task_name,problem_type,instruction,instance,solution,obj,instance_variant,solution_variant,context_index,input_format,input_index_base
AP3,AP3,"Many people depend on a tidy schedule at the courier shop: each rider takes on one restaurant and one delivery patch, and every restaurant and every patch must be taken by exactly one rider — no overlaps, no gaps. Each rider’s trip length for their restaurant-plus-zone choice is known, and the best overall plan is simply the one with the smallest sum of those trip lengths across all riders. The exact restaurants, zones, riders, and measured distances are shown below.

There are 8 couriers and corresponding restaurants and delivery zones with indices A, B, C, D, E, F, G, H; the following lines list every rider/restaurant/zone triple and its measured trip length.
Meaning: costs form a 3D tensor. For each fixed rider_id=i, you are given a restaurant_id×delivery_zone_id matrix whose entry at row restaurant_id=j and column delivery_zone_id=k equals riding_distance(i,j,k). You must pick exactly one (j,k) for every i, with all restaurant_id and all delivery_zone_id used exactly once.
riding_distance_tensor (per-rider_id markdown matrices):
## rider_id=A
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 89 | 9 | 90 | 88 | 16 | 40 | 75 | 85 |
| B | 68 | 22 | 2 | 63 | 58 | 0 | 41 | 62 |
| C | 48 | 94 | 80 | 85 | 30 | 51 | 11 | 97 |
| D | 84 | 82 | 51 | 46 | 24 | 16 | 56 | 99 |
| E | 48 | 62 | 58 | 98 | 43 | 28 | 99 | 40 |
| F | 70 | 63 | 68 | 25 | 71 | 76 | 6 | 38 |
| G | 99 | 63 | 61 | 67 | 88 | 11 | 9 | 87 |
| H | 70 | 6 | 40 | 65 | 35 | 70 | 80 | 98 |

## rider_id=B
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 16 | 91 | 3 | 17 | 24 | 81 | 36 | 17 |
| B | 59 | 36 | 15 | 89 | 74 | 33 | 87 | 49 |
| C | 20 | 28 | 60 | 24 | 0 | 5 | 66 | 88 |
| D | 8 | 31 | 53 | 37 | 65 | 52 | 37 | 94 |
| E | 28 | 15 | 12 | 54 | 30 | 66 | 53 | 82 |
| F | 49 | 69 | 50 | 17 | 35 | 16 | 81 | 35 |
| G | 96 | 78 | 12 | 21 | 86 | 28 | 95 | 97 |
| H | 13 | 0 | 26 | 13 | 91 | 68 | 8 | 67 |

## rider_id=C
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 24 | 19 | 85 | 28 | 60 | 61 | 66 | 86 |
| B | 66 | 40 | 93 | 67 | 43 | 90 | 30 | 13 |
| C | 46 | 78 | 56 | 84 | 24 | 16 | 14 | 53 |
| D | 51 | 83 | 56 | 43 | 45 | 60 | 28 | 85 |
| E | 76 | 21 | 94 | 55 | 13 | 65 | 95 | 15 |
| F | 83 | 93 | 31 | 85 | 61 | 38 | 45 | 0 |
| G | 86 | 99 | 32 | 21 | 60 | 8 | 50 | 50 |
| H | 40 | 92 | 81 | 93 | 91 | 94 | 94 | 65 |

## rider_id=D
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 38 | 13 | 99 | 55 | 26 | 77 | 41 | 44 |
| B | 73 | 30 | 32 | 57 | 25 | 60 | 81 | 26 |
| C | 98 | 30 | 95 | 57 | 26 | 89 | 16 | 69 |
| D | 2 | 65 | 98 | 55 | 65 | 2 | 7 | 87 |
| E | 29 | 76 | 75 | 61 | 16 | 57 | 39 | 6 |
| F | 17 | 24 | 68 | 65 | 80 | 91 | 22 | 3 |
| G | 77 | 54 | 37 | 32 | 39 | 14 | 62 | 0 |
| H | 11 | 56 | 85 | 79 | 32 | 25 | 14 | 64 |

## rider_id=E
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 57 | 55 | 36 | 66 | 71 | 34 | 91 | 10 |
| B | 23 | 39 | 57 | 47 | 45 | 94 | 27 | 89 |
| C | 22 | 20 | 98 | 80 | 50 | 9 | 25 | 13 |
| D | 81 | 74 | 63 | 65 | 21 | 19 | 30 | 98 |
| E | 67 | 20 | 32 | 42 | 89 | 30 | 93 | 78 |
| F | 50 | 92 | 68 | 1 | 99 | 61 | 20 | 77 |
| G | 34 | 88 | 18 | 67 | 15 | 44 | 41 | 72 |
| H | 12 | 6 | 18 | 54 | 69 | 39 | 10 | 61 |

## rider_id=F
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 27 | 74 | 63 | 74 | 74 | 8 | 84 | 97 |
| B | 86 | 0 | 0 | 62 | 67 | 52 | 20 | 81 |
| C | 90 | 67 | 49 | 65 | 62 | 53 | 37 | 13 |
| D | 0 | 50 | 99 | 55 | 44 | 13 | 3 | 61 |
| E | 83 | 71 | 53 | 23 | 82 | 33 | 92 | 71 |
| F | 6 | 40 | 2 | 78 | 68 | 19 | 27 | 66 |
| G | 3 | 5 | 44 | 82 | 81 | 40 | 97 | 50 |
| H | 84 | 28 | 71 | 84 | 73 | 49 | 78 | 65 |

## rider_id=G
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 38 | 46 | 46 | 17 | 4 | 95 | 16 | 55 |
| B | 91 | 82 | 33 | 91 | 28 | 51 | 75 | 79 |
| C | 8 | 12 | 95 | 79 | 99 | 3 | 62 | 84 |
| D | 54 | 91 | 26 | 85 | 49 | 78 | 40 | 87 |
| E | 85 | 77 | 60 | 58 | 71 | 95 | 41 | 43 |
| F | 97 | 85 | 11 | 86 | 71 | 86 | 34 | 32 |
| G | 87 | 25 | 22 | 30 | 82 | 45 | 50 | 4 |
| H | 5 | 30 | 17 | 76 | 38 | 38 | 85 | 26 |

## rider_id=H
| restaurant_id\delivery_zone_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 18 | 24 | 30 | 13 | 15 | 64 | 76 | 12 |
| B | 97 | 46 | 5 | 43 | 82 | 30 | 2 | 33 |
| C | 19 | 18 | 82 | 44 | 96 | 47 | 14 | 11 |
| D | 95 | 82 | 35 | 95 | 81 | 93 | 76 | 80 |
| E | 21 | 10 | 18 | 9 | 19 | 9 | 57 | 66 |
| F | 12 | 3 | 45 | 85 | 8 | 31 | 53 | 12 |
| G | 35 | 71 | 40 | 2 | 66 | 8 | 6 | 74 |
| H | 28 | 38 | 43 | 49 | 29 | 37 | 62 | 62 |
Choose the assignment that minimizes the total sum of the listed trip lengths across all 8 couriers.

I'll keep the final plan tidy in a small JSON sketch like this — just the shape of what I'll return:

{
  ""solution"": [
    [<i_id>, <j_id>, <k_id>],
    ...
  ]
}

This means ""solution"" is a list of triples. Each triple picks one rider (first entry), one restaurant (second entry), and one delivery patch (third entry). Think of each triple as one rider's assigned restaurant-and-patch pair. This block is only a sketch of the expected shape, not the actual answer.

Please use the exact identifiers from the instance input — don't 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”.""","{'cost_tensor': [[[89, 9, 90, 88, 16, 40, 75, 85], [68, 22, 2, 63, 58, 0, 41, 62], [48, 94, 80, 85, 30, 51, 11, 97], [84, 82, 51, 46, 24, 16, 56, 99], [48, 62, 58, 98, 43, 28, 99, 40], [70, 63, 68, 25, 71, 76, 6, 38], [99, 63, 61, 67, 88, 11, 9, 87], [70, 6, 40, 65, 35, 70, 80, 98]], [[16, 91, 3, 17, 24, 81, 36, 17], [59, 36, 15, 89, 74, 33, 87, 49], [20, 28, 60, 24, 0, 5, 66, 88], [8, 31, 53, 37, 65, 52, 37, 94], [28, 15, 12, 54, 30, 66, 53, 82], [49, 69, 50, 17, 35, 16, 81, 35], [96, 78, 12, 21, 86, 28, 95, 97], [13, 0, 26, 13, 91, 68, 8, 67]], [[24, 19, 85, 28, 60, 61, 66, 86], [66, 40, 93, 67, 43, 90, 30, 13], [46, 78, 56, 84, 24, 16, 14, 53], [51, 83, 56, 43, 45, 60, 28, 85], [76, 21, 94, 55, 13, 65, 95, 15], [83, 93, 31, 85, 61, 38, 45, 0], [86, 99, 32, 21, 60, 8, 50, 50], [40, 92, 81, 93, 91, 94, 94, 65]], [[38, 13, 99, 55, 26, 77, 41, 44], [73, 30, 32, 57, 25, 60, 81, 26], [98, 30, 95, 57, 26, 89, 16, 69], [2, 65, 98, 55, 65, 2, 7, 87], [29, 76, 75, 61, 16, 57, 39, 6], [17, 24, 68, 65, 80, 91, 22, 3], [77, 54, 37, 32, 39, 14, 62, 0], [11, 56, 85, 79, 32, 25, 14, 64]], [[57, 55, 36, 66, 71, 34, 91, 10], [23, 39, 57, 47, 45, 94, 27, 89], [22, 20, 98, 80, 50, 9, 25, 13], [81, 74, 63, 65, 21, 19, 30, 98], [67, 20, 32, 42, 89, 30, 93, 78], [50, 92, 68, 1, 99, 61, 20, 77], [34, 88, 18, 67, 15, 44, 41, 72], [12, 6, 18, 54, 69, 39, 10, 61]], [[27, 74, 63, 74, 74, 8, 84, 97], [86, 0, 0, 62, 67, 52, 20, 81], [90, 67, 49, 65, 62, 53, 37, 13], [0, 50, 99, 55, 44, 13, 3, 61], [83, 71, 53, 23, 82, 33, 92, 71], [6, 40, 2, 78, 68, 19, 27, 66], [3, 5, 44, 82, 81, 40, 97, 50], [84, 28, 71, 84, 73, 49, 78, 65]], [[38, 46, 46, 17, 4, 95, 16, 55], [91, 82, 33, 91, 28, 51, 75, 79], [8, 12, 95, 79, 99, 3, 62, 84], [54, 91, 26, 85, 49, 78, 40, 87], [85, 77, 60, 58, 71, 95, 41, 43], [97, 85, 11, 86, 71, 86, 34, 32], [87, 25, 22, 30, 82, 45, 50, 4], [5, 30, 17, 76, 38, 38, 85, 26]], [[18, 24, 30, 13, 15, 64, 76, 12], [97, 46, 5, 43, 82, 30, 2, 33], [19, 18, 82, 44, 96, 47, 14, 11], [95, 82, 35, 95, 81, 93, 76, 80], [21, 10, 18, 9, 19, 9, 57, 66], [12, 3, 45, 85, 8, 31, 53, 12], [35, 71, 40, 2, 66, 8, 6, 74], [28, 38, 43, 49, 29, 37, 62, 62]]], 'objective': 28.0}","[[0, 7, 1], [1, 0, 2], [2, 4, 4], [3, 6, 7], [4, 5, 3], [5, 3, 0], [6, 2, 5], [7, 1, 6]]",28.0,"{'problem_type': 'AP3', 'n': 8, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 89}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 9}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 90}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 88}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 16}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 40}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 75}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 85}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 68}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 22}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 2}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 63}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 58}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 0}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 41}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 62}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 48}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 94}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 80}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 85}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 30}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 51}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 11}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 97}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 84}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 82}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 51}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 46}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 24}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 16}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 56}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 99}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 48}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 62}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 58}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 98}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 43}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 28}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 99}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 40}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 70}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 63}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 68}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 25}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 71}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 76}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 6}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 38}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 99}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 63}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 61}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 67}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 88}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 11}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 9}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 87}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 70}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 6}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 40}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 65}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 35}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 70}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 80}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 98}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 16}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 91}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 3}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 17}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 24}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 81}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 36}, {'i': 'B', 'j': 'A', 'k': 'H', 'cost': 17}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 59}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 36}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 15}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 89}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 74}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 33}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 87}, {'i': 'B', 'j': 'B', 'k': 'H', 'cost': 49}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 20}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 28}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 60}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 24}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 0}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 5}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 66}, {'i': 'B', 'j': 'C', 'k': 'H', 'cost': 88}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 8}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 31}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 53}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 37}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 65}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 52}, {'i': 'B', 'j': 'D', 'k': 'G', 'cost': 37}, {'i': 'B', 'j': 'D', 'k': 'H', 'cost': 94}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 28}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 15}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 12}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 54}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 30}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 66}, {'i': 'B', 'j': 'E', 'k': 'G', 'cost': 53}, {'i': 'B', 'j': 'E', 'k': 'H', 'cost': 82}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 49}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 69}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 50}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 17}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 35}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 16}, {'i': 'B', 'j': 'F', 'k': 'G', 'cost': 81}, {'i': 'B', 'j': 'F', 'k': 'H', 'cost': 35}, {'i': 'B', 'j': 'G', 'k': 'A', 'cost': 96}, {'i': 'B', 'j': 'G', 'k': 'B', 'cost': 78}, {'i': 'B', 'j': 'G', 'k': 'C', 'cost': 12}, {'i': 'B', 'j': 'G', 'k': 'D', 'cost': 21}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 86}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 28}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 95}, {'i': 'B', 'j': 'G', 'k': 'H', 'cost': 97}, {'i': 'B', 'j': 'H', 'k': 'A', 'cost': 13}, {'i': 'B', 'j': 'H', 'k': 'B', 'cost': 0}, {'i': 'B', 'j': 'H', 'k': 'C', 'cost': 26}, {'i': 'B', 'j': 'H', 'k': 'D', 'cost': 13}, {'i': 'B', 'j': 'H', 'k': 'E', 'cost': 91}, {'i': 'B', 'j': 'H', 'k': 'F', 'cost': 68}, {'i': 'B', 'j': 'H', 'k': 'G', 'cost': 8}, {'i': 'B', 'j': 'H', 'k': 'H', 'cost': 67}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 24}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 19}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 85}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 28}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 60}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 61}, {'i': 'C', 'j': 'A', 'k': 'G', 'cost': 66}, {'i': 'C', 'j': 'A', 'k': 'H', 'cost': 86}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 66}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 40}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 93}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 67}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 43}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 90}, {'i': 'C', 'j': 'B', 'k': 'G', 'cost': 30}, {'i': 'C', 'j': 'B', 'k': 'H', 'cost': 13}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 46}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 78}, {'i': 'C', 'j': 'C', 'k': 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'cost': 66}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 12}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 3}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 45}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 85}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 8}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 31}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 53}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 12}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 35}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 71}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 40}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 66}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 8}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 6}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 74}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 28}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 38}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 43}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 49}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 29}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 37}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 62}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 62}]}","[['A', 'H', 'B'], ['B', 'A', 'C'], ['C', 'E', 'E'], ['D', 'G', 'H'], ['E', 'F', 'D'], ['F', 'D', 'A'], ['G', 'C', 'F'], ['H', 'B', 'G']]",1,nl,names
AP3,AP3,"We had a stack of speaker bios, a list of rooms, and a list of time slots — and the task was to match each speaker with exactly one room and one slot so every room and every slot ends up with a single speaker. Someone assigned a cost to each possible speaker-room-time combo, and the idea was to pick the lineup whose costs add up to the least amount overall. Nothing could be duplicated or skipped: one speaker, one room, one slot each. The concrete details are shown below.

We had 6 keynote speakers, the same number of rooms and time slots, labeled A, B, C, D, E, F.

*Meaning: costs form a 3D tensor. For each fixed speaker_id=i, you are given a room_id×time_slot_id matrix whose entry at row room_id=j and column time_slot_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all room_id and all time_slot_id used exactly once.*

**assignment_cost_tensor (per-speaker_id markdown matrices)**

## speaker_id=A
| room_id\time_slot_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 62 | 78 | 26 | 68 | 95 | 93 |
| B | 98 | 31 | 53 | 87 | 78 | 24 |
| C | 73 | 79 | 82 | 98 | 71 | 73 |
| D | 8 | 55 | 25 | 66 | 53 | 71 |
| E | 82 | 52 | 76 | 89 | 86 | 45 |
| F | 24 | 48 | 59 | 66 | 28 | 64 |

## speaker_id=B
| room_id\time_slot_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 58 | 41 | 83 | 22 | 66 | 91 |
| B | 31 | 16 | 52 | 91 | 14 | 57 |
| C | 89 | 8 | 10 | 81 | 45 | 16 |
| D | 41 | 63 | 77 | 49 | 73 | 98 |
| E | 89 | 3 | 65 | 7 | 6 | 44 |
| F | 64 | 73 | 21 | 6 | 9 | 27 |

## speaker_id=C
| room_id\time_slot_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 68 | 92 | 51 | 99 | 18 | 53 |
| B | 25 | 30 | 89 | 38 | 86 | 18 |
| C | 11 | 83 | 95 | 53 | 91 | 88 |
| D | 14 | 24 | 56 | 81 | 12 | 22 |
| E | 34 | 70 | 23 | 31 | 60 | 98 |
| F | 78 | 71 | 15 | 99 | 15 | 96 |

## speaker_id=D
| room_id\time_slot_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 43 | 25 | 39 | 43 | 73 | 1 |
| B | 34 | 64 | 60 | 73 | 1 | 22 |
| C | 86 | 47 | 60 | 78 | 80 | 62 |
| D | 42 | 9 | 90 | 28 | 48 | 90 |
| E | 63 | 27 | 18 | 52 | 7 | 3 |
| F | 96 | 86 | 44 | 25 | 53 | 2 |

## speaker_id=E
| room_id\time_slot_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 79 | 42 | 79 | 72 | 45 | 91 |
| B | 84 | 73 | 53 | 11 | 37 | 48 |
| C | 75 | 17 | 34 | 16 | 37 | 19 |
| D | 29 | 79 | 80 | 94 | 10 | 17 |
| E | 10 | 32 | 41 | 44 | 17 | 73 |
| F | 56 | 26 | 85 | 86 | 92 | 47 |

## speaker_id=F
| room_id\time_slot_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 54 | 95 | 64 | 98 | 84 | 50 |
| B | 45 | 49 | 98 | 39 | 58 | 37 |
| C | 79 | 83 | 93 | 76 | 60 | 81 |
| D | 77 | 23 | 26 | 76 | 84 | 59 |
| E | 0 | 87 | 22 | 58 | 83 | 97 |
| F | 15 | 99 | 53 | 51 | 76 | 45 |

We then selected 6 of these triples so every speaker, room, and time slot was used exactly once.

I'll show the shape of the reply I need in a quick JSON sketch so it's clear how to return the matchings.

{
  ""solution"": [
    [<speaker_id>, <room_id>, <slot_id>],
    ...
  ]
}

Here ""solution"" is a list of triples — one triple per speaker — and each triple is the speaker identifier, the room identifier, and the time-slot identifier in that order. Think of it like filling out a little form: each row says which room and which slot a given speaker gets.

This JSON block is just an example of the shape I want, not the actual assignment.

Please 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"".","{'cost_tensor': [[[62, 78, 26, 68, 95, 93], [98, 31, 53, 87, 78, 24], [73, 79, 82, 98, 71, 73], [8, 55, 25, 66, 53, 71], [82, 52, 76, 89, 86, 45], [24, 48, 59, 66, 28, 64]], [[58, 41, 83, 22, 66, 91], [31, 16, 52, 91, 14, 57], [89, 8, 10, 81, 45, 16], [41, 63, 77, 49, 73, 98], [89, 3, 65, 7, 6, 44], [64, 73, 21, 6, 9, 27]], [[68, 92, 51, 99, 18, 53], [25, 30, 89, 38, 86, 18], [11, 83, 95, 53, 91, 88], [14, 24, 56, 81, 12, 22], [34, 70, 23, 31, 60, 98], [78, 71, 15, 99, 15, 96]], [[43, 25, 39, 43, 73, 1], [34, 64, 60, 73, 1, 22], [86, 47, 60, 78, 80, 62], [42, 9, 90, 28, 48, 90], [63, 27, 18, 52, 7, 3], [96, 86, 44, 25, 53, 2]], [[79, 42, 79, 72, 45, 91], [84, 73, 53, 11, 37, 48], [75, 17, 34, 16, 37, 19], [29, 79, 80, 94, 10, 17], [10, 32, 41, 44, 17, 73], [56, 26, 85, 86, 92, 47]], [[54, 95, 64, 98, 84, 50], [45, 49, 98, 39, 58, 37], [79, 83, 93, 76, 60, 81], [77, 23, 26, 76, 84, 59], [0, 87, 22, 58, 83, 97], [15, 99, 53, 51, 76, 45]]], 'objective': 59.0}","[[0, 0, 2], [1, 2, 1], [2, 3, 4], [3, 5, 5], [4, 1, 3], [5, 4, 0]]",59.0,"{'problem_type': 'AP3', 'n': 6, 'ids': ['A', 'B', 'C', 'D', 'E', 'F'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 62}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 78}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 26}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 68}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 95}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 93}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 98}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 31}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 53}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 87}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 78}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 24}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 73}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 79}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 82}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 98}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 71}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 73}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 8}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 55}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 25}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 66}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 53}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 71}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 82}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 52}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 76}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 89}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 86}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 45}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 24}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 48}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 59}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 66}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 28}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 64}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 58}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 41}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 83}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 22}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 66}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 91}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 31}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 16}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 52}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 91}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 14}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 57}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 89}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 8}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 10}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 81}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 45}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 16}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 41}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 63}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 77}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 49}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 73}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 98}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 89}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 3}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 65}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 7}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 6}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 44}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 64}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 73}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 21}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 6}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 9}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 27}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 68}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 92}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 51}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 99}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 18}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 53}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 25}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 30}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 89}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 38}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 86}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 18}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 11}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 83}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 95}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 53}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 91}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 88}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 14}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 24}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 56}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 81}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 12}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 22}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 34}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 70}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 23}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 31}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 60}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 98}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 78}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 71}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 15}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 99}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 15}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 96}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 43}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 25}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 39}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 43}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 73}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 1}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 34}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 64}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 60}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 73}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 1}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 22}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 86}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 47}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 60}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 78}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 80}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 62}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 42}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 9}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 90}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 28}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 48}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 90}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 63}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 27}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 18}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 52}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 7}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 3}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 96}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 86}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 44}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 25}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 53}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 2}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 79}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 42}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 79}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 72}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 45}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 91}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 84}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 73}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 53}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 11}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 37}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 48}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 75}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 17}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 34}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 16}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 37}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 19}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 29}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 79}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 80}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 94}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 10}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 17}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 10}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 32}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 41}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 44}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 17}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 73}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 56}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 26}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 85}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 86}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 92}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 47}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 54}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 95}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 64}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 98}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 84}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 50}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 45}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 49}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 98}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 39}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 58}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 37}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 79}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 83}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 93}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 76}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 60}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 81}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 77}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 23}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 26}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 76}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 84}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 59}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 0}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 87}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 22}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 58}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 83}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 97}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 15}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 99}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 53}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 51}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 76}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 45}]}","[['A', 'A', 'C'], ['B', 'C', 'B'], ['C', 'D', 'E'], ['D', 'F', 'F'], ['E', 'B', 'D'], ['F', 'E', 'A']]",2,markdown_table,names
AP3,AP3,"A plant manager faces a tidy constraint: assign every product to one machine and one shift, don’t let machines or shifts be reused, and don’t leave any machine or shift empty. Each product+machine+shift choice has a specific cost attached, so the practical way to compare plans is to add up those costs for the chosen assignments and pick the set that results in the lowest total spend. The exact options and numbers are listed below.

{
  ""num_products"": 8,
  ""index_identifiers"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8
  ]
}

# Meaning: costs form a 3D tensor. For each fixed product_id=i, you are given a machine_id×shift_id matrix whose entry at row machine_id=j and column shift_id=k equals production_cost(i,j,k). You must pick exactly one (j,k) for every i, with all machine_id and all shift_id used exactly once.
# production_cost_tensor (per-product_id markdown matrices)

## product_id=1
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 39 | 11 | 19 | 34 | 16 | 88 | 5 | 67 |
| 2 | 32 | 37 | 0 | 50 | 38 | 53 | 1 | 14 |
| 3 | 94 | 48 | 1 | 54 | 64 | 75 | 90 | 60 |
| 4 | 97 | 52 | 25 | 99 | 66 | 58 | 28 | 20 |
| 5 | 5 | 96 | 29 | 31 | 2 | 98 | 88 | 98 |
| 6 | 67 | 72 | 63 | 8 | 57 | 40 | 49 | 67 |
| 7 | 35 | 23 | 44 | 94 | 84 | 4 | 70 | 90 |
| 8 | 66 | 53 | 66 | 24 | 2 | 32 | 70 | 97 |

## product_id=2
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 12 | 62 | 14 | 49 | 15 | 22 | 4 | 16 |
| 2 | 80 | 27 | 17 | 39 | 2 | 75 | 68 | 28 |
| 3 | 23 | 96 | 18 | 65 | 44 | 4 | 81 | 91 |
| 4 | 14 | 24 | 26 | 27 | 3 | 62 | 14 | 79 |
| 5 | 19 | 73 | 69 | 20 | 40 | 3 | 69 | 89 |
| 6 | 14 | 6 | 6 | 21 | 3 | 77 | 87 | 67 |
| 7 | 51 | 6 | 31 | 30 | 81 | 40 | 5 | 95 |
| 8 | 60 | 28 | 94 | 62 | 36 | 49 | 9 | 0 |

## product_id=3
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 71 | 68 | 93 | 77 | 61 | 38 | 73 | 48 |
| 2 | 44 | 95 | 54 | 30 | 51 | 97 | 72 | 75 |
| 3 | 44 | 7 | 40 | 39 | 66 | 20 | 20 | 86 |
| 4 | 64 | 92 | 58 | 14 | 50 | 55 | 93 | 31 |
| 5 | 63 | 27 | 60 | 42 | 94 | 78 | 89 | 81 |
| 6 | 88 | 2 | 3 | 33 | 20 | 74 | 75 | 30 |
| 7 | 55 | 54 | 76 | 72 | 93 | 65 | 1 | 66 |
| 8 | 60 | 27 | 75 | 65 | 24 | 76 | 46 | 34 |

## product_id=4
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 29 | 36 | 2 | 72 | 63 | 69 | 45 | 46 |
| 2 | 96 | 71 | 3 | 70 | 34 | 67 | 98 | 2 |
| 3 | 73 | 72 | 55 | 44 | 28 | 15 | 23 | 76 |
| 4 | 58 | 35 | 71 | 30 | 71 | 50 | 86 | 98 |
| 5 | 52 | 96 | 86 | 8 | 18 | 63 | 56 | 15 |
| 6 | 18 | 78 | 30 | 41 | 53 | 61 | 2 | 70 |
| 7 | 83 | 67 | 61 | 0 | 62 | 76 | 27 | 45 |
| 8 | 99 | 99 | 43 | 4 | 11 | 4 | 97 | 9 |

## product_id=5
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 20 | 6 | 46 | 76 | 13 | 67 | 35 | 83 |
| 2 | 30 | 33 | 85 | 76 | 25 | 23 | 54 | 50 |
| 3 | 0 | 78 | 32 | 14 | 98 | 77 | 27 | 57 |
| 4 | 29 | 93 | 21 | 74 | 18 | 85 | 64 | 96 |
| 5 | 86 | 2 | 73 | 91 | 17 | 3 | 9 | 54 |
| 6 | 76 | 19 | 85 | 23 | 0 | 56 | 82 | 81 |
| 7 | 19 | 77 | 97 | 34 | 35 | 59 | 41 | 37 |
| 8 | 60 | 60 | 20 | 64 | 98 | 75 | 96 | 86 |

## product_id=6
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 76 | 94 | 38 | 47 | 16 | 95 | 16 | 73 |
| 2 | 41 | 15 | 97 | 23 | 47 | 77 | 58 | 47 |
| 3 | 96 | 53 | 70 | 69 | 21 | 30 | 17 | 73 |
| 4 | 47 | 82 | 10 | 20 | 11 | 64 | 13 | 81 |
| 5 | 84 | 99 | 43 | 66 | 81 | 49 | 85 | 79 |
| 6 | 82 | 83 | 70 | 40 | 33 | 92 | 59 | 63 |
| 7 | 81 | 83 | 75 | 35 | 99 | 91 | 53 | 78 |
| 8 | 27 | 1 | 5 | 67 | 40 | 54 | 91 | 82 |

## product_id=7
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 24 | 71 | 68 | 57 | 12 | 33 | 21 | 38 |
| 2 | 71 | 2 | 90 | 1 | 46 | 6 | 5 | 21 |
| 3 | 51 | 4 | 56 | 34 | 0 | 90 | 44 | 76 |
| 4 | 49 | 75 | 84 | 23 | 4 | 47 | 92 | 64 |
| 5 | 35 | 69 | 9 | 66 | 47 | 32 | 28 | 61 |
| 6 | 84 | 57 | 81 | 21 | 49 | 20 | 76 | 6 |
| 7 | 69 | 51 | 28 | 12 | 19 | 34 | 47 | 48 |
| 8 | 29 | 34 | 51 | 39 | 58 | 80 | 26 | 66 |

## product_id=8
| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 54 | 68 | 19 | 7 | 84 | 10 | 53 | 29 |
| 2 | 15 | 91 | 41 | 90 | 55 | 92 | 87 | 84 |
| 3 | 39 | 27 | 68 | 10 | 23 | 65 | 71 | 49 |
| 4 | 16 | 63 | 85 | 39 | 38 | 44 | 72 | 74 |
| 5 | 0 | 96 | 28 | 1 | 14 | 86 | 9 | 43 |
| 6 | 15 | 90 | 64 | 25 | 58 | 53 | 41 | 13 |
| 7 | 44 | 47 | 61 | 49 | 42 | 82 | 95 | 39 |
| 8 | 20 | 70 | 60 | 69 | 92 | 46 | 55 | 10 |

If you want to give the plan in a machine-friendly way, just use a little JSON like this one — nothing fancy, just a list of triples showing which product goes to which machine and which shift:

{
  ""solution"": [
    [<i_id>, <j_id>, <k_id>],
    ...
  ]
}

Think of each inner triple as [product_id, machine_id, shift_id] — one triple for each product, in plain, human terms. This JSON is just a sketch of the shape I expect, not the actual answer.

Please make sure you use the identifiers exactly as they appear in 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”.","{'cost_tensor': [[[39, 11, 19, 34, 16, 88, 5, 67], [32, 37, 0, 50, 38, 53, 1, 14], [94, 48, 1, 54, 64, 75, 90, 60], [97, 52, 25, 99, 66, 58, 28, 20], [5, 96, 29, 31, 2, 98, 88, 98], [67, 72, 63, 8, 57, 40, 49, 67], [35, 23, 44, 94, 84, 4, 70, 90], [66, 53, 66, 24, 2, 32, 70, 97]], [[12, 62, 14, 49, 15, 22, 4, 16], [80, 27, 17, 39, 2, 75, 68, 28], [23, 96, 18, 65, 44, 4, 81, 91], [14, 24, 26, 27, 3, 62, 14, 79], [19, 73, 69, 20, 40, 3, 69, 89], [14, 6, 6, 21, 3, 77, 87, 67], [51, 6, 31, 30, 81, 40, 5, 95], [60, 28, 94, 62, 36, 49, 9, 0]], [[71, 68, 93, 77, 61, 38, 73, 48], [44, 95, 54, 30, 51, 97, 72, 75], [44, 7, 40, 39, 66, 20, 20, 86], [64, 92, 58, 14, 50, 55, 93, 31], [63, 27, 60, 42, 94, 78, 89, 81], [88, 2, 3, 33, 20, 74, 75, 30], [55, 54, 76, 72, 93, 65, 1, 66], [60, 27, 75, 65, 24, 76, 46, 34]], [[29, 36, 2, 72, 63, 69, 45, 46], [96, 71, 3, 70, 34, 67, 98, 2], [73, 72, 55, 44, 28, 15, 23, 76], [58, 35, 71, 30, 71, 50, 86, 98], [52, 96, 86, 8, 18, 63, 56, 15], [18, 78, 30, 41, 53, 61, 2, 70], [83, 67, 61, 0, 62, 76, 27, 45], [99, 99, 43, 4, 11, 4, 97, 9]], [[20, 6, 46, 76, 13, 67, 35, 83], [30, 33, 85, 76, 25, 23, 54, 50], [0, 78, 32, 14, 98, 77, 27, 57], [29, 93, 21, 74, 18, 85, 64, 96], [86, 2, 73, 91, 17, 3, 9, 54], [76, 19, 85, 23, 0, 56, 82, 81], [19, 77, 97, 34, 35, 59, 41, 37], [60, 60, 20, 64, 98, 75, 96, 86]], [[76, 94, 38, 47, 16, 95, 16, 73], [41, 15, 97, 23, 47, 77, 58, 47], [96, 53, 70, 69, 21, 30, 17, 73], [47, 82, 10, 20, 11, 64, 13, 81], [84, 99, 43, 66, 81, 49, 85, 79], [82, 83, 70, 40, 33, 92, 59, 63], [81, 83, 75, 35, 99, 91, 53, 78], [27, 1, 5, 67, 40, 54, 91, 82]], [[24, 71, 68, 57, 12, 33, 21, 38], [71, 2, 90, 1, 46, 6, 5, 21], [51, 4, 56, 34, 0, 90, 44, 76], [49, 75, 84, 23, 4, 47, 92, 64], [35, 69, 9, 66, 47, 32, 28, 61], [84, 57, 81, 21, 49, 20, 76, 6], [69, 51, 28, 12, 19, 34, 47, 48], [29, 34, 51, 39, 58, 80, 26, 66]], [[54, 68, 19, 7, 84, 10, 53, 29], [15, 91, 41, 90, 55, 92, 87, 84], [39, 27, 68, 10, 23, 65, 71, 49], [16, 63, 85, 39, 38, 44, 72, 74], [0, 96, 28, 1, 14, 86, 9, 43], [15, 90, 64, 25, 58, 53, 41, 13], [44, 47, 61, 49, 42, 82, 95, 39], [20, 70, 60, 69, 92, 46, 55, 10]]], 'objective': 19.0}","[[0, 6, 5], [1, 0, 6], [2, 5, 2], [3, 1, 7], [4, 2, 0], [5, 7, 1], [6, 3, 4], [7, 4, 3]]",19.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 39}, {'i': 1, 'j': 1, 'k': 2, 'cost': 11}, {'i': 1, 'j': 1, 'k': 3, 'cost': 19}, {'i': 1, 'j': 1, 'k': 4, 'cost': 34}, {'i': 1, 'j': 1, 'k': 5, 'cost': 16}, {'i': 1, 'j': 1, 'k': 6, 'cost': 88}, {'i': 1, 'j': 1, 'k': 7, 'cost': 5}, {'i': 1, 'j': 1, 'k': 8, 'cost': 67}, {'i': 1, 'j': 2, 'k': 1, 'cost': 32}, {'i': 1, 'j': 2, 'k': 2, 'cost': 37}, {'i': 1, 'j': 2, 'k': 3, 'cost': 0}, {'i': 1, 'j': 2, 'k': 4, 'cost': 50}, {'i': 1, 'j': 2, 'k': 5, 'cost': 38}, {'i': 1, 'j': 2, 'k': 6, 'cost': 53}, {'i': 1, 'j': 2, 'k': 7, 'cost': 1}, {'i': 1, 'j': 2, 'k': 8, 'cost': 14}, {'i': 1, 'j': 3, 'k': 1, 'cost': 94}, {'i': 1, 'j': 3, 'k': 2, 'cost': 48}, {'i': 1, 'j': 3, 'k': 3, 'cost': 1}, {'i': 1, 'j': 3, 'k': 4, 'cost': 54}, {'i': 1, 'j': 3, 'k': 5, 'cost': 64}, {'i': 1, 'j': 3, 'k': 6, 'cost': 75}, {'i': 1, 'j': 3, 'k': 7, 'cost': 90}, {'i': 1, 'j': 3, 'k': 8, 'cost': 60}, {'i': 1, 'j': 4, 'k': 1, 'cost': 97}, {'i': 1, 'j': 4, 'k': 2, 'cost': 52}, {'i': 1, 'j': 4, 'k': 3, 'cost': 25}, {'i': 1, 'j': 4, 'k': 4, 'cost': 99}, {'i': 1, 'j': 4, 'k': 5, 'cost': 66}, {'i': 1, 'j': 4, 'k': 6, 'cost': 58}, {'i': 1, 'j': 4, 'k': 7, 'cost': 28}, {'i': 1, 'j': 4, 'k': 8, 'cost': 20}, {'i': 1, 'j': 5, 'k': 1, 'cost': 5}, {'i': 1, 'j': 5, 'k': 2, 'cost': 96}, {'i': 1, 'j': 5, 'k': 3, 'cost': 29}, {'i': 1, 'j': 5, 'k': 4, 'cost': 31}, {'i': 1, 'j': 5, 'k': 5, 'cost': 2}, {'i': 1, 'j': 5, 'k': 6, 'cost': 98}, {'i': 1, 'j': 5, 'k': 7, 'cost': 88}, {'i': 1, 'j': 5, 'k': 8, 'cost': 98}, {'i': 1, 'j': 6, 'k': 1, 'cost': 67}, {'i': 1, 'j': 6, 'k': 2, 'cost': 72}, {'i': 1, 'j': 6, 'k': 3, 'cost': 63}, {'i': 1, 'j': 6, 'k': 4, 'cost': 8}, {'i': 1, 'j': 6, 'k': 5, 'cost': 57}, {'i': 1, 'j': 6, 'k': 6, 'cost': 40}, {'i': 1, 'j': 6, 'k': 7, 'cost': 49}, {'i': 1, 'j': 6, 'k': 8, 'cost': 67}, {'i': 1, 'j': 7, 'k': 1, 'cost': 35}, {'i': 1, 'j': 7, 'k': 2, 'cost': 23}, {'i': 1, 'j': 7, 'k': 3, 'cost': 44}, {'i': 1, 'j': 7, 'k': 4, 'cost': 94}, {'i': 1, 'j': 7, 'k': 5, 'cost': 84}, {'i': 1, 'j': 7, 'k': 6, 'cost': 4}, {'i': 1, 'j': 7, 'k': 7, 'cost': 70}, {'i': 1, 'j': 7, 'k': 8, 'cost': 90}, {'i': 1, 'j': 8, 'k': 1, 'cost': 66}, {'i': 1, 'j': 8, 'k': 2, 'cost': 53}, {'i': 1, 'j': 8, 'k': 3, 'cost': 66}, {'i': 1, 'j': 8, 'k': 4, 'cost': 24}, {'i': 1, 'j': 8, 'k': 5, 'cost': 2}, {'i': 1, 'j': 8, 'k': 6, 'cost': 32}, {'i': 1, 'j': 8, 'k': 7, 'cost': 70}, {'i': 1, 'j': 8, 'k': 8, 'cost': 97}, {'i': 2, 'j': 1, 'k': 1, 'cost': 12}, {'i': 2, 'j': 1, 'k': 2, 'cost': 62}, {'i': 2, 'j': 1, 'k': 3, 'cost': 14}, {'i': 2, 'j': 1, 'k': 4, 'cost': 49}, {'i': 2, 'j': 1, 'k': 5, 'cost': 15}, {'i': 2, 'j': 1, 'k': 6, 'cost': 22}, {'i': 2, 'j': 1, 'k': 7, 'cost': 4}, {'i': 2, 'j': 1, 'k': 8, 'cost': 16}, {'i': 2, 'j': 2, 'k': 1, 'cost': 80}, {'i': 2, 'j': 2, 'k': 2, 'cost': 27}, {'i': 2, 'j': 2, 'k': 3, 'cost': 17}, {'i': 2, 'j': 2, 'k': 4, 'cost': 39}, {'i': 2, 'j': 2, 'k': 5, 'cost': 2}, {'i': 2, 'j': 2, 'k': 6, 'cost': 75}, {'i': 2, 'j': 2, 'k': 7, 'cost': 68}, {'i': 2, 'j': 2, 'k': 8, 'cost': 28}, {'i': 2, 'j': 3, 'k': 1, 'cost': 23}, {'i': 2, 'j': 3, 'k': 2, 'cost': 96}, {'i': 2, 'j': 3, 'k': 3, 'cost': 18}, {'i': 2, 'j': 3, 'k': 4, 'cost': 65}, {'i': 2, 'j': 3, 'k': 5, 'cost': 44}, {'i': 2, 'j': 3, 'k': 6, 'cost': 4}, {'i': 2, 'j': 3, 'k': 7, 'cost': 81}, {'i': 2, 'j': 3, 'k': 8, 'cost': 91}, {'i': 2, 'j': 4, 'k': 1, 'cost': 14}, {'i': 2, 'j': 4, 'k': 2, 'cost': 24}, {'i': 2, 'j': 4, 'k': 3, 'cost': 26}, {'i': 2, 'j': 4, 'k': 4, 'cost': 27}, {'i': 2, 'j': 4, 'k': 5, 'cost': 3}, {'i': 2, 'j': 4, 'k': 6, 'cost': 62}, {'i': 2, 'j': 4, 'k': 7, 'cost': 14}, {'i': 2, 'j': 4, 'k': 8, 'cost': 79}, {'i': 2, 'j': 5, 'k': 1, 'cost': 19}, {'i': 2, 'j': 5, 'k': 2, 'cost': 73}, {'i': 2, 'j': 5, 'k': 3, 'cost': 69}, {'i': 2, 'j': 5, 'k': 4, 'cost': 20}, {'i': 2, 'j': 5, 'k': 5, 'cost': 40}, {'i': 2, 'j': 5, 'k': 6, 'cost': 3}, {'i': 2, 'j': 5, 'k': 7, 'cost': 69}, {'i': 2, 'j': 5, 'k': 8, 'cost': 89}, {'i': 2, 'j': 6, 'k': 1, 'cost': 14}, {'i': 2, 'j': 6, 'k': 2, 'cost': 6}, {'i': 2, 'j': 6, 'k': 3, 'cost': 6}, {'i': 2, 'j': 6, 'k': 4, 'cost': 21}, {'i': 2, 'j': 6, 'k': 5, 'cost': 3}, {'i': 2, 'j': 6, 'k': 6, 'cost': 77}, {'i': 2, 'j': 6, 'k': 7, 'cost': 87}, {'i': 2, 'j': 6, 'k': 8, 'cost': 67}, {'i': 2, 'j': 7, 'k': 1, 'cost': 51}, {'i': 2, 'j': 7, 'k': 2, 'cost': 6}, {'i': 2, 'j': 7, 'k': 3, 'cost': 31}, {'i': 2, 'j': 7, 'k': 4, 'cost': 30}, {'i': 2, 'j': 7, 'k': 5, 'cost': 81}, {'i': 2, 'j': 7, 'k': 6, 'cost': 40}, {'i': 2, 'j': 7, 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4, 'k': 1, 'cost': 49}, {'i': 7, 'j': 4, 'k': 2, 'cost': 75}, {'i': 7, 'j': 4, 'k': 3, 'cost': 84}, {'i': 7, 'j': 4, 'k': 4, 'cost': 23}, {'i': 7, 'j': 4, 'k': 5, 'cost': 4}, {'i': 7, 'j': 4, 'k': 6, 'cost': 47}, {'i': 7, 'j': 4, 'k': 7, 'cost': 92}, {'i': 7, 'j': 4, 'k': 8, 'cost': 64}, {'i': 7, 'j': 5, 'k': 1, 'cost': 35}, {'i': 7, 'j': 5, 'k': 2, 'cost': 69}, {'i': 7, 'j': 5, 'k': 3, 'cost': 9}, {'i': 7, 'j': 5, 'k': 4, 'cost': 66}, {'i': 7, 'j': 5, 'k': 5, 'cost': 47}, {'i': 7, 'j': 5, 'k': 6, 'cost': 32}, {'i': 7, 'j': 5, 'k': 7, 'cost': 28}, {'i': 7, 'j': 5, 'k': 8, 'cost': 61}, {'i': 7, 'j': 6, 'k': 1, 'cost': 84}, {'i': 7, 'j': 6, 'k': 2, 'cost': 57}, {'i': 7, 'j': 6, 'k': 3, 'cost': 81}, {'i': 7, 'j': 6, 'k': 4, 'cost': 21}, {'i': 7, 'j': 6, 'k': 5, 'cost': 49}, {'i': 7, 'j': 6, 'k': 6, 'cost': 20}, {'i': 7, 'j': 6, 'k': 7, 'cost': 76}, {'i': 7, 'j': 6, 'k': 8, 'cost': 6}, {'i': 7, 'j': 7, 'k': 1, 'cost': 69}, {'i': 7, 'j': 7, 'k': 2, 'cost': 51}, {'i': 7, 'j': 7, 'k': 3, 'cost': 28}, {'i': 7, 'j': 7, 'k': 4, 'cost': 12}, {'i': 7, 'j': 7, 'k': 5, 'cost': 19}, {'i': 7, 'j': 7, 'k': 6, 'cost': 34}, {'i': 7, 'j': 7, 'k': 7, 'cost': 47}, {'i': 7, 'j': 7, 'k': 8, 'cost': 48}, {'i': 7, 'j': 8, 'k': 1, 'cost': 29}, {'i': 7, 'j': 8, 'k': 2, 'cost': 34}, {'i': 7, 'j': 8, 'k': 3, 'cost': 51}, {'i': 7, 'j': 8, 'k': 4, 'cost': 39}, {'i': 7, 'j': 8, 'k': 5, 'cost': 58}, {'i': 7, 'j': 8, 'k': 6, 'cost': 80}, {'i': 7, 'j': 8, 'k': 7, 'cost': 26}, {'i': 7, 'j': 8, 'k': 8, 'cost': 66}, {'i': 8, 'j': 1, 'k': 1, 'cost': 54}, {'i': 8, 'j': 1, 'k': 2, 'cost': 68}, {'i': 8, 'j': 1, 'k': 3, 'cost': 19}, {'i': 8, 'j': 1, 'k': 4, 'cost': 7}, {'i': 8, 'j': 1, 'k': 5, 'cost': 84}, {'i': 8, 'j': 1, 'k': 6, 'cost': 10}, {'i': 8, 'j': 1, 'k': 7, 'cost': 53}, {'i': 8, 'j': 1, 'k': 8, 'cost': 29}, {'i': 8, 'j': 2, 'k': 1, 'cost': 15}, {'i': 8, 'j': 2, 'k': 2, 'cost': 91}, {'i': 8, 'j': 2, 'k': 3, 'cost': 41}, {'i': 8, 'j': 2, 'k': 4, 'cost': 90}, {'i': 8, 'j': 2, 'k': 5, 'cost': 55}, {'i': 8, 'j': 2, 'k': 6, 'cost': 92}, {'i': 8, 'j': 2, 'k': 7, 'cost': 87}, {'i': 8, 'j': 2, 'k': 8, 'cost': 84}, {'i': 8, 'j': 3, 'k': 1, 'cost': 39}, {'i': 8, 'j': 3, 'k': 2, 'cost': 27}, {'i': 8, 'j': 3, 'k': 3, 'cost': 68}, {'i': 8, 'j': 3, 'k': 4, 'cost': 10}, {'i': 8, 'j': 3, 'k': 5, 'cost': 23}, {'i': 8, 'j': 3, 'k': 6, 'cost': 65}, {'i': 8, 'j': 3, 'k': 7, 'cost': 71}, {'i': 8, 'j': 3, 'k': 8, 'cost': 49}, {'i': 8, 'j': 4, 'k': 1, 'cost': 16}, {'i': 8, 'j': 4, 'k': 2, 'cost': 63}, {'i': 8, 'j': 4, 'k': 3, 'cost': 85}, {'i': 8, 'j': 4, 'k': 4, 'cost': 39}, {'i': 8, 'j': 4, 'k': 5, 'cost': 38}, {'i': 8, 'j': 4, 'k': 6, 'cost': 44}, {'i': 8, 'j': 4, 'k': 7, 'cost': 72}, {'i': 8, 'j': 4, 'k': 8, 'cost': 74}, {'i': 8, 'j': 5, 'k': 1, 'cost': 0}, {'i': 8, 'j': 5, 'k': 2, 'cost': 96}, {'i': 8, 'j': 5, 'k': 3, 'cost': 28}, {'i': 8, 'j': 5, 'k': 4, 'cost': 1}, {'i': 8, 'j': 5, 'k': 5, 'cost': 14}, {'i': 8, 'j': 5, 'k': 6, 'cost': 86}, {'i': 8, 'j': 5, 'k': 7, 'cost': 9}, {'i': 8, 'j': 5, 'k': 8, 'cost': 43}, {'i': 8, 'j': 6, 'k': 1, 'cost': 15}, {'i': 8, 'j': 6, 'k': 2, 'cost': 90}, {'i': 8, 'j': 6, 'k': 3, 'cost': 64}, {'i': 8, 'j': 6, 'k': 4, 'cost': 25}, {'i': 8, 'j': 6, 'k': 5, 'cost': 58}, {'i': 8, 'j': 6, 'k': 6, 'cost': 53}, {'i': 8, 'j': 6, 'k': 7, 'cost': 41}, {'i': 8, 'j': 6, 'k': 8, 'cost': 13}, {'i': 8, 'j': 7, 'k': 1, 'cost': 44}, {'i': 8, 'j': 7, 'k': 2, 'cost': 47}, {'i': 8, 'j': 7, 'k': 3, 'cost': 61}, {'i': 8, 'j': 7, 'k': 4, 'cost': 49}, {'i': 8, 'j': 7, 'k': 5, 'cost': 42}, {'i': 8, 'j': 7, 'k': 6, 'cost': 82}, {'i': 8, 'j': 7, 'k': 7, 'cost': 95}, {'i': 8, 'j': 7, 'k': 8, 'cost': 39}, {'i': 8, 'j': 8, 'k': 1, 'cost': 20}, {'i': 8, 'j': 8, 'k': 2, 'cost': 70}, {'i': 8, 'j': 8, 'k': 3, 'cost': 60}, {'i': 8, 'j': 8, 'k': 4, 'cost': 69}, {'i': 8, 'j': 8, 'k': 5, 'cost': 92}, {'i': 8, 'j': 8, 'k': 6, 'cost': 46}, {'i': 8, 'j': 8, 'k': 7, 'cost': 55}, {'i': 8, 'j': 8, 'k': 8, 'cost': 10}]}","[[1, 7, 6], [2, 1, 7], [3, 6, 3], [4, 2, 8], [5, 3, 1], [6, 8, 2], [7, 4, 5], [8, 5, 4]]",3,json,1
AP3,AP3,"Many people on the placement panel are deciding who works on what and under whom: every student must be matched to one project and one supervisor, and every project and supervisor must go to only one student. Each choice comes with a mismatch penalty, and the committee judges a full matching by summing those penalties for all students—the lower that total sum, the better the outcome. Assignments can’t be reused or skipped; it’s a strict one-to-one pairing across the three groups. The concrete list and penalties are provided below.

There are 8 students, 8 projects and 8 supervisors, identified as 1, 2, 3, 4, 5, 6, 7, 8.
Meaning: costs form a 3D tensor. For each fixed student_id=i, you are given a project_id×supervisor_id matrix whose entry at row project_id=j and column supervisor_id=k equals mismatch_penalty(i,j,k). You must pick exactly one (j,k) for every i, with all project_id and all supervisor_id used exactly once.
mismatch_penalty_tensor (per-student_id markdown matrices):
## student_id=1
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 58 | 59 | 97 | 80 | 2 | 91 | 53 | 90 |
| 2 | 85 | 19 | 41 | 86 | 49 | 11 | 7 | 8 |
| 3 | 79 | 83 | 4 | 43 | 27 | 0 | 41 | 9 |
| 4 | 36 | 36 | 89 | 19 | 45 | 3 | 38 | 74 |
| 5 | 31 | 22 | 70 | 68 | 48 | 82 | 28 | 37 |
| 6 | 32 | 68 | 92 | 58 | 85 | 43 | 32 | 22 |
| 7 | 40 | 31 | 53 | 67 | 36 | 2 | 75 | 92 |
| 8 | 26 | 83 | 47 | 88 | 22 | 7 | 90 | 60 |

## student_id=2
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 12 | 79 | 10 | 9 | 9 | 14 | 4 | 87 |
| 2 | 16 | 21 | 83 | 72 | 25 | 12 | 37 | 23 |
| 3 | 72 | 49 | 30 | 4 | 72 | 52 | 42 | 79 |
| 4 | 27 | 36 | 24 | 23 | 9 | 54 | 80 | 59 |
| 5 | 22 | 84 | 83 | 74 | 13 | 6 | 41 | 51 |
| 6 | 21 | 48 | 3 | 21 | 85 | 24 | 94 | 32 |
| 7 | 39 | 78 | 56 | 16 | 70 | 70 | 76 | 71 |
| 8 | 65 | 56 | 55 | 55 | 81 | 33 | 71 | 38 |

## student_id=3
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 62 | 97 | 8 | 60 | 48 | 75 | 33 | 97 |
| 2 | 11 | 40 | 79 | 75 | 50 | 96 | 13 | 68 |
| 3 | 98 | 50 | 78 | 77 | 86 | 30 | 58 | 99 |
| 4 | 36 | 32 | 16 | 84 | 52 | 2 | 72 | 2 |
| 5 | 15 | 1 | 89 | 84 | 66 | 99 | 38 | 34 |
| 6 | 33 | 79 | 79 | 22 | 19 | 34 | 11 | 57 |
| 7 | 45 | 35 | 57 | 50 | 48 | 39 | 68 | 75 |
| 8 | 80 | 58 | 30 | 0 | 3 | 3 | 11 | 59 |

## student_id=4
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 91 | 99 | 70 | 76 | 23 | 14 | 95 | 37 |
| 2 | 27 | 36 | 16 | 26 | 26 | 75 | 50 | 58 |
| 3 | 93 | 83 | 17 | 23 | 13 | 35 | 15 | 58 |
| 4 | 90 | 72 | 52 | 92 | 9 | 20 | 55 | 1 |
| 5 | 56 | 86 | 32 | 59 | 69 | 91 | 37 | 56 |
| 6 | 79 | 70 | 34 | 81 | 44 | 70 | 59 | 93 |
| 7 | 83 | 24 | 76 | 68 | 85 | 5 | 66 | 4 |
| 8 | 85 | 14 | 11 | 34 | 69 | 49 | 84 | 80 |

## student_id=5
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 7 | 13 | 91 | 35 | 19 | 76 | 39 | 17 |
| 2 | 71 | 75 | 29 | 94 | 27 | 63 | 36 | 43 |
| 3 | 58 | 87 | 50 | 59 | 69 | 34 | 88 | 67 |
| 4 | 61 | 23 | 65 | 2 | 73 | 49 | 13 | 3 |
| 5 | 10 | 72 | 85 | 98 | 7 | 63 | 19 | 84 |
| 6 | 69 | 61 | 17 | 62 | 89 | 75 | 84 | 96 |
| 7 | 60 | 3 | 56 | 70 | 70 | 9 | 49 | 2 |
| 8 | 72 | 90 | 72 | 25 | 88 | 19 | 9 | 23 |

## student_id=6
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 93 | 77 | 91 | 40 | 16 | 79 | 0 | 38 |
| 2 | 31 | 7 | 48 | 47 | 20 | 85 | 14 | 7 |
| 3 | 56 | 92 | 22 | 56 | 12 | 6 | 12 | 71 |
| 4 | 83 | 59 | 94 | 42 | 15 | 41 | 38 | 55 |
| 5 | 85 | 32 | 22 | 9 | 27 | 86 | 93 | 99 |
| 6 | 80 | 36 | 72 | 61 | 47 | 12 | 66 | 15 |
| 7 | 49 | 63 | 0 | 0 | 39 | 61 | 53 | 32 |
| 8 | 44 | 79 | 73 | 3 | 96 | 88 | 31 | 1 |

## student_id=7
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 15 | 51 | 53 | 96 | 22 | 11 | 23 | 49 |
| 2 | 34 | 83 | 4 | 53 | 59 | 59 | 82 | 50 |
| 3 | 33 | 13 | 1 | 71 | 35 | 7 | 71 | 66 |
| 4 | 42 | 65 | 55 | 1 | 9 | 81 | 33 | 57 |
| 5 | 4 | 12 | 25 | 67 | 59 | 76 | 64 | 40 |
| 6 | 18 | 17 | 14 | 12 | 7 | 74 | 36 | 2 |
| 7 | 51 | 71 | 40 | 42 | 3 | 30 | 34 | 28 |
| 8 | 8 | 62 | 96 | 75 | 22 | 38 | 57 | 71 |

## student_id=8
| project_id\supervisor_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 42 | 60 | 77 | 62 | 19 | 68 | 39 | 15 |
| 2 | 50 | 86 | 71 | 39 | 38 | 57 | 89 | 46 |
| 3 | 24 | 93 | 63 | 95 | 95 | 18 | 62 | 30 |
| 4 | 37 | 36 | 33 | 48 | 46 | 22 | 72 | 91 |
| 5 | 6 | 1 | 88 | 99 | 53 | 21 | 79 | 61 |
| 6 | 48 | 5 | 6 | 7 | 17 | 33 | 32 | 0 |
| 7 | 97 | 81 | 30 | 4 | 3 | 7 | 75 | 51 |
| 8 | 7 | 11 | 4 | 17 | 59 | 35 | 91 | 6 |
The committee will sum the listed mismatch penalties to judge each complete matching.

If you want to hand back a matching, just use this simple JSON shape — it's the format I expect for a proposed assignment:

{
  ""solution"": [
    [<student_id>, <project_id>, <supervisor_id>],
    ...
  ]
}

Each inner list is one complete choice: the student, then the project they get, then the supervisor. The ""solution"" array is just the full list of those triples for everyone. This is only a sketch of the shape I want — replace the placeholders with the actual IDs from the instance when you submit a real matching.

