosk F, the walking distance is 77.\nFrom location H to candidate kiosk G, the walking distance is 174.\nFrom location H to candidate kiosk I, the walking distance is 56.\nFrom location H to candidate kiosk J, the walking distance is 93.\nFrom location H to candidate kiosk K, the walking distance is 93.\nFrom location H to candidate kiosk L, the walking distance is 59.\nFrom location H to candidate kiosk M, the walking distance is 156.\nFrom location H to candidate kiosk N, the walking distance is 192.\nFrom location H to candidate kiosk O, the walking distance is 88.\nFrom location H to candidate kiosk P, the walking distance is 57.\nFrom location H to candidate kiosk Q, the walking distance is 140.\nFrom location I to candidate kiosk A, the walking distance is 211.\nFrom location I to candidate kiosk B, the walking distance is 139.\nFrom location I to candidate kiosk C, the walking distance is 123.\nFrom location I to candidate kiosk D, the walking distance is 176.\nFrom location I to candidate kiosk E, the walking distance is 135.\nFrom location I to candidate kiosk F, the walking distance is 21.\nFrom location I to candidate kiosk G, the walking distance is 119.\nFrom location I to candidate kiosk H, the walking distance is 56.\nFrom location I to candidate kiosk J, the walking distance is 143.\nFrom location I to candidate kiosk K, the walking distance is 147.\nFrom location I to candidate kiosk L, the walking distance is 115.\nFrom location I to candidate kiosk M, the walking distance is 170.\nFrom location I to candidate kiosk N, the walking distance is 136.\nFrom location I to candidate kiosk O, the walking distance is 102.\nFrom location I to candidate kiosk P, the walking distance is 71.\nFrom location I to candidate kiosk Q, the walking distance is 154.\nFrom location J to candidate kiosk A, the walking distance is 123.\nFrom location J to candidate kiosk B, the walking distance is 61.\nFrom location J to candidate kiosk C, the walking distance is 38.\nFrom location J to candidate kiosk D, the walking distance is 98.\nFrom location J to candidate kiosk E, the walking distance is 152.\nFrom location J to candidate kiosk F, the walking distance is 122.\nFrom location J to candidate kiosk G, the walking distance is 81.\nFrom location J to candidate kiosk H, the walking distance is 93.\nFrom location J to candidate kiosk I, the walking distance is 143.\nFrom location J to candidate kiosk K, the walking distance is 154.\nFrom location J to candidate kiosk L, the walking distance is 152.\nFrom location J to candidate kiosk M, the walking distance is 141.\nFrom location J to candidate kiosk N, the walking distance is 127.\nFrom location J to candidate kiosk O, the walking distance is 125.\nFrom location J to candidate kiosk P, the walking distance is 126.\nFrom location J to candidate kiosk Q, the walking distance is 193.\nFrom location K to candidate kiosk A, the walking distance is 168.\nFrom location K to candidate kiosk B, the walking distance is 111.\nFrom location K to candidate kiosk C, the walking distance is 134.\nFrom location K to candidate kiosk D, the walking distance is 148.\nFrom location K to candidate kiosk E, the walking distance is 175.\nFrom location K to candidate kiosk F, the walking distance is 126.\nFrom location K to candidate kiosk G, the walking distance is 119.\nFrom location K to candidate kiosk H, the walking distance is 93.\nFrom location K to candidate kiosk I, the walking distance is 147.\nFrom location K to candidate kiosk J, the walking distance is 154.\nFrom location K to candidate kiosk L, the walking distance is 34.\nFrom location K to candidate kiosk M, the walking distance is 95.\nFrom location K to candidate kiosk N, the walking distance is 164.\nFrom location K to candidate kiosk O, the walking distance is 143.\nFrom location K to candidate kiosk P, the walking distance is 131.\nFrom location K to candidate kiosk Q, the walking distance is 188.\nFrom location L to candidate kiosk A, the walking distance is 202.\nFrom location L to candidate kiosk B, the walking distance is 145.\nFrom location L to candidate kiosk C, the walking distance is 167.\nFrom location L to candidate kiosk D, the walking distance is 182.\nFrom location L to candidate kiosk E, the walking distance is 197.\nFrom location L to candidate kiosk F, the walking distance is 136.\nFrom location L to candidate kiosk G, the walking distance is 153.\nFrom location L to candidate kiosk H, the walking distance is 59.\nFrom location L to candidate kiosk I, the walking distance is 115.\nFrom location L to candidate kiosk J, the walking distance is 152.\nFrom location L to candidate kiosk K, the walking distance is 34.\nFrom location L to candidate kiosk M, the walking distance is 129.\nFrom location L to candidate kiosk N, the walking distance is 186.\nFrom location L to candidate kiosk O, the walking distance is 109.\nFrom location L to candidate kiosk P, the walking distance is 97.\nFrom location L to candidate kiosk Q, the walking distance is 154.\nFrom location M to candidate kiosk A, the walking distance is 152.\nFrom location M to candidate kiosk B, the walking distance is 80.\nFrom location M to candidate kiosk C, the walking distance is 103.\nFrom location M to candidate kiosk D, the walking distance is 117.\nFrom location M to candidate kiosk E, the walking distance is 180.\nFrom location M to candidate kiosk F, the walking distance is 175.\nFrom location M to candidate kiosk G, the walking distance is 88.\nFrom location M to candidate kiosk H, the walking distance is 156.\nFrom location M to candidate kiosk I, the walking distance is 170.\nFrom location M to candidate kiosk J, the walking distance is 141.\nFrom location M to candidate kiosk K, the walking distance is 95.\nFrom location M to candidate kiosk L, the walking distance is 129.\nFrom location M to candidate kiosk N, the walking distance is 161.\nFrom location M to candidate kiosk O, the walking distance is 154.\nFrom location M to candidate kiosk P, the walking distance is 123.\nFrom location M to candidate kiosk Q, the walking distance is 149.\nFrom location N to candidate kiosk A, the walking distance is 204.\nFrom location N to candidate kiosk B, the walking distance is 93.\nFrom location N to candidate kiosk C, the walking distance is 109.\nFrom location N to candidate kiosk D, the walking distance is 130.\nFrom location N to candidate kiosk E, the walking distance is 193.\nFrom location N to candidate kiosk F, the walking distance is 115.\nFrom location N to candidate kiosk G, the walking distance is 73.\nFrom location N to candidate kiosk H, the walking distance is 192.\nFrom location N to candidate kiosk I, the walking distance is 136.\nFrom location N to candidate kiosk J, the walking distance is 127.\nFrom location N to candidate kiosk K, the walking distance is 164.\nFrom location N to candidate kiosk L, the walking distance is 186.\nFrom location N to candidate kiosk M, the walking distance is 161.\nFrom location N to candidate kiosk O, the walking distance is 106.\nFrom location N to candidate kiosk P, the walking distance is 137.\nFrom location N to candidate kiosk Q, the walking distance is 150.\nFrom location O to candidate kiosk A, the walking distance is 176.\nFrom location O to candidate kiosk B, the walking distance is 127.\nFrom location O to candidate kiosk C, the walking distance is 104.\nFrom location O to candidate kiosk D, the walking distance is 164.\nFrom location O to candidate kiosk E, the walking distance is 136.\nFrom location O to candidate kiosk F, the walking distance is 107.\nFrom location O to candidate kiosk G, the walking distance is 147.\nFrom location O to candidate kiosk H, the walking distance is 88.\nFrom location O to candidate kiosk I, the walking distance is 102.\nFrom location O to candidate kiosk J, the walking distance is 125.\nFrom location O to candidate kiosk K, the walking distance is 143.\nFrom location O to candidate kiosk L, the walking distance is 109.\nFrom location O to candidate kiosk M, the walking distance is 154.\nFrom location O to candidate kiosk N, the walking distance is 106.\nFrom location O to candidate kiosk P, the walking distance is 31.\nFrom location O to candidate kiosk Q, the walking distance is 114.\nFrom location P to candidate kiosk A, the walking distance is 146.\nFrom location P to candidate kiosk B, the walking distance is 111.\nFrom location P to candidate kiosk C, the walking distance is 88.\nFrom location P to candidate kiosk D, the walking distance is 148.\nFrom location P to candidate kiosk E, the walking distance is 120.\nFrom location P to candidate kiosk F, the walking distance is 76.\nFrom location P to candidate kiosk G, the walking distance is 131.\nFrom location P to candidate kiosk H, the walking distance is 57.\nFrom location P to candidate kiosk I, the walking distance is 71.\nFrom location P to candidate kiosk J, the walking distance is 126.\nFrom location P to candidate kiosk K, the walking distance is 131.\nFrom location P to candidate kiosk L, the walking distance is 97.\nFrom location P to candidate kiosk M, the walking distance is 123.\nFrom location P to candidate kiosk N, the walking distance is 137.\nFrom location P to candidate kiosk O, the walking distance is 31.\nFrom location P to candidate kiosk Q, the walking distance is 83.\nFrom location Q to candidate kiosk A, the walking distance is 171.\nFrom location Q to candidate kiosk B, the walking distance is 171.\nFrom location Q to candidate kiosk C, the walking distance is 171.\nFrom location Q to candidate kiosk D, the walking distance is 208.\nFrom location Q to candidate kiosk E, the walking distance is 196.\nFrom location Q to candidate kiosk F, the walking distance is 159.\nFrom location Q to candidate kiosk G, the walking distance is 179.\nFrom location Q to candidate kiosk H, the walking distance is 140.\nFrom location Q to candidate kiosk I, the walking distance is 154.\nFrom location Q to candidate kiosk J, the walking distance is 193.\nFrom location Q to candidate kiosk K, the walking distance is 188.\nFrom location Q to candidate kiosk L, the walking distance is 154.\nFrom location Q to candidate kiosk M, the walking distance is 149.\nFrom location Q to candidate kiosk N, the walking distance is 150.\nFrom location Q to candidate kiosk O, the walking distance is 114.\nFrom location Q to candidate kiosk P, the walking distance is 83.\nThey'll sum these distances for every building-to-kiosk assignment to judge how reasonable the choices are.\n\nAlso, when you send the picked spots back, it'd be great if you stick to this simple JSON layout so it's easy to load and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis is just a sketch of the shape I need:\n- \"selected\" is the list of kiosk locations you decide to open.\n- \"assignments\" lists, for every campus building (in the same order as the instance), which opened kiosk that building is assigned to.\n\nQuick note: that JSON is only the expected shape, not the actual answer — fill in the real identifiers from the instance when you respond. And please use the exact identifiers from the input with no renaming or new labels — they need to match exactly as given. \n\n- for example: \"Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".\"", "instance": { "distance_matrix": [ [ 0, 174, 156, 211, 116, 199, 182, 155, 211, 123, 168, 202, 152, 204, 176, 146, 171 ], [ 174, 0, 23, 37, 134, 118, 20, 154, 139, 61, 111, 145, 80, 93, 127, 111, 171 ], [ 156, 23, 0, 60, 116, 102, 43, 131, 123, 38, 134, 167, 103, 109, 104, 88, 171 ], [ 211, 37, 60, 0, 117, 155, 57, 191, 176, 98, 148, 182, 117, 130, 164, 148, 208 ], [ 116, 134, 116, 117, 0, 134, 142, 157, 135, 152, 175, 197, 180, 193, 136, 120, 196 ], [ 199, 118, 102, 155, 134, 0, 98, 77, 21, 122, 126, 136, 175, 115, 107, 76, 159 ], [ 182, 20, 43, 57, 142, 98, 0, 174, 119, 81, 119, 153, 88, 73, 147, 131, 179 ], [ 155, 154, 131, 191, 157, 77, 174, 0, 56, 93, 93, 59, 156, 192, 88, 57, 140 ], [ 211, 139, 123, 176, 135, 21, 119, 56, 0, 143, 147, 115, 170, 136, 102, 71, 154 ], [ 123, 61, 38, 98, 152, 122, 81, 93, 143, 0, 154, 152, 141, 127, 125, 126, 193 ], [ 168, 111, 134, 148, 175, 126, 119, 93, 147, 154, 0, 34, 95, 164, 143, 131, 188 ], [ 202, 145, 167, 182, 197, 136, 153, 59, 115, 152, 34, 0, 129, 186, 109, 97, 154 ], [ 152, 80, 103, 117, 180, 175, 88, 156, 170, 141, 95, 129, 0, 161, 154, 123, 149 ], [ 204, 93, 109, 130, 193, 115, 73, 192, 136, 127, 164, 186, 161, 0, 106, 137, 150 ], [ 176, 127, 104, 164, 136, 107, 147, 88, 102, 125, 143, 109, 154, 106, 0, 31, 114 ], [ 146, 111, 88, 148, 120, 76, 131, 57, 71, 126, 131, 97, 123, 137, 31, 0, 83 ], [ 171, 171, 171, 208, 196, 159, 179, 140, 154, 193, 188, 154, 149, 150, 114, 83, 0 ] ], "p": 2, "objective": 1106.0 }, "solution": { "facilities": [ 1, 15 ], "assignments": [ 15, 1, 1, 1, 15, 15, 1, 15, 15, 1, 1, 15, 1, 1, 15, 15, 15 ] }, "obj": 1106.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 2, "sites": [ { "id": "A", "distances": { "A": 0, "B": 174, "C": 156, "D": 211, "E": 116, "F": 199, "G": 182, "H": 155, "I": 211, "J": 123, "K": 168, "L": 202, "M": 152, "N": 204, "O": 176, "P": 146, "Q": 171 } }, { "id": "B", "distances": { "A": 174, "B": 0, "C": 23, "D": 37, "E": 134, "F": 118, "G": 20, "H": 154, "I": 139, "J": 61, "K": 111, "L": 145, "M": 80, "N": 93, "O": 127, "P": 111, "Q": 171 } }, { "id": "C", "distances": { "A": 156, "B": 23, "C": 0, "D": 60, "E": 116, "F": 102, "G": 43, "H": 131, "I": 123, "J": 38, "K": 134, "L": 167, "M": 103, "N": 109, "O": 104, "P": 88, "Q": 171 } }, { "id": "D", "distances": { "A": 211, "B": 37, "C": 60, "D": 0, "E": 117, "F": 155, "G": 57, "H": 191, "I": 176, "J": 98, "K": 148, "L": 182, "M": 117, "N": 130, "O": 164, "P": 148, "Q": 208 } }, { "id": "E", "distances": { "A": 116, "B": 134, "C": 116, "D": 117, "E": 0, "F": 134, "G": 142, "H": 157, "I": 135, "J": 152, "K": 175, "L": 197, "M": 180, "N": 193, "O": 136, "P": 120, "Q": 196 } }, { "id": "F", "distances": { "A": 199, "B": 118, "C": 102, "D": 155, "E": 134, "F": 0, "G": 98, "H": 77, "I": 21, "J": 122, "K": 126, "L": 136, "M": 175, "N": 115, "O": 107, "P": 76, "Q": 159 } }, { "id": "G", "distances": { "A": 182, "B": 20, "C": 43, "D": 57, "E": 142, "F": 98, "G": 0, "H": 174, "I": 119, "J": 81, "K": 119, "L": 153, "M": 88, "N": 73, "O": 147, "P": 131, "Q": 179 } }, { "id": "H", "distances": { "A": 155, "B": 154, "C": 131, "D": 191, "E": 157, "F": 77, "G": 174, "H": 0, "I": 56, "J": 93, "K": 93, "L": 59, "M": 156, "N": 192, "O": 88, "P": 57, "Q": 140 } }, { "id": "I", "distances": { "A": 211, "B": 139, "C": 123, "D": 176, "E": 135, "F": 21, "G": 119, "H": 56, "I": 0, "J": 143, "K": 147, "L": 115, "M": 170, "N": 136, "O": 102, "P": 71, "Q": 154 } }, { "id": "J", "distances": { "A": 123, "B": 61, "C": 38, "D": 98, "E": 152, "F": 122, "G": 81, "H": 93, "I": 143, "J": 0, "K": 154, "L": 152, "M": 141, "N": 127, "O": 125, "P": 126, "Q": 193 } }, { "id": "K", "distances": { "A": 168, "B": 111, "C": 134, "D": 148, "E": 175, "F": 126, "G": 119, "H": 93, "I": 147, "J": 154, "K": 0, "L": 34, "M": 95, "N": 164, "O": 143, "P": 131, "Q": 188 } }, { "id": "L", "distances": { "A": 202, "B": 145, "C": 167, "D": 182, "E": 197, "F": 136, "G": 153, "H": 59, "I": 115, "J": 152, "K": 34, "L": 0, "M": 129, "N": 186, "O": 109, "P": 97, "Q": 154 } }, { "id": "M", "distances": { "A": 152, "B": 80, "C": 103, "D": 117, "E": 180, "F": 175, "G": 88, "H": 156, "I": 170, "J": 141, "K": 95, "L": 129, "M": 0, "N": 161, "O": 154, "P": 123, "Q": 149 } }, { "id": "N", "distances": { "A": 204, "B": 93, "C": 109, "D": 130, "E": 193, "F": 115, "G": 73, "H": 192, "I": 136, "J": 127, "K": 164, "L": 186, "M": 161, "N": 0, "O": 106, "P": 137, "Q": 150 } }, { "id": "O", "distances": { "A": 176, "B": 127, "C": 104, "D": 164, "E": 136, "F": 107, "G": 147, "H": 88, "I": 102, "J": 125, "K": 143, "L": 109, "M": 154, "N": 106, "O": 0, "P": 31, "Q": 114 } }, { "id": "P", "distances": { "A": 146, "B": 111, "C": 88, "D": 148, "E": 120, "F": 76, "G": 131, "H": 57, "I": 71, "J": 126, "K": 131, "L": 97, "M": 123, "N": 137, "O": 31, "P": 0, "Q": 83 } }, { "id": "Q", "distances": { "A": 171, "B": 171, "C": 171, "D": 208, "E": 196, "F": 159, "G": 179, "H": 140, "I": 154, "J": 193, "K": 188, "L": 154, "M": 149, "N": 150, "O": 114, "P": 83, "Q": 0 } } ], "objective": 1106.0 }, "solution_variant": { "selected": [ "B", "P" ], "assignments": [ "P", "B", "B", "B", "P", "P", "B", "P", "P", "B", "B", "P", "B", "B", "P", "P", "P" ] }, "context_index": 43, "input_format": "markdown_table", "input_index_base": "names" }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Back at the office the task is to pick a set number of food bank satellite sites from a given list and make one-to-one links between each community zone and an open site. The better arrangement is the one that minimizes how far everyone has to go overall: measure the distance for each zone to its assigned site, add those distances together, and the smallest sum is best. Each zone must be assigned to exactly one open site, and only the listed properties can be used. The exact locations and travel distances are provided below.