Please make sure all identifiers are used exactly as they appear in the instance input — no renaming and no 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”.","{'cost_tensor': [[[58, 59, 97, 80, 2, 91, 53, 90], [85, 19, 41, 86, 49, 11, 7, 8], [79, 83, 4, 43, 27, 0, 41, 9], [36, 36, 89, 19, 45, 3, 38, 74], [31, 22, 70, 68, 48, 82, 28, 37], [32, 68, 92, 58, 85, 43, 32, 22], [40, 31, 53, 67, 36, 2, 75, 92], [26, 83, 47, 88, 22, 7, 90, 60]], [[12, 79, 10, 9, 9, 14, 4, 87], [16, 21, 83, 72, 25, 12, 37, 23], [72, 49, 30, 4, 72, 52, 42, 79], [27, 36, 24, 23, 9, 54, 80, 59], [22, 84, 83, 74, 13, 6, 41, 51], [21, 48, 3, 21, 85, 24, 94, 32], [39, 78, 56, 16, 70, 70, 76, 71], [65, 56, 55, 55, 81, 33, 71, 38]], [[62, 97, 8, 60, 48, 75, 33, 97], [11, 40, 79, 75, 50, 96, 13, 68], [98, 50, 78, 77, 86, 30, 58, 99], [36, 32, 16, 84, 52, 2, 72, 2], [15, 1, 89, 84, 66, 99, 38, 34], [33, 79, 79, 22, 19, 34, 11, 57], [45, 35, 57, 50, 48, 39, 68, 75], [80, 58, 30, 0, 3, 3, 11, 59]], [[91, 99, 70, 76, 23, 14, 95, 37], [27, 36, 16, 26, 26, 75, 50, 58], [93, 83, 17, 23, 13, 35, 15, 58], [90, 72, 52, 92, 9, 20, 55, 1], [56, 86, 32, 59, 69, 91, 37, 56], [79, 70, 34, 81, 44, 70, 59, 93], [83, 24, 76, 68, 85, 5, 66, 4], [85, 14, 11, 34, 69, 49, 84, 80]], [[7, 13, 91, 35, 19, 76, 39, 17], [71, 75, 29, 94, 27, 63, 36, 43], [58, 87, 50, 59, 69, 34, 88, 67], [61, 23, 65, 2, 73, 49, 13, 3], [10, 72, 85, 98, 7, 63, 19, 84], [69, 61, 17, 62, 89, 75, 84, 96], [60, 3, 56, 70, 70, 9, 49, 2], [72, 90, 72, 25, 88, 19, 9, 23]], [[93, 77, 91, 40, 16, 79, 0, 38], [31, 7, 48, 47, 20, 85, 14, 7], [56, 92, 22, 56, 12, 6, 12, 71], [83, 59, 94, 42, 15, 41, 38, 55], [85, 32, 22, 9, 27, 86, 93, 99], [80, 36, 72, 61, 47, 12, 66, 15], [49, 63, 0, 0, 39, 61, 53, 32], [44, 79, 73, 3, 96, 88, 31, 1]], [[15, 51, 53, 96, 22, 11, 23, 49], [34, 83, 4, 53, 59, 59, 82, 50], [33, 13, 1, 71, 35, 7, 71, 66], [42, 65, 55, 1, 9, 81, 33, 57], [4, 12, 25, 67, 59, 76, 64, 40], [18, 17, 14, 12, 7, 74, 36, 2], [51, 71, 40, 42, 3, 30, 34, 28], [8, 62, 96, 75, 22, 38, 57, 71]], [[42, 60, 77, 62, 19, 68, 39, 15], [50, 86, 71, 39, 38, 57, 89, 46], [24, 93, 63, 95, 95, 18, 62, 30], [37, 36, 33, 48, 46, 22, 72, 91], [6, 1, 88, 99, 53, 21, 79, 61], [48, 5, 6, 7, 17, 33, 32, 0], [97, 81, 30, 4, 3, 7, 75, 51], [7, 11, 4, 17, 59, 35, 91, 6]]], 'objective': 27.0}","[[0, 2, 5], [1, 0, 6], [2, 7, 4], [3, 3, 7], [4, 4, 0], [5, 6, 3], [6, 1, 2], [7, 5, 1]]",27.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 58}, {'i': 1, 'j': 1, 'k': 2, 'cost': 59}, {'i': 1, 'j': 1, 'k': 3, 'cost': 97}, {'i': 1, 'j': 1, 'k': 4, 'cost': 80}, {'i': 1, 'j': 1, 'k': 5, 'cost': 2}, {'i': 1, 'j': 1, 'k': 6, 'cost': 91}, {'i': 1, 'j': 1, 'k': 7, 'cost': 53}, {'i': 1, 'j': 1, 'k': 8, 'cost': 90}, {'i': 1, 'j': 2, 'k': 1, 'cost': 85}, {'i': 1, 'j': 2, 'k': 2, 'cost': 19}, {'i': 1, 'j': 2, 'k': 3, 'cost': 41}, {'i': 1, 'j': 2, 'k': 4, 'cost': 86}, {'i': 1, 'j': 2, 'k': 5, 'cost': 49}, {'i': 1, 'j': 2, 'k': 6, 'cost': 11}, {'i': 1, 'j': 2, 'k': 7, 'cost': 7}, {'i': 1, 'j': 2, 'k': 8, 'cost': 8}, {'i': 1, 'j': 3, 'k': 1, 'cost': 79}, {'i': 1, 'j': 3, 'k': 2, 'cost': 83}, {'i': 1, 'j': 3, 'k': 3, 'cost': 4}, {'i': 1, 'j': 3, 'k': 4, 'cost': 43}, {'i': 1, 'j': 3, 'k': 5, 'cost': 27}, {'i': 1, 'j': 3, 'k': 6, 'cost': 0}, {'i': 1, 'j': 3, 'k': 7, 'cost': 41}, {'i': 1, 'j': 3, 'k': 8, 'cost': 9}, {'i': 1, 'j': 4, 'k': 1, 'cost': 36}, {'i': 1, 'j': 4, 'k': 2, 'cost': 36}, {'i': 1, 'j': 4, 'k': 3, 'cost': 89}, {'i': 1, 'j': 4, 'k': 4, 'cost': 19}, {'i': 1, 'j': 4, 'k': 5, 'cost': 45}, {'i': 1, 'j': 4, 'k': 6, 'cost': 3}, {'i': 1, 'j': 4, 'k': 7, 'cost': 38}, {'i': 1, 'j': 4, 'k': 8, 'cost': 74}, {'i': 1, 'j': 5, 'k': 1, 'cost': 31}, {'i': 1, 'j': 5, 'k': 2, 'cost': 22}, {'i': 1, 'j': 5, 'k': 3, 'cost': 70}, {'i': 1, 'j': 5, 'k': 4, 'cost': 68}, {'i': 1, 'j': 5, 'k': 5, 'cost': 48}, {'i': 1, 'j': 5, 'k': 6, 'cost': 82}, {'i': 1, 'j': 5, 'k': 7, 'cost': 28}, {'i': 1, 'j': 5, 'k': 8, 'cost': 37}, {'i': 1, 'j': 6, 'k': 1, 'cost': 32}, {'i': 1, 'j': 6, 'k': 2, 'cost': 68}, {'i': 1, 'j': 6, 'k': 3, 'cost': 92}, {'i': 1, 'j': 6, 'k': 4, 'cost': 58}, {'i': 1, 'j': 6, 'k': 5, 'cost': 85}, {'i': 1, 'j': 6, 'k': 6, 'cost': 43}, {'i': 1, 'j': 6, 'k': 7, 'cost': 32}, {'i': 1, 'j': 6, 'k': 8, 'cost': 22}, {'i': 1, 'j': 7, 'k': 1, 'cost': 40}, {'i': 1, 'j': 7, 'k': 2, 'cost': 31}, {'i': 1, 'j': 7, 'k': 3, 'cost': 53}, {'i': 1, 'j': 7, 'k': 4, 'cost': 67}, {'i': 1, 'j': 7, 'k': 5, 'cost': 36}, {'i': 1, 'j': 7, 'k': 6, 'cost': 2}, {'i': 1, 'j': 7, 'k': 7, 'cost': 75}, {'i': 1, 'j': 7, 'k': 8, 'cost': 92}, {'i': 1, 'j': 8, 'k': 1, 'cost': 26}, {'i': 1, 'j': 8, 'k': 2, 'cost': 83}, {'i': 1, 'j': 8, 'k': 3, 'cost': 47}, {'i': 1, 'j': 8, 'k': 4, 'cost': 88}, {'i': 1, 'j': 8, 'k': 5, 'cost': 22}, {'i': 1, 'j': 8, 'k': 6, 'cost': 7}, {'i': 1, 'j': 8, 'k': 7, 'cost': 90}, {'i': 1, 'j': 8, 'k': 8, 'cost': 60}, {'i': 2, 'j': 1, 'k': 1, 'cost': 12}, {'i': 2, 'j': 1, 'k': 2, 'cost': 79}, 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'cost': 42}, {'i': 7, 'j': 4, 'k': 2, 'cost': 65}, {'i': 7, 'j': 4, 'k': 3, 'cost': 55}, {'i': 7, 'j': 4, 'k': 4, 'cost': 1}, {'i': 7, 'j': 4, 'k': 5, 'cost': 9}, {'i': 7, 'j': 4, 'k': 6, 'cost': 81}, {'i': 7, 'j': 4, 'k': 7, 'cost': 33}, {'i': 7, 'j': 4, 'k': 8, 'cost': 57}, {'i': 7, 'j': 5, 'k': 1, 'cost': 4}, {'i': 7, 'j': 5, 'k': 2, 'cost': 12}, {'i': 7, 'j': 5, 'k': 3, 'cost': 25}, {'i': 7, 'j': 5, 'k': 4, 'cost': 67}, {'i': 7, 'j': 5, 'k': 5, 'cost': 59}, {'i': 7, 'j': 5, 'k': 6, 'cost': 76}, {'i': 7, 'j': 5, 'k': 7, 'cost': 64}, {'i': 7, 'j': 5, 'k': 8, 'cost': 40}, {'i': 7, 'j': 6, 'k': 1, 'cost': 18}, {'i': 7, 'j': 6, 'k': 2, 'cost': 17}, {'i': 7, 'j': 6, 'k': 3, 'cost': 14}, {'i': 7, 'j': 6, 'k': 4, 'cost': 12}, {'i': 7, 'j': 6, 'k': 5, 'cost': 7}, {'i': 7, 'j': 6, 'k': 6, 'cost': 74}, {'i': 7, 'j': 6, 'k': 7, 'cost': 36}, {'i': 7, 'j': 6, 'k': 8, 'cost': 2}, {'i': 7, 'j': 7, 'k': 1, 'cost': 51}, {'i': 7, 'j': 7, 'k': 2, 'cost': 71}, {'i': 7, 'j': 7, 'k': 3, 'cost': 40}, {'i': 7, 'j': 7, 'k': 4, 'cost': 42}, {'i': 7, 'j': 7, 'k': 5, 'cost': 3}, {'i': 7, 'j': 7, 'k': 6, 'cost': 30}, {'i': 7, 'j': 7, 'k': 7, 'cost': 34}, {'i': 7, 'j': 7, 'k': 8, 'cost': 28}, {'i': 7, 'j': 8, 'k': 1, 'cost': 8}, {'i': 7, 'j': 8, 'k': 2, 'cost': 62}, {'i': 7, 'j': 8, 'k': 3, 'cost': 96}, {'i': 7, 'j': 8, 'k': 4, 'cost': 75}, {'i': 7, 'j': 8, 'k': 5, 'cost': 22}, {'i': 7, 'j': 8, 'k': 6, 'cost': 38}, {'i': 7, 'j': 8, 'k': 7, 'cost': 57}, {'i': 7, 'j': 8, 'k': 8, 'cost': 71}, {'i': 8, 'j': 1, 'k': 1, 'cost': 42}, {'i': 8, 'j': 1, 'k': 2, 'cost': 60}, {'i': 8, 'j': 1, 'k': 3, 'cost': 77}, {'i': 8, 'j': 1, 'k': 4, 'cost': 62}, {'i': 8, 'j': 1, 'k': 5, 'cost': 19}, {'i': 8, 'j': 1, 'k': 6, 'cost': 68}, {'i': 8, 'j': 1, 'k': 7, 'cost': 39}, {'i': 8, 'j': 1, 'k': 8, 'cost': 15}, {'i': 8, 'j': 2, 'k': 1, 'cost': 50}, {'i': 8, 'j': 2, 'k': 2, 'cost': 86}, {'i': 8, 'j': 2, 'k': 3, 'cost': 71}, {'i': 8, 'j': 2, 'k': 4, 'cost': 39}, {'i': 8, 'j': 2, 'k': 5, 'cost': 38}, {'i': 8, 'j': 2, 'k': 6, 'cost': 57}, {'i': 8, 'j': 2, 'k': 7, 'cost': 89}, {'i': 8, 'j': 2, 'k': 8, 'cost': 46}, {'i': 8, 'j': 3, 'k': 1, 'cost': 24}, {'i': 8, 'j': 3, 'k': 2, 'cost': 93}, {'i': 8, 'j': 3, 'k': 3, 'cost': 63}, {'i': 8, 'j': 3, 'k': 4, 'cost': 95}, {'i': 8, 'j': 3, 'k': 5, 'cost': 95}, {'i': 8, 'j': 3, 'k': 6, 'cost': 18}, {'i': 8, 'j': 3, 'k': 7, 'cost': 62}, {'i': 8, 'j': 3, 'k': 8, 'cost': 30}, {'i': 8, 'j': 4, 'k': 1, 'cost': 37}, {'i': 8, 'j': 4, 'k': 2, 'cost': 36}, {'i': 8, 'j': 4, 'k': 3, 'cost': 33}, {'i': 8, 'j': 4, 'k': 4, 'cost': 48}, {'i': 8, 'j': 4, 'k': 5, 'cost': 46}, {'i': 8, 'j': 4, 'k': 6, 'cost': 22}, {'i': 8, 'j': 4, 'k': 7, 'cost': 72}, {'i': 8, 'j': 4, 'k': 8, 'cost': 91}, {'i': 8, 'j': 5, 'k': 1, 'cost': 6}, {'i': 8, 'j': 5, 'k': 2, 'cost': 1}, {'i': 8, 'j': 5, 'k': 3, 'cost': 88}, {'i': 8, 'j': 5, 'k': 4, 'cost': 99}, {'i': 8, 'j': 5, 'k': 5, 'cost': 53}, {'i': 8, 'j': 5, 'k': 6, 'cost': 21}, {'i': 8, 'j': 5, 'k': 7, 'cost': 79}, {'i': 8, 'j': 5, 'k': 8, 'cost': 61}, {'i': 8, 'j': 6, 'k': 1, 'cost': 48}, {'i': 8, 'j': 6, 'k': 2, 'cost': 5}, {'i': 8, 'j': 6, 'k': 3, 'cost': 6}, {'i': 8, 'j': 6, 'k': 4, 'cost': 7}, {'i': 8, 'j': 6, 'k': 5, 'cost': 17}, {'i': 8, 'j': 6, 'k': 6, 'cost': 33}, {'i': 8, 'j': 6, 'k': 7, 'cost': 32}, {'i': 8, 'j': 6, 'k': 8, 'cost': 0}, {'i': 8, 'j': 7, 'k': 1, 'cost': 97}, {'i': 8, 'j': 7, 'k': 2, 'cost': 81}, {'i': 8, 'j': 7, 'k': 3, 'cost': 30}, {'i': 8, 'j': 7, 'k': 4, 'cost': 4}, {'i': 8, 'j': 7, 'k': 5, 'cost': 3}, {'i': 8, 'j': 7, 'k': 6, 'cost': 7}, {'i': 8, 'j': 7, 'k': 7, 'cost': 75}, {'i': 8, 'j': 7, 'k': 8, 'cost': 51}, {'i': 8, 'j': 8, 'k': 1, 'cost': 7}, {'i': 8, 'j': 8, 'k': 2, 'cost': 11}, {'i': 8, 'j': 8, 'k': 3, 'cost': 4}, {'i': 8, 'j': 8, 'k': 4, 'cost': 17}, {'i': 8, 'j': 8, 'k': 5, 'cost': 59}, {'i': 8, 'j': 8, 'k': 6, 'cost': 35}, {'i': 8, 'j': 8, 'k': 7, 'cost': 91}, {'i': 8, 'j': 8, 'k': 8, 'cost': 6}]}","[[1, 3, 6], [2, 1, 7], [3, 8, 5], [4, 4, 8], [5, 5, 1], [6, 7, 4], [7, 2, 3], [8, 6, 2]]",4,nl,1
AP3,AP3,"Recently the studio scheduled a lineup of shoots and needed to match each model with one photographer and one backdrop, ensuring no photographer or backdrop handled more than one model. Every pairing came with a predicted retouch time, and the total retouch time for the day is simply the sum of the chosen pairings’ times — the team wanted that total to be as low as possible. The concrete options and numbers follow below.

# num_models=6
# model_ids=0, 1, 2, 3, 4, 5

# Meaning: costs form a 3D tensor. For each fixed model_id=i, you are given a photographer_id×backdrop_id matrix whose entry at row photographer_id=j and column backdrop_id=k equals expected_retouch_time(i,j,k). You must pick exactly one (j,k) for every i, with all photographer_id and all backdrop_id used exactly once.
# expected_retouch_time_tensor (per-model_id markdown matrices)

## model_id=0
| photographer_id\backdrop_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 68 | 25 | 19 | 32 | 80 | 50 |
| 1 | 85 | 39 | 98 | 79 | 85 | 5 |
| 2 | 17 | 42 | 54 | 11 | 72 | 68 |
| 3 | 74 | 61 | 70 | 55 | 83 | 53 |
| 4 | 60 | 64 | 92 | 22 | 85 | 73 |
| 5 | 49 | 70 | 65 | 79 | 18 | 47 |

## model_id=1
| photographer_id\backdrop_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 91 | 57 | 95 | 27 | 33 | 59 |
| 1 | 0 | 63 | 44 | 70 | 5 | 5 |
| 2 | 81 | 39 | 39 | 16 | 14 | 25 |
| 3 | 94 | 54 | 86 | 61 | 52 | 93 |
| 4 | 8 | 71 | 73 | 8 | 44 | 73 |
| 5 | 25 | 63 | 90 | 45 | 97 | 9 |

## model_id=2
| photographer_id\backdrop_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 18 | 45 | 13 | 84 | 97 | 97 |
| 1 | 88 | 62 | 70 | 67 | 65 | 13 |
| 2 | 0 | 60 | 74 | 71 | 47 | 17 |
| 3 | 60 | 14 | 97 | 64 | 26 | 8 |
| 4 | 80 | 96 | 5 | 14 | 94 | 25 |
| 5 | 39 | 19 | 73 | 62 | 14 | 21 |

## model_id=3
| photographer_id\backdrop_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 56 | 0 | 24 | 80 | 87 | 74 |
| 1 | 70 | 32 | 69 | 3 | 36 | 85 |
| 2 | 71 | 24 | 85 | 93 | 38 | 16 |
| 3 | 96 | 14 | 14 | 64 | 44 | 63 |
| 4 | 82 | 83 | 15 | 63 | 92 | 66 |
| 5 | 96 | 62 | 25 | 91 | 70 | 21 |

## model_id=4
| photographer_id\backdrop_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 74 | 44 | 3 | 11 | 10 | 84 |
| 1 | 28 | 94 | 31 | 1 | 44 | 56 |
| 2 | 97 | 85 | 73 | 99 | 28 | 55 |
| 3 | 87 | 10 | 30 | 83 | 29 | 91 |
| 4 | 72 | 68 | 1 | 96 | 8 | 42 |
| 5 | 86 | 82 | 58 | 30 | 61 | 75 |

## model_id=5
| photographer_id\backdrop_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 79 | 16 | 69 | 50 | 75 | 28 |
| 1 | 74 | 97 | 55 | 35 | 11 | 72 |
| 2 | 38 | 27 | 56 | 40 | 87 | 56 |
| 3 | 62 | 59 | 17 | 21 | 24 | 61 |
| 4 | 42 | 42 | 29 | 10 | 34 | 84 |
| 5 | 66 | 69 | 98 | 63 | 53 | 55 |

If you want to give the final plan, just stick to a tiny JSON layout like this — super simple and easy to read:

{
  ""solution"": [
    [<model_id>, <photographer_id>, <backdrop_id>],
    ...
  ]
}

Here ""solution"" is a list of triples. Each triple is the chosen model, the chosen photographer, and the chosen backdrop for that model (in that order). Think of it like filling out a short form: one row per model with the three ids you picked. This JSON is just a sketch showing the shape I expect, not the actual answer.

Please make sure every identifier you use matches exactly what appears in the instance input — no renaming, no 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”.","{'cost_tensor': [[[68, 25, 19, 32, 80, 50], [85, 39, 98, 79, 85, 5], [17, 42, 54, 11, 72, 68], [74, 61, 70, 55, 83, 53], [60, 64, 92, 22, 85, 73], [49, 70, 65, 79, 18, 47]], [[91, 57, 95, 27, 33, 59], [0, 63, 44, 70, 5, 5], [81, 39, 39, 16, 14, 25], [94, 54, 86, 61, 52, 93], [8, 71, 73, 8, 44, 73], [25, 63, 90, 45, 97, 9]], [[18, 45, 13, 84, 97, 97], [88, 62, 70, 67, 65, 13], [0, 60, 74, 71, 47, 17], [60, 14, 97, 64, 26, 8], [80, 96, 5, 14, 94, 25], [39, 19, 73, 62, 14, 21]], [[56, 0, 24, 80, 87, 74], [70, 32, 69, 3, 36, 85], [71, 24, 85, 93, 38, 16], [96, 14, 14, 64, 44, 63], [82, 83, 15, 63, 92, 66], [96, 62, 25, 91, 70, 21]], [[74, 44, 3, 11, 10, 84], [28, 94, 31, 1, 44, 56], [97, 85, 73, 99, 28, 55], [87, 10, 30, 83, 29, 91], [72, 68, 1, 96, 8, 42], [86, 82, 58, 30, 61, 75]], [[79, 16, 69, 50, 75, 28], [74, 97, 55, 35, 11, 72], [38, 27, 56, 40, 87, 56], [62, 59, 17, 21, 24, 61], [42, 42, 29, 10, 34, 84], [66, 69, 98, 63, 53, 55]]], 'objective': 45.0}","[[0, 5, 4], [1, 1, 5], [2, 2, 0], [3, 0, 1], [4, 4, 2], [5, 3, 3]]",45.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 68}, {'i': 0, 'j': 0, 'k': 1, 'cost': 25}, {'i': 0, 'j': 0, 'k': 2, 'cost': 19}, {'i': 0, 'j': 0, 'k': 3, 'cost': 32}, {'i': 0, 'j': 0, 'k': 4, 'cost': 80}, {'i': 0, 'j': 0, 'k': 5, 'cost': 50}, {'i': 0, 'j': 1, 'k': 0, 'cost': 85}, {'i': 0, 'j': 1, 'k': 1, 'cost': 39}, {'i': 0, 'j': 1, 'k': 2, 'cost': 98}, {'i': 0, 'j': 1, 'k': 3, 'cost': 79}, {'i': 0, 'j': 1, 'k': 4, 'cost': 85}, {'i': 0, 'j': 1, 'k': 5, 'cost': 5}, {'i': 0, 'j': 2, 'k': 0, 'cost': 17}, {'i': 0, 'j': 2, 'k': 1, 'cost': 42}, {'i': 0, 'j': 2, 'k': 2, 'cost': 54}, {'i': 0, 'j': 2, 'k': 3, 'cost': 11}, {'i': 0, 'j': 2, 'k': 4, 'cost': 72}, {'i': 0, 'j': 2, 'k': 5, 'cost': 68}, {'i': 0, 'j': 3, 'k': 0, 'cost': 74}, {'i': 0, 'j': 3, 'k': 1, 'cost': 61}, {'i': 0, 'j': 3, 'k': 2, 'cost': 70}, {'i': 0, 'j': 3, 'k': 3, 'cost': 55}, {'i': 0, 'j': 3, 'k': 4, 'cost': 83}, {'i': 0, 'j': 3, 'k': 5, 'cost': 53}, {'i': 0, 'j': 4, 'k': 0, 'cost': 60}, {'i': 0, 'j': 4, 'k': 1, 'cost': 64}, {'i': 0, 'j': 4, 'k': 2, 'cost': 92}, {'i': 0, 'j': 4, 'k': 3, 'cost': 22}, {'i': 0, 'j': 4, 'k': 4, 'cost': 85}, {'i': 0, 'j': 4, 'k': 5, 'cost': 73}, {'i': 0, 'j': 5, 'k': 0, 'cost': 49}, {'i': 0, 'j': 5, 'k': 1, 'cost': 70}, {'i': 0, 'j': 5, 'k': 2, 'cost': 65}, {'i': 0, 'j': 5, 'k': 3, 'cost': 79}, {'i': 0, 'j': 5, 'k': 4, 'cost': 18}, {'i': 0, 'j': 5, 'k': 5, 'cost': 47}, {'i': 1, 'j': 0, 'k': 0, 'cost': 91}, {'i': 1, 'j': 0, 'k': 1, 'cost': 57}, {'i': 1, 'j': 0, 'k': 2, 'cost': 95}, {'i': 1, 'j': 0, 'k': 3, 'cost': 27}, {'i': 1, 'j': 0, 'k': 4, 'cost': 33}, {'i': 1, 'j': 0, 'k': 5, 'cost': 59}, {'i': 1, 'j': 1, 'k': 0, 'cost': 0}, {'i': 1, 'j': 1, 'k': 1, 'cost': 63}, {'i': 1, 'j': 1, 'k': 2, 'cost': 44}, {'i': 1, 'j': 1, 'k': 3, 'cost': 70}, {'i': 1, 'j': 1, 'k': 4, 'cost': 5}, {'i': 1, 'j': 1, 'k': 5, 'cost': 5}, {'i': 1, 'j': 2, 'k': 0, 'cost': 81}, {'i': 1, 'j': 2, 'k': 1, 'cost': 39}, {'i': 1, 'j': 2, 'k': 2, 'cost': 39}, {'i': 1, 'j': 2, 'k': 3, 'cost': 16}, {'i': 1, 'j': 2, 'k': 4, 'cost': 14}, {'i': 1, 'j': 2, 'k': 5, 'cost': 25}, {'i': 1, 'j': 3, 'k': 0, 'cost': 94}, {'i': 1, 'j': 3, 'k': 1, 'cost': 54}, {'i': 1, 'j': 3, 'k': 2, 'cost': 86}, {'i': 1, 'j': 3, 'k': 3, 'cost': 61}, {'i': 1, 'j': 3, 'k': 4, 'cost': 52}, {'i': 1, 'j': 3, 'k': 5, 'cost': 93}, {'i': 1, 'j': 4, 'k': 0, 'cost': 8}, {'i': 1, 'j': 4, 'k': 1, 'cost': 71}, {'i': 1, 'j': 4, 'k': 2, 'cost': 73}, {'i': 1, 'j': 4, 'k': 3, 'cost': 8}, {'i': 1, 'j': 4, 'k': 4, 'cost': 44}, {'i': 1, 'j': 4, 'k': 5, 'cost': 73}, {'i': 1, 'j': 5, 'k': 0, 'cost': 25}, {'i': 1, 'j': 5, 'k': 1, 'cost': 63}, {'i': 1, 'j': 5, 'k': 2, 'cost': 90}, {'i': 1, 'j': 5, 'k': 3, 'cost': 45}, {'i': 1, 'j': 5, 'k': 4, 'cost': 97}, {'i': 1, 'j': 5, 'k': 5, 'cost': 9}, {'i': 2, 'j': 0, 'k': 0, 'cost': 18}, {'i': 2, 'j': 0, 'k': 1, 'cost': 45}, {'i': 2, 'j': 0, 'k': 2, 'cost': 13}, {'i': 2, 'j': 0, 'k': 3, 'cost': 84}, {'i': 2, 'j': 0, 'k': 4, 'cost': 97}, {'i': 2, 'j': 0, 'k': 5, 'cost': 97}, {'i': 2, 'j': 1, 'k': 0, 'cost': 88}, {'i': 2, 'j': 1, 'k': 1, 'cost': 62}, {'i': 2, 'j': 1, 'k': 2, 'cost': 70}, {'i': 2, 'j': 1, 'k': 3, 'cost': 67}, {'i': 2, 'j': 1, 'k': 4, 'cost': 65}, {'i': 2, 'j': 1, 'k': 5, 'cost': 13}, {'i': 2, 'j': 2, 'k': 0, 'cost': 0}, {'i': 2, 'j': 2, 'k': 1, 'cost': 60}, {'i': 2, 'j': 2, 'k': 2, 'cost': 74}, {'i': 2, 'j': 2, 'k': 3, 'cost': 71}, {'i': 2, 'j': 2, 'k': 4, 'cost': 47}, {'i': 2, 'j': 2, 'k': 5, 'cost': 17}, {'i': 2, 'j': 3, 'k': 0, 'cost': 60}, {'i': 2, 'j': 3, 'k': 1, 'cost': 14}, {'i': 2, 'j': 3, 'k': 2, 'cost': 97}, {'i': 2, 'j': 3, 'k': 3, 'cost': 64}, {'i': 2, 'j': 3, 'k': 4, 'cost': 26}, {'i': 2, 'j': 3, 'k': 5, 'cost': 8}, {'i': 2, 'j': 4, 'k': 0, 'cost': 80}, {'i': 2, 'j': 4, 'k': 1, 'cost': 96}, {'i': 2, 'j': 4, 'k': 2, 'cost': 5}, {'i': 2, 'j': 4, 'k': 3, 'cost': 14}, {'i': 2, 'j': 4, 'k': 4, 'cost': 94}, {'i': 2, 'j': 4, 'k': 5, 'cost': 25}, {'i': 2, 'j': 5, 'k': 0, 'cost': 39}, {'i': 2, 'j': 5, 'k': 1, 'cost': 19}, {'i': 2, 'j': 5, 'k': 2, 'cost': 73}, {'i': 2, 'j': 5, 'k': 3, 'cost': 62}, {'i': 2, 'j': 5, 'k': 4, 'cost': 14}, {'i': 2, 'j': 5, 'k': 5, 'cost': 21}, {'i': 3, 'j': 0, 'k': 0, 'cost': 56}, {'i': 3, 'j': 0, 'k': 1, 'cost': 0}, {'i': 3, 'j': 0, 'k': 2, 'cost': 24}, {'i': 3, 'j': 0, 'k': 3, 'cost': 80}, {'i': 3, 'j': 0, 'k': 4, 'cost': 87}, {'i': 3, 'j': 0, 'k': 5, 'cost': 74}, {'i': 3, 'j': 1, 'k': 0, 'cost': 70}, {'i': 3, 'j': 1, 'k': 1, 'cost': 32}, {'i': 3, 'j': 1, 'k': 2, 'cost': 69}, {'i': 3, 'j': 1, 'k': 3, 'cost': 3}, {'i': 3, 'j': 1, 'k': 4, 'cost': 36}, {'i': 3, 'j': 1, 'k': 5, 'cost': 85}, {'i': 3, 'j': 2, 'k': 0, 'cost': 71}, {'i': 3, 'j': 2, 'k': 1, 'cost': 24}, {'i': 3, 'j': 2, 'k': 2, 'cost': 85}, {'i': 3, 'j': 2, 'k': 3, 'cost': 93}, {'i': 3, 'j': 2, 'k': 4, 'cost': 38}, {'i': 3, 'j': 2, 'k': 5, 'cost': 16}, {'i': 3, 'j': 3, 'k': 0, 'cost': 96}, {'i': 3, 'j': 3, 'k': 1, 'cost': 14}, {'i': 3, 'j': 3, 'k': 2, 'cost': 14}, {'i': 3, 'j': 3, 'k': 3, 'cost': 64}, {'i': 3, 'j': 3, 'k': 4, 'cost': 44}, {'i': 3, 'j': 3, 'k': 5, 'cost': 63}, {'i': 3, 'j': 4, 'k': 0, 'cost': 82}, {'i': 3, 'j': 4, 'k': 1, 'cost': 83}, {'i': 3, 'j': 4, 'k': 2, 'cost': 15}, {'i': 3, 'j': 4, 'k': 3, 'cost': 63}, {'i': 3, 'j': 4, 'k': 4, 'cost': 92}, {'i': 3, 'j': 4, 'k': 5, 'cost': 66}, {'i': 3, 'j': 5, 'k': 0, 'cost': 96}, {'i': 3, 'j': 5, 'k': 1, 'cost': 62}, {'i': 3, 'j': 5, 'k': 2, 'cost': 25}, {'i': 3, 'j': 5, 'k': 3, 'cost': 91}, {'i': 3, 'j': 5, 'k': 4, 'cost': 70}, {'i': 3, 'j': 5, 'k': 5, 'cost': 21}, {'i': 4, 'j': 0, 'k': 0, 'cost': 74}, {'i': 4, 'j': 0, 'k': 1, 'cost': 44}, {'i': 4, 'j': 0, 'k': 2, 'cost': 3}, {'i': 4, 'j': 0, 'k': 3, 'cost': 11}, {'i': 4, 'j': 0, 'k': 4, 'cost': 10}, {'i': 4, 'j': 0, 'k': 5, 'cost': 84}, {'i': 4, 'j': 1, 'k': 0, 'cost': 28}, {'i': 4, 'j': 1, 'k': 1, 'cost': 94}, {'i': 4, 'j': 1, 'k': 2, 'cost': 31}, {'i': 4, 'j': 1, 'k': 3, 'cost': 1}, {'i': 4, 'j': 1, 'k': 4, 'cost': 44}, {'i': 4, 'j': 1, 'k': 5, 'cost': 56}, {'i': 4, 'j': 2, 'k': 0, 'cost': 97}, {'i': 4, 'j': 2, 'k': 1, 'cost': 85}, {'i': 4, 'j': 2, 'k': 2, 'cost': 73}, {'i': 4, 'j': 2, 'k': 3, 'cost': 99}, {'i': 4, 'j': 2, 'k': 4, 'cost': 28}, {'i': 4, 'j': 2, 'k': 5, 'cost': 55}, {'i': 4, 'j': 3, 'k': 0, 'cost': 87}, {'i': 4, 'j': 3, 'k': 1, 'cost': 10}, {'i': 4, 'j': 3, 'k': 2, 'cost': 30}, {'i': 4, 'j': 3, 'k': 3, 'cost': 83}, {'i': 4, 'j': 3, 'k': 4, 'cost': 29}, {'i': 4, 'j': 3, 'k': 5, 'cost': 91}, {'i': 4, 'j': 4, 'k': 0, 'cost': 72}, {'i': 4, 'j': 4, 'k': 1, 'cost': 68}, {'i': 4, 'j': 4, 'k': 2, 'cost': 1}, {'i': 4, 'j': 4, 'k': 3, 'cost': 96}, {'i': 4, 'j': 4, 'k': 4, 'cost': 8}, {'i': 4, 'j': 4, 'k': 5, 'cost': 42}, {'i': 4, 'j': 5, 'k': 0, 'cost': 86}, {'i': 4, 'j': 5, 'k': 1, 'cost': 82}, {'i': 4, 'j': 5, 'k': 2, 'cost': 58}, {'i': 4, 'j': 5, 'k': 3, 'cost': 30}, {'i': 4, 'j': 5, 'k': 4, 'cost': 61}, {'i': 4, 'j': 5, 'k': 5, 'cost': 75}, {'i': 5, 'j': 0, 'k': 0, 'cost': 79}, {'i': 5, 'j': 0, 'k': 1, 'cost': 16}, {'i': 5, 'j': 0, 'k': 2, 'cost': 69}, {'i': 5, 'j': 0, 'k': 3, 'cost': 50}, {'i': 5, 'j': 0, 'k': 4, 'cost': 75}, {'i': 5, 'j': 0, 'k': 5, 'cost': 28}, {'i': 5, 'j': 1, 'k': 0, 'cost': 74}, {'i': 5, 'j': 1, 'k': 1, 'cost': 97}, {'i': 5, 'j': 1, 'k': 2, 'cost': 55}, {'i': 5, 'j': 1, 'k': 3, 'cost': 35}, {'i': 5, 'j': 1, 'k': 4, 'cost': 11}, {'i': 5, 'j': 1, 'k': 5, 'cost': 72}, {'i': 5, 'j': 2, 'k': 0, 'cost': 38}, {'i': 5, 'j': 2, 'k': 1, 'cost': 27}, {'i': 5, 'j': 2, 'k': 2, 'cost': 56}, {'i': 5, 'j': 2, 'k': 3, 'cost': 40}, {'i': 5, 'j': 2, 'k': 4, 'cost': 87}, {'i': 5, 'j': 2, 'k': 5, 'cost': 56}, {'i': 5, 'j': 3, 'k': 0, 'cost': 62}, {'i': 5, 'j': 3, 'k': 1, 'cost': 59}, {'i': 5, 'j': 3, 'k': 2, 'cost': 17}, {'i': 5, 'j': 3, 'k': 3, 'cost': 21}, {'i': 5, 'j': 3, 'k': 4, 'cost': 24}, {'i': 5, 'j': 3, 'k': 5, 'cost': 61}, {'i': 5, 'j': 4, 'k': 0, 'cost': 42}, {'i': 5, 'j': 4, 'k': 1, 'cost': 42}, {'i': 5, 'j': 4, 'k': 2, 'cost': 29}, {'i': 5, 'j': 4, 'k': 3, 'cost': 10}, {'i': 5, 'j': 4, 'k': 4, 'cost': 34}, {'i': 5, 'j': 4, 'k': 5, 'cost': 84}, {'i': 5, 'j': 5, 'k': 0, 'cost': 66}, {'i': 5, 'j': 5, 'k': 1, 'cost': 69}, {'i': 5, 'j': 5, 'k': 2, 'cost': 98}, {'i': 5, 'j': 5, 'k': 3, 'cost': 63}, {'i': 5, 'j': 5, 'k': 4, 'cost': 53}, {'i': 5, 'j': 5, 'k': 5, 'cost': 55}]}","[[0, 5, 4], [1, 1, 5], [2, 2, 0], [3, 0, 1], [4, 4, 2], [5, 3, 3]]",5,csv,0
AP3,AP3,"There’s a little catering puzzle at hand: match each table with one appetizer vendor and one dessert vendor, making sure no vendor is assigned to more than one table and no table is left without its two servers. What makes one arrangement nicer than another is the total price — just add each table’s appetizer cost and dessert cost, then add those totals — and the goal is to keep that final sum as small as possible. The specific tables, vendors, and costs appear below.

{
  ""num_tables"": 7,
  ""index_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6
  ]
}

# Meaning: costs form a 3D tensor. For each fixed table_id=i, you are given a appetizer_vendor_id×dessert_vendor_id matrix whose entry at row appetizer_vendor_id=j and column dessert_vendor_id=k equals catering_cost(i,j,k). You must pick exactly one (j,k) for every i, with all appetizer_vendor_id and all dessert_vendor_id used exactly once.
# catering_cost_tensor (per-table_id markdown matrices)

## table_id=0
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 74 | 16 | 65 | 50 | 67 | 40 | 34 |
| 1 | 83 | 51 | 57 | 37 | 11 | 67 | 33 |
| 2 | 60 | 85 | 19 | 66 | 26 | 81 | 0 |
| 3 | 57 | 7 | 8 | 13 | 50 | 77 | 57 |
| 4 | 11 | 56 | 67 | 82 | 80 | 60 | 90 |
| 5 | 64 | 82 | 67 | 63 | 43 | 39 | 30 |
| 6 | 81 | 70 | 81 | 20 | 5 | 71 | 62 |

## table_id=1
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 22 | 46 | 92 | 68 | 59 | 76 | 69 |
| 1 | 24 | 26 | 42 | 21 | 20 | 84 | 90 |
| 2 | 65 | 50 | 95 | 6 | 17 | 29 | 88 |
| 3 | 99 | 68 | 92 | 65 | 38 | 55 | 93 |
| 4 | 72 | 34 | 14 | 68 | 97 | 18 | 78 |
| 5 | 99 | 36 | 14 | 39 | 33 | 99 | 0 |
| 6 | 90 | 16 | 89 | 47 | 15 | 45 | 17 |

## table_id=2
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 11 | 23 | 38 | 36 | 38 | 42 | 88 |
| 1 | 7 | 86 | 43 | 33 | 90 | 53 | 80 |
| 2 | 57 | 36 | 67 | 88 | 0 | 55 | 83 |
| 3 | 71 | 82 | 38 | 35 | 13 | 94 | 26 |
| 4 | 11 | 1 | 16 | 42 | 13 | 15 | 87 |
| 5 | 42 | 11 | 58 | 11 | 6 | 47 | 0 |
| 6 | 61 | 93 | 85 | 76 | 28 | 42 | 69 |

## table_id=3
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 51 | 47 | 45 | 28 | 35 | 55 | 77 |
| 1 | 56 | 82 | 38 | 93 | 16 | 63 | 28 |
| 2 | 57 | 3 | 44 | 71 | 78 | 75 | 55 |
| 3 | 83 | 57 | 60 | 88 | 3 | 51 | 5 |
| 4 | 87 | 16 | 2 | 81 | 20 | 0 | 34 |
| 5 | 61 | 5 | 5 | 8 | 77 | 73 | 28 |
| 6 | 59 | 19 | 92 | 42 | 51 | 6 | 16 |

## table_id=4
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 59 | 84 | 29 | 99 | 34 | 93 | 73 |
| 1 | 27 | 18 | 32 | 93 | 69 | 27 | 61 |
| 2 | 39 | 25 | 23 | 66 | 68 | 71 | 25 |
| 3 | 29 | 34 | 48 | 51 | 69 | 77 | 42 |
| 4 | 13 | 90 | 57 | 32 | 21 | 91 | 25 |
| 5 | 84 | 97 | 35 | 95 | 93 | 65 | 86 |
| 6 | 32 | 42 | 81 | 30 | 74 | 92 | 51 |

## table_id=5
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 3 | 50 | 58 | 48 | 69 | 81 | 67 |
| 1 | 23 | 49 | 80 | 71 | 72 | 9 | 56 |
| 2 | 28 | 24 | 53 | 30 | 35 | 74 | 62 |
| 3 | 51 | 5 | 47 | 1 | 19 | 71 | 3 |
| 4 | 50 | 82 | 16 | 89 | 71 | 59 | 19 |
| 5 | 93 | 17 | 77 | 87 | 51 | 63 | 25 |
| 6 | 80 | 60 | 76 | 71 | 38 | 7 | 21 |

## table_id=6
| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 10 | 49 | 30 | 24 | 94 | 98 |
| 1 | 2 | 77 | 86 | 18 | 96 | 20 | 39 |
| 2 | 97 | 72 | 32 | 70 | 93 | 66 | 87 |
| 3 | 41 | 10 | 46 | 65 | 12 | 84 | 0 |
| 4 | 9 | 3 | 67 | 99 | 71 | 23 | 23 |
| 5 | 17 | 42 | 11 | 48 | 96 | 54 | 46 |
| 6 | 51 | 19 | 50 | 51 | 32 | 9 | 19 |

Also, when you send back the matching, please use this simple JSON layout so it's easy to read and parse:

{
  ""solution"": [
    [<table_id>, <appetizer_id>, <dessert_id>],
    ...
  ]
}

Each inner array is one trio: the table, its appetizer vendor, and its dessert vendor. Think of it as a quick form — list one triple per table. This JSON is just a sketch of the shape we want, not the actual answer.

Please be sure to use the exact identifiers from the instance input — no renaming and 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”.","{'cost_tensor': [[[74, 16, 65, 50, 67, 40, 34], [83, 51, 57, 37, 11, 67, 33], [60, 85, 19, 66, 26, 81, 0], [57, 7, 8, 13, 50, 77, 57], [11, 56, 67, 82, 80, 60, 90], [64, 82, 67, 63, 43, 39, 30], [81, 70, 81, 20, 5, 71, 62]], [[22, 46, 92, 68, 59, 76, 69], [24, 26, 42, 21, 20, 84, 90], [65, 50, 95, 6, 17, 29, 88], [99, 68, 92, 65, 38, 55, 93], [72, 34, 14, 68, 97, 18, 78], [99, 36, 14, 39, 33, 99, 0], [90, 16, 89, 47, 15, 45, 17]], [[11, 23, 38, 36, 38, 42, 88], [7, 86, 43, 33, 90, 53, 80], [57, 36, 67, 88, 0, 55, 83], [71, 82, 38, 35, 13, 94, 26], [11, 1, 16, 42, 13, 15, 87], [42, 11, 58, 11, 6, 47, 0], [61, 93, 85, 76, 28, 42, 69]], [[51, 47, 45, 28, 35, 55, 77], [56, 82, 38, 93, 16, 63, 28], [57, 3, 44, 71, 78, 75, 55], [83, 57, 60, 88, 3, 51, 5], [87, 16, 2, 81, 20, 0, 34], [61, 5, 5, 8, 77, 73, 28], [59, 19, 92, 42, 51, 6, 16]], [[59, 84, 29, 99, 34, 93, 73], [27, 18, 32, 93, 69, 27, 61], [39, 25, 23, 66, 68, 71, 25], [29, 34, 48, 51, 69, 77, 42], [13, 90, 57, 32, 21, 91, 25], [84, 97, 35, 95, 93, 65, 86], [32, 42, 81, 30, 74, 92, 51]], [[3, 50, 58, 48, 69, 81, 67], [23, 49, 80, 71, 72, 9, 56], [28, 24, 53, 30, 35, 74, 62], [51, 5, 47, 1, 19, 71, 3], [50, 82, 16, 89, 71, 59, 19], [93, 17, 77, 87, 51, 63, 25], [80, 60, 76, 71, 38, 7, 21]], [[1, 10, 49, 30, 24, 94, 98], [2, 77, 86, 18, 96, 20, 39], [97, 72, 32, 70, 93, 66, 87], [41, 10, 46, 65, 12, 84, 0], [9, 3, 67, 99, 71, 23, 23], [17, 42, 11, 48, 96, 54, 46], [51, 19, 50, 51, 32, 9, 19]]], 'objective': 41.0}","[[0, 3, 3], [1, 5, 6], [2, 2, 4], [3, 4, 2], [4, 1, 1], [5, 6, 5], [6, 0, 0]]",41.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [0, 1, 2, 3, 4, 5, 6], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 74}, {'i': 0, 'j': 0, 'k': 1, 'cost': 16}, {'i': 0, 'j': 0, 'k': 2, 'cost': 65}, {'i': 0, 'j': 0, 'k': 3, 'cost': 50}, {'i': 0, 'j': 0, 'k': 4, 'cost': 67}, {'i': 0, 'j': 0, 'k': 5, 'cost': 40}, {'i': 0, 'j': 0, 'k': 6, 'cost': 34}, {'i': 0, 'j': 1, 'k': 0, 'cost': 83}, {'i': 0, 'j': 1, 'k': 1, 'cost': 51}, {'i': 0, 'j': 1, 'k': 2, 'cost': 57}, {'i': 0, 'j': 1, 'k': 3, 'cost': 37}, {'i': 0, 'j': 1, 'k': 4, 'cost': 11}, {'i': 0, 'j': 1, 'k': 5, 'cost': 67}, {'i': 0, 'j': 1, 'k': 6, 'cost': 33}, {'i': 0, 'j': 2, 'k': 0, 'cost': 60}, {'i': 0, 'j': 2, 'k': 1, 'cost': 85}, {'i': 0, 'j': 2, 'k': 2, 'cost': 19}, {'i': 0, 'j': 2, 'k': 3, 'cost': 66}, {'i': 0, 'j': 2, 'k': 4, 'cost': 26}, {'i': 0, 'j': 2, 'k': 5, 'cost': 81}, {'i': 0, 'j': 2, 'k': 6, 'cost': 0}, {'i': 0, 'j': 3, 'k': 0, 'cost': 57}, {'i': 0, 'j': 3, 'k': 1, 'cost': 7}, {'i': 0, 'j': 3, 'k': 2, 'cost': 8}, {'i': 0, 'j': 3, 'k': 3, 'cost': 13}, {'i': 0, 'j': 3, 'k': 4, 'cost': 50}, {'i': 0, 'j': 3, 'k': 5, 'cost': 77}, {'i': 0, 'j': 3, 'k': 6, 'cost': 57}, {'i': 0, 'j': 4, 'k': 0, 'cost': 11}, {'i': 0, 'j': 4, 'k': 1, 'cost': 56}, {'i': 0, 'j': 4, 'k': 2, 'cost': 67}, {'i': 0, 'j': 4, 'k': 3, 'cost': 82}, {'i': 0, 'j': 4, 'k': 4, 'cost': 80}, {'i': 0, 'j': 4, 'k': 5, 'cost': 60}, {'i': 0, 'j': 4, 'k': 6, 'cost': 90}, {'i': 0, 'j': 5, 'k': 0, 'cost': 64}, {'i': 0, 'j': 5, 'k': 1, 'cost': 82}, {'i': 0, 'j': 5, 'k': 2, 'cost': 67}, {'i': 0, 'j': 5, 'k': 3, 'cost': 63}, {'i': 0, 'j': 5, 'k': 4, 'cost': 43}, {'i': 0, 'j': 5, 'k': 5, 'cost': 39}, {'i': 0, 'j': 5, 'k': 6, 'cost': 30}, {'i': 0, 'j': 6, 'k': 0, 'cost': 81}, {'i': 0, 'j': 6, 'k': 1, 'cost': 70}, {'i': 0, 'j': 6, 'k': 2, 'cost': 81}, {'i': 0, 'j': 6, 'k': 3, 'cost': 20}, {'i': 0, 'j': 6, 'k': 4, 'cost': 5}, {'i': 0, 'j': 6, 'k': 5, 'cost': 71}, {'i': 0, 'j': 6, 'k': 6, 'cost': 62}, {'i': 1, 'j': 0, 'k': 0, 'cost': 22}, {'i': 1, 'j': 0, 'k': 1, 'cost': 46}, {'i': 1, 'j': 0, 'k': 2, 'cost': 92}, {'i': 1, 'j': 0, 'k': 3, 'cost': 68}, {'i': 1, 'j': 0, 'k': 4, 'cost': 59}, {'i': 1, 'j': 0, 'k': 5, 'cost': 76}, {'i': 1, 'j': 0, 'k': 6, 'cost': 69}, {'i': 1, 'j': 1, 'k': 0, 'cost': 24}, {'i': 1, 'j': 1, 'k': 1, 'cost': 26}, {'i': 1, 'j': 1, 'k': 2, 'cost': 42}, {'i': 1, 'j': 1, 'k': 3, 'cost': 21}, {'i': 1, 'j': 1, 'k': 4, 'cost': 20}, {'i': 1, 'j': 1, 'k': 5, 'cost': 84}, {'i': 1, 'j': 1, 'k': 6, 'cost': 90}, {'i': 1, 'j': 2, 'k': 0, 'cost': 65}, {'i': 1, 'j': 2, 'k': 1, 'cost': 50}, {'i': 1, 'j': 2, 'k': 2, 'cost': 95}, {'i': 1, 'j': 2, 'k': 3, 'cost': 6}, {'i': 1, 'j': 2, 'k': 4, 'cost': 17}, {'i': 1, 'j': 2, 'k': 5, 'cost': 29}, {'i': 1, 'j': 2, 'k': 6, 'cost': 88}, {'i': 1, 'j': 3, 'k': 0, 'cost': 99}, {'i': 1, 'j': 3, 'k': 1, 'cost': 68}, {'i': 1, 'j': 3, 'k': 2, 'cost': 92}, {'i': 1, 'j': 3, 'k': 3, 'cost': 65}, {'i': 1, 'j': 3, 'k': 4, 'cost': 38}, {'i': 1, 'j': 3, 'k': 5, 'cost': 55}, {'i': 1, 'j': 3, 'k': 6, 'cost': 93}, {'i': 1, 'j': 4, 'k': 0, 'cost': 72}, {'i': 1, 'j': 4, 'k': 1, 'cost': 34}, {'i': 1, 'j': 4, 'k': 2, 'cost': 14}, {'i': 1, 'j': 4, 'k': 3, 'cost': 68}, {'i': 1, 'j': 4, 'k': 4, 'cost': 97}, {'i': 1, 'j': 4, 'k': 5, 'cost': 18}, {'i': 1, 'j': 4, 'k': 6, 'cost': 78}, {'i': 1, 'j': 5, 'k': 0, 'cost': 99}, {'i': 1, 'j': 5, 'k': 1, 'cost': 36}, {'i': 1, 'j': 5, 'k': 2, 'cost': 14}, {'i': 1, 'j': 5, 'k': 3, 'cost': 39}, {'i': 1, 'j': 5, 'k': 4, 'cost': 33}, {'i': 1, 'j': 5, 'k': 5, 'cost': 99}, {'i': 1, 'j': 5, 'k': 6, 'cost': 0}, {'i': 1, 'j': 6, 'k': 0, 'cost': 90}, {'i': 1, 'j': 6, 'k': 1, 'cost': 16}, {'i': 1, 'j': 6, 'k': 2, 'cost': 89}, {'i': 1, 'j': 6, 'k': 3, 'cost': 47}, {'i': 1, 'j': 6, 'k': 4, 'cost': 15}, {'i': 1, 'j': 6, 'k': 5, 'cost': 45}, {'i': 1, 'j': 6, 'k': 6, 'cost': 17}, {'i': 2, 'j': 0, 'k': 0, 'cost': 11}, {'i': 2, 'j': 0, 'k': 1, 'cost': 23}, {'i': 2, 'j': 0, 'k': 2, 'cost': 38}, {'i': 2, 'j': 0, 'k': 3, 'cost': 36}, {'i': 2, 'j': 0, 'k': 4, 'cost': 38}, {'i': 2, 'j': 0, 'k': 5, 'cost': 42}, {'i': 2, 'j': 0, 'k': 6, 'cost': 88}, {'i': 2, 'j': 1, 'k': 0, 'cost': 7}, {'i': 2, 'j': 1, 'k': 1, 'cost': 86}, {'i': 2, 'j': 1, 'k': 2, 'cost': 43}, {'i': 2, 'j': 1, 'k': 3, 'cost': 33}, {'i': 2, 'j': 1, 'k': 4, 'cost': 90}, {'i': 2, 'j': 1, 'k': 5, 'cost': 53}, {'i': 2, 'j': 1, 'k': 6, 'cost': 80}, {'i': 2, 'j': 2, 'k': 0, 'cost': 57}, {'i': 2, 'j': 2, 'k': 1, 'cost': 36}, {'i': 2, 'j': 2, 'k': 2, 'cost': 67}, {'i': 2, 'j': 2, 'k': 3, 'cost': 88}, {'i': 2, 'j': 2, 'k': 4, 'cost': 0}, {'i': 2, 'j': 2, 'k': 5, 'cost': 55}, {'i': 2, 'j': 2, 'k': 6, 'cost': 83}, {'i': 2, 'j': 3, 'k': 0, 'cost': 71}, {'i': 2, 'j': 3, 'k': 1, 'cost': 82}, {'i': 2, 'j': 3, 'k': 2, 'cost': 38}, {'i': 2, 'j': 3, 'k': 3, 'cost': 35}, {'i': 2, 'j': 3, 'k': 4, 'cost': 13}, {'i': 2, 'j': 3, 'k': 5, 'cost': 94}, {'i': 2, 'j': 3, 'k': 6, 'cost': 26}, {'i': 2, 'j': 4, 'k': 0, 'cost': 11}, {'i': 2, 'j': 4, 'k': 1, 'cost': 1}, {'i': 2, 'j': 4, 'k': 2, 'cost': 16}, {'i': 2, 'j': 4, 'k': 3, 'cost': 42}, {'i': 2, 'j': 4, 'k': 4, 'cost': 13}, {'i': 2, 'j': 4, 'k': 5, 'cost': 15}, {'i': 2, 'j': 4, 'k': 6, 'cost': 87}, {'i': 2, 'j': 5, 'k': 0, 'cost': 42}, {'i': 2, 'j': 5, 'k': 1, 'cost': 11}, {'i': 2, 'j': 5, 'k': 2, 'cost': 58}, {'i': 2, 'j': 5, 'k': 3, 'cost': 11}, {'i': 2, 'j': 5, 'k': 4, 'cost': 6}, {'i': 2, 'j': 5, 'k': 5, 'cost': 47}, {'i': 2, 'j': 5, 'k': 6, 'cost': 0}, {'i': 2, 'j': 6, 'k': 0, 'cost': 61}, {'i': 2, 'j': 6, 'k': 1, 'cost': 93}, {'i': 2, 'j': 6, 'k': 2, 'cost': 85}, {'i': 2, 'j': 6, 'k': 3, 'cost': 76}, {'i': 2, 'j': 6, 'k': 4, 'cost': 28}, {'i': 2, 'j': 6, 'k': 5, 'cost': 42}, {'i': 2, 'j': 6, 'k': 6, 'cost': 69}, {'i': 3, 'j': 0, 'k': 0, 'cost': 51}, {'i': 3, 'j': 0, 'k': 1, 'cost': 47}, {'i': 3, 'j': 0, 'k': 2, 'cost': 45}, {'i': 3, 'j': 0, 'k': 3, 'cost': 28}, {'i': 3, 'j': 0, 'k': 4, 'cost': 35}, {'i': 3, 'j': 0, 'k': 5, 'cost': 55}, {'i': 3, 'j': 0, 'k': 6, 'cost': 77}, {'i': 3, 'j': 1, 'k': 0, 'cost': 56}, {'i': 3, 'j': 1, 'k': 1, 'cost': 82}, {'i': 3, 'j': 1, 'k': 2, 'cost': 38}, {'i': 3, 'j': 1, 'k': 3, 'cost': 93}, {'i': 3, 'j': 1, 'k': 4, 'cost': 16}, {'i': 3, 'j': 1, 'k': 5, 'cost': 63}, {'i': 3, 'j': 1, 'k': 6, 'cost': 28}, {'i': 3, 'j': 2, 'k': 0, 'cost': 57}, {'i': 3, 'j': 2, 'k': 1, 'cost': 3}, {'i': 3, 'j': 2, 'k': 2, 'cost': 44}, {'i': 3, 'j': 2, 'k': 3, 'cost': 71}, {'i': 3, 'j': 2, 'k': 4, 'cost': 78}, {'i': 3, 'j': 2, 'k': 5, 'cost': 75}, {'i': 3, 'j': 2, 'k': 6, 'cost': 55}, {'i': 3, 'j': 3, 'k': 0, 'cost': 83}, {'i': 3, 'j': 3, 'k': 1, 'cost': 57}, {'i': 3, 'j': 3, 'k': 2, 'cost': 60}, {'i': 3, 'j': 3, 'k': 3, 'cost': 88}, {'i': 3, 'j': 3, 'k': 4, 'cost': 3}, {'i': 3, 'j': 3, 'k': 5, 'cost': 51}, {'i': 3, 'j': 3, 'k': 6, 'cost': 5}, {'i': 3, 'j': 4, 'k': 0, 'cost': 87}, {'i': 3, 'j': 4, 'k': 1, 'cost': 16}, {'i': 3, 'j': 4, 'k': 2, 'cost': 2}, {'i': 3, 'j': 4, 'k': 3, 'cost': 81}, {'i': 3, 'j': 4, 'k': 4, 'cost': 20}, {'i': 3, 'j': 4, 'k': 5, 'cost': 0}, {'i': 3, 'j': 4, 'k': 6, 'cost': 34}, {'i': 3, 'j': 5, 'k': 0, 'cost': 61}, {'i': 3, 'j': 5, 'k': 1, 'cost': 5}, {'i': 3, 'j': 5, 'k': 2, 'cost': 5}, {'i': 3, 'j': 5, 'k': 3, 'cost': 8}, {'i': 3, 'j': 5, 'k': 4, 'cost': 77}, {'i': 3, 'j': 5, 'k': 5, 'cost': 73}, {'i': 3, 'j': 5, 'k': 6, 'cost': 28}, {'i': 3, 'j': 6, 'k': 0, 'cost': 59}, {'i': 3, 'j': 6, 'k': 1, 'cost': 19}, {'i': 3, 'j': 6, 'k': 2, 'cost': 92}, {'i': 3, 'j': 6, 'k': 3, 'cost': 42}, {'i': 3, 'j': 6, 'k': 4, 'cost': 51}, {'i': 3, 'j': 6, 'k': 5, 'cost': 6}, {'i': 3, 'j': 6, 'k': 6, 'cost': 16}, {'i': 4, 'j': 0, 'k': 0, 'cost': 59}, {'i': 4, 'j': 0, 'k': 1, 'cost': 84}, {'i': 4, 'j': 0, 'k': 2, 'cost': 29}, {'i': 4, 'j': 0, 'k': 3, 'cost': 99}, {'i': 4, 'j': 0, 'k': 4, 'cost': 34}, {'i': 4, 'j': 0, 'k': 5, 'cost': 93}, {'i': 4, 'j': 0, 'k': 6, 'cost': 73}, {'i': 4, 'j': 1, 'k': 0, 'cost': 27}, {'i': 4, 'j': 1, 'k': 1, 'cost': 18}, {'i': 4, 'j': 1, 'k': 2, 'cost': 32}, {'i': 4, 'j': 1, 'k': 3, 'cost': 93}, {'i': 4, 'j': 1, 'k': 4, 'cost': 69}, {'i': 4, 'j': 1, 'k': 5, 'cost': 27}, {'i': 4, 'j': 1, 'k': 6, 'cost': 61}, {'i': 4, 'j': 2, 'k': 0, 'cost': 39}, {'i': 4, 'j': 2, 'k': 1, 'cost': 25}, {'i': 4, 'j': 2, 'k': 2, 'cost': 23}, {'i': 4, 'j': 2, 'k': 3, 'cost': 66}, {'i': 4, 'j': 2, 'k': 4, 'cost': 68}, {'i': 4, 'j': 2, 'k': 5, 'cost': 71}, {'i': 4, 'j': 2, 'k': 6, 'cost': 25}, {'i': 4, 'j': 3, 'k': 0, 'cost': 29}, {'i': 4, 'j': 3, 'k': 1, 'cost': 34}, {'i': 4, 'j': 3, 'k': 2, 'cost': 48}, {'i': 4, 'j': 3, 'k': 3, 'cost': 51}, {'i': 4, 'j': 3, 'k': 4, 'cost': 69}, {'i': 4, 'j': 3, 'k': 5, 'cost': 77}, {'i': 4, 'j': 3, 'k': 6, 'cost': 42}, {'i': 4, 'j': 4, 'k': 0, 'cost': 13}, {'i': 4, 'j': 4, 'k': 1, 'cost': 90}, {'i': 4, 'j': 4, 'k': 2, 'cost': 57}, {'i': 4, 'j': 4, 'k': 3, 'cost': 32}, {'i': 4, 'j': 4, 'k': 4, 'cost': 21}, {'i': 4, 'j': 4, 'k': 5, 'cost': 91}, {'i': 4, 'j': 4, 'k': 6, 'cost': 25}, {'i': 4, 'j': 5, 'k': 0, 'cost': 84}, {'i': 4, 'j': 5, 'k': 1, 'cost': 97}, {'i': 4, 'j': 5, 'k': 2, 'cost': 35}, {'i': 4, 'j': 5, 'k': 3, 'cost': 95}, {'i': 4, 'j': 5, 'k': 4, 'cost': 93}, {'i': 4, 'j': 5, 'k': 5, 'cost': 65}, {'i': 4, 'j': 5, 'k': 6, 'cost': 86}, {'i': 4, 'j': 6, 'k': 0, 'cost': 32}, {'i': 4, 'j': 6, 'k': 1, 'cost': 42}, {'i': 4, 'j': 6, 'k': 2, 'cost': 81}, {'i': 4, 'j': 6, 'k': 3, 'cost': 30}, {'i': 4, 'j': 6, 'k': 4, 'cost': 74}, {'i': 4, 'j': 6, 'k': 5, 'cost': 92}, {'i': 4, 'j': 6, 'k': 6, 'cost': 51}, {'i': 5, 'j': 0, 'k': 0, 'cost': 3}, {'i': 5, 'j': 0, 'k': 1, 'cost': 50}, {'i': 5, 'j': 0, 'k': 2, 'cost': 58}, {'i': 5, 'j': 0, 'k': 3, 'cost': 48}, {'i': 5, 'j': 0, 'k': 4, 'cost': 69}, {'i': 5, 'j': 0, 'k': 5, 'cost': 81}, {'i': 5, 'j': 0, 'k': 6, 'cost': 67}, {'i': 5, 'j': 1, 'k': 0, 'cost': 23}, {'i': 5, 'j': 1, 'k': 1, 'cost': 49}, {'i': 5, 'j': 1, 'k': 2, 'cost': 80}, {'i': 5, 'j': 1, 'k': 3, 'cost': 71}, {'i': 5, 'j': 1, 'k': 4, 'cost': 72}, {'i': 5, 'j': 1, 'k': 5, 'cost': 9}, {'i': 5, 'j': 1, 'k': 6, 'cost': 56}, {'i': 5, 'j': 2, 'k': 0, 'cost': 28}, {'i': 5, 'j': 2, 'k': 1, 'cost': 24}, {'i': 5, 'j': 2, 'k': 2, 'cost': 53}, {'i': 5, 'j': 2, 'k': 3, 'cost': 30}, {'i': 5, 'j': 2, 'k': 4, 'cost': 35}, {'i': 5, 'j': 2, 'k': 5, 'cost': 74}, {'i': 5, 'j': 2, 'k': 6, 'cost': 62}, {'i': 5, 'j': 3, 'k': 0, 'cost': 51}, {'i': 5, 'j': 3, 'k': 1, 'cost': 5}, {'i': 5, 'j': 3, 'k': 2, 'cost': 47}, {'i': 5, 'j': 3, 'k': 3, 'cost': 1}, {'i': 5, 'j': 3, 'k': 4, 'cost': 19}, {'i': 5, 'j': 3, 'k': 5, 'cost': 71}, {'i': 5, 'j': 3, 'k': 6, 'cost': 3}, {'i': 5, 'j': 4, 'k': 0, 'cost': 50}, {'i': 5, 'j': 4, 'k': 1, 'cost': 82}, {'i': 5, 'j': 4, 'k': 2, 'cost': 16}, {'i': 5, 'j': 4, 'k': 3, 'cost': 89}, {'i': 5, 'j': 4, 'k': 4, 'cost': 71}, {'i': 5, 'j': 4, 'k': 5, 'cost': 59}, {'i': 5, 'j': 4, 'k': 6, 'cost': 19}, {'i': 5, 'j': 5, 'k': 0, 'cost': 93}, {'i': 5, 'j': 5, 'k': 1, 'cost': 17}, {'i': 5, 'j': 5, 'k': 2, 'cost': 77}, {'i': 5, 'j': 5, 'k': 3, 'cost': 87}, {'i': 5, 'j': 5, 'k': 4, 'cost': 51}, {'i': 5, 'j': 5, 'k': 5, 'cost': 63}, {'i': 5, 'j': 5, 'k': 6, 'cost': 25}, {'i': 5, 'j': 6, 'k': 0, 'cost': 80}, {'i': 5, 'j': 6, 'k': 1, 'cost': 60}, {'i': 5, 'j': 6, 'k': 2, 'cost': 76}, {'i': 5, 'j': 6, 'k': 3, 'cost': 71}, {'i': 5, 'j': 6, 'k': 4, 'cost': 38}, {'i': 5, 'j': 6, 'k': 5, 'cost': 7}, {'i': 5, 'j': 6, 'k': 6, 'cost': 21}, {'i': 6, 'j': 0, 'k': 0, 'cost': 1}, {'i': 6, 'j': 0, 'k': 1, 'cost': 10}, {'i': 6, 'j': 0, 'k': 2, 'cost': 49}, {'i': 6, 'j': 0, 'k': 3, 'cost': 30}, {'i': 6, 'j': 0, 'k': 4, 'cost': 24}, {'i': 6, 'j': 0, 'k': 5, 'cost': 94}, {'i': 6, 'j': 0, 'k': 6, 'cost': 98}, {'i': 6, 'j': 1, 'k': 0, 'cost': 2}, {'i': 6, 'j': 1, 'k': 1, 'cost': 77}, {'i': 6, 'j': 1, 'k': 2, 'cost': 86}, {'i': 6, 'j': 1, 'k': 3, 'cost': 18}, {'i': 6, 'j': 1, 'k': 4, 'cost': 96}, {'i': 6, 'j': 1, 'k': 5, 'cost': 20}, {'i': 6, 'j': 1, 'k': 6, 'cost': 39}, {'i': 6, 'j': 2, 'k': 0, 'cost': 97}, {'i': 6, 'j': 2, 'k': 1, 'cost': 72}, {'i': 6, 'j': 2, 'k': 2, 'cost': 32}, {'i': 6, 'j': 2, 'k': 3, 'cost': 70}, {'i': 6, 'j': 2, 'k': 4, 'cost': 93}, {'i': 6, 'j': 2, 'k': 5, 'cost': 66}, {'i': 6, 'j': 2, 'k': 6, 'cost': 87}, {'i': 6, 'j': 3, 'k': 0, 'cost': 41}, {'i': 6, 'j': 3, 'k': 1, 'cost': 10}, {'i': 6, 'j': 3, 'k': 2, 'cost': 46}, {'i': 6, 'j': 3, 'k': 3, 'cost': 65}, {'i': 6, 'j': 3, 'k': 4, 'cost': 12}, {'i': 6, 'j': 3, 'k': 5, 'cost': 84}, {'i': 6, 'j': 3, 'k': 6, 'cost': 0}, {'i': 6, 'j': 4, 'k': 0, 'cost': 9}, {'i': 6, 'j': 4, 'k': 1, 'cost': 3}, {'i': 6, 'j': 4, 'k': 2, 'cost': 67}, {'i': 6, 'j': 4, 'k': 3, 'cost': 99}, {'i': 6, 'j': 4, 'k': 4, 'cost': 71}, {'i': 6, 'j': 4, 'k': 5, 'cost': 23}, {'i': 6, 'j': 4, 'k': 6, 'cost': 23}, {'i': 6, 'j': 5, 'k': 0, 'cost': 17}, {'i': 6, 'j': 5, 'k': 1, 'cost': 42}, {'i': 6, 'j': 5, 'k': 2, 'cost': 11}, {'i': 6, 'j': 5, 'k': 3, 'cost': 48}, {'i': 6, 'j': 5, 'k': 4, 'cost': 96}, {'i': 6, 'j': 5, 'k': 5, 'cost': 54}, {'i': 6, 'j': 5, 'k': 6, 'cost': 46}, {'i': 6, 'j': 6, 'k': 0, 'cost': 51}, {'i': 6, 'j': 6, 'k': 1, 'cost': 19}, {'i': 6, 'j': 6, 'k': 2, 'cost': 50}, {'i': 6, 'j': 6, 'k': 3, 'cost': 51}, {'i': 6, 'j': 6, 'k': 4, 'cost': 32}, {'i': 6, 'j': 6, 'k': 5, 'cost': 9}, {'i': 6, 'j': 6, 'k': 6, 'cost': 19}]}","[[0, 3, 3], [1, 5, 6], [2, 2, 4], [3, 4, 2], [4, 1, 1], [5, 6, 5], [6, 0, 0]]",6,json,0
AP3,AP3,"I watched the loading crew puzzle over a stack of pallets and a list of trucks and routes — each pallet needs exactly one truck and exactly one delivery route. The trick is that no truck can take more than one pallet and no route gets used twice, so everything has to line up one-for-one. What makes one way better than another is simple: how much fuel all the trips will eat up. For every pallet, check the fuel that truck would use on the chosen route, add those fuel numbers together, and the arrangement with the smallest total fuel is the one to pick. The actual trucks, routes, and fuel numbers are shown below.

{
  ""num_pallets"": 7,
  ""pallet_truck_route_identifiers"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6
  ]
}

# Meaning: costs form a 3D tensor. For each fixed pallet_id=i, you are given a truck_id×route_id matrix whose entry at row truck_id=j and column route_id=k equals fuel_cost(i,j,k). You must pick exactly one (j,k) for every i, with all truck_id and all route_id used exactly once.
# fuel_cost_tensor (per-pallet_id markdown matrices)

## pallet_id=0
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 21 | 85 | 90 | 92 | 46 | 88 | 56 |
| 1 | 38 | 23 | 5 | 24 | 65 | 54 | 46 |
| 2 | 66 | 88 | 87 | 97 | 60 | 14 | 36 |
| 3 | 90 | 53 | 19 | 24 | 67 | 52 | 59 |
| 4 | 89 | 88 | 3 | 35 | 45 | 83 | 78 |
| 5 | 82 | 25 | 14 | 79 | 99 | 75 | 76 |
| 6 | 81 | 67 | 33 | 57 | 44 | 4 | 56 |

## pallet_id=1
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 87 | 38 | 81 | 88 | 81 | 11 | 63 |
| 1 | 48 | 44 | 91 | 76 | 96 | 51 | 96 |
| 2 | 2 | 7 | 52 | 88 | 74 | 21 | 41 |
| 3 | 63 | 96 | 41 | 98 | 76 | 18 | 31 |
| 4 | 96 | 37 | 18 | 83 | 89 | 63 | 39 |
| 5 | 38 | 68 | 70 | 38 | 32 | 4 | 29 |
| 6 | 35 | 75 | 88 | 76 | 81 | 10 | 80 |

## pallet_id=2
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 69 | 56 | 73 | 31 | 10 | 40 | 90 |
| 1 | 12 | 58 | 44 | 94 | 65 | 52 | 28 |
| 2 | 42 | 91 | 92 | 71 | 8 | 57 | 71 |
| 3 | 43 | 98 | 81 | 22 | 36 | 86 | 82 |
| 4 | 66 | 30 | 38 | 82 | 58 | 85 | 66 |
| 5 | 89 | 20 | 36 | 28 | 29 | 24 | 92 |
| 6 | 24 | 67 | 82 | 58 | 32 | 77 | 23 |

## pallet_id=3
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 38 | 88 | 82 | 48 | 43 | 19 | 26 |
| 1 | 80 | 6 | 24 | 54 | 76 | 56 | 5 |
| 2 | 12 | 67 | 8 | 23 | 75 | 43 | 36 |
| 3 | 74 | 11 | 72 | 79 | 50 | 46 | 20 |
| 4 | 9 | 16 | 29 | 85 | 4 | 94 | 70 |
| 5 | 0 | 22 | 53 | 95 | 9 | 11 | 35 |
| 6 | 64 | 61 | 82 | 83 | 12 | 59 | 84 |

## pallet_id=4
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 78 | 82 | 0 | 72 | 2 | 74 | 82 |
| 1 | 8 | 15 | 57 | 84 | 79 | 75 | 75 |
| 2 | 21 | 42 | 45 | 22 | 67 | 20 | 29 |
| 3 | 94 | 4 | 13 | 59 | 41 | 33 | 67 |
| 4 | 73 | 87 | 63 | 30 | 47 | 40 | 14 |
| 5 | 97 | 42 | 83 | 58 | 13 | 26 | 83 |
| 6 | 46 | 71 | 65 | 11 | 22 | 3 | 27 |

## pallet_id=5
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 38 | 4 | 41 | 9 | 60 | 21 | 86 |
| 1 | 45 | 40 | 27 | 42 | 72 | 24 | 0 |
| 2 | 25 | 17 | 35 | 88 | 99 | 90 | 75 |
| 3 | 36 | 88 | 56 | 90 | 22 | 58 | 19 |
| 4 | 64 | 48 | 76 | 79 | 45 | 73 | 56 |
| 5 | 98 | 11 | 24 | 77 | 78 | 88 | 58 |
| 6 | 24 | 95 | 12 | 56 | 34 | 13 | 35 |

## pallet_id=6
| truck_id\route_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 13 | 37 | 42 | 33 | 10 | 46 | 10 |
| 1 | 90 | 11 | 62 | 75 | 43 | 4 | 18 |
| 2 | 9 | 90 | 52 | 85 | 69 | 35 | 64 |
| 3 | 77 | 7 | 76 | 14 | 0 | 55 | 71 |
| 4 | 41 | 1 | 61 | 77 | 73 | 32 | 70 |
| 5 | 26 | 66 | 32 | 87 | 55 | 10 | 82 |
| 6 | 73 | 71 | 17 | 26 | 85 | 16 | 47 |

If you want to hand me the matching in a neat, machine-friendly way, just use a tiny JSON snippet like this:

{
  ""solution"": [
    [""<pallet_id>"", ""<truck_id>"", ""<route_id>""],
    ...
  ]
}

Each inner array is one selected triple: the pallet, the truck assigned to it, and the route chosen for that truck. Think of it like a simple form: one line per pallet saying which truck and which route go with it. This JSON is just a sketch of the shape I expect — not the actual answer.

Please make sure to use the exact identifiers from the instance input — don't 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”.""","{'cost_tensor': [[[21, 85, 90, 92, 46, 88, 56], [38, 23, 5, 24, 65, 54, 46], [66, 88, 87, 97, 60, 14, 36], [90, 53, 19, 24, 67, 52, 59], [89, 88, 3, 35, 45, 83, 78], [82, 25, 14, 79, 99, 75, 76], [81, 67, 33, 57, 44, 4, 56]], [[87, 38, 81, 88, 81, 11, 63], [48, 44, 91, 76, 96, 51, 96], [2, 7, 52, 88, 74, 21, 41], [63, 96, 41, 98, 76, 18, 31], [96, 37, 18, 83, 89, 63, 39], [38, 68, 70, 38, 32, 4, 29], [35, 75, 88, 76, 81, 10, 80]], [[69, 56, 73, 31, 10, 40, 90], [12, 58, 44, 94, 65, 52, 28], [42, 91, 92, 71, 8, 57, 71], [43, 98, 81, 22, 36, 86, 82], [66, 30, 38, 82, 58, 85, 66], [89, 20, 36, 28, 29, 24, 92], [24, 67, 82, 58, 32, 77, 23]], [[38, 88, 82, 48, 43, 19, 26], [80, 6, 24, 54, 76, 56, 5], [12, 67, 8, 23, 75, 43, 36], [74, 11, 72, 79, 50, 46, 20], [9, 16, 29, 85, 4, 94, 70], [0, 22, 53, 95, 9, 11, 35], [64, 61, 82, 83, 12, 59, 84]], [[78, 82, 0, 72, 2, 74, 82], [8, 15, 57, 84, 79, 75, 75], [21, 42, 45, 22, 67, 20, 29], [94, 4, 13, 59, 41, 33, 67], [73, 87, 63, 30, 47, 40, 14], [97, 42, 83, 58, 13, 26, 83], [46, 71, 65, 11, 22, 3, 27]], [[38, 4, 41, 9, 60, 21, 86], [45, 40, 27, 42, 72, 24, 0], [25, 17, 35, 88, 99, 90, 75], [36, 88, 56, 90, 22, 58, 19], [64, 48, 76, 79, 45, 73, 56], [98, 11, 24, 77, 78, 88, 58], [24, 95, 12, 56, 34, 13, 35]], [[13, 37, 42, 33, 10, 46, 10], [90, 11, 62, 75, 43, 4, 18], [9, 90, 52, 85, 69, 35, 64], [77, 7, 76, 14, 0, 55, 71], [41, 1, 61, 77, 73, 32, 70], [26, 66, 32, 87, 55, 10, 82], [73, 71, 17, 26, 85, 16, 47]]], 'objective': 37.0}","[[0, 4, 2], [1, 2, 1], [2, 0, 4], [3, 5, 0], [4, 6, 5], [5, 1, 6], [6, 3, 3]]",37.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [0, 1, 2, 3, 4, 5, 6], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 21}, {'i': 0, 'j': 0, 'k': 1, 'cost': 85}, {'i': 0, 'j': 0, 'k': 2, 'cost': 90}, {'i': 0, 'j': 0, 'k': 3, 'cost': 92}, {'i': 0, 'j': 0, 'k': 4, 'cost': 46}, {'i': 0, 'j': 0, 'k': 5, 'cost': 88}, {'i': 0, 'j': 0, 'k': 6, 'cost': 56}, {'i': 0, 'j': 1, 'k': 0, 'cost': 38}, {'i': 0, 'j': 1, 'k': 1, 'cost': 23}, {'i': 0, 'j': 1, 'k': 2, 'cost': 5}, {'i': 0, 'j': 1, 'k': 3, 'cost': 24}, {'i': 0, 'j': 1, 'k': 4, 'cost': 65}, {'i': 0, 'j': 1, 'k': 5, 'cost': 54}, {'i': 0, 'j': 1, 'k': 6, 'cost': 46}, {'i': 0, 'j': 2, 'k': 0, 'cost': 66}, {'i': 0, 'j': 2, 'k': 1, 'cost': 88}, {'i': 0, 'j': 2, 'k': 2, 'cost': 87}, {'i': 0, 'j': 2, 'k': 3, 'cost': 97}, {'i': 0, 'j': 2, 'k': 4, 'cost': 60}, {'i': 0, 'j': 2, 'k': 5, 'cost': 14}, {'i': 0, 'j': 2, 'k': 6, 'cost': 36}, {'i': 0, 'j': 3, 'k': 0, 'cost': 90}, {'i': 0, 'j': 3, 'k': 1, 'cost': 53}, {'i': 0, 'j': 3, 'k': 2, 'cost': 19}, {'i': 0, 'j': 3, 'k': 3, 'cost': 24}, {'i': 0, 'j': 3, 'k': 4, 'cost': 67}, {'i': 0, 'j': 3, 'k': 5, 'cost': 52}, {'i': 0, 'j': 3, 'k': 6, 'cost': 59}, {'i': 0, 'j': 4, 'k': 0, 'cost': 89}, {'i': 0, 'j': 4, 'k': 1, 'cost': 88}, {'i': 0, 'j': 4, 'k': 2, 'cost': 3}, {'i': 0, 'j': 4, 'k': 3, 'cost': 35}, {'i': 0, 'j': 4, 'k': 4, 'cost': 45}, {'i': 0, 'j': 4, 'k': 5, 'cost': 83}, {'i': 0, 'j': 4, 'k': 6, 'cost': 78}, {'i': 0, 'j': 5, 'k': 0, 'cost': 82}, {'i': 0, 'j': 5, 'k': 1, 'cost': 25}, {'i': 0, 'j': 5, 'k': 2, 'cost': 14}, {'i': 0, 'j': 5, 'k': 3, 'cost': 79}, {'i': 0, 'j': 5, 'k': 4, 'cost': 99}, {'i': 0, 'j': 5, 'k': 5, 'cost': 75}, {'i': 0, 'j': 5, 'k': 6, 'cost': 76}, {'i': 0, 'j': 6, 'k': 0, 'cost': 81}, {'i': 0, 'j': 6, 'k': 1, 'cost': 67}, {'i': 0, 'j': 6, 'k': 2, 'cost': 33}, {'i': 0, 'j': 6, 'k': 3, 'cost': 57}, {'i': 0, 'j': 6, 'k': 4, 'cost': 44}, {'i': 0, 'j': 6, 'k': 5, 'cost': 4}, {'i': 0, 'j': 6, 'k': 6, 'cost': 56}, {'i': 1, 'j': 0, 'k': 0, 'cost': 87}, {'i': 1, 'j': 0, 'k': 1, 'cost': 38}, {'i': 1, 'j': 0, 'k': 2, 'cost': 81}, {'i': 1, 'j': 0, 'k': 3, 'cost': 88}, {'i': 1, 'j': 0, 'k': 4, 'cost': 81}, {'i': 1, 'j': 0, 'k': 5, 'cost': 11}, {'i': 1, 'j': 0, 'k': 6, 'cost': 63}, {'i': 1, 'j': 1, 'k': 0, 'cost': 48}, {'i': 1, 'j': 1, 'k': 1, 'cost': 44}, {'i': 1, 'j': 1, 'k': 2, 'cost': 91}, {'i': 1, 'j': 1, 'k': 3, 'cost': 76}, {'i': 1, 'j': 1, 'k': 4, 'cost': 96}, {'i': 1, 'j': 1, 'k': 5, 'cost': 51}, {'i': 1, 'j': 1, 'k': 6, 'cost': 96}, {'i': 1, 'j': 2, 'k': 0, 'cost': 2}, {'i': 1, 'j': 2, 'k': 1, 'cost': 7}, {'i': 1, 'j': 2, 'k': 2, 'cost': 52}, {'i': 1, 'j': 2, 'k': 3, 'cost': 88}, {'i': 1, 'j': 2, 'k': 4, 'cost': 74}, {'i': 1, 'j': 2, 'k': 5, 'cost': 21}, {'i': 1, 'j': 2, 'k': 6, 'cost': 41}, {'i': 1, 'j': 3, 'k': 0, 'cost': 63}, {'i': 1, 'j': 3, 'k': 1, 'cost': 96}, {'i': 1, 'j': 3, 'k': 2, 'cost': 41}, {'i': 1, 'j': 3, 'k': 3, 'cost': 98}, {'i': 1, 'j': 3, 'k': 4, 'cost': 76}, {'i': 1, 'j': 3, 'k': 5, 'cost': 18}, {'i': 1, 'j': 3, 'k': 6, 'cost': 31}, {'i': 1, 'j': 4, 'k': 0, 'cost': 96}, {'i': 1, 'j': 4, 'k': 1, 'cost': 37}, {'i': 1, 'j': 4, 'k': 2, 'cost': 18}, {'i': 1, 'j': 4, 'k': 3, 'cost': 83}, {'i': 1, 'j': 4, 'k': 4, 'cost': 89}, {'i': 1, 'j': 4, 'k': 5, 'cost': 63}, {'i': 1, 'j': 4, 'k': 6, 'cost': 39}, {'i': 1, 'j': 5, 'k': 0, 'cost': 38}, {'i': 1, 'j': 5, 'k': 1, 'cost': 68}, {'i': 1, 'j': 5, 'k': 2, 'cost': 70}, {'i': 1, 'j': 5, 'k': 3, 'cost': 38}, {'i': 1, 'j': 5, 'k': 4, 'cost': 32}, {'i': 1, 'j': 5, 'k': 5, 'cost': 4}, {'i': 1, 'j': 5, 'k': 6, 'cost': 29}, {'i': 1, 'j': 6, 'k': 0, 'cost': 35}, {'i': 1, 'j': 6, 'k': 1, 'cost': 75}, {'i': 1, 'j': 6, 'k': 2, 'cost': 88}, {'i': 1, 'j': 6, 'k': 3, 'cost': 76}, {'i': 1, 'j': 6, 'k': 4, 'cost': 81}, {'i': 1, 'j': 6, 'k': 5, 'cost': 10}, {'i': 1, 'j': 6, 'k': 6, 'cost': 80}, {'i': 2, 'j': 0, 'k': 0, 'cost': 69}, {'i': 2, 'j': 0, 'k': 1, 'cost': 56}, {'i': 2, 'j': 0, 'k': 2, 'cost': 73}, {'i': 2, 'j': 0, 'k': 3, 'cost': 31}, {'i': 2, 'j': 0, 'k': 4, 'cost': 10}, {'i': 2, 'j': 0, 'k': 5, 'cost': 40}, {'i': 2, 'j': 0, 'k': 6, 'cost': 90}, {'i': 2, 'j': 1, 'k': 0, 'cost': 12}, {'i': 2, 'j': 1, 'k': 1, 'cost': 58}, {'i': 2, 'j': 1, 'k': 2, 'cost': 44}, {'i': 2, 'j': 1, 'k': 3, 'cost': 94}, {'i': 2, 'j': 1, 'k': 4, 'cost': 65}, {'i': 2, 'j': 1, 'k': 5, 'cost': 52}, {'i': 2, 'j': 1, 'k': 6, 'cost': 28}, {'i': 2, 'j': 2, 'k': 0, 'cost': 42}, {'i': 2, 'j': 2, 'k': 1, 'cost': 91}, {'i': 2, 'j': 2, 'k': 2, 'cost': 92}, {'i': 2, 'j': 2, 'k': 3, 'cost': 71}, {'i': 2, 'j': 2, 'k': 4, 'cost': 8}, {'i': 2, 'j': 2, 'k': 5, 'cost': 57}, {'i': 2, 'j': 2, 'k': 6, 'cost': 71}, {'i': 2, 'j': 3, 'k': 0, 'cost': 43}, {'i': 2, 'j': 3, 'k': 1, 'cost': 98}, {'i': 2, 'j': 3, 'k': 2, 'cost': 81}, {'i': 2, 'j': 3, 'k': 3, 'cost': 22}, {'i': 2, 'j': 3, 'k': 4, 'cost': 36}, {'i': 2, 'j': 3, 'k': 5, 'cost': 86}, {'i': 2, 'j': 3, 'k': 6, 'cost': 82}, {'i': 2, 'j': 4, 'k': 0, 'cost': 66}, {'i': 2, 'j': 4, 'k': 1, 'cost': 30}, {'i': 2, 'j': 4, 'k': 2, 'cost': 38}, {'i': 2, 'j': 4, 'k': 3, 'cost': 82}, {'i': 2, 'j': 4, 'k': 4, 'cost': 58}, {'i': 2, 'j': 4, 'k': 5, 'cost': 85}, {'i': 2, 'j': 4, 'k': 6, 'cost': 66}, {'i': 2, 'j': 5, 'k': 0, 'cost': 89}, {'i': 2, 'j': 5, 'k': 1, 'cost': 20}, {'i': 2, 'j': 5, 'k': 2, 'cost': 36}, {'i': 2, 'j': 5, 'k': 3, 'cost': 28}, {'i': 2, 'j': 5, 'k': 4, 'cost': 29}, {'i': 2, 'j': 5, 'k': 5, 'cost': 24}, {'i': 2, 'j': 5, 'k': 6, 'cost': 92}, {'i': 2, 'j': 6, 'k': 0, 'cost': 24}, {'i': 2, 'j': 6, 'k': 1, 'cost': 67}, {'i': 2, 'j': 6, 'k': 2, 'cost': 82}, {'i': 2, 'j': 6, 'k': 3, 'cost': 58}, {'i': 2, 'j': 6, 'k': 4, 'cost': 32}, {'i': 2, 'j': 6, 'k': 5, 'cost': 77}, {'i': 2, 'j': 6, 'k': 6, 'cost': 23}, {'i': 3, 'j': 0, 'k': 0, 'cost': 38}, {'i': 3, 'j': 0, 'k': 1, 'cost': 88}, {'i': 3, 'j': 0, 'k': 2, 'cost': 82}, {'i': 3, 'j': 0, 'k': 3, 'cost': 48}, {'i': 3, 'j': 0, 'k': 4, 'cost': 43}, {'i': 3, 'j': 0, 'k': 5, 'cost': 19}, {'i': 3, 'j': 0, 'k': 6, 'cost': 26}, {'i': 3, 'j': 1, 'k': 0, 'cost': 80}, {'i': 3, 'j': 1, 'k': 1, 'cost': 6}, {'i': 3, 'j': 1, 'k': 2, 'cost': 24}, {'i': 3, 'j': 1, 'k': 3, 'cost': 54}, {'i': 3, 'j': 1, 'k': 4, 'cost': 76}, {'i': 3, 'j': 1, 'k': 5, 'cost': 56}, {'i': 3, 'j': 1, 'k': 6, 'cost': 5}, {'i': 3, 'j': 2, 'k': 0, 'cost': 12}, {'i': 3, 'j': 2, 'k': 1, 'cost': 67}, {'i': 3, 'j': 2, 'k': 2, 'cost': 8}, {'i': 3, 'j': 2, 'k': 3, 'cost': 23}, {'i': 3, 'j': 2, 'k': 4, 'cost': 75}, {'i': 3, 'j': 2, 'k': 5, 'cost': 43}, {'i': 3, 'j': 2, 'k': 6, 'cost': 36}, {'i': 3, 'j': 3, 'k': 0, 'cost': 74}, {'i': 3, 'j': 3, 'k': 1, 'cost': 11}, {'i': 3, 'j': 3, 'k': 2, 'cost': 72}, {'i': 3, 'j': 3, 'k': 3, 'cost': 79}, {'i': 3, 'j': 3, 'k': 4, 'cost': 50}, {'i': 3, 'j': 3, 'k': 5, 'cost': 46}, {'i': 3, 'j': 3, 'k': 6, 'cost': 20}, {'i': 3, 'j': 4, 'k': 0, 'cost': 9}, {'i': 3, 'j': 4, 'k': 1, 'cost': 16}, {'i': 3, 'j': 4, 'k': 2, 'cost': 29}, {'i': 3, 'j': 4, 'k': 3, 'cost': 85}, {'i': 3, 'j': 4, 'k': 4, 'cost': 4}, {'i': 3, 'j': 4, 'k': 5, 'cost': 94}, {'i': 3, 'j': 4, 'k': 6, 'cost': 70}, {'i': 3, 'j': 5, 'k': 0, 'cost': 0}, {'i': 3, 'j': 5, 'k': 1, 'cost': 22}, {'i': 3, 'j': 5, 'k': 2, 'cost': 53}, {'i': 3, 'j': 5, 'k': 3, 'cost': 95}, {'i': 3, 'j': 5, 'k': 4, 'cost': 9}, {'i': 3, 'j': 5, 'k': 5, 'cost': 11}, {'i': 3, 'j': 5, 'k': 6, 'cost': 35}, {'i': 3, 'j': 6, 'k': 0, 'cost': 64}, {'i': 3, 'j': 6, 'k': 1, 'cost': 61}, {'i': 3, 'j': 6, 'k': 2, 'cost': 82}, {'i': 3, 'j': 6, 'k': 3, 'cost': 83}, {'i': 3, 'j': 6, 'k': 4, 'cost': 12}, {'i': 3, 'j': 6, 'k': 5, 'cost': 59}, {'i': 3, 'j': 6, 'k': 6, 'cost': 84}, {'i': 4, 'j': 0, 'k': 0, 'cost': 78}, {'i': 4, 'j': 0, 'k': 1, 'cost': 82}, {'i': 4, 'j': 0, 'k': 2, 'cost': 0}, {'i': 4, 'j': 0, 'k': 3, 'cost': 72}, {'i': 4, 'j': 0, 'k': 4, 'cost': 2}, {'i': 4, 'j': 0, 'k': 5, 'cost': 74}, {'i': 4, 'j': 0, 'k': 6, 'cost': 82}, {'i': 4, 'j': 1, 'k': 0, 'cost': 8}, {'i': 4, 'j': 1, 'k': 1, 'cost': 15}, {'i': 4, 'j': 1, 'k': 2, 'cost': 57}, {'i': 4, 'j': 1, 'k': 3, 'cost': 84}, {'i': 4, 'j': 1, 'k': 4, 'cost': 79}, {'i': 4, 'j': 1, 'k': 5, 'cost': 75}, {'i': 4, 'j': 1, 'k': 6, 'cost': 75}, {'i': 4, 'j': 2, 'k': 0, 'cost': 21}, {'i': 4, 'j': 2, 'k': 1, 'cost': 42}, {'i': 4, 'j': 2, 'k': 2, 'cost': 45}, {'i': 4, 'j': 2, 'k': 3, 'cost': 22}, {'i': 4, 'j': 2, 'k': 4, 'cost': 67}, {'i': 4, 'j': 2, 'k': 5, 'cost': 20}, {'i': 4, 'j': 2, 'k': 6, 'cost': 29}, {'i': 4, 'j': 3, 'k': 0, 'cost': 94}, {'i': 4, 'j': 3, 'k': 1, 'cost': 4}, {'i': 4, 'j': 3, 'k': 2, 'cost': 13}, {'i': 4, 'j': 3, 'k': 3, 'cost': 59}, {'i': 4, 'j': 3, 'k': 4, 'cost': 41}, {'i': 4, 'j': 3, 'k': 5, 'cost': 33}, {'i': 4, 'j': 3, 'k': 6, 'cost': 67}, {'i': 4, 'j': 4, 'k': 0, 'cost': 73}, {'i': 4, 'j': 4, 'k': 1, 'cost': 87}, {'i': 4, 'j': 4, 'k': 2, 'cost': 63}, {'i': 4, 'j': 4, 'k': 3, 'cost': 30}, {'i': 4, 'j': 4, 'k': 4, 'cost': 47}, {'i': 4, 'j': 4, 'k': 5, 'cost': 40}, {'i': 4, 'j': 4, 'k': 6, 'cost': 14}, {'i': 4, 'j': 5, 'k': 0, 'cost': 97}, {'i': 4, 'j': 5, 'k': 1, 'cost': 42}, {'i': 4, 'j': 5, 'k': 2, 'cost': 83}, {'i': 4, 'j': 5, 'k': 3, 'cost': 58}, {'i': 4, 'j': 5, 'k': 4, 'cost': 13}, {'i': 4, 'j': 5, 'k': 5, 'cost': 26}, {'i': 4, 'j': 5, 'k': 6, 'cost': 83}, {'i': 4, 'j': 6, 'k': 0, 'cost': 46}, {'i': 4, 'j': 6, 'k': 1, 'cost': 71}, {'i': 4, 'j': 6, 'k': 2, 'cost': 65}, {'i': 4, 'j': 6, 'k': 3, 'cost': 11}, {'i': 4, 'j': 6, 'k': 4, 'cost': 22}, {'i': 4, 'j': 6, 'k': 5, 'cost': 3}, {'i': 4, 'j': 6, 'k': 6, 'cost': 27}, {'i': 5, 'j': 0, 'k': 0, 'cost': 38}, {'i': 5, 'j': 0, 'k': 1, 'cost': 4}, {'i': 5, 'j': 0, 'k': 2, 'cost': 41}, {'i': 5, 'j': 0, 'k': 3, 'cost': 9}, {'i': 5, 'j': 0, 'k': 4, 'cost': 60}, {'i': 5, 'j': 0, 'k': 5, 'cost': 21}, {'i': 5, 'j': 0, 'k': 6, 'cost': 86}, {'i': 5, 'j': 1, 'k': 0, 'cost': 45}, {'i': 5, 'j': 1, 'k': 1, 'cost': 40}, {'i': 5, 'j': 1, 'k': 2, 'cost': 27}, {'i': 5, 'j': 1, 'k': 3, 'cost': 42}, {'i': 5, 'j': 1, 'k': 4, 'cost': 72}, {'i': 5, 'j': 1, 'k': 5, 'cost': 24}, {'i': 5, 'j': 1, 'k': 6, 'cost': 0}, {'i': 5, 'j': 2, 'k': 0, 'cost': 25}, {'i': 5, 'j': 2, 'k': 1, 'cost': 17}, {'i': 5, 'j': 2, 'k': 2, 'cost': 35}, {'i': 5, 'j': 2, 'k': 3, 'cost': 88}, {'i': 5, 'j': 2, 'k': 4, 'cost': 99}, {'i': 5, 'j': 2, 'k': 5, 'cost': 90}, {'i': 5, 'j': 2, 'k': 6, 'cost': 75}, {'i': 5, 'j': 3, 'k': 0, 'cost': 36}, {'i': 5, 'j': 3, 'k': 1, 'cost': 88}, {'i': 5, 'j': 3, 'k': 2, 'cost': 56}, {'i': 5, 'j': 3, 'k': 3, 'cost': 90}, {'i': 5, 'j': 3, 'k': 4, 'cost': 22}, {'i': 5, 'j': 3, 'k': 5, 'cost': 58}, {'i': 5, 'j': 3, 'k': 6, 'cost': 19}, {'i': 5, 'j': 4, 'k': 0, 'cost': 64}, {'i': 5, 'j': 4, 'k': 1, 'cost': 48}, {'i': 5, 'j': 4, 'k': 2, 'cost': 76}, {'i': 5, 'j': 4, 'k': 3, 'cost': 79}, {'i': 5, 'j': 4, 'k': 4, 'cost': 45}, {'i': 5, 'j': 4, 'k': 5, 'cost': 73}, {'i': 5, 'j': 4, 'k': 6, 'cost': 56}, {'i': 5, 'j': 5, 'k': 0, 'cost': 98}, {'i': 5, 'j': 5, 'k': 1, 'cost': 11}, {'i': 5, 'j': 5, 'k': 2, 'cost': 24}, {'i': 5, 'j': 5, 'k': 3, 'cost': 77}, {'i': 5, 'j': 5, 'k': 4, 'cost': 78}, {'i': 5, 'j': 5, 'k': 5, 'cost': 88}, {'i': 5, 'j': 5, 'k': 6, 'cost': 58}, {'i': 5, 'j': 6, 'k': 0, 'cost': 24}, {'i': 5, 'j': 6, 'k': 1, 'cost': 95}, {'i': 5, 'j': 6, 'k': 2, 'cost': 12}, {'i': 5, 'j': 6, 'k': 3, 'cost': 56}, {'i': 5, 'j': 6, 'k': 4, 'cost': 34}, {'i': 5, 'j': 6, 'k': 5, 'cost': 13}, {'i': 5, 'j': 6, 'k': 6, 'cost': 35}, {'i': 6, 'j': 0, 'k': 0, 'cost': 13}, {'i': 6, 'j': 0, 'k': 1, 'cost': 37}, {'i': 6, 'j': 0, 'k': 2, 'cost': 42}, {'i': 6, 'j': 0, 'k': 3, 'cost': 33}, {'i': 6, 'j': 0, 'k': 4, 'cost': 10}, {'i': 6, 'j': 0, 'k': 5, 'cost': 46}, {'i': 6, 'j': 0, 'k': 6, 'cost': 10}, {'i': 6, 'j': 1, 'k': 0, 'cost': 90}, {'i': 6, 'j': 1, 'k': 1, 'cost': 11}, {'i': 6, 'j': 1, 'k': 2, 'cost': 62}, {'i': 6, 'j': 1, 'k': 3, 'cost': 75}, {'i': 6, 'j': 1, 'k': 4, 'cost': 43}, {'i': 6, 'j': 1, 'k': 5, 'cost': 4}, {'i': 6, 'j': 1, 'k': 6, 'cost': 18}, {'i': 6, 'j': 2, 'k': 0, 'cost': 9}, {'i': 6, 'j': 2, 'k': 1, 'cost': 90}, {'i': 6, 'j': 2, 'k': 2, 'cost': 52}, {'i': 6, 'j': 2, 'k': 3, 'cost': 85}, {'i': 6, 'j': 2, 'k': 4, 'cost': 69}, {'i': 6, 'j': 2, 'k': 5, 'cost': 35}, {'i': 6, 'j': 2, 'k': 6, 'cost': 64}, {'i': 6, 'j': 3, 'k': 0, 'cost': 77}, {'i': 6, 'j': 3, 'k': 1, 'cost': 7}, {'i': 6, 'j': 3, 'k': 2, 'cost': 76}, {'i': 6, 'j': 3, 'k': 3, 'cost': 14}, {'i': 6, 'j': 3, 'k': 4, 'cost': 0}, {'i': 6, 'j': 3, 'k': 5, 'cost': 55}, {'i': 6, 'j': 3, 'k': 6, 'cost': 71}, {'i': 6, 'j': 4, 'k': 0, 'cost': 41}, {'i': 6, 'j': 4, 'k': 1, 'cost': 1}, {'i': 6, 'j': 4, 'k': 2, 'cost': 61}, {'i': 6, 'j': 4, 'k': 3, 'cost': 77}, {'i': 6, 'j': 4, 'k': 4, 'cost': 73}, {'i': 6, 'j': 4, 'k': 5, 'cost': 32}, {'i': 6, 'j': 4, 'k': 6, 'cost': 70}, {'i': 6, 'j': 5, 'k': 0, 'cost': 26}, {'i': 6, 'j': 5, 'k': 1, 'cost': 66}, {'i': 6, 'j': 5, 'k': 2, 'cost': 32}, {'i': 6, 'j': 5, 'k': 3, 'cost': 87}, {'i': 6, 'j': 5, 'k': 4, 'cost': 55}, {'i': 6, 'j': 5, 'k': 5, 'cost': 10}, {'i': 6, 'j': 5, 'k': 6, 'cost': 82}, {'i': 6, 'j': 6, 'k': 0, 'cost': 73}, {'i': 6, 'j': 6, 'k': 1, 'cost': 71}, {'i': 6, 'j': 6, 'k': 2, 'cost': 17}, {'i': 6, 'j': 6, 'k': 3, 'cost': 26}, {'i': 6, 'j': 6, 'k': 4, 'cost': 85}, {'i': 6, 'j': 6, 'k': 5, 'cost': 16}, {'i': 6, 'j': 6, 'k': 6, 'cost': 47}]}","[[0, 4, 2], [1, 2, 1], [2, 0, 4], [3, 5, 0], [4, 6, 5], [5, 1, 6], [6, 3, 3]]",7,json,0
AP3,AP3,"Picture this: a closet of outfits and a drawer of accessories, and a team of clients who each need one of each, with each outfit and accessory going to exactly one person. Every possible assignment carries a price for each client (outfit plus accessory), and the final cost is the sum of all those client costs — the aim is to make that grand total as small as possible while still giving everyone one outfit and one accessory. No sharing, no extras left behind. The specific items and their costs are shown below.

Below are the 6 clients (1, 2, 3, 4, 5, 6) and every outfit+accessory option with its cost:
Meaning: costs form a 3D tensor. For each fixed client_id=i, you are given a outfit_id×accessory_id matrix whose entry at row outfit_id=j and column accessory_id=k equals combined_cost(i,j,k). You must pick exactly one (j,k) for every i, with all outfit_id and all accessory_id used exactly once.
combined_cost_tensor (per-client_id markdown matrices):
## client_id=1
| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 4 | 98 | 27 | 53 | 31 | 76 |
| 2 | 6 | 68 | 57 | 13 | 63 | 17 |
| 3 | 57 | 54 | 12 | 54 | 5 | 15 |
| 4 | 74 | 50 | 78 | 91 | 91 | 69 |
| 5 | 36 | 46 | 44 | 82 | 97 | 64 |
| 6 | 94 | 89 | 82 | 29 | 54 | 68 |

## client_id=2
| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 32 | 96 | 51 | 70 | 87 | 75 |
| 2 | 0 | 4 | 43 | 19 | 90 | 78 |
| 3 | 17 | 8 | 38 | 39 | 14 | 1 |
| 4 | 0 | 5 | 76 | 66 | 98 | 16 |
| 5 | 53 | 48 | 97 | 74 | 33 | 31 |
| 6 | 58 | 31 | 94 | 47 | 43 | 98 |

## client_id=3
| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 12 | 44 | 71 | 59 | 41 | 14 |
| 2 | 78 | 46 | 70 | 27 | 7 | 82 |
| 3 | 70 | 50 | 35 | 57 | 51 | 89 |
| 4 | 32 | 45 | 25 | 33 | 55 | 35 |
| 5 | 27 | 42 | 38 | 26 | 28 | 60 |
| 6 | 37 | 76 | 99 | 35 | 54 | 76 |

## client_id=4
| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 83 | 67 | 36 | 15 | 57 | 80 |
| 2 | 94 | 79 | 11 | 41 | 16 | 66 |
| 3 | 51 | 77 | 8 | 95 | 47 | 53 |
| 4 | 88 | 66 | 53 | 13 | 95 | 67 |
| 5 | 55 | 61 | 91 | 30 | 47 | 41 |
| 6 | 34 | 47 | 95 | 93 | 20 | 78 |

## client_id=5
| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 10 | 58 | 21 | 56 | 44 | 80 |
| 2 | 9 | 13 | 64 | 85 | 36 | 49 |
| 3 | 56 | 9 | 16 | 27 | 4 | 39 |
| 4 | 51 | 21 | 45 | 79 | 98 | 15 |
| 5 | 24 | 43 | 58 | 42 | 1 | 48 |
| 6 | 86 | 83 | 73 | 99 | 24 | 42 |

## client_id=6
| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 10 | 25 | 73 | 96 | 60 | 34 |
| 2 | 73 | 70 | 15 | 6 | 35 | 98 |
| 3 | 97 | 9 | 16 | 40 | 95 | 62 |
| 4 | 53 | 77 | 62 | 82 | 98 | 25 |
| 5 | 13 | 74 | 49 | 36 | 47 | 99 |
| 6 | 50 | 99 | 5 | 36 | 82 | 15 |
Assign exactly one line to each client so every outfit and accessory is used once and the grand total is as small as possible.

Oh, and one more thing — when you send the assignment back, it's handy if you use a tiny JSON sketch like this so everything's clean and easy to check:

{
  ""solution"": [
    [<client_id>, <outfit_id>, <accessory_id>]
  ]
}

It's just a simple list of triples: each inner array is one client with their chosen outfit and accessory. The ""solution"" array should contain one triple for each client. This is only the shape I expect — not the actual answer.

Please make sure you use the exact identifiers from the instance input, without renaming or inventing new labels. To be clear:
- 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”.""","{'cost_tensor': [[[4, 98, 27, 53, 31, 76], [6, 68, 57, 13, 63, 17], [57, 54, 12, 54, 5, 15], [74, 50, 78, 91, 91, 69], [36, 46, 44, 82, 97, 64], [94, 89, 82, 29, 54, 68]], [[32, 96, 51, 70, 87, 75], [0, 4, 43, 19, 90, 78], [17, 8, 38, 39, 14, 1], [0, 5, 76, 66, 98, 16], [53, 48, 97, 74, 33, 31], [58, 31, 94, 47, 43, 98]], [[12, 44, 71, 59, 41, 14], [78, 46, 70, 27, 7, 82], [70, 50, 35, 57, 51, 89], [32, 45, 25, 33, 55, 35], [27, 42, 38, 26, 28, 60], [37, 76, 99, 35, 54, 76]], [[83, 67, 36, 15, 57, 80], [94, 79, 11, 41, 16, 66], [51, 77, 8, 95, 47, 53], [88, 66, 53, 13, 95, 67], [55, 61, 91, 30, 47, 41], [34, 47, 95, 93, 20, 78]], [[10, 58, 21, 56, 44, 80], [9, 13, 64, 85, 36, 49], [56, 9, 16, 27, 4, 39], [51, 21, 45, 79, 98, 15], [24, 43, 58, 42, 1, 48], [86, 83, 73, 99, 24, 42]], [[10, 25, 73, 96, 60, 34], [73, 70, 15, 6, 35, 98], [97, 9, 16, 40, 95, 62], [53, 77, 62, 82, 98, 25], [13, 74, 49, 36, 47, 99], [50, 99, 5, 36, 82, 15]]], 'objective': 47.0}","[[0, 1, 0], [1, 2, 1], [2, 0, 5], [3, 3, 3], [4, 4, 4], [5, 5, 2]]",47.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 4}, {'i': 1, 'j': 1, 'k': 2, 'cost': 98}, {'i': 1, 'j': 1, 'k': 3, 'cost': 27}, {'i': 1, 'j': 1, 'k': 4, 'cost': 53}, {'i': 1, 'j': 1, 'k': 5, 'cost': 31}, {'i': 1, 'j': 1, 'k': 6, 'cost': 76}, {'i': 1, 'j': 2, 'k': 1, 'cost': 6}, {'i': 1, 'j': 2, 'k': 2, 'cost': 68}, {'i': 1, 'j': 2, 'k': 3, 'cost': 57}, {'i': 1, 'j': 2, 'k': 4, 'cost': 13}, {'i': 1, 'j': 2, 'k': 5, 'cost': 63}, {'i': 1, 'j': 2, 'k': 6, 'cost': 17}, {'i': 1, 'j': 3, 'k': 1, 'cost': 57}, {'i': 1, 'j': 3, 'k': 2, 'cost': 54}, {'i': 1, 'j': 3, 'k': 3, 'cost': 12}, {'i': 1, 'j': 3, 'k': 4, 'cost': 54}, {'i': 1, 'j': 3, 'k': 5, 'cost': 5}, {'i': 1, 'j': 3, 'k': 6, 'cost': 15}, {'i': 1, 'j': 4, 'k': 1, 'cost': 74}, {'i': 1, 'j': 4, 'k': 2, 'cost': 50}, {'i': 1, 'j': 4, 'k': 3, 'cost': 78}, {'i': 1, 'j': 4, 'k': 4, 'cost': 91}, {'i': 1, 'j': 4, 'k': 5, 'cost': 91}, {'i': 1, 'j': 4, 'k': 6, 'cost': 69}, {'i': 1, 'j': 5, 'k': 1, 'cost': 36}, {'i': 1, 'j': 5, 'k': 2, 'cost': 46}, {'i': 1, 'j': 5, 'k': 3, 'cost': 44}, {'i': 1, 'j': 5, 'k': 4, 'cost': 82}, {'i': 1, 'j': 5, 'k': 5, 'cost': 97}, {'i': 1, 'j': 5, 'k': 6, 'cost': 64}, {'i': 1, 'j': 6, 'k': 1, 'cost': 94}, {'i': 1, 'j': 6, 'k': 2, 'cost': 89}, {'i': 1, 'j': 6, 'k': 3, 'cost': 82}, {'i': 1, 'j': 6, 'k': 4, 'cost': 29}, {'i': 1, 'j': 6, 'k': 5, 'cost': 54}, {'i': 1, 'j': 6, 'k': 6, 'cost': 68}, {'i': 2, 'j': 1, 'k': 1, 'cost': 32}, {'i': 2, 'j': 1, 'k': 2, 'cost': 96}, {'i': 2, 'j': 1, 'k': 3, 'cost': 51}, {'i': 2, 'j': 1, 'k': 4, 'cost': 70}, {'i': 2, 'j': 1, 'k': 5, 'cost': 87}, {'i': 2, 'j': 1, 'k': 6, 'cost': 75}, {'i': 2, 'j': 2, 'k': 1, 'cost': 0}, {'i': 2, 'j': 2, 'k': 2, 'cost': 4}, {'i': 2, 'j': 2, 'k': 3, 'cost': 43}, {'i': 2, 'j': 2, 'k': 4, 'cost': 19}, {'i': 2, 'j': 2, 'k': 5, 'cost': 90}, {'i': 2, 'j': 2, 'k': 6, 'cost': 78}, {'i': 2, 'j': 3, 'k': 1, 'cost': 17}, {'i': 2, 'j': 3, 'k': 2, 'cost': 8}, {'i': 2, 'j': 3, 'k': 3, 'cost': 38}, {'i': 2, 'j': 3, 'k': 4, 'cost': 39}, {'i': 2, 'j': 3, 'k': 5, 'cost': 14}, {'i': 2, 'j': 3, 'k': 6, 'cost': 1}, {'i': 2, 'j': 4, 'k': 1, 'cost': 0}, {'i': 2, 'j': 4, 'k': 2, 'cost': 5}, {'i': 2, 'j': 4, 'k': 3, 'cost': 76}, {'i': 2, 'j': 4, 'k': 4, 'cost': 66}, {'i': 2, 'j': 4, 'k': 5, 'cost': 98}, {'i': 2, 'j': 4, 'k': 6, 'cost': 16}, {'i': 2, 'j': 5, 'k': 1, 'cost': 53}, {'i': 2, 'j': 5, 'k': 2, 'cost': 48}, {'i': 2, 'j': 5, 'k': 3, 'cost': 97}, {'i': 2, 'j': 5, 'k': 4, 'cost': 74}, {'i': 2, 'j': 5, 'k': 5, 'cost': 33}, {'i': 2, 'j': 5, 'k': 6, 'cost': 31}, {'i': 2, 'j': 6, 'k': 1, 'cost': 58}, {'i': 2, 'j': 6, 'k': 2, 'cost': 31}, {'i': 2, 'j': 6, 'k': 3, 'cost': 94}, {'i': 2, 'j': 6, 'k': 4, 'cost': 47}, {'i': 2, 'j': 6, 'k': 5, 'cost': 43}, {'i': 2, 'j': 6, 'k': 6, 'cost': 98}, {'i': 3, 'j': 1, 'k': 1, 'cost': 12}, {'i': 3, 'j': 1, 'k': 2, 'cost': 44}, {'i': 3, 'j': 1, 'k': 3, 'cost': 71}, {'i': 3, 'j': 1, 'k': 4, 'cost': 59}, {'i': 3, 'j': 1, 'k': 5, 'cost': 41}, {'i': 3, 'j': 1, 'k': 6, 'cost': 14}, {'i': 3, 'j': 2, 'k': 1, 'cost': 78}, {'i': 3, 'j': 2, 'k': 2, 'cost': 46}, {'i': 3, 'j': 2, 'k': 3, 'cost': 70}, {'i': 3, 'j': 2, 'k': 4, 'cost': 27}, {'i': 3, 'j': 2, 'k': 5, 'cost': 7}, {'i': 3, 'j': 2, 'k': 6, 'cost': 82}, {'i': 3, 'j': 3, 'k': 1, 'cost': 70}, {'i': 3, 'j': 3, 'k': 2, 'cost': 50}, {'i': 3, 'j': 3, 'k': 3, 'cost': 35}, {'i': 3, 'j': 3, 'k': 4, 'cost': 57}, {'i': 3, 'j': 3, 'k': 5, 'cost': 51}, {'i': 3, 'j': 3, 'k': 6, 'cost': 89}, {'i': 3, 'j': 4, 'k': 1, 'cost': 32}, {'i': 3, 'j': 4, 'k': 2, 'cost': 45}, {'i': 3, 'j': 4, 'k': 3, 'cost': 25}, {'i': 3, 'j': 4, 'k': 4, 'cost': 33}, {'i': 3, 'j': 4, 'k': 5, 'cost': 55}, {'i': 3, 'j': 4, 'k': 6, 'cost': 35}, {'i': 3, 'j': 5, 'k': 1, 'cost': 27}, {'i': 3, 'j': 5, 'k': 2, 'cost': 42}, {'i': 3, 'j': 5, 'k': 3, 'cost': 38}, {'i': 3, 'j': 5, 'k': 4, 'cost': 26}, {'i': 3, 'j': 5, 'k': 5, 'cost': 28}, {'i': 3, 'j': 5, 'k': 6, 'cost': 60}, {'i': 3, 'j': 6, 'k': 1, 'cost': 37}, {'i': 3, 'j': 6, 'k': 2, 'cost': 76}, {'i': 3, 'j': 6, 'k': 3, 'cost': 99}, {'i': 3, 'j': 6, 'k': 4, 'cost': 35}, {'i': 3, 'j': 6, 'k': 5, 'cost': 54}, {'i': 3, 'j': 6, 'k': 6, 'cost': 76}, {'i': 4, 'j': 1, 'k': 1, 'cost': 83}, {'i': 4, 'j': 1, 'k': 2, 'cost': 67}, {'i': 4, 'j': 1, 'k': 3, 'cost': 36}, {'i': 4, 'j': 1, 'k': 4, 'cost': 15}, {'i': 4, 'j': 1, 'k': 5, 'cost': 57}, {'i': 4, 'j': 1, 'k': 6, 'cost': 80}, {'i': 4, 'j': 2, 'k': 1, 'cost': 94}, {'i': 4, 'j': 2, 'k': 2, 'cost': 79}, {'i': 4, 'j': 2, 'k': 3, 'cost': 11}, {'i': 4, 'j': 2, 'k': 4, 'cost': 41}, {'i': 4, 'j': 2, 'k': 5, 'cost': 16}, {'i': 4, 'j': 2, 'k': 6, 'cost': 66}, {'i': 4, 'j': 3, 'k': 1, 'cost': 51}, {'i': 4, 'j': 3, 'k': 2, 'cost': 77}, {'i': 4, 'j': 3, 'k': 3, 'cost': 8}, {'i': 4, 'j': 3, 'k': 4, 'cost': 95}, {'i': 4, 'j': 3, 'k': 5, 'cost': 47}, {'i': 4, 'j': 3, 'k': 6, 'cost': 53}, {'i': 4, 'j': 4, 'k': 1, 'cost': 88}, {'i': 4, 'j': 4, 'k': 2, 'cost': 66}, {'i': 4, 'j': 4, 'k': 3, 'cost': 53}, {'i': 4, 'j': 4, 'k': 4, 'cost': 13}, {'i': 4, 'j': 4, 'k': 5, 'cost': 95}, {'i': 4, 'j': 4, 'k': 6, 'cost': 67}, {'i': 4, 'j': 5, 'k': 1, 'cost': 55}, {'i': 4, 'j': 5, 'k': 2, 'cost': 61}, {'i': 4, 'j': 5, 'k': 3, 'cost': 91}, {'i': 4, 'j': 5, 'k': 4, 'cost': 30}, {'i': 4, 'j': 5, 'k': 5, 'cost': 47}, {'i': 4, 'j': 5, 'k': 6, 'cost': 41}, {'i': 4, 'j': 6, 'k': 1, 'cost': 34}, {'i': 4, 'j': 6, 'k': 2, 'cost': 47}, {'i': 4, 'j': 6, 'k': 3, 'cost': 95}, {'i': 4, 'j': 6, 'k': 4, 'cost': 93}, {'i': 4, 'j': 6, 'k': 5, 'cost': 20}, {'i': 4, 'j': 6, 'k': 6, 'cost': 78}, {'i': 5, 'j': 1, 'k': 1, 'cost': 10}, {'i': 5, 'j': 1, 'k': 2, 'cost': 58}, {'i': 5, 'j': 1, 'k': 3, 'cost': 21}, {'i': 5, 'j': 1, 'k': 4, 'cost': 56}, {'i': 5, 'j': 1, 'k': 5, 'cost': 44}, {'i': 5, 'j': 1, 'k': 6, 'cost': 80}, {'i': 5, 'j': 2, 'k': 1, 'cost': 9}, {'i': 5, 'j': 2, 'k': 2, 'cost': 13}, {'i': 5, 'j': 2, 'k': 3, 'cost': 64}, {'i': 5, 'j': 2, 'k': 4, 'cost': 85}, {'i': 5, 'j': 2, 'k': 5, 'cost': 36}, {'i': 5, 'j': 2, 'k': 6, 'cost': 49}, {'i': 5, 'j': 3, 'k': 1, 'cost': 56}, {'i': 5, 'j': 3, 'k': 2, 'cost': 9}, {'i': 5, 'j': 3, 'k': 3, 'cost': 16}, {'i': 5, 'j': 3, 'k': 4, 'cost': 27}, {'i': 5, 'j': 3, 'k': 5, 'cost': 4}, {'i': 5, 'j': 3, 'k': 6, 'cost': 39}, {'i': 5, 'j': 4, 'k': 1, 'cost': 51}, {'i': 5, 'j': 4, 'k': 2, 'cost': 21}, {'i': 5, 'j': 4, 'k': 3, 'cost': 45}, {'i': 5, 'j': 4, 'k': 4, 'cost': 79}, {'i': 5, 'j': 4, 'k': 5, 'cost': 98}, {'i': 5, 'j': 4, 'k': 6, 'cost': 15}, {'i': 5, 'j': 5, 'k': 1, 'cost': 24}, {'i': 5, 'j': 5, 'k': 2, 'cost': 43}, {'i': 5, 'j': 5, 'k': 3, 'cost': 58}, {'i': 5, 'j': 5, 'k': 4, 'cost': 42}, {'i': 5, 'j': 5, 'k': 5, 'cost': 1}, {'i': 5, 'j': 5, 'k': 6, 'cost': 48}, {'i': 5, 'j': 6, 'k': 1, 'cost': 86}, {'i': 5, 'j': 6, 'k': 2, 'cost': 83}, {'i': 5, 'j': 6, 'k': 3, 'cost': 73}, {'i': 5, 'j': 6, 'k': 4, 'cost': 99}, {'i': 5, 'j': 6, 'k': 5, 'cost': 24}, {'i': 5, 'j': 6, 'k': 6, 'cost': 42}, {'i': 6, 'j': 1, 'k': 1, 'cost': 10}, {'i': 6, 'j': 1, 'k': 2, 'cost': 25}, {'i': 6, 'j': 1, 'k': 3, 'cost': 73}, {'i': 6, 'j': 1, 'k': 4, 'cost': 96}, {'i': 6, 'j': 1, 'k': 5, 'cost': 60}, {'i': 6, 'j': 1, 'k': 6, 'cost': 34}, {'i': 6, 'j': 2, 'k': 1, 'cost': 73}, {'i': 6, 'j': 2, 'k': 2, 'cost': 70}, {'i': 6, 'j': 2, 'k': 3, 'cost': 15}, {'i': 6, 'j': 2, 'k': 4, 'cost': 6}, {'i': 6, 'j': 2, 'k': 5, 'cost': 35}, {'i': 6, 'j': 2, 'k': 6, 'cost': 98}, {'i': 6, 'j': 3, 'k': 1, 'cost': 97}, {'i': 6, 'j': 3, 'k': 2, 'cost': 9}, {'i': 6, 'j': 3, 'k': 3, 'cost': 16}, {'i': 6, 'j': 3, 'k': 4, 'cost': 40}, {'i': 6, 'j': 3, 'k': 5, 'cost': 95}, {'i': 6, 'j': 3, 'k': 6, 'cost': 62}, {'i': 6, 'j': 4, 'k': 1, 'cost': 53}, {'i': 6, 'j': 4, 'k': 2, 'cost': 77}, {'i': 6, 'j': 4, 'k': 3, 'cost': 62}, {'i': 6, 'j': 4, 'k': 4, 'cost': 82}, {'i': 6, 'j': 4, 'k': 5, 'cost': 98}, {'i': 6, 'j': 4, 'k': 6, 'cost': 25}, {'i': 6, 'j': 5, 'k': 1, 'cost': 13}, {'i': 6, 'j': 5, 'k': 2, 'cost': 74}, {'i': 6, 'j': 5, 'k': 3, 'cost': 49}, {'i': 6, 'j': 5, 'k': 4, 'cost': 36}, {'i': 6, 'j': 5, 'k': 5, 'cost': 47}, {'i': 6, 'j': 5, 'k': 6, 'cost': 99}, {'i': 6, 'j': 6, 'k': 1, 'cost': 50}, {'i': 6, 'j': 6, 'k': 2, 'cost': 99}, {'i': 6, 'j': 6, 'k': 3, 'cost': 5}, {'i': 6, 'j': 6, 'k': 4, 'cost': 36}, {'i': 6, 'j': 6, 'k': 5, 'cost': 82}, {'i': 6, 'j': 6, 'k': 6, 'cost': 15}]}","[[1, 2, 1], [2, 3, 2], [3, 1, 6], [4, 4, 4], [5, 5, 5], [6, 6, 3]]",8,nl,1
AP3,AP3,"I remember helping put together a tiny music festival where every band needed exactly one stage and exactly one time slot, and every stage and every time had to host just one band—no double bookings and no empty spots. The job was to pick which stage-and-time pair each band gets so that, when looking at the expected clash for each band, the total of those clash costs (just add up each band's expected conflict cost for its assigned stage and time) is as small as possible. The concrete lineup and the numbers for those expected clashes are shown below.