\n\n{\n \"total_locations\": 17,\n \"satellites_to_open\": 6,\n \"location_ids\": [\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16,\n 17\n ],\n \"data\": [\n {\n \"from_location_id\": 1,\n \"to_location_id\": 2,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 3,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 4,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 5,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 6,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 7,\n \"travel_distance\": 19\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 8,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 9,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 10,\n \"travel_distance\": 30\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 11,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 12,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 13,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 14,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 15,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 16,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 17,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 1,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 3,\n \"travel_distance\": 27\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 4,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 5,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 6,\n \"travel_distance\": 18\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 7,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 8,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 9,\n \"travel_distance\": 14\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 10,\n \"travel_distance\": 18\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 11,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 12,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 13,\n \"travel_distance\": 5\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 14,\n \"travel_distance\": 24\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 15,\n \"travel_distance\": 20\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 16,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 17,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 1,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 2,\n \"travel_distance\": 27\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 4,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 5,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 6,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 7,\n \"travel_distance\": 24\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 8,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 9,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 10,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 11,\n \"travel_distance\": 50\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 12,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 13,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 14,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 15,\n \"travel_distance\": 30\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 16,\n \"travel_distance\": 20\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 17,\n \"travel_distance\": 37\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 1,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 2,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 3,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 5,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 6,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 7,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 8,\n \"travel_distance\": 37\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 9,\n \"travel_distance\": 19\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 10,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 11,\n \"travel_distance\": 45\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 12,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 13,\n \"travel_distance\": 37\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 14,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 15,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 16,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 17,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 1,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 2,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 3,\n \"travel_distance\": 25\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 4,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 6,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 7,\n \"travel_distance\": 30\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 8,\n \"travel_distance\": 29\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 9,\n \"travel_distance\": 42\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 10,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 11,\n \"travel_distance\": 53\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 12,\n \"travel_distance\": 22\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 13,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 14,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 15,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 16,\n \"travel_distance\": 36\n },\n {\n \"from_location_id\": 5,\n \"to_location_id\": 17,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 1,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 2,\n \"travel_distance\": 18\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 3,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 4,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 5,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 7,\n \"travel_distance\": 32\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 8,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 9,\n 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\"travel_distance\": 22\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 7,\n \"travel_distance\": 27\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 8,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 9,\n \"travel_distance\": 28\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 10,\n \"travel_distance\": 16\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 11,\n \"travel_distance\": 50\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 12,\n \"travel_distance\": 40\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 13,\n \"travel_distance\": 31\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 14,\n \"travel_distance\": 43\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 15,\n \"travel_distance\": 26\n },\n {\n \"from_location_id\": 16,\n \"to_location_id\": 17,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 1,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 2,\n \"travel_distance\": 33\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 3,\n \"travel_distance\": 37\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 4,\n \"travel_distance\": 44\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 5,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 6,\n \"travel_distance\": 39\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 7,\n \"travel_distance\": 41\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 8,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 9,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 10,\n \"travel_distance\": 35\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 11,\n \"travel_distance\": 47\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 12,\n \"travel_distance\": 50\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 13,\n \"travel_distance\": 38\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 14,\n \"travel_distance\": 34\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 15,\n \"travel_distance\": 27\n },\n {\n \"from_location_id\": 17,\n \"to_location_id\": 16,\n \"travel_distance\": 44\n }\n ]\n}\n\nAlso, to keep things machine-friendly, please return the final choice in this simple JSON shape (just a quick heads-up — it's just the shape, not the answer itself):\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of satellite sites we decide to open, and \"assignments\" as, for each community zone (in the same order as the input), which open site that zone is linked to. Super casual: picked sites go in the selected list; every zone points to one of those picked sites in the assignments list.\n\nThis JSON is just a sketch of the expected shape, not the actual filled-in answer. Please make sure to use the exact identifiers from the instance input — do not rename them or invent new labels. \n\nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 31, 25, 41, 34, 34, 19, 28, 22, 30, 39, 44, 36, 31, 38, 26, 35 ], [ 31, 0, 27, 32, 28, 18, 32, 25, 14, 18, 25, 36, 5, 24, 20, 29, 33 ], [ 25, 27, 0, 28, 25, 26, 24, 26, 22, 34, 50, 33, 32, 33, 30, 20, 37 ], [ 41, 32, 28, 0, 39, 39, 36, 37, 19, 26, 45, 40, 37, 34, 34, 42, 44 ], [ 34, 28, 25, 39, 0, 34, 30, 29, 42, 32, 53, 22, 33, 34, 33, 36, 38 ], [ 34, 18, 26, 39, 34, 0, 32, 26, 32, 26, 37, 22, 21, 26, 32, 22, 39 ], [ 19, 32, 24, 36, 30, 32, 0, 33, 27, 31, 39, 38, 37, 27, 39, 27, 41 ], [ 28, 25, 26, 37, 29, 26, 33, 0, 29, 33, 28, 33, 30, 33, 25, 34, 38 ], [ 22, 14, 22, 19, 42, 32, 27, 29, 0, 32, 37, 47, 19, 38, 34, 28, 34 ], [ 30, 18, 34, 26, 32, 26, 31, 33, 32, 0, 43, 44, 23, 27, 32, 16, 35 ], [ 39, 25, 50, 45, 53, 37, 39, 28, 37, 43, 0, 55, 30, 45, 45, 50, 47 ], [ 44, 36, 33, 40, 22, 22, 38, 33, 47, 44, 55, 0, 39, 48, 37, 40, 50 ], [ 36, 5, 32, 37, 33, 21, 37, 30, 19, 23, 30, 39, 0, 29, 25, 31, 38 ], [ 31, 24, 33, 34, 34, 26, 27, 33, 38, 27, 45, 48, 29, 0, 18, 43, 34 ], [ 38, 20, 30, 34, 33, 32, 39, 25, 34, 32, 45, 37, 25, 18, 0, 26, 27 ], [ 26, 29, 20, 42, 36, 22, 27, 34, 28, 16, 50, 40, 31, 43, 26, 0, 44 ], [ 35, 33, 37, 44, 38, 39, 41, 38, 34, 35, 47, 50, 38, 34, 27, 44, 0 ] ], "p": 6, "objective": 208.0 }, "solution": { "facilities": [ 1, 3, 4, 6, 15, 16 ], "assignments": [ 6, 1, 15, 3, 4, 1, 6, 1, 1, 15, 1, 4, 1, 1, 1, 15, 16 ] }, "obj": 208.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 17, "num_open": 6, "sites": [ { "id": 1, "distances": { "1": 0, "2": 31, "3": 25, "4": 41, "5": 34, "6": 34, "7": 19, "8": 28, "9": 22, "10": 30, "11": 39, "12": 44, "13": 36, "14": 31, "15": 38, "16": 26, "17": 35 } }, { "id": 2, "distances": { "1": 31, "2": 0, "3": 27, "4": 32, "5": 28, "6": 18, "7": 32, "8": 25, "9": 14, "10": 18, "11": 25, "12": 36, "13": 5, "14": 24, "15": 20, "16": 29, "17": 33 } }, { "id": 3, "distances": { "1": 25, "2": 27, "3": 0, "4": 28, "5": 25, "6": 26, "7": 24, "8": 26, "9": 22, "10": 34, "11": 50, "12": 33, "13": 32, "14": 33, "15": 30, "16": 20, "17": 37 } }, { "id": 4, "distances": { "1": 41, "2": 32, "3": 28, "4": 0, "5": 39, "6": 39, "7": 36, "8": 37, "9": 19, "10": 26, "11": 45, "12": 40, "13": 37, "14": 34, "15": 34, "16": 42, "17": 44 } }, { "id": 5, "distances": { "1": 34, "2": 28, "3": 25, "4": 39, "5": 0, "6": 34, "7": 30, "8": 29, "9": 42, "10": 32, "11": 53, "12": 22, "13": 33, "14": 34, "15": 33, "16": 36, "17": 38 } }, { "id": 6, "distances": { "1": 34, "2": 18, "3": 26, "4": 39, "5": 34, "6": 0, "7": 32, "8": 26, "9": 32, "10": 26, "11": 37, "12": 22, "13": 21, "14": 26, "15": 32, "16": 22, "17": 39 } }, { "id": 7, "distances": { "1": 19, "2": 32, "3": 24, "4": 36, "5": 30, "6": 32, "7": 0, "8": 33, "9": 27, "10": 31, "11": 39, "12": 38, "13": 37, "14": 27, "15": 39, "16": 27, "17": 41 } }, { "id": 8, "distances": { "1": 28, "2": 25, "3": 26, "4": 37, "5": 29, "6": 26, "7": 33, "8": 0, "9": 29, "10": 33, "11": 28, "12": 33, "13": 30, "14": 33, "15": 25, "16": 34, "17": 38 } }, { "id": 9, "distances": { "1": 22, "2": 14, "3": 22, "4": 19, "5": 42, "6": 32, "7": 27, "8": 29, "9": 0, "10": 32, "11": 37, "12": 47, "13": 19, "14": 38, "15": 34, "16": 28, "17": 34 } }, { "id": 10, "distances": { "1": 30, "2": 18, "3": 34, "4": 26, "5": 32, "6": 26, "7": 31, "8": 33, "9": 32, "10": 0, "11": 43, "12": 44, "13": 23, "14": 27, "15": 32, "16": 16, "17": 35 } }, { "id": 11, "distances": { "1": 39, "2": 25, "3": 50, "4": 45, "5": 53, "6": 37, "7": 39, "8": 28, "9": 37, "10": 43, "11": 0, "12": 55, "13": 30, "14": 45, "15": 45, "16": 50, "17": 47 } }, { "id": 12, "distances": { "1": 44, "2": 36, "3": 33, "4": 40, "5": 22, "6": 22, "7": 38, "8": 33, "9": 47, "10": 44, "11": 55, "12": 0, "13": 39, "14": 48, "15": 37, "16": 40, "17": 50 } }, { "id": 13, "distances": { "1": 36, "2": 5, "3": 32, "4": 37, "5": 33, "6": 21, "7": 37, "8": 30, "9": 19, "10": 23, "11": 30, "12": 39, "13": 0, "14": 29, "15": 25, "16": 31, "17": 38 } }, { "id": 14, "distances": { "1": 31, "2": 24, "3": 33, "4": 34, "5": 34, "6": 26, "7": 27, "8": 33, "9": 38, "10": 27, "11": 45, "12": 48, "13": 29, "14": 0, "15": 18, "16": 43, "17": 34 } }, { "id": 15, "distances": { "1": 38, "2": 20, "3": 30, "4": 34, "5": 33, "6": 32, "7": 39, "8": 25, "9": 34, "10": 32, "11": 45, "12": 37, "13": 25, "14": 18, "15": 0, "16": 26, "17": 27 } }, { "id": 16, "distances": { "1": 26, "2": 29, "3": 20, "4": 42, "5": 36, "6": 22, "7": 27, "8": 34, "9": 28, "10": 16, "11": 50, "12": 40, "13": 31, "14": 43, "15": 26, "16": 0, "17": 44 } }, { "id": 17, "distances": { "1": 35, "2": 33, "3": 37, "4": 44, "5": 38, "6": 39, "7": 41, "8": 38, "9": 34, "10": 35, "11": 47, "12": 50, "13": 38, "14": 34, "15": 27, "16": 44, "17": 0 } } ], "objective": 208.0 }, "solution_variant": { "selected": [ 2, 4, 5, 7, 16, 17 ], "assignments": [ 7, 2, 16, 4, 5, 2, 7, 2, 2, 16, 2, 5, 2, 2, 2, 16, 17 ] }, "context_index": 44, "input_format": "json", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "I’m the transit planner trying to pick a handful of park-and-ride sites from a bigger list, then link every suburb to one of the opened sites so people can drive there before hopping on transit. The trick is to pick exactly the allowed number of lots and make sure every suburb is sent to one—and only one—of those open lots. A better plan is simply the one where, when all the suburbs’ trips are added up, the total miles (or minutes) people drive to their assigned lot is as small as possible. The actual candidate lots, suburbs and the distances between them are shown below.\n\n{\n \"total_locations\": 20,\n \"num_lots_to_open\": 2,\n \"location_ids\": [\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16,\n 17,\n 18,\n 19,\n 20\n ],\n \"data\": [\n {\n \"from_location_id\": 1,\n \"to_location_id\": 2,\n \"drive_distance\": 61\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 3,\n \"drive_distance\": 59\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 4,\n \"drive_distance\": 68\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 5,\n \"drive_distance\": 22\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 6,\n \"drive_distance\": 83\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 7,\n \"drive_distance\": 43\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 8,\n \"drive_distance\": 62\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 9,\n \"drive_distance\": 64\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 10,\n \"drive_distance\": 106\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 11,\n \"drive_distance\": 58\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 12,\n \"drive_distance\": 54\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 13,\n \"drive_distance\": 32\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 14,\n \"drive_distance\": 90\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 15,\n \"drive_distance\": 56\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 16,\n \"drive_distance\": 77\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 17,\n \"drive_distance\": 68\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 18,\n \"drive_distance\": 49\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 19,\n \"drive_distance\": 64\n },\n {\n \"from_location_id\": 1,\n \"to_location_id\": 20,\n \"drive_distance\": 58\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 1,\n \"drive_distance\": 61\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 3,\n \"drive_distance\": 29\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 4,\n \"drive_distance\": 48\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 5,\n \"drive_distance\": 59\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 6,\n \"drive_distance\": 31\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 7,\n \"drive_distance\": 47\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 8,\n \"drive_distance\": 45\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 9,\n \"drive_distance\": 47\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 10,\n \"drive_distance\": 90\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 11,\n \"drive_distance\": 42\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 12,\n \"drive_distance\": 37\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 13,\n \"drive_distance\": 47\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 14,\n \"drive_distance\": 95\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 15,\n \"drive_distance\": 44\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 16,\n \"drive_distance\": 76\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 17,\n \"drive_distance\": 49\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 18,\n \"drive_distance\": 50\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 19,\n \"drive_distance\": 44\n },\n {\n \"from_location_id\": 2,\n \"to_location_id\": 20,\n \"drive_distance\": 31\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 1,\n \"drive_distance\": 59\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 2,\n \"drive_distance\": 29\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 4,\n \"drive_distance\": 50\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 5,\n \"drive_distance\": 56\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 6,\n \"drive_distance\": 40\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 7,\n \"drive_distance\": 31\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 8,\n \"drive_distance\": 32\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 9,\n \"drive_distance\": 35\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 10,\n \"drive_distance\": 81\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 11,\n \"drive_distance\": 46\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 12,\n \"drive_distance\": 29\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 13,\n \"drive_distance\": 27\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 14,\n \"drive_distance\": 75\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 15,\n \"drive_distance\": 38\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 16,\n \"drive_distance\": 67\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 17,\n \"drive_distance\": 39\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 18,\n \"drive_distance\": 45\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 19,\n \"drive_distance\": 35\n },\n {\n \"from_location_id\": 3,\n \"to_location_id\": 20,\n \"drive_distance\": 41\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 1,\n \"drive_distance\": 68\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 2,\n \"drive_distance\": 48\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 3,\n \"drive_distance\": 50\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 5,\n \"drive_distance\": 58\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 6,\n \"drive_distance\": 67\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 7,\n \"drive_distance\": 55\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 8,\n \"drive_distance\": 52\n },\n {\n \"from_location_id\": 4,\n \"to_location_id\": 9,\n \"drive_distance\": 57\n },\n {\n \"from_location_id\": 4,\n 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5,\n \"drive_distance\": 85\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 7,\n \"drive_distance\": 69\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 8,\n \"drive_distance\": 67\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 9,\n \"drive_distance\": 70\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 10,\n \"drive_distance\": 69\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 11,\n \"drive_distance\": 64\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 12,\n \"drive_distance\": 68\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 13,\n \"drive_distance\": 67\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 14,\n \"drive_distance\": 115\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 15,\n \"drive_distance\": 63\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 16,\n \"drive_distance\": 62\n },\n {\n \"from_location_id\": 6,\n \"to_location_id\": 17,\n \"drive_distance\": 60\n },\n {\n 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10,\n \"drive_distance\": 92\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 11,\n \"drive_distance\": 27\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 12,\n \"drive_distance\": 26\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 13,\n \"drive_distance\": 20\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 14,\n \"drive_distance\": 86\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 15,\n \"drive_distance\": 49\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 16,\n \"drive_distance\": 49\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 17,\n \"drive_distance\": 39\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 18,\n \"drive_distance\": 35\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 19,\n \"drive_distance\": 34\n },\n {\n \"from_location_id\": 7,\n \"to_location_id\": 20,\n \"drive_distance\": 44\n },\n {\n \"from_location_id\": 8,\n \"to_location_id\": 1,\n \"drive_distance\": 62\n },\n {\n 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\"drive_distance\": 29\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 9,\n \"drive_distance\": 20\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 10,\n \"drive_distance\": 92\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 11,\n \"drive_distance\": 55\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 12,\n \"drive_distance\": 39\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 13,\n \"drive_distance\": 46\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 14,\n \"drive_distance\": 79\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 15,\n \"drive_distance\": 45\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 16,\n \"drive_distance\": 77\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 17,\n \"drive_distance\": 55\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 18,\n \"drive_distance\": 58\n },\n {\n \"from_location_id\": 19,\n \"to_location_id\": 20,\n \"drive_distance\": 36\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 1,\n \"drive_distance\": 58\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 2,\n \"drive_distance\": 31\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 3,\n \"drive_distance\": 41\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 4,\n \"drive_distance\": 45\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 5,\n \"drive_distance\": 39\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 6,\n \"drive_distance\": 53\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 7,\n \"drive_distance\": 44\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 8,\n \"drive_distance\": 42\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 9,\n \"drive_distance\": 46\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 10,\n \"drive_distance\": 98\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 11,\n \"drive_distance\": 39\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 12,\n \"drive_distance\": 51\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 13,\n \"drive_distance\": 48\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 14,\n \"drive_distance\": 68\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 15,\n \"drive_distance\": 41\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 16,\n \"drive_distance\": 75\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 17,\n \"drive_distance\": 62\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 18,\n \"drive_distance\": 37\n },\n {\n \"from_location_id\": 20,\n \"to_location_id\": 19,\n \"drive_distance\": 36\n }\n ]\n}\n\nAlso, when you send back the plan, just stick to this simple JSON shape so I can read it automatically:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis is just a sketch of the shape I need. \"selected\" is where you list the lots you choose to open (one placeholder per chosen lot), and \"assignments\" lists, for every suburb in the same order as the instance input, which opened lot that suburb is sent to. Keep it casual—think of \"selected\" as the checked boxes and \"assignments\" as the dropdown choices next to each suburb.\n\nPlease don’t rename any of the actual identifiers from the instance input when you fill this in — use them exactly as given, and don’t introduce new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 61, 59, 68, 22, 83, 43, 62, 64, 106, 58, 54, 32, 90, 56, 77, 68, 49, 64, 58 ], [ 61, 0, 29, 48, 59, 31, 47, 45, 47, 90, 42, 37, 47, 95, 44, 76, 49, 50, 44, 31 ], [ 59, 29, 0, 50, 56, 40, 31, 32, 35, 81, 46, 29, 27, 75, 38, 67, 39, 45, 35, 41 ], [ 68, 48, 50, 0, 58, 67, 55, 52, 57, 91, 50, 43, 59, 107, 12, 85, 57, 37, 57, 45 ], [ 22, 59, 56, 58, 0, 85, 33, 52, 54, 103, 48, 51, 36, 94, 46, 70, 54, 53, 54, 39 ], [ 83, 31, 40, 67, 85, 0, 69, 67, 70, 69, 64, 68, 67, 115, 63, 62, 60, 65, 55, 53 ], [ 43, 47, 31, 55, 33, 69, 0, 31, 27, 92, 27, 26, 20, 86, 49, 49, 39, 35, 34, 44 ], [ 62, 45, 32, 52, 52, 67, 31, 0, 49, 95, 46, 41, 37, 94, 40, 68, 58, 53, 29, 42 ], [ 64, 47, 35, 57, 54, 70, 27, 49, 0, 107, 53, 48, 42, 90, 45, 76, 66, 61, 20, 46 ], [ 106, 90, 81, 91, 103, 69, 92, 95, 107, 0, 105, 78, 88, 150, 79, 123, 101, 62, 92, 98 ], [ 58, 42, 46, 50, 48, 64, 27, 46, 53, 105, 0, 45, 39, 94, 44, 64, 54, 50, 55, 39 ], [ 54, 37, 29, 43, 51, 68, 26, 41, 48, 78, 45, 0, 22, 88, 31, 64, 57, 34, 39, 51 ], [ 32, 47, 27, 59, 36, 67, 20, 37, 42, 88, 39, 22, 0, 82, 49, 61, 51, 37, 46, 48 ], [ 90, 95, 75, 107, 94, 115, 86, 94, 90, 150, 94, 88, 82, 0, 95, 121, 100, 93, 79, 68 ], [ 56, 44, 38, 12, 46, 63, 49, 40, 45, 79, 44, 31, 49, 95, 0, 76, 51, 25, 45, 41 ], [ 77, 76, 67, 85, 70, 62, 49, 68, 76, 123, 64, 64, 61, 121, 76, 0, 28, 66, 77, 75 ], [ 68, 49, 39, 57, 54, 60, 39, 58, 66, 101, 54, 57, 51, 100, 51, 28, 0, 52, 55, 62 ], [ 49, 50, 45, 37, 53, 65, 35, 53, 61, 62, 50, 34, 37, 93, 25, 66, 52, 0, 58, 37 ], [ 64, 44, 35, 57, 54, 55, 34, 29, 20, 92, 55, 39, 46, 79, 45, 77, 55, 58, 0, 36 ], [ 58, 31, 41, 45, 39, 53, 44, 42, 46, 98, 39, 51, 48, 68, 41, 75, 62, 37, 36, 0 ] ], "p": 2, "objective": 710.0 }, "solution": { "facilities": [ 6, 14 ], "assignments": [ 6, 14, 6, 14, 6, 14, 6, 6, 6, 14, 6, 6, 6, 6, 14, 6, 6, 14, 6, 14 ] }, "obj": 710.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 20, "num_open": 2, "sites": [ { "id": 1, "distances": { "1": 0, "2": 61, "3": 59, "4": 68, "5": 22, "6": 83, "7": 43, "8": 62, "9": 64, "10": 106, "11": 58, "12": 54, "13": 32, "14": 90, "15": 56, "16": 77, "17": 68, "18": 49, "19": 64, "20": 58 } }, { "id": 2, "distances": { "1": 61, "2": 0, "3": 29, "4": 48, "5": 59, "6": 31, "7": 47, "8": 45, "9": 47, "10": 90, "11": 42, "12": 37, "13": 47, "14": 95, "15": 44, "16": 76, "17": 49, "18": 50, "19": 44, "20": 31 } }, { "id": 3, "distances": { "1": 59, "2": 29, "3": 0, "4": 50, "5": 56, "6": 40, "7": 31, "8": 32, "9": 35, "10": 81, "11": 46, "12": 29, "13": 27, "14": 75, "15": 38, "16": 67, "17": 39, "18": 45, "19": 35, "20": 41 } }, { "id": 4, "distances": { "1": 68, "2": 48, "3": 50, "4": 0, "5": 58, "6": 67, "7": 55, "8": 52, "9": 57, "10": 91, "11": 50, "12": 43, "13": 59, "14": 107, "15": 12, "16": 85, "17": 57, "18": 37, "19": 57, "20": 45 } }, { "id": 5, "distances": { "1": 22, "2": 59, "3": 56, "4": 58, "5": 0, "6": 85, "7": 33, "8": 52, "9": 54, "10": 103, "11": 48, "12": 51, "13": 36, "14": 94, "15": 46, "16": 70, "17": 54, "18": 53, "19": 54, "20": 39 } }, { "id": 6, "distances": { "1": 83, "2": 31, "3": 40, "4": 67, "5": 85, "6": 0, "7": 69, "8": 67, "9": 70, "10": 69, "11": 64, "12": 68, "13": 67, "14": 115, "15": 63, "16": 62, "17": 60, "18": 65, "19": 55, "20": 53 } }, { "id": 7, "distances": { "1": 43, "2": 47, "3": 31, "4": 55, "5": 33, "6": 69, "7": 0, "8": 31, "9": 27, "10": 92, "11": 27, "12": 26, "13": 20, "14": 86, "15": 49, "16": 49, "17": 39, "18": 35, "19": 34, "20": 44 } }, { "id": 8, "distances": { "1": 62, "2": 45, "3": 32, "4": 52, "5": 52, "6": 67, "7": 31, "8": 0, "9": 49, "10": 95, "11": 46, "12": 41, "13": 37, "14": 94, "15": 40, "16": 68, "17": 58, "18": 53, "19": 29, "20": 42 } }, { "id": 9, "distances": { "1": 64, "2": 47, "3": 35, "4": 57, "5": 54, "6": 70, "7": 27, "8": 49, "9": 0, "10": 107, "11": 53, "12": 48, "13": 42, "14": 90, "15": 45, "16": 76, "17": 66, "18": 61, "19": 20, "20": 46 } }, { "id": 10, "distances": { "1": 106, "2": 90, "3": 81, "4": 91, "5": 103, "6": 69, "7": 92, "8": 95, "9": 107, "10": 0, "11": 105, "12": 78, "13": 88, "14": 150, "15": 79, "16": 123, "17": 101, "18": 62, "19": 92, "20": 98 } }, { "id": 11, "distances": { "1": 58, "2": 42, "3": 46, "4": 50, "5": 48, "6": 64, "7": 27, "8": 46, "9": 53, "10": 105, "11": 0, "12": 45, "13": 39, "14": 94, "15": 44, "16": 64, "17": 54, "18": 50, "19": 55, "20": 39 } }, { "id": 12, "distances": { "1": 54, "2": 37, "3": 29, "4": 43, "5": 51, "6": 68, "7": 26, "8": 41, "9": 48, "10": 78, "11": 45, "12": 0, "13": 22, "14": 88, "15": 31, "16": 64, "17": 57, "18": 34, "19": 39, "20": 51 } }, { "id": 13, "distances": { "1": 32, "2": 47, "3": 27, "4": 59, "5": 36, "6": 67, "7": 20, "8": 37, "9": 42, "10": 88, "11": 39, "12": 22, "13": 0, "14": 82, "15": 49, "16": 61, "17": 51, "18": 37, "19": 46, "20": 48 } }, { "id": 14, "distances": { "1": 90, "2": 95, "3": 75, "4": 107, "5": 94, "6": 115, "7": 86, "8": 94, "9": 90, "10": 150, "11": 94, "12": 88, "13": 82, "14": 0, "15": 95, "16": 121, "17": 100, "18": 93, "19": 79, "20": 68 } }, { "id": 15, "distances": { "1": 56, "2": 44, "3": 38, "4": 12, "5": 46, "6": 63, "7": 49, "8": 40, "9": 45, "10": 79, "11": 44, "12": 31, "13": 49, "14": 95, "15": 0, "16": 76, "17": 51, "18": 25, "19": 45, "20": 41 } }, { "id": 16, "distances": { "1": 77, "2": 76, "3": 67, "4": 85, "5": 70, "6": 62, "7": 49, "8": 68, "9": 76, "10": 123, "11": 64, "12": 64, "13": 61, "14": 121, "15": 76, "16": 0, "17": 28, "18": 66, "19": 77, "20": 75 } }, { "id": 17, "distances": { "1": 68, "2": 49, "3": 39, "4": 57, "5": 54, "6": 60, "7": 39, "8": 58, "9": 66, "10": 101, "11": 54, "12": 57, "13": 51, "14": 100, "15": 51, "16": 28, "17": 0, "18": 52, "19": 55, "20": 62 } }, { "id": 18, "distances": { "1": 49, "2": 50, "3": 45, "4": 37, "5": 53, "6": 65, "7": 35, "8": 53, "9": 61, "10": 62, "11": 50, "12": 34, "13": 37, "14": 93, "15": 25, "16": 66, "17": 52, "18": 0, "19": 58, "20": 37 } }, { "id": 19, "distances": { "1": 64, "2": 44, "3": 35, "4": 57, "5": 54, "6": 55, "7": 34, "8": 29, "9": 20, "10": 92, "11": 55, "12": 39, "13": 46, "14": 79, "15": 45, "16": 77, "17": 55, "18": 58, "19": 0, "20": 36 } }, { "id": 20, "distances": { "1": 58, "2": 31, "3": 41, "4": 45, "5": 39, "6": 53, "7": 44, "8": 42, "9": 46, "10": 98, "11": 39, "12": 51, "13": 48, "14": 68, "15": 41, "16": 75, "17": 62, "18": 37, "19": 36, "20": 0 } } ], "objective": 710.0 }, "solution_variant": { "selected": [ 7, 15 ], "assignments": [ 7, 15, 7, 15, 7, 15, 7, 7, 7, 15, 7, 7, 7, 7, 15, 7, 7, 15, 7, 15 ] }, "context_index": 45, "input_format": "json", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Recently the parks team was asked to pick a set number of clearings for dog play areas and to route every neighborhood park to a single chosen site. The aim is to minimize how far everyone walks overall — computed by summing each park’s distance to the play area it’s sent to. Practically, that means opening exactly the allotted number of clearings and assigning each park to one, and only one, open play area so nothing’s left out or doubled. The concrete map and distance numbers follow below.