{
  ""num_bands"": 7,
  ""lineup_identifiers"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6
  ]
}

# Meaning: costs form a 3D tensor. For each fixed band_id=i, you are given a stage_id×time_slot_id matrix whose entry at row stage_id=j and column time_slot_id=k equals expected_conflict_cost(i,j,k). You must pick exactly one (j,k) for every i, with all stage_id and all time_slot_id used exactly once.
# expected_conflict_cost_tensor (per-band_id markdown matrices)

## band_id=0
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 21 | 72 | 65 | 37 | 19 | 23 | 49 |
| 1 | 36 | 23 | 96 | 80 | 57 | 59 | 2 |
| 2 | 40 | 6 | 17 | 62 | 67 | 42 | 29 |
| 3 | 78 | 16 | 47 | 76 | 13 | 71 | 34 |
| 4 | 36 | 65 | 48 | 99 | 43 | 37 | 76 |
| 5 | 56 | 55 | 4 | 71 | 27 | 38 | 32 |
| 6 | 34 | 74 | 59 | 56 | 51 | 52 | 33 |

## band_id=1
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 36 | 26 | 43 | 50 | 60 | 58 | 8 |
| 1 | 72 | 92 | 99 | 55 | 64 | 1 | 26 |
| 2 | 23 | 34 | 39 | 91 | 74 | 49 | 87 |
| 3 | 24 | 68 | 17 | 66 | 46 | 4 | 12 |
| 4 | 93 | 35 | 86 | 29 | 32 | 12 | 99 |
| 5 | 14 | 34 | 77 | 84 | 21 | 80 | 78 |
| 6 | 87 | 20 | 37 | 25 | 64 | 36 | 69 |

## band_id=2
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 97 | 83 | 98 | 20 | 4 | 84 | 54 |
| 1 | 89 | 10 | 52 | 44 | 55 | 81 | 8 |
| 2 | 71 | 22 | 9 | 29 | 4 | 71 | 40 |
| 3 | 71 | 66 | 28 | 82 | 22 | 29 | 50 |
| 4 | 22 | 97 | 40 | 50 | 34 | 54 | 54 |
| 5 | 42 | 13 | 53 | 83 | 32 | 79 | 13 |
| 6 | 2 | 76 | 85 | 21 | 74 | 55 | 32 |

## band_id=3
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 83 | 53 | 60 | 82 | 63 | 50 | 79 |
| 1 | 65 | 1 | 15 | 33 | 44 | 57 | 72 |
| 2 | 83 | 80 | 48 | 99 | 14 | 66 | 55 |
| 3 | 71 | 42 | 61 | 34 | 34 | 28 | 25 |
| 4 | 94 | 61 | 75 | 73 | 84 | 67 | 74 |
| 5 | 62 | 75 | 51 | 57 | 2 | 71 | 13 |
| 6 | 16 | 92 | 75 | 45 | 92 | 61 | 41 |

## band_id=4
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 64 | 88 | 55 | 61 | 86 | 51 | 80 |
| 1 | 45 | 74 | 3 | 65 | 47 | 23 | 92 |
| 2 | 55 | 50 | 61 | 35 | 3 | 59 | 16 |
| 3 | 31 | 81 | 40 | 62 | 9 | 56 | 7 |
| 4 | 49 | 12 | 77 | 75 | 58 | 80 | 88 |
| 5 | 26 | 18 | 81 | 98 | 41 | 27 | 1 |
| 6 | 38 | 29 | 74 | 99 | 84 | 2 | 41 |

## band_id=5
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 86 | 39 | 44 | 89 | 87 | 46 | 23 |
| 1 | 36 | 48 | 78 | 72 | 39 | 91 | 21 |
| 2 | 88 | 30 | 84 | 90 | 64 | 66 | 63 |
| 3 | 81 | 4 | 10 | 75 | 80 | 51 | 37 |
| 4 | 35 | 58 | 85 | 21 | 15 | 13 | 54 |
| 5 | 11 | 17 | 83 | 91 | 0 | 6 | 96 |
| 6 | 19 | 34 | 59 | 63 | 83 | 19 | 54 |

## band_id=6
| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 88 | 95 | 62 | 4 | 55 | 74 | 97 |
| 1 | 76 | 13 | 78 | 91 | 8 | 99 | 46 |
| 2 | 18 | 8 | 57 | 0 | 85 | 25 | 84 |
| 3 | 60 | 98 | 9 | 11 | 35 | 53 | 2 |
| 4 | 89 | 87 | 37 | 48 | 42 | 5 | 60 |
| 5 | 53 | 62 | 92 | 74 | 66 | 46 | 86 |
| 6 | 97 | 96 | 67 | 75 | 76 | 49 | 69 |

And to keep things tidy when you send the final assignment back, here’s the little JSON shape I like to use — just a quick sketch of what your answer should look like.

{
  ""solution"": [
    [<band_id>, <stage_id>, <time_slot_id>],
    ...
  ]
}

The ""solution"" entry is just a list of triples: each inner list picks one band, the stage they play on, and the time slot they get. Think of each triple as ""band goes to this stage at this time."" This block is only a sketch of the expected shape, not the actual answer.

Please make sure you use the exact identifiers from the instance input — don’t 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”.""","{'cost_tensor': [[[21, 72, 65, 37, 19, 23, 49], [36, 23, 96, 80, 57, 59, 2], [40, 6, 17, 62, 67, 42, 29], [78, 16, 47, 76, 13, 71, 34], [36, 65, 48, 99, 43, 37, 76], [56, 55, 4, 71, 27, 38, 32], [34, 74, 59, 56, 51, 52, 33]], [[36, 26, 43, 50, 60, 58, 8], [72, 92, 99, 55, 64, 1, 26], [23, 34, 39, 91, 74, 49, 87], [24, 68, 17, 66, 46, 4, 12], [93, 35, 86, 29, 32, 12, 99], [14, 34, 77, 84, 21, 80, 78], [87, 20, 37, 25, 64, 36, 69]], [[97, 83, 98, 20, 4, 84, 54], [89, 10, 52, 44, 55, 81, 8], [71, 22, 9, 29, 4, 71, 40], [71, 66, 28, 82, 22, 29, 50], [22, 97, 40, 50, 34, 54, 54], [42, 13, 53, 83, 32, 79, 13], [2, 76, 85, 21, 74, 55, 32]], [[83, 53, 60, 82, 63, 50, 79], [65, 1, 15, 33, 44, 57, 72], [83, 80, 48, 99, 14, 66, 55], [71, 42, 61, 34, 34, 28, 25], [94, 61, 75, 73, 84, 67, 74], [62, 75, 51, 57, 2, 71, 13], [16, 92, 75, 45, 92, 61, 41]], [[64, 88, 55, 61, 86, 51, 80], [45, 74, 3, 65, 47, 23, 92], [55, 50, 61, 35, 3, 59, 16], [31, 81, 40, 62, 9, 56, 7], [49, 12, 77, 75, 58, 80, 88], [26, 18, 81, 98, 41, 27, 1], [38, 29, 74, 99, 84, 2, 41]], [[86, 39, 44, 89, 87, 46, 23], [36, 48, 78, 72, 39, 91, 21], [88, 30, 84, 90, 64, 66, 63], [81, 4, 10, 75, 80, 51, 37], [35, 58, 85, 21, 15, 13, 54], [11, 17, 83, 91, 0, 6, 96], [19, 34, 59, 63, 83, 19, 54]], [[88, 95, 62, 4, 55, 74, 97], [76, 13, 78, 91, 8, 99, 46], [18, 8, 57, 0, 85, 25, 84], [60, 98, 9, 11, 35, 53, 2], [89, 87, 37, 48, 42, 5, 60], [53, 62, 92, 74, 66, 46, 86], [97, 96, 67, 75, 76, 49, 69]]], 'objective': 37.0}","[[0, 5, 2], [1, 0, 6], [2, 6, 0], [3, 1, 1], [4, 3, 4], [5, 4, 5], [6, 2, 3]]",37.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [0, 1, 2, 3, 4, 5, 6], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 21}, {'i': 0, 'j': 0, 'k': 1, 'cost': 72}, {'i': 0, 'j': 0, 'k': 2, 'cost': 65}, {'i': 0, 'j': 0, 'k': 3, 'cost': 37}, {'i': 0, 'j': 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{'i': 6, 'j': 0, 'k': 0, 'cost': 88}, {'i': 6, 'j': 0, 'k': 1, 'cost': 95}, {'i': 6, 'j': 0, 'k': 2, 'cost': 62}, {'i': 6, 'j': 0, 'k': 3, 'cost': 4}, {'i': 6, 'j': 0, 'k': 4, 'cost': 55}, {'i': 6, 'j': 0, 'k': 5, 'cost': 74}, {'i': 6, 'j': 0, 'k': 6, 'cost': 97}, {'i': 6, 'j': 1, 'k': 0, 'cost': 76}, {'i': 6, 'j': 1, 'k': 1, 'cost': 13}, {'i': 6, 'j': 1, 'k': 2, 'cost': 78}, {'i': 6, 'j': 1, 'k': 3, 'cost': 91}, {'i': 6, 'j': 1, 'k': 4, 'cost': 8}, {'i': 6, 'j': 1, 'k': 5, 'cost': 99}, {'i': 6, 'j': 1, 'k': 6, 'cost': 46}, {'i': 6, 'j': 2, 'k': 0, 'cost': 18}, {'i': 6, 'j': 2, 'k': 1, 'cost': 8}, {'i': 6, 'j': 2, 'k': 2, 'cost': 57}, {'i': 6, 'j': 2, 'k': 3, 'cost': 0}, {'i': 6, 'j': 2, 'k': 4, 'cost': 85}, {'i': 6, 'j': 2, 'k': 5, 'cost': 25}, {'i': 6, 'j': 2, 'k': 6, 'cost': 84}, {'i': 6, 'j': 3, 'k': 0, 'cost': 60}, {'i': 6, 'j': 3, 'k': 1, 'cost': 98}, {'i': 6, 'j': 3, 'k': 2, 'cost': 9}, {'i': 6, 'j': 3, 'k': 3, 'cost': 11}, {'i': 6, 'j': 3, 'k': 4, 'cost': 35}, {'i': 6, 'j': 3, 'k': 5, 'cost': 53}, {'i': 6, 'j': 3, 'k': 6, 'cost': 2}, {'i': 6, 'j': 4, 'k': 0, 'cost': 89}, {'i': 6, 'j': 4, 'k': 1, 'cost': 87}, {'i': 6, 'j': 4, 'k': 2, 'cost': 37}, {'i': 6, 'j': 4, 'k': 3, 'cost': 48}, {'i': 6, 'j': 4, 'k': 4, 'cost': 42}, {'i': 6, 'j': 4, 'k': 5, 'cost': 5}, {'i': 6, 'j': 4, 'k': 6, 'cost': 60}, {'i': 6, 'j': 5, 'k': 0, 'cost': 53}, {'i': 6, 'j': 5, 'k': 1, 'cost': 62}, {'i': 6, 'j': 5, 'k': 2, 'cost': 92}, {'i': 6, 'j': 5, 'k': 3, 'cost': 74}, {'i': 6, 'j': 5, 'k': 4, 'cost': 66}, {'i': 6, 'j': 5, 'k': 5, 'cost': 46}, {'i': 6, 'j': 5, 'k': 6, 'cost': 86}, {'i': 6, 'j': 6, 'k': 0, 'cost': 97}, {'i': 6, 'j': 6, 'k': 1, 'cost': 96}, {'i': 6, 'j': 6, 'k': 2, 'cost': 67}, {'i': 6, 'j': 6, 'k': 3, 'cost': 75}, {'i': 6, 'j': 6, 'k': 4, 'cost': 76}, {'i': 6, 'j': 6, 'k': 5, 'cost': 49}, {'i': 6, 'j': 6, 'k': 6, 'cost': 69}]}","[[0, 5, 2], [1, 0, 6], [2, 6, 0], [3, 1, 1], [4, 3, 4], [5, 4, 5], [6, 2, 3]]",9,json,0
AP3,AP3,"We joked that it was like seating people for a dinner — every document needs a single translator and a single language combination at the table. Each possible match has a fee, and the whole idea is to make the final bill as small as it can be by summing the fees for all chosen matches. Rules of the dinner: every document gets one seat, every translator gets one seat, and every language pair is used only once. The exact list of documents, translators, language pairs, and their costs follows below.

{
  ""num_documents"": 6,
  ""index_identifiers"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F""
  ]
}

# Meaning: costs form a 3D tensor. For each fixed document_id=i, you are given a translator_id×language_pair_id matrix whose entry at row translator_id=j and column language_pair_id=k equals translation_fee(i,j,k). You must pick exactly one (j,k) for every i, with all translator_id and all language_pair_id used exactly once.
# translation_fee_tensor (per-document_id markdown matrices)

## document_id=A
| translator_id\language_pair_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 4 | 30 | 87 | 93 | 8 | 64 |
| B | 46 | 31 | 40 | 50 | 16 | 53 |
| C | 59 | 28 | 3 | 48 | 93 | 70 |
| D | 92 | 64 | 33 | 18 | 17 | 24 |
| E | 97 | 80 | 40 | 70 | 7 | 34 |
| F | 71 | 4 | 31 | 43 | 65 | 51 |

## document_id=B
| translator_id\language_pair_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 85 | 33 | 60 | 25 | 96 | 70 |
| B | 82 | 16 | 23 | 2 | 99 | 8 |
| C | 75 | 2 | 2 | 44 | 10 | 12 |
| D | 78 | 69 | 10 | 79 | 68 | 90 |
| E | 97 | 20 | 60 | 61 | 19 | 4 |
| F | 5 | 36 | 95 | 29 | 12 | 10 |

## document_id=C
| translator_id\language_pair_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 83 | 15 | 72 | 60 | 76 | 77 |
| B | 96 | 29 | 43 | 18 | 68 | 74 |
| C | 56 | 68 | 54 | 37 | 53 | 84 |
| D | 45 | 56 | 40 | 44 | 22 | 88 |
| E | 96 | 43 | 6 | 15 | 79 | 86 |
| F | 98 | 36 | 67 | 34 | 38 | 75 |

## document_id=D
| translator_id\language_pair_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 2 | 46 | 92 | 31 | 68 | 12 |
| B | 87 | 56 | 85 | 0 | 2 | 74 |
| C | 90 | 10 | 39 | 33 | 9 | 90 |
| D | 87 | 53 | 55 | 66 | 10 | 64 |
| E | 39 | 65 | 79 | 32 | 70 | 5 |
| F | 56 | 10 | 27 | 90 | 24 | 84 |

## document_id=E
| translator_id\language_pair_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 74 | 56 | 16 | 60 | 52 | 63 |
| B | 59 | 51 | 35 | 55 | 85 | 60 |
| C | 24 | 38 | 20 | 44 | 30 | 15 |
| D | 20 | 23 | 43 | 0 | 49 | 4 |
| E | 82 | 38 | 8 | 99 | 62 | 91 |
| F | 48 | 20 | 26 | 71 | 37 | 35 |

## document_id=F
| translator_id\language_pair_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 45 | 67 | 52 | 9 | 76 | 23 |
| B | 94 | 2 | 91 | 14 | 79 | 15 |
| C | 86 | 81 | 38 | 92 | 97 | 34 |
| D | 32 | 2 | 40 | 8 | 72 | 91 |
| E | 39 | 97 | 61 | 65 | 35 | 20 |
| F | 4 | 89 | 58 | 83 | 32 | 52 |

I'll keep the final answer in a simple JSON shape so it's easy to check automatically. Here’s the sketch of how I want the solution formatted:

{
  ""solution"": [
    [<doc_id>, <translator_id>, <langpair_id>],
    ...
  ]
}

This says ""solution"" is a list of triples. Each triple is one document matched with one translator and one language pair (in that order). It's just a quick form — the JSON above is the expected shape, not the actual assignment itself.

Please make sure to 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”.""","{'cost_tensor': [[[4, 30, 87, 93, 8, 64], [46, 31, 40, 50, 16, 53], [59, 28, 3, 48, 93, 70], [92, 64, 33, 18, 17, 24], [97, 80, 40, 70, 7, 34], [71, 4, 31, 43, 65, 51]], [[85, 33, 60, 25, 96, 70], [82, 16, 23, 2, 99, 8], [75, 2, 2, 44, 10, 12], [78, 69, 10, 79, 68, 90], [97, 20, 60, 61, 19, 4], [5, 36, 95, 29, 12, 10]], [[83, 15, 72, 60, 76, 77], [96, 29, 43, 18, 68, 74], [56, 68, 54, 37, 53, 84], [45, 56, 40, 44, 22, 88], [96, 43, 6, 15, 79, 86], [98, 36, 67, 34, 38, 75]], [[2, 46, 92, 31, 68, 12], [87, 56, 85, 0, 2, 74], [90, 10, 39, 33, 9, 90], [87, 53, 55, 66, 10, 64], [39, 65, 79, 32, 70, 5], [56, 10, 27, 90, 24, 84]], [[74, 56, 16, 60, 52, 63], [59, 51, 35, 55, 85, 60], [24, 38, 20, 44, 30, 15], [20, 23, 43, 0, 49, 4], [82, 38, 8, 99, 62, 91], [48, 20, 26, 71, 37, 35]], [[45, 67, 52, 9, 76, 23], [94, 2, 91, 14, 79, 15], [86, 81, 38, 92, 97, 34], [32, 2, 40, 8, 72, 91], [39, 97, 61, 65, 35, 20], [4, 89, 58, 83, 32, 52]]], 'objective': 24.0}","[[0, 0, 4], [1, 2, 1], [2, 4, 2], [3, 1, 3], [4, 3, 5], [5, 5, 0]]",24.0,"{'problem_type': 'AP3', 'n': 6, 'ids': ['A', 'B', 'C', 'D', 'E', 'F'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 4}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 30}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 87}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 93}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 8}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 64}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 46}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 31}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 40}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 50}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 16}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 53}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 59}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 28}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 3}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 48}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 93}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 70}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 92}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 64}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 33}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 18}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 17}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 24}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 97}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 80}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 40}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 70}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 7}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 34}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 71}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 4}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 31}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 43}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 65}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 51}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 85}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 33}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 60}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 25}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 96}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 70}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 82}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 16}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 23}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 2}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 99}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 8}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 75}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 2}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 2}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 44}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 10}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 12}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 78}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 69}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 10}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 79}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 68}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 90}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 97}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 20}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 60}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 61}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 19}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 4}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 5}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 36}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 95}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 29}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 12}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 10}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 83}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 15}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 72}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 60}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 76}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 77}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 96}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 29}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 43}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 18}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 68}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 74}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 56}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 68}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 54}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 37}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 53}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 84}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 45}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 56}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 40}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 44}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 22}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 88}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 96}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 43}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 6}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 15}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 79}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 86}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 98}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 36}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 67}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 34}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 38}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 75}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 2}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 46}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 92}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 31}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 68}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 12}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 87}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 56}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 85}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 0}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 2}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 74}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 90}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 10}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 39}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 33}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 9}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 90}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 87}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 53}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 55}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 66}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 10}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 64}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 39}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 65}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 79}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 32}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 70}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 5}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 56}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 10}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 27}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 90}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 24}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 84}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 74}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 56}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 16}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 60}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 52}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 63}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 59}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 51}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 35}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 55}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 85}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 60}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 24}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 38}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 20}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 44}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 30}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 15}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 20}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 23}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 43}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 0}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 49}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 4}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 82}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 38}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 8}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 99}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 62}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 91}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 48}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 20}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 26}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 71}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 37}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 35}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 45}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 67}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 52}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 9}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 76}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 23}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 94}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 2}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 91}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 14}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 79}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 15}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 86}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 81}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 38}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 92}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 97}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 34}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 32}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 2}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 40}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 8}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 72}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 91}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 39}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 97}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 61}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 65}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 35}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 20}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 4}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 89}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 58}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 83}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 32}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 52}]}","[['A', 'A', 'E'], ['B', 'C', 'B'], ['C', 'E', 'C'], ['D', 'B', 'D'], ['E', 'D', 'F'], ['F', 'F', 'A']]",10,json,names
AP3,AP3,"There’s a morning rush at a print shop: a stack of customer jobs, a row of printers, and a row of finishing stations. The trick is to pair each job with one printer and one finishing station, making sure every printer is used by exactly one job and every finisher by exactly one job — nothing gets assigned twice or left out. One plan is better than another if it gets all the work done sooner; you can tell by adding each job’s printing time and its finishing time and summing those up for the whole batch, then choosing the assignment with the lowest total. The specific job times and machine options appear below.

# num_orders=8
# index_identifiers=A, B, C, D, E, F, G, H

# Meaning: costs form a 3D tensor. For each fixed order_id=i, you are given a printer_id×finisher_id matrix whose entry at row printer_id=j and column finisher_id=k equals total_processing_time(i,j,k). You must pick exactly one (j,k) for every i, with all printer_id and all finisher_id used exactly once.
# total_processing_time_tensor (per-order_id markdown matrices)

## order_id=A
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 51 | 38 | 3 | 21 | 58 | 30 | 47 | 69 |
| B | 42 | 71 | 26 | 54 | 26 | 50 | 3 | 74 |
| C | 82 | 28 | 47 | 22 | 8 | 83 | 73 | 20 |
| D | 91 | 33 | 43 | 26 | 24 | 90 | 95 | 63 |
| E | 80 | 84 | 74 | 85 | 2 | 93 | 81 | 61 |
| F | 48 | 17 | 46 | 46 | 21 | 97 | 35 | 19 |
| G | 26 | 83 | 92 | 57 | 12 | 72 | 18 | 40 |
| H | 61 | 91 | 92 | 88 | 46 | 89 | 14 | 22 |

## order_id=B
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 57 | 32 | 0 | 0 | 66 | 74 | 48 | 23 |
| B | 56 | 65 | 83 | 48 | 56 | 29 | 67 | 21 |
| C | 67 | 25 | 31 | 64 | 50 | 74 | 25 | 13 |
| D | 37 | 87 | 95 | 41 | 3 | 65 | 65 | 77 |
| E | 55 | 32 | 61 | 85 | 59 | 65 | 65 | 24 |
| F | 72 | 98 | 62 | 69 | 56 | 9 | 84 | 58 |
| G | 12 | 93 | 47 | 60 | 8 | 45 | 27 | 30 |
| H | 87 | 85 | 74 | 28 | 9 | 39 | 45 | 61 |

## order_id=C
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 98 | 65 | 92 | 14 | 27 | 10 | 62 | 71 |
| B | 39 | 10 | 21 | 20 | 5 | 82 | 80 | 10 |
| C | 49 | 19 | 44 | 45 | 40 | 22 | 0 | 3 |
| D | 85 | 50 | 28 | 79 | 74 | 65 | 47 | 80 |
| E | 1 | 42 | 66 | 65 | 46 | 71 | 41 | 90 |
| F | 97 | 26 | 79 | 32 | 85 | 8 | 17 | 81 |
| G | 93 | 87 | 39 | 61 | 31 | 61 | 63 | 54 |
| H | 99 | 98 | 29 | 32 | 96 | 36 | 48 | 17 |

## order_id=D
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 71 | 32 | 6 | 86 | 77 | 47 | 95 | 74 |
| B | 4 | 88 | 6 | 73 | 69 | 28 | 58 | 63 |
| C | 51 | 39 | 6 | 83 | 57 | 40 | 77 | 61 |
| D | 28 | 57 | 31 | 10 | 12 | 16 | 14 | 98 |
| E | 4 | 53 | 30 | 55 | 6 | 52 | 23 | 57 |
| F | 89 | 7 | 75 | 22 | 62 | 93 | 53 | 2 |
| G | 90 | 57 | 6 | 28 | 29 | 69 | 92 | 38 |
| H | 66 | 62 | 81 | 48 | 12 | 97 | 62 | 70 |

## order_id=E
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 39 | 68 | 0 | 47 | 58 | 68 | 61 | 50 |
| B | 86 | 8 | 21 | 98 | 59 | 45 | 81 | 73 |
| C | 43 | 22 | 95 | 8 | 84 | 26 | 52 | 38 |
| D | 37 | 3 | 96 | 81 | 44 | 15 | 69 | 81 |
| E | 37 | 31 | 9 | 71 | 22 | 97 | 34 | 30 |
| F | 6 | 76 | 13 | 47 | 96 | 2 | 79 | 36 |
| G | 50 | 52 | 51 | 23 | 66 | 70 | 89 | 86 |
| H | 81 | 46 | 1 | 48 | 52 | 62 | 31 | 14 |

## order_id=F
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 1 | 2 | 54 | 67 | 18 | 46 | 27 | 46 |
| B | 6 | 51 | 52 | 43 | 55 | 91 | 39 | 35 |
| C | 21 | 59 | 84 | 59 | 59 | 94 | 90 | 34 |
| D | 30 | 52 | 77 | 1 | 13 | 23 | 3 | 47 |
| E | 87 | 78 | 71 | 94 | 12 | 2 | 37 | 48 |
| F | 33 | 47 | 7 | 71 | 41 | 1 | 15 | 42 |
| G | 4 | 16 | 68 | 18 | 78 | 49 | 60 | 48 |
| H | 84 | 96 | 94 | 25 | 50 | 25 | 24 | 96 |

## order_id=G
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 12 | 36 | 61 | 0 | 94 | 31 | 59 | 68 |
| B | 25 | 33 | 61 | 1 | 89 | 15 | 12 | 78 |
| C | 39 | 53 | 2 | 78 | 50 | 18 | 62 | 23 |
| D | 81 | 23 | 31 | 7 | 91 | 51 | 26 | 1 |
| E | 67 | 54 | 80 | 1 | 25 | 13 | 63 | 81 |
| F | 55 | 33 | 14 | 81 | 93 | 16 | 34 | 32 |
| G | 1 | 39 | 54 | 88 | 97 | 14 | 15 | 49 |
| H | 16 | 5 | 44 | 17 | 49 | 69 | 38 | 90 |

## order_id=H
| printer_id\finisher_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 46 | 17 | 32 | 96 | 52 | 46 | 85 | 92 |
| B | 57 | 33 | 78 | 33 | 35 | 38 | 45 | 91 |
| C | 19 | 54 | 93 | 53 | 8 | 16 | 42 | 38 |
| D | 82 | 78 | 61 | 14 | 15 | 63 | 27 | 79 |
| E | 72 | 50 | 54 | 0 | 93 | 71 | 52 | 21 |
| F | 54 | 6 | 19 | 38 | 9 | 7 | 7 | 63 |
| G | 30 | 52 | 32 | 89 | 89 | 22 | 19 | 67 |
| H | 39 | 61 | 20 | 20 | 81 | 48 | 26 | 15 |

If you want to send me the final pairing in a neat, machine-friendly way, just use a small JSON snippet like this — nothing fancy, just a list of the chosen triples.

{
  ""solution"": [
    [<i_id>, <j_id>, <k_id>],
    ...
  ]
}

This shows the shape I expect: ""solution"" holds an array of triples, and each triple is one job matched to one printer and one finisher. Think of each inner list as ""job i goes to printer j and finisher k"" — super simple, like filling out a form.

This JSON is just a sketch of the shape I need, not the actual answer. Please be sure to use the identifiers exactly as they appear in 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”.""","{'cost_tensor': [[[51, 38, 3, 21, 58, 30, 47, 69], [42, 71, 26, 54, 26, 50, 3, 74], [82, 28, 47, 22, 8, 83, 73, 20], [91, 33, 43, 26, 24, 90, 95, 63], [80, 84, 74, 85, 2, 93, 81, 61], [48, 17, 46, 46, 21, 97, 35, 19], [26, 83, 92, 57, 12, 72, 18, 40], [61, 91, 92, 88, 46, 89, 14, 22]], [[57, 32, 0, 0, 66, 74, 48, 23], [56, 65, 83, 48, 56, 29, 67, 21], [67, 25, 31, 64, 50, 74, 25, 13], [37, 87, 95, 41, 3, 65, 65, 77], [55, 32, 61, 85, 59, 65, 65, 24], [72, 98, 62, 69, 56, 9, 84, 58], [12, 93, 47, 60, 8, 45, 27, 30], [87, 85, 74, 28, 9, 39, 45, 61]], [[98, 65, 92, 14, 27, 10, 62, 71], [39, 10, 21, 20, 5, 82, 80, 10], [49, 19, 44, 45, 40, 22, 0, 3], [85, 50, 28, 79, 74, 65, 47, 80], [1, 42, 66, 65, 46, 71, 41, 90], [97, 26, 79, 32, 85, 8, 17, 81], [93, 87, 39, 61, 31, 61, 63, 54], [99, 98, 29, 32, 96, 36, 48, 17]], [[71, 32, 6, 86, 77, 47, 95, 74], [4, 88, 6, 73, 69, 28, 58, 63], [51, 39, 6, 83, 57, 40, 77, 61], [28, 57, 31, 10, 12, 16, 14, 98], [4, 53, 30, 55, 6, 52, 23, 57], [89, 7, 75, 22, 62, 93, 53, 2], [90, 57, 6, 28, 29, 69, 92, 38], [66, 62, 81, 48, 12, 97, 62, 70]], [[39, 68, 0, 47, 58, 68, 61, 50], [86, 8, 21, 98, 59, 45, 81, 73], [43, 22, 95, 8, 84, 26, 52, 38], [37, 3, 96, 81, 44, 15, 69, 81], [37, 31, 9, 71, 22, 97, 34, 30], [6, 76, 13, 47, 96, 2, 79, 36], [50, 52, 51, 23, 66, 70, 89, 86], [81, 46, 1, 48, 52, 62, 31, 14]], [[1, 2, 54, 67, 18, 46, 27, 46], [6, 51, 52, 43, 55, 91, 39, 35], [21, 59, 84, 59, 59, 94, 90, 34], [30, 52, 77, 1, 13, 23, 3, 47], [87, 78, 71, 94, 12, 2, 37, 48], [33, 47, 7, 71, 41, 1, 15, 42], [4, 16, 68, 18, 78, 49, 60, 48], [84, 96, 94, 25, 50, 25, 24, 96]], [[12, 36, 61, 0, 94, 31, 59, 68], [25, 33, 61, 1, 89, 15, 12, 78], [39, 53, 2, 78, 50, 18, 62, 23], [81, 23, 31, 7, 91, 51, 26, 1], [67, 54, 80, 1, 25, 13, 63, 81], [55, 33, 14, 81, 93, 16, 34, 32], [1, 39, 54, 88, 97, 14, 15, 49], [16, 5, 44, 17, 49, 69, 38, 90]], [[46, 17, 32, 96, 52, 46, 85, 92], [57, 33, 78, 33, 35, 38, 45, 91], [19, 54, 93, 53, 8, 16, 42, 38], [82, 78, 61, 14, 15, 63, 27, 79], [72, 50, 54, 0, 93, 71, 52, 21], [54, 6, 19, 38, 9, 7, 7, 63], [30, 52, 32, 89, 89, 22, 19, 67], [39, 61, 20, 20, 81, 48, 26, 15]]], 'objective': 23.0}","[[0, 1, 6], [1, 0, 2], [2, 2, 7], [3, 7, 4], [4, 3, 1], [5, 5, 5], [6, 6, 0], [7, 4, 3]]",23.0,"{'problem_type': 'AP3', 'n': 8, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 51}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 38}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 3}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 21}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 58}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 30}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 47}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 69}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 42}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 71}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 26}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 54}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 26}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 50}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 3}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 74}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 82}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 28}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 47}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 22}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 8}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 83}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 73}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 20}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 91}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 33}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 43}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 26}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 24}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 90}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 95}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 63}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 80}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 84}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 74}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 85}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 2}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 93}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 81}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 61}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 48}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 17}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 46}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 46}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 21}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 97}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 35}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 19}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 26}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 83}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 92}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 57}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 12}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 72}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 18}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 40}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 61}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 91}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 92}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 88}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 46}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 89}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 14}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 22}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 57}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 32}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 0}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 0}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 66}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 74}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 48}, {'i': 'B', 'j': 'A', 'k': 'H', 'cost': 23}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 56}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 65}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 83}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 48}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 56}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 29}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 67}, {'i': 'B', 'j': 'B', 'k': 'H', 'cost': 21}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 67}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 25}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 31}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 64}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 50}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 74}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 25}, {'i': 'B', 'j': 'C', 'k': 'H', 'cost': 13}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 37}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 87}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 95}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 41}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 3}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 65}, {'i': 'B', 'j': 'D', 'k': 'G', 'cost': 65}, {'i': 'B', 'j': 'D', 'k': 'H', 'cost': 77}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 55}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 32}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 61}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 85}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 59}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 65}, {'i': 'B', 'j': 'E', 'k': 'G', 'cost': 65}, {'i': 'B', 'j': 'E', 'k': 'H', 'cost': 24}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 72}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 98}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 62}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 69}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 56}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 9}, {'i': 'B', 'j': 'F', 'k': 'G', 'cost': 84}, {'i': 'B', 'j': 'F', 'k': 'H', 'cost': 58}, {'i': 'B', 'j': 'G', 'k': 'A', 'cost': 12}, {'i': 'B', 'j': 'G', 'k': 'B', 'cost': 93}, {'i': 'B', 'j': 'G', 'k': 'C', 'cost': 47}, {'i': 'B', 'j': 'G', 'k': 'D', 'cost': 60}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 8}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 45}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 27}, {'i': 'B', 'j': 'G', 'k': 'H', 'cost': 30}, {'i': 'B', 'j': 'H', 'k': 'A', 'cost': 87}, {'i': 'B', 'j': 'H', 'k': 'B', 'cost': 85}, {'i': 'B', 'j': 'H', 'k': 'C', 'cost': 74}, {'i': 'B', 'j': 'H', 'k': 'D', 'cost': 28}, {'i': 'B', 'j': 'H', 'k': 'E', 'cost': 9}, {'i': 'B', 'j': 'H', 'k': 'F', 'cost': 39}, {'i': 'B', 'j': 'H', 'k': 'G', 'cost': 45}, {'i': 'B', 'j': 'H', 'k': 'H', 'cost': 61}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 98}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 65}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 92}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 14}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 27}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 10}, {'i': 'C', 'j': 'A', 'k': 'G', 'cost': 62}, {'i': 'C', 'j': 'A', 'k': 'H', 'cost': 71}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 39}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 10}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 21}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 20}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 5}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 82}, {'i': 'C', 'j': 'B', 'k': 'G', 'cost': 80}, {'i': 'C', 'j': 'B', 'k': 'H', 'cost': 10}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 49}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 19}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 44}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 45}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 40}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 22}, {'i': 'C', 'j': 'C', 'k': 'G', 'cost': 0}, {'i': 'C', 'j': 'C', 'k': 'H', 'cost': 3}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 85}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 50}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 28}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 79}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 74}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 65}, {'i': 'C', 'j': 'D', 'k': 'G', 'cost': 47}, {'i': 'C', 'j': 'D', 'k': 'H', 'cost': 80}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 1}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 42}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 66}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 65}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 46}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 71}, {'i': 'C', 'j': 'E', 'k': 'G', 'cost': 41}, {'i': 'C', 'j': 'E', 'k': 'H', 'cost': 90}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 97}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 26}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 79}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 32}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 85}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 8}, {'i': 'C', 'j': 'F', 'k': 'G', 'cost': 17}, {'i': 'C', 'j': 'F', 'k': 'H', 'cost': 81}, {'i': 'C', 'j': 'G', 'k': 'A', 'cost': 93}, {'i': 'C', 'j': 'G', 'k': 'B', 'cost': 87}, {'i': 'C', 'j': 'G', 'k': 'C', 'cost': 39}, {'i': 'C', 'j': 'G', 'k': 'D', 'cost': 61}, {'i': 'C', 'j': 'G', 'k': 'E', 'cost': 31}, {'i': 'C', 'j': 'G', 'k': 'F', 'cost': 61}, {'i': 'C', 'j': 'G', 'k': 'G', 'cost': 63}, {'i': 'C', 'j': 'G', 'k': 'H', 'cost': 54}, {'i': 'C', 'j': 'H', 'k': 'A', 'cost': 99}, {'i': 'C', 'j': 'H', 'k': 'B', 'cost': 98}, {'i': 'C', 'j': 'H', 'k': 'C', 'cost': 29}, {'i': 'C', 'j': 'H', 'k': 'D', 'cost': 32}, {'i': 'C', 'j': 'H', 'k': 'E', 'cost': 96}, {'i': 'C', 'j': 'H', 'k': 'F', 'cost': 36}, {'i': 'C', 'j': 'H', 'k': 'G', 'cost': 48}, {'i': 'C', 'j': 'H', 'k': 'H', 'cost': 17}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 71}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 32}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 6}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 86}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 77}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 47}, {'i': 'D', 'j': 'A', 'k': 'G', 'cost': 95}, {'i': 'D', 'j': 'A', 'k': 'H', 'cost': 74}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 4}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 88}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 6}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 73}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 69}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 28}, {'i': 'D', 'j': 'B', 'k': 'G', 'cost': 58}, {'i': 'D', 'j': 'B', 'k': 'H', 'cost': 63}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 51}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 39}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 6}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 83}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 57}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 40}, {'i': 'D', 'j': 'C', 'k': 'G', 'cost': 77}, {'i': 'D', 'j': 'C', 'k': 'H', 'cost': 61}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 28}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 57}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 31}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 10}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 12}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 16}, {'i': 'D', 'j': 'D', 'k': 'G', 'cost': 14}, {'i': 'D', 'j': 'D', 'k': 'H', 'cost': 98}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 4}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 53}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 30}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 55}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 6}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 52}, {'i': 'D', 'j': 'E', 'k': 'G', 'cost': 23}, {'i': 'D', 'j': 'E', 'k': 'H', 'cost': 57}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 89}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 7}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 75}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 22}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 62}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 93}, {'i': 'D', 'j': 'F', 'k': 'G', 'cost': 53}, {'i': 'D', 'j': 'F', 'k': 'H', 'cost': 2}, {'i': 'D', 'j': 'G', 'k': 'A', 'cost': 90}, {'i': 'D', 'j': 'G', 'k': 'B', 'cost': 57}, {'i': 'D', 'j': 'G', 'k': 'C', 'cost': 6}, {'i': 'D', 'j': 'G', 'k': 'D', 'cost': 28}, {'i': 'D', 'j': 'G', 'k': 'E', 'cost': 29}, {'i': 'D', 'j': 'G', 'k': 'F', 'cost': 69}, {'i': 'D', 'j': 'G', 'k': 'G', 'cost': 92}, {'i': 'D', 'j': 'G', 'k': 'H', 'cost': 38}, {'i': 'D', 'j': 'H', 'k': 'A', 'cost': 66}, {'i': 'D', 'j': 'H', 'k': 'B', 'cost': 62}, {'i': 'D', 'j': 'H', 'k': 'C', 'cost': 81}, {'i': 'D', 'j': 'H', 'k': 'D', 'cost': 48}, {'i': 'D', 'j': 'H', 'k': 'E', 'cost': 12}, {'i': 'D', 'j': 'H', 'k': 'F', 'cost': 97}, {'i': 'D', 'j': 'H', 'k': 'G', 'cost': 62}, {'i': 'D', 'j': 'H', 'k': 'H', 'cost': 70}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 39}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 68}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 0}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 47}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 58}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 68}, {'i': 'E', 'j': 'A', 'k': 'G', 'cost': 61}, {'i': 'E', 'j': 'A', 'k': 'H', 'cost': 50}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 86}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 8}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 21}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 98}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 59}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 45}, {'i': 'E', 'j': 'B', 'k': 'G', 'cost': 81}, {'i': 'E', 'j': 'B', 'k': 'H', 'cost': 73}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 43}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 22}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 95}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 8}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 84}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 26}, {'i': 'E', 'j': 'C', 'k': 'G', 'cost': 52}, {'i': 'E', 'j': 'C', 'k': 'H', 'cost': 38}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 37}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 3}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 96}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 81}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 44}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 15}, {'i': 'E', 'j': 'D', 'k': 'G', 'cost': 69}, {'i': 'E', 'j': 'D', 'k': 'H', 'cost': 81}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 37}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 31}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 9}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 71}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 22}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 97}, {'i': 'E', 'j': 'E', 'k': 'G', 'cost': 34}, {'i': 'E', 'j': 'E', 'k': 'H', 'cost': 30}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 6}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 76}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 13}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 47}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 96}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 2}, {'i': 'E', 'j': 'F', 'k': 'G', 'cost': 79}, {'i': 'E', 'j': 'F', 'k': 'H', 'cost': 36}, {'i': 'E', 'j': 'G', 'k': 'A', 'cost': 50}, {'i': 'E', 'j': 'G', 'k': 'B', 'cost': 52}, {'i': 'E', 'j': 'G', 'k': 'C', 'cost': 51}, {'i': 'E', 'j': 'G', 'k': 'D', 'cost': 23}, {'i': 'E', 'j': 'G', 'k': 'E', 'cost': 66}, {'i': 'E', 'j': 'G', 'k': 'F', 'cost': 70}, {'i': 'E', 'j': 'G', 'k': 'G', 'cost': 89}, {'i': 'E', 'j': 'G', 'k': 'H', 'cost': 86}, {'i': 'E', 'j': 'H', 'k': 'A', 'cost': 81}, {'i': 'E', 'j': 'H', 'k': 'B', 'cost': 46}, {'i': 'E', 'j': 'H', 'k': 'C', 'cost': 1}, {'i': 'E', 'j': 'H', 'k': 'D', 'cost': 48}, {'i': 'E', 'j': 'H', 'k': 'E', 'cost': 52}, {'i': 'E', 'j': 'H', 'k': 'F', 'cost': 62}, {'i': 'E', 'j': 'H', 'k': 'G', 'cost': 31}, {'i': 'E', 'j': 'H', 'k': 'H', 'cost': 14}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 1}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 2}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 54}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 67}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 18}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 46}, {'i': 'F', 'j': 'A', 'k': 'G', 'cost': 27}, {'i': 'F', 'j': 'A', 'k': 'H', 'cost': 46}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 6}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 51}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 52}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 43}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 55}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 91}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 39}, {'i': 'F', 'j': 'B', 'k': 'H', 'cost': 35}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 21}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 59}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 84}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 59}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 59}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 94}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 90}, {'i': 'F', 'j': 'C', 'k': 'H', 'cost': 34}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 30}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 52}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 77}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 1}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 13}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 23}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 3}, {'i': 'F', 'j': 'D', 'k': 'H', 'cost': 47}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 87}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 78}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 71}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 94}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 12}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 2}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 37}, {'i': 'F', 'j': 'E', 'k': 'H', 'cost': 48}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 33}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 47}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 7}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 71}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 41}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 1}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 15}, {'i': 'F', 'j': 'F', 'k': 'H', 'cost': 42}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 4}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 16}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 68}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 18}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 78}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 49}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 60}, {'i': 'F', 'j': 'G', 'k': 'H', 'cost': 48}, {'i': 'F', 'j': 'H', 'k': 'A', 'cost': 84}, {'i': 'F', 'j': 'H', 'k': 'B', 'cost': 96}, {'i': 'F', 'j': 'H', 'k': 'C', 'cost': 94}, {'i': 'F', 'j': 'H', 'k': 'D', 'cost': 25}, {'i': 'F', 'j': 'H', 'k': 'E', 'cost': 50}, {'i': 'F', 'j': 'H', 'k': 'F', 'cost': 25}, {'i': 'F', 'j': 'H', 'k': 'G', 'cost': 24}, {'i': 'F', 'j': 'H', 'k': 'H', 'cost': 96}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 12}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 36}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 61}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 0}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 94}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 31}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 59}, {'i': 'G', 'j': 'A', 'k': 'H', 'cost': 68}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 25}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 33}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 61}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 1}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 89}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 15}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 12}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 78}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 39}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 53}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 2}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 78}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 50}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 18}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 62}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 23}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 81}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 23}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 31}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 7}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 91}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 51}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 26}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 1}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 67}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 54}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 80}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 1}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 25}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 13}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 63}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 81}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 55}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 33}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 14}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 81}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 93}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 16}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 34}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 32}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 1}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 39}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 54}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 88}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 97}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 14}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 15}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 49}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 16}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 5}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 44}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 17}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 49}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 69}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 38}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 90}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 46}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 17}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 32}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 96}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 52}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 46}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 85}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 92}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 57}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 33}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 78}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 33}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 35}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 38}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 45}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 91}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 19}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 54}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 93}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 53}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 8}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 16}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 42}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 38}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 82}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 78}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 61}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 14}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 15}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 63}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 27}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 79}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 72}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 50}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 54}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 0}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 93}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 71}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 52}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 21}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 54}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 6}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 19}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 38}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 9}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 7}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 7}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 63}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 30}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 52}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 32}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 89}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 89}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 22}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 19}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 67}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 39}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 61}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 20}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 20}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 81}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 48}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 26}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 15}]}","[['A', 'B', 'G'], ['B', 'A', 'C'], ['C', 'C', 'H'], ['D', 'H', 'E'], ['E', 'D', 'B'], ['F', 'F', 'F'], ['G', 'G', 'A'], ['H', 'E', 'D']]",11,csv,names
AP3,AP3,"Someone in charge of the quarterly push needed to assign each campaign to exactly one outlet and one calendar week, making sure each outlet runs one campaign and each week gets one campaign — nothing gets repeated or skipped. Each campaign+outlet+week combo has a price, so the sensible plan was to choose the arrangement that makes the total spend as low as possible by adding up the costs of all the chosen combos. The full breakdown of campaigns, channels, weeks and costs appears below.

{
  ""num_campaigns"": 8,
  ""campaign_ids"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8
  ]
}

# Meaning: costs form a 3D tensor. For each fixed campaign_id=i, you are given a channel_id×week_id matrix whose entry at row channel_id=j and column week_id=k equals combo_cost(i,j,k). You must pick exactly one (j,k) for every i, with all channel_id and all week_id used exactly once.
# combo_cost_tensor (per-campaign_id markdown matrices)

## campaign_id=1
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 7 | 4 | 63 | 28 | 45 | 54 | 32 | 49 |
| 2 | 34 | 72 | 58 | 0 | 1 | 88 | 70 | 12 |
| 3 | 41 | 2 | 37 | 68 | 0 | 52 | 73 | 22 |
| 4 | 43 | 46 | 88 | 68 | 6 | 27 | 44 | 1 |
| 5 | 88 | 54 | 96 | 86 | 26 | 91 | 75 | 24 |
| 6 | 84 | 63 | 77 | 4 | 99 | 73 | 75 | 61 |
| 7 | 16 | 89 | 50 | 51 | 50 | 17 | 29 | 79 |
| 8 | 58 | 21 | 20 | 24 | 90 | 91 | 10 | 18 |

## campaign_id=2
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 43 | 27 | 14 | 10 | 70 | 97 | 6 | 4 |
| 2 | 94 | 22 | 82 | 16 | 43 | 39 | 3 | 21 |
| 3 | 84 | 97 | 88 | 21 | 99 | 36 | 20 | 72 |
| 4 | 82 | 91 | 26 | 91 | 61 | 93 | 81 | 2 |
| 5 | 90 | 52 | 81 | 6 | 98 | 80 | 57 | 86 |
| 6 | 29 | 50 | 12 | 64 | 62 | 27 | 56 | 69 |
| 7 | 45 | 67 | 21 | 86 | 60 | 52 | 17 | 26 |
| 8 | 21 | 28 | 83 | 51 | 3 | 15 | 10 | 20 |

## campaign_id=3
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 7 | 25 | 6 | 39 | 15 | 8 | 66 | 86 |
| 2 | 41 | 86 | 3 | 37 | 40 | 63 | 2 | 29 |
| 3 | 66 | 7 | 93 | 45 | 13 | 73 | 58 | 83 |
| 4 | 9 | 47 | 89 | 44 | 13 | 34 | 14 | 9 |
| 5 | 13 | 26 | 95 | 28 | 38 | 66 | 28 | 9 |
| 6 | 91 | 76 | 75 | 55 | 47 | 6 | 45 | 7 |
| 7 | 68 | 81 | 51 | 81 | 98 | 89 | 73 | 88 |
| 8 | 70 | 72 | 72 | 11 | 38 | 59 | 17 | 14 |

## campaign_id=4
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 64 | 89 | 92 | 89 | 15 | 74 | 47 | 58 |
| 2 | 9 | 65 | 37 | 1 | 38 | 27 | 62 | 66 |
| 3 | 17 | 55 | 62 | 4 | 50 | 35 | 79 | 24 |
| 4 | 78 | 36 | 76 | 72 | 79 | 47 | 17 | 26 |
| 5 | 14 | 92 | 35 | 51 | 60 | 40 | 97 | 81 |
| 6 | 54 | 36 | 50 | 58 | 56 | 72 | 43 | 60 |
| 7 | 80 | 96 | 32 | 29 | 16 | 83 | 52 | 12 |
| 8 | 36 | 64 | 35 | 46 | 69 | 64 | 45 | 25 |

## campaign_id=5
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 69 | 2 | 7 | 48 | 42 | 37 | 54 | 87 |
| 2 | 12 | 84 | 9 | 62 | 93 | 27 | 83 | 72 |
| 3 | 1 | 72 | 23 | 13 | 72 | 28 | 6 | 5 |
| 4 | 51 | 27 | 77 | 54 | 73 | 85 | 82 | 50 |
| 5 | 15 | 80 | 68 | 48 | 61 | 52 | 23 | 14 |
| 6 | 14 | 35 | 0 | 85 | 97 | 78 | 31 | 60 |
| 7 | 11 | 66 | 73 | 92 | 30 | 93 | 3 | 63 |
| 8 | 31 | 12 | 65 | 59 | 22 | 81 | 25 | 8 |

## campaign_id=6
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 24 | 79 | 86 | 82 | 87 | 60 | 39 | 84 |
| 2 | 43 | 82 | 36 | 61 | 96 | 47 | 45 | 71 |
| 3 | 7 | 37 | 51 | 72 | 76 | 30 | 44 | 55 |
| 4 | 24 | 15 | 9 | 88 | 91 | 32 | 55 | 27 |
| 5 | 83 | 94 | 47 | 62 | 74 | 16 | 51 | 99 |
| 6 | 15 | 60 | 46 | 36 | 72 | 31 | 2 | 55 |
| 7 | 43 | 46 | 37 | 93 | 73 | 64 | 27 | 2 |
| 8 | 39 | 61 | 90 | 0 | 18 | 60 | 57 | 26 |

## campaign_id=7
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 70 | 62 | 90 | 26 | 3 | 82 | 63 | 47 |
| 2 | 0 | 31 | 73 | 78 | 20 | 43 | 68 | 5 |
| 3 | 48 | 50 | 45 | 7 | 93 | 42 | 35 | 23 |
| 4 | 24 | 0 | 51 | 65 | 52 | 21 | 47 | 12 |
| 5 | 19 | 26 | 6 | 21 | 88 | 14 | 53 | 75 |
| 6 | 86 | 42 | 11 | 94 | 57 | 44 | 13 | 75 |
| 7 | 21 | 3 | 23 | 75 | 18 | 34 | 36 | 32 |
| 8 | 68 | 11 | 28 | 29 | 16 | 15 | 23 | 56 |

## campaign_id=8
| channel_id\week_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 84 | 14 | 64 | 71 | 49 | 41 | 20 | 30 |
| 2 | 50 | 83 | 1 | 42 | 63 | 38 | 86 | 14 |
| 3 | 32 | 56 | 53 | 66 | 39 | 31 | 82 | 42 |
| 4 | 22 | 93 | 64 | 42 | 83 | 81 | 73 | 1 |
| 5 | 44 | 34 | 56 | 35 | 82 | 26 | 94 | 88 |
| 6 | 27 | 70 | 61 | 78 | 37 | 80 | 87 | 98 |
| 7 | 26 | 58 | 54 | 61 | 57 | 46 | 8 | 61 |
| 8 | 80 | 18 | 61 | 74 | 15 | 67 | 55 | 37 |

If you want the final plan in a simple, machine-friendly shape, just follow this JSON layout for the reply (keeps everything predictable and easy to check):

{
  ""solution"": [
    [<campaign_id>, <outlet_id>, <week_id>],
    ...
  ]
}

Each inner triple is one chosen combo: the campaign, the outlet assigned to it, and the calendar week it will run in — basically [campaign, outlet, week]. This is just a sketch of the expected shape, not the actual assignment.