\n\n{\n \"total_locations\": 16,\n \"play_areas_to_open\": 5,\n \"location_ids\": [\n 1,\n 2,\n 3,\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13,\n 14,\n 15,\n 16\n ],\n \"data\": [\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 2,\n \"travel_distance\": 132\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 3,\n \"travel_distance\": 157\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 4,\n \"travel_distance\": 137\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 5,\n \"travel_distance\": 203\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 6,\n \"travel_distance\": 108\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 7,\n \"travel_distance\": 64\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 8,\n \"travel_distance\": 130\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 9,\n \"travel_distance\": 138\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 10,\n \"travel_distance\": 143\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 11,\n \"travel_distance\": 188\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 12,\n \"travel_distance\": 119\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 13,\n \"travel_distance\": 97\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 14,\n \"travel_distance\": 160\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 15,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 1,\n \"target_clearing_id\": 16,\n \"travel_distance\": 178\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 1,\n \"travel_distance\": 132\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 3,\n \"travel_distance\": 155\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 4,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 5,\n \"travel_distance\": 127\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 6,\n \"travel_distance\": 79\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 7,\n \"travel_distance\": 126\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 8,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 9,\n \"travel_distance\": 42\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 10,\n \"travel_distance\": 30\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 11,\n \"travel_distance\": 75\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 12,\n \"travel_distance\": 63\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 13,\n \"travel_distance\": 41\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 14,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 15,\n \"travel_distance\": 91\n },\n {\n \"source_park_id\": 2,\n \"target_clearing_id\": 16,\n \"travel_distance\": 120\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 1,\n \"travel_distance\": 157\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 2,\n \"travel_distance\": 155\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 4,\n \"travel_distance\": 112\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 5,\n \"travel_distance\": 216\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 6,\n \"travel_distance\": 113\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 7,\n \"travel_distance\": 103\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 8,\n \"travel_distance\": 185\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 9,\n \"travel_distance\": 113\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 10,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 11,\n \"travel_distance\": 178\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 12,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 13,\n \"travel_distance\": 156\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 14,\n \"travel_distance\": 153\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 15,\n \"travel_distance\": 167\n },\n {\n \"source_park_id\": 3,\n \"target_clearing_id\": 16,\n \"travel_distance\": 153\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 1,\n \"travel_distance\": 137\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 2,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 3,\n \"travel_distance\": 112\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 5,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 6,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 7,\n \"travel_distance\": 83\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 8,\n \"travel_distance\": 111\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 9,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 10,\n \"travel_distance\": 113\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 11,\n \"travel_distance\": 158\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 12,\n \"travel_distance\": 114\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 13,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 14,\n \"travel_distance\": 133\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 15,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 4,\n \"target_clearing_id\": 16,\n \"travel_distance\": 92\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 1,\n \"travel_distance\": 203\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 2,\n \"travel_distance\": 127\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 3,\n \"travel_distance\": 216\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 4,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 6,\n \"travel_distance\": 185\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 7,\n \"travel_distance\": 181\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 8,\n \"travel_distance\": 149\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 9,\n \"travel_distance\": 131\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 10,\n \"travel_distance\": 97\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 11,\n \"travel_distance\": 142\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 12,\n \"travel_distance\": 184\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 13,\n \"travel_distance\": 162\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 14,\n \"travel_distance\": 225\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 15,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 5,\n \"target_clearing_id\": 16,\n \"travel_distance\": 186\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 1,\n \"travel_distance\": 108\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 2,\n \"travel_distance\": 79\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 3,\n \"travel_distance\": 113\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 4,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 5,\n \"travel_distance\": 185\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 7,\n \"travel_distance\": 84\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 8,\n \"travel_distance\": 118\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 9,\n \"travel_distance\": 94\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 10,\n \"travel_distance\": 109\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 11,\n \"travel_distance\": 143\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 12,\n \"travel_distance\": 94\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 13,\n \"travel_distance\": 72\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 14,\n \"travel_distance\": 52\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 15,\n \"travel_distance\": 128\n },\n {\n \"source_park_id\": 6,\n \"target_clearing_id\": 16,\n \"travel_distance\": 118\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 1,\n \"travel_distance\": 64\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 2,\n \"travel_distance\": 126\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 3,\n \"travel_distance\": 103\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 4,\n \"travel_distance\": 83\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 5,\n \"travel_distance\": 181\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 6,\n \"travel_distance\": 84\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 8,\n \"travel_distance\": 108\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 9,\n \"travel_distance\": 84\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 10,\n \"travel_distance\": 118\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 11,\n \"travel_distance\": 149\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 12,\n \"travel_distance\": 105\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 13,\n \"travel_distance\": 112\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 14,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 15,\n \"travel_distance\": 138\n },\n {\n \"source_park_id\": 7,\n \"target_clearing_id\": 16,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 1,\n \"travel_distance\": 130\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 2,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 3,\n \"travel_distance\": 185\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 4,\n \"travel_distance\": 111\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 5,\n \"travel_distance\": 149\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 6,\n \"travel_distance\": 118\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 7,\n \"travel_distance\": 108\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 9,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 10,\n \"travel_distance\": 135\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 11,\n \"travel_distance\": 180\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 12,\n \"travel_distance\": 111\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 13,\n \"travel_distance\": 89\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 14,\n \"travel_distance\": 170\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 15,\n \"travel_distance\": 139\n },\n {\n \"source_park_id\": 8,\n \"target_clearing_id\": 16,\n \"travel_distance\": 165\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 1,\n \"travel_distance\": 138\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 2,\n \"travel_distance\": 42\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 3,\n \"travel_distance\": 113\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 4,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 5,\n \"travel_distance\": 131\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 6,\n \"travel_distance\": 94\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 7,\n \"travel_distance\": 84\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 8,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 10,\n \"travel_distance\": 34\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 11,\n \"travel_distance\": 79\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 12,\n \"travel_distance\": 105\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 13,\n \"travel_distance\": 83\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 14,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 15,\n \"travel_distance\": 133\n },\n {\n \"source_park_id\": 9,\n \"target_clearing_id\": 16,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 1,\n \"travel_distance\": 143\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 2,\n \"travel_distance\": 30\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 3,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 4,\n \"travel_distance\": 113\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 5,\n \"travel_distance\": 97\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 6,\n \"travel_distance\": 109\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 7,\n \"travel_distance\": 118\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 8,\n \"travel_distance\": 135\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 9,\n \"travel_distance\": 34\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 11,\n \"travel_distance\": 45\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 12,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 13,\n \"travel_distance\": 71\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 14,\n \"travel_distance\": 154\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 15,\n \"travel_distance\": 121\n },\n {\n \"source_park_id\": 10,\n \"target_clearing_id\": 16,\n \"travel_distance\": 112\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 1,\n \"travel_distance\": 188\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 2,\n \"travel_distance\": 75\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 3,\n \"travel_distance\": 178\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 4,\n \"travel_distance\": 158\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 5,\n \"travel_distance\": 142\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 6,\n \"travel_distance\": 143\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 7,\n \"travel_distance\": 149\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 8,\n \"travel_distance\": 180\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 9,\n \"travel_distance\": 79\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 10,\n \"travel_distance\": 45\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 12,\n \"travel_distance\": 138\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 13,\n \"travel_distance\": 116\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 14,\n \"travel_distance\": 187\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 15,\n \"travel_distance\": 166\n },\n {\n \"source_park_id\": 11,\n \"target_clearing_id\": 16,\n \"travel_distance\": 157\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 1,\n \"travel_distance\": 119\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 2,\n \"travel_distance\": 63\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 3,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 4,\n \"travel_distance\": 114\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 5,\n \"travel_distance\": 184\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 6,\n \"travel_distance\": 94\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 7,\n \"travel_distance\": 105\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 8,\n \"travel_distance\": 111\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 9,\n \"travel_distance\": 105\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 10,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 11,\n \"travel_distance\": 138\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 13,\n \"travel_distance\": 22\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 14,\n \"travel_distance\": 139\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 15,\n \"travel_distance\": 78\n },\n {\n \"source_park_id\": 12,\n \"target_clearing_id\": 16,\n \"travel_distance\": 139\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 1,\n \"travel_distance\": 97\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 2,\n \"travel_distance\": 41\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 3,\n \"travel_distance\": 156\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 4,\n \"travel_distance\": 93\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 5,\n \"travel_distance\": 162\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 6,\n \"travel_distance\": 72\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 7,\n \"travel_distance\": 112\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 8,\n \"travel_distance\": 89\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 9,\n \"travel_distance\": 83\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 10,\n \"travel_distance\": 71\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 11,\n \"travel_distance\": 116\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 12,\n \"travel_distance\": 22\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 14,\n \"travel_distance\": 117\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 15,\n \"travel_distance\": 56\n },\n {\n \"source_park_id\": 13,\n \"target_clearing_id\": 16,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 1,\n \"travel_distance\": 160\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 2,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 3,\n \"travel_distance\": 153\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 4,\n \"travel_distance\": 133\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 5,\n \"travel_distance\": 225\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 6,\n \"travel_distance\": 52\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 7,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 8,\n \"travel_distance\": 170\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 9,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 10,\n \"travel_distance\": 154\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 11,\n \"travel_distance\": 187\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 12,\n \"travel_distance\": 139\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 13,\n \"travel_distance\": 117\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 15,\n \"travel_distance\": 173\n },\n {\n \"source_park_id\": 14,\n \"target_clearing_id\": 16,\n \"travel_distance\": 162\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 1,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 2,\n \"travel_distance\": 91\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 3,\n \"travel_distance\": 167\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 4,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 5,\n \"travel_distance\": 134\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 6,\n \"travel_distance\": 128\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 7,\n \"travel_distance\": 138\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 8,\n \"travel_distance\": 139\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 9,\n \"travel_distance\": 133\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 10,\n \"travel_distance\": 121\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 11,\n \"travel_distance\": 166\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 12,\n \"travel_distance\": 78\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 13,\n \"travel_distance\": 56\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 14,\n \"travel_distance\": 173\n },\n {\n \"source_park_id\": 15,\n \"target_clearing_id\": 16,\n \"travel_distance\": 156\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 1,\n \"travel_distance\": 178\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 2,\n \"travel_distance\": 120\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 3,\n \"travel_distance\": 153\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 4,\n \"travel_distance\": 92\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 5,\n \"travel_distance\": 186\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 6,\n \"travel_distance\": 118\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 7,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 8,\n \"travel_distance\": 165\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 9,\n \"travel_distance\": 124\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 10,\n \"travel_distance\": 112\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 11,\n \"travel_distance\": 157\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 12,\n \"travel_distance\": 139\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 13,\n \"travel_distance\": 147\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 14,\n \"travel_distance\": 162\n },\n {\n \"source_park_id\": 16,\n \"target_clearing_id\": 15,\n \"travel_distance\": 156\n }\n ]\n}\n\nAlso, when you send the actual answer, please follow this simple JSON layout so I can read it easily — just a casual sketch of the shape we expect:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list which clearings (the play-area sites) you decide to open. \"assignments\" is a parallel list that says, for each park in the same order they appear in the instance, which open site that park is routed to. Super informal: \"selected\" = open spots, \"assignments\" = which open spot each park uses.