Please 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”
- a capital letter followed by digits like “A1” or “X7”","{'cost_tensor': [[[7, 4, 63, 28, 45, 54, 32, 49], [34, 72, 58, 0, 1, 88, 70, 12], [41, 2, 37, 68, 0, 52, 73, 22], [43, 46, 88, 68, 6, 27, 44, 1], [88, 54, 96, 86, 26, 91, 75, 24], [84, 63, 77, 4, 99, 73, 75, 61], [16, 89, 50, 51, 50, 17, 29, 79], [58, 21, 20, 24, 90, 91, 10, 18]], [[43, 27, 14, 10, 70, 97, 6, 4], [94, 22, 82, 16, 43, 39, 3, 21], [84, 97, 88, 21, 99, 36, 20, 72], [82, 91, 26, 91, 61, 93, 81, 2], [90, 52, 81, 6, 98, 80, 57, 86], [29, 50, 12, 64, 62, 27, 56, 69], [45, 67, 21, 86, 60, 52, 17, 26], [21, 28, 83, 51, 3, 15, 10, 20]], [[7, 25, 6, 39, 15, 8, 66, 86], [41, 86, 3, 37, 40, 63, 2, 29], [66, 7, 93, 45, 13, 73, 58, 83], [9, 47, 89, 44, 13, 34, 14, 9], [13, 26, 95, 28, 38, 66, 28, 9], [91, 76, 75, 55, 47, 6, 45, 7], [68, 81, 51, 81, 98, 89, 73, 88], [70, 72, 72, 11, 38, 59, 17, 14]], [[64, 89, 92, 89, 15, 74, 47, 58], [9, 65, 37, 1, 38, 27, 62, 66], [17, 55, 62, 4, 50, 35, 79, 24], [78, 36, 76, 72, 79, 47, 17, 26], [14, 92, 35, 51, 60, 40, 97, 81], [54, 36, 50, 58, 56, 72, 43, 60], [80, 96, 32, 29, 16, 83, 52, 12], [36, 64, 35, 46, 69, 64, 45, 25]], [[69, 2, 7, 48, 42, 37, 54, 87], [12, 84, 9, 62, 93, 27, 83, 72], [1, 72, 23, 13, 72, 28, 6, 5], [51, 27, 77, 54, 73, 85, 82, 50], [15, 80, 68, 48, 61, 52, 23, 14], [14, 35, 0, 85, 97, 78, 31, 60], [11, 66, 73, 92, 30, 93, 3, 63], [31, 12, 65, 59, 22, 81, 25, 8]], [[24, 79, 86, 82, 87, 60, 39, 84], [43, 82, 36, 61, 96, 47, 45, 71], [7, 37, 51, 72, 76, 30, 44, 55], [24, 15, 9, 88, 91, 32, 55, 27], [83, 94, 47, 62, 74, 16, 51, 99], [15, 60, 46, 36, 72, 31, 2, 55], [43, 46, 37, 93, 73, 64, 27, 2], [39, 61, 90, 0, 18, 60, 57, 26]], [[70, 62, 90, 26, 3, 82, 63, 47], [0, 31, 73, 78, 20, 43, 68, 5], [48, 50, 45, 7, 93, 42, 35, 23], [24, 0, 51, 65, 52, 21, 47, 12], [19, 26, 6, 21, 88, 14, 53, 75], [86, 42, 11, 94, 57, 44, 13, 75], [21, 3, 23, 75, 18, 34, 36, 32], [68, 11, 28, 29, 16, 15, 23, 56]], [[84, 14, 64, 71, 49, 41, 20, 30], [50, 83, 1, 42, 63, 38, 86, 14], [32, 56, 53, 66, 39, 31, 82, 42], [22, 93, 64, 42, 83, 81, 73, 1], [44, 34, 56, 35, 82, 26, 94, 88], [27, 70, 61, 78, 37, 80, 87, 98], [26, 58, 54, 61, 57, 46, 8, 61], [80, 18, 61, 74, 15, 67, 55, 37]]], 'objective': 28.0}","[[0, 2, 4], [1, 0, 7], [2, 5, 5], [3, 4, 0], [4, 6, 6], [5, 7, 3], [6, 3, 1], [7, 1, 2]]",28.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 7}, {'i': 1, 'j': 1, 'k': 2, 'cost': 4}, {'i': 1, 'j': 1, 'k': 3, 'cost': 63}, {'i': 1, 'j': 1, 'k': 4, 'cost': 28}, {'i': 1, 'j': 1, 'k': 5, 'cost': 45}, {'i': 1, 'j': 1, 'k': 6, 'cost': 54}, {'i': 1, 'j': 1, 'k': 7, 'cost': 32}, {'i': 1, 'j': 1, 'k': 8, 'cost': 49}, {'i': 1, 'j': 2, 'k': 1, 'cost': 34}, {'i': 1, 'j': 2, 'k': 2, 'cost': 72}, {'i': 1, 'j': 2, 'k': 3, 'cost': 58}, {'i': 1, 'j': 2, 'k': 4, 'cost': 0}, {'i': 1, 'j': 2, 'k': 5, 'cost': 1}, {'i': 1, 'j': 2, 'k': 6, 'cost': 88}, {'i': 1, 'j': 2, 'k': 7, 'cost': 70}, {'i': 1, 'j': 2, 'k': 8, 'cost': 12}, {'i': 1, 'j': 3, 'k': 1, 'cost': 41}, {'i': 1, 'j': 3, 'k': 2, 'cost': 2}, {'i': 1, 'j': 3, 'k': 3, 'cost': 37}, {'i': 1, 'j': 3, 'k': 4, 'cost': 68}, {'i': 1, 'j': 3, 'k': 5, 'cost': 0}, {'i': 1, 'j': 3, 'k': 6, 'cost': 52}, {'i': 1, 'j': 3, 'k': 7, 'cost': 73}, {'i': 1, 'j': 3, 'k': 8, 'cost': 22}, {'i': 1, 'j': 4, 'k': 1, 'cost': 43}, {'i': 1, 'j': 4, 'k': 2, 'cost': 46}, {'i': 1, 'j': 4, 'k': 3, 'cost': 88}, {'i': 1, 'j': 4, 'k': 4, 'cost': 68}, {'i': 1, 'j': 4, 'k': 5, 'cost': 6}, {'i': 1, 'j': 4, 'k': 6, 'cost': 27}, {'i': 1, 'j': 4, 'k': 7, 'cost': 44}, {'i': 1, 'j': 4, 'k': 8, 'cost': 1}, {'i': 1, 'j': 5, 'k': 1, 'cost': 88}, {'i': 1, 'j': 5, 'k': 2, 'cost': 54}, {'i': 1, 'j': 5, 'k': 3, 'cost': 96}, {'i': 1, 'j': 5, 'k': 4, 'cost': 86}, {'i': 1, 'j': 5, 'k': 5, 'cost': 26}, {'i': 1, 'j': 5, 'k': 6, 'cost': 91}, {'i': 1, 'j': 5, 'k': 7, 'cost': 75}, {'i': 1, 'j': 5, 'k': 8, 'cost': 24}, {'i': 1, 'j': 6, 'k': 1, 'cost': 84}, {'i': 1, 'j': 6, 'k': 2, 'cost': 63}, {'i': 1, 'j': 6, 'k': 3, 'cost': 77}, {'i': 1, 'j': 6, 'k': 4, 'cost': 4}, {'i': 1, 'j': 6, 'k': 5, 'cost': 99}, {'i': 1, 'j': 6, 'k': 6, 'cost': 73}, {'i': 1, 'j': 6, 'k': 7, 'cost': 75}, {'i': 1, 'j': 6, 'k': 8, 'cost': 61}, {'i': 1, 'j': 7, 'k': 1, 'cost': 16}, {'i': 1, 'j': 7, 'k': 2, 'cost': 89}, {'i': 1, 'j': 7, 'k': 3, 'cost': 50}, {'i': 1, 'j': 7, 'k': 4, 'cost': 51}, {'i': 1, 'j': 7, 'k': 5, 'cost': 50}, {'i': 1, 'j': 7, 'k': 6, 'cost': 17}, {'i': 1, 'j': 7, 'k': 7, 'cost': 29}, {'i': 1, 'j': 7, 'k': 8, 'cost': 79}, {'i': 1, 'j': 8, 'k': 1, 'cost': 58}, {'i': 1, 'j': 8, 'k': 2, 'cost': 21}, {'i': 1, 'j': 8, 'k': 3, 'cost': 20}, {'i': 1, 'j': 8, 'k': 4, 'cost': 24}, {'i': 1, 'j': 8, 'k': 5, 'cost': 90}, {'i': 1, 'j': 8, 'k': 6, 'cost': 91}, {'i': 1, 'j': 8, 'k': 7, 'cost': 10}, {'i': 1, 'j': 8, 'k': 8, 'cost': 18}, {'i': 2, 'j': 1, 'k': 1, 'cost': 43}, {'i': 2, 'j': 1, 'k': 2, 'cost': 27}, {'i': 2, 'j': 1, 'k': 3, 'cost': 14}, {'i': 2, 'j': 1, 'k': 4, 'cost': 10}, {'i': 2, 'j': 1, 'k': 5, 'cost': 70}, {'i': 2, 'j': 1, 'k': 6, 'cost': 97}, {'i': 2, 'j': 1, 'k': 7, 'cost': 6}, {'i': 2, 'j': 1, 'k': 8, 'cost': 4}, {'i': 2, 'j': 2, 'k': 1, 'cost': 94}, {'i': 2, 'j': 2, 'k': 2, 'cost': 22}, {'i': 2, 'j': 2, 'k': 3, 'cost': 82}, {'i': 2, 'j': 2, 'k': 4, 'cost': 16}, {'i': 2, 'j': 2, 'k': 5, 'cost': 43}, {'i': 2, 'j': 2, 'k': 6, 'cost': 39}, {'i': 2, 'j': 2, 'k': 7, 'cost': 3}, {'i': 2, 'j': 2, 'k': 8, 'cost': 21}, {'i': 2, 'j': 3, 'k': 1, 'cost': 84}, {'i': 2, 'j': 3, 'k': 2, 'cost': 97}, {'i': 2, 'j': 3, 'k': 3, 'cost': 88}, {'i': 2, 'j': 3, 'k': 4, 'cost': 21}, {'i': 2, 'j': 3, 'k': 5, 'cost': 99}, {'i': 2, 'j': 3, 'k': 6, 'cost': 36}, {'i': 2, 'j': 3, 'k': 7, 'cost': 20}, {'i': 2, 'j': 3, 'k': 8, 'cost': 72}, {'i': 2, 'j': 4, 'k': 1, 'cost': 82}, {'i': 2, 'j': 4, 'k': 2, 'cost': 91}, {'i': 2, 'j': 4, 'k': 3, 'cost': 26}, {'i': 2, 'j': 4, 'k': 4, 'cost': 91}, {'i': 2, 'j': 4, 'k': 5, 'cost': 61}, {'i': 2, 'j': 4, 'k': 6, 'cost': 93}, {'i': 2, 'j': 4, 'k': 7, 'cost': 81}, {'i': 2, 'j': 4, 'k': 8, 'cost': 2}, {'i': 2, 'j': 5, 'k': 1, 'cost': 90}, {'i': 2, 'j': 5, 'k': 2, 'cost': 52}, {'i': 2, 'j': 5, 'k': 3, 'cost': 81}, {'i': 2, 'j': 5, 'k': 4, 'cost': 6}, {'i': 2, 'j': 5, 'k': 5, 'cost': 98}, {'i': 2, 'j': 5, 'k': 6, 'cost': 80}, {'i': 2, 'j': 5, 'k': 7, 'cost': 57}, {'i': 2, 'j': 5, 'k': 8, 'cost': 86}, {'i': 2, 'j': 6, 'k': 1, 'cost': 29}, {'i': 2, 'j': 6, 'k': 2, 'cost': 50}, {'i': 2, 'j': 6, 'k': 3, 'cost': 12}, {'i': 2, 'j': 6, 'k': 4, 'cost': 64}, {'i': 2, 'j': 6, 'k': 5, 'cost': 62}, {'i': 2, 'j': 6, 'k': 6, 'cost': 27}, {'i': 2, 'j': 6, 'k': 7, 'cost': 56}, {'i': 2, 'j': 6, 'k': 8, 'cost': 69}, {'i': 2, 'j': 7, 'k': 1, 'cost': 45}, {'i': 2, 'j': 7, 'k': 2, 'cost': 67}, {'i': 2, 'j': 7, 'k': 3, 'cost': 21}, {'i': 2, 'j': 7, 'k': 4, 'cost': 86}, {'i': 2, 'j': 7, 'k': 5, 'cost': 60}, {'i': 2, 'j': 7, 'k': 6, 'cost': 52}, {'i': 2, 'j': 7, 'k': 7, 'cost': 17}, {'i': 2, 'j': 7, 'k': 8, 'cost': 26}, {'i': 2, 'j': 8, 'k': 1, 'cost': 21}, {'i': 2, 'j': 8, 'k': 2, 'cost': 28}, {'i': 2, 'j': 8, 'k': 3, 'cost': 83}, {'i': 2, 'j': 8, 'k': 4, 'cost': 51}, {'i': 2, 'j': 8, 'k': 5, 'cost': 3}, {'i': 2, 'j': 8, 'k': 6, 'cost': 15}, {'i': 2, 'j': 8, 'k': 7, 'cost': 10}, {'i': 2, 'j': 8, 'k': 8, 'cost': 20}, {'i': 3, 'j': 1, 'k': 1, 'cost': 7}, {'i': 3, 'j': 1, 'k': 2, 'cost': 25}, {'i': 3, 'j': 1, 'k': 3, 'cost': 6}, {'i': 3, 'j': 1, 'k': 4, 'cost': 39}, {'i': 3, 'j': 1, 'k': 5, 'cost': 15}, {'i': 3, 'j': 1, 'k': 6, 'cost': 8}, {'i': 3, 'j': 1, 'k': 7, 'cost': 66}, {'i': 3, 'j': 1, 'k': 8, 'cost': 86}, {'i': 3, 'j': 2, 'k': 1, 'cost': 41}, {'i': 3, 'j': 2, 'k': 2, 'cost': 86}, {'i': 3, 'j': 2, 'k': 3, 'cost': 3}, {'i': 3, 'j': 2, 'k': 4, 'cost': 37}, {'i': 3, 'j': 2, 'k': 5, 'cost': 40}, {'i': 3, 'j': 2, 'k': 6, 'cost': 63}, {'i': 3, 'j': 2, 'k': 7, 'cost': 2}, {'i': 3, 'j': 2, 'k': 8, 'cost': 29}, {'i': 3, 'j': 3, 'k': 1, 'cost': 66}, {'i': 3, 'j': 3, 'k': 2, 'cost': 7}, {'i': 3, 'j': 3, 'k': 3, 'cost': 93}, {'i': 3, 'j': 3, 'k': 4, 'cost': 45}, {'i': 3, 'j': 3, 'k': 5, 'cost': 13}, {'i': 3, 'j': 3, 'k': 6, 'cost': 73}, {'i': 3, 'j': 3, 'k': 7, 'cost': 58}, {'i': 3, 'j': 3, 'k': 8, 'cost': 83}, {'i': 3, 'j': 4, 'k': 1, 'cost': 9}, {'i': 3, 'j': 4, 'k': 2, 'cost': 47}, {'i': 3, 'j': 4, 'k': 3, 'cost': 89}, {'i': 3, 'j': 4, 'k': 4, 'cost': 44}, {'i': 3, 'j': 4, 'k': 5, 'cost': 13}, {'i': 3, 'j': 4, 'k': 6, 'cost': 34}, {'i': 3, 'j': 4, 'k': 7, 'cost': 14}, {'i': 3, 'j': 4, 'k': 8, 'cost': 9}, {'i': 3, 'j': 5, 'k': 1, 'cost': 13}, {'i': 3, 'j': 5, 'k': 2, 'cost': 26}, {'i': 3, 'j': 5, 'k': 3, 'cost': 95}, {'i': 3, 'j': 5, 'k': 4, 'cost': 28}, {'i': 3, 'j': 5, 'k': 5, 'cost': 38}, {'i': 3, 'j': 5, 'k': 6, 'cost': 66}, {'i': 3, 'j': 5, 'k': 7, 'cost': 28}, {'i': 3, 'j': 5, 'k': 8, 'cost': 9}, {'i': 3, 'j': 6, 'k': 1, 'cost': 91}, {'i': 3, 'j': 6, 'k': 2, 'cost': 76}, {'i': 3, 'j': 6, 'k': 3, 'cost': 75}, {'i': 3, 'j': 6, 'k': 4, 'cost': 55}, {'i': 3, 'j': 6, 'k': 5, 'cost': 47}, {'i': 3, 'j': 6, 'k': 6, 'cost': 6}, {'i': 3, 'j': 6, 'k': 7, 'cost': 45}, {'i': 3, 'j': 6, 'k': 8, 'cost': 7}, {'i': 3, 'j': 7, 'k': 1, 'cost': 68}, {'i': 3, 'j': 7, 'k': 2, 'cost': 81}, {'i': 3, 'j': 7, 'k': 3, 'cost': 51}, {'i': 3, 'j': 7, 'k': 4, 'cost': 81}, {'i': 3, 'j': 7, 'k': 5, 'cost': 98}, {'i': 3, 'j': 7, 'k': 6, 'cost': 89}, {'i': 3, 'j': 7, 'k': 7, 'cost': 73}, {'i': 3, 'j': 7, 'k': 8, 'cost': 88}, {'i': 3, 'j': 8, 'k': 1, 'cost': 70}, {'i': 3, 'j': 8, 'k': 2, 'cost': 72}, {'i': 3, 'j': 8, 'k': 3, 'cost': 72}, {'i': 3, 'j': 8, 'k': 4, 'cost': 11}, {'i': 3, 'j': 8, 'k': 5, 'cost': 38}, {'i': 3, 'j': 8, 'k': 6, 'cost': 59}, {'i': 3, 'j': 8, 'k': 7, 'cost': 17}, {'i': 3, 'j': 8, 'k': 8, 'cost': 14}, {'i': 4, 'j': 1, 'k': 1, 'cost': 64}, {'i': 4, 'j': 1, 'k': 2, 'cost': 89}, {'i': 4, 'j': 1, 'k': 3, 'cost': 92}, {'i': 4, 'j': 1, 'k': 4, 'cost': 89}, {'i': 4, 'j': 1, 'k': 5, 'cost': 15}, {'i': 4, 'j': 1, 'k': 6, 'cost': 74}, {'i': 4, 'j': 1, 'k': 7, 'cost': 47}, {'i': 4, 'j': 1, 'k': 8, 'cost': 58}, {'i': 4, 'j': 2, 'k': 1, 'cost': 9}, {'i': 4, 'j': 2, 'k': 2, 'cost': 65}, {'i': 4, 'j': 2, 'k': 3, 'cost': 37}, {'i': 4, 'j': 2, 'k': 4, 'cost': 1}, {'i': 4, 'j': 2, 'k': 5, 'cost': 38}, {'i': 4, 'j': 2, 'k': 6, 'cost': 27}, {'i': 4, 'j': 2, 'k': 7, 'cost': 62}, {'i': 4, 'j': 2, 'k': 8, 'cost': 66}, {'i': 4, 'j': 3, 'k': 1, 'cost': 17}, {'i': 4, 'j': 3, 'k': 2, 'cost': 55}, {'i': 4, 'j': 3, 'k': 3, 'cost': 62}, {'i': 4, 'j': 3, 'k': 4, 'cost': 4}, {'i': 4, 'j': 3, 'k': 5, 'cost': 50}, {'i': 4, 'j': 3, 'k': 6, 'cost': 35}, {'i': 4, 'j': 3, 'k': 7, 'cost': 79}, {'i': 4, 'j': 3, 'k': 8, 'cost': 24}, {'i': 4, 'j': 4, 'k': 1, 'cost': 78}, {'i': 4, 'j': 4, 'k': 2, 'cost': 36}, {'i': 4, 'j': 4, 'k': 3, 'cost': 76}, {'i': 4, 'j': 4, 'k': 4, 'cost': 72}, {'i': 4, 'j': 4, 'k': 5, 'cost': 79}, {'i': 4, 'j': 4, 'k': 6, 'cost': 47}, {'i': 4, 'j': 4, 'k': 7, 'cost': 17}, {'i': 4, 'j': 4, 'k': 8, 'cost': 26}, {'i': 4, 'j': 5, 'k': 1, 'cost': 14}, {'i': 4, 'j': 5, 'k': 2, 'cost': 92}, {'i': 4, 'j': 5, 'k': 3, 'cost': 35}, {'i': 4, 'j': 5, 'k': 4, 'cost': 51}, {'i': 4, 'j': 5, 'k': 5, 'cost': 60}, {'i': 4, 'j': 5, 'k': 6, 'cost': 40}, {'i': 4, 'j': 5, 'k': 7, 'cost': 97}, {'i': 4, 'j': 5, 'k': 8, 'cost': 81}, {'i': 4, 'j': 6, 'k': 1, 'cost': 54}, {'i': 4, 'j': 6, 'k': 2, 'cost': 36}, {'i': 4, 'j': 6, 'k': 3, 'cost': 50}, {'i': 4, 'j': 6, 'k': 4, 'cost': 58}, {'i': 4, 'j': 6, 'k': 5, 'cost': 56}, {'i': 4, 'j': 6, 'k': 6, 'cost': 72}, {'i': 4, 'j': 6, 'k': 7, 'cost': 43}, {'i': 4, 'j': 6, 'k': 8, 'cost': 60}, {'i': 4, 'j': 7, 'k': 1, 'cost': 80}, {'i': 4, 'j': 7, 'k': 2, 'cost': 96}, {'i': 4, 'j': 7, 'k': 3, 'cost': 32}, {'i': 4, 'j': 7, 'k': 4, 'cost': 29}, {'i': 4, 'j': 7, 'k': 5, 'cost': 16}, {'i': 4, 'j': 7, 'k': 6, 'cost': 83}, {'i': 4, 'j': 7, 'k': 7, 'cost': 52}, {'i': 4, 'j': 7, 'k': 8, 'cost': 12}, {'i': 4, 'j': 8, 'k': 1, 'cost': 36}, {'i': 4, 'j': 8, 'k': 2, 'cost': 64}, {'i': 4, 'j': 8, 'k': 3, 'cost': 35}, {'i': 4, 'j': 8, 'k': 4, 'cost': 46}, {'i': 4, 'j': 8, 'k': 5, 'cost': 69}, {'i': 4, 'j': 8, 'k': 6, 'cost': 64}, {'i': 4, 'j': 8, 'k': 7, 'cost': 45}, {'i': 4, 'j': 8, 'k': 8, 'cost': 25}, {'i': 5, 'j': 1, 'k': 1, 'cost': 69}, {'i': 5, 'j': 1, 'k': 2, 'cost': 2}, {'i': 5, 'j': 1, 'k': 3, 'cost': 7}, {'i': 5, 'j': 1, 'k': 4, 'cost': 48}, {'i': 5, 'j': 1, 'k': 5, 'cost': 42}, {'i': 5, 'j': 1, 'k': 6, 'cost': 37}, {'i': 5, 'j': 1, 'k': 7, 'cost': 54}, {'i': 5, 'j': 1, 'k': 8, 'cost': 87}, {'i': 5, 'j': 2, 'k': 1, 'cost': 12}, {'i': 5, 'j': 2, 'k': 2, 'cost': 84}, {'i': 5, 'j': 2, 'k': 3, 'cost': 9}, {'i': 5, 'j': 2, 'k': 4, 'cost': 62}, {'i': 5, 'j': 2, 'k': 5, 'cost': 93}, {'i': 5, 'j': 2, 'k': 6, 'cost': 27}, {'i': 5, 'j': 2, 'k': 7, 'cost': 83}, {'i': 5, 'j': 2, 'k': 8, 'cost': 72}, {'i': 5, 'j': 3, 'k': 1, 'cost': 1}, {'i': 5, 'j': 3, 'k': 2, 'cost': 72}, {'i': 5, 'j': 3, 'k': 3, 'cost': 23}, {'i': 5, 'j': 3, 'k': 4, 'cost': 13}, {'i': 5, 'j': 3, 'k': 5, 'cost': 72}, {'i': 5, 'j': 3, 'k': 6, 'cost': 28}, {'i': 5, 'j': 3, 'k': 7, 'cost': 6}, {'i': 5, 'j': 3, 'k': 8, 'cost': 5}, {'i': 5, 'j': 4, 'k': 1, 'cost': 51}, {'i': 5, 'j': 4, 'k': 2, 'cost': 27}, {'i': 5, 'j': 4, 'k': 3, 'cost': 77}, {'i': 5, 'j': 4, 'k': 4, 'cost': 54}, {'i': 5, 'j': 4, 'k': 5, 'cost': 73}, {'i': 5, 'j': 4, 'k': 6, 'cost': 85}, {'i': 5, 'j': 4, 'k': 7, 'cost': 82}, {'i': 5, 'j': 4, 'k': 8, 'cost': 50}, {'i': 5, 'j': 5, 'k': 1, 'cost': 15}, {'i': 5, 'j': 5, 'k': 2, 'cost': 80}, {'i': 5, 'j': 5, 'k': 3, 'cost': 68}, {'i': 5, 'j': 5, 'k': 4, 'cost': 48}, {'i': 5, 'j': 5, 'k': 5, 'cost': 61}, {'i': 5, 'j': 5, 'k': 6, 'cost': 52}, {'i': 5, 'j': 5, 'k': 7, 'cost': 23}, {'i': 5, 'j': 5, 'k': 8, 'cost': 14}, {'i': 5, 'j': 6, 'k': 1, 'cost': 14}, {'i': 5, 'j': 6, 'k': 2, 'cost': 35}, {'i': 5, 'j': 6, 'k': 3, 'cost': 0}, {'i': 5, 'j': 6, 'k': 4, 'cost': 85}, {'i': 5, 'j': 6, 'k': 5, 'cost': 97}, {'i': 5, 'j': 6, 'k': 6, 'cost': 78}, {'i': 5, 'j': 6, 'k': 7, 'cost': 31}, {'i': 5, 'j': 6, 'k': 8, 'cost': 60}, {'i': 5, 'j': 7, 'k': 1, 'cost': 11}, {'i': 5, 'j': 7, 'k': 2, 'cost': 66}, {'i': 5, 'j': 7, 'k': 3, 'cost': 73}, {'i': 5, 'j': 7, 'k': 4, 'cost': 92}, {'i': 5, 'j': 7, 'k': 5, 'cost': 30}, {'i': 5, 'j': 7, 'k': 6, 'cost': 93}, {'i': 5, 'j': 7, 'k': 7, 'cost': 3}, {'i': 5, 'j': 7, 'k': 8, 'cost': 63}, {'i': 5, 'j': 8, 'k': 1, 'cost': 31}, {'i': 5, 'j': 8, 'k': 2, 'cost': 12}, {'i': 5, 'j': 8, 'k': 3, 'cost': 65}, {'i': 5, 'j': 8, 'k': 4, 'cost': 59}, {'i': 5, 'j': 8, 'k': 5, 'cost': 22}, {'i': 5, 'j': 8, 'k': 6, 'cost': 81}, {'i': 5, 'j': 8, 'k': 7, 'cost': 25}, {'i': 5, 'j': 8, 'k': 8, 'cost': 8}, {'i': 6, 'j': 1, 'k': 1, 'cost': 24}, {'i': 6, 'j': 1, 'k': 2, 'cost': 79}, {'i': 6, 'j': 1, 'k': 3, 'cost': 86}, {'i': 6, 'j': 1, 'k': 4, 'cost': 82}, {'i': 6, 'j': 1, 'k': 5, 'cost': 87}, {'i': 6, 'j': 1, 'k': 6, 'cost': 60}, {'i': 6, 'j': 1, 'k': 7, 'cost': 39}, {'i': 6, 'j': 1, 'k': 8, 'cost': 84}, {'i': 6, 'j': 2, 'k': 1, 'cost': 43}, {'i': 6, 'j': 2, 'k': 2, 'cost': 82}, {'i': 6, 'j': 2, 'k': 3, 'cost': 36}, {'i': 6, 'j': 2, 'k': 4, 'cost': 61}, {'i': 6, 'j': 2, 'k': 5, 'cost': 96}, {'i': 6, 'j': 2, 'k': 6, 'cost': 47}, {'i': 6, 'j': 2, 'k': 7, 'cost': 45}, {'i': 6, 'j': 2, 'k': 8, 'cost': 71}, {'i': 6, 'j': 3, 'k': 1, 'cost': 7}, {'i': 6, 'j': 3, 'k': 2, 'cost': 37}, {'i': 6, 'j': 3, 'k': 3, 'cost': 51}, {'i': 6, 'j': 3, 'k': 4, 'cost': 72}, {'i': 6, 'j': 3, 'k': 5, 'cost': 76}, {'i': 6, 'j': 3, 'k': 6, 'cost': 30}, {'i': 6, 'j': 3, 'k': 7, 'cost': 44}, {'i': 6, 'j': 3, 'k': 8, 'cost': 55}, {'i': 6, 'j': 4, 'k': 1, 'cost': 24}, {'i': 6, 'j': 4, 'k': 2, 'cost': 15}, {'i': 6, 'j': 4, 'k': 3, 'cost': 9}, {'i': 6, 'j': 4, 'k': 4, 'cost': 88}, {'i': 6, 'j': 4, 'k': 5, 'cost': 91}, {'i': 6, 'j': 4, 'k': 6, 'cost': 32}, {'i': 6, 'j': 4, 'k': 7, 'cost': 55}, {'i': 6, 'j': 4, 'k': 8, 'cost': 27}, {'i': 6, 'j': 5, 'k': 1, 'cost': 83}, {'i': 6, 'j': 5, 'k': 2, 'cost': 94}, {'i': 6, 'j': 5, 'k': 3, 'cost': 47}, {'i': 6, 'j': 5, 'k': 4, 'cost': 62}, {'i': 6, 'j': 5, 'k': 5, 'cost': 74}, {'i': 6, 'j': 5, 'k': 6, 'cost': 16}, {'i': 6, 'j': 5, 'k': 7, 'cost': 51}, {'i': 6, 'j': 5, 'k': 8, 'cost': 99}, {'i': 6, 'j': 6, 'k': 1, 'cost': 15}, {'i': 6, 'j': 6, 'k': 2, 'cost': 60}, {'i': 6, 'j': 6, 'k': 3, 'cost': 46}, {'i': 6, 'j': 6, 'k': 4, 'cost': 36}, {'i': 6, 'j': 6, 'k': 5, 'cost': 72}, {'i': 6, 'j': 6, 'k': 6, 'cost': 31}, {'i': 6, 'j': 6, 'k': 7, 'cost': 2}, {'i': 6, 'j': 6, 'k': 8, 'cost': 55}, {'i': 6, 'j': 7, 'k': 1, 'cost': 43}, {'i': 6, 'j': 7, 'k': 2, 'cost': 46}, {'i': 6, 'j': 7, 'k': 3, 'cost': 37}, {'i': 6, 'j': 7, 'k': 4, 'cost': 93}, {'i': 6, 'j': 7, 'k': 5, 'cost': 73}, {'i': 6, 'j': 7, 'k': 6, 'cost': 64}, {'i': 6, 'j': 7, 'k': 7, 'cost': 27}, {'i': 6, 'j': 7, 'k': 8, 'cost': 2}, {'i': 6, 'j': 8, 'k': 1, 'cost': 39}, {'i': 6, 'j': 8, 'k': 2, 'cost': 61}, {'i': 6, 'j': 8, 'k': 3, 'cost': 90}, {'i': 6, 'j': 8, 'k': 4, 'cost': 0}, {'i': 6, 'j': 8, 'k': 5, 'cost': 18}, {'i': 6, 'j': 8, 'k': 6, 'cost': 60}, {'i': 6, 'j': 8, 'k': 7, 'cost': 57}, {'i': 6, 'j': 8, 'k': 8, 'cost': 26}, {'i': 7, 'j': 1, 'k': 1, 'cost': 70}, {'i': 7, 'j': 1, 'k': 2, 'cost': 62}, {'i': 7, 'j': 1, 'k': 3, 'cost': 90}, {'i': 7, 'j': 1, 'k': 4, 'cost': 26}, {'i': 7, 'j': 1, 'k': 5, 'cost': 3}, {'i': 7, 'j': 1, 'k': 6, 'cost': 82}, {'i': 7, 'j': 1, 'k': 7, 'cost': 63}, {'i': 7, 'j': 1, 'k': 8, 'cost': 47}, {'i': 7, 'j': 2, 'k': 1, 'cost': 0}, {'i': 7, 'j': 2, 'k': 2, 'cost': 31}, {'i': 7, 'j': 2, 'k': 3, 'cost': 73}, {'i': 7, 'j': 2, 'k': 4, 'cost': 78}, {'i': 7, 'j': 2, 'k': 5, 'cost': 20}, {'i': 7, 'j': 2, 'k': 6, 'cost': 43}, {'i': 7, 'j': 2, 'k': 7, 'cost': 68}, {'i': 7, 'j': 2, 'k': 8, 'cost': 5}, {'i': 7, 'j': 3, 'k': 1, 'cost': 48}, {'i': 7, 'j': 3, 'k': 2, 'cost': 50}, {'i': 7, 'j': 3, 'k': 3, 'cost': 45}, {'i': 7, 'j': 3, 'k': 4, 'cost': 7}, {'i': 7, 'j': 3, 'k': 5, 'cost': 93}, {'i': 7, 'j': 3, 'k': 6, 'cost': 42}, {'i': 7, 'j': 3, 'k': 7, 'cost': 35}, {'i': 7, 'j': 3, 'k': 8, 'cost': 23}, {'i': 7, 'j': 4, 'k': 1, 'cost': 24}, {'i': 7, 'j': 4, 'k': 2, 'cost': 0}, {'i': 7, 'j': 4, 'k': 3, 'cost': 51}, {'i': 7, 'j': 4, 'k': 4, 'cost': 65}, {'i': 7, 'j': 4, 'k': 5, 'cost': 52}, {'i': 7, 'j': 4, 'k': 6, 'cost': 21}, {'i': 7, 'j': 4, 'k': 7, 'cost': 47}, {'i': 7, 'j': 4, 'k': 8, 'cost': 12}, {'i': 7, 'j': 5, 'k': 1, 'cost': 19}, {'i': 7, 'j': 5, 'k': 2, 'cost': 26}, {'i': 7, 'j': 5, 'k': 3, 'cost': 6}, {'i': 7, 'j': 5, 'k': 4, 'cost': 21}, {'i': 7, 'j': 5, 'k': 5, 'cost': 88}, {'i': 7, 'j': 5, 'k': 6, 'cost': 14}, {'i': 7, 'j': 5, 'k': 7, 'cost': 53}, {'i': 7, 'j': 5, 'k': 8, 'cost': 75}, {'i': 7, 'j': 6, 'k': 1, 'cost': 86}, {'i': 7, 'j': 6, 'k': 2, 'cost': 42}, {'i': 7, 'j': 6, 'k': 3, 'cost': 11}, {'i': 7, 'j': 6, 'k': 4, 'cost': 94}, {'i': 7, 'j': 6, 'k': 5, 'cost': 57}, {'i': 7, 'j': 6, 'k': 6, 'cost': 44}, {'i': 7, 'j': 6, 'k': 7, 'cost': 13}, {'i': 7, 'j': 6, 'k': 8, 'cost': 75}, {'i': 7, 'j': 7, 'k': 1, 'cost': 21}, {'i': 7, 'j': 7, 'k': 2, 'cost': 3}, {'i': 7, 'j': 7, 'k': 3, 'cost': 23}, {'i': 7, 'j': 7, 'k': 4, 'cost': 75}, {'i': 7, 'j': 7, 'k': 5, 'cost': 18}, {'i': 7, 'j': 7, 'k': 6, 'cost': 34}, {'i': 7, 'j': 7, 'k': 7, 'cost': 36}, {'i': 7, 'j': 7, 'k': 8, 'cost': 32}, {'i': 7, 'j': 8, 'k': 1, 'cost': 68}, {'i': 7, 'j': 8, 'k': 2, 'cost': 11}, {'i': 7, 'j': 8, 'k': 3, 'cost': 28}, {'i': 7, 'j': 8, 'k': 4, 'cost': 29}, {'i': 7, 'j': 8, 'k': 5, 'cost': 16}, {'i': 7, 'j': 8, 'k': 6, 'cost': 15}, {'i': 7, 'j': 8, 'k': 7, 'cost': 23}, {'i': 7, 'j': 8, 'k': 8, 'cost': 56}, {'i': 8, 'j': 1, 'k': 1, 'cost': 84}, {'i': 8, 'j': 1, 'k': 2, 'cost': 14}, {'i': 8, 'j': 1, 'k': 3, 'cost': 64}, {'i': 8, 'j': 1, 'k': 4, 'cost': 71}, {'i': 8, 'j': 1, 'k': 5, 'cost': 49}, {'i': 8, 'j': 1, 'k': 6, 'cost': 41}, {'i': 8, 'j': 1, 'k': 7, 'cost': 20}, {'i': 8, 'j': 1, 'k': 8, 'cost': 30}, {'i': 8, 'j': 2, 'k': 1, 'cost': 50}, {'i': 8, 'j': 2, 'k': 2, 'cost': 83}, {'i': 8, 'j': 2, 'k': 3, 'cost': 1}, {'i': 8, 'j': 2, 'k': 4, 'cost': 42}, {'i': 8, 'j': 2, 'k': 5, 'cost': 63}, {'i': 8, 'j': 2, 'k': 6, 'cost': 38}, {'i': 8, 'j': 2, 'k': 7, 'cost': 86}, {'i': 8, 'j': 2, 'k': 8, 'cost': 14}, {'i': 8, 'j': 3, 'k': 1, 'cost': 32}, {'i': 8, 'j': 3, 'k': 2, 'cost': 56}, {'i': 8, 'j': 3, 'k': 3, 'cost': 53}, {'i': 8, 'j': 3, 'k': 4, 'cost': 66}, {'i': 8, 'j': 3, 'k': 5, 'cost': 39}, {'i': 8, 'j': 3, 'k': 6, 'cost': 31}, {'i': 8, 'j': 3, 'k': 7, 'cost': 82}, {'i': 8, 'j': 3, 'k': 8, 'cost': 42}, {'i': 8, 'j': 4, 'k': 1, 'cost': 22}, {'i': 8, 'j': 4, 'k': 2, 'cost': 93}, {'i': 8, 'j': 4, 'k': 3, 'cost': 64}, {'i': 8, 'j': 4, 'k': 4, 'cost': 42}, {'i': 8, 'j': 4, 'k': 5, 'cost': 83}, {'i': 8, 'j': 4, 'k': 6, 'cost': 81}, {'i': 8, 'j': 4, 'k': 7, 'cost': 73}, {'i': 8, 'j': 4, 'k': 8, 'cost': 1}, {'i': 8, 'j': 5, 'k': 1, 'cost': 44}, {'i': 8, 'j': 5, 'k': 2, 'cost': 34}, {'i': 8, 'j': 5, 'k': 3, 'cost': 56}, {'i': 8, 'j': 5, 'k': 4, 'cost': 35}, {'i': 8, 'j': 5, 'k': 5, 'cost': 82}, {'i': 8, 'j': 5, 'k': 6, 'cost': 26}, {'i': 8, 'j': 5, 'k': 7, 'cost': 94}, {'i': 8, 'j': 5, 'k': 8, 'cost': 88}, {'i': 8, 'j': 6, 'k': 1, 'cost': 27}, {'i': 8, 'j': 6, 'k': 2, 'cost': 70}, {'i': 8, 'j': 6, 'k': 3, 'cost': 61}, {'i': 8, 'j': 6, 'k': 4, 'cost': 78}, {'i': 8, 'j': 6, 'k': 5, 'cost': 37}, {'i': 8, 'j': 6, 'k': 6, 'cost': 80}, {'i': 8, 'j': 6, 'k': 7, 'cost': 87}, {'i': 8, 'j': 6, 'k': 8, 'cost': 98}, {'i': 8, 'j': 7, 'k': 1, 'cost': 26}, {'i': 8, 'j': 7, 'k': 2, 'cost': 58}, {'i': 8, 'j': 7, 'k': 3, 'cost': 54}, {'i': 8, 'j': 7, 'k': 4, 'cost': 61}, {'i': 8, 'j': 7, 'k': 5, 'cost': 57}, {'i': 8, 'j': 7, 'k': 6, 'cost': 46}, {'i': 8, 'j': 7, 'k': 7, 'cost': 8}, {'i': 8, 'j': 7, 'k': 8, 'cost': 61}, {'i': 8, 'j': 8, 'k': 1, 'cost': 80}, {'i': 8, 'j': 8, 'k': 2, 'cost': 18}, {'i': 8, 'j': 8, 'k': 3, 'cost': 61}, {'i': 8, 'j': 8, 'k': 4, 'cost': 74}, {'i': 8, 'j': 8, 'k': 5, 'cost': 15}, {'i': 8, 'j': 8, 'k': 6, 'cost': 67}, {'i': 8, 'j': 8, 'k': 7, 'cost': 55}, {'i': 8, 'j': 8, 'k': 8, 'cost': 37}]}","[[1, 3, 5], [2, 1, 8], [3, 6, 6], [4, 5, 1], [5, 7, 7], [6, 8, 4], [7, 4, 2], [8, 2, 3]]",12,json,1
AP3,AP3,"We turned chore night into a little matchmaking problem: every family member needs one specific chore and one specific cleaning day, and every chore and every day has to be claimed by exactly one person. The best arrangement is the one where, after totaling each person’s discomfort score for the task and day they get, that overall sum is as low as possible. No job or day can be left unassigned or duplicated — it’s one person, one task, one day all the way. The exact tasks, days, and the inconvenience scores are listed below.

We have 7 family members — A, B, C, D, E, F, G — each needing one chore and one day.

*Meaning: costs form a 3D tensor. For each fixed member_id=i, you are given a chore_id×cleaning_day_id matrix whose entry at row chore_id=j and column cleaning_day_id=k equals inconvenience_score(i,j,k). You must pick exactly one (j,k) for every i, with all chore_id and all cleaning_day_id used exactly once.*

**inconvenience_score_tensor (per-member_id markdown matrices)**

## member_id=A
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 87 | 50 | 36 | 50 | 49 | 44 | 68 |
| B | 14 | 6 | 21 | 34 | 68 | 80 | 95 |
| C | 22 | 38 | 25 | 92 | 58 | 29 | 90 |
| D | 26 | 63 | 92 | 74 | 7 | 73 | 28 |
| E | 50 | 18 | 26 | 72 | 30 | 80 | 58 |
| F | 98 | 63 | 4 | 11 | 62 | 78 | 78 |
| G | 89 | 46 | 17 | 85 | 66 | 63 | 31 |

## member_id=B
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 59 | 36 | 4 | 45 | 53 | 88 | 73 |
| B | 79 | 21 | 26 | 55 | 93 | 72 | 80 |
| C | 33 | 78 | 83 | 62 | 20 | 96 | 91 |
| D | 71 | 75 | 96 | 78 | 33 | 56 | 31 |
| E | 97 | 63 | 99 | 97 | 93 | 15 | 33 |
| F | 96 | 6 | 17 | 48 | 30 | 93 | 45 |
| G | 95 | 95 | 87 | 59 | 54 | 17 | 3 |

## member_id=C
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 84 | 12 | 52 | 74 | 85 | 22 | 5 |
| B | 9 | 24 | 45 | 56 | 45 | 90 | 81 |
| C | 48 | 75 | 89 | 65 | 21 | 9 | 20 |
| D | 47 | 28 | 30 | 83 | 16 | 67 | 20 |
| E | 94 | 33 | 33 | 73 | 54 | 3 | 48 |
| F | 92 | 94 | 66 | 30 | 62 | 77 | 54 |
| G | 87 | 67 | 92 | 21 | 78 | 27 | 9 |

## member_id=D
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 58 | 14 | 34 | 52 | 51 | 66 | 32 |
| B | 83 | 28 | 51 | 99 | 21 | 80 | 71 |
| C | 39 | 19 | 4 | 90 | 84 | 76 | 13 |
| D | 5 | 3 | 18 | 88 | 26 | 51 | 51 |
| E | 8 | 11 | 77 | 76 | 5 | 71 | 42 |
| F | 72 | 64 | 84 | 76 | 25 | 28 | 28 |
| G | 93 | 24 | 75 | 2 | 28 | 77 | 6 |

## member_id=E
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 31 | 71 | 60 | 3 | 12 | 72 | 51 |
| B | 53 | 96 | 2 | 14 | 36 | 58 | 91 |
| C | 70 | 68 | 81 | 67 | 98 | 59 | 46 |
| D | 46 | 81 | 4 | 2 | 44 | 60 | 20 |
| E | 74 | 2 | 59 | 29 | 49 | 80 | 25 |
| F | 97 | 10 | 44 | 75 | 32 | 66 | 71 |
| G | 1 | 48 | 28 | 41 | 46 | 47 | 2 |

## member_id=F
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 49 | 32 | 21 | 56 | 79 | 64 | 7 |
| B | 53 | 65 | 59 | 98 | 86 | 65 | 64 |
| C | 35 | 95 | 73 | 43 | 41 | 71 | 92 |
| D | 13 | 77 | 39 | 61 | 92 | 49 | 9 |
| E | 18 | 59 | 46 | 15 | 40 | 80 | 94 |
| F | 66 | 91 | 12 | 29 | 17 | 97 | 60 |
| G | 40 | 23 | 56 | 40 | 62 | 78 | 89 |

## member_id=G
| chore_id\cleaning_day_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 65 | 81 | 57 | 9 | 22 | 49 | 95 |
| B | 54 | 88 | 66 | 21 | 4 | 79 | 96 |
| C | 97 | 70 | 47 | 46 | 9 | 22 | 37 |
| D | 11 | 18 | 30 | 11 | 78 | 22 | 3 |
| E | 64 | 18 | 53 | 6 | 33 | 67 | 87 |
| F | 69 | 59 | 40 | 56 | 85 | 30 | 9 |
| G | 69 | 95 | 39 | 97 | 87 | 17 | 31 |

We will choose the 7 triples that minimize the total inconvenience.

Also, when you hand back the matching, please use this simple JSON layout so I can read it straight away — just a quick sketch of the shape I expect:

{
  ""solution"": [
    [<person_id>, <chore_id>, <day_id>],
    ...
  ]
}

Think of each triple as one row in a little table: the first spot is the family member, the second is the chore they get, and the third is the day they’ll do it. This block is only a sketch of the expected shape, not the actual answer — I just want the final assignment to follow that exact structure.

Important: use the identifiers exactly as they appear in the instance input — do not rename them and do not introduce any 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”.","{'cost_tensor': [[[87, 50, 36, 50, 49, 44, 68], [14, 6, 21, 34, 68, 80, 95], [22, 38, 25, 92, 58, 29, 90], [26, 63, 92, 74, 7, 73, 28], [50, 18, 26, 72, 30, 80, 58], [98, 63, 4, 11, 62, 78, 78], [89, 46, 17, 85, 66, 63, 31]], [[59, 36, 4, 45, 53, 88, 73], [79, 21, 26, 55, 93, 72, 80], [33, 78, 83, 62, 20, 96, 91], [71, 75, 96, 78, 33, 56, 31], [97, 63, 99, 97, 93, 15, 33], [96, 6, 17, 48, 30, 93, 45], [95, 95, 87, 59, 54, 17, 3]], [[84, 12, 52, 74, 85, 22, 5], [9, 24, 45, 56, 45, 90, 81], [48, 75, 89, 65, 21, 9, 20], [47, 28, 30, 83, 16, 67, 20], [94, 33, 33, 73, 54, 3, 48], [92, 94, 66, 30, 62, 77, 54], [87, 67, 92, 21, 78, 27, 9]], [[58, 14, 34, 52, 51, 66, 32], [83, 28, 51, 99, 21, 80, 71], [39, 19, 4, 90, 84, 76, 13], [5, 3, 18, 88, 26, 51, 51], [8, 11, 77, 76, 5, 71, 42], [72, 64, 84, 76, 25, 28, 28], [93, 24, 75, 2, 28, 77, 6]], [[31, 71, 60, 3, 12, 72, 51], [53, 96, 2, 14, 36, 58, 91], [70, 68, 81, 67, 98, 59, 46], [46, 81, 4, 2, 44, 60, 20], [74, 2, 59, 29, 49, 80, 25], [97, 10, 44, 75, 32, 66, 71], [1, 48, 28, 41, 46, 47, 2]], [[49, 32, 21, 56, 79, 64, 7], [53, 65, 59, 98, 86, 65, 64], [35, 95, 73, 43, 41, 71, 92], [13, 77, 39, 61, 92, 49, 9], [18, 59, 46, 15, 40, 80, 94], [66, 91, 12, 29, 17, 97, 60], [40, 23, 56, 40, 62, 78, 89]], [[65, 81, 57, 9, 22, 49, 95], [54, 88, 66, 21, 4, 79, 96], [97, 70, 47, 46, 9, 22, 37], [11, 18, 30, 11, 78, 22, 3], [64, 18, 53, 6, 33, 67, 87], [69, 59, 40, 56, 85, 30, 9], [69, 95, 39, 97, 87, 17, 31]]], 'objective': 41.0}","[[0, 1, 1], [1, 6, 6], [2, 4, 5], [3, 3, 0], [4, 0, 3], [5, 5, 2], [6, 2, 4]]",41.0,"{'problem_type': 'AP3', 'n': 7, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 87}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 50}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 36}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 50}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 49}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 44}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 68}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 14}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 6}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 21}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 34}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 68}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 80}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 95}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 22}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 38}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 25}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 92}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 58}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 29}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 90}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 26}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 63}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 92}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 74}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 7}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 73}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 28}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 50}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 26}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 72}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 30}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 80}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 58}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 98}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 63}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 4}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 11}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 62}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 78}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 78}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 89}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 46}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 17}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 85}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 66}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 63}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 31}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 59}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 36}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 4}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 45}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 53}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 88}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 73}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 79}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 21}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 26}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 55}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 93}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 72}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 80}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 33}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 78}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 83}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 62}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 20}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 96}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 91}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 71}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 75}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 96}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 78}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 33}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 56}, {'i': 'B', 'j': 'D', 'k': 'G', 'cost': 31}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 97}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 63}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 99}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 97}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 93}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 15}, {'i': 'B', 'j': 'E', 'k': 'G', 'cost': 33}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 96}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 6}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 17}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 48}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 30}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 93}, {'i': 'B', 'j': 'F', 'k': 'G', 'cost': 45}, {'i': 'B', 'j': 'G', 'k': 'A', 'cost': 95}, {'i': 'B', 'j': 'G', 'k': 'B', 'cost': 95}, {'i': 'B', 'j': 'G', 'k': 'C', 'cost': 87}, {'i': 'B', 'j': 'G', 'k': 'D', 'cost': 59}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 54}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 17}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 3}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 84}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 12}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 52}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 74}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 85}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 22}, {'i': 'C', 'j': 'A', 'k': 'G', 'cost': 5}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 9}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 24}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 45}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 56}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 45}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 90}, {'i': 'C', 'j': 'B', 'k': 'G', 'cost': 81}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 48}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 75}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 89}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 65}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 21}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 9}, {'i': 'C', 'j': 'C', 'k': 'G', 'cost': 20}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 47}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 28}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 30}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 83}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 16}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 67}, {'i': 'C', 'j': 'D', 'k': 'G', 'cost': 20}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 94}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 33}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 33}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 73}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 54}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 3}, {'i': 'C', 'j': 'E', 'k': 'G', 'cost': 48}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 92}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 94}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 66}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 30}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 62}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 77}, {'i': 'C', 'j': 'F', 'k': 'G', 'cost': 54}, {'i': 'C', 'j': 'G', 'k': 'A', 'cost': 87}, {'i': 'C', 'j': 'G', 'k': 'B', 'cost': 67}, {'i': 'C', 'j': 'G', 'k': 'C', 'cost': 92}, {'i': 'C', 'j': 'G', 'k': 'D', 'cost': 21}, {'i': 'C', 'j': 'G', 'k': 'E', 'cost': 78}, {'i': 'C', 'j': 'G', 'k': 'F', 'cost': 27}, {'i': 'C', 'j': 'G', 'k': 'G', 'cost': 9}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 58}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 14}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 34}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 52}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 51}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 66}, {'i': 'D', 'j': 'A', 'k': 'G', 'cost': 32}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 83}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 28}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 51}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 99}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 21}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 80}, {'i': 'D', 'j': 'B', 'k': 'G', 'cost': 71}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 39}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 19}, 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'cost': 76}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 25}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 28}, {'i': 'D', 'j': 'F', 'k': 'G', 'cost': 28}, {'i': 'D', 'j': 'G', 'k': 'A', 'cost': 93}, {'i': 'D', 'j': 'G', 'k': 'B', 'cost': 24}, {'i': 'D', 'j': 'G', 'k': 'C', 'cost': 75}, {'i': 'D', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'D', 'j': 'G', 'k': 'E', 'cost': 28}, {'i': 'D', 'j': 'G', 'k': 'F', 'cost': 77}, {'i': 'D', 'j': 'G', 'k': 'G', 'cost': 6}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 31}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 71}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 60}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 3}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 12}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 72}, {'i': 'E', 'j': 'A', 'k': 'G', 'cost': 51}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 53}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 96}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 2}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 14}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 36}, {'i': 'E', 'j': 'B', 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'cost': 15}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 40}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 80}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 94}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 66}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 91}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 12}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 29}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 17}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 97}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 60}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 40}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 23}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 56}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 40}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 62}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 78}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 89}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 65}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 81}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 57}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 9}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 22}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 49}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 95}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 54}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 88}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 66}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 21}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 4}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 79}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 96}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 97}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 70}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 47}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 46}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 9}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 22}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 37}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 11}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 18}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 30}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 11}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 78}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 22}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 3}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 64}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 18}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 53}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 6}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 33}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 67}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 87}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 69}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 59}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 40}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 56}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 85}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 30}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 9}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 69}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 95}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 39}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 97}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 87}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 17}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 31}]}","[['A', 'B', 'B'], ['B', 'G', 'G'], ['C', 'E', 'F'], ['D', 'D', 'A'], ['E', 'A', 'D'], ['F', 'F', 'C'], ['G', 'C', 'E']]",13,markdown_table,names
AP3,AP3,"Recently the manager asked the team to pair tables, waiters, and wine matchings in a way that keeps the night moving smoothly. The constraint was clear: each table gets a single waiter and a single wine pairing, and every waiter and every wine pairing has to be matched to exactly one table — no repeats, no omissions. Each possible triple has a service-time value, and the aim was to choose the collection of triples that produces the smallest possible total when those times are all added together. The detailed list of tables, waiters, wine choices, and their service times appears below.

There are 7 tables (and thus 7 waiters and 7 wine pairings), identified as A, B, C, D, E, F, G.

*Meaning: costs form a 3D tensor. For each fixed table_id=i, you are given a waiter_id×wine_pairing_id matrix whose entry at row waiter_id=j and column wine_pairing_id=k equals service_time(i,j,k). You must pick exactly one (j,k) for every i, with all waiter_id and all wine_pairing_id used exactly once.*

**service_time_tensor (per-table_id markdown matrices)**

## table_id=A
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 28 | 13 | 74 | 19 | 98 | 66 | 41 |
| B | 64 | 35 | 21 | 5 | 43 | 52 | 41 |
| C | 88 | 73 | 53 | 6 | 16 | 24 | 15 |
| D | 37 | 79 | 53 | 77 | 10 | 33 | 4 |
| E | 22 | 77 | 13 | 36 | 97 | 9 | 4 |
| F | 44 | 66 | 86 | 0 | 18 | 14 | 77 |
| G | 87 | 46 | 49 | 97 | 74 | 72 | 23 |

## table_id=B
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 91 | 2 | 85 | 52 | 63 | 39 | 39 |
| B | 0 | 38 | 84 | 77 | 41 | 24 | 57 |
| C | 11 | 57 | 20 | 10 | 49 | 35 | 59 |
| D | 23 | 87 | 83 | 20 | 26 | 71 | 80 |
| E | 32 | 53 | 96 | 78 | 37 | 61 | 43 |
| F | 60 | 12 | 85 | 12 | 19 | 18 | 89 |
| G | 1 | 79 | 66 | 81 | 35 | 62 | 17 |

## table_id=C
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 25 | 13 | 83 | 54 | 81 | 29 | 65 |
| B | 57 | 13 | 70 | 38 | 56 | 39 | 81 |
| C | 8 | 90 | 30 | 75 | 62 | 31 | 51 |
| D | 41 | 41 | 77 | 84 | 56 | 63 | 7 |
| E | 19 | 76 | 22 | 71 | 82 | 45 | 39 |
| F | 95 | 97 | 91 | 84 | 62 | 52 | 15 |
| G | 67 | 47 | 97 | 35 | 27 | 50 | 32 |

## table_id=D
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 38 | 14 | 16 | 24 | 63 | 69 | 65 |
| B | 91 | 53 | 92 | 41 | 93 | 85 | 15 |
| C | 18 | 9 | 10 | 8 | 46 | 21 | 68 |
| D | 77 | 45 | 57 | 83 | 64 | 84 | 30 |
| E | 83 | 21 | 72 | 37 | 42 | 44 | 20 |
| F | 83 | 0 | 24 | 11 | 28 | 32 | 98 |
| G | 68 | 43 | 66 | 79 | 87 | 62 | 42 |

## table_id=E
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 42 | 86 | 53 | 95 | 22 | 95 | 96 |
| B | 18 | 82 | 52 | 50 | 17 | 73 | 52 |
| C | 73 | 61 | 8 | 94 | 75 | 57 | 40 |
| D | 2 | 17 | 83 | 15 | 5 | 19 | 35 |
| E | 8 | 20 | 92 | 89 | 90 | 53 | 28 |
| F | 49 | 85 | 8 | 17 | 69 | 25 | 92 |
| G | 53 | 27 | 69 | 77 | 86 | 9 | 75 |

## table_id=F
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 8 | 6 | 13 | 72 | 93 | 91 | 77 |
| B | 11 | 90 | 3 | 69 | 55 | 14 | 82 |
| C | 65 | 86 | 9 | 45 | 12 | 45 | 74 |
| D | 90 | 46 | 55 | 13 | 60 | 42 | 3 |
| E | 65 | 96 | 21 | 77 | 15 | 66 | 22 |
| F | 11 | 67 | 88 | 23 | 41 | 76 | 29 |
| G | 93 | 83 | 75 | 14 | 99 | 11 | 17 |

## table_id=G
| waiter_id\wine_pairing_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 19 | 85 | 58 | 4 | 17 | 66 | 85 |
| B | 45 | 89 | 82 | 82 | 10 | 99 | 37 |
| C | 59 | 15 | 53 | 61 | 15 | 94 | 38 |
| D | 66 | 37 | 16 | 35 | 1 | 86 | 91 |
| E | 52 | 45 | 14 | 82 | 27 | 64 | 68 |
| F | 30 | 77 | 55 | 37 | 95 | 59 | 7 |
| G | 42 | 71 | 31 | 58 | 11 | 56 | 11 |

The team will choose the triples that yield the smallest possible total service time.

If you want the final matching in a compact, machine-friendly way, I usually just drop it into a tiny JSON snippet like this for clarity.

{
  ""solution"": [
    [<table_id>, <waiter_id>, <wine_id>],
    ...
  ]
}

This is just a sketch of the shape I mean: ""solution"" holds a list of triples, and each triple is the table identifier, the waiter identifier, and the wine-pairing identifier chosen for that table. Think of it like filling out a simple form — one row per table, with the assigned waiter and wine next to it.

This JSON is only the expected shape, not the actual matching — I'll fill in the real triples from the instance when you want them. Please make sure to use the exact identifiers as they appear in the instance input — do not 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”.","{'cost_tensor': [[[28, 13, 74, 19, 98, 66, 41], [64, 35, 21, 5, 43, 52, 41], [88, 73, 53, 6, 16, 24, 15], [37, 79, 53, 77, 10, 33, 4], [22, 77, 13, 36, 97, 9, 4], [44, 66, 86, 0, 18, 14, 77], [87, 46, 49, 97, 74, 72, 23]], [[91, 2, 85, 52, 63, 39, 39], [0, 38, 84, 77, 41, 24, 57], [11, 57, 20, 10, 49, 35, 59], [23, 87, 83, 20, 26, 71, 80], [32, 53, 96, 78, 37, 61, 43], [60, 12, 85, 12, 19, 18, 89], [1, 79, 66, 81, 35, 62, 17]], [[25, 13, 83, 54, 81, 29, 65], [57, 13, 70, 38, 56, 39, 81], [8, 90, 30, 75, 62, 31, 51], [41, 41, 77, 84, 56, 63, 7], [19, 76, 22, 71, 82, 45, 39], [95, 97, 91, 84, 62, 52, 15], [67, 47, 97, 35, 27, 50, 32]], [[38, 14, 16, 24, 63, 69, 65], [91, 53, 92, 41, 93, 85, 15], [18, 9, 10, 8, 46, 21, 68], [77, 45, 57, 83, 64, 84, 30], [83, 21, 72, 37, 42, 44, 20], [83, 0, 24, 11, 28, 32, 98], [68, 43, 66, 79, 87, 62, 42]], [[42, 86, 53, 95, 22, 95, 96], [18, 82, 52, 50, 17, 73, 52], [73, 61, 8, 94, 75, 57, 40], [2, 17, 83, 15, 5, 19, 35], [8, 20, 92, 89, 90, 53, 28], [49, 85, 8, 17, 69, 25, 92], [53, 27, 69, 77, 86, 9, 75]], [[8, 6, 13, 72, 93, 91, 77], [11, 90, 3, 69, 55, 14, 82], [65, 86, 9, 45, 12, 45, 74], [90, 46, 55, 13, 60, 42, 3], [65, 96, 21, 77, 15, 66, 22], [11, 67, 88, 23, 41, 76, 29], [93, 83, 75, 14, 99, 11, 17]], [[19, 85, 58, 4, 17, 66, 85], [45, 89, 82, 82, 10, 99, 37], [59, 15, 53, 61, 15, 94, 38], [66, 37, 16, 35, 1, 86, 91], [52, 45, 14, 82, 27, 64, 68], [30, 77, 55, 37, 95, 59, 7], [42, 71, 31, 58, 11, 56, 11]]], 'objective': 38.0}","[[0, 4, 6], [1, 0, 1], [2, 2, 0], [3, 5, 3], [4, 6, 5], [5, 1, 2], [6, 3, 4]]",38.0,"{'problem_type': 'AP3', 'n': 7, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 28}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 13}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 74}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 19}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 98}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 66}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 41}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 64}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 35}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 21}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 5}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 43}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 52}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 41}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 88}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 73}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 53}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 6}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 16}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 24}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 15}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 37}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 79}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 53}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 77}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 10}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 33}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 4}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 22}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 77}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 13}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 36}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 97}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 9}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 4}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 44}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 66}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 86}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 0}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 18}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 14}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 77}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 87}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 46}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 49}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 97}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 74}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 72}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 23}, {'i': 'B', 'j': 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81}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 35}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 62}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 17}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 25}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 13}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 83}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 54}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 81}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 29}, {'i': 'C', 'j': 'A', 'k': 'G', 'cost': 65}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 57}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 13}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 70}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 38}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 56}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 39}, {'i': 'C', 'j': 'B', 'k': 'G', 'cost': 81}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 8}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 90}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 30}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 75}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 62}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 31}, {'i': 'C', 'j': 'C', 'k': 'G', 'cost': 51}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 41}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 41}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 77}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 84}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 56}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 63}, {'i': 'C', 'j': 'D', 'k': 'G', 'cost': 7}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 19}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 76}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 22}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 71}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 82}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 45}, {'i': 'C', 'j': 'E', 'k': 'G', 'cost': 39}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 95}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 97}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 91}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 84}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 62}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 52}, {'i': 'C', 'j': 'F', 'k': 'G', 'cost': 15}, {'i': 'C', 'j': 'G', 'k': 'A', 'cost': 67}, {'i': 'C', 'j': 'G', 'k': 'B', 'cost': 47}, {'i': 'C', 'j': 'G', 'k': 'C', 'cost': 97}, {'i': 'C', 'j': 'G', 'k': 'D', 'cost': 35}, {'i': 'C', 'j': 'G', 'k': 'E', 'cost': 27}, {'i': 'C', 'j': 'G', 'k': 'F', 'cost': 50}, {'i': 'C', 'j': 'G', 'k': 'G', 'cost': 32}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 38}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 14}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 16}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 24}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 63}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 69}, {'i': 'D', 'j': 'A', 'k': 'G', 'cost': 65}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 91}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 53}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 92}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 41}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 93}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 85}, {'i': 'D', 'j': 'B', 'k': 'G', 'cost': 15}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 18}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 9}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 10}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 8}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 46}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 21}, {'i': 'D', 'j': 'C', 'k': 'G', 'cost': 68}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 77}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 45}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 57}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 83}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 64}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 84}, {'i': 'D', 'j': 'D', 'k': 'G', 'cost': 30}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 83}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 21}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 72}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 37}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 42}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 44}, {'i': 'D', 'j': 'E', 'k': 'G', 'cost': 20}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 83}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 0}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 24}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 11}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 28}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 32}, {'i': 'D', 'j': 'F', 'k': 'G', 'cost': 98}, {'i': 'D', 'j': 'G', 'k': 'A', 'cost': 68}, {'i': 'D', 'j': 'G', 'k': 'B', 'cost': 43}, {'i': 'D', 'j': 'G', 'k': 'C', 'cost': 66}, {'i': 'D', 'j': 'G', 'k': 'D', 'cost': 79}, {'i': 'D', 'j': 'G', 'k': 'E', 'cost': 87}, {'i': 'D', 'j': 'G', 'k': 'F', 'cost': 62}, {'i': 'D', 'j': 'G', 'k': 'G', 'cost': 42}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 42}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 86}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 53}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 95}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 22}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 95}, {'i': 'E', 'j': 'A', 'k': 'G', 'cost': 96}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 18}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 82}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 52}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 50}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 17}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 73}, {'i': 'E', 'j': 'B', 'k': 'G', 'cost': 52}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 73}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 61}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 8}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 94}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 75}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 57}, {'i': 'E', 'j': 'C', 'k': 'G', 'cost': 40}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 2}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 17}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 83}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 15}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 5}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 19}, {'i': 'E', 'j': 'D', 'k': 'G', 'cost': 35}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 8}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 20}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 92}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 89}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 90}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 53}, {'i': 'E', 'j': 'E', 'k': 'G', 'cost': 28}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 49}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 85}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 8}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 17}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 69}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 25}, {'i': 'E', 'j': 'F', 'k': 'G', 'cost': 92}, {'i': 'E', 'j': 'G', 'k': 'A', 'cost': 53}, {'i': 'E', 'j': 'G', 'k': 'B', 'cost': 27}, {'i': 'E', 'j': 'G', 'k': 'C', 'cost': 69}, {'i': 'E', 'j': 'G', 'k': 'D', 'cost': 77}, {'i': 'E', 'j': 'G', 'k': 'E', 'cost': 86}, {'i': 'E', 'j': 'G', 'k': 'F', 'cost': 9}, {'i': 'E', 'j': 'G', 'k': 'G', 'cost': 75}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 8}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 6}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 13}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 72}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 93}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 91}, {'i': 'F', 'j': 'A', 'k': 'G', 'cost': 77}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 11}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 90}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 3}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 69}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 55}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 14}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 82}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 65}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 86}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 9}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 45}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 12}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 45}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 74}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 90}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 46}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 55}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 13}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 60}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 42}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 3}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 65}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 96}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 21}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 77}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 15}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 66}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 22}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 11}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 67}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 88}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 23}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 41}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 76}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 29}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 93}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 83}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 75}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 14}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 99}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 11}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 17}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 19}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 85}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 58}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 4}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 17}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 66}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 85}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 45}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 89}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 82}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 82}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 10}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 99}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 37}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 59}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 15}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 53}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 61}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 15}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 94}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 38}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 66}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 37}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 16}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 35}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 1}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 86}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 91}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 52}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 45}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 14}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 82}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 27}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 64}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 68}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 30}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 77}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 55}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 37}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 95}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 59}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 7}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 42}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 71}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 31}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 58}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 11}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 56}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 11}]}","[['A', 'E', 'G'], ['B', 'A', 'B'], ['C', 'C', 'A'], ['D', 'F', 'D'], ['E', 'G', 'F'], ['F', 'B', 'C'], ['G', 'D', 'E']]",14,markdown_table,names
AP3,AP3,"I was on a team trying to put together a smooth college timetable: every course needs one classroom and one time slot, and there happen to be exactly as many rooms and times as courses. The trick is to pick for each course a room-and-time pair so that no room or time gets used more than once and nothing is left unassigned, and the whole schedule causes as few student clashes as possible — to check that, just add up the clash cost for every course’s chosen room and time. Concrete details for the specific instance are shown below.

# num_courses=8
# course_ids=A, B, C, D, E, F, G, H

# Meaning: costs form a 3D tensor. For each fixed course_id=i, you are given a room_id×time_slot_id matrix whose entry at row room_id=j and column time_slot_id=k equals conflict_cost(i,j,k). You must pick exactly one (j,k) for every i, with all room_id and all time_slot_id used exactly once.
# conflict_cost_tensor (per-course_id markdown matrices)

## course_id=A
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 50 | 49 | 23 | 94 | 18 | 68 | 74 | 73 |
| B | 83 | 1 | 97 | 42 | 33 | 34 | 99 | 27 |
| C | 21 | 25 | 41 | 59 | 94 | 37 | 55 | 11 |
| D | 36 | 47 | 43 | 71 | 49 | 77 | 32 | 85 |
| E | 78 | 70 | 63 | 65 | 41 | 3 | 91 | 41 |
| F | 31 | 31 | 51 | 83 | 84 | 60 | 79 | 2 |
| G | 97 | 99 | 53 | 74 | 83 | 50 | 58 | 11 |
| H | 83 | 4 | 41 | 52 | 55 | 76 | 92 | 45 |

## course_id=B
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 4 | 4 | 14 | 33 | 44 | 46 | 58 | 7 |
| B | 9 | 41 | 80 | 68 | 45 | 15 | 42 | 65 |
| C | 29 | 89 | 94 | 39 | 78 | 48 | 30 | 3 |
| D | 62 | 40 | 99 | 59 | 77 | 12 | 54 | 8 |
| E | 56 | 32 | 89 | 37 | 68 | 49 | 65 | 40 |
| F | 48 | 81 | 95 | 64 | 66 | 23 | 8 | 76 |
| G | 86 | 2 | 28 | 58 | 45 | 76 | 84 | 2 |
| H | 98 | 56 | 50 | 10 | 62 | 83 | 37 | 62 |

## course_id=C
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 42 | 13 | 45 | 36 | 0 | 15 | 53 | 3 |
| B | 89 | 1 | 8 | 47 | 94 | 77 | 18 | 82 |
| C | 15 | 89 | 78 | 44 | 66 | 43 | 20 | 29 |
| D | 63 | 29 | 51 | 41 | 59 | 25 | 71 | 48 |
| E | 27 | 69 | 45 | 26 | 70 | 70 | 93 | 39 |
| F | 21 | 32 | 91 | 78 | 0 | 72 | 34 | 20 |
| G | 15 | 28 | 40 | 71 | 40 | 37 | 21 | 33 |
| H | 91 | 97 | 65 | 29 | 18 | 82 | 20 | 0 |

## course_id=D
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 61 | 66 | 68 | 43 | 98 | 64 | 59 | 25 |
| B | 62 | 35 | 91 | 34 | 5 | 52 | 53 | 72 |
| C | 6 | 14 | 9 | 0 | 52 | 79 | 20 | 94 |
| D | 13 | 88 | 74 | 71 | 92 | 46 | 49 | 40 |
| E | 94 | 85 | 46 | 10 | 67 | 63 | 71 | 91 |
| F | 95 | 30 | 65 | 9 | 12 | 13 | 81 | 89 |
| G | 35 | 14 | 28 | 9 | 9 | 60 | 28 | 3 |
| H | 29 | 98 | 12 | 65 | 50 | 41 | 6 | 9 |

## course_id=E
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 91 | 50 | 5 | 71 | 58 | 70 | 47 | 27 |
| B | 15 | 8 | 16 | 4 | 12 | 43 | 99 | 12 |
| C | 21 | 71 | 66 | 45 | 35 | 52 | 3 | 74 |
| D | 39 | 9 | 15 | 3 | 7 | 84 | 57 | 37 |
| E | 7 | 16 | 7 | 66 | 91 | 38 | 56 | 33 |
| F | 27 | 13 | 77 | 87 | 23 | 27 | 27 | 54 |
| G | 5 | 35 | 26 | 46 | 77 | 84 | 26 | 50 |
| H | 18 | 90 | 56 | 76 | 55 | 76 | 87 | 6 |

## course_id=F
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 62 | 33 | 56 | 62 | 95 | 68 | 20 | 90 |
| B | 95 | 93 | 74 | 71 | 60 | 9 | 21 | 95 |
| C | 73 | 59 | 46 | 18 | 59 | 11 | 43 | 67 |
| D | 8 | 41 | 32 | 50 | 3 | 15 | 82 | 34 |
| E | 37 | 18 | 74 | 14 | 40 | 44 | 26 | 8 |
| F | 51 | 95 | 74 | 37 | 14 | 3 | 61 | 20 |
| G | 39 | 27 | 83 | 87 | 72 | 0 | 40 | 13 |
| H | 0 | 13 | 3 | 62 | 38 | 59 | 27 | 56 |

## course_id=G
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 10 | 91 | 20 | 1 | 48 | 49 | 20 | 77 |
| B | 2 | 66 | 33 | 90 | 57 | 48 | 64 | 99 |
| C | 11 | 28 | 68 | 81 | 42 | 89 | 3 | 34 |
| D | 74 | 27 | 7 | 23 | 50 | 56 | 47 | 78 |
| E | 93 | 89 | 26 | 95 | 42 | 3 | 73 | 80 |
| F | 8 | 26 | 18 | 52 | 7 | 36 | 69 | 68 |
| G | 97 | 41 | 24 | 63 | 44 | 88 | 30 | 48 |
| H | 44 | 97 | 49 | 81 | 92 | 48 | 13 | 86 |

## course_id=H
| room_id\time_slot_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 97 | 98 | 71 | 84 | 39 | 38 | 32 | 29 |
| B | 98 | 13 | 50 | 96 | 65 | 55 | 98 | 29 |
| C | 20 | 48 | 78 | 19 | 86 | 12 | 2 | 45 |
| D | 90 | 12 | 87 | 9 | 48 | 78 | 61 | 95 |
| E | 37 | 82 | 78 | 33 | 68 | 46 | 39 | 91 |
| F | 23 | 90 | 69 | 65 | 67 | 11 | 82 | 8 |
| G | 58 | 87 | 71 | 76 | 8 | 46 | 51 | 59 |
| H | 9 | 44 | 44 | 55 | 28 | 93 | 31 | 40 |

If you want the final schedule in a simple, copy-pasteable shape, here's the little JSON sketch I expect for the answer — nothing fancy, just a list of triples showing which course goes to which room and which time.

{
  ""solution"": [
    [<course_id>, <room_id>, <time_id>],
    ...
  ]
}

Think of each triple as ""course, room, time"" in that order. This JSON is just the shape I want you to follow — fill in the actual course/room/time identifiers from the instance when you give the real answer.

Please make sure you use the identifiers exactly as they appear in 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”.""","{'cost_tensor': [[[50, 49, 23, 94, 18, 68, 74, 73], [83, 1, 97, 42, 33, 34, 99, 27], [21, 25, 41, 59, 94, 37, 55, 11], [36, 47, 43, 71, 49, 77, 32, 85], [78, 70, 63, 65, 41, 3, 91, 41], [31, 31, 51, 83, 84, 60, 79, 2], [97, 99, 53, 74, 83, 50, 58, 11], [83, 4, 41, 52, 55, 76, 92, 45]], [[4, 4, 14, 33, 44, 46, 58, 7], [9, 41, 80, 68, 45, 15, 42, 65], [29, 89, 94, 39, 78, 48, 30, 3], [62, 40, 99, 59, 77, 12, 54, 8], [56, 32, 89, 37, 68, 49, 65, 40], [48, 81, 95, 64, 66, 23, 8, 76], [86, 2, 28, 58, 45, 76, 84, 2], [98, 56, 50, 10, 62, 83, 37, 62]], [[42, 13, 45, 36, 0, 15, 53, 3], [89, 1, 8, 47, 94, 77, 18, 82], [15, 89, 78, 44, 66, 43, 20, 29], [63, 29, 51, 41, 59, 25, 71, 48], [27, 69, 45, 26, 70, 70, 93, 39], [21, 32, 91, 78, 0, 72, 34, 20], [15, 28, 40, 71, 40, 37, 21, 33], [91, 97, 65, 29, 18, 82, 20, 0]], [[61, 66, 68, 43, 98, 64, 59, 25], [62, 35, 91, 34, 5, 52, 53, 72], [6, 14, 9, 0, 52, 79, 20, 94], [13, 88, 74, 71, 92, 46, 49, 40], [94, 85, 46, 10, 67, 63, 71, 91], [95, 30, 65, 9, 12, 13, 81, 89], [35, 14, 28, 9, 9, 60, 28, 3], [29, 98, 12, 65, 50, 41, 6, 9]], [[91, 50, 5, 71, 58, 70, 47, 27], [15, 8, 16, 4, 12, 43, 99, 12], [21, 71, 66, 45, 35, 52, 3, 74], [39, 9, 15, 3, 7, 84, 57, 37], [7, 16, 7, 66, 91, 38, 56, 33], [27, 13, 77, 87, 23, 27, 27, 54], [5, 35, 26, 46, 77, 84, 26, 50], [18, 90, 56, 76, 55, 76, 87, 6]], [[62, 33, 56, 62, 95, 68, 20, 90], [95, 93, 74, 71, 60, 9, 21, 95], [73, 59, 46, 18, 59, 11, 43, 67], [8, 41, 32, 50, 3, 15, 82, 34], [37, 18, 74, 14, 40, 44, 26, 8], [51, 95, 74, 37, 14, 3, 61, 20], [39, 27, 83, 87, 72, 0, 40, 13], [0, 13, 3, 62, 38, 59, 27, 56]], [[10, 91, 20, 1, 48, 49, 20, 77], [2, 66, 33, 90, 57, 48, 64, 99], [11, 28, 68, 81, 42, 89, 3, 34], [74, 27, 7, 23, 50, 56, 47, 78], [93, 89, 26, 95, 42, 3, 73, 80], [8, 26, 18, 52, 7, 36, 69, 68], [97, 41, 24, 63, 44, 88, 30, 48], [44, 97, 49, 81, 92, 48, 13, 86]], [[97, 98, 71, 84, 39, 38, 32, 29], [98, 13, 50, 96, 65, 55, 98, 29], [20, 48, 78, 19, 86, 12, 2, 45], [90, 12, 87, 9, 48, 78, 61, 95], [37, 82, 78, 33, 68, 46, 39, 91], [23, 90, 69, 65, 67, 11, 82, 8], [58, 87, 71, 76, 8, 46, 51, 59], [9, 44, 44, 55, 28, 93, 31, 40]]], 'objective': 19.0}","[[0, 1, 1], [1, 0, 0], [2, 5, 4], [3, 6, 7], [4, 3, 3], [5, 7, 2], [6, 4, 5], [7, 2, 6]]",19.0,"{'problem_type': 'AP3', 'n': 8, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 50}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 49}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 23}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 94}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 18}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 68}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 74}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 73}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 83}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 1}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 97}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 42}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 33}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 34}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 99}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 27}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 21}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 25}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 41}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 59}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 94}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 37}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 55}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 11}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 36}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 47}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 43}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 71}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 49}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 77}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 32}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 85}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 78}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 70}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 63}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 65}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 41}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 3}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 91}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 41}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 31}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 31}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 51}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 83}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 84}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 60}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 79}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 2}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 97}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 99}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 53}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 74}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 83}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 50}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 58}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 11}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 83}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 4}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 41}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 52}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 55}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 76}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 92}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 45}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 4}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 4}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 14}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 33}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 44}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 46}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 58}, {'i': 'B', 'j': 'A', 'k': 'H', 'cost': 7}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 9}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 41}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 80}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 68}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 45}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 15}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 42}, {'i': 'B', 'j': 'B', 'k': 'H', 'cost': 65}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 29}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 89}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 94}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 39}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 78}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 48}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 30}, {'i': 'B', 'j': 'C', 'k': 'H', 'cost': 3}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 62}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 40}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 99}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 59}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 77}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 12}, {'i': 'B', 'j': 'D', 'k': 'G', 'cost': 54}, {'i': 'B', 'j': 'D', 'k': 'H', 'cost': 8}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 56}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 32}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 89}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 37}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 68}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 49}, {'i': 'B', 'j': 'E', 'k': 'G', 'cost': 65}, {'i': 'B', 'j': 'E', 'k': 'H', 'cost': 40}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 48}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 81}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 95}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 64}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 66}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 23}, {'i': 'B', 'j': 'F', 'k': 'G', 'cost': 8}, {'i': 'B', 'j': 'F', 'k': 'H', 'cost': 76}, {'i': 'B', 'j': 'G', 'k': 'A', 'cost': 86}, {'i': 'B', 'j': 'G', 'k': 'B', 'cost': 2}, {'i': 'B', 'j': 'G', 'k': 'C', 'cost': 28}, {'i': 'B', 'j': 'G', 'k': 'D', 'cost': 58}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 45}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 76}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 84}, {'i': 'B', 'j': 'G', 'k': 'H', 'cost': 2}, {'i': 'B', 'j': 'H', 'k': 'A', 'cost': 98}, {'i': 'B', 'j': 'H', 'k': 'B', 'cost': 56}, {'i': 'B', 'j': 'H', 'k': 'C', 'cost': 50}, {'i': 'B', 'j': 'H', 'k': 'D', 'cost': 10}, {'i': 'B', 'j': 'H', 'k': 'E', 'cost': 62}, {'i': 'B', 'j': 'H', 'k': 'F', 'cost': 83}, {'i': 'B', 'j': 'H', 'k': 'G', 'cost': 37}, {'i': 'B', 'j': 'H', 'k': 'H', 'cost': 62}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 42}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 13}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 45}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 36}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 0}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 15}, {'i': 'C', 'j': 'A', 'k': 'G', 'cost': 53}, {'i': 'C', 'j': 'A', 'k': 'H', 'cost': 3}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 89}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 1}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 8}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 47}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 94}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 77}, {'i': 'C', 'j': 'B', 'k': 'G', 'cost': 18}, {'i': 'C', 'j': 'B', 'k': 'H', 'cost': 82}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 15}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 89}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 78}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 44}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 66}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 43}, {'i': 'C', 'j': 'C', 'k': 'G', 'cost': 20}, {'i': 'C', 'j': 'C', 'k': 'H', 'cost': 29}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 63}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 29}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 51}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 41}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 59}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 25}, {'i': 'C', 'j': 'D', 'k': 'G', 'cost': 71}, {'i': 'C', 'j': 'D', 'k': 'H', 'cost': 48}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 27}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 69}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 45}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 26}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 70}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 70}, {'i': 'C', 'j': 'E', 'k': 'G', 'cost': 93}, {'i': 'C', 'j': 'E', 'k': 'H', 'cost': 39}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 21}, {'i': 'C', 'j': 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'F', 'cost': 13}, {'i': 'D', 'j': 'F', 'k': 'G', 'cost': 81}, {'i': 'D', 'j': 'F', 'k': 'H', 'cost': 89}, {'i': 'D', 'j': 'G', 'k': 'A', 'cost': 35}, {'i': 'D', 'j': 'G', 'k': 'B', 'cost': 14}, {'i': 'D', 'j': 'G', 'k': 'C', 'cost': 28}, {'i': 'D', 'j': 'G', 'k': 'D', 'cost': 9}, {'i': 'D', 'j': 'G', 'k': 'E', 'cost': 9}, {'i': 'D', 'j': 'G', 'k': 'F', 'cost': 60}, {'i': 'D', 'j': 'G', 'k': 'G', 'cost': 28}, {'i': 'D', 'j': 'G', 'k': 'H', 'cost': 3}, {'i': 'D', 'j': 'H', 'k': 'A', 'cost': 29}, {'i': 'D', 'j': 'H', 'k': 'B', 'cost': 98}, {'i': 'D', 'j': 'H', 'k': 'C', 'cost': 12}, {'i': 'D', 'j': 'H', 'k': 'D', 'cost': 65}, {'i': 'D', 'j': 'H', 'k': 'E', 'cost': 50}, {'i': 'D', 'j': 'H', 'k': 'F', 'cost': 41}, {'i': 'D', 'j': 'H', 'k': 'G', 'cost': 6}, {'i': 'D', 'j': 'H', 'k': 'H', 'cost': 9}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 91}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 50}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 5}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 71}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 58}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 70}, {'i': 'E', 'j': 'A', 'k': 'G', 'cost': 47}, {'i': 'E', 'j': 'A', 'k': 'H', 'cost': 27}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 15}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 8}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 16}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 4}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 12}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 43}, {'i': 'E', 'j': 'B', 'k': 'G', 'cost': 99}, {'i': 'E', 'j': 'B', 'k': 'H', 'cost': 12}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 21}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 71}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 66}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 45}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 35}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 52}, {'i': 'E', 'j': 'C', 'k': 'G', 'cost': 3}, {'i': 'E', 'j': 'C', 'k': 'H', 'cost': 74}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 39}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 9}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 15}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 3}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 7}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 84}, {'i': 'E', 'j': 'D', 'k': 'G', 'cost': 57}, {'i': 'E', 'j': 'D', 'k': 'H', 'cost': 37}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 7}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 16}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 7}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 66}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 91}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 38}, {'i': 'E', 'j': 'E', 'k': 'G', 'cost': 56}, {'i': 'E', 'j': 'E', 'k': 'H', 'cost': 33}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 27}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 13}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 77}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 87}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 23}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 27}, {'i': 'E', 'j': 'F', 'k': 'G', 'cost': 27}, {'i': 'E', 'j': 'F', 'k': 'H', 'cost': 54}, {'i': 'E', 'j': 'G', 'k': 'A', 'cost': 5}, {'i': 'E', 'j': 'G', 'k': 'B', 'cost': 35}, {'i': 'E', 'j': 'G', 'k': 'C', 'cost': 26}, {'i': 'E', 'j': 'G', 'k': 'D', 'cost': 46}, {'i': 'E', 'j': 'G', 'k': 'E', 'cost': 77}, {'i': 'E', 'j': 'G', 'k': 'F', 'cost': 84}, {'i': 'E', 'j': 'G', 'k': 'G', 'cost': 26}, {'i': 'E', 'j': 'G', 'k': 'H', 'cost': 50}, {'i': 'E', 'j': 'H', 'k': 'A', 'cost': 18}, {'i': 'E', 'j': 'H', 'k': 'B', 'cost': 90}, {'i': 'E', 'j': 'H', 'k': 'C', 'cost': 56}, {'i': 'E', 'j': 'H', 'k': 'D', 'cost': 76}, {'i': 'E', 'j': 'H', 'k': 'E', 'cost': 55}, {'i': 'E', 'j': 'H', 'k': 'F', 'cost': 76}, {'i': 'E', 'j': 'H', 'k': 'G', 'cost': 87}, {'i': 'E', 'j': 'H', 'k': 'H', 'cost': 6}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 62}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 33}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 56}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 62}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 95}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 68}, {'i': 'F', 'j': 'A', 'k': 'G', 'cost': 20}, {'i': 'F', 'j': 'A', 'k': 'H', 'cost': 90}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 95}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 93}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 74}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 71}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 60}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 9}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 21}, {'i': 'F', 'j': 'B', 'k': 'H', 'cost': 95}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 73}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 59}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 46}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 18}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 59}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 11}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 43}, {'i': 'F', 'j': 'C', 'k': 'H', 'cost': 67}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 8}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 41}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 32}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 50}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 3}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 15}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 82}, {'i': 'F', 'j': 'D', 'k': 'H', 'cost': 34}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 37}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 18}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 74}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 14}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 40}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 44}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 26}, {'i': 'F', 'j': 'E', 'k': 'H', 'cost': 8}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 51}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 95}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 74}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 37}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 14}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 3}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 61}, {'i': 'F', 'j': 'F', 'k': 'H', 'cost': 20}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 39}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 27}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 83}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 87}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 72}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 0}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 40}, {'i': 'F', 'j': 'G', 'k': 'H', 'cost': 13}, {'i': 'F', 'j': 'H', 'k': 'A', 'cost': 0}, {'i': 'F', 'j': 'H', 'k': 'B', 'cost': 13}, {'i': 'F', 'j': 'H', 'k': 'C', 'cost': 3}, {'i': 'F', 'j': 'H', 'k': 'D', 'cost': 62}, {'i': 'F', 'j': 'H', 'k': 'E', 'cost': 38}, {'i': 'F', 'j': 'H', 'k': 'F', 'cost': 59}, {'i': 'F', 'j': 'H', 'k': 'G', 'cost': 27}, {'i': 'F', 'j': 'H', 'k': 'H', 'cost': 56}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 10}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 91}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 20}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 1}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 48}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 49}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 20}, {'i': 'G', 'j': 'A', 'k': 'H', 'cost': 77}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 2}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 66}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 33}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 90}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 57}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 48}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 64}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 99}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 11}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 28}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 68}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 81}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 42}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 89}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 3}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 34}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 74}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 27}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 7}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 23}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 50}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 56}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 47}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 78}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 93}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 89}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 26}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 95}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 42}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 3}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 73}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 80}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 8}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 26}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 18}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 52}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 7}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 36}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 69}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 68}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 97}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 41}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 24}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 63}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 44}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 88}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 30}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 48}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 44}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 97}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 49}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 81}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 92}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 48}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 13}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 86}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 97}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 98}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 71}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 84}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 39}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 38}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 32}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 29}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 98}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 13}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 50}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 96}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 65}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 55}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 98}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 29}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 20}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 48}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 78}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 19}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 86}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 12}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 2}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 45}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 90}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 12}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 87}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 9}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 48}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 78}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 61}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 95}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 37}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 82}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 78}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 33}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 68}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 46}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 39}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 91}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 23}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 90}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 69}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 65}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 67}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 11}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 82}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 8}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 58}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 87}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 71}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 76}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 8}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 46}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 51}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 59}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 9}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 44}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 44}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 55}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 28}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 93}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 31}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 40}]}","[['A', 'B', 'B'], ['B', 'A', 'A'], ['C', 'F', 'E'], ['D', 'G', 'H'], ['E', 'D', 'D'], ['F', 'H', 'C'], ['G', 'E', 'F'], ['H', 'C', 'G']]",15,csv,names
AP3,AP3,"There’s a production puzzle: a set of scenes, a set of DPs, and a set of locations, all the same size. The team must pair each scene with exactly one DP and one location, making sure no DP or location gets reused. Each possible pairing carries a setup charge, and the whole point is to choose the pairings so the sum of those charges across all scenes comes out the lowest. Everything must be assigned exactly once; the detailed options and costs follow below.

There are 6 scenes, identified as 0, 1, 2, 3, 4, 5.
Meaning: costs form a 3D tensor. For each fixed scene_id=i, you are given a dp_id×location_id matrix whose entry at row dp_id=j and column location_id=k equals setup_cost(i,j,k). You must pick exactly one (j,k) for every i, with all dp_id and all location_id used exactly once.
setup_cost_tensor (per-scene_id markdown matrices):
## scene_id=0
| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 32 | 57 | 80 | 32 | 48 | 95 |
| 1 | 87 | 71 | 10 | 99 | 74 | 46 |
| 2 | 12 | 18 | 62 | 58 | 7 | 61 |
| 3 | 97 | 36 | 95 | 86 | 9 | 55 |
| 4 | 46 | 2 | 52 | 9 | 30 | 91 |
| 5 | 12 | 18 | 64 | 74 | 45 | 86 |

## scene_id=1
| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 94 | 65 | 20 | 67 | 50 | 13 |
| 1 | 24 | 28 | 19 | 72 | 66 | 41 |
| 2 | 40 | 37 | 77 | 92 | 33 | 4 |
| 3 | 87 | 56 | 17 | 66 | 85 | 4 |
| 4 | 29 | 44 | 0 | 22 | 14 | 77 |
| 5 | 0 | 87 | 97 | 66 | 72 | 23 |

## scene_id=2
| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 86 | 65 | 18 | 49 | 54 | 31 |
| 1 | 40 | 38 | 24 | 80 | 69 | 65 |
| 2 | 90 | 77 | 83 | 81 | 84 | 30 |
| 3 | 67 | 34 | 58 | 62 | 55 | 51 |
| 4 | 55 | 83 | 11 | 88 | 32 | 98 |
| 5 | 62 | 68 | 79 | 75 | 62 | 42 |

## scene_id=3
| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 75 | 25 | 81 | 41 | 57 | 22 |
| 1 | 15 | 98 | 33 | 1 | 95 | 80 |
| 2 | 1 | 48 | 62 | 1 | 73 | 67 |
| 3 | 95 | 5 | 88 | 48 | 69 | 67 |
| 4 | 69 | 19 | 89 | 68 | 60 | 74 |
| 5 | 37 | 18 | 12 | 45 | 49 | 66 |

## scene_id=4
| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 53 | 59 | 33 | 79 | 26 | 10 |
| 1 | 54 | 8 | 72 | 74 | 91 | 77 |
| 2 | 79 | 90 | 13 | 87 | 42 | 3 |
| 3 | 45 | 80 | 92 | 86 | 45 | 37 |
| 4 | 84 | 11 | 23 | 24 | 76 | 29 |
| 5 | 84 | 93 | 14 | 58 | 11 | 17 |

## scene_id=5
| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 66 | 38 | 8 | 2 | 11 | 20 |
| 1 | 50 | 19 | 4 | 15 | 66 | 85 |
| 2 | 84 | 66 | 35 | 90 | 86 | 91 |
| 3 | 3 | 57 | 72 | 8 | 0 | 22 |
| 4 | 99 | 30 | 37 | 66 | 59 | 7 |
| 5 | 75 | 42 | 58 | 54 | 56 | 11 |
Select exactly one line for each of the 6 scenes so every DP and location is used once and the total setup charge is minimized.

Also, when you return the final assignments, please use this simple JSON shape so it's easy to parse and check.

{
  ""solution"": [
    [""<scene_id>"", ""<dp_id>"", ""<location_id>""],
    [""<scene_id>"", ""<dp_id>"", ""<location_id>""],
    [""<scene_id>"", ""<dp_id>"", ""<location_id>""]
  ]
}

Think of ""solution"" as a list of little forms: each inner array is one chosen triple (scene, DP, location) in that order. The angle-bracket placeholders above are just a sketch of the shape — replace them with the actual IDs from the instance when you submit your answer.

Please make sure to use the identifiers exactly as they appear in 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”.""","{'cost_tensor': [[[32, 57, 80, 32, 48, 95], [87, 71, 10, 99, 74, 46], [12, 18, 62, 58, 7, 61], [97, 36, 95, 86, 9, 55], [46, 2, 52, 9, 30, 91], [12, 18, 64, 74, 45, 86]], [[94, 65, 20, 67, 50, 13], [24, 28, 19, 72, 66, 41], [40, 37, 77, 92, 33, 4], [87, 56, 17, 66, 85, 4], [29, 44, 0, 22, 14, 77], [0, 87, 97, 66, 72, 23]], [[86, 65, 18, 49, 54, 31], [40, 38, 24, 80, 69, 65], [90, 77, 83, 81, 84, 30], [67, 34, 58, 62, 55, 51], [55, 83, 11, 88, 32, 98], [62, 68, 79, 75, 62, 42]], [[75, 25, 81, 41, 57, 22], [15, 98, 33, 1, 95, 80], [1, 48, 62, 1, 73, 67], [95, 5, 88, 48, 69, 67], [69, 19, 89, 68, 60, 74], [37, 18, 12, 45, 49, 66]], [[53, 59, 33, 79, 26, 10], [54, 8, 72, 74, 91, 77], [79, 90, 13, 87, 42, 3], [45, 80, 92, 86, 45, 37], [84, 11, 23, 24, 76, 29], [84, 93, 14, 58, 11, 17]], [[66, 38, 8, 2, 11, 20], [50, 19, 4, 15, 66, 85], [84, 66, 35, 90, 86, 91], [3, 57, 72, 8, 0, 22], [99, 30, 37, 66, 59, 7], [75, 42, 58, 54, 56, 11]]], 'objective': 24.0}","[[0, 4, 1], [1, 5, 0], [2, 0, 2], [3, 1, 3], [4, 2, 5], [5, 3, 4]]",24.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 32}, {'i': 0, 'j': 0, 'k': 1, 'cost': 57}, {'i': 0, 'j': 0, 'k': 2, 'cost': 80}, {'i': 0, 'j': 0, 'k': 3, 'cost': 32}, {'i': 0, 'j': 0, 'k': 4, 'cost': 48}, {'i': 0, 'j': 0, 'k': 5, 'cost': 95}, {'i': 0, 'j': 1, 'k': 0, 'cost': 87}, {'i': 0, 'j': 1, 'k': 1, 'cost': 71}, {'i': 0, 'j': 1, 'k': 2, 'cost': 10}, {'i': 0, 'j': 1, 'k': 3, 'cost': 99}, {'i': 0, 'j': 1, 'k': 4, 'cost': 74}, {'i': 0, 'j': 1, 'k': 5, 'cost': 46}, {'i': 0, 'j': 2, 'k': 0, 'cost': 12}, {'i': 0, 'j': 2, 'k': 1, 'cost': 18}, {'i': 0, 'j': 2, 'k': 2, 'cost': 62}, {'i': 0, 'j': 2, 'k': 3, 'cost': 58}, {'i': 0, 'j': 2, 'k': 4, 'cost': 7}, {'i': 0, 'j': 2, 'k': 5, 'cost': 61}, {'i': 0, 'j': 3, 'k': 0, 'cost': 97}, {'i': 0, 'j': 3, 'k': 1, 'cost': 36}, {'i': 0, 'j': 3, 'k': 2, 'cost': 95}, {'i': 0, 'j': 3, 'k': 3, 'cost': 86}, {'i': 0, 'j': 3, 'k': 4, 'cost': 9}, {'i': 0, 'j': 3, 'k': 5, 'cost': 55}, {'i': 0, 'j': 4, 'k': 0, 'cost': 46}, {'i': 0, 'j': 4, 'k': 1, 'cost': 2}, {'i': 0, 'j': 4, 'k': 2, 'cost': 52}, {'i': 0, 'j': 4, 'k': 3, 'cost': 9}, {'i': 0, 'j': 4, 'k': 4, 'cost': 30}, {'i': 0, 'j': 4, 'k': 5, 'cost': 91}, {'i': 0, 'j': 5, 'k': 0, 'cost': 12}, {'i': 0, 'j': 5, 'k': 1, 'cost': 18}, {'i': 0, 'j': 5, 'k': 2, 'cost': 64}, {'i': 0, 'j': 5, 'k': 3, 'cost': 74}, {'i': 0, 'j': 5, 'k': 4, 'cost': 45}, {'i': 0, 'j': 5, 'k': 5, 'cost': 86}, {'i': 1, 'j': 0, 'k': 0, 'cost': 94}, {'i': 1, 'j': 0, 'k': 1, 'cost': 65}, {'i': 1, 'j': 0, 'k': 2, 'cost': 20}, {'i': 1, 'j': 0, 'k': 3, 'cost': 67}, {'i': 1, 'j': 0, 'k': 4, 'cost': 50}, {'i': 1, 'j': 0, 'k': 5, 'cost': 13}, {'i': 1, 'j': 1, 'k': 0, 'cost': 24}, {'i': 1, 'j': 1, 'k': 1, 'cost': 28}, {'i': 1, 'j': 1, 'k': 2, 'cost': 19}, {'i': 1, 'j': 1, 'k': 3, 'cost': 72}, {'i': 1, 'j': 1, 'k': 4, 'cost': 66}, {'i': 1, 'j': 1, 'k': 5, 'cost': 41}, {'i': 1, 'j': 2, 'k': 0, 'cost': 40}, {'i': 1, 'j': 2, 'k': 1, 'cost': 37}, {'i': 1, 'j': 2, 'k': 2, 'cost': 77}, {'i': 1, 'j': 2, 'k': 3, 'cost': 92}, {'i': 1, 'j': 2, 'k': 4, 'cost': 33}, {'i': 1, 'j': 2, 'k': 5, 'cost': 4}, {'i': 1, 'j': 3, 'k': 0, 'cost': 87}, {'i': 1, 'j': 3, 'k': 1, 'cost': 56}, {'i': 1, 'j': 3, 'k': 2, 'cost': 17}, {'i': 1, 'j': 3, 'k': 3, 'cost': 66}, {'i': 1, 'j': 3, 'k': 4, 'cost': 85}, {'i': 1, 'j': 3, 'k': 5, 'cost': 4}, {'i': 1, 'j': 4, 'k': 0, 'cost': 29}, {'i': 1, 'j': 4, 'k': 1, 'cost': 44}, {'i': 1, 'j': 4, 'k': 2, 'cost': 0}, {'i': 1, 'j': 4, 'k': 3, 'cost': 22}, {'i': 1, 'j': 4, 'k': 4, 'cost': 14}, {'i': 1, 'j': 4, 'k': 5, 'cost': 77}, {'i': 1, 'j': 5, 'k': 0, 'cost': 0}, {'i': 1, 'j': 5, 'k': 1, 'cost': 87}, {'i': 1, 'j': 5, 'k': 2, 'cost': 97}, {'i': 1, 'j': 5, 'k': 3, 'cost': 66}, {'i': 1, 'j': 5, 'k': 4, 'cost': 72}, {'i': 1, 'j': 5, 'k': 5, 'cost': 23}, {'i': 2, 'j': 0, 'k': 0, 'cost': 86}, {'i': 2, 'j': 0, 'k': 1, 'cost': 65}, {'i': 2, 'j': 0, 'k': 2, 'cost': 18}, {'i': 2, 'j': 0, 'k': 3, 'cost': 49}, {'i': 2, 'j': 0, 'k': 4, 'cost': 54}, {'i': 2, 'j': 0, 'k': 5, 'cost': 31}, {'i': 2, 'j': 1, 'k': 0, 'cost': 40}, {'i': 2, 'j': 1, 'k': 1, 'cost': 38}, {'i': 2, 'j': 1, 'k': 2, 'cost': 24}, {'i': 2, 'j': 1, 'k': 3, 'cost': 80}, {'i': 2, 'j': 1, 'k': 4, 'cost': 69}, {'i': 2, 'j': 1, 'k': 5, 'cost': 65}, {'i': 2, 'j': 2, 'k': 0, 'cost': 90}, {'i': 2, 'j': 2, 'k': 1, 'cost': 77}, {'i': 2, 'j': 2, 'k': 2, 'cost': 83}, {'i': 2, 'j': 2, 'k': 3, 'cost': 81}, {'i': 2, 'j': 2, 'k': 4, 'cost': 84}, {'i': 2, 'j': 2, 'k': 5, 'cost': 30}, {'i': 2, 'j': 3, 'k': 0, 'cost': 67}, {'i': 2, 'j': 3, 'k': 1, 'cost': 34}, {'i': 2, 'j': 3, 'k': 2, 'cost': 58}, {'i': 2, 'j': 3, 'k': 3, 'cost': 62}, {'i': 2, 'j': 3, 'k': 4, 'cost': 55}, {'i': 2, 'j': 3, 'k': 5, 'cost': 51}, {'i': 2, 'j': 4, 'k': 0, 'cost': 55}, {'i': 2, 'j': 4, 'k': 1, 'cost': 83}, {'i': 2, 'j': 4, 'k': 2, 'cost': 11}, {'i': 2, 'j': 4, 'k': 3, 'cost': 88}, {'i': 2, 'j': 4, 'k': 4, 'cost': 32}, {'i': 2, 'j': 4, 'k': 5, 'cost': 98}, {'i': 2, 'j': 5, 'k': 0, 'cost': 62}, {'i': 2, 'j': 5, 'k': 1, 'cost': 68}, {'i': 2, 'j': 5, 'k': 2, 'cost': 79}, {'i': 2, 'j': 5, 'k': 3, 'cost': 75}, {'i': 2, 'j': 5, 'k': 4, 'cost': 62}, {'i': 2, 'j': 5, 'k': 5, 'cost': 42}, {'i': 3, 'j': 0, 'k': 0, 'cost': 75}, {'i': 3, 'j': 0, 'k': 1, 'cost': 25}, {'i': 3, 'j': 0, 'k': 2, 'cost': 81}, {'i': 3, 'j': 0, 'k': 3, 'cost': 41}, {'i': 3, 'j': 0, 'k': 4, 'cost': 57}, {'i': 3, 'j': 0, 'k': 5, 'cost': 22}, {'i': 3, 'j': 1, 'k': 0, 'cost': 15}, {'i': 3, 'j': 1, 'k': 1, 'cost': 98}, {'i': 3, 'j': 1, 'k': 2, 'cost': 33}, {'i': 3, 'j': 1, 'k': 3, 'cost': 1}, {'i': 3, 'j': 1, 'k': 4, 'cost': 95}, {'i': 3, 'j': 1, 'k': 5, 'cost': 80}, {'i': 3, 'j': 2, 'k': 0, 'cost': 1}, {'i': 3, 'j': 2, 'k': 1, 'cost': 48}, {'i': 3, 'j': 2, 'k': 2, 'cost': 62}, {'i': 3, 'j': 2, 'k': 3, 'cost': 1}, {'i': 3, 'j': 2, 'k': 4, 'cost': 73}, {'i': 3, 'j': 2, 'k': 5, 'cost': 67}, {'i': 3, 'j': 3, 'k': 0, 'cost': 95}, {'i': 3, 'j': 3, 'k': 1, 'cost': 5}, {'i': 3, 'j': 3, 'k': 2, 'cost': 88}, {'i': 3, 'j': 3, 'k': 3, 'cost': 48}, {'i': 3, 'j': 3, 'k': 4, 'cost': 69}, {'i': 3, 'j': 3, 'k': 5, 'cost': 67}, {'i': 3, 'j': 4, 'k': 0, 'cost': 69}, {'i': 3, 'j': 4, 'k': 1, 'cost': 19}, {'i': 3, 'j': 4, 'k': 2, 'cost': 89}, {'i': 3, 'j': 4, 'k': 3, 'cost': 68}, {'i': 3, 'j': 4, 'k': 4, 'cost': 60}, {'i': 3, 'j': 4, 'k': 5, 'cost': 74}, {'i': 3, 'j': 5, 'k': 0, 'cost': 37}, {'i': 3, 'j': 5, 'k': 1, 'cost': 18}, {'i': 3, 'j': 5, 'k': 2, 'cost': 12}, {'i': 3, 'j': 5, 'k': 3, 'cost': 45}, {'i': 3, 'j': 5, 'k': 4, 'cost': 49}, {'i': 3, 'j': 5, 'k': 5, 'cost': 66}, {'i': 4, 'j': 0, 'k': 0, 'cost': 53}, {'i': 4, 'j': 0, 'k': 1, 'cost': 59}, {'i': 4, 'j': 0, 'k': 2, 'cost': 33}, {'i': 4, 'j': 0, 'k': 3, 'cost': 79}, {'i': 4, 'j': 0, 'k': 4, 'cost': 26}, {'i': 4, 'j': 0, 'k': 5, 'cost': 10}, {'i': 4, 'j': 1, 'k': 0, 'cost': 54}, {'i': 4, 'j': 1, 'k': 1, 'cost': 8}, {'i': 4, 'j': 1, 'k': 2, 'cost': 72}, {'i': 4, 'j': 1, 'k': 3, 'cost': 74}, {'i': 4, 'j': 1, 'k': 4, 'cost': 91}, {'i': 4, 'j': 1, 'k': 5, 'cost': 77}, {'i': 4, 'j': 2, 'k': 0, 'cost': 79}, {'i': 4, 'j': 2, 'k': 1, 'cost': 90}, {'i': 4, 'j': 2, 'k': 2, 'cost': 13}, {'i': 4, 'j': 2, 'k': 3, 'cost': 87}, {'i': 4, 'j': 2, 'k': 4, 'cost': 42}, {'i': 4, 'j': 2, 'k': 5, 'cost': 3}, {'i': 4, 'j': 3, 'k': 0, 'cost': 45}, {'i': 4, 'j': 3, 'k': 1, 'cost': 80}, {'i': 4, 'j': 3, 'k': 2, 'cost': 92}, {'i': 4, 'j': 3, 'k': 3, 'cost': 86}, {'i': 4, 'j': 3, 'k': 4, 'cost': 45}, {'i': 4, 'j': 3, 'k': 5, 'cost': 37}, {'i': 4, 'j': 4, 'k': 0, 'cost': 84}, {'i': 4, 'j': 4, 'k': 1, 'cost': 11}, {'i': 4, 'j': 4, 'k': 2, 'cost': 23}, {'i': 4, 'j': 4, 'k': 3, 'cost': 24}, {'i': 4, 'j': 4, 'k': 4, 'cost': 76}, {'i': 4, 'j': 4, 'k': 5, 'cost': 29}, {'i': 4, 'j': 5, 'k': 0, 'cost': 84}, {'i': 4, 'j': 5, 'k': 1, 'cost': 93}, {'i': 4, 'j': 5, 'k': 2, 'cost': 14}, {'i': 4, 'j': 5, 'k': 3, 'cost': 58}, {'i': 4, 'j': 5, 'k': 4, 'cost': 11}, {'i': 4, 'j': 5, 'k': 5, 'cost': 17}, {'i': 5, 'j': 0, 'k': 0, 'cost': 66}, {'i': 5, 'j': 0, 'k': 1, 'cost': 38}, {'i': 5, 'j': 0, 'k': 2, 'cost': 8}, {'i': 5, 'j': 0, 'k': 3, 'cost': 2}, {'i': 5, 'j': 0, 'k': 4, 'cost': 11}, {'i': 5, 'j': 0, 'k': 5, 'cost': 20}, {'i': 5, 'j': 1, 'k': 0, 'cost': 50}, {'i': 5, 'j': 1, 'k': 1, 'cost': 19}, {'i': 5, 'j': 1, 'k': 2, 'cost': 4}, {'i': 5, 'j': 1, 'k': 3, 'cost': 15}, {'i': 5, 'j': 1, 'k': 4, 'cost': 66}, {'i': 5, 'j': 1, 'k': 5, 'cost': 85}, {'i': 5, 'j': 2, 'k': 0, 'cost': 84}, {'i': 5, 'j': 2, 'k': 1, 'cost': 66}, {'i': 5, 'j': 2, 'k': 2, 'cost': 35}, {'i': 5, 'j': 2, 'k': 3, 'cost': 90}, {'i': 5, 'j': 2, 'k': 4, 'cost': 86}, {'i': 5, 'j': 2, 'k': 5, 'cost': 91}, {'i': 5, 'j': 3, 'k': 0, 'cost': 3}, {'i': 5, 'j': 3, 'k': 1, 'cost': 57}, {'i': 5, 'j': 3, 'k': 2, 'cost': 72}, {'i': 5, 'j': 3, 'k': 3, 'cost': 8}, {'i': 5, 'j': 3, 'k': 4, 'cost': 0}, {'i': 5, 'j': 3, 'k': 5, 'cost': 22}, {'i': 5, 'j': 4, 'k': 0, 'cost': 99}, {'i': 5, 'j': 4, 'k': 1, 'cost': 30}, {'i': 5, 'j': 4, 'k': 2, 'cost': 37}, {'i': 5, 'j': 4, 'k': 3, 'cost': 66}, {'i': 5, 'j': 4, 'k': 4, 'cost': 59}, {'i': 5, 'j': 4, 'k': 5, 'cost': 7}, {'i': 5, 'j': 5, 'k': 0, 'cost': 75}, {'i': 5, 'j': 5, 'k': 1, 'cost': 42}, {'i': 5, 'j': 5, 'k': 2, 'cost': 58}, {'i': 5, 'j': 5, 'k': 3, 'cost': 54}, {'i': 5, 'j': 5, 'k': 4, 'cost': 56}, {'i': 5, 'j': 5, 'k': 5, 'cost': 11}]}","[[0, 4, 1], [1, 5, 0], [2, 0, 2], [3, 1, 3], [4, 2, 5], [5, 3, 4]]",16,nl,0
AP3,AP3,"On a busy catering team there are exactly as many menus as there are chefs and as there are suppliers, so the puzzle is to give each menu one chef and one supplier while using every chef and every supplier once. Each possible assignment comes with an ingredient cost, and the plan is to choose those assignments so the grand total of all ingredient costs is as small as it can be — add together the cost for each day’s chosen chef-and-supplier pair to get that total. The exact lineup and cost numbers are shown below.

The 7 menus are listed as A, B, C, D, E, F, G.
Meaning: costs form a 3D tensor. For each fixed menu_id=i, you are given a chef_id×supplier_id matrix whose entry at row chef_id=j and column supplier_id=k equals ingredient_cost(i,j,k). You must pick exactly one (j,k) for every i, with all chef_id and all supplier_id used exactly once.
ingredient_cost_tensor (per-menu_id markdown matrices):
## menu_id=A
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 23 | 11 | 48 | 53 | 10 | 9 | 67 |
| B | 7 | 94 | 47 | 85 | 25 | 60 | 93 |
| C | 79 | 93 | 40 | 53 | 29 | 45 | 10 |
| D | 23 | 78 | 99 | 12 | 5 | 30 | 19 |
| E | 78 | 64 | 88 | 18 | 72 | 17 | 18 |
| F | 61 | 52 | 55 | 7 | 3 | 56 | 9 |
| G | 3 | 29 | 50 | 80 | 81 | 10 | 69 |

## menu_id=B
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 52 | 0 | 28 | 3 | 19 | 92 | 76 |
| B | 97 | 19 | 55 | 54 | 77 | 60 | 8 |
| C | 8 | 17 | 72 | 48 | 69 | 76 | 41 |
| D | 75 | 41 | 66 | 5 | 50 | 55 | 37 |
| E | 92 | 46 | 88 | 75 | 5 | 33 | 59 |
| F | 51 | 10 | 24 | 25 | 13 | 30 | 5 |
| G | 22 | 76 | 69 | 2 | 15 | 52 | 88 |

## menu_id=C
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 24 | 50 | 37 | 78 | 74 | 15 | 87 |
| B | 16 | 8 | 47 | 34 | 80 | 2 | 27 |
| C | 70 | 24 | 59 | 61 | 75 | 64 | 55 |
| D | 12 | 26 | 50 | 99 | 64 | 99 | 18 |
| E | 12 | 66 | 7 | 34 | 5 | 21 | 85 |
| F | 14 | 25 | 56 | 96 | 17 | 42 | 57 |
| G | 81 | 90 | 23 | 45 | 10 | 27 | 76 |

## menu_id=D
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 52 | 67 | 48 | 61 | 46 | 63 | 0 |
| B | 53 | 93 | 96 | 75 | 91 | 85 | 89 |
| C | 14 | 5 | 95 | 77 | 37 | 87 | 70 |
| D | 95 | 63 | 31 | 66 | 88 | 34 | 62 |
| E | 23 | 4 | 74 | 86 | 78 | 90 | 94 |
| F | 70 | 94 | 37 | 35 | 63 | 23 | 38 |
| G | 51 | 23 | 52 | 50 | 53 | 77 | 10 |

## menu_id=E
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 33 | 32 | 86 | 32 | 17 | 19 | 10 |
| B | 31 | 29 | 22 | 39 | 54 | 78 | 63 |
| C | 92 | 80 | 49 | 54 | 43 | 39 | 91 |
| D | 76 | 88 | 98 | 58 | 78 | 89 | 30 |
| E | 77 | 98 | 25 | 16 | 87 | 32 | 69 |
| F | 30 | 57 | 0 | 91 | 3 | 94 | 19 |
| G | 8 | 17 | 87 | 75 | 6 | 92 | 14 |

## menu_id=F
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 82 | 70 | 91 | 77 | 66 | 47 | 25 |
| B | 84 | 9 | 64 | 50 | 79 | 2 | 1 |
| C | 70 | 88 | 60 | 99 | 84 | 79 | 64 |
| D | 58 | 37 | 99 | 8 | 75 | 74 | 7 |
| E | 11 | 41 | 77 | 15 | 43 | 80 | 87 |
| F | 84 | 69 | 64 | 21 | 34 | 68 | 68 |
| G | 75 | 45 | 29 | 68 | 97 | 65 | 30 |

## menu_id=G
| chef_id\supplier_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 52 | 86 | 41 | 10 | 96 | 97 | 76 |
| B | 94 | 61 | 2 | 13 | 87 | 33 | 28 |
| C | 8 | 75 | 87 | 2 | 75 | 21 | 90 |
| D | 13 | 24 | 36 | 25 | 61 | 94 | 6 |
| E | 8 | 54 | 16 | 36 | 1 | 72 | 81 |
| F | 48 | 66 | 98 | 72 | 26 | 97 | 97 |
| G | 64 | 2 | 11 | 25 | 69 | 47 | 6 |
Select one triple for each of the 7 menus so the sum of ingredient costs is minimized.

If you want to hand the solution back in a tidy, machine-friendly way, just drop it into a tiny JSON object like this:

{
  ""solution"": [
    [<menu_id>, <chef_id>, <supplier_id>],
    ...
  ]
}

Think of each inner triple as one menu's pick: the menu, the chef chosen for it, and the supplier chosen for it. This is just a sketch showing the shape I expect — when you give the actual answer, replace those placeholders with the real IDs from the instance.

Please make sure you use the identifiers exactly as they appear in the input — don't 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”.""","{'cost_tensor': [[[23, 11, 48, 53, 10, 9, 67], [7, 94, 47, 85, 25, 60, 93], [79, 93, 40, 53, 29, 45, 10], [23, 78, 99, 12, 5, 30, 19], [78, 64, 88, 18, 72, 17, 18], [61, 52, 55, 7, 3, 56, 9], [3, 29, 50, 80, 81, 10, 69]], [[52, 0, 28, 3, 19, 92, 76], [97, 19, 55, 54, 77, 60, 8], [8, 17, 72, 48, 69, 76, 41], [75, 41, 66, 5, 50, 55, 37], [92, 46, 88, 75, 5, 33, 59], [51, 10, 24, 25, 13, 30, 5], [22, 76, 69, 2, 15, 52, 88]], [[24, 50, 37, 78, 74, 15, 87], [16, 8, 47, 34, 80, 2, 27], [70, 24, 59, 61, 75, 64, 55], [12, 26, 50, 99, 64, 99, 18], [12, 66, 7, 34, 5, 21, 85], [14, 25, 56, 96, 17, 42, 57], [81, 90, 23, 45, 10, 27, 76]], [[52, 67, 48, 61, 46, 63, 0], [53, 93, 96, 75, 91, 85, 89], [14, 5, 95, 77, 37, 87, 70], [95, 63, 31, 66, 88, 34, 62], [23, 4, 74, 86, 78, 90, 94], [70, 94, 37, 35, 63, 23, 38], [51, 23, 52, 50, 53, 77, 10]], [[33, 32, 86, 32, 17, 19, 10], [31, 29, 22, 39, 54, 78, 63], [92, 80, 49, 54, 43, 39, 91], [76, 88, 98, 58, 78, 89, 30], [77, 98, 25, 16, 87, 32, 69], [30, 57, 0, 91, 3, 94, 19], [8, 17, 87, 75, 6, 92, 14]], [[82, 70, 91, 77, 66, 47, 25], [84, 9, 64, 50, 79, 2, 1], [70, 88, 60, 99, 84, 79, 64], [58, 37, 99, 8, 75, 74, 7], [11, 41, 77, 15, 43, 80, 87], [84, 69, 64, 21, 34, 68, 68], [75, 45, 29, 68, 97, 65, 30]], [[52, 86, 41, 10, 96, 97, 76], [94, 61, 2, 13, 87, 33, 28], [8, 75, 87, 2, 75, 21, 90], [13, 24, 36, 25, 61, 94, 6], [8, 54, 16, 36, 1, 72, 81], [48, 66, 98, 72, 26, 97, 97], [64, 2, 11, 25, 69, 47, 6]]], 'objective': 21.0}","[[0, 6, 0], [1, 0, 3], [2, 1, 5], [3, 2, 1], [4, 5, 2], [5, 3, 6], [6, 4, 4]]",21.0,"{'problem_type': 'AP3', 'n': 7, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 23}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 11}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 48}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 53}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 10}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 9}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 67}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 7}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 94}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 47}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 85}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 25}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 60}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 93}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 79}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 93}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 40}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 53}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 29}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 45}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 10}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 23}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 78}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 99}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 12}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 5}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 30}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 19}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 78}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 64}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 88}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 72}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 17}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 18}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 61}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 52}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 55}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 7}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 3}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 56}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 9}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 3}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 29}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 50}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 80}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 81}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 10}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 69}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 52}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 0}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 28}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 3}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 19}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 92}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 76}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 97}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 19}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 55}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 54}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 77}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 60}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 8}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 8}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 17}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 72}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 48}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 69}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 76}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 41}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 75}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 41}, 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'cost': 9}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 64}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 50}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 79}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 2}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 1}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 70}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 88}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 60}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 99}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 84}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 79}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 64}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 58}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 37}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 99}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 8}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 75}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 74}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 7}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 11}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 41}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 77}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 15}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 43}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 80}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 87}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 84}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 69}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 64}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 21}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 34}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 68}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 68}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 75}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 45}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 29}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 68}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 97}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 65}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 30}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 52}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 86}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 41}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 10}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 96}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 97}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 76}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 94}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 61}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 2}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 13}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 87}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 33}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 28}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 8}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 75}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 87}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 2}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 75}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 21}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 90}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 13}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 24}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 36}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 25}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 61}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 94}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 6}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 8}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 54}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 16}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 36}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 1}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 72}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 81}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 48}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 66}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 98}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 72}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 26}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 97}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 97}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 64}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 2}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 11}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 25}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 69}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 47}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 6}]}","[['A', 'G', 'A'], ['B', 'A', 'D'], ['C', 'B', 'F'], ['D', 'C', 'B'], ['E', 'F', 'C'], ['F', 'D', 'G'], ['G', 'E', 'E']]",17,nl,names
AP3,AP3,"Someone at the front desk needs a clean plan: every incoming patient must be matched to one specialist and one room, and no specialist or room can be assigned more than once. Each trio choice comes with an expected wait plus transfer penalty, and the plan’s quality is just the sum of those penalties across all patients — lower is better. The detailed list of patients, specialists, rooms and the corresponding wait/transfer values appears below.

{
  ""num_patients"": 6,
  ""patient_ids"": [
    0,
    1,
    2,
    3,
    4,
    5
  ]
}

# Meaning: costs form a 3D tensor. For each fixed patient_id=i, you are given a specialist_id×room_id matrix whose entry at row specialist_id=j and column room_id=k equals expected_wait_transfer_cost(i,j,k). You must pick exactly one (j,k) for every i, with all specialist_id and all room_id used exactly once.
# expected_wait_transfer_cost_tensor (per-patient_id markdown matrices)

## patient_id=0
| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 85 | 74 | 86 | 78 | 79 | 9 |
| 1 | 6 | 84 | 81 | 58 | 72 | 90 |
| 2 | 11 | 16 | 10 | 35 | 42 | 71 |
| 3 | 48 | 54 | 80 | 25 | 19 | 64 |
| 4 | 72 | 96 | 48 | 64 | 43 | 30 |
| 5 | 94 | 17 | 99 | 53 | 30 | 7 |

## patient_id=1
| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 39 | 84 | 20 | 35 | 62 | 73 |
| 1 | 54 | 99 | 31 | 80 | 52 | 34 |
| 2 | 55 | 47 | 60 | 1 | 56 | 53 |
| 3 | 92 | 14 | 35 | 45 | 44 | 11 |
| 4 | 33 | 30 | 72 | 86 | 25 | 99 |
| 5 | 46 | 37 | 55 | 71 | 87 | 36 |

## patient_id=2
| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 0 | 22 | 47 | 19 | 29 | 56 |
| 1 | 34 | 7 | 12 | 15 | 27 | 91 |
| 2 | 87 | 42 | 75 | 92 | 1 | 42 |
| 3 | 77 | 76 | 73 | 89 | 1 | 40 |
| 4 | 28 | 34 | 70 | 56 | 14 | 40 |
| 5 | 28 | 2 | 70 | 69 | 96 | 66 |

## patient_id=3
| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 38 | 6 | 46 | 27 | 50 | 4 |
| 1 | 52 | 61 | 95 | 54 | 39 | 36 |
| 2 | 27 | 53 | 24 | 60 | 87 | 4 |
| 3 | 1 | 74 | 20 | 2 | 60 | 54 |
| 4 | 81 | 49 | 62 | 78 | 73 | 28 |
| 5 | 39 | 84 | 17 | 70 | 96 | 3 |

## patient_id=4
| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 16 | 82 | 53 | 14 | 15 | 21 |
| 1 | 70 | 76 | 6 | 72 | 28 | 85 |
| 2 | 88 | 27 | 78 | 71 | 83 | 57 |
| 3 | 89 | 8 | 46 | 42 | 66 | 37 |
| 4 | 70 | 5 | 75 | 97 | 63 | 89 |
| 5 | 85 | 85 | 22 | 69 | 33 | 24 |

## patient_id=5
| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 47 | 9 | 40 | 9 | 34 | 2 |
| 1 | 93 | 44 | 15 | 9 | 14 | 94 |
| 2 | 34 | 43 | 93 | 93 | 79 | 67 |
| 3 | 35 | 56 | 48 | 95 | 14 | 58 |
| 4 | 68 | 79 | 49 | 91 | 75 | 96 |
| 5 | 43 | 76 | 2 | 51 | 26 | 40 |

Oh, and when you send the actual assignment back, please use this simple JSON sketch so it's easy to parse:

{
  ""solution"": [
    [""<patient_id>"", ""<specialist_id>"", ""<room_id>""],
    ...
  ]
}

Just to keep it friendly: ""solution"" is a list of triples — each triple picks the patient, the specialist, and the room assigned to them. Think of each small array as one filled-out row on a scheduling form.

This is just the expected shape, not the real answer — fill in the real IDs from the instance when you submit the plan. Please use the IDs exactly as they appear in the input — no renaming and no 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”.","{'cost_tensor': [[[85, 74, 86, 78, 79, 9], [6, 84, 81, 58, 72, 90], [11, 16, 10, 35, 42, 71], [48, 54, 80, 25, 19, 64], [72, 96, 48, 64, 43, 30], [94, 17, 99, 53, 30, 7]], [[39, 84, 20, 35, 62, 73], [54, 99, 31, 80, 52, 34], [55, 47, 60, 1, 56, 53], [92, 14, 35, 45, 44, 11], [33, 30, 72, 86, 25, 99], [46, 37, 55, 71, 87, 36]], [[0, 22, 47, 19, 29, 56], [34, 7, 12, 15, 27, 91], [87, 42, 75, 92, 1, 42], [77, 76, 73, 89, 1, 40], [28, 34, 70, 56, 14, 40], [28, 2, 70, 69, 96, 66]], [[38, 6, 46, 27, 50, 4], [52, 61, 95, 54, 39, 36], [27, 53, 24, 60, 87, 4], [1, 74, 20, 2, 60, 54], [81, 49, 62, 78, 73, 28], [39, 84, 17, 70, 96, 3]], [[16, 82, 53, 14, 15, 21], [70, 76, 6, 72, 28, 85], [88, 27, 78, 71, 83, 57], [89, 8, 46, 42, 66, 37], [70, 5, 75, 97, 63, 89], [85, 85, 22, 69, 33, 24]], [[47, 9, 40, 9, 34, 2], [93, 44, 15, 9, 14, 94], [34, 43, 93, 93, 79, 67], [35, 56, 48, 95, 14, 58], [68, 79, 49, 91, 75, 96], [43, 76, 2, 51, 26, 40]]], 'objective': 19.0}","[[0, 1, 0], [1, 2, 3], [2, 3, 4], [3, 0, 5], [4, 4, 1], [5, 5, 2]]",19.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 85}, {'i': 0, 'j': 0, 'k': 1, 'cost': 74}, {'i': 0, 'j': 0, 'k': 2, 'cost': 86}, {'i': 0, 'j': 0, 'k': 3, 'cost': 78}, {'i': 0, 'j': 0, 'k': 4, 'cost': 79}, {'i': 0, 'j': 0, 'k': 5, 'cost': 9}, {'i': 0, 'j': 1, 'k': 0, 'cost': 6}, {'i': 0, 'j': 1, 'k': 1, 'cost': 84}, {'i': 0, 'j': 1, 'k': 2, 'cost': 81}, {'i': 0, 'j': 1, 'k': 3, 'cost': 58}, {'i': 0, 'j': 1, 'k': 4, 'cost': 72}, {'i': 0, 'j': 1, 'k': 5, 'cost': 90}, {'i': 0, 'j': 2, 'k': 0, 'cost': 11}, {'i': 0, 'j': 2, 'k': 1, 'cost': 16}, {'i': 0, 'j': 2, 'k': 2, 'cost': 10}, {'i': 0, 'j': 2, 'k': 3, 'cost': 35}, {'i': 0, 'j': 2, 'k': 4, 'cost': 42}, {'i': 0, 'j': 2, 'k': 5, 'cost': 71}, {'i': 0, 'j': 3, 'k': 0, 'cost': 48}, {'i': 0, 'j': 3, 'k': 1, 'cost': 54}, {'i': 0, 'j': 3, 'k': 2, 'cost': 80}, {'i': 0, 'j': 3, 'k': 3, 'cost': 25}, {'i': 0, 'j': 3, 'k': 4, 'cost': 19}, {'i': 0, 'j': 3, 'k': 5, 'cost': 64}, {'i': 0, 'j': 4, 'k': 0, 'cost': 72}, {'i': 0, 'j': 4, 'k': 1, 'cost': 96}, {'i': 0, 'j': 4, 'k': 2, 'cost': 48}, {'i': 0, 'j': 4, 'k': 3, 'cost': 64}, {'i': 0, 'j': 4, 'k': 4, 'cost': 43}, {'i': 0, 'j': 4, 'k': 5, 'cost': 30}, {'i': 0, 'j': 5, 'k': 0, 'cost': 94}, {'i': 0, 'j': 5, 'k': 1, 'cost': 17}, {'i': 0, 'j': 5, 'k': 2, 'cost': 99}, {'i': 0, 'j': 5, 'k': 3, 'cost': 53}, {'i': 0, 'j': 5, 'k': 4, 'cost': 30}, {'i': 0, 'j': 5, 'k': 5, 'cost': 7}, {'i': 1, 'j': 0, 'k': 0, 'cost': 39}, {'i': 1, 'j': 0, 'k': 1, 'cost': 84}, {'i': 1, 'j': 0, 'k': 2, 'cost': 20}, {'i': 1, 'j': 0, 'k': 3, 'cost': 35}, {'i': 1, 'j': 0, 'k': 4, 'cost': 62}, {'i': 1, 'j': 0, 'k': 5, 'cost': 73}, {'i': 1, 'j': 1, 'k': 0, 'cost': 54}, {'i': 1, 'j': 1, 'k': 1, 'cost': 99}, {'i': 1, 'j': 1, 'k': 2, 'cost': 31}, {'i': 1, 'j': 1, 'k': 3, 'cost': 80}, {'i': 1, 'j': 1, 'k': 4, 'cost': 52}, {'i': 1, 'j': 1, 'k': 5, 'cost': 34}, {'i': 1, 'j': 2, 'k': 0, 'cost': 55}, {'i': 1, 'j': 2, 'k': 1, 'cost': 47}, {'i': 1, 'j': 2, 'k': 2, 'cost': 60}, {'i': 1, 'j': 2, 'k': 3, 'cost': 1}, {'i': 1, 'j': 2, 'k': 4, 'cost': 56}, {'i': 1, 'j': 2, 'k': 5, 'cost': 53}, {'i': 1, 'j': 3, 'k': 0, 'cost': 92}, {'i': 1, 'j': 3, 'k': 1, 'cost': 14}, {'i': 1, 'j': 3, 'k': 2, 'cost': 35}, {'i': 1, 'j': 3, 'k': 3, 'cost': 45}, {'i': 1, 'j': 3, 'k': 4, 'cost': 44}, {'i': 1, 'j': 3, 'k': 5, 'cost': 11}, {'i': 1, 'j': 4, 'k': 0, 'cost': 33}, {'i': 1, 'j': 4, 'k': 1, 'cost': 30}, {'i': 1, 'j': 4, 'k': 2, 'cost': 72}, {'i': 1, 'j': 4, 'k': 3, 'cost': 86}, {'i': 1, 'j': 4, 'k': 4, 'cost': 25}, {'i': 1, 'j': 4, 'k': 5, 'cost': 99}, {'i': 1, 'j': 5, 'k': 0, 'cost': 46}, {'i': 1, 'j': 5, 'k': 1, 'cost': 37}, {'i': 1, 'j': 5, 'k': 2, 'cost': 55}, {'i': 1, 'j': 5, 'k': 3, 'cost': 71}, {'i': 1, 'j': 5, 'k': 4, 'cost': 87}, {'i': 1, 'j': 5, 'k': 5, 'cost': 36}, {'i': 2, 'j': 0, 'k': 0, 'cost': 0}, {'i': 2, 'j': 0, 'k': 1, 'cost': 22}, {'i': 2, 'j': 0, 'k': 2, 'cost': 47}, {'i': 2, 'j': 0, 'k': 3, 'cost': 19}, {'i': 2, 'j': 0, 'k': 4, 'cost': 29}, {'i': 2, 'j': 0, 'k': 5, 'cost': 56}, {'i': 2, 'j': 1, 'k': 0, 'cost': 34}, {'i': 2, 'j': 1, 'k': 1, 'cost': 7}, {'i': 2, 'j': 1, 'k': 2, 'cost': 12}, {'i': 2, 'j': 1, 'k': 3, 'cost': 15}, {'i': 2, 'j': 1, 'k': 4, 'cost': 27}, {'i': 2, 'j': 1, 'k': 5, 'cost': 91}, {'i': 2, 'j': 2, 'k': 0, 'cost': 87}, {'i': 2, 'j': 2, 'k': 1, 'cost': 42}, {'i': 2, 'j': 2, 'k': 2, 'cost': 75}, {'i': 2, 'j': 2, 'k': 3, 'cost': 92}, {'i': 2, 'j': 2, 'k': 4, 'cost': 1}, {'i': 2, 'j': 2, 'k': 5, 'cost': 42}, {'i': 2, 'j': 3, 'k': 0, 'cost': 77}, {'i': 2, 'j': 3, 'k': 1, 'cost': 76}, {'i': 2, 'j': 3, 'k': 2, 'cost': 73}, {'i': 2, 'j': 3, 'k': 3, 'cost': 89}, {'i': 2, 'j': 3, 'k': 4, 'cost': 1}, {'i': 2, 'j': 3, 'k': 5, 'cost': 40}, {'i': 2, 'j': 4, 'k': 0, 'cost': 28}, {'i': 2, 'j': 4, 'k': 1, 'cost': 34}, {'i': 2, 'j': 4, 'k': 2, 'cost': 70}, {'i': 2, 'j': 4, 'k': 3, 'cost': 56}, {'i': 2, 'j': 4, 'k': 4, 'cost': 14}, {'i': 2, 'j': 4, 'k': 5, 'cost': 40}, {'i': 2, 'j': 5, 'k': 0, 'cost': 28}, {'i': 2, 'j': 5, 'k': 1, 'cost': 2}, {'i': 2, 'j': 5, 'k': 2, 'cost': 70}, {'i': 2, 'j': 5, 'k': 3, 'cost': 69}, {'i': 2, 'j': 5, 'k': 4, 'cost': 96}, {'i': 2, 'j': 5, 'k': 5, 'cost': 66}, {'i': 3, 'j': 0, 'k': 0, 'cost': 38}, {'i': 3, 'j': 0, 'k': 1, 'cost': 6}, {'i': 3, 'j': 0, 'k': 2, 'cost': 46}, {'i': 3, 'j': 0, 'k': 3, 'cost': 27}, {'i': 3, 'j': 0, 'k': 4, 'cost': 50}, {'i': 3, 'j': 0, 'k': 5, 'cost': 4}, {'i': 3, 'j': 1, 'k': 0, 'cost': 52}, {'i': 3, 'j': 1, 'k': 1, 'cost': 61}, {'i': 3, 'j': 1, 'k': 2, 'cost': 95}, {'i': 3, 'j': 1, 'k': 3, 'cost': 54}, {'i': 3, 'j': 1, 'k': 4, 'cost': 39}, {'i': 3, 'j': 1, 'k': 5, 'cost': 36}, {'i': 3, 'j': 2, 'k': 0, 'cost': 27}, {'i': 3, 'j': 2, 'k': 1, 'cost': 53}, {'i': 3, 'j': 2, 'k': 2, 'cost': 24}, {'i': 3, 'j': 2, 'k': 3, 'cost': 60}, {'i': 3, 'j': 2, 'k': 4, 'cost': 87}, {'i': 3, 'j': 2, 'k': 5, 'cost': 4}, {'i': 3, 'j': 3, 'k': 0, 'cost': 1}, {'i': 3, 'j': 3, 'k': 1, 'cost': 74}, {'i': 3, 'j': 3, 'k': 2, 'cost': 20}, {'i': 3, 'j': 3, 'k': 3, 'cost': 2}, {'i': 3, 'j': 3, 'k': 4, 'cost': 60}, {'i': 3, 'j': 3, 'k': 5, 'cost': 54}, {'i': 3, 'j': 4, 'k': 0, 'cost': 81}, {'i': 3, 'j': 4, 'k': 1, 'cost': 49}, {'i': 3, 'j': 4, 'k': 2, 'cost': 62}, {'i': 3, 'j': 4, 'k': 3, 'cost': 78}, {'i': 3, 'j': 4, 'k': 4, 'cost': 73}, {'i': 3, 'j': 4, 'k': 5, 'cost': 28}, {'i': 3, 'j': 5, 'k': 0, 'cost': 39}, {'i': 3, 'j': 5, 'k': 1, 'cost': 84}, {'i': 3, 'j': 5, 'k': 2, 'cost': 17}, {'i': 3, 'j': 5, 'k': 3, 'cost': 70}, {'i': 3, 'j': 5, 'k': 4, 'cost': 96}, {'i': 3, 'j': 5, 'k': 5, 'cost': 3}, {'i': 4, 'j': 0, 'k': 0, 'cost': 16}, {'i': 4, 'j': 0, 'k': 1, 'cost': 82}, {'i': 4, 'j': 0, 'k': 2, 'cost': 53}, {'i': 4, 'j': 0, 'k': 3, 'cost': 14}, {'i': 4, 'j': 0, 'k': 4, 'cost': 15}, {'i': 4, 'j': 0, 'k': 5, 'cost': 21}, {'i': 4, 'j': 1, 'k': 0, 'cost': 70}, {'i': 4, 'j': 1, 'k': 1, 'cost': 76}, {'i': 4, 'j': 1, 'k': 2, 'cost': 6}, {'i': 4, 'j': 1, 'k': 3, 'cost': 72}, {'i': 4, 'j': 1, 'k': 4, 'cost': 28}, {'i': 4, 'j': 1, 'k': 5, 'cost': 85}, {'i': 4, 'j': 2, 'k': 0, 'cost': 88}, {'i': 4, 'j': 2, 'k': 1, 'cost': 27}, {'i': 4, 'j': 2, 'k': 2, 'cost': 78}, {'i': 4, 'j': 2, 'k': 3, 'cost': 71}, {'i': 4, 'j': 2, 'k': 4, 'cost': 83}, {'i': 4, 'j': 2, 'k': 5, 'cost': 57}, {'i': 4, 'j': 3, 'k': 0, 'cost': 89}, {'i': 4, 'j': 3, 'k': 1, 'cost': 8}, {'i': 4, 'j': 3, 'k': 2, 'cost': 46}, {'i': 4, 'j': 3, 'k': 3, 'cost': 42}, {'i': 4, 'j': 3, 'k': 4, 'cost': 66}, {'i': 4, 'j': 3, 'k': 5, 'cost': 37}, {'i': 4, 'j': 4, 'k': 0, 'cost': 70}, {'i': 4, 'j': 4, 'k': 1, 'cost': 5}, {'i': 4, 'j': 4, 'k': 2, 'cost': 75}, {'i': 4, 'j': 4, 'k': 3, 'cost': 97}, {'i': 4, 'j': 4, 'k': 4, 'cost': 63}, {'i': 4, 'j': 4, 'k': 5, 'cost': 89}, {'i': 4, 'j': 5, 'k': 0, 'cost': 85}, {'i': 4, 'j': 5, 'k': 1, 'cost': 85}, {'i': 4, 'j': 5, 'k': 2, 'cost': 22}, {'i': 4, 'j': 5, 'k': 3, 'cost': 69}, {'i': 4, 'j': 5, 'k': 4, 'cost': 33}, {'i': 4, 'j': 5, 'k': 5, 'cost': 24}, {'i': 5, 'j': 0, 'k': 0, 'cost': 47}, {'i': 5, 'j': 0, 'k': 1, 'cost': 9}, {'i': 5, 'j': 0, 'k': 2, 'cost': 40}, {'i': 5, 'j': 0, 'k': 3, 'cost': 9}, {'i': 5, 'j': 0, 'k': 4, 'cost': 34}, {'i': 5, 'j': 0, 'k': 5, 'cost': 2}, {'i': 5, 'j': 1, 'k': 0, 'cost': 93}, {'i': 5, 'j': 1, 'k': 1, 'cost': 44}, {'i': 5, 'j': 1, 'k': 2, 'cost': 15}, {'i': 5, 'j': 1, 'k': 3, 'cost': 9}, {'i': 5, 'j': 1, 'k': 4, 'cost': 14}, {'i': 5, 'j': 1, 'k': 5, 'cost': 94}, {'i': 5, 'j': 2, 'k': 0, 'cost': 34}, {'i': 5, 'j': 2, 'k': 1, 'cost': 43}, {'i': 5, 'j': 2, 'k': 2, 'cost': 93}, {'i': 5, 'j': 2, 'k': 3, 'cost': 93}, {'i': 5, 'j': 2, 'k': 4, 'cost': 79}, {'i': 5, 'j': 2, 'k': 5, 'cost': 67}, {'i': 5, 'j': 3, 'k': 0, 'cost': 35}, {'i': 5, 'j': 3, 'k': 1, 'cost': 56}, {'i': 5, 'j': 3, 'k': 2, 'cost': 48}, {'i': 5, 'j': 3, 'k': 3, 'cost': 95}, {'i': 5, 'j': 3, 'k': 4, 'cost': 14}, {'i': 5, 'j': 3, 'k': 5, 'cost': 58}, {'i': 5, 'j': 4, 'k': 0, 'cost': 68}, {'i': 5, 'j': 4, 'k': 1, 'cost': 79}, {'i': 5, 'j': 4, 'k': 2, 'cost': 49}, {'i': 5, 'j': 4, 'k': 3, 'cost': 91}, {'i': 5, 'j': 4, 'k': 4, 'cost': 75}, {'i': 5, 'j': 4, 'k': 5, 'cost': 96}, {'i': 5, 'j': 5, 'k': 0, 'cost': 43}, {'i': 5, 'j': 5, 'k': 1, 'cost': 76}, {'i': 5, 'j': 5, 'k': 2, 'cost': 2}, {'i': 5, 'j': 5, 'k': 3, 'cost': 51}, {'i': 5, 'j': 5, 'k': 4, 'cost': 26}, {'i': 5, 'j': 5, 'k': 5, 'cost': 40}]}","[[0, 1, 0], [1, 2, 3], [2, 3, 4], [3, 0, 5], [4, 4, 1], [5, 5, 2]]",18,json,0
AP3,AP3,"At a busy production house the task is simple to say and tricky to do: give each content creator a single camera kit and a single editing slot, making sure every kit and every slot goes to exactly one creator. Every possible trio of person, kit and slot has a turnaround time, and the right set of choices is the one where the total turnaround — the sum of each chosen trio’s time — comes out the lowest. The full list of creators, kits, slots and their times appears below.

# num_creators_kits_slots=7
# index_identifiers=1, 2, 3, 4, 5, 6, 7

# Meaning: costs form a 3D tensor. For each fixed creator_id=i, you are given a camera_kit_id×editing_slot_id matrix whose entry at row camera_kit_id=j and column editing_slot_id=k equals turnaround_time(i,j,k). You must pick exactly one (j,k) for every i, with all camera_kit_id and all editing_slot_id used exactly once.
# turnaround_time_tensor (per-creator_id markdown matrices)

## creator_id=1
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 76 | 14 | 31 | 47 | 56 | 78 | 18 |
| 2 | 65 | 15 | 24 | 27 | 87 | 49 | 8 |
| 3 | 94 | 17 | 85 | 13 | 22 | 79 | 51 |
| 4 | 94 | 88 | 20 | 22 | 88 | 70 | 40 |
| 5 | 84 | 87 | 74 | 33 | 8 | 74 | 99 |
| 6 | 80 | 75 | 97 | 63 | 48 | 44 | 51 |
| 7 | 83 | 41 | 33 | 77 | 17 | 25 | 53 |

## creator_id=2
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 29 | 42 | 41 | 72 | 33 | 98 | 85 |
| 2 | 42 | 2 | 93 | 52 | 68 | 26 | 13 |
| 3 | 52 | 47 | 0 | 22 | 59 | 13 | 21 |
| 4 | 32 | 54 | 38 | 18 | 5 | 44 | 60 |
| 5 | 94 | 92 | 65 | 62 | 22 | 87 | 39 |
| 6 | 92 | 12 | 11 | 77 | 93 | 14 | 17 |
| 7 | 0 | 18 | 43 | 66 | 96 | 6 | 9 |

## creator_id=3
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 12 | 21 | 22 | 53 | 20 | 31 | 30 |
| 2 | 71 | 86 | 94 | 81 | 44 | 67 | 69 |
| 3 | 11 | 18 | 36 | 5 | 21 | 37 | 53 |
| 4 | 78 | 54 | 14 | 79 | 79 | 1 | 19 |
| 5 | 26 | 35 | 6 | 76 | 78 | 19 | 10 |
| 6 | 49 | 27 | 75 | 45 | 65 | 51 | 18 |
| 7 | 0 | 73 | 46 | 50 | 12 | 39 | 95 |

## creator_id=4
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 84 | 28 | 9 | 76 | 80 | 84 | 65 |
| 2 | 78 | 76 | 60 | 23 | 43 | 99 | 13 |
| 3 | 26 | 69 | 28 | 14 | 30 | 2 | 38 |
| 4 | 62 | 98 | 63 | 93 | 21 | 4 | 8 |
| 5 | 81 | 1 | 44 | 21 | 96 | 88 | 77 |
| 6 | 70 | 62 | 84 | 97 | 29 | 87 | 40 |
| 7 | 3 | 31 | 42 | 95 | 95 | 5 | 36 |

## creator_id=5
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 69 | 18 | 10 | 79 | 53 | 63 | 96 |
| 2 | 94 | 72 | 56 | 38 | 86 | 75 | 16 |
| 3 | 7 | 90 | 21 | 20 | 86 | 52 | 81 |
| 4 | 66 | 85 | 94 | 68 | 13 | 48 | 99 |
| 5 | 33 | 81 | 72 | 2 | 25 | 56 | 14 |
| 6 | 77 | 48 | 94 | 97 | 18 | 45 | 98 |
| 7 | 99 | 93 | 10 | 30 | 38 | 95 | 94 |

## creator_id=6
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 14 | 40 | 77 | 34 | 7 | 34 | 3 |
| 2 | 28 | 1 | 94 | 97 | 57 | 27 | 14 |
| 3 | 84 | 73 | 90 | 75 | 19 | 82 | 43 |
| 4 | 48 | 22 | 82 | 76 | 68 | 53 | 5 |
| 5 | 81 | 60 | 70 | 45 | 31 | 83 | 69 |
| 6 | 27 | 29 | 83 | 78 | 86 | 68 | 47 |
| 7 | 17 | 26 | 69 | 21 | 25 | 66 | 79 |

## creator_id=7
| camera_kit_id\editing_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 9 | 12 | 89 | 99 | 44 | 84 | 3 |
| 2 | 99 | 52 | 45 | 69 | 73 | 39 | 59 |
| 3 | 58 | 21 | 58 | 45 | 10 | 65 | 42 |
| 4 | 53 | 37 | 34 | 85 | 71 | 6 | 97 |
| 5 | 32 | 64 | 45 | 41 | 47 | 93 | 91 |
| 6 | 0 | 2 | 20 | 89 | 33 | 91 | 42 |
| 7 | 67 | 69 | 3 | 13 | 25 | 61 | 5 |

If you want to send back the chosen assignment, you can just paste it in a small JSON snippet like this:

{
  ""solution"": [
    [<creator_id>, <kit_id>, <slot_id>],
    ...
  ]
}

This is just a simple sketch: ""solution"" holds a list of triples, and each triple is one creator paired with the kit and the editing slot assigned to them, in that order. Replace the placeholders with the actual IDs from the instance when you reply.

Please be sure to use the identifiers exactly as they appear in the instance input — no renaming and 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”.""","{'cost_tensor': [[[76, 14, 31, 47, 56, 78, 18], [65, 15, 24, 27, 87, 49, 8], [94, 17, 85, 13, 22, 79, 51], [94, 88, 20, 22, 88, 70, 40], [84, 87, 74, 33, 8, 74, 99], [80, 75, 97, 63, 48, 44, 51], [83, 41, 33, 77, 17, 25, 53]], [[29, 42, 41, 72, 33, 98, 85], [42, 2, 93, 52, 68, 26, 13], [52, 47, 0, 22, 59, 13, 21], [32, 54, 38, 18, 5, 44, 60], [94, 92, 65, 62, 22, 87, 39], [92, 12, 11, 77, 93, 14, 17], [0, 18, 43, 66, 96, 6, 9]], [[12, 21, 22, 53, 20, 31, 30], [71, 86, 94, 81, 44, 67, 69], [11, 18, 36, 5, 21, 37, 53], [78, 54, 14, 79, 79, 1, 19], [26, 35, 6, 76, 78, 19, 10], [49, 27, 75, 45, 65, 51, 18], [0, 73, 46, 50, 12, 39, 95]], [[84, 28, 9, 76, 80, 84, 65], [78, 76, 60, 23, 43, 99, 13], [26, 69, 28, 14, 30, 2, 38], [62, 98, 63, 93, 21, 4, 8], [81, 1, 44, 21, 96, 88, 77], [70, 62, 84, 97, 29, 87, 40], [3, 31, 42, 95, 95, 5, 36]], [[69, 18, 10, 79, 53, 63, 96], [94, 72, 56, 38, 86, 75, 16], [7, 90, 21, 20, 86, 52, 81], [66, 85, 94, 68, 13, 48, 99], [33, 81, 72, 2, 25, 56, 14], [77, 48, 94, 97, 18, 45, 98], [99, 93, 10, 30, 38, 95, 94]], [[14, 40, 77, 34, 7, 34, 3], [28, 1, 94, 97, 57, 27, 14], [84, 73, 90, 75, 19, 82, 43], [48, 22, 82, 76, 68, 53, 5], [81, 60, 70, 45, 31, 83, 69], [27, 29, 83, 78, 86, 68, 47], [17, 26, 69, 21, 25, 66, 79]], [[9, 12, 89, 99, 44, 84, 3], [99, 52, 45, 69, 73, 39, 59], [58, 21, 58, 45, 10, 65, 42], [53, 37, 34, 85, 71, 6, 97], [32, 64, 45, 41, 47, 93, 91], [0, 2, 20, 89, 33, 91, 42], [67, 69, 3, 13, 25, 61, 5]]], 'objective': 23.0}","[[0, 1, 6], [1, 2, 2], [2, 3, 5], [3, 6, 0], [4, 4, 3], [5, 0, 4], [6, 5, 1]]",23.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [1, 2, 3, 4, 5, 6, 7], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 76}, {'i': 1, 'j': 1, 'k': 2, 'cost': 14}, {'i': 1, 'j': 1, 'k': 3, 'cost': 31}, {'i': 1, 'j': 1, 'k': 4, 'cost': 47}, {'i': 1, 'j': 1, 'k': 5, 'cost': 56}, {'i': 1, 'j': 1, 'k': 6, 'cost': 78}, {'i': 1, 'j': 1, 'k': 7, 'cost': 18}, {'i': 1, 'j': 2, 'k': 1, 'cost': 65}, {'i': 1, 'j': 2, 'k': 2, 'cost': 15}, {'i': 1, 'j': 2, 'k': 3, 'cost': 24}, {'i': 1, 'j': 2, 'k': 4, 'cost': 27}, {'i': 1, 'j': 2, 'k': 5, 'cost': 87}, {'i': 1, 'j': 2, 'k': 6, 'cost': 49}, {'i': 1, 'j': 2, 'k': 7, 'cost': 8}, {'i': 1, 'j': 3, 'k': 1, 'cost': 94}, {'i': 1, 'j': 3, 'k': 2, 'cost': 17}, {'i': 1, 'j': 3, 'k': 3, 'cost': 85}, {'i': 1, 'j': 3, 'k': 4, 'cost': 13}, {'i': 1, 'j': 3, 'k': 5, 'cost': 22}, {'i': 1, 'j': 3, 'k': 6, 'cost': 79}, {'i': 1, 'j': 3, 'k': 7, 'cost': 51}, {'i': 1, 'j': 4, 'k': 1, 'cost': 94}, {'i': 1, 'j': 4, 'k': 2, 'cost': 88}, {'i': 1, 'j': 4, 'k': 3, 'cost': 20}, {'i': 1, 'j': 4, 'k': 4, 'cost': 22}, {'i': 1, 'j': 4, 'k': 5, 'cost': 88}, {'i': 1, 'j': 4, 'k': 6, 'cost': 70}, {'i': 1, 'j': 4, 'k': 7, 'cost': 40}, {'i': 1, 'j': 5, 'k': 1, 'cost': 84}, {'i': 1, 'j': 5, 'k': 2, 'cost': 87}, {'i': 1, 'j': 5, 'k': 3, 'cost': 74}, {'i': 1, 'j': 5, 'k': 4, 'cost': 33}, {'i': 1, 'j': 5, 'k': 5, 'cost': 8}, {'i': 1, 'j': 5, 'k': 6, 'cost': 74}, {'i': 1, 'j': 5, 'k': 7, 'cost': 99}, {'i': 1, 'j': 6, 'k': 1, 'cost': 80}, {'i': 1, 'j': 6, 'k': 2, 'cost': 75}, {'i': 1, 'j': 6, 'k': 3, 'cost': 97}, {'i': 1, 'j': 6, 'k': 4, 'cost': 63}, {'i': 1, 'j': 6, 'k': 5, 'cost': 48}, {'i': 1, 'j': 6, 'k': 6, 'cost': 44}, {'i': 1, 'j': 6, 'k': 7, 'cost': 51}, {'i': 1, 'j': 7, 'k': 1, 'cost': 83}, {'i': 1, 'j': 7, 'k': 2, 'cost': 41}, {'i': 1, 'j': 7, 'k': 3, 'cost': 33}, {'i': 1, 'j': 7, 'k': 4, 'cost': 77}, {'i': 1, 'j': 7, 'k': 5, 'cost': 17}, {'i': 1, 'j': 7, 'k': 6, 'cost': 25}, {'i': 1, 'j': 7, 'k': 7, 'cost': 53}, {'i': 2, 'j': 1, 'k': 1, 'cost': 29}, {'i': 2, 'j': 1, 'k': 2, 'cost': 42}, {'i': 2, 'j': 1, 'k': 3, 'cost': 41}, {'i': 2, 'j': 1, 'k': 4, 'cost': 72}, {'i': 2, 'j': 1, 'k': 5, 'cost': 33}, {'i': 2, 'j': 1, 'k': 6, 'cost': 98}, {'i': 2, 'j': 1, 'k': 7, 'cost': 85}, {'i': 2, 'j': 2, 'k': 1, 'cost': 42}, {'i': 2, 'j': 2, 'k': 2, 'cost': 2}, {'i': 2, 'j': 2, 'k': 3, 'cost': 93}, {'i': 2, 'j': 2, 'k': 4, 'cost': 52}, {'i': 2, 'j': 2, 'k': 5, 'cost': 68}, {'i': 2, 'j': 2, 'k': 6, 'cost': 26}, {'i': 2, 'j': 2, 'k': 7, 'cost': 13}, {'i': 2, 'j': 3, 'k': 1, 'cost': 52}, {'i': 2, 'j': 3, 'k': 2, 'cost': 47}, {'i': 2, 'j': 3, 'k': 3, 'cost': 0}, {'i': 2, 'j': 3, 'k': 4, 'cost': 22}, {'i': 2, 'j': 3, 'k': 5, 'cost': 59}, {'i': 2, 'j': 3, 'k': 6, 'cost': 13}, {'i': 2, 'j': 3, 'k': 7, 'cost': 21}, {'i': 2, 'j': 4, 'k': 1, 'cost': 32}, {'i': 2, 'j': 4, 'k': 2, 'cost': 54}, {'i': 2, 'j': 4, 'k': 3, 'cost': 38}, {'i': 2, 'j': 4, 'k': 4, 'cost': 18}, {'i': 2, 'j': 4, 'k': 5, 'cost': 5}, {'i': 2, 'j': 4, 'k': 6, 'cost': 44}, {'i': 2, 'j': 4, 'k': 7, 'cost': 60}, {'i': 2, 'j': 5, 'k': 1, 'cost': 94}, {'i': 2, 'j': 5, 'k': 2, 'cost': 92}, {'i': 2, 'j': 5, 'k': 3, 'cost': 65}, {'i': 2, 'j': 5, 'k': 4, 'cost': 62}, {'i': 2, 'j': 5, 'k': 5, 'cost': 22}, {'i': 2, 'j': 5, 'k': 6, 'cost': 87}, {'i': 2, 'j': 5, 'k': 7, 'cost': 39}, {'i': 2, 'j': 6, 'k': 1, 'cost': 92}, {'i': 2, 'j': 6, 'k': 2, 'cost': 12}, {'i': 2, 'j': 6, 'k': 3, 'cost': 11}, {'i': 2, 'j': 6, 'k': 4, 'cost': 77}, {'i': 2, 'j': 6, 'k': 5, 'cost': 93}, {'i': 2, 'j': 6, 'k': 6, 'cost': 14}, {'i': 2, 'j': 6, 'k': 7, 'cost': 17}, {'i': 2, 'j': 7, 'k': 1, 'cost': 0}, {'i': 2, 'j': 7, 'k': 2, 'cost': 18}, {'i': 2, 'j': 7, 'k': 3, 'cost': 43}, {'i': 2, 'j': 7, 'k': 4, 'cost': 66}, {'i': 2, 'j': 7, 'k': 5, 'cost': 96}, {'i': 2, 'j': 7, 'k': 6, 'cost': 6}, {'i': 2, 'j': 7, 'k': 7, 'cost': 9}, {'i': 3, 'j': 1, 'k': 1, 'cost': 12}, {'i': 3, 'j': 1, 'k': 2, 'cost': 21}, {'i': 3, 'j': 1, 'k': 3, 'cost': 22}, {'i': 3, 'j': 1, 'k': 4, 'cost': 53}, {'i': 3, 'j': 1, 'k': 5, 'cost': 20}, {'i': 3, 'j': 1, 'k': 6, 'cost': 31}, {'i': 3, 'j': 1, 'k': 7, 'cost': 30}, {'i': 3, 'j': 2, 'k': 1, 'cost': 71}, {'i': 3, 'j': 2, 'k': 2, 'cost': 86}, {'i': 3, 'j': 2, 'k': 3, 'cost': 94}, {'i': 3, 'j': 2, 'k': 4, 'cost': 81}, {'i': 3, 'j': 2, 'k': 5, 'cost': 44}, {'i': 3, 'j': 2, 'k': 6, 'cost': 67}, {'i': 3, 'j': 2, 'k': 7, 'cost': 69}, {'i': 3, 'j': 3, 'k': 1, 'cost': 11}, {'i': 3, 'j': 3, 'k': 2, 'cost': 18}, {'i': 3, 'j': 3, 'k': 3, 'cost': 36}, {'i': 3, 'j': 3, 'k': 4, 'cost': 5}, {'i': 3, 'j': 3, 'k': 5, 'cost': 21}, {'i': 3, 'j': 3, 'k': 6, 'cost': 37}, {'i': 3, 'j': 3, 'k': 7, 'cost': 53}, {'i': 3, 'j': 4, 'k': 1, 'cost': 78}, {'i': 3, 'j': 4, 'k': 2, 'cost': 54}, {'i': 3, 'j': 4, 'k': 3, 'cost': 14}, {'i': 3, 'j': 4, 'k': 4, 'cost': 79}, {'i': 3, 'j': 4, 'k': 5, 'cost': 79}, {'i': 3, 'j': 4, 'k': 6, 'cost': 1}, {'i': 3, 'j': 4, 'k': 7, 'cost': 19}, {'i': 3, 'j': 5, 'k': 1, 'cost': 26}, {'i': 3, 'j': 5, 'k': 2, 'cost': 35}, {'i': 3, 'j': 5, 'k': 3, 'cost': 6}, {'i': 3, 'j': 5, 'k': 4, 'cost': 76}, {'i': 3, 'j': 5, 'k': 5, 'cost': 78}, {'i': 3, 'j': 5, 'k': 6, 'cost': 19}, {'i': 3, 'j': 5, 'k': 7, 'cost': 10}, {'i': 3, 'j': 6, 'k': 1, 'cost': 49}, {'i': 3, 'j': 6, 'k': 2, 'cost': 27}, {'i': 3, 'j': 6, 'k': 3, 'cost': 75}, {'i': 3, 'j': 6, 'k': 4, 'cost': 45}, {'i': 3, 'j': 6, 'k': 5, 'cost': 65}, {'i': 3, 'j': 6, 'k': 6, 'cost': 51}, {'i': 3, 'j': 6, 'k': 7, 'cost': 18}, {'i': 3, 'j': 7, 'k': 1, 'cost': 0}, {'i': 3, 'j': 7, 'k': 2, 'cost': 73}, {'i': 3, 'j': 7, 'k': 3, 'cost': 46}, {'i': 3, 'j': 7, 'k': 4, 'cost': 50}, {'i': 3, 'j': 7, 'k': 5, 'cost': 12}, {'i': 3, 'j': 7, 'k': 6, 'cost': 39}, {'i': 3, 'j': 7, 'k': 7, 'cost': 95}, {'i': 4, 'j': 1, 'k': 1, 'cost': 84}, {'i': 4, 'j': 1, 'k': 2, 'cost': 28}, {'i': 4, 'j': 1, 'k': 3, 'cost': 9}, {'i': 4, 'j': 1, 'k': 4, 'cost': 76}, {'i': 4, 'j': 1, 'k': 5, 'cost': 80}, {'i': 4, 'j': 1, 'k': 6, 'cost': 84}, {'i': 4, 'j': 1, 'k': 7, 'cost': 65}, {'i': 4, 'j': 2, 'k': 1, 'cost': 78}, {'i': 4, 'j': 2, 'k': 2, 'cost': 76}, {'i': 4, 'j': 2, 'k': 3, 'cost': 60}, {'i': 4, 'j': 2, 'k': 4, 'cost': 23}, {'i': 4, 'j': 2, 'k': 5, 'cost': 43}, {'i': 4, 'j': 2, 'k': 6, 'cost': 99}, {'i': 4, 'j': 2, 'k': 7, 'cost': 13}, {'i': 4, 'j': 3, 'k': 1, 'cost': 26}, {'i': 4, 'j': 3, 'k': 2, 'cost': 69}, {'i': 4, 'j': 3, 'k': 3, 'cost': 28}, {'i': 4, 'j': 3, 'k': 4, 'cost': 14}, {'i': 4, 'j': 3, 'k': 5, 'cost': 30}, {'i': 4, 'j': 3, 'k': 6, 'cost': 2}, {'i': 4, 'j': 3, 'k': 7, 'cost': 38}, {'i': 4, 'j': 4, 'k': 1, 'cost': 62}, {'i': 4, 'j': 4, 'k': 2, 'cost': 98}, {'i': 4, 'j': 4, 'k': 3, 'cost': 63}, {'i': 4, 'j': 4, 'k': 4, 'cost': 93}, {'i': 4, 'j': 4, 'k': 5, 'cost': 21}, {'i': 4, 'j': 4, 'k': 6, 'cost': 4}, {'i': 4, 'j': 4, 'k': 7, 'cost': 8}, {'i': 4, 'j': 5, 'k': 1, 'cost': 81}, {'i': 4, 'j': 5, 'k': 2, 'cost': 1}, {'i': 4, 'j': 5, 'k': 3, 'cost': 44}, {'i': 4, 'j': 5, 'k': 4, 'cost': 21}, {'i': 4, 'j': 5, 'k': 5, 'cost': 96}, {'i': 4, 'j': 5, 'k': 6, 'cost': 88}, {'i': 4, 'j': 5, 'k': 7, 'cost': 77}, {'i': 4, 'j': 6, 'k': 1, 'cost': 70}, {'i': 4, 'j': 6, 'k': 2, 'cost': 62}, {'i': 4, 'j': 6, 'k': 3, 'cost': 84}, {'i': 4, 'j': 6, 'k': 4, 'cost': 97}, {'i': 4, 'j': 6, 'k': 5, 'cost': 29}, {'i': 4, 'j': 6, 'k': 6, 'cost': 87}, {'i': 4, 'j': 6, 'k': 7, 'cost': 40}, {'i': 4, 'j': 7, 'k': 1, 'cost': 3}, {'i': 4, 'j': 7, 'k': 2, 'cost': 31}, {'i': 4, 'j': 7, 'k': 3, 'cost': 42}, {'i': 4, 'j': 7, 'k': 4, 'cost': 95}, {'i': 4, 'j': 7, 'k': 5, 'cost': 95}, {'i': 4, 'j': 7, 'k': 6, 'cost': 5}, {'i': 4, 'j': 7, 'k': 7, 'cost': 36}, {'i': 5, 'j': 1, 'k': 1, 'cost': 69}, {'i': 5, 'j': 1, 'k': 2, 'cost': 18}, {'i': 5, 'j': 1, 'k': 3, 'cost': 10}, {'i': 5, 'j': 1, 'k': 4, 'cost': 79}, {'i': 5, 'j': 1, 'k': 5, 'cost': 53}, {'i': 5, 'j': 1, 'k': 6, 'cost': 63}, {'i': 5, 'j': 1, 'k': 7, 'cost': 96}, {'i': 5, 'j': 2, 'k': 1, 'cost': 94}, {'i': 5, 'j': 2, 'k': 2, 'cost': 72}, {'i': 5, 'j': 2, 'k': 3, 'cost': 56}, {'i': 5, 'j': 2, 'k': 4, 'cost': 38}, {'i': 5, 'j': 2, 'k': 5, 'cost': 86}, {'i': 5, 'j': 2, 'k': 6, 'cost': 75}, {'i': 5, 'j': 2, 'k': 7, 'cost': 16}, {'i': 5, 'j': 3, 'k': 1, 'cost': 7}, {'i': 5, 'j': 3, 'k': 2, 'cost': 90}, {'i': 5, 'j': 3, 'k': 3, 'cost': 21}, {'i': 5, 'j': 3, 'k': 4, 'cost': 20}, {'i': 5, 'j': 3, 'k': 5, 'cost': 86}, {'i': 5, 'j': 3, 'k': 6, 'cost': 52}, {'i': 5, 'j': 3, 'k': 7, 'cost': 81}, {'i': 5, 'j': 4, 'k': 1, 'cost': 66}, {'i': 5, 'j': 4, 'k': 2, 'cost': 85}, {'i': 5, 'j': 4, 'k': 3, 'cost': 94}, {'i': 5, 'j': 4, 'k': 4, 'cost': 68}, {'i': 5, 'j': 4, 'k': 5, 'cost': 13}, {'i': 5, 'j': 4, 'k': 6, 'cost': 48}, {'i': 5, 'j': 4, 'k': 7, 'cost': 99}, {'i': 5, 'j': 5, 'k': 1, 'cost': 33}, {'i': 5, 'j': 5, 'k': 2, 'cost': 81}, {'i': 5, 'j': 5, 'k': 3, 'cost': 72}, {'i': 5, 'j': 5, 'k': 4, 'cost': 2}, {'i': 5, 'j': 5, 'k': 5, 'cost': 25}, {'i': 5, 'j': 5, 'k': 6, 'cost': 56}, {'i': 5, 'j': 5, 'k': 7, 'cost': 14}, {'i': 5, 'j': 6, 'k': 1, 'cost': 77}, {'i': 5, 'j': 6, 'k': 2, 'cost': 48}, {'i': 5, 'j': 6, 'k': 3, 'cost': 94}, {'i': 5, 'j': 6, 'k': 4, 'cost': 97}, {'i': 5, 'j': 6, 'k': 5, 'cost': 18}, {'i': 5, 'j': 6, 'k': 6, 'cost': 45}, {'i': 5, 'j': 6, 'k': 7, 'cost': 98}, {'i': 5, 'j': 7, 'k': 1, 'cost': 99}, {'i': 5, 'j': 7, 'k': 2, 'cost': 93}, {'i': 5, 'j': 7, 'k': 3, 'cost': 10}, {'i': 5, 'j': 7, 'k': 4, 'cost': 30}, {'i': 5, 'j': 7, 'k': 5, 'cost': 38}, {'i': 5, 'j': 7, 'k': 6, 'cost': 95}, {'i': 5, 'j': 7, 'k': 7, 'cost': 94}, {'i': 6, 'j': 1, 'k': 1, 'cost': 14}, {'i': 6, 'j': 1, 'k': 2, 'cost': 40}, {'i': 6, 'j': 1, 'k': 3, 'cost': 77}, {'i': 6, 'j': 1, 'k': 4, 'cost': 34}, {'i': 6, 'j': 1, 'k': 5, 'cost': 7}, {'i': 6, 'j': 1, 'k': 6, 'cost': 34}, {'i': 6, 'j': 1, 'k': 7, 'cost': 3}, {'i': 6, 'j': 2, 'k': 1, 'cost': 28}, {'i': 6, 'j': 2, 'k': 2, 'cost': 1}, {'i': 6, 'j': 2, 'k': 3, 'cost': 94}, {'i': 6, 'j': 2, 'k': 4, 'cost': 97}, {'i': 6, 'j': 2, 'k': 5, 'cost': 57}, {'i': 6, 'j': 2, 'k': 6, 'cost': 27}, {'i': 6, 'j': 2, 'k': 7, 'cost': 14}, {'i': 6, 'j': 3, 'k': 1, 'cost': 84}, {'i': 6, 'j': 3, 'k': 2, 'cost': 73}, {'i': 6, 'j': 3, 'k': 3, 'cost': 90}, {'i': 6, 'j': 3, 'k': 4, 'cost': 75}, {'i': 6, 'j': 3, 'k': 5, 'cost': 19}, {'i': 6, 'j': 3, 'k': 6, 'cost': 82}, {'i': 6, 'j': 3, 'k': 7, 'cost': 43}, {'i': 6, 'j': 4, 'k': 1, 'cost': 48}, {'i': 6, 'j': 4, 'k': 2, 'cost': 22}, {'i': 6, 'j': 4, 'k': 3, 'cost': 82}, {'i': 6, 'j': 4, 'k': 4, 'cost': 76}, {'i': 6, 'j': 4, 'k': 5, 'cost': 68}, {'i': 6, 'j': 4, 'k': 6, 'cost': 53}, {'i': 6, 'j': 4, 'k': 7, 'cost': 5}, {'i': 6, 'j': 5, 'k': 1, 'cost': 81}, {'i': 6, 'j': 5, 'k': 2, 'cost': 60}, {'i': 6, 'j': 5, 'k': 3, 'cost': 70}, {'i': 6, 'j': 5, 'k': 4, 'cost': 45}, {'i': 6, 'j': 5, 'k': 5, 'cost': 31}, {'i': 6, 'j': 5, 'k': 6, 'cost': 83}, {'i': 6, 'j': 5, 'k': 7, 'cost': 69}, {'i': 6, 'j': 6, 'k': 1, 'cost': 27}, {'i': 6, 'j': 6, 'k': 2, 'cost': 29}, {'i': 6, 'j': 6, 'k': 3, 'cost': 83}, {'i': 6, 'j': 6, 'k': 4, 'cost': 78}, {'i': 6, 'j': 6, 'k': 5, 'cost': 86}, {'i': 6, 'j': 6, 'k': 6, 'cost': 68}, {'i': 6, 'j': 6, 'k': 7, 'cost': 47}, {'i': 6, 'j': 7, 'k': 1, 'cost': 17}, {'i': 6, 'j': 7, 'k': 2, 'cost': 26}, {'i': 6, 'j': 7, 'k': 3, 'cost': 69}, {'i': 6, 'j': 7, 'k': 4, 'cost': 21}, {'i': 6, 'j': 7, 'k': 5, 'cost': 25}, {'i': 6, 'j': 7, 'k': 6, 'cost': 66}, {'i': 6, 'j': 7, 'k': 7, 'cost': 79}, {'i': 7, 'j': 1, 'k': 1, 'cost': 9}, {'i': 7, 'j': 1, 'k': 2, 'cost': 12}, {'i': 7, 'j': 1, 'k': 3, 'cost': 89}, {'i': 7, 'j': 1, 'k': 4, 'cost': 99}, {'i': 7, 'j': 1, 'k': 5, 'cost': 44}, {'i': 7, 'j': 1, 'k': 6, 'cost': 84}, {'i': 7, 'j': 1, 'k': 7, 'cost': 3}, {'i': 7, 'j': 2, 'k': 1, 'cost': 99}, {'i': 7, 'j': 2, 'k': 2, 'cost': 52}, {'i': 7, 'j': 2, 'k': 3, 'cost': 45}, {'i': 7, 'j': 2, 'k': 4, 'cost': 69}, {'i': 7, 'j': 2, 'k': 5, 'cost': 73}, {'i': 7, 'j': 2, 'k': 6, 'cost': 39}, {'i': 7, 'j': 2, 'k': 7, 'cost': 59}, {'i': 7, 'j': 3, 'k': 1, 'cost': 58}, {'i': 7, 'j': 3, 'k': 2, 'cost': 21}, {'i': 7, 'j': 3, 'k': 3, 'cost': 58}, {'i': 7, 'j': 3, 'k': 4, 'cost': 45}, {'i': 7, 'j': 3, 'k': 5, 'cost': 10}, {'i': 7, 'j': 3, 'k': 6, 'cost': 65}, {'i': 7, 'j': 3, 'k': 7, 'cost': 42}, {'i': 7, 'j': 4, 'k': 1, 'cost': 53}, {'i': 7, 'j': 4, 'k': 2, 'cost': 37}, {'i': 7, 'j': 4, 'k': 3, 'cost': 34}, {'i': 7, 'j': 4, 'k': 4, 'cost': 85}, {'i': 7, 'j': 4, 'k': 5, 'cost': 71}, {'i': 7, 'j': 4, 'k': 6, 'cost': 6}, {'i': 7, 'j': 4, 'k': 7, 'cost': 97}, {'i': 7, 'j': 5, 'k': 1, 'cost': 32}, {'i': 7, 'j': 5, 'k': 2, 'cost': 64}, {'i': 7, 'j': 5, 'k': 3, 'cost': 45}, {'i': 7, 'j': 5, 'k': 4, 'cost': 41}, {'i': 7, 'j': 5, 'k': 5, 'cost': 47}, {'i': 7, 'j': 5, 'k': 6, 'cost': 93}, {'i': 7, 'j': 5, 'k': 7, 'cost': 91}, {'i': 7, 'j': 6, 'k': 1, 'cost': 0}, {'i': 7, 'j': 6, 'k': 2, 'cost': 2}, {'i': 7, 'j': 6, 'k': 3, 'cost': 20}, {'i': 7, 'j': 6, 'k': 4, 'cost': 89}, {'i': 7, 'j': 6, 'k': 5, 'cost': 33}, {'i': 7, 'j': 6, 'k': 6, 'cost': 91}, {'i': 7, 'j': 6, 'k': 7, 'cost': 42}, {'i': 7, 'j': 7, 'k': 1, 'cost': 67}, {'i': 7, 'j': 7, 'k': 2, 'cost': 69}, {'i': 7, 'j': 7, 'k': 3, 'cost': 3}, {'i': 7, 'j': 7, 'k': 4, 'cost': 13}, {'i': 7, 'j': 7, 'k': 5, 'cost': 25}, {'i': 7, 'j': 7, 'k': 6, 'cost': 61}, {'i': 7, 'j': 7, 'k': 7, 'cost': 5}]}","[[1, 2, 7], [2, 3, 3], [3, 4, 6], [4, 7, 1], [5, 5, 4], [6, 1, 5], [7, 6, 2]]",19,csv,1
AP3,AP3,"Someone in the team described it like this: every prototype needs one tester and one test rig, and every tester and every rig can only be used once. So the task is to decide, for each prototype, which tester and which rig to pair with it, making sure there are no duplicates or leftovers. What counts as a better plan is simply the one with the smallest combined testing cost — calculate that by summing the cost of each prototype’s assigned tester-and-rig. The concrete cost table is shown below.

{
  ""num_prototypes"": 8,
  ""prototype_ids"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8
  ]
}

# Meaning: costs form a 3D tensor. For each fixed prototype_id=i, you are given a tester_id×rig_id matrix whose entry at row tester_id=j and column rig_id=k equals test_cost(i,j,k). You must pick exactly one (j,k) for every i, with all tester_id and all rig_id used exactly once.
# test_cost_tensor (per-prototype_id markdown matrices)

## prototype_id=1
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 59 | 46 | 24 | 6 | 18 | 41 | 0 | 45 |
| 2 | 5 | 67 | 2 | 86 | 97 | 62 | 40 | 15 |
| 3 | 42 | 99 | 30 | 60 | 78 | 3 | 4 | 32 |
| 4 | 36 | 18 | 46 | 40 | 56 | 98 | 93 | 54 |
| 5 | 17 | 66 | 27 | 61 | 28 | 51 | 38 | 13 |
| 6 | 13 | 65 | 93 | 10 | 18 | 31 | 68 | 22 |
| 7 | 16 | 21 | 92 | 80 | 13 | 91 | 57 | 73 |
| 8 | 91 | 60 | 71 | 19 | 6 | 38 | 36 | 3 |

## prototype_id=2
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 49 | 54 | 25 | 75 | 98 | 82 | 60 | 78 |
| 2 | 91 | 34 | 54 | 90 | 90 | 21 | 0 | 1 |
| 3 | 48 | 27 | 92 | 55 | 84 | 7 | 18 | 11 |
| 4 | 67 | 13 | 73 | 99 | 71 | 48 | 22 | 53 |
| 5 | 77 | 68 | 5 | 1 | 21 | 55 | 8 | 70 |
| 6 | 82 | 27 | 69 | 55 | 84 | 20 | 90 | 0 |
| 7 | 70 | 80 | 61 | 71 | 7 | 53 | 63 | 66 |
| 8 | 9 | 41 | 40 | 58 | 60 | 91 | 62 | 88 |

## prototype_id=3
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 84 | 61 | 40 | 54 | 62 | 26 | 5 | 40 |
| 2 | 87 | 60 | 45 | 11 | 3 | 78 | 42 | 40 |
| 3 | 48 | 62 | 84 | 61 | 51 | 72 | 22 | 11 |
| 4 | 44 | 41 | 14 | 52 | 32 | 44 | 91 | 34 |
| 5 | 24 | 40 | 2 | 26 | 76 | 76 | 24 | 33 |
| 6 | 96 | 59 | 5 | 76 | 0 | 89 | 89 | 35 |
| 7 | 17 | 47 | 72 | 50 | 48 | 76 | 57 | 71 |
| 8 | 50 | 58 | 67 | 62 | 40 | 77 | 4 | 5 |

## prototype_id=4
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 34 | 90 | 39 | 36 | 3 | 9 | 99 | 17 |
| 2 | 70 | 98 | 71 | 38 | 0 | 70 | 61 | 6 |
| 3 | 2 | 75 | 50 | 72 | 77 | 91 | 73 | 13 |
| 4 | 83 | 72 | 4 | 79 | 3 | 84 | 62 | 50 |
| 5 | 2 | 97 | 36 | 46 | 73 | 37 | 89 | 84 |
| 6 | 82 | 12 | 46 | 39 | 78 | 63 | 26 | 97 |
| 7 | 21 | 68 | 46 | 27 | 81 | 71 | 37 | 75 |
| 8 | 31 | 33 | 73 | 99 | 22 | 9 | 2 | 34 |

## prototype_id=5
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 15 | 54 | 45 | 77 | 7 | 77 | 88 | 28 |
| 2 | 74 | 93 | 57 | 66 | 99 | 65 | 68 | 19 |
| 3 | 31 | 20 | 73 | 59 | 81 | 21 | 55 | 31 |
| 4 | 29 | 38 | 5 | 1 | 42 | 68 | 66 | 86 |
| 5 | 23 | 58 | 81 | 12 | 66 | 70 | 7 | 80 |
| 6 | 96 | 11 | 43 | 29 | 79 | 52 | 85 | 46 |
| 7 | 50 | 81 | 97 | 4 | 14 | 23 | 39 | 85 |
| 8 | 68 | 77 | 28 | 38 | 88 | 45 | 44 | 44 |

## prototype_id=6
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 25 | 79 | 51 | 15 | 35 | 24 | 86 | 42 |
| 2 | 23 | 49 | 77 | 24 | 51 | 30 | 65 | 66 |
| 3 | 40 | 63 | 93 | 53 | 18 | 16 | 1 | 21 |
| 4 | 52 | 4 | 47 | 81 | 63 | 8 | 48 | 83 |
| 5 | 94 | 39 | 76 | 11 | 74 | 78 | 21 | 34 |
| 6 | 9 | 13 | 23 | 44 | 93 | 92 | 49 | 7 |
| 7 | 19 | 91 | 6 | 86 | 77 | 41 | 74 | 8 |
| 8 | 66 | 6 | 93 | 90 | 62 | 94 | 31 | 97 |

## prototype_id=7
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 67 | 76 | 96 | 50 | 18 | 90 | 35 | 15 |
| 2 | 52 | 40 | 63 | 79 | 71 | 41 | 44 | 11 |
| 3 | 84 | 69 | 17 | 77 | 44 | 45 | 49 | 28 |
| 4 | 1 | 62 | 93 | 28 | 21 | 80 | 89 | 15 |
| 5 | 71 | 82 | 98 | 83 | 58 | 33 | 32 | 27 |
| 6 | 76 | 73 | 48 | 59 | 82 | 29 | 37 | 45 |
| 7 | 39 | 72 | 3 | 5 | 43 | 38 | 62 | 64 |
| 8 | 89 | 6 | 37 | 95 | 8 | 67 | 82 | 94 |

## prototype_id=8
| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 54 | 79 | 77 | 0 | 90 | 68 | 64 | 55 |
| 2 | 67 | 66 | 62 | 61 | 22 | 52 | 14 | 15 |
| 3 | 18 | 63 | 3 | 55 | 40 | 11 | 34 | 30 |
| 4 | 69 | 1 | 93 | 25 | 11 | 24 | 66 | 11 |
| 5 | 39 | 12 | 40 | 4 | 63 | 92 | 61 | 60 |
| 6 | 51 | 95 | 61 | 64 | 40 | 89 | 64 | 23 |
| 7 | 46 | 98 | 53 | 81 | 43 | 11 | 89 | 95 |
| 8 | 74 | 23 | 30 | 14 | 89 | 59 | 93 | 10 |

Oh, and when you send the assignment back, please use this simple JSON shape so it's easy to parse:

{
  ""solution"": [
    [<prototype_id>, <tester_id>, <rig_id>],
    ...
  ]
}

This just sketches the shape I expect: ""solution"" is a list, and each inner triple picks the prototype together with the tester and the rig you want to pair it with. Think of each triple like filling out a single line on a form: which prototype, which tester, which rig. It's just a template — not the actual assignments.