\n\nThis is just the shape I want, not the actual solution values.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 132, 157, 137, 203, 108, 64, 130, 138, 143, 188, 119, 97, 160, 147, 178 ], [ 132, 0, 155, 134, 127, 79, 126, 124, 42, 30, 75, 63, 41, 124, 91, 120 ], [ 157, 155, 0, 112, 216, 113, 103, 185, 113, 147, 178, 134, 156, 153, 167, 153 ], [ 137, 134, 112, 0, 147, 93, 83, 111, 93, 113, 158, 114, 93, 133, 147, 92 ], [ 203, 127, 216, 147, 0, 185, 181, 149, 131, 97, 142, 184, 162, 225, 134, 186 ], [ 108, 79, 113, 93, 185, 0, 84, 118, 94, 109, 143, 94, 72, 52, 128, 118 ], [ 64, 126, 103, 83, 181, 84, 0, 108, 84, 118, 149, 105, 112, 124, 138, 124 ], [ 130, 124, 185, 111, 149, 118, 108, 0, 147, 135, 180, 111, 89, 170, 139, 165 ], [ 138, 42, 113, 93, 131, 94, 84, 147, 0, 34, 79, 105, 83, 134, 133, 124 ], [ 143, 30, 147, 113, 97, 109, 118, 135, 34, 0, 45, 93, 71, 154, 121, 112 ], [ 188, 75, 178, 158, 142, 143, 149, 180, 79, 45, 0, 138, 116, 187, 166, 157 ], [ 119, 63, 134, 114, 184, 94, 105, 111, 105, 93, 138, 0, 22, 139, 78, 139 ], [ 97, 41, 156, 93, 162, 72, 112, 89, 83, 71, 116, 22, 0, 117, 56, 147 ], [ 160, 124, 153, 133, 225, 52, 124, 170, 134, 154, 187, 139, 117, 0, 173, 162 ], [ 147, 91, 167, 147, 134, 128, 138, 139, 133, 121, 166, 78, 56, 173, 0, 156 ], [ 178, 120, 153, 92, 186, 118, 124, 165, 124, 112, 157, 139, 147, 162, 156, 0 ] ], "p": 5, "objective": 675.0 }, "solution": { "facilities": [ 5, 6, 9, 12, 15 ], "assignments": [ 6, 9, 6, 6, 9, 5, 6, 12, 9, 9, 9, 12, 12, 5, 12, 15 ] }, "obj": 675.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 5, "sites": [ { "id": 1, "distances": { "1": 0, "2": 132, "3": 157, "4": 137, "5": 203, "6": 108, "7": 64, "8": 130, "9": 138, "10": 143, "11": 188, "12": 119, "13": 97, "14": 160, "15": 147, "16": 178 } }, { "id": 2, "distances": { "1": 132, "2": 0, "3": 155, "4": 134, "5": 127, "6": 79, "7": 126, "8": 124, "9": 42, "10": 30, "11": 75, "12": 63, "13": 41, "14": 124, "15": 91, "16": 120 } }, { "id": 3, "distances": { "1": 157, "2": 155, "3": 0, "4": 112, "5": 216, "6": 113, "7": 103, "8": 185, "9": 113, "10": 147, "11": 178, "12": 134, "13": 156, "14": 153, "15": 167, "16": 153 } }, { "id": 4, "distances": { "1": 137, "2": 134, "3": 112, "4": 0, "5": 147, "6": 93, "7": 83, "8": 111, "9": 93, "10": 113, "11": 158, "12": 114, "13": 93, "14": 133, "15": 147, "16": 92 } }, { "id": 5, "distances": { "1": 203, "2": 127, "3": 216, "4": 147, "5": 0, "6": 185, "7": 181, "8": 149, "9": 131, "10": 97, "11": 142, "12": 184, "13": 162, "14": 225, "15": 134, "16": 186 } }, { "id": 6, "distances": { "1": 108, "2": 79, "3": 113, "4": 93, "5": 185, "6": 0, "7": 84, "8": 118, "9": 94, "10": 109, "11": 143, "12": 94, "13": 72, "14": 52, "15": 128, "16": 118 } }, { "id": 7, "distances": { "1": 64, "2": 126, "3": 103, "4": 83, "5": 181, "6": 84, "7": 0, "8": 108, "9": 84, "10": 118, "11": 149, "12": 105, "13": 112, "14": 124, "15": 138, "16": 124 } }, { "id": 8, "distances": { "1": 130, "2": 124, "3": 185, "4": 111, "5": 149, "6": 118, "7": 108, "8": 0, "9": 147, "10": 135, "11": 180, "12": 111, "13": 89, "14": 170, "15": 139, "16": 165 } }, { "id": 9, "distances": { "1": 138, "2": 42, "3": 113, "4": 93, "5": 131, "6": 94, "7": 84, "8": 147, "9": 0, "10": 34, "11": 79, "12": 105, "13": 83, "14": 134, "15": 133, "16": 124 } }, { "id": 10, "distances": { "1": 143, "2": 30, "3": 147, "4": 113, "5": 97, "6": 109, "7": 118, "8": 135, "9": 34, "10": 0, "11": 45, "12": 93, "13": 71, "14": 154, "15": 121, "16": 112 } }, { "id": 11, "distances": { "1": 188, "2": 75, "3": 178, "4": 158, "5": 142, "6": 143, "7": 149, "8": 180, "9": 79, "10": 45, "11": 0, "12": 138, "13": 116, "14": 187, "15": 166, "16": 157 } }, { "id": 12, "distances": { "1": 119, "2": 63, "3": 134, "4": 114, "5": 184, "6": 94, "7": 105, "8": 111, "9": 105, "10": 93, "11": 138, "12": 0, "13": 22, "14": 139, "15": 78, "16": 139 } }, { "id": 13, "distances": { "1": 97, "2": 41, "3": 156, "4": 93, "5": 162, "6": 72, "7": 112, "8": 89, "9": 83, "10": 71, "11": 116, "12": 22, "13": 0, "14": 117, "15": 56, "16": 147 } }, { "id": 14, "distances": { "1": 160, "2": 124, "3": 153, "4": 133, "5": 225, "6": 52, "7": 124, "8": 170, "9": 134, "10": 154, "11": 187, "12": 139, "13": 117, "14": 0, "15": 173, "16": 162 } }, { "id": 15, "distances": { "1": 147, "2": 91, "3": 167, "4": 147, "5": 134, "6": 128, "7": 138, "8": 139, "9": 133, "10": 121, "11": 166, "12": 78, "13": 56, "14": 173, "15": 0, "16": 156 } }, { "id": 16, "distances": { "1": 178, "2": 120, "3": 153, "4": 92, "5": 186, "6": 118, "7": 124, "8": 165, "9": 124, "10": 112, "11": 157, "12": 139, "13": 147, "14": 162, "15": 156, "16": 0 } } ], "objective": 675.0 }, "solution_variant": { "selected": [ 6, 7, 10, 13, 16 ], "assignments": [ 7, 10, 7, 7, 10, 6, 7, 13, 10, 10, 10, 13, 13, 6, 13, 16 ] }, "context_index": 46, "input_format": "json", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Out in town there are several possible spots for water refill points, but only a limited number can be activated. The task is to choose which spots to open and assign every block to one of the opened spots so that no block is left without a single assigned station. The best choice is the one that makes the combined travel as small as possible: calculate the plan’s score by adding up the distance from each block to its assigned station, and the lower that sum, the better. The exact site options and pairwise distances are listed below.\n\nThere are 18 candidate locations, exactly 2 stations may be activated, and the location identifiers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.\nTravel distance from 0 to 1 is 26.\nTravel distance from 0 to 2 is 41.\nTravel distance from 0 to 3 is 33.\nTravel distance from 0 to 4 is 50.\nTravel distance from 0 to 5 is 46.\nTravel distance from 0 to 6 is 26.\nTravel distance from 0 to 7 is 53.\nTravel distance from 0 to 8 is 46.\nTravel distance from 0 to 9 is 23.\nTravel distance from 0 to 10 is 33.\nTravel distance from 0 to 11 is 60.\nTravel distance from 0 to 12 is 30.\nTravel distance from 0 to 13 is 34.\nTravel distance from 0 to 14 is 37.\nTravel distance from 0 to 15 is 32.\nTravel distance from 0 to 16 is 18.\nTravel distance from 0 to 17 is 40.\nTravel distance from 1 to 0 is 26.\nTravel distance from 1 to 2 is 39.\nTravel distance from 1 to 3 is 33.\nTravel distance from 1 to 4 is 45.\nTravel distance from 1 to 5 is 44.\nTravel distance from 1 to 6 is 17.\nTravel distance from 1 to 7 is 63.\nTravel distance from 1 to 8 is 45.\nTravel distance from 1 to 9 is 43.\nTravel distance from 1 to 10 is 37.\nTravel distance from 1 to 11 is 65.\nTravel distance from 1 to 12 is 20.\nTravel distance from 1 to 13 is 35.\nTravel distance from 1 to 14 is 31.\nTravel distance from 1 to 15 is 26.\nTravel distance from 1 to 16 is 21.\nTravel distance from 1 to 17 is 18.\nTravel distance from 2 to 0 is 41.\nTravel distance from 2 to 1 is 39.\nTravel distance from 2 to 3 is 49.\nTravel distance from 2 to 4 is 46.\nTravel distance from 2 to 5 is 15.\nTravel distance from 2 to 6 is 52.\nTravel distance from 2 to 7 is 45.\nTravel distance from 2 to 8 is 45.\nTravel distance from 2 to 9 is 51.\nTravel distance from 2 to 10 is 46.\nTravel distance from 2 to 11 is 64.\nTravel distance from 2 to 12 is 46.\nTravel distance from 2 to 13 is 35.\nTravel distance from 2 to 14 is 32.\nTravel distance from 2 to 15 is 45.\nTravel distance from 2 to 16 is 44.\nTravel distance from 2 to 17 is 56.\nTravel distance from 3 to 0 is 33.\nTravel distance from 3 to 1 is 33.\nTravel distance from 3 to 2 is 49.\nTravel distance from 3 to 4 is 35.\nTravel distance from 3 to 5 is 45.\nTravel distance from 3 to 6 is 39.\nTravel distance from 3 to 7 is 44.\nTravel distance from 3 to 8 is 44.\nTravel distance from 3 to 9 is 33.\nTravel distance from 3 to 10 is 37.\nTravel distance from 3 to 11 is 78.\nTravel distance from 3 to 12 is 34.\nTravel distance from 3 to 13 is 27.\nTravel distance from 3 to 14 is 33.\nTravel distance from 3 to 15 is 29.\nTravel distance from 3 to 16 is 21.\nTravel distance from 3 to 17 is 46.\nTravel distance from 4 to 0 is 50.\nTravel distance from 4 to 1 is 45.\nTravel distance from 4 to 2 is 46.\nTravel distance from 4 to 3 is 35.\nTravel distance from 4 to 5 is 31.\nTravel distance from 4 to 6 is 56.\nTravel distance from 4 to 7 is 45.\nTravel distance from 4 to 8 is 47.\nTravel distance from 4 to 9 is 55.\nTravel distance from 4 to 10 is 36.\nTravel distance from 4 to 11 is 70.\nTravel distance from 4 to 12 is 52.\nTravel distance from 4 to 13 is 50.\nTravel distance from 4 to 14 is 14.\nTravel distance from 4 to 15 is 47.\nTravel distance from 4 to 16 is 48.\nTravel distance from 4 to 17 is 58.\nTravel distance from 5 to 0 is 46.\nTravel distance from 5 to 1 is 44.\nTravel distance from 5 to 2 is 15.\nTravel distance from 5 to 3 is 45.\nTravel distance from 5 to 4 is 31.\nTravel distance from 5 to 6 is 52.\nTravel distance from 5 to 7 is 52.\nTravel distance from 5 to 8 is 58.\nTravel distance from 5 to 9 is 53.\nTravel distance from 5 to 10 is 43.\nTravel distance from 5 to 11 is 69.\nTravel distance from 5 to 12 is 45.\nTravel distance from 5 to 13 is 40.\nTravel distance from 5 to 14 is 17.\nTravel distance from 5 to 15 is 50.\nTravel distance from 5 to 16 is 42.\nTravel distance from 5 to 17 is 52.\nTravel distance from 6 to 0 is 26.\nTravel distance from 6 to 1 is 17.\nTravel distance from 6 to 2 is 52.\nTravel distance from 6 to 3 is 39.\nTravel distance from 6 to 4 is 56.\nTravel distance from 6 to 5 is 52.\nTravel distance from 6 to 7 is 57.\nTravel distance from 6 to 8 is 51.\nTravel distance from 6 to 9 is 45.\nTravel distance from 6 to 10 is 39.\nTravel distance from 6 to 11 is 67.\nTravel distance from 6 to 12 is 19.\nTravel distance from 6 to 13 is 47.\nTravel distance from 6 to 14 is 45.\nTravel distance from 6 to 15 is 43.\nTravel distance from 6 to 16 is 20.\nTravel distance from 6 to 17 is 35.\nTravel distance from 7 to 0 is 53.\nTravel distance from 7 to 1 is 63.\nTravel distance from 7 to 2 is 45.\nTravel distance from 7 to 3 is 44.\nTravel distance from 7 to 4 is 45.\nTravel distance from 7 to 5 is 52.\nTravel distance from 7 to 6 is 57.\nTravel distance from 7 to 8 is 66.\nTravel distance from 7 to 9 is 57.\nTravel distance from 7 to 10 is 57.\nTravel distance from 7 to 11 is 91.\nTravel distance from 7 to 12 is 51.\nTravel distance from 7 to 13 is 57.\nTravel distance from 7 to 14 is 35.\nTravel distance from 7 to 15 is 63.\nTravel distance from 7 to 16 is 49.\nTravel distance from 7 to 17 is 67.\nTravel distance from 8 to 0 is 46.\nTravel distance from 8 to 1 is 45.\nTravel distance from 8 to 2 is 45.\nTravel distance from 8 to 3 is 44.\nTravel distance from 8 to 4 is 47.\nTravel distance from 8 to 5 is 58.\nTravel distance from 8 to 6 is 51.\nTravel distance from 8 to 7 is 66.\nTravel distance from 8 to 9 is 54.\nTravel distance from 8 to 10 is 51.\nTravel distance from 8 to 11 is 58.\nTravel distance from 8 to 12 is 47.\nTravel distance from 8 to 13 is 47.\nTravel distance from 8 to 14 is 45.\nTravel distance from 8 to 15 is 48.\nTravel distance from 8 to 16 is 47.\nTravel distance from 8 to 17 is 41.\nTravel distance from 9 to 0 is 23.\nTravel distance from 9 to 1 is 43.\nTravel distance from 9 to 2 is 51.\nTravel distance from 9 to 3 is 33.\nTravel distance from 9 to 4 is 55.\nTravel distance from 9 to 5 is 53.\nTravel distance from 9 to 6 is 45.\nTravel distance from 9 to 7 is 57.\nTravel distance from 9 to 8 is 54.\nTravel distance from 9 to 10 is 47.\nTravel distance from 9 to 11 is 80.\nTravel distance from 9 to 12 is 49.\nTravel distance from 9 to 13 is 49.\nTravel distance from 9 to 14 is 45.\nTravel distance from 9 to 15 is 27.\nTravel distance from 9 to 16 is 41.\nTravel distance from 9 to 17 is 50.\nTravel distance from 10 to 0 is 33.\nTravel distance from 10 to 1 is 37.\nTravel distance from 10 to 2 is 46.\nTravel distance from 10 to 3 is 37.\nTravel distance from 10 to 4 is 36.\nTravel distance from 10 to 5 is 43.\nTravel distance from 10 to 6 is 39.\nTravel distance from 10 to 7 is 57.\nTravel distance from 10 to 8 is 51.\nTravel distance from 10 to 9 is 47.\nTravel distance from 10 to 11 is 72.\nTravel distance from 10 to 12 is 40.\nTravel distance from 10 to 13 is 52.\nTravel distance from 10 to 14 is 26.\nTravel distance from 10 to 15 is 43.\nTravel distance from 10 to 16 is 29.\nTravel distance from 10 to 17 is 44.\nTravel distance from 11 to 0 is 60.\nTravel distance from 11 to 1 is 65.\nTravel distance from 11 to 2 is 64.\nTravel distance from 11 to 3 is 78.\nTravel distance from 11 to 4 is 70.\nTravel distance from 11 to 5 is 69.\nTravel distance from 11 to 6 is 67.\nTravel distance from 11 to 7 is 91.\nTravel distance from 11 to 8 is 58.\nTravel distance from 11 to 9 is 80.\nTravel distance from 11 to 10 is 72.\nTravel distance from 11 to 12 is 70.\nTravel distance from 11 to 13 is 79.\nTravel distance from 11 to 14 is 56.\nTravel distance from 11 to 15 is 78.\nTravel distance from 11 to 16 is 57.\nTravel distance from 11 to 17 is 79.\nTravel distance from 12 to 0 is 30.\nTravel distance from 12 to 1 is 20.\nTravel distance from 12 to 2 is 46.\nTravel distance from 12 to 3 is 34.\nTravel distance from 12 to 4 is 52.\nTravel distance from 12 to 5 is 45.\nTravel distance from 12 to 6 is 19.\nTravel distance from 12 to 7 is 51.\nTravel distance from 12 to 8 is 47.\nTravel distance from 12 to 9 is 49.\nTravel distance from 12 to 10 is 40.\nTravel distance from 12 to 11 is 70.\nTravel distance from 12 to 13 is 33.\nTravel distance from 12 to 14 is 38.\nTravel distance from 12 to 15 is 35.\nTravel distance from 12 to 16 is 23.\nTravel distance from 12 to 17 is 38.\nTravel distance from 13 to 0 is 34.\nTravel distance from 13 to 1 is 35.\nTravel distance from 13 to 2 is 35.\nTravel distance from 13 to 3 is 27.\nTravel distance from 13 to 4 is 50.\nTravel distance from 13 to 5 is 40.\nTravel distance from 13 to 6 is 47.\nTravel distance from 13 to 7 is 57.\nTravel distance from 13 to 8 is 47.\nTravel distance from 13 to 9 is 49.\nTravel distance from 13 to 10 is 52.\nTravel distance from 13 to 11 is 79.\nTravel distance from 13 to 12 is 33.\nTravel distance from 13 to 14 is 36.\nTravel distance from 13 to 15 is 22.\nTravel distance from 13 to 16 is 42.\nTravel distance from 13 to 17 is 39.\nTravel distance from 14 to 0 is 37.\nTravel distance from 14 to 1 is 31.\nTravel distance from 14 to 2 is 32.\nTravel distance from 14 to 3 is 33.\nTravel distance from 14 to 4 is 14.\nTravel distance from 14 to 5 is 17.\nTravel distance from 14 to 6 is 45.\nTravel distance from 14 to 7 is 35.\nTravel distance from 14 to 8 is 45.\nTravel distance from 14 to 9 is 45.\nTravel distance from 14 to 10 is 26.\nTravel distance from 14 to 11 is 56.\nTravel distance from 14 to 12 is 38.\nTravel distance from 14 to 13 is 36.\nTravel distance from 14 to 15 is 35.\nTravel distance from 14 to 16 is 35.\nTravel distance from 14 to 17 is 45.\nTravel distance from 15 to 0 is 32.\nTravel distance from 15 to 1 is 26.\nTravel distance from 15 to 2 is 45.\nTravel distance from 15 to 3 is 29.\nTravel distance from 15 to 4 is 47.\nTravel distance from 15 to 5 is 50.\nTravel distance from 15 to 6 is 43.\nTravel distance from 15 to 7 is 63.\nTravel distance from 15 to 8 is 48.\nTravel distance from 15 to 9 is 27.\nTravel distance from 15 to 10 is 43.\nTravel distance from 15 to 11 is 78.\nTravel distance from 15 to 12 is 35.\nTravel distance from 15 to 13 is 22.\nTravel distance from 15 to 14 is 35.\nTravel distance from 15 to 16 is 33.\nTravel distance from 15 to 17 is 25.\nTravel distance from 16 to 0 is 18.\nTravel distance from 16 to 1 is 21.\nTravel distance from 16 to 2 is 44.\nTravel distance from 16 to 3 is 21.\nTravel distance from 16 to 4 is 48.\nTravel distance from 16 to 5 is 42.\nTravel distance from 16 to 6 is 20.\nTravel distance from 16 to 7 is 49.\nTravel distance from 16 to 8 is 47.\nTravel distance from 16 to 9 is 41.\nTravel distance from 16 to 10 is 29.\nTravel distance from 16 to 11 is 57.\nTravel distance from 16 to 12 is 23.\nTravel distance from 16 to 13 is 42.\nTravel distance from 16 to 14 is 35.\nTravel distance from 16 to 15 is 33.\nTravel distance from 16 to 17 is 36.\nTravel distance from 17 to 0 is 40.\nTravel distance from 17 to 1 is 18.\nTravel distance from 17 to 2 is 56.\nTravel distance from 17 to 3 is 46.\nTravel distance from 17 to 4 is 58.\nTravel distance from 17 to 5 is 52.\nTravel distance from 17 to 6 is 35.\nTravel distance from 17 to 7 is 67.\nTravel distance from 17 to 8 is 41.\nTravel distance from 17 to 9 is 50.\nTravel distance from 17 to 10 is 44.\nTravel distance from 17 to 11 is 79.\nTravel distance from 17 to 12 is 38.\nTravel distance from 17 to 13 is 39.\nTravel distance from 17 to 14 is 45.\nTravel distance from 17 to 15 is 25.\nTravel distance from 17 to 16 is 36.\nUse these distances to sum the travel from every block to its assigned station and obtain the plan’s score for opening 2 stations.\n\nIf you want to share a proposed plan, just drop it in this simple JSON shape so I can read it easily — something like:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nHere \"selected\" is the list of refill spots you decide to open, and \"assignments\" is a matching list that says, for each block, which opened spot it should use. Think of it like filling out a little form: pick the sites to activate, then point every block to one of them. This JSON is just a sketch of the expected shape, not the actual answer — I'll need the real identifiers from the instance to compute the best plan.\n\nPlease make sure all identifiers in your reply match exactly what's in the instance input — do not rename or invent labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "distance_matrix": [ [ 0, 26, 41, 33, 50, 46, 26, 53, 46, 23, 33, 60, 30, 34, 37, 32, 18, 40 ], [ 26, 0, 39, 33, 45, 44, 17, 63, 45, 43, 37, 65, 20, 35, 31, 26, 21, 18 ], [ 41, 39, 0, 49, 46, 15, 52, 45, 45, 51, 46, 64, 46, 35, 32, 45, 44, 56 ], [ 33, 33, 49, 0, 35, 45, 39, 44, 44, 33, 37, 78, 34, 27, 33, 29, 21, 46 ], [ 50, 45, 46, 35, 0, 31, 56, 45, 47, 55, 36, 70, 52, 50, 14, 47, 48, 58 ], [ 46, 44, 15, 45, 31, 0, 52, 52, 58, 53, 43, 69, 45, 40, 17, 50, 42, 52 ], [ 26, 17, 52, 39, 56, 52, 0, 57, 51, 45, 39, 67, 19, 47, 45, 43, 20, 35 ], [ 53, 63, 45, 44, 45, 52, 57, 0, 66, 57, 57, 91, 51, 57, 35, 63, 49, 67 ], [ 46, 45, 45, 44, 47, 58, 51, 66, 0, 54, 51, 58, 47, 47, 45, 48, 47, 41 ], [ 23, 43, 51, 33, 55, 53, 45, 57, 54, 0, 47, 80, 49, 49, 45, 27, 41, 50 ], [ 33, 37, 46, 37, 36, 43, 39, 57, 51, 47, 0, 72, 40, 52, 26, 43, 29, 44 ], [ 60, 65, 64, 78, 70, 69, 67, 91, 58, 80, 72, 0, 70, 79, 56, 78, 57, 79 ], [ 30, 20, 46, 34, 52, 45, 19, 51, 47, 49, 40, 70, 0, 33, 38, 35, 23, 38 ], [ 34, 35, 35, 27, 50, 40, 47, 57, 47, 49, 52, 79, 33, 0, 36, 22, 42, 39 ], [ 37, 31, 32, 33, 14, 17, 45, 35, 45, 45, 26, 56, 38, 36, 0, 35, 35, 45 ], [ 32, 26, 45, 29, 47, 50, 43, 63, 48, 27, 43, 78, 35, 22, 35, 0, 33, 25 ], [ 18, 21, 44, 21, 48, 42, 20, 49, 47, 41, 29, 57, 23, 42, 35, 33, 0, 36 ], [ 40, 18, 56, 46, 58, 52, 35, 67, 41, 50, 44, 79, 38, 39, 45, 25, 36, 0 ] ], "p": 2, "objective": 464.0 }, "solution": { "facilities": [ 1, 14 ], "assignments": [ 1, 1, 14, 14, 14, 14, 1, 14, 1, 1, 14, 14, 1, 1, 14, 1, 1, 1 ] }, "obj": 464.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 2, "sites": [ { "id": 0, "distances": { "0": 0, "1": 26, "2": 41, "3": 33, "4": 50, "5": 46, "6": 26, "7": 53, "8": 46, "9": 23, "10": 33, "11": 60, "12": 30, "13": 34, "14": 37, "15": 32, "16": 18, "17": 40 } }, { "id": 1, "distances": { "0": 26, "1": 0, "2": 39, "3": 33, "4": 45, "5": 44, "6": 17, "7": 63, "8": 45, "9": 43, "10": 37, "11": 65, "12": 20, "13": 35, "14": 31, "15": 26, "16": 21, "17": 18 } }, { "id": 2, "distances": { "0": 41, "1": 39, "2": 0, "3": 49, "4": 46, "5": 15, "6": 52, "7": 45, "8": 45, "9": 51, "10": 46, "11": 64, "12": 46, "13": 35, "14": 32, "15": 45, "16": 44, "17": 56 } }, { "id": 3, "distances": { "0": 33, "1": 33, "2": 49, "3": 0, "4": 35, "5": 45, "6": 39, "7": 44, "8": 44, "9": 33, "10": 37, "11": 78, "12": 34, "13": 27, "14": 33, "15": 29, "16": 21, "17": 46 } }, { "id": 4, "distances": { "0": 50, "1": 45, "2": 46, "3": 35, "4": 0, "5": 31, "6": 56, "7": 45, "8": 47, "9": 55, "10": 36, "11": 70, "12": 52, "13": 50, "14": 14, "15": 47, "16": 48, "17": 58 } }, { "id": 5, "distances": { "0": 46, "1": 44, "2": 15, "3": 45, "4": 31, "5": 0, "6": 52, "7": 52, "8": 58, "9": 53, "10": 43, "11": 69, "12": 45, "13": 40, "14": 17, "15": 50, "16": 42, "17": 52 } }, { "id": 6, "distances": { "0": 26, "1": 17, "2": 52, "3": 39, "4": 56, "5": 52, "6": 0, "7": 57, "8": 51, "9": 45, "10": 39, "11": 67, "12": 19, "13": 47, "14": 45, "15": 43, "16": 20, "17": 35 } }, { "id": 7, "distances": { "0": 53, "1": 63, "2": 45, "3": 44, "4": 45, "5": 52, "6": 57, "7": 0, "8": 66, "9": 57, "10": 57, "11": 91, "12": 51, "13": 57, "14": 35, "15": 63, "16": 49, "17": 67 } }, { "id": 8, "distances": { "0": 46, "1": 45, "2": 45, "3": 44, "4": 47, "5": 58, "6": 51, "7": 66, "8": 0, "9": 54, "10": 51, "11": 58, "12": 47, "13": 47, "14": 45, "15": 48, "16": 47, "17": 41 } }, { "id": 9, "distances": { "0": 23, "1": 43, "2": 51, "3": 33, "4": 55, "5": 53, "6": 45, "7": 57, "8": 54, "9": 0, "10": 47, "11": 80, "12": 49, "13": 49, "14": 45, "15": 27, "16": 41, "17": 50 } }, { "id": 10, "distances": { "0": 33, "1": 37, "2": 46, "3": 37, "4": 36, "5": 43, "6": 39, "7": 57, "8": 51, "9": 47, "10": 0, "11": 72, "12": 40, "13": 52, "14": 26, "15": 43, "16": 29, "17": 44 } }, { "id": 11, "distances": { "0": 60, "1": 65, "2": 64, "3": 78, "4": 70, "5": 69, "6": 67, "7": 91, "8": 58, "9": 80, "10": 72, "11": 0, "12": 70, "13": 79, "14": 56, "15": 78, "16": 57, "17": 79 } }, { "id": 12, "distances": { "0": 30, "1": 20, "2": 46, "3": 34, "4": 52, "5": 45, "6": 19, "7": 51, "8": 47, "9": 49, "10": 40, "11": 70, "12": 0, "13": 33, "14": 38, "15": 35, "16": 23, "17": 38 } }, { "id": 13, "distances": { "0": 34, "1": 35, "2": 35, "3": 27, "4": 50, "5": 40, "6": 47, "7": 57, "8": 47, "9": 49, "10": 52, "11": 79, "12": 33, "13": 0, "14": 36, "15": 22, "16": 42, "17": 39 } }, { "id": 14, "distances": { "0": 37, "1": 31, "2": 32, "3": 33, "4": 14, "5": 17, "6": 45, "7": 35, "8": 45, "9": 45, "10": 26, "11": 56, "12": 38, "13": 36, "14": 0, "15": 35, "16": 35, "17": 45 } }, { "id": 15, "distances": { "0": 32, "1": 26, "2": 45, "3": 29, "4": 47, "5": 50, "6": 43, "7": 63, "8": 48, "9": 27, "10": 43, "11": 78, "12": 35, "13": 22, "14": 35, "15": 0, "16": 33, "17": 25 } }, { "id": 16, "distances": { "0": 18, "1": 21, "2": 44, "3": 21, "4": 48, "5": 42, "6": 20, "7": 49, "8": 47, "9": 41, "10": 29, "11": 57, "12": 23, "13": 42, "14": 35, "15": 33, "16": 0, "17": 36 } }, { "id": 17, "distances": { "0": 40, "1": 18, "2": 56, "3": 46, "4": 58, "5": 52, "6": 35, "7": 67, "8": 41, "9": 50, "10": 44, "11": 79, "12": 38, "13": 39, "14": 45, "15": 25, "16": 36, "17": 0 } } ], "objective": 464.0 }, "solution_variant": { "selected": [ 1, 14 ], "assignments": [ 1, 1, 14, 14, 14, 14, 1, 14, 1, 1, 14, 14, 1, 1, 14, 1, 1, 1 ] }, "context_index": 47, "input_format": "nl", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "On a slow afternoon the ops manager was sketching a map: pick a fixed number of stroller rental kiosks from the suggested sites and link each entrance area to a single open kiosk (nothing gets left out or doubled up). The practical yardstick is clear — for each entrance figure the walk to its linked kiosk, sum all those walks, and the arrangement with the smallest total walking distance makes shoppers happiest. The detailed site options and distances are given below.\n\nThe ops manager recorded 16 total locations, must open 5 kiosks, and listed the locations as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.\nEntrance 0 to kiosk 1: walking distance 37.\nEntrance 0 to kiosk 2: walking distance 36.\nEntrance 0 to kiosk 3: walking distance 26.\nEntrance 0 to kiosk 4: walking distance 53.\nEntrance 0 to kiosk 5: walking distance 31.\nEntrance 0 to kiosk 6: walking distance 66.\nEntrance 0 to kiosk 7: walking distance 20.\nEntrance 0 to kiosk 8: walking distance 47.\nEntrance 0 to kiosk 9: walking distance 54.\nEntrance 0 to kiosk 10: walking distance 52.\nEntrance 0 to kiosk 11: walking distance 41.\nEntrance 0 to kiosk 12: walking distance 48.\nEntrance 0 to kiosk 13: walking distance 53.\nEntrance 0 to kiosk 14: walking distance 22.\nEntrance 0 to kiosk 15: walking distance 40.\nEntrance 1 to kiosk 0: walking distance 37.\nEntrance 1 to kiosk 2: walking distance 43.\nEntrance 1 to kiosk 3: walking distance 11.\nEntrance 1 to kiosk 4: walking distance 58.\nEntrance 1 to kiosk 5: walking distance 39.\nEntrance 1 to kiosk 6: walking distance 51.\nEntrance 1 to kiosk 7: walking distance 31.\nEntrance 1 to kiosk 8: walking distance 37.\nEntrance 1 to kiosk 9: walking distance 44.\nEntrance 1 to kiosk 10: walking distance 50.\nEntrance 1 to kiosk 11: walking distance 44.\nEntrance 1 to kiosk 12: walking distance 35.\nEntrance 1 to kiosk 13: walking distance 49.\nEntrance 1 to kiosk 14: walking distance 37.\nEntrance 1 to kiosk 15: walking distance 26.\nEntrance 2 to kiosk 0: walking distance 36.\nEntrance 2 to kiosk 1: walking distance 43.\nEntrance 2 to kiosk 3: walking distance 40.\nEntrance 2 to kiosk 4: walking distance 37.\nEntrance 2 to kiosk 5: walking distance 37.\nEntrance 2 to kiosk 6: walking distance 48.\nEntrance 2 to kiosk 7: walking distance 34.\nEntrance 2 to kiosk 8: walking distance 36.\nEntrance 2 to kiosk 9: walking distance 23.\nEntrance 2 to kiosk 10: walking distance 61.\nEntrance 2 to kiosk 11: walking distance 36.\nEntrance 2 to kiosk 12: walking distance 35.\nEntrance 2 to kiosk 13: walking distance 31.\nEntrance 2 to kiosk 14: walking distance 33.\nEntrance 2 to kiosk 15: walking distance 27.\nEntrance 3 to kiosk 0: walking distance 26.\nEntrance 3 to kiosk 1: walking distance 11.\nEntrance 3 to kiosk 2: walking distance 40.\nEntrance 3 to kiosk 4: walking distance 64.\nEntrance 3 to kiosk 5: walking distance 28.\nEntrance 3 to kiosk 6: walking distance 54.\nEntrance 3 to kiosk 7: walking distance 24.\nEntrance 3 to kiosk 8: walking distance 48.\nEntrance 3 to kiosk 9: walking distance 54.\nEntrance 3 to kiosk 10: walking distance 56.\nEntrance 3 to kiosk 11: walking distance 55.\nEntrance 3 to kiosk 12: walking distance 46.\nEntrance 3 to kiosk 13: walking distance 60.\nEntrance 3 to kiosk 14: walking distance 26.\nEntrance 3 to kiosk 15: walking distance 37.\nEntrance 4 to kiosk 0: walking distance 53.\nEntrance 4 to kiosk 1: walking distance 58.\nEntrance 4 to kiosk 2: walking distance 37.\nEntrance 4 to kiosk 3: walking distance 64.\nEntrance 4 to kiosk 5: walking distance 52.\nEntrance 4 to kiosk 6: walking distance 60.\nEntrance 4 to kiosk 7: walking distance 49.\nEntrance 4 to kiosk 8: walking distance 40.\nEntrance 4 to kiosk 9: walking distance 44.\nEntrance 4 to kiosk 10: walking distance 66.\nEntrance 4 to kiosk 11: walking distance 42.\nEntrance 4 to kiosk 12: walking distance 45.\nEntrance 4 to kiosk 13: walking distance 23.\nEntrance 4 to kiosk 14: walking distance 50.\nEntrance 4 to kiosk 15: walking distance 44.\nEntrance 5 to kiosk 0: walking distance 31.\nEntrance 5 to kiosk 1: walking distance 39.\nEntrance 5 to kiosk 2: walking distance 37.\nEntrance 5 to kiosk 3: walking distance 28.\nEntrance 5 to kiosk 4: walking distance 52.\nEntrance 5 to kiosk 6: walking distance 49.\nEntrance 5 to kiosk 7: walking distance 29.\nEntrance 5 to kiosk 8: walking distance 43.\nEntrance 5 to kiosk 9: walking distance 33.\nEntrance 5 to kiosk 10: walking distance 45.\nEntrance 5 to kiosk 11: walking distance 37.\nEntrance 5 to kiosk 12: walking distance 38.\nEntrance 5 to kiosk 13: walking distance 52.\nEntrance 5 to kiosk 14: walking distance 15.\nEntrance 5 to kiosk 15: walking distance 24.\nEntrance 6 to kiosk 0: walking distance 66.\nEntrance 6 to kiosk 1: walking distance 51.\nEntrance 6 to kiosk 2: walking distance 48.\nEntrance 6 to kiosk 3: walking distance 54.\nEntrance 6 to kiosk 4: walking distance 60.\nEntrance 6 to kiosk 5: walking distance 49.\nEntrance 6 to kiosk 7: walking distance 46.\nEntrance 6 to kiosk 8: walking distance 53.\nEntrance 6 to kiosk 9: walking distance 46.\nEntrance 6 to kiosk 10: walking distance 70.\nEntrance 6 to kiosk 11: walking distance 44.\nEntrance 6 to kiosk 12: walking distance 45.\nEntrance 6 to kiosk 13: walking distance 64.\nEntrance 6 to kiosk 14: walking distance 62.\nEntrance 6 to kiosk 15: walking distance 41.\nEntrance 7 to kiosk 0: walking distance 20.\nEntrance 7 to kiosk 1: walking distance 31.\nEntrance 7 to kiosk 2: walking distance 34.\nEntrance 7 to kiosk 3: walking distance 24.\nEntrance 7 to kiosk 4: walking distance 49.\nEntrance 7 to kiosk 5: walking distance 29.\nEntrance 7 to kiosk 6: walking distance 46.\nEntrance 7 to kiosk 8: walking distance 40.\nEntrance 7 to kiosk 9: walking distance 39.\nEntrance 7 to kiosk 10: walking distance 50.\nEntrance 7 to kiosk 11: walking distance 42.\nEntrance 7 to kiosk 12: walking distance 35.\nEntrance 7 to kiosk 13: walking distance 44.\nEntrance 7 to kiosk 14: walking distance 20.\nEntrance 7 to kiosk 15: walking distance 21.\nEntrance 8 to kiosk 0: walking distance 47.\nEntrance 8 to kiosk 1: walking distance 37.\nEntrance 8 to kiosk 2: walking distance 36.\nEntrance 8 to kiosk 3: walking distance 48.\nEntrance 8 to kiosk 4: walking distance 40.\nEntrance 8 to kiosk 5: walking distance 43.\nEntrance 8 to kiosk 6: walking distance 53.\nEntrance 8 to kiosk 7: walking distance 40.\nEntrance 8 to kiosk 9: walking distance 41.\nEntrance 8 to kiosk 10: walking distance 52.\nEntrance 8 to kiosk 11: walking distance 41.\nEntrance 8 to kiosk 12: walking distance 38.\nEntrance 8 to kiosk 13: walking distance 25.\nEntrance 8 to kiosk 14: walking distance 47.\nEntrance 8 to kiosk 15: walking distance 35.\nEntrance 9 to kiosk 0: walking distance 54.\nEntrance 9 to kiosk 1: walking distance 44.\nEntrance 9 to kiosk 2: walking distance 23.\nEntrance 9 to kiosk 3: walking distance 54.\nEntrance 9 to kiosk 4: walking distance 44.\nEntrance 9 to kiosk 5: walking distance 33.\nEntrance 9 to kiosk 6: walking distance 46.\nEntrance 9 to kiosk 7: walking distance 39.\nEntrance 9 to kiosk 8: walking distance 41.\nEntrance 9 to kiosk 10: walking distance 63.\nEntrance 9 to kiosk 11: walking distance 47.\nEntrance 9 to kiosk 12: walking distance 34.\nEntrance 9 to kiosk 13: walking distance 29.\nEntrance 9 to kiosk 14: walking distance 42.\nEntrance 9 to kiosk 15: walking distance 18.\nEntrance 10 to kiosk 0: walking distance 52.\nEntrance 10 to kiosk 1: walking distance 50.\nEntrance 10 to kiosk 2: walking distance 61.\nEntrance 10 to kiosk 3: walking distance 56.\nEntrance 10 to kiosk 4: walking distance 66.\nEntrance 10 to kiosk 5: walking distance 45.\nEntrance 10 to kiosk 6: walking distance 70.\nEntrance 10 to kiosk 7: walking distance 50.\nEntrance 10 to kiosk 8: walking distance 52.\nEntrance 10 to kiosk 9: walking distance 63.\nEntrance 10 to kiosk 11: walking distance 56.\nEntrance 10 to kiosk 12: walking distance 49.\nEntrance 10 to kiosk 13: walking distance 46.\nEntrance 10 to kiosk 14: walking distance 30.\nEntrance 10 to kiosk 15: walking distance 53.\nEntrance 11 to kiosk 0: walking distance 41.\nEntrance 11 to kiosk 1: walking distance 44.\nEntrance 11 to kiosk 2: walking distance 36.\nEntrance 11 to kiosk 3: walking distance 55.\nEntrance 11 to kiosk 4: walking distance 42.\nEntrance 11 to kiosk 5: walking distance 37.\nEntrance 11 to kiosk 6: walking distance 44.\nEntrance 11 to kiosk 7: walking distance 42.\nEntrance 11 to kiosk 8: walking distance 41.\nEntrance 11 to kiosk 9: walking distance 47.\nEntrance 11 to kiosk 10: walking distance 56.\nEntrance 11 to kiosk 12: walking distance 33.\nEntrance 11 to kiosk 13: walking distance 47.\nEntrance 11 to kiosk 14: walking distance 45.\nEntrance 11 to kiosk 15: walking distance 31.\nEntrance 12 to kiosk 0: walking distance 48.\nEntrance 12 to kiosk 1: walking distance 35.\nEntrance 12 to kiosk 2: walking distance 35.\nEntrance 12 to kiosk 3: walking distance 46.\nEntrance 12 to kiosk 4: walking distance 45.\nEntrance 12 to kiosk 5: walking distance 38.\nEntrance 12 to kiosk 6: walking distance 45.\nEntrance 12 to kiosk 7: walking distance 35.\nEntrance 12 to kiosk 8: walking distance 38.\nEntrance 12 to kiosk 9: walking distance 34.\nEntrance 12 to kiosk 10: walking distance 49.\nEntrance 12 to kiosk 11: walking distance 33.\nEntrance 12 to kiosk 13: walking distance 33.\nEntrance 12 to kiosk 14: walking distance 37.\nEntrance 12 to kiosk 15: walking distance 30.\nEntrance 13 to kiosk 0: walking distance 53.\nEntrance 13 to kiosk 1: walking distance 49.\nEntrance 13 to kiosk 2: walking distance 31.\nEntrance 13 to kiosk 3: walking distance 60.\nEntrance 13 to kiosk 4: walking distance 23.\nEntrance 13 to kiosk 5: walking distance 52.\nEntrance 13 to kiosk 6: walking distance 64.\nEntrance 13 to kiosk 7: walking distance 44.\nEntrance 13 to kiosk 8: walking distance 25.\nEntrance 13 to kiosk 9: walking distance 29.\nEntrance 13 to kiosk 10: walking distance 46.\nEntrance 13 to kiosk 11: walking distance 47.\nEntrance 13 to kiosk 12: walking distance 33.\nEntrance 13 to kiosk 14: walking distance 56.\nEntrance 13 to kiosk 15: walking distance 39.\nEntrance 14 to kiosk 0: walking distance 22.\nEntrance 14 to kiosk 1: walking distance 37.\nEntrance 14 to kiosk 2: walking distance 33.\nEntrance 14 to kiosk 3: walking distance 26.\nEntrance 14 to kiosk 4: walking distance 50.\nEntrance 14 to kiosk 5: walking distance 15.\nEntrance 14 to kiosk 6: walking distance 62.\nEntrance 14 to kiosk 7: walking distance 20.\nEntrance 14 to kiosk 8: walking distance 47.\nEntrance 14 to kiosk 9: walking distance 42.\nEntrance 14 to kiosk 10: walking distance 30.\nEntrance 14 to kiosk 11: walking distance 45.\nEntrance 14 to kiosk 12: walking distance 37.\nEntrance 14 to kiosk 13: walking distance 56.\nEntrance 14 to kiosk 15: walking distance 24.\nEntrance 15 to kiosk 0: walking distance 40.\nEntrance 15 to kiosk 1: walking distance 26.\nEntrance 15 to kiosk 2: walking distance 27.\nEntrance 15 to kiosk 3: walking distance 37.\nEntrance 15 to kiosk 4: walking distance 44.\nEntrance 15 to kiosk 5: walking distance 24.\nEntrance 15 to kiosk 6: walking distance 41.\nEntrance 15 to kiosk 7: walking distance 21.\nEntrance 15 to kiosk 8: walking distance 35.\nEntrance 15 to kiosk 9: walking distance 18.\nEntrance 15 to kiosk 10: walking distance 53.\nEntrance 15 to kiosk 11: walking distance 31.\nEntrance 15 to kiosk 12: walking distance 30.\nEntrance 15 to kiosk 13: walking distance 39.\nEntrance 15 to kiosk 14: walking distance 24.\nThe ops manager will sum these walking distances to evaluate and choose the 5-kiosk arrangement among the 16 locations that minimizes total walking.\n\nIf you want the answer in a neat, machine-friendly shape, just follow this relaxed JSON layout — nothing fancy, just a simple form that matches the story:\n\n{\n \"solution\": {\n \"selected\": [\"\", \"\", ...],\n \"assignments\": [\"\", \"\", ...]\n }\n}\n\n\"selected\" is where you'd list the kiosk sites you decide to open (placeholders for the actual site identifiers). \"assignments\" lists, for each entrance, which opened kiosk that entrance is linked to — again placeholders showing the shape. Think of it like filling out a little form: which kiosks are open, and which kiosk each entrance walks to.\n\nThis JSON is just a sketch of the expected shape, not the real answer.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "distance_matrix": [ [ 0, 37, 36, 26, 53, 31, 66, 20, 47, 54, 52, 41, 48, 53, 22, 40 ], [ 37, 0, 43, 11, 58, 39, 51, 31, 37, 44, 50, 44, 35, 49, 37, 26 ], [ 36, 43, 0, 40, 37, 37, 48, 34, 36, 23, 61, 36, 35, 31, 33, 27 ], [ 26, 11, 40, 0, 64, 28, 54, 24, 48, 54, 56, 55, 46, 60, 26, 37 ], [ 53, 58, 37, 64, 0, 52, 60, 49, 40, 44, 66, 42, 45, 23, 50, 44 ], [ 31, 39, 37, 28, 52, 0, 49, 29, 43, 33, 45, 37, 38, 52, 15, 24 ], [ 66, 51, 48, 54, 60, 49, 0, 46, 53, 46, 70, 44, 45, 64, 62, 41 ], [ 20, 31, 34, 24, 49, 29, 46, 0, 40, 39, 50, 42, 35, 44, 20, 21 ], [ 47, 37, 36, 48, 40, 43, 53, 40, 0, 41, 52, 41, 38, 25, 47, 35 ], [ 54, 44, 23, 54, 44, 33, 46, 39, 41, 0, 63, 47, 34, 29, 42, 18 ], [ 52, 50, 61, 56, 66, 45, 70, 50, 52, 63, 0, 56, 49, 46, 30, 53 ], [ 41, 44, 36, 55, 42, 37, 44, 42, 41, 47, 56, 0, 33, 47, 45, 31 ], [ 48, 35, 35, 46, 45, 38, 45, 35, 38, 34, 49, 33, 0, 33, 37, 30 ], [ 53, 49, 31, 60, 23, 52, 64, 44, 25, 29, 46, 47, 33, 0, 56, 39 ], [ 22, 37, 33, 26, 50, 15, 62, 20, 47, 42, 30, 45, 37, 56, 0, 24 ], [ 40, 26, 27, 37, 44, 24, 41, 21, 35, 18, 53, 31, 30, 39, 24, 0 ] ], "p": 5, "objective": 252.0 }, "solution": { "facilities": [ 1, 6, 13, 14, 15 ], "assignments": [ 14, 1, 15, 1, 13, 14, 6, 14, 13, 15, 14, 15, 15, 13, 14, 15 ] }, "obj": 252.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 16, "num_open": 5, "sites": [ { "id": 0, "distances": { "0": 0, "1": 37, "2": 36, "3": 26, "4": 53, "5": 31, "6": 66, "7": 20, "8": 47, "9": 54, "10": 52, "11": 41, "12": 48, "13": 53, "14": 22, "15": 40 } }, { "id": 1, "distances": { "0": 37, "1": 0, "2": 43, "3": 11, "4": 58, "5": 39, "6": 51, "7": 31, "8": 37, "9": 44, "10": 50, "11": 44, "12": 35, "13": 49, "14": 37, "15": 26 } }, { "id": 2, "distances": { "0": 36, "1": 43, "2": 0, "3": 40, "4": 37, "5": 37, "6": 48, "7": 34, "8": 36, "9": 23, "10": 61, "11": 36, "12": 35, "13": 31, "14": 33, "15": 27 } }, { "id": 3, "distances": { "0": 26, "1": 11, "2": 40, "3": 0, "4": 64, "5": 28, "6": 54, "7": 24, "8": 48, "9": 54, "10": 56, "11": 55, "12": 46, "13": 60, "14": 26, "15": 37 } }, { "id": 4, "distances": { "0": 53, "1": 58, "2": 37, "3": 64, "4": 0, "5": 52, "6": 60, "7": 49, "8": 40, "9": 44, "10": 66, "11": 42, "12": 45, "13": 23, "14": 50, "15": 44 } }, { "id": 5, "distances": { "0": 31, "1": 39, "2": 37, "3": 28, "4": 52, "5": 0, "6": 49, "7": 29, "8": 43, "9": 33, "10": 45, "11": 37, "12": 38, "13": 52, "14": 15, "15": 24 } }, { "id": 6, "distances": { "0": 66, "1": 51, "2": 48, "3": 54, "4": 60, "5": 49, "6": 0, "7": 46, "8": 53, "9": 46, "10": 70, "11": 44, "12": 45, "13": 64, "14": 62, "15": 41 } }, { "id": 7, "distances": { "0": 20, "1": 31, "2": 34, "3": 24, "4": 49, "5": 29, "6": 46, "7": 0, "8": 40, "9": 39, "10": 50, "11": 42, "12": 35, "13": 44, "14": 20, "15": 21 } }, { "id": 8, "distances": { "0": 47, "1": 37, "2": 36, "3": 48, "4": 40, "5": 43, "6": 53, "7": 40, "8": 0, "9": 41, "10": 52, "11": 41, "12": 38, "13": 25, "14": 47, "15": 35 } }, { "id": 9, "distances": { "0": 54, "1": 44, "2": 23, "3": 54, "4": 44, "5": 33, "6": 46, "7": 39, "8": 41, "9": 0, "10": 63, "11": 47, "12": 34, "13": 29, "14": 42, "15": 18 } }, { "id": 10, "distances": { "0": 52, "1": 50, "2": 61, "3": 56, "4": 66, "5": 45, "6": 70, "7": 50, "8": 52, "9": 63, "10": 0, "11": 56, "12": 49, "13": 46, "14": 30, "15": 53 } }, { "id": 11, "distances": { "0": 41, "1": 44, "2": 36, "3": 55, "4": 42, "5": 37, "6": 44, "7": 42, "8": 41, "9": 47, "10": 56, "11": 0, "12": 33, "13": 47, "14": 45, "15": 31 } }, { "id": 12, "distances": { "0": 48, "1": 35, "2": 35, "3": 46, "4": 45, "5": 38, "6": 45, "7": 35, "8": 38, "9": 34, "10": 49, "11": 33, "12": 0, "13": 33, "14": 37, "15": 30 } }, { "id": 13, "distances": { "0": 53, "1": 49, "2": 31, "3": 60, "4": 23, "5": 52, "6": 64, "7": 44, "8": 25, "9": 29, "10": 46, "11": 47, "12": 33, "13": 0, "14": 56, "15": 39 } }, { "id": 14, "distances": { "0": 22, "1": 37, "2": 33, "3": 26, "4": 50, "5": 15, "6": 62, "7": 20, "8": 47, "9": 42, "10": 30, "11": 45, "12": 37, "13": 56, "14": 0, "15": 24 } }, { "id": 15, "distances": { "0": 40, "1": 26, "2": 27, "3": 37, "4": 44, "5": 24, "6": 41, "7": 21, "8": 35, "9": 18, "10": 53, "11": 31, "12": 30, "13": 39, "14": 24, "15": 0 } } ], "objective": 252.0 }, "solution_variant": { "selected": [ 1, 6, 13, 14, 15 ], "assignments": [ 14, 1, 15, 1, 13, 14, 6, 14, 13, 15, 14, 15, 15, 13, 14, 15 ] }, "context_index": 48, "input_format": "nl", "input_index_base": 0 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Back in the planning meeting the job was to pick a fixed number of pop-up locations from several candidate spots and assign every attending neighborhood to one chosen stall. What counts as a better plan is how little it makes everyone travel overall: for each neighborhood take its distance to the stall it’s assigned to, sum those distances across all neighborhoods, and pick the arrangement with the lowest total. Every neighborhood must be assigned to exactly one open stall, and the number of stalls is set in advance. The detailed list of locations and pairwise distances is provided below.\n\n# total_candidate_locations=18\n# num_stalls_to_open=1\n# location_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18\norigin_location_id,destination_location_id,travel_distance\n1,2,59\n1,3,24\n1,4,28\n1,5,37\n1,6,65\n1,7,37\n1,8,50\n1,9,57\n1,10,51\n1,11,60\n1,12,60\n1,13,58\n1,14,41\n1,15,49\n1,16,54\n1,17,40\n1,18,41\n2,1,59\n2,3,53\n2,4,53\n2,5,63\n2,6,60\n2,7,55\n2,8,64\n2,9,69\n2,10,59\n2,11,66\n2,12,65\n2,13,64\n2,14,70\n2,15,51\n2,16,71\n2,17,49\n2,18,40\n3,1,24\n3,2,53\n3,4,35\n3,5,22\n3,6,55\n3,7,13\n3,8,31\n3,9,35\n3,10,38\n3,11,41\n3,12,36\n3,13,54\n3,14,56\n3,15,33\n3,16,30\n3,17,16\n3,18,22\n4,1,28\n4,2,53\n4,3,35\n4,5,34\n4,6,50\n4,7,37\n4,8,46\n4,9,35\n4,10,38\n4,11,32\n4,12,35\n4,13,53\n4,14,50\n4,15,22\n4,16,43\n4,17,31\n4,18,13\n5,1,37\n5,2,63\n5,3,22\n5,4,34\n5,6,48\n5,7,35\n5,8,42\n5,9,40\n5,10,56\n5,11,35\n5,12,53\n5,13,62\n5,14,55\n5,15,16\n5,16,26\n5,17,38\n5,18,23\n6,1,65\n6,2,60\n6,3,55\n6,4,50\n6,5,48\n6,7,68\n6,8,54\n6,9,64\n6,10,43\n6,11,70\n6,12,54\n6,13,86\n6,14,82\n6,15,32\n6,16,65\n6,17,39\n6,18,43\n7,1,37\n7,2,55\n7,3,13\n7,4,37\n7,5,35\n7,6,68\n7,8,44\n7,9,38\n7,10,51\n7,11,51\n7,12,49\n7,13,60\n7,14,64\n7,15,38\n7,16,43\n7,17,29\n7,18,34\n8,1,50\n8,2,64\n8,3,31\n8,4,46\n8,5,42\n8,6,54\n8,7,44\n8,9,40\n8,10,49\n8,11,52\n8,12,59\n8,13,64\n8,14,39\n8,15,44\n8,16,30\n8,17,15\n8,18,33\n9,1,57\n9,2,69\n9,3,35\n9,4,35\n9,5,40\n9,6,64\n9,7,38\n9,8,40\n9,10,53\n9,11,41\n9,12,54\n9,13,62\n9,14,57\n9,15,34\n9,16,28\n9,17,25\n9,18,32\n10,1,51\n10,2,59\n10,3,38\n10,4,38\n10,5,56\n10,6,43\n10,7,51\n10,8,49\n10,9,53\n10,11,50\n10,12,57\n10,13,64\n10,14,62\n10,15,44\n10,16,59\n10,17,34\n10,18,35\n11,1,60\n11,2,66\n11,3,41\n11,4,32\n11,5,35\n11,6,70\n11,7,51\n11,8,52\n11,9,41\n11,10,50\n11,12,51\n11,13,67\n11,14,67\n11,15,38\n11,16,49\n11,17,37\n11,18,29\n12,1,60\n12,2,65\n12,3,36\n12,4,35\n12,5,53\n12,6,54\n12,7,49\n12,8,59\n12,9,54\n12,10,57\n12,11,51\n12,13,62\n12,14,72\n12,15,41\n12,16,51\n12,17,44\n12,18,32\n13,1,58\n13,2,64\n13,3,54\n13,4,53\n13,5,62\n13,6,86\n13,7,60\n13,8,64\n13,9,62\n13,10,64\n13,11,67\n13,12,62\n13,14,53\n13,15,62\n13,16,70\n13,17,50\n13,18,53\n14,1,41\n14,2,70\n14,3,56\n14,4,50\n14,5,55\n14,6,82\n14,7,64\n14,8,39\n14,9,57\n14,10,62\n14,11,67\n14,12,72\n14,13,53\n14,15,59\n14,16,43\n14,17,54\n14,18,50\n15,1,49\n15,2,51\n15,3,33\n15,4,22\n15,5,16\n15,6,32\n15,7,38\n15,8,44\n15,9,34\n15,10,44\n15,11,38\n15,12,41\n15,13,62\n15,14,59\n15,16,42\n15,17,29\n15,18,11\n16,1,54\n16,2,71\n16,3,30\n16,4,43\n16,5,26\n16,6,65\n16,7,43\n16,8,30\n16,9,28\n16,10,59\n16,11,49\n16,12,51\n16,13,70\n16,14,43\n16,15,42\n16,17,37\n16,18,40\n17,1,40\n17,2,49\n17,3,16\n17,4,31\n17,5,38\n17,6,39\n17,7,29\n17,8,15\n17,9,25\n17,10,34\n17,11,37\n17,12,44\n17,13,50\n17,14,54\n17,15,29\n17,16,37\n17,18,18\n18,1,41\n18,2,40\n18,3,22\n18,4,13\n18,5,23\n18,6,43\n18,7,34\n18,8,33\n18,9,32\n18,10,35\n18,11,29\n18,12,32\n18,13,53\n18,14,50\n18,15,11\n18,16,40\n18,17,18\n\nIf you want the final reply in a simple machine-friendly shape, just follow this little JSON sketch for how I expect the answer to be laid out.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis is just a template showing the shape I expect: \"selected\" lists which pop-up stalls you decide to open, and \"assignments\" lists, for every neighborhood in the same order as the instance input, which opened stall that neighborhood is assigned to. Think of it like a short form: pick the open sites, then say which site each neighborhood goes to.\n\nThis JSON is only a sketch of the expected shape, not the actual answer. Also, be sure to use the exact identifiers from the instance input — don't rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "distance_matrix": [ [ 0, 59, 24, 28, 37, 65, 37, 50, 57, 51, 60, 60, 58, 41, 49, 54, 40, 41 ], [ 59, 0, 53, 53, 63, 60, 55, 64, 69, 59, 66, 65, 64, 70, 51, 71, 49, 40 ], [ 24, 53, 0, 35, 22, 55, 13, 31, 35, 38, 41, 36, 54, 56, 33, 30, 16, 22 ], [ 28, 53, 35, 0, 34, 50, 37, 46, 35, 38, 32, 35, 53, 50, 22, 43, 31, 13 ], [ 37, 63, 22, 34, 0, 48, 35, 42, 40, 56, 35, 53, 62, 55, 16, 26, 38, 23 ], [ 65, 60, 55, 50, 48, 0, 68, 54, 64, 43, 70, 54, 86, 82, 32, 65, 39, 43 ], [ 37, 55, 13, 37, 35, 68, 0, 44, 38, 51, 51, 49, 60, 64, 38, 43, 29, 34 ], [ 50, 64, 31, 46, 42, 54, 44, 0, 40, 49, 52, 59, 64, 39, 44, 30, 15, 33 ], [ 57, 69, 35, 35, 40, 64, 38, 40, 0, 53, 41, 54, 62, 57, 34, 28, 25, 32 ], [ 51, 59, 38, 38, 56, 43, 51, 49, 53, 0, 50, 57, 64, 62, 44, 59, 34, 35 ], [ 60, 66, 41, 32, 35, 70, 51, 52, 41, 50, 0, 51, 67, 67, 38, 49, 37, 29 ], [ 60, 65, 36, 35, 53, 54, 49, 59, 54, 57, 51, 0, 62, 72, 41, 51, 44, 32 ], [ 58, 64, 54, 53, 62, 86, 60, 64, 62, 64, 67, 62, 0, 53, 62, 70, 50, 53 ], [ 41, 70, 56, 50, 55, 82, 64, 39, 57, 62, 67, 72, 53, 0, 59, 43, 54, 50 ], [ 49, 51, 33, 22, 16, 32, 38, 44, 34, 44, 38, 41, 62, 59, 0, 42, 29, 11 ], [ 54, 71, 30, 43, 26, 65, 43, 30, 28, 59, 49, 51, 70, 43, 42, 0, 37, 40 ], [ 40, 49, 16, 31, 38, 39, 29, 15, 25, 34, 37, 44, 50, 54, 29, 37, 0, 18 ], [ 41, 40, 22, 13, 23, 43, 34, 33, 32, 35, 29, 32, 53, 50, 11, 40, 18, 0 ] ], "p": 1, "objective": 549.0 }, "solution": { "facilities": [ 17 ], "assignments": [ 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17 ] }, "obj": 549.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 1, "sites": [ { "id": 1, "distances": { "1": 0, "2": 59, "3": 24, "4": 28, "5": 37, "6": 65, "7": 37, "8": 50, "9": 57, "10": 51, "11": 60, "12": 60, "13": 58, "14": 41, "15": 49, "16": 54, "17": 40, "18": 41 } }, { "id": 2, "distances": { "1": 59, "2": 0, "3": 53, "4": 53, "5": 63, "6": 60, "7": 55, "8": 64, "9": 69, "10": 59, "11": 66, "12": 65, "13": 64, "14": 70, "15": 51, "16": 71, "17": 49, "18": 40 } }, { "id": 3, "distances": { "1": 24, "2": 53, "3": 0, "4": 35, "5": 22, "6": 55, "7": 13, "8": 31, "9": 35, "10": 38, "11": 41, "12": 36, "13": 54, "14": 56, "15": 33, "16": 30, "17": 16, "18": 22 } }, { "id": 4, "distances": { "1": 28, "2": 53, "3": 35, "4": 0, "5": 34, "6": 50, "7": 37, "8": 46, "9": 35, "10": 38, "11": 32, "12": 35, "13": 53, "14": 50, "15": 22, "16": 43, "17": 31, "18": 13 } }, { "id": 5, "distances": { "1": 37, "2": 63, "3": 22, "4": 34, "5": 0, "6": 48, "7": 35, "8": 42, "9": 40, "10": 56, "11": 35, "12": 53, "13": 62, "14": 55, "15": 16, "16": 26, "17": 38, "18": 23 } }, { "id": 6, "distances": { "1": 65, "2": 60, "3": 55, "4": 50, "5": 48, "6": 0, "7": 68, "8": 54, "9": 64, "10": 43, "11": 70, "12": 54, "13": 86, "14": 82, "15": 32, "16": 65, "17": 39, "18": 43 } }, { "id": 7, "distances": { "1": 37, "2": 55, "3": 13, "4": 37, "5": 35, "6": 68, "7": 0, "8": 44, "9": 38, "10": 51, "11": 51, "12": 49, "13": 60, "14": 64, "15": 38, "16": 43, "17": 29, "18": 34 } }, { "id": 8, "distances": { "1": 50, "2": 64, "3": 31, "4": 46, "5": 42, "6": 54, "7": 44, "8": 0, "9": 40, "10": 49, "11": 52, "12": 59, "13": 64, "14": 39, "15": 44, "16": 30, "17": 15, "18": 33 } }, { "id": 9, "distances": { "1": 57, "2": 69, "3": 35, "4": 35, "5": 40, "6": 64, "7": 38, "8": 40, "9": 0, "10": 53, "11": 41, "12": 54, "13": 62, "14": 57, "15": 34, "16": 28, "17": 25, "18": 32 } }, { "id": 10, "distances": { "1": 51, "2": 59, "3": 38, "4": 38, "5": 56, "6": 43, "7": 51, "8": 49, "9": 53, "10": 0, "11": 50, "12": 57, "13": 64, "14": 62, "15": 44, "16": 59, "17": 34, "18": 35 } }, { "id": 11, "distances": { "1": 60, "2": 66, "3": 41, "4": 32, "5": 35, "6": 70, "7": 51, "8": 52, "9": 41, "10": 50, "11": 0, "12": 51, "13": 67, "14": 67, "15": 38, "16": 49, "17": 37, "18": 29 } }, { "id": 12, "distances": { "1": 60, "2": 65, "3": 36, "4": 35, "5": 53, "6": 54, "7": 49, "8": 59, "9": 54, "10": 57, "11": 51, "12": 0, "13": 62, "14": 72, "15": 41, "16": 51, "17": 44, "18": 32 } }, { "id": 13, "distances": { "1": 58, "2": 64, "3": 54, "4": 53, "5": 62, "6": 86, "7": 60, "8": 64, "9": 62, "10": 64, "11": 67, "12": 62, "13": 0, "14": 53, "15": 62, "16": 70, "17": 50, "18": 53 } }, { "id": 14, "distances": { "1": 41, "2": 70, "3": 56, "4": 50, "5": 55, "6": 82, "7": 64, "8": 39, "9": 57, "10": 62, "11": 67, "12": 72, "13": 53, "14": 0, "15": 59, "16": 43, "17": 54, "18": 50 } }, { "id": 15, "distances": { "1": 49, "2": 51, "3": 33, "4": 22, "5": 16, "6": 32, "7": 38, "8": 44, "9": 34, "10": 44, "11": 38, "12": 41, "13": 62, "14": 59, "15": 0, "16": 42, "17": 29, "18": 11 } }, { "id": 16, "distances": { "1": 54, "2": 71, "3": 30, "4": 43, "5": 26, "6": 65, "7": 43, "8": 30, "9": 28, "10": 59, "11": 49, "12": 51, "13": 70, "14": 43, "15": 42, "16": 0, "17": 37, "18": 40 } }, { "id": 17, "distances": { "1": 40, "2": 49, "3": 16, "4": 31, "5": 38, "6": 39, "7": 29, "8": 15, "9": 25, "10": 34, "11": 37, "12": 44, "13": 50, "14": 54, "15": 29, "16": 37, "17": 0, "18": 18 } }, { "id": 18, "distances": { "1": 41, "2": 40, "3": 22, "4": 13, "5": 23, "6": 43, "7": 34, "8": 33, "9": 32, "10": 35, "11": 29, "12": 32, "13": 53, "14": 50, "15": 11, "16": 40, "17": 18, "18": 0 } } ], "objective": 549.0 }, "solution_variant": { "selected": [ 18 ], "assignments": [ 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18 ] }, "context_index": 49, "input_format": "csv", "input_index_base": 1 }, { "task_name": "PMED", "problem_type": "PMED", "instruction": "Around town the goal is to open a set number of recycling drop‑off sites chosen from several possible places, and then link every residential block to one of the opened sites — every block must have one assignment and only one. The best arrangement is simply the one that keeps the total walking or driving distance lowest: sum the distance for every block to its assigned site, and pick the setup with the smallest total. The full list of candidate locations and the distance data is shown below.\n\nThere are 18 locations listed; exactly 2 drop-off centers must be opened, and the location identifiers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.\nDistance from 1 to 2 is 39.\nDistance from 1 to 3 is 92.\nDistance from 1 to 4 is 122.\nDistance from 1 to 5 is 110.\nDistance from 1 to 6 is 64.\nDistance from 1 to 7 is 153.\nDistance from 1 to 8 is 160.\nDistance from 1 to 9 is 181.\nDistance from 1 to 10 is 104.\nDistance from 1 to 11 is 48.\nDistance from 1 to 12 is 136.\nDistance from 1 to 13 is 184.\nDistance from 1 to 14 is 121.\nDistance from 1 to 15 is 83.\nDistance from 1 to 16 is 65.\nDistance from 1 to 17 is 147.\nDistance from 1 to 18 is 117.\nDistance from 2 to 1 is 39.\nDistance from 2 to 3 is 53.\nDistance from 2 to 4 is 120.\nDistance from 2 to 5 is 144.\nDistance from 2 to 6 is 103.\nDistance from 2 to 7 is 114.\nDistance from 2 to 8 is 181.\nDistance from 2 to 9 is 174.\nDistance from 2 to 10 is 99.\nDistance from 2 to 11 is 43.\nDistance from 2 to 12 is 97.\nDistance from 2 to 13 is 145.\nDistance from 2 to 14 is 82.\nDistance from 2 to 15 is 44.\nDistance from 2 to 16 is 26.\nDistance from 2 to 17 is 186.\nDistance from 2 to 18 is 156.\nDistance from 3 to 1 is 92.\nDistance from 3 to 2 is 53.\nDistance from 3 to 4 is 67.\nDistance from 3 to 5 is 123.\nDistance from 3 to 6 is 153.\nDistance from 3 to 7 is 99.\nDistance from 3 to 8 is 160.\nDistance from 3 to 9 is 159.\nDistance from 3 to 10 is 102.\nDistance from 3 to 11 is 96.\nDistance from 3 to 12 is 82.\nDistance from 3 to 13 is 130.\nDistance from 3 to 14 is 67.\nDistance from 3 to 15 is 29.\nDistance from 3 to 16 is 41.\nDistance from 3 to 17 is 195.\nDistance from 3 to 18 is 130.\nDistance from 4 to 1 is 122.\nDistance from 4 to 2 is 120.\nDistance from 4 to 3 is 67.\nDistance from 4 to 5 is 123.\nDistance from 4 to 6 is 86.\nDistance from 4 to 7 is 112.\nDistance from 4 to 8 is 104.\nDistance from 4 to 9 is 174.\nDistance from 4 to 10 is 124.\nDistance from 4 to 11 is 88.\nDistance from 4 to 12 is 149.\nDistance from 4 to 13 is 106.\nDistance from 4 to 14 is 134.\nDistance from 4 to 15 is 96.\nDistance from 4 to 16 is 108.\nDistance from 4 to 17 is 200.\nDistance from 4 to 18 is 63.\nDistance from 5 to 1 is 110.\nDistance from 5 to 2 is 144.\nDistance from 5 to 3 is 123.\nDistance from 5 to 4 is 123.\nDistance from 5 to 6 is 98.\nDistance from 5 to 7 is 94.\nDistance from 5 to 8 is 106.\nDistance from 5 to 9 is 137.\nDistance from 5 to 10 is 105.\nDistance from 5 to 11 is 158.\nDistance from 5 to 12 is 173.\nDistance from 5 to 13 is 135.\nDistance from 5 to 14 is 146.\nDistance from 5 to 15 is 120.\nDistance from 5 to 16 is 132.\nDistance from 5 to 17 is 233.\nDistance from 5 to 18 is 107.\nDistance from 6 to 1 is 64.\nDistance from 6 to 2 is 103.\nDistance from 6 to 3 is 153.\nDistance from 6 to 4 is 86.\nDistance from 6 to 5 is 98.\nDistance from 6 to 7 is 173.\nDistance from 6 to 8 is 143.\nDistance from 6 to 9 is 174.\nDistance from 6 to 10 is 137.\nDistance from 6 to 11 is 112.\nDistance from 6 to 12 is 130.\nDistance from 6 to 13 is 164.\nDistance from 6 to 14 is 163.\nDistance from 6 to 15 is 125.\nDistance from 6 to 16 is 129.\nDistance from 6 to 17 is 147.\nDistance from 6 to 18 is 147.\nDistance from 7 to 1 is 153.\nDistance from 7 to 2 is 114.\nDistance from 7 to 3 is 99.\nDistance from 7 to 4 is 112.\nDistance from 7 to 5 is 94.\nDistance from 7 to 6 is 173.\nDistance from 7 to 8 is 148.\nDistance from 7 to 9 is 128.\nDistance from 7 to 10 is 158.\nDistance from 7 to 11 is 157.\nDistance from 7 to 12 is 123.\nDistance from 7 to 13 is 105.\nDistance from 7 to 14 is 52.\nDistance from 7 to 15 is 70.\nDistance from 7 to 16 is 102.\nDistance from 7 to 17 is 171.\nDistance from 7 to 18 is 105.\nDistance from 8 to 1 is 160.\nDistance from 8 to 2 is 181.\nDistance from 8 to 3 is 160.\nDistance from 8 to 4 is 104.\nDistance from 8 to 5 is 106.\nDistance from 8 to 6 is 143.\nDistance from 8 to 7 is 148.\nDistance from 8 to 9 is 133.\nDistance from 8 to 10 is 151.\nDistance from 8 to 11 is 192.\nDistance from 8 to 12 is 210.\nDistance from 8 to 13 is 201.\nDistance from 8 to 14 is 195.\nDistance from 8 to 15 is 157.\nDistance from 8 to 16 is 169.\nDistance from 8 to 17 is 229.\nDistance from 8 to 18 is 115.\nDistance from 9 to 1 is 181.\nDistance from 9 to 2 is 174.\nDistance from 9 to 3 is 159.\nDistance from 9 to 4 is 174.\nDistance from 9 to 5 is 137.\nDistance from 9 to 6 is 174.\nDistance from 9 to 7 is 128.\nDistance from 9 to 8 is 133.\nDistance from 9 to 10 is 100.\nDistance from 9 to 11 is 139.\nDistance from 9 to 12 is 183.\nDistance from 9 to 13 is 136.\nDistance from 9 to 14 is 112.\nDistance from 9 to 15 is 130.\nDistance from 9 to 16 is 162.\nDistance from 9 to 17 is 118.\nDistance from 9 to 18 is 161.\nDistance from 10 to 1 is 104.\nDistance from 10 to 2 is 99.\nDistance from 10 to 3 is 102.\nDistance from 10 to 4 is 124.\nDistance from 10 to 5 is 105.\nDistance from 10 to 6 is 137.\nDistance from 10 to 7 is 158.\nDistance from 10 to 8 is 151.\nDistance from 10 to 9 is 100.\nDistance from 10 to 11 is 56.\nDistance from 10 to 12 is 152.\nDistance from 10 to 13 is 151.\nDistance from 10 to 14 is 126.\nDistance from 10 to 15 is 99.\nDistance from 10 to 16 is 111.\nDistance from 10 to 17 is 218.\nDistance from 10 to 18 is 61.\nDistance from 11 to 1 is 48.\nDistance from 11 to 2 is 43.\nDistance from 11 to 3 is 96.\nDistance from 11 to 4 is 88.\nDistance from 11 to 5 is 158.\nDistance from 11 to 6 is 112.\nDistance from 11 to 7 is 157.\nDistance from 11 to 8 is 192.\nDistance from 11 to 9 is 139.\nDistance from 11 to 10 is 56.\nDistance from 11 to 12 is 140.\nDistance from 11 to 13 is 162.\nDistance from 11 to 14 is 125.\nDistance from 11 to 15 is 87.\nDistance from 11 to 16 is 69.\nDistance from 11 to 17 is 171.\nDistance from 11 to 18 is 117.\nDistance from 12 to 1 is 136.\nDistance from 12 to 2 is 97.\nDistance from 12 to 3 is 82.\nDistance from 12 to 4 is 149.\nDistance from 12 to 5 is 173.\nDistance from 12 to 6 is 130.\nDistance from 12 to 7 is 123.\nDistance from 12 to 8 is 210.\nDistance from 12 to 9 is 183.\nDistance from 12 to 10 is 152.\nDistance from 12 to 11 is 140.\nDistance from 12 to 13 is 48.\nDistance from 12 to 14 is 91.\nDistance from 12 to 15 is 53.\nDistance from 12 to 16 is 85.\nDistance from 12 to 17 is 171.\nDistance from 12 to 18 is 138.\nDistance from 13 to 1 is 184.\nDistance from 13 to 2 is 145.\nDistance from 13 to 3 is 130.\nDistance from 13 to 4 is 106.\nDistance from 13 to 5 is 135.\nDistance from 13 to 6 is 164.\nDistance from 13 to 7 is 105.\nDistance from 13 to 8 is 201.\nDistance from 13 to 9 is 136.\nDistance from 13 to 10 is 151.\nDistance from 13 to 11 is 162.\nDistance from 13 to 12 is 48.\nDistance from 13 to 14 is 139.\nDistance from 13 to 15 is 101.\nDistance from 13 to 16 is 133.\nDistance from 13 to 17 is 219.\nDistance from 13 to 18 is 90.\nDistance from 14 to 1 is 121.\nDistance from 14 to 2 is 82.\nDistance from 14 to 3 is 67.\nDistance from 14 to 4 is 134.\nDistance from 14 to 5 is 146.\nDistance from 14 to 6 is 163.\nDistance from 14 to 7 is 52.\nDistance from 14 to 8 is 195.\nDistance from 14 to 9 is 112.\nDistance from 14 to 10 is 126.\nDistance from 14 to 11 is 125.\nDistance from 14 to 12 is 91.\nDistance from 14 to 13 is 139.\nDistance from 14 to 15 is 38.\nDistance from 14 to 16 is 70.\nDistance from 14 to 17 is 204.\nDistance from 14 to 18 is 118.\nDistance from 15 to 1 is 83.\nDistance from 15 to 2 is 44.\nDistance from 15 to 3 is 29.\nDistance from 15 to 4 is 96.\nDistance from 15 to 5 is 120.\nDistance from 15 to 6 is 125.\nDistance from 15 to 7 is 70.\nDistance from 15 to 8 is 157.\nDistance from 15 to 9 is 130.\nDistance from 15 to 10 is 99.\nDistance from 15 to 11 is 87.\nDistance from 15 to 12 is 53.\nDistance from 15 to 13 is 101.\nDistance from 15 to 14 is 38.\nDistance from 15 to 16 is 32.\nDistance from 15 to 17 is 166.\nDistance from 15 to 18 is 137.\nDistance from 16 to 1 is 65.\nDistance from 16 to 2 is 26.\nDistance from 16 to 3 is 41.\nDistance from 16 to 4 is 108.\nDistance from 16 to 5 is 132.\nDistance from 16 to 6 is 129.\nDistance from 16 to 7 is 102.\nDistance from 16 to 8 is 169.\nDistance from 16 to 9 is 162.\nDistance from 16 to 10 is 111.\nDistance from 16 to 11 is 69.\nDistance from 16 to 12 is 85.\nDistance from 16 to 13 is 133.\nDistance from 16 to 14 is 70.\nDistance from 16 to 15 is 32.\nDistance from 16 to 17 is 198.\nDistance from 16 to 18 is 169.\nDistance from 17 to 1 is 147.\nDistance from 17 to 2 is 186.\nDistance from 17 to 3 is 195.\nDistance from 17 to 4 is 200.\nDistance from 17 to 5 is 233.\nDistance from 17 to 6 is 147.\nDistance from 17 to 7 is 171.\nDistance from 17 to 8 is 229.\nDistance from 17 to 9 is 118.\nDistance from 17 to 10 is 218.\nDistance from 17 to 11 is 171.\nDistance from 17 to 12 is 171.\nDistance from 17 to 13 is 219.\nDistance from 17 to 14 is 204.\nDistance from 17 to 15 is 166.\nDistance from 17 to 16 is 198.\nDistance from 17 to 18 is 198.\nDistance from 18 to 1 is 117.\nDistance from 18 to 2 is 156.\nDistance from 18 to 3 is 130.\nDistance from 18 to 4 is 63.\nDistance from 18 to 5 is 107.\nDistance from 18 to 6 is 147.\nDistance from 18 to 7 is 105.\nDistance from 18 to 8 is 115.\nDistance from 18 to 9 is 161.\nDistance from 18 to 10 is 61.\nDistance from 18 to 11 is 117.\nDistance from 18 to 12 is 138.\nDistance from 18 to 13 is 90.\nDistance from 18 to 14 is 118.\nDistance from 18 to 15 is 137.\nDistance from 18 to 16 is 169.\nDistance from 18 to 17 is 198.\nThese pairwise travel distances are provided to compute assignments and select the arrangement with the lowest total travel.\n\nI'll return the result in a small JSON object so it's easy to read and plug into whatever you use next. Here's the shape I'll follow:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of drop-off sites we decide to open. \"assignments\" is a list that, in order, tells which opened site each residential block is assigned to (one entry per block). This is just a sketch of the expected format, not the actual final answer.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "distance_matrix": [ [ 0, 39, 92, 122, 110, 64, 153, 160, 181, 104, 48, 136, 184, 121, 83, 65, 147, 117 ], [ 39, 0, 53, 120, 144, 103, 114, 181, 174, 99, 43, 97, 145, 82, 44, 26, 186, 156 ], [ 92, 53, 0, 67, 123, 153, 99, 160, 159, 102, 96, 82, 130, 67, 29, 41, 195, 130 ], [ 122, 120, 67, 0, 123, 86, 112, 104, 174, 124, 88, 149, 106, 134, 96, 108, 200, 63 ], [ 110, 144, 123, 123, 0, 98, 94, 106, 137, 105, 158, 173, 135, 146, 120, 132, 233, 107 ], [ 64, 103, 153, 86, 98, 0, 173, 143, 174, 137, 112, 130, 164, 163, 125, 129, 147, 147 ], [ 153, 114, 99, 112, 94, 173, 0, 148, 128, 158, 157, 123, 105, 52, 70, 102, 171, 105 ], [ 160, 181, 160, 104, 106, 143, 148, 0, 133, 151, 192, 210, 201, 195, 157, 169, 229, 115 ], [ 181, 174, 159, 174, 137, 174, 128, 133, 0, 100, 139, 183, 136, 112, 130, 162, 118, 161 ], [ 104, 99, 102, 124, 105, 137, 158, 151, 100, 0, 56, 152, 151, 126, 99, 111, 218, 61 ], [ 48, 43, 96, 88, 158, 112, 157, 192, 139, 56, 0, 140, 162, 125, 87, 69, 171, 117 ], [ 136, 97, 82, 149, 173, 130, 123, 210, 183, 152, 140, 0, 48, 91, 53, 85, 171, 138 ], [ 184, 145, 130, 106, 135, 164, 105, 201, 136, 151, 162, 48, 0, 139, 101, 133, 219, 90 ], [ 121, 82, 67, 134, 146, 163, 52, 195, 112, 126, 125, 91, 139, 0, 38, 70, 204, 118 ], [ 83, 44, 29, 96, 120, 125, 70, 157, 130, 99, 87, 53, 101, 38, 0, 32, 166, 137 ], [ 65, 26, 41, 108, 132, 129, 102, 169, 162, 111, 69, 85, 133, 70, 32, 0, 198, 169 ], [ 147, 186, 195, 200, 233, 147, 171, 229, 118, 218, 171, 171, 219, 204, 166, 198, 0, 198 ], [ 117, 156, 130, 63, 107, 147, 105, 115, 161, 61, 117, 138, 90, 118, 137, 169, 198, 0 ] ], "p": 2, "objective": 1293.0 }, "solution": { "facilities": [ 14, 17 ], "assignments": [ 14, 14, 14, 17, 17, 14, 14, 17, 14, 17, 14, 14, 17, 14, 14, 14, 14, 17 ] }, "obj": 1293.0, "instance_variant": { "problem_type": "PMED", "num_nodes": 18, "num_open": 2, "sites": [ { "id": 1, "distances": { "1": 0, "2": 39, "3": 92, "4": 122, "5": 110, "6": 64, "7": 153, "8": 160, "9": 181, "10": 104, "11": 48, "12": 136, "13": 184, "14": 121, "15": 83, "16": 65, "17": 147, "18": 117 } }, { "id": 2, "distances": { "1": 39, "2": 0, "3": 53, "4": 120, "5": 144, "6": 103, "7": 114, "8": 181, "9": 174, "10": 99, "11": 43, "12": 97, "13": 145, "14": 82, "15": 44, "16": 26, "17": 186, "18": 156 } }, { "id": 3, "distances": { "1": 92, "2": 53, "3": 0, "4": 67, "5": 123, "6": 153, "7": 99, "8": 160, "9": 159, "10": 102, "11": 96, "12": 82, "13": 130, "14": 67, "15": 29, "16": 41, "17": 195, "18": 130 } }, { "id": 4, "distances": { "1": 122, "2": 120, "3": 67, "4": 0, "5": 123, "6": 86, "7": 112, "8": 104, "9": 174, "10": 124, "11": 88, "12": 149, "13": 106, "14": 134, "15": 96, "16": 108, "17": 200, "18": 63 } }, { "id": 5, "distances": { "1": 110, "2": 144, "3": 123, "4": 123, "5": 0, "6": 98, "7": 94, "8": 106, "9": 137, "10": 105, "11": 158, "12": 173, "13": 135, "14": 146, "15": 120, "16": 132, "17": 233, "18": 107 } }, { "id": 6, "distances": { "1": 64, "2": 103, "3": 153, "4": 86, "5": 98, "6": 0, "7": 173, "8": 143, "9": 174, "10": 137, "11": 112, "12": 130, "13": 164, "14": 163, "15": 125, "16": 129, "17": 147, "18": 147 } }, { "id": 7, "distances": { "1": 153, "2": 114, "3": 99, "4": 112, "5": 94, "6": 173, "7": 0, "8": 148, "9": 128, "10": 158, "11": 157, "12": 123, "13": 105, "14": 52, "15": 70, "16": 102, "17": 171, "18": 105 } }, { "id": 8, "distances": { "1": 160, "2": 181, "3": 160, "4": 104, "5": 106, "6": 143, "7": 148, "8": 0, "9": 133, "10": 151, "11": 192, "12": 210, "13": 201, "14": 195, "15": 157, "16": 169, "17": 229, "18": 115 } }, { "id": 9, "distances": { "1": 181, "2": 174, "3": 159, "4": 174, "5": 137, "6": 174, "7": 128, "8": 133, "9": 0, "10": 100, "11": 139, "12": 183, "13": 136, "14": 112, "15": 130, "16": 162, "17": 118, "18": 161 } }, { "id": 10, "distances": { "1": 104, "2": 99, "3": 102, "4": 124, "5": 105, "6": 137, "7": 158, "8": 151, "9": 100, "10": 0, "11": 56, "12": 152, "13": 151, "14": 126, "15": 99, "16": 111, "17": 218, "18": 61 } }, { "id": 11, "distances": { "1": 48, "2": 43, "3": 96, "4": 88, "5": 158, "6": 112, "7": 157, "8": 192, "9": 139, "10": 56, "11": 0, "12": 140, "13": 162, "14": 125, "15": 87, "16": 69, "17": 171, "18": 117 } }, { "id": 12, "distances": { "1": 136, "2": 97, "3": 82, "4": 149, "5": 173, "6": 130, "7": 123, "8": 210, "9": 183, "10": 152, "11": 140, "12": 0, "13": 48, "14": 91, "15": 53, "16": 85, "17": 171, "18": 138 } }, { "id": 13, "distances": { "1": 184, "2": 145, "3": 130, "4": 106, "5": 135, "6": 164, "7": 105, "8": 201, "9": 136, "10": 151, "11": 162, "12": 48, "13": 0, "14": 139, "15": 101, "16": 133, "17": 219, "18": 90 } }, { "id": 14, "distances": { "1": 121, "2": 82, "3": 67, "4": 134, "5": 146, "6": 163, "7": 52, "8": 195, "9": 112, "10": 126, "11": 125, "12": 91, "13": 139, "14": 0, "15": 38, "16": 70, "17": 204, "18": 118 } }, { "id": 15, "distances": { "1": 83, "2": 44, "3": 29, "4": 96, "5": 120, "6": 125, "7": 70, "8": 157, "9": 130, "10": 99, "11": 87, "12": 53, "13": 101, "14": 38, "15": 0, "16": 32, "17": 166, "18": 137 } }, { "id": 16, "distances": { "1": 65, "2": 26, "3": 41, "4": 108, "5": 132, "6": 129, "7": 102, "8": 169, "9": 162, "10": 111, "11": 69, "12": 85, "13": 133, "14": 70, "15": 32, "16": 0, "17": 198, "18": 169 } }, { "id": 17, "distances": { "1": 147, "2": 186, "3": 195, "4": 200, "5": 233, "6": 147, "7": 171, "8": 229, "9": 118, "10": 218, "11": 171, "12": 171, "13": 219, "14": 204, "15": 166, "16": 198, "17": 0, "18": 198 } }, { "id": 18, "distances": { "1": 117, "2": 156, "3": 130, "4": 63, "5": 107, "6": 147, "7": 105, "8": 115, "9": 161, "10": 61, "11": 117, "12": 138, "13": 90, "14": 118, "15": 137, "16": 169, "17": 198, "18": 0 } } ], "objective": 1293.0 }, "solution_variant": { "selected": [ 15, 18 ], "assignments": [ 15, 15, 15, 18, 18, 15, 15, 18, 15, 18, 15, 15, 18, 15, 15, 15, 15, 18 ] }, "context_index": 50, "input_format": "nl", "input_index_base": 1 } ]