Please make sure to use the exact identifiers from the instance input — no renaming, no made-up 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”.""","{'cost_tensor': [[[59, 46, 24, 6, 18, 41, 0, 45], [5, 67, 2, 86, 97, 62, 40, 15], [42, 99, 30, 60, 78, 3, 4, 32], [36, 18, 46, 40, 56, 98, 93, 54], [17, 66, 27, 61, 28, 51, 38, 13], [13, 65, 93, 10, 18, 31, 68, 22], [16, 21, 92, 80, 13, 91, 57, 73], [91, 60, 71, 19, 6, 38, 36, 3]], [[49, 54, 25, 75, 98, 82, 60, 78], [91, 34, 54, 90, 90, 21, 0, 1], [48, 27, 92, 55, 84, 7, 18, 11], [67, 13, 73, 99, 71, 48, 22, 53], [77, 68, 5, 1, 21, 55, 8, 70], [82, 27, 69, 55, 84, 20, 90, 0], [70, 80, 61, 71, 7, 53, 63, 66], [9, 41, 40, 58, 60, 91, 62, 88]], [[84, 61, 40, 54, 62, 26, 5, 40], [87, 60, 45, 11, 3, 78, 42, 40], [48, 62, 84, 61, 51, 72, 22, 11], [44, 41, 14, 52, 32, 44, 91, 34], [24, 40, 2, 26, 76, 76, 24, 33], [96, 59, 5, 76, 0, 89, 89, 35], [17, 47, 72, 50, 48, 76, 57, 71], [50, 58, 67, 62, 40, 77, 4, 5]], [[34, 90, 39, 36, 3, 9, 99, 17], [70, 98, 71, 38, 0, 70, 61, 6], [2, 75, 50, 72, 77, 91, 73, 13], [83, 72, 4, 79, 3, 84, 62, 50], [2, 97, 36, 46, 73, 37, 89, 84], [82, 12, 46, 39, 78, 63, 26, 97], [21, 68, 46, 27, 81, 71, 37, 75], [31, 33, 73, 99, 22, 9, 2, 34]], [[15, 54, 45, 77, 7, 77, 88, 28], [74, 93, 57, 66, 99, 65, 68, 19], [31, 20, 73, 59, 81, 21, 55, 31], [29, 38, 5, 1, 42, 68, 66, 86], [23, 58, 81, 12, 66, 70, 7, 80], [96, 11, 43, 29, 79, 52, 85, 46], [50, 81, 97, 4, 14, 23, 39, 85], [68, 77, 28, 38, 88, 45, 44, 44]], [[25, 79, 51, 15, 35, 24, 86, 42], [23, 49, 77, 24, 51, 30, 65, 66], [40, 63, 93, 53, 18, 16, 1, 21], [52, 4, 47, 81, 63, 8, 48, 83], [94, 39, 76, 11, 74, 78, 21, 34], [9, 13, 23, 44, 93, 92, 49, 7], [19, 91, 6, 86, 77, 41, 74, 8], [66, 6, 93, 90, 62, 94, 31, 97]], [[67, 76, 96, 50, 18, 90, 35, 15], [52, 40, 63, 79, 71, 41, 44, 11], [84, 69, 17, 77, 44, 45, 49, 28], [1, 62, 93, 28, 21, 80, 89, 15], [71, 82, 98, 83, 58, 33, 32, 27], [76, 73, 48, 59, 82, 29, 37, 45], [39, 72, 3, 5, 43, 38, 62, 64], [89, 6, 37, 95, 8, 67, 82, 94]], [[54, 79, 77, 0, 90, 68, 64, 55], [67, 66, 62, 61, 22, 52, 14, 15], [18, 63, 3, 55, 40, 11, 34, 30], [69, 1, 93, 25, 11, 24, 66, 11], [39, 12, 40, 4, 63, 92, 61, 60], [51, 95, 61, 64, 40, 89, 64, 23], [46, 98, 53, 81, 43, 11, 89, 95], [74, 23, 30, 14, 89, 59, 93, 10]]], 'objective': 24.0}","[[0, 0, 6], [1, 1, 7], [2, 5, 4], [3, 4, 0], [4, 3, 3], [5, 7, 1], [6, 6, 2], [7, 2, 5]]",24.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 59}, {'i': 1, 'j': 1, 'k': 2, 'cost': 46}, {'i': 1, 'j': 1, 'k': 3, 'cost': 24}, {'i': 1, 'j': 1, 'k': 4, 'cost': 6}, {'i': 1, 'j': 1, 'k': 5, 'cost': 18}, {'i': 1, 'j': 1, 'k': 6, 'cost': 41}, {'i': 1, 'j': 1, 'k': 7, 'cost': 0}, {'i': 1, 'j': 1, 'k': 8, 'cost': 45}, {'i': 1, 'j': 2, 'k': 1, 'cost': 5}, {'i': 1, 'j': 2, 'k': 2, 'cost': 67}, {'i': 1, 'j': 2, 'k': 3, 'cost': 2}, {'i': 1, 'j': 2, 'k': 4, 'cost': 86}, {'i': 1, 'j': 2, 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{'i': 6, 'j': 5, 'k': 4, 'cost': 11}, {'i': 6, 'j': 5, 'k': 5, 'cost': 74}, {'i': 6, 'j': 5, 'k': 6, 'cost': 78}, {'i': 6, 'j': 5, 'k': 7, 'cost': 21}, {'i': 6, 'j': 5, 'k': 8, 'cost': 34}, {'i': 6, 'j': 6, 'k': 1, 'cost': 9}, {'i': 6, 'j': 6, 'k': 2, 'cost': 13}, {'i': 6, 'j': 6, 'k': 3, 'cost': 23}, {'i': 6, 'j': 6, 'k': 4, 'cost': 44}, {'i': 6, 'j': 6, 'k': 5, 'cost': 93}, {'i': 6, 'j': 6, 'k': 6, 'cost': 92}, {'i': 6, 'j': 6, 'k': 7, 'cost': 49}, {'i': 6, 'j': 6, 'k': 8, 'cost': 7}, {'i': 6, 'j': 7, 'k': 1, 'cost': 19}, {'i': 6, 'j': 7, 'k': 2, 'cost': 91}, {'i': 6, 'j': 7, 'k': 3, 'cost': 6}, {'i': 6, 'j': 7, 'k': 4, 'cost': 86}, {'i': 6, 'j': 7, 'k': 5, 'cost': 77}, {'i': 6, 'j': 7, 'k': 6, 'cost': 41}, {'i': 6, 'j': 7, 'k': 7, 'cost': 74}, {'i': 6, 'j': 7, 'k': 8, 'cost': 8}, {'i': 6, 'j': 8, 'k': 1, 'cost': 66}, {'i': 6, 'j': 8, 'k': 2, 'cost': 6}, {'i': 6, 'j': 8, 'k': 3, 'cost': 93}, {'i': 6, 'j': 8, 'k': 4, 'cost': 90}, {'i': 6, 'j': 8, 'k': 5, 'cost': 62}, {'i': 6, 'j': 8, 'k': 6, 'cost': 94}, {'i': 6, 'j': 8, 'k': 7, 'cost': 31}, {'i': 6, 'j': 8, 'k': 8, 'cost': 97}, {'i': 7, 'j': 1, 'k': 1, 'cost': 67}, {'i': 7, 'j': 1, 'k': 2, 'cost': 76}, {'i': 7, 'j': 1, 'k': 3, 'cost': 96}, {'i': 7, 'j': 1, 'k': 4, 'cost': 50}, {'i': 7, 'j': 1, 'k': 5, 'cost': 18}, {'i': 7, 'j': 1, 'k': 6, 'cost': 90}, {'i': 7, 'j': 1, 'k': 7, 'cost': 35}, {'i': 7, 'j': 1, 'k': 8, 'cost': 15}, {'i': 7, 'j': 2, 'k': 1, 'cost': 52}, {'i': 7, 'j': 2, 'k': 2, 'cost': 40}, {'i': 7, 'j': 2, 'k': 3, 'cost': 63}, {'i': 7, 'j': 2, 'k': 4, 'cost': 79}, {'i': 7, 'j': 2, 'k': 5, 'cost': 71}, {'i': 7, 'j': 2, 'k': 6, 'cost': 41}, {'i': 7, 'j': 2, 'k': 7, 'cost': 44}, {'i': 7, 'j': 2, 'k': 8, 'cost': 11}, {'i': 7, 'j': 3, 'k': 1, 'cost': 84}, {'i': 7, 'j': 3, 'k': 2, 'cost': 69}, {'i': 7, 'j': 3, 'k': 3, 'cost': 17}, {'i': 7, 'j': 3, 'k': 4, 'cost': 77}, {'i': 7, 'j': 3, 'k': 5, 'cost': 44}, {'i': 7, 'j': 3, 'k': 6, 'cost': 45}, {'i': 7, 'j': 3, 'k': 7, 'cost': 49}, {'i': 7, 'j': 3, 'k': 8, 'cost': 28}, {'i': 7, 'j': 4, 'k': 1, 'cost': 1}, {'i': 7, 'j': 4, 'k': 2, 'cost': 62}, {'i': 7, 'j': 4, 'k': 3, 'cost': 93}, {'i': 7, 'j': 4, 'k': 4, 'cost': 28}, {'i': 7, 'j': 4, 'k': 5, 'cost': 21}, {'i': 7, 'j': 4, 'k': 6, 'cost': 80}, {'i': 7, 'j': 4, 'k': 7, 'cost': 89}, {'i': 7, 'j': 4, 'k': 8, 'cost': 15}, {'i': 7, 'j': 5, 'k': 1, 'cost': 71}, {'i': 7, 'j': 5, 'k': 2, 'cost': 82}, {'i': 7, 'j': 5, 'k': 3, 'cost': 98}, {'i': 7, 'j': 5, 'k': 4, 'cost': 83}, {'i': 7, 'j': 5, 'k': 5, 'cost': 58}, {'i': 7, 'j': 5, 'k': 6, 'cost': 33}, {'i': 7, 'j': 5, 'k': 7, 'cost': 32}, {'i': 7, 'j': 5, 'k': 8, 'cost': 27}, {'i': 7, 'j': 6, 'k': 1, 'cost': 76}, {'i': 7, 'j': 6, 'k': 2, 'cost': 73}, {'i': 7, 'j': 6, 'k': 3, 'cost': 48}, {'i': 7, 'j': 6, 'k': 4, 'cost': 59}, {'i': 7, 'j': 6, 'k': 5, 'cost': 82}, {'i': 7, 'j': 6, 'k': 6, 'cost': 29}, {'i': 7, 'j': 6, 'k': 7, 'cost': 37}, {'i': 7, 'j': 6, 'k': 8, 'cost': 45}, {'i': 7, 'j': 7, 'k': 1, 'cost': 39}, {'i': 7, 'j': 7, 'k': 2, 'cost': 72}, {'i': 7, 'j': 7, 'k': 3, 'cost': 3}, {'i': 7, 'j': 7, 'k': 4, 'cost': 5}, {'i': 7, 'j': 7, 'k': 5, 'cost': 43}, {'i': 7, 'j': 7, 'k': 6, 'cost': 38}, {'i': 7, 'j': 7, 'k': 7, 'cost': 62}, {'i': 7, 'j': 7, 'k': 8, 'cost': 64}, {'i': 7, 'j': 8, 'k': 1, 'cost': 89}, {'i': 7, 'j': 8, 'k': 2, 'cost': 6}, {'i': 7, 'j': 8, 'k': 3, 'cost': 37}, {'i': 7, 'j': 8, 'k': 4, 'cost': 95}, {'i': 7, 'j': 8, 'k': 5, 'cost': 8}, {'i': 7, 'j': 8, 'k': 6, 'cost': 67}, {'i': 7, 'j': 8, 'k': 7, 'cost': 82}, {'i': 7, 'j': 8, 'k': 8, 'cost': 94}, {'i': 8, 'j': 1, 'k': 1, 'cost': 54}, {'i': 8, 'j': 1, 'k': 2, 'cost': 79}, {'i': 8, 'j': 1, 'k': 3, 'cost': 77}, {'i': 8, 'j': 1, 'k': 4, 'cost': 0}, {'i': 8, 'j': 1, 'k': 5, 'cost': 90}, {'i': 8, 'j': 1, 'k': 6, 'cost': 68}, {'i': 8, 'j': 1, 'k': 7, 'cost': 64}, {'i': 8, 'j': 1, 'k': 8, 'cost': 55}, {'i': 8, 'j': 2, 'k': 1, 'cost': 67}, {'i': 8, 'j': 2, 'k': 2, 'cost': 66}, {'i': 8, 'j': 2, 'k': 3, 'cost': 62}, {'i': 8, 'j': 2, 'k': 4, 'cost': 61}, {'i': 8, 'j': 2, 'k': 5, 'cost': 22}, {'i': 8, 'j': 2, 'k': 6, 'cost': 52}, {'i': 8, 'j': 2, 'k': 7, 'cost': 14}, {'i': 8, 'j': 2, 'k': 8, 'cost': 15}, {'i': 8, 'j': 3, 'k': 1, 'cost': 18}, {'i': 8, 'j': 3, 'k': 2, 'cost': 63}, {'i': 8, 'j': 3, 'k': 3, 'cost': 3}, {'i': 8, 'j': 3, 'k': 4, 'cost': 55}, {'i': 8, 'j': 3, 'k': 5, 'cost': 40}, {'i': 8, 'j': 3, 'k': 6, 'cost': 11}, {'i': 8, 'j': 3, 'k': 7, 'cost': 34}, {'i': 8, 'j': 3, 'k': 8, 'cost': 30}, {'i': 8, 'j': 4, 'k': 1, 'cost': 69}, {'i': 8, 'j': 4, 'k': 2, 'cost': 1}, {'i': 8, 'j': 4, 'k': 3, 'cost': 93}, {'i': 8, 'j': 4, 'k': 4, 'cost': 25}, {'i': 8, 'j': 4, 'k': 5, 'cost': 11}, {'i': 8, 'j': 4, 'k': 6, 'cost': 24}, {'i': 8, 'j': 4, 'k': 7, 'cost': 66}, {'i': 8, 'j': 4, 'k': 8, 'cost': 11}, {'i': 8, 'j': 5, 'k': 1, 'cost': 39}, {'i': 8, 'j': 5, 'k': 2, 'cost': 12}, {'i': 8, 'j': 5, 'k': 3, 'cost': 40}, {'i': 8, 'j': 5, 'k': 4, 'cost': 4}, {'i': 8, 'j': 5, 'k': 5, 'cost': 63}, {'i': 8, 'j': 5, 'k': 6, 'cost': 92}, {'i': 8, 'j': 5, 'k': 7, 'cost': 61}, {'i': 8, 'j': 5, 'k': 8, 'cost': 60}, {'i': 8, 'j': 6, 'k': 1, 'cost': 51}, {'i': 8, 'j': 6, 'k': 2, 'cost': 95}, {'i': 8, 'j': 6, 'k': 3, 'cost': 61}, {'i': 8, 'j': 6, 'k': 4, 'cost': 64}, {'i': 8, 'j': 6, 'k': 5, 'cost': 40}, {'i': 8, 'j': 6, 'k': 6, 'cost': 89}, {'i': 8, 'j': 6, 'k': 7, 'cost': 64}, {'i': 8, 'j': 6, 'k': 8, 'cost': 23}, {'i': 8, 'j': 7, 'k': 1, 'cost': 46}, {'i': 8, 'j': 7, 'k': 2, 'cost': 98}, {'i': 8, 'j': 7, 'k': 3, 'cost': 53}, {'i': 8, 'j': 7, 'k': 4, 'cost': 81}, {'i': 8, 'j': 7, 'k': 5, 'cost': 43}, {'i': 8, 'j': 7, 'k': 6, 'cost': 11}, {'i': 8, 'j': 7, 'k': 7, 'cost': 89}, {'i': 8, 'j': 7, 'k': 8, 'cost': 95}, {'i': 8, 'j': 8, 'k': 1, 'cost': 74}, {'i': 8, 'j': 8, 'k': 2, 'cost': 23}, {'i': 8, 'j': 8, 'k': 3, 'cost': 30}, {'i': 8, 'j': 8, 'k': 4, 'cost': 14}, {'i': 8, 'j': 8, 'k': 5, 'cost': 89}, {'i': 8, 'j': 8, 'k': 6, 'cost': 59}, {'i': 8, 'j': 8, 'k': 7, 'cost': 93}, {'i': 8, 'j': 8, 'k': 8, 'cost': 10}]}","[[1, 1, 7], [2, 2, 8], [3, 6, 5], [4, 5, 1], [5, 4, 4], [6, 8, 2], [7, 7, 3], [8, 3, 6]]",20,json,1
AP3,AP3,"I manage a small photo studio and have a stack of bookings that all need a photographer and an equipment kit. The job is to pick one photographer and one kit for each shoot so that every photographer and every kit gets used once and nothing is left sitting idle or doubled up. For each shoot the cost is the photographer’s fee plus the kit rental, and the idea is to pick pairings that keep the overall bill as low as possible by adding up those fees across all shoots. The exact shoots, people, kits, and prices are shown below.

I have 6 shoots to schedule, labeled 0, 1, 2, 3, 4, 5.

*Meaning: costs form a 3D tensor. For each fixed shoot_id=i, you are given a photographer_id×kit_id matrix whose entry at row photographer_id=j and column kit_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all photographer_id and all kit_id used exactly once.*

**assignment_cost_tensor (per-shoot_id markdown matrices)**

## shoot_id=0
| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 39 | 62 | 10 | 40 | 78 | 51 |
| 1 | 19 | 72 | 15 | 33 | 58 | 53 |
| 2 | 39 | 60 | 40 | 8 | 59 | 94 |
| 3 | 17 | 98 | 91 | 90 | 57 | 65 |
| 4 | 44 | 59 | 52 | 82 | 58 | 37 |
| 5 | 17 | 80 | 98 | 93 | 62 | 22 |

## shoot_id=1
| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 35 | 17 | 5 | 28 | 30 | 92 |
| 1 | 12 | 52 | 95 | 91 | 54 | 67 |
| 2 | 25 | 19 | 77 | 11 | 33 | 67 |
| 3 | 69 | 86 | 26 | 73 | 99 | 24 |
| 4 | 21 | 64 | 14 | 96 | 72 | 70 |
| 5 | 67 | 92 | 40 | 39 | 9 | 95 |

## shoot_id=2
| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 55 | 16 | 80 | 36 | 24 | 10 |
| 1 | 84 | 45 | 84 | 50 | 39 | 64 |
| 2 | 26 | 5 | 27 | 28 | 5 | 52 |
| 3 | 88 | 35 | 94 | 2 | 97 | 82 |
| 4 | 42 | 37 | 62 | 65 | 16 | 49 |
| 5 | 43 | 88 | 88 | 39 | 27 | 71 |

## shoot_id=3
| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 44 | 24 | 15 | 25 | 23 | 37 |
| 1 | 15 | 31 | 26 | 94 | 66 | 58 |
| 2 | 98 | 38 | 45 | 88 | 99 | 1 |
| 3 | 69 | 95 | 21 | 28 | 13 | 57 |
| 4 | 52 | 64 | 2 | 58 | 31 | 57 |
| 5 | 87 | 34 | 39 | 91 | 95 | 96 |

## shoot_id=4
| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 23 | 15 | 78 | 27 | 85 | 6 |
| 1 | 10 | 1 | 39 | 38 | 0 | 52 |
| 2 | 1 | 91 | 72 | 99 | 49 | 84 |
| 3 | 99 | 79 | 89 | 10 | 35 | 88 |
| 4 | 52 | 35 | 90 | 3 | 96 | 22 |
| 5 | 90 | 85 | 9 | 77 | 15 | 88 |

## shoot_id=5
| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 29 | 0 | 47 | 44 | 44 | 22 |
| 1 | 94 | 89 | 0 | 67 | 64 | 2 |
| 2 | 40 | 40 | 17 | 43 | 9 | 94 |
| 3 | 57 | 97 | 55 | 24 | 7 | 21 |
| 4 | 8 | 33 | 28 | 55 | 97 | 30 |
| 5 | 43 | 18 | 74 | 15 | 55 | 3 |

I'll pick pairings that minimize the total cost across all 6 shoots.

Oh, and when you send back the actual matchings, a simple JSON sketch like this works great:

{
  ""solution"": [
    [<shoot_id>, <photographer_id>, <kit_id>],
    ...
  ]
}

""solution"" is just a list of triples: each triple assigns one photographer and one equipment kit to a single shoot. Think of each inner list as [shoot_id, photographer_id, kit_id]. This block is only the expected shape — a template — not the real answer.

Please use the exact identifiers given 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"".","{'cost_tensor': [[[39, 62, 10, 40, 78, 51], [19, 72, 15, 33, 58, 53], [39, 60, 40, 8, 59, 94], [17, 98, 91, 90, 57, 65], [44, 59, 52, 82, 58, 37], [17, 80, 98, 93, 62, 22]], [[35, 17, 5, 28, 30, 92], [12, 52, 95, 91, 54, 67], [25, 19, 77, 11, 33, 67], [69, 86, 26, 73, 99, 24], [21, 64, 14, 96, 72, 70], [67, 92, 40, 39, 9, 95]], [[55, 16, 80, 36, 24, 10], [84, 45, 84, 50, 39, 64], [26, 5, 27, 28, 5, 52], [88, 35, 94, 2, 97, 82], [42, 37, 62, 65, 16, 49], [43, 88, 88, 39, 27, 71]], [[44, 24, 15, 25, 23, 37], [15, 31, 26, 94, 66, 58], [98, 38, 45, 88, 99, 1], [69, 95, 21, 28, 13, 57], [52, 64, 2, 58, 31, 57], [87, 34, 39, 91, 95, 96]], [[23, 15, 78, 27, 85, 6], [10, 1, 39, 38, 0, 52], [1, 91, 72, 99, 49, 84], [99, 79, 89, 10, 35, 88], [52, 35, 90, 3, 96, 22], [90, 85, 9, 77, 15, 88]], [[29, 0, 47, 44, 44, 22], [94, 89, 0, 67, 64, 2], [40, 40, 17, 43, 9, 94], [57, 97, 55, 24, 7, 21], [8, 33, 28, 55, 97, 30], [43, 18, 74, 15, 55, 3]]], 'objective': 31.0}","[[0, 0, 2], [1, 5, 4], [2, 3, 3], [3, 2, 5], [4, 1, 1], [5, 4, 0]]",31.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 39}, {'i': 0, 'j': 0, 'k': 1, 'cost': 62}, {'i': 0, 'j': 0, 'k': 2, 'cost': 10}, {'i': 0, 'j': 0, 'k': 3, 'cost': 40}, {'i': 0, 'j': 0, 'k': 4, 'cost': 78}, {'i': 0, 'j': 0, 'k': 5, 'cost': 51}, {'i': 0, 'j': 1, 'k': 0, 'cost': 19}, {'i': 0, 'j': 1, 'k': 1, 'cost': 72}, {'i': 0, 'j': 1, 'k': 2, 'cost': 15}, {'i': 0, 'j': 1, 'k': 3, 'cost': 33}, {'i': 0, 'j': 1, 'k': 4, 'cost': 58}, {'i': 0, 'j': 1, 'k': 5, 'cost': 53}, {'i': 0, 'j': 2, 'k': 0, 'cost': 39}, {'i': 0, 'j': 2, 'k': 1, 'cost': 60}, {'i': 0, 'j': 2, 'k': 2, 'cost': 40}, {'i': 0, 'j': 2, 'k': 3, 'cost': 8}, {'i': 0, 'j': 2, 'k': 4, 'cost': 59}, {'i': 0, 'j': 2, 'k': 5, 'cost': 94}, {'i': 0, 'j': 3, 'k': 0, 'cost': 17}, {'i': 0, 'j': 3, 'k': 1, 'cost': 98}, {'i': 0, 'j': 3, 'k': 2, 'cost': 91}, {'i': 0, 'j': 3, 'k': 3, 'cost': 90}, {'i': 0, 'j': 3, 'k': 4, 'cost': 57}, {'i': 0, 'j': 3, 'k': 5, 'cost': 65}, {'i': 0, 'j': 4, 'k': 0, 'cost': 44}, {'i': 0, 'j': 4, 'k': 1, 'cost': 59}, {'i': 0, 'j': 4, 'k': 2, 'cost': 52}, {'i': 0, 'j': 4, 'k': 3, 'cost': 82}, {'i': 0, 'j': 4, 'k': 4, 'cost': 58}, {'i': 0, 'j': 4, 'k': 5, 'cost': 37}, {'i': 0, 'j': 5, 'k': 0, 'cost': 17}, {'i': 0, 'j': 5, 'k': 1, 'cost': 80}, {'i': 0, 'j': 5, 'k': 2, 'cost': 98}, {'i': 0, 'j': 5, 'k': 3, 'cost': 93}, {'i': 0, 'j': 5, 'k': 4, 'cost': 62}, {'i': 0, 'j': 5, 'k': 5, 'cost': 22}, {'i': 1, 'j': 0, 'k': 0, 'cost': 35}, {'i': 1, 'j': 0, 'k': 1, 'cost': 17}, {'i': 1, 'j': 0, 'k': 2, 'cost': 5}, {'i': 1, 'j': 0, 'k': 3, 'cost': 28}, {'i': 1, 'j': 0, 'k': 4, 'cost': 30}, {'i': 1, 'j': 0, 'k': 5, 'cost': 92}, {'i': 1, 'j': 1, 'k': 0, 'cost': 12}, {'i': 1, 'j': 1, 'k': 1, 'cost': 52}, {'i': 1, 'j': 1, 'k': 2, 'cost': 95}, {'i': 1, 'j': 1, 'k': 3, 'cost': 91}, {'i': 1, 'j': 1, 'k': 4, 'cost': 54}, {'i': 1, 'j': 1, 'k': 5, 'cost': 67}, {'i': 1, 'j': 2, 'k': 0, 'cost': 25}, {'i': 1, 'j': 2, 'k': 1, 'cost': 19}, {'i': 1, 'j': 2, 'k': 2, 'cost': 77}, {'i': 1, 'j': 2, 'k': 3, 'cost': 11}, {'i': 1, 'j': 2, 'k': 4, 'cost': 33}, {'i': 1, 'j': 2, 'k': 5, 'cost': 67}, {'i': 1, 'j': 3, 'k': 0, 'cost': 69}, {'i': 1, 'j': 3, 'k': 1, 'cost': 86}, {'i': 1, 'j': 3, 'k': 2, 'cost': 26}, {'i': 1, 'j': 3, 'k': 3, 'cost': 73}, {'i': 1, 'j': 3, 'k': 4, 'cost': 99}, {'i': 1, 'j': 3, 'k': 5, 'cost': 24}, {'i': 1, 'j': 4, 'k': 0, 'cost': 21}, {'i': 1, 'j': 4, 'k': 1, 'cost': 64}, {'i': 1, 'j': 4, 'k': 2, 'cost': 14}, {'i': 1, 'j': 4, 'k': 3, 'cost': 96}, {'i': 1, 'j': 4, 'k': 4, 'cost': 72}, {'i': 1, 'j': 4, 'k': 5, 'cost': 70}, {'i': 1, 'j': 5, 'k': 0, 'cost': 67}, {'i': 1, 'j': 5, 'k': 1, 'cost': 92}, {'i': 1, 'j': 5, 'k': 2, 'cost': 40}, {'i': 1, 'j': 5, 'k': 3, 'cost': 39}, {'i': 1, 'j': 5, 'k': 4, 'cost': 9}, {'i': 1, 'j': 5, 'k': 5, 'cost': 95}, {'i': 2, 'j': 0, 'k': 0, 'cost': 55}, {'i': 2, 'j': 0, 'k': 1, 'cost': 16}, {'i': 2, 'j': 0, 'k': 2, 'cost': 80}, {'i': 2, 'j': 0, 'k': 3, 'cost': 36}, {'i': 2, 'j': 0, 'k': 4, 'cost': 24}, {'i': 2, 'j': 0, 'k': 5, 'cost': 10}, {'i': 2, 'j': 1, 'k': 0, 'cost': 84}, {'i': 2, 'j': 1, 'k': 1, 'cost': 45}, {'i': 2, 'j': 1, 'k': 2, 'cost': 84}, {'i': 2, 'j': 1, 'k': 3, 'cost': 50}, {'i': 2, 'j': 1, 'k': 4, 'cost': 39}, {'i': 2, 'j': 1, 'k': 5, 'cost': 64}, {'i': 2, 'j': 2, 'k': 0, 'cost': 26}, {'i': 2, 'j': 2, 'k': 1, 'cost': 5}, {'i': 2, 'j': 2, 'k': 2, 'cost': 27}, {'i': 2, 'j': 2, 'k': 3, 'cost': 28}, {'i': 2, 'j': 2, 'k': 4, 'cost': 5}, {'i': 2, 'j': 2, 'k': 5, 'cost': 52}, {'i': 2, 'j': 3, 'k': 0, 'cost': 88}, {'i': 2, 'j': 3, 'k': 1, 'cost': 35}, {'i': 2, 'j': 3, 'k': 2, 'cost': 94}, {'i': 2, 'j': 3, 'k': 3, 'cost': 2}, {'i': 2, 'j': 3, 'k': 4, 'cost': 97}, {'i': 2, 'j': 3, 'k': 5, 'cost': 82}, {'i': 2, 'j': 4, 'k': 0, 'cost': 42}, {'i': 2, 'j': 4, 'k': 1, 'cost': 37}, {'i': 2, 'j': 4, 'k': 2, 'cost': 62}, {'i': 2, 'j': 4, 'k': 3, 'cost': 65}, {'i': 2, 'j': 4, 'k': 4, 'cost': 16}, {'i': 2, 'j': 4, 'k': 5, 'cost': 49}, {'i': 2, 'j': 5, 'k': 0, 'cost': 43}, {'i': 2, 'j': 5, 'k': 1, 'cost': 88}, {'i': 2, 'j': 5, 'k': 2, 'cost': 88}, {'i': 2, 'j': 5, 'k': 3, 'cost': 39}, {'i': 2, 'j': 5, 'k': 4, 'cost': 27}, {'i': 2, 'j': 5, 'k': 5, 'cost': 71}, {'i': 3, 'j': 0, 'k': 0, 'cost': 44}, {'i': 3, 'j': 0, 'k': 1, 'cost': 24}, {'i': 3, 'j': 0, 'k': 2, 'cost': 15}, {'i': 3, 'j': 0, 'k': 3, 'cost': 25}, {'i': 3, 'j': 0, 'k': 4, 'cost': 23}, {'i': 3, 'j': 0, 'k': 5, 'cost': 37}, {'i': 3, 'j': 1, 'k': 0, 'cost': 15}, {'i': 3, 'j': 1, 'k': 1, 'cost': 31}, {'i': 3, 'j': 1, 'k': 2, 'cost': 26}, {'i': 3, 'j': 1, 'k': 3, 'cost': 94}, {'i': 3, 'j': 1, 'k': 4, 'cost': 66}, {'i': 3, 'j': 1, 'k': 5, 'cost': 58}, {'i': 3, 'j': 2, 'k': 0, 'cost': 98}, {'i': 3, 'j': 2, 'k': 1, 'cost': 38}, {'i': 3, 'j': 2, 'k': 2, 'cost': 45}, {'i': 3, 'j': 2, 'k': 3, 'cost': 88}, {'i': 3, 'j': 2, 'k': 4, 'cost': 99}, {'i': 3, 'j': 2, 'k': 5, 'cost': 1}, {'i': 3, 'j': 3, 'k': 0, 'cost': 69}, {'i': 3, 'j': 3, 'k': 1, 'cost': 95}, {'i': 3, 'j': 3, 'k': 2, 'cost': 21}, {'i': 3, 'j': 3, 'k': 3, 'cost': 28}, {'i': 3, 'j': 3, 'k': 4, 'cost': 13}, {'i': 3, 'j': 3, 'k': 5, 'cost': 57}, {'i': 3, 'j': 4, 'k': 0, 'cost': 52}, {'i': 3, 'j': 4, 'k': 1, 'cost': 64}, {'i': 3, 'j': 4, 'k': 2, 'cost': 2}, {'i': 3, 'j': 4, 'k': 3, 'cost': 58}, {'i': 3, 'j': 4, 'k': 4, 'cost': 31}, {'i': 3, 'j': 4, 'k': 5, 'cost': 57}, {'i': 3, 'j': 5, 'k': 0, 'cost': 87}, {'i': 3, 'j': 5, 'k': 1, 'cost': 34}, {'i': 3, 'j': 5, 'k': 2, 'cost': 39}, {'i': 3, 'j': 5, 'k': 3, 'cost': 91}, {'i': 3, 'j': 5, 'k': 4, 'cost': 95}, {'i': 3, 'j': 5, 'k': 5, 'cost': 96}, {'i': 4, 'j': 0, 'k': 0, 'cost': 23}, {'i': 4, 'j': 0, 'k': 1, 'cost': 15}, {'i': 4, 'j': 0, 'k': 2, 'cost': 78}, {'i': 4, 'j': 0, 'k': 3, 'cost': 27}, {'i': 4, 'j': 0, 'k': 4, 'cost': 85}, {'i': 4, 'j': 0, 'k': 5, 'cost': 6}, {'i': 4, 'j': 1, 'k': 0, 'cost': 10}, {'i': 4, 'j': 1, 'k': 1, 'cost': 1}, {'i': 4, 'j': 1, 'k': 2, 'cost': 39}, {'i': 4, 'j': 1, 'k': 3, 'cost': 38}, {'i': 4, 'j': 1, 'k': 4, 'cost': 0}, {'i': 4, 'j': 1, 'k': 5, 'cost': 52}, {'i': 4, 'j': 2, 'k': 0, 'cost': 1}, {'i': 4, 'j': 2, 'k': 1, 'cost': 91}, {'i': 4, 'j': 2, 'k': 2, 'cost': 72}, {'i': 4, 'j': 2, 'k': 3, 'cost': 99}, {'i': 4, 'j': 2, 'k': 4, 'cost': 49}, {'i': 4, 'j': 2, 'k': 5, 'cost': 84}, {'i': 4, 'j': 3, 'k': 0, 'cost': 99}, {'i': 4, 'j': 3, 'k': 1, 'cost': 79}, {'i': 4, 'j': 3, 'k': 2, 'cost': 89}, {'i': 4, 'j': 3, 'k': 3, 'cost': 10}, {'i': 4, 'j': 3, 'k': 4, 'cost': 35}, {'i': 4, 'j': 3, 'k': 5, 'cost': 88}, {'i': 4, 'j': 4, 'k': 0, 'cost': 52}, {'i': 4, 'j': 4, 'k': 1, 'cost': 35}, {'i': 4, 'j': 4, 'k': 2, 'cost': 90}, {'i': 4, 'j': 4, 'k': 3, 'cost': 3}, {'i': 4, 'j': 4, 'k': 4, 'cost': 96}, {'i': 4, 'j': 4, 'k': 5, 'cost': 22}, {'i': 4, 'j': 5, 'k': 0, 'cost': 90}, {'i': 4, 'j': 5, 'k': 1, 'cost': 85}, {'i': 4, 'j': 5, 'k': 2, 'cost': 9}, {'i': 4, 'j': 5, 'k': 3, 'cost': 77}, {'i': 4, 'j': 5, 'k': 4, 'cost': 15}, {'i': 4, 'j': 5, 'k': 5, 'cost': 88}, {'i': 5, 'j': 0, 'k': 0, 'cost': 29}, {'i': 5, 'j': 0, 'k': 1, 'cost': 0}, {'i': 5, 'j': 0, 'k': 2, 'cost': 47}, {'i': 5, 'j': 0, 'k': 3, 'cost': 44}, {'i': 5, 'j': 0, 'k': 4, 'cost': 44}, {'i': 5, 'j': 0, 'k': 5, 'cost': 22}, {'i': 5, 'j': 1, 'k': 0, 'cost': 94}, {'i': 5, 'j': 1, 'k': 1, 'cost': 89}, {'i': 5, 'j': 1, 'k': 2, 'cost': 0}, {'i': 5, 'j': 1, 'k': 3, 'cost': 67}, {'i': 5, 'j': 1, 'k': 4, 'cost': 64}, {'i': 5, 'j': 1, 'k': 5, 'cost': 2}, {'i': 5, 'j': 2, 'k': 0, 'cost': 40}, {'i': 5, 'j': 2, 'k': 1, 'cost': 40}, {'i': 5, 'j': 2, 'k': 2, 'cost': 17}, {'i': 5, 'j': 2, 'k': 3, 'cost': 43}, {'i': 5, 'j': 2, 'k': 4, 'cost': 9}, {'i': 5, 'j': 2, 'k': 5, 'cost': 94}, {'i': 5, 'j': 3, 'k': 0, 'cost': 57}, {'i': 5, 'j': 3, 'k': 1, 'cost': 97}, {'i': 5, 'j': 3, 'k': 2, 'cost': 55}, {'i': 5, 'j': 3, 'k': 3, 'cost': 24}, {'i': 5, 'j': 3, 'k': 4, 'cost': 7}, {'i': 5, 'j': 3, 'k': 5, 'cost': 21}, {'i': 5, 'j': 4, 'k': 0, 'cost': 8}, {'i': 5, 'j': 4, 'k': 1, 'cost': 33}, {'i': 5, 'j': 4, 'k': 2, 'cost': 28}, {'i': 5, 'j': 4, 'k': 3, 'cost': 55}, {'i': 5, 'j': 4, 'k': 4, 'cost': 97}, {'i': 5, 'j': 4, 'k': 5, 'cost': 30}, {'i': 5, 'j': 5, 'k': 0, 'cost': 43}, {'i': 5, 'j': 5, 'k': 1, 'cost': 18}, {'i': 5, 'j': 5, 'k': 2, 'cost': 74}, {'i': 5, 'j': 5, 'k': 3, 'cost': 15}, {'i': 5, 'j': 5, 'k': 4, 'cost': 55}, {'i': 5, 'j': 5, 'k': 5, 'cost': 3}]}","[[0, 0, 2], [1, 5, 4], [2, 3, 3], [3, 2, 5], [4, 1, 1], [5, 4, 0]]",21,markdown_table,0
AP3,AP3,"A friend who runs a courier service described it this way: there are as many jobs as there are drivers and vans, so each job gets paired with a single driver and a single van, and every driver and van gets used exactly once. Each possible pairing has fuel and time figures attached, and the aim is to choose pairings so that, after summing fuel and time for every job, the overall total is as small as possible. The detailed list of combos and their costs appears below.

# num_orders=6
# index_identifiers=1, 2, 3, 4, 5, 6

# Meaning: costs form a 3D tensor. For each fixed order_id=i, you are given a driver_id×van_id matrix whose entry at row driver_id=j and column van_id=k equals fuel_time_cost(i,j,k). You must pick exactly one (j,k) for every i, with all driver_id and all van_id used exactly once.
# fuel_time_cost_tensor (per-order_id markdown matrices)

## order_id=1
| driver_id\van_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 26 | 46 | 2 | 17 | 57 | 14 |
| 2 | 43 | 37 | 27 | 22 | 49 | 30 |
| 3 | 44 | 73 | 65 | 26 | 35 | 75 |
| 4 | 81 | 39 | 38 | 70 | 7 | 7 |
| 5 | 3 | 18 | 73 | 93 | 82 | 61 |
| 6 | 18 | 17 | 10 | 28 | 99 | 12 |

## order_id=2
| driver_id\van_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 5 | 40 | 90 | 62 | 71 | 42 |
| 2 | 85 | 22 | 12 | 83 | 90 | 60 |
| 3 | 27 | 79 | 75 | 14 | 31 | 31 |
| 4 | 56 | 94 | 87 | 50 | 54 | 87 |
| 5 | 2 | 25 | 71 | 31 | 83 | 70 |
| 6 | 84 | 44 | 92 | 71 | 25 | 82 |

## order_id=3
| driver_id\van_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 38 | 99 | 72 | 45 | 47 | 31 |
| 2 | 43 | 16 | 71 | 78 | 97 | 30 |
| 3 | 47 | 62 | 11 | 70 | 86 | 13 |
| 4 | 9 | 0 | 43 | 47 | 3 | 38 |
| 5 | 30 | 66 | 92 | 17 | 94 | 34 |
| 6 | 76 | 52 | 96 | 76 | 27 | 67 |

## order_id=4
| driver_id\van_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 58 | 24 | 83 | 52 | 84 | 34 |
| 2 | 81 | 55 | 74 | 53 | 55 | 98 |
| 3 | 65 | 90 | 94 | 16 | 97 | 64 |
| 4 | 81 | 31 | 88 | 78 | 27 | 2 |
| 5 | 69 | 22 | 32 | 52 | 23 | 46 |
| 6 | 95 | 60 | 54 | 77 | 59 | 72 |

## order_id=5
| driver_id\van_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 59 | 65 | 27 | 73 | 56 | 73 |
| 2 | 3 | 30 | 19 | 27 | 87 | 90 |
| 3 | 84 | 64 | 10 | 51 | 94 | 86 |
| 4 | 48 | 55 | 50 | 22 | 86 | 48 |
| 5 | 17 | 8 | 10 | 87 | 73 | 22 |
| 6 | 65 | 54 | 50 | 7 | 50 | 48 |

## order_id=6
| driver_id\van_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 47 | 71 | 73 | 99 | 49 | 32 |
| 2 | 19 | 12 | 86 | 79 | 25 | 73 |
| 3 | 10 | 69 | 28 | 29 | 62 | 37 |
| 4 | 94 | 74 | 93 | 80 | 88 | 1 |
| 5 | 17 | 88 | 6 | 84 | 52 | 22 |
| 6 | 10 | 84 | 38 | 28 | 25 | 61 |

If you want to hand the chosen pairings to me in a neat, machine-friendly way, just use this JSON shape:

{
  ""solution"": [
    [<i_id>, <j_id>, <k_id>],
    ...
  ]
}

Here ""solution"" is a list of triples. Each triple [i, j, k] means: job i is done by driver j using van k. Think of it like filling out a simple form — one triple per job, and together they describe all the pairings. This JSON block is only a sketch of the expected shape, not the actual answer.

Please 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""
- a capital letter followed by digits like ""A1"" or ""X7""","{'cost_tensor': [[[26, 46, 2, 17, 57, 14], [43, 37, 27, 22, 49, 30], [44, 73, 65, 26, 35, 75], [81, 39, 38, 70, 7, 7], [3, 18, 73, 93, 82, 61], [18, 17, 10, 28, 99, 12]], [[5, 40, 90, 62, 71, 42], [85, 22, 12, 83, 90, 60], [27, 79, 75, 14, 31, 31], [56, 94, 87, 50, 54, 87], [2, 25, 71, 31, 83, 70], [84, 44, 92, 71, 25, 82]], [[38, 99, 72, 45, 47, 31], [43, 16, 71, 78, 97, 30], [47, 62, 11, 70, 86, 13], [9, 0, 43, 47, 3, 38], [30, 66, 92, 17, 94, 34], [76, 52, 96, 76, 27, 67]], [[58, 24, 83, 52, 84, 34], [81, 55, 74, 53, 55, 98], [65, 90, 94, 16, 97, 64], [81, 31, 88, 78, 27, 2], [69, 22, 32, 52, 23, 46], [95, 60, 54, 77, 59, 72]], [[59, 65, 27, 73, 56, 73], [3, 30, 19, 27, 87, 90], [84, 64, 10, 51, 94, 86], [48, 55, 50, 22, 86, 48], [17, 8, 10, 87, 73, 22], [65, 54, 50, 7, 50, 48]], [[47, 71, 73, 99, 49, 32], [19, 12, 86, 79, 25, 73], [10, 69, 28, 29, 62, 37], [94, 74, 93, 80, 88, 1], [17, 88, 6, 84, 52, 22], [10, 84, 38, 28, 25, 61]]], 'objective': 58.0}","[[0, 5, 5], [1, 0, 0], [2, 3, 4], [3, 2, 3], [4, 4, 2], [5, 1, 1]]",58.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 26}, {'i': 1, 'j': 1, 'k': 2, 'cost': 46}, {'i': 1, 'j': 1, 'k': 3, 'cost': 2}, {'i': 1, 'j': 1, 'k': 4, 'cost': 17}, {'i': 1, 'j': 1, 'k': 5, 'cost': 57}, {'i': 1, 'j': 1, 'k': 6, 'cost': 14}, {'i': 1, 'j': 2, 'k': 1, 'cost': 43}, {'i': 1, 'j': 2, 'k': 2, 'cost': 37}, {'i': 1, 'j': 2, 'k': 3, 'cost': 27}, {'i': 1, 'j': 2, 'k': 4, 'cost': 22}, {'i': 1, 'j': 2, 'k': 5, 'cost': 49}, {'i': 1, 'j': 2, 'k': 6, 'cost': 30}, {'i': 1, 'j': 3, 'k': 1, 'cost': 44}, {'i': 1, 'j': 3, 'k': 2, 'cost': 73}, {'i': 1, 'j': 3, 'k': 3, 'cost': 65}, {'i': 1, 'j': 3, 'k': 4, 'cost': 26}, {'i': 1, 'j': 3, 'k': 5, 'cost': 35}, {'i': 1, 'j': 3, 'k': 6, 'cost': 75}, {'i': 1, 'j': 4, 'k': 1, 'cost': 81}, {'i': 1, 'j': 4, 'k': 2, 'cost': 39}, {'i': 1, 'j': 4, 'k': 3, 'cost': 38}, {'i': 1, 'j': 4, 'k': 4, 'cost': 70}, {'i': 1, 'j': 4, 'k': 5, 'cost': 7}, {'i': 1, 'j': 4, 'k': 6, 'cost': 7}, {'i': 1, 'j': 5, 'k': 1, 'cost': 3}, {'i': 1, 'j': 5, 'k': 2, 'cost': 18}, {'i': 1, 'j': 5, 'k': 3, 'cost': 73}, {'i': 1, 'j': 5, 'k': 4, 'cost': 93}, {'i': 1, 'j': 5, 'k': 5, 'cost': 82}, {'i': 1, 'j': 5, 'k': 6, 'cost': 61}, {'i': 1, 'j': 6, 'k': 1, 'cost': 18}, {'i': 1, 'j': 6, 'k': 2, 'cost': 17}, {'i': 1, 'j': 6, 'k': 3, 'cost': 10}, {'i': 1, 'j': 6, 'k': 4, 'cost': 28}, {'i': 1, 'j': 6, 'k': 5, 'cost': 99}, {'i': 1, 'j': 6, 'k': 6, 'cost': 12}, {'i': 2, 'j': 1, 'k': 1, 'cost': 5}, {'i': 2, 'j': 1, 'k': 2, 'cost': 40}, {'i': 2, 'j': 1, 'k': 3, 'cost': 90}, {'i': 2, 'j': 1, 'k': 4, 'cost': 62}, {'i': 2, 'j': 1, 'k': 5, 'cost': 71}, {'i': 2, 'j': 1, 'k': 6, 'cost': 42}, {'i': 2, 'j': 2, 'k': 1, 'cost': 85}, {'i': 2, 'j': 2, 'k': 2, 'cost': 22}, {'i': 2, 'j': 2, 'k': 3, 'cost': 12}, {'i': 2, 'j': 2, 'k': 4, 'cost': 83}, {'i': 2, 'j': 2, 'k': 5, 'cost': 90}, {'i': 2, 'j': 2, 'k': 6, 'cost': 60}, {'i': 2, 'j': 3, 'k': 1, 'cost': 27}, {'i': 2, 'j': 3, 'k': 2, 'cost': 79}, {'i': 2, 'j': 3, 'k': 3, 'cost': 75}, {'i': 2, 'j': 3, 'k': 4, 'cost': 14}, {'i': 2, 'j': 3, 'k': 5, 'cost': 31}, {'i': 2, 'j': 3, 'k': 6, 'cost': 31}, {'i': 2, 'j': 4, 'k': 1, 'cost': 56}, {'i': 2, 'j': 4, 'k': 2, 'cost': 94}, {'i': 2, 'j': 4, 'k': 3, 'cost': 87}, {'i': 2, 'j': 4, 'k': 4, 'cost': 50}, {'i': 2, 'j': 4, 'k': 5, 'cost': 54}, {'i': 2, 'j': 4, 'k': 6, 'cost': 87}, {'i': 2, 'j': 5, 'k': 1, 'cost': 2}, {'i': 2, 'j': 5, 'k': 2, 'cost': 25}, {'i': 2, 'j': 5, 'k': 3, 'cost': 71}, {'i': 2, 'j': 5, 'k': 4, 'cost': 31}, {'i': 2, 'j': 5, 'k': 5, 'cost': 83}, {'i': 2, 'j': 5, 'k': 6, 'cost': 70}, {'i': 2, 'j': 6, 'k': 1, 'cost': 84}, {'i': 2, 'j': 6, 'k': 2, 'cost': 44}, {'i': 2, 'j': 6, 'k': 3, 'cost': 92}, {'i': 2, 'j': 6, 'k': 4, 'cost': 71}, {'i': 2, 'j': 6, 'k': 5, 'cost': 25}, {'i': 2, 'j': 6, 'k': 6, 'cost': 82}, {'i': 3, 'j': 1, 'k': 1, 'cost': 38}, {'i': 3, 'j': 1, 'k': 2, 'cost': 99}, {'i': 3, 'j': 1, 'k': 3, 'cost': 72}, {'i': 3, 'j': 1, 'k': 4, 'cost': 45}, {'i': 3, 'j': 1, 'k': 5, 'cost': 47}, {'i': 3, 'j': 1, 'k': 6, 'cost': 31}, {'i': 3, 'j': 2, 'k': 1, 'cost': 43}, {'i': 3, 'j': 2, 'k': 2, 'cost': 16}, {'i': 3, 'j': 2, 'k': 3, 'cost': 71}, {'i': 3, 'j': 2, 'k': 4, 'cost': 78}, {'i': 3, 'j': 2, 'k': 5, 'cost': 97}, {'i': 3, 'j': 2, 'k': 6, 'cost': 30}, {'i': 3, 'j': 3, 'k': 1, 'cost': 47}, {'i': 3, 'j': 3, 'k': 2, 'cost': 62}, {'i': 3, 'j': 3, 'k': 3, 'cost': 11}, {'i': 3, 'j': 3, 'k': 4, 'cost': 70}, {'i': 3, 'j': 3, 'k': 5, 'cost': 86}, {'i': 3, 'j': 3, 'k': 6, 'cost': 13}, {'i': 3, 'j': 4, 'k': 1, 'cost': 9}, {'i': 3, 'j': 4, 'k': 2, 'cost': 0}, {'i': 3, 'j': 4, 'k': 3, 'cost': 43}, {'i': 3, 'j': 4, 'k': 4, 'cost': 47}, {'i': 3, 'j': 4, 'k': 5, 'cost': 3}, {'i': 3, 'j': 4, 'k': 6, 'cost': 38}, {'i': 3, 'j': 5, 'k': 1, 'cost': 30}, {'i': 3, 'j': 5, 'k': 2, 'cost': 66}, {'i': 3, 'j': 5, 'k': 3, 'cost': 92}, {'i': 3, 'j': 5, 'k': 4, 'cost': 17}, {'i': 3, 'j': 5, 'k': 5, 'cost': 94}, {'i': 3, 'j': 5, 'k': 6, 'cost': 34}, {'i': 3, 'j': 6, 'k': 1, 'cost': 76}, {'i': 3, 'j': 6, 'k': 2, 'cost': 52}, {'i': 3, 'j': 6, 'k': 3, 'cost': 96}, {'i': 3, 'j': 6, 'k': 4, 'cost': 76}, {'i': 3, 'j': 6, 'k': 5, 'cost': 27}, {'i': 3, 'j': 6, 'k': 6, 'cost': 67}, {'i': 4, 'j': 1, 'k': 1, 'cost': 58}, {'i': 4, 'j': 1, 'k': 2, 'cost': 24}, {'i': 4, 'j': 1, 'k': 3, 'cost': 83}, {'i': 4, 'j': 1, 'k': 4, 'cost': 52}, {'i': 4, 'j': 1, 'k': 5, 'cost': 84}, {'i': 4, 'j': 1, 'k': 6, 'cost': 34}, {'i': 4, 'j': 2, 'k': 1, 'cost': 81}, {'i': 4, 'j': 2, 'k': 2, 'cost': 55}, {'i': 4, 'j': 2, 'k': 3, 'cost': 74}, {'i': 4, 'j': 2, 'k': 4, 'cost': 53}, {'i': 4, 'j': 2, 'k': 5, 'cost': 55}, {'i': 4, 'j': 2, 'k': 6, 'cost': 98}, {'i': 4, 'j': 3, 'k': 1, 'cost': 65}, {'i': 4, 'j': 3, 'k': 2, 'cost': 90}, {'i': 4, 'j': 3, 'k': 3, 'cost': 94}, {'i': 4, 'j': 3, 'k': 4, 'cost': 16}, {'i': 4, 'j': 3, 'k': 5, 'cost': 97}, {'i': 4, 'j': 3, 'k': 6, 'cost': 64}, {'i': 4, 'j': 4, 'k': 1, 'cost': 81}, {'i': 4, 'j': 4, 'k': 2, 'cost': 31}, {'i': 4, 'j': 4, 'k': 3, 'cost': 88}, {'i': 4, 'j': 4, 'k': 4, 'cost': 78}, {'i': 4, 'j': 4, 'k': 5, 'cost': 27}, {'i': 4, 'j': 4, 'k': 6, 'cost': 2}, {'i': 4, 'j': 5, 'k': 1, 'cost': 69}, {'i': 4, 'j': 5, 'k': 2, 'cost': 22}, {'i': 4, 'j': 5, 'k': 3, 'cost': 32}, {'i': 4, 'j': 5, 'k': 4, 'cost': 52}, {'i': 4, 'j': 5, 'k': 5, 'cost': 23}, {'i': 4, 'j': 5, 'k': 6, 'cost': 46}, {'i': 4, 'j': 6, 'k': 1, 'cost': 95}, {'i': 4, 'j': 6, 'k': 2, 'cost': 60}, {'i': 4, 'j': 6, 'k': 3, 'cost': 54}, {'i': 4, 'j': 6, 'k': 4, 'cost': 77}, {'i': 4, 'j': 6, 'k': 5, 'cost': 59}, {'i': 4, 'j': 6, 'k': 6, 'cost': 72}, {'i': 5, 'j': 1, 'k': 1, 'cost': 59}, {'i': 5, 'j': 1, 'k': 2, 'cost': 65}, {'i': 5, 'j': 1, 'k': 3, 'cost': 27}, {'i': 5, 'j': 1, 'k': 4, 'cost': 73}, {'i': 5, 'j': 1, 'k': 5, 'cost': 56}, {'i': 5, 'j': 1, 'k': 6, 'cost': 73}, {'i': 5, 'j': 2, 'k': 1, 'cost': 3}, {'i': 5, 'j': 2, 'k': 2, 'cost': 30}, {'i': 5, 'j': 2, 'k': 3, 'cost': 19}, {'i': 5, 'j': 2, 'k': 4, 'cost': 27}, {'i': 5, 'j': 2, 'k': 5, 'cost': 87}, {'i': 5, 'j': 2, 'k': 6, 'cost': 90}, {'i': 5, 'j': 3, 'k': 1, 'cost': 84}, {'i': 5, 'j': 3, 'k': 2, 'cost': 64}, {'i': 5, 'j': 3, 'k': 3, 'cost': 10}, {'i': 5, 'j': 3, 'k': 4, 'cost': 51}, {'i': 5, 'j': 3, 'k': 5, 'cost': 94}, {'i': 5, 'j': 3, 'k': 6, 'cost': 86}, {'i': 5, 'j': 4, 'k': 1, 'cost': 48}, {'i': 5, 'j': 4, 'k': 2, 'cost': 55}, {'i': 5, 'j': 4, 'k': 3, 'cost': 50}, {'i': 5, 'j': 4, 'k': 4, 'cost': 22}, {'i': 5, 'j': 4, 'k': 5, 'cost': 86}, {'i': 5, 'j': 4, 'k': 6, 'cost': 48}, {'i': 5, 'j': 5, 'k': 1, 'cost': 17}, {'i': 5, 'j': 5, 'k': 2, 'cost': 8}, {'i': 5, 'j': 5, 'k': 3, 'cost': 10}, {'i': 5, 'j': 5, 'k': 4, 'cost': 87}, {'i': 5, 'j': 5, 'k': 5, 'cost': 73}, {'i': 5, 'j': 5, 'k': 6, 'cost': 22}, {'i': 5, 'j': 6, 'k': 1, 'cost': 65}, {'i': 5, 'j': 6, 'k': 2, 'cost': 54}, {'i': 5, 'j': 6, 'k': 3, 'cost': 50}, {'i': 5, 'j': 6, 'k': 4, 'cost': 7}, {'i': 5, 'j': 6, 'k': 5, 'cost': 50}, {'i': 5, 'j': 6, 'k': 6, 'cost': 48}, {'i': 6, 'j': 1, 'k': 1, 'cost': 47}, {'i': 6, 'j': 1, 'k': 2, 'cost': 71}, {'i': 6, 'j': 1, 'k': 3, 'cost': 73}, {'i': 6, 'j': 1, 'k': 4, 'cost': 99}, {'i': 6, 'j': 1, 'k': 5, 'cost': 49}, {'i': 6, 'j': 1, 'k': 6, 'cost': 32}, {'i': 6, 'j': 2, 'k': 1, 'cost': 19}, {'i': 6, 'j': 2, 'k': 2, 'cost': 12}, {'i': 6, 'j': 2, 'k': 3, 'cost': 86}, {'i': 6, 'j': 2, 'k': 4, 'cost': 79}, {'i': 6, 'j': 2, 'k': 5, 'cost': 25}, {'i': 6, 'j': 2, 'k': 6, 'cost': 73}, {'i': 6, 'j': 3, 'k': 1, 'cost': 10}, {'i': 6, 'j': 3, 'k': 2, 'cost': 69}, {'i': 6, 'j': 3, 'k': 3, 'cost': 28}, {'i': 6, 'j': 3, 'k': 4, 'cost': 29}, {'i': 6, 'j': 3, 'k': 5, 'cost': 62}, {'i': 6, 'j': 3, 'k': 6, 'cost': 37}, {'i': 6, 'j': 4, 'k': 1, 'cost': 94}, {'i': 6, 'j': 4, 'k': 2, 'cost': 74}, {'i': 6, 'j': 4, 'k': 3, 'cost': 93}, {'i': 6, 'j': 4, 'k': 4, 'cost': 80}, {'i': 6, 'j': 4, 'k': 5, 'cost': 88}, {'i': 6, 'j': 4, 'k': 6, 'cost': 1}, {'i': 6, 'j': 5, 'k': 1, 'cost': 17}, {'i': 6, 'j': 5, 'k': 2, 'cost': 88}, {'i': 6, 'j': 5, 'k': 3, 'cost': 6}, {'i': 6, 'j': 5, 'k': 4, 'cost': 84}, {'i': 6, 'j': 5, 'k': 5, 'cost': 52}, {'i': 6, 'j': 5, 'k': 6, 'cost': 22}, {'i': 6, 'j': 6, 'k': 1, 'cost': 10}, {'i': 6, 'j': 6, 'k': 2, 'cost': 84}, {'i': 6, 'j': 6, 'k': 3, 'cost': 38}, {'i': 6, 'j': 6, 'k': 4, 'cost': 28}, {'i': 6, 'j': 6, 'k': 5, 'cost': 25}, {'i': 6, 'j': 6, 'k': 6, 'cost': 61}]}","[[1, 6, 6], [2, 1, 1], [3, 4, 5], [4, 3, 4], [5, 5, 3], [6, 2, 2]]",22,csv,1
AP3,AP3,"Someone on the events team has to pair each scheduled activity with a single volunteer and a single station so that no volunteer or station is used more than once and nothing is left out. The goal is clear in plain terms — minimize the whole staffing charge by adding up the cost for each activity’s volunteer-and-station match and keeping that overall sum as small as possible. The full list of activities, volunteers, stations and their costs appears below.

# num_activities=6
# activity_ids=0, 1, 2, 3, 4, 5

# Meaning: costs form a 3D tensor. For each fixed activity_id=i, you are given a volunteer_id×station_id matrix whose entry at row volunteer_id=j and column station_id=k equals staffing_cost(i,j,k). You must pick exactly one (j,k) for every i, with all volunteer_id and all station_id used exactly once.
# staffing_cost_tensor (per-activity_id markdown matrices)

## activity_id=0
| volunteer_id\station_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 76 | 19 | 93 | 55 | 3 | 61 |
| 1 | 65 | 14 | 10 | 51 | 56 | 17 |
| 2 | 65 | 82 | 27 | 58 | 93 | 87 |
| 3 | 11 | 84 | 36 | 41 | 88 | 76 |
| 4 | 71 | 75 | 16 | 40 | 69 | 54 |
| 5 | 25 | 32 | 27 | 52 | 49 | 66 |

## activity_id=1
| volunteer_id\station_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 21 | 88 | 16 | 3 | 65 | 32 |
| 1 | 5 | 24 | 89 | 28 | 81 | 36 |
| 2 | 82 | 95 | 51 | 69 | 12 | 73 |
| 3 | 52 | 46 | 77 | 18 | 47 | 71 |
| 4 | 28 | 54 | 37 | 9 | 37 | 95 |
| 5 | 75 | 46 | 83 | 18 | 10 | 2 |

## activity_id=2
| volunteer_id\station_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 60 | 6 | 70 | 86 | 63 | 90 |
| 1 | 83 | 58 | 10 | 29 | 59 | 95 |
| 2 | 49 | 13 | 32 | 51 | 90 | 0 |
| 3 | 91 | 13 | 40 | 89 | 36 | 89 |
| 4 | 79 | 65 | 63 | 4 | 91 | 4 |
| 5 | 97 | 56 | 96 | 35 | 76 | 49 |

## activity_id=3
| volunteer_id\station_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 50 | 86 | 31 | 88 | 87 | 57 |
| 1 | 46 | 53 | 32 | 38 | 5 | 38 |
| 2 | 26 | 94 | 16 | 17 | 39 | 72 |
| 3 | 57 | 66 | 52 | 11 | 28 | 8 |
| 4 | 45 | 92 | 48 | 46 | 89 | 16 |
| 5 | 74 | 24 | 78 | 83 | 5 | 67 |

## activity_id=4
| volunteer_id\station_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 95 | 62 | 24 | 0 | 13 | 64 |
| 1 | 71 | 45 | 6 | 97 | 84 | 7 |
| 2 | 55 | 75 | 84 | 40 | 81 | 76 |
| 3 | 24 | 4 | 60 | 8 | 8 | 51 |
| 4 | 22 | 4 | 72 | 94 | 95 | 77 |
| 5 | 53 | 36 | 61 | 71 | 0 | 52 |

## activity_id=5
| volunteer_id\station_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 89 | 75 | 87 | 50 | 17 | 47 |
| 1 | 69 | 86 | 13 | 17 | 20 | 67 |
| 2 | 33 | 14 | 70 | 30 | 2 | 49 |
| 3 | 7 | 94 | 96 | 21 | 60 | 23 |
| 4 | 66 | 30 | 8 | 78 | 23 | 99 |
| 5 | 34 | 40 | 28 | 69 | 61 | 56 |

You can send back the matching in a simple JSON shape like this — casual and machine-friendly at the same time.

{
  ""solution"": [
    [<activity_id>, <volunteer_id>, <station_id>],
    ...
  ]
}

Each little triple is one activity matched with its volunteer and station. The outer array collects one triple per activity so everything is assigned once. This JSON is just a sketch of the shape I want you to use, not the actual answer itself.

Please make sure you use the exact identifiers from the instance input — don’t 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”.""","{'cost_tensor': [[[76, 19, 93, 55, 3, 61], [65, 14, 10, 51, 56, 17], [65, 82, 27, 58, 93, 87], [11, 84, 36, 41, 88, 76], [71, 75, 16, 40, 69, 54], [25, 32, 27, 52, 49, 66]], [[21, 88, 16, 3, 65, 32], [5, 24, 89, 28, 81, 36], [82, 95, 51, 69, 12, 73], [52, 46, 77, 18, 47, 71], [28, 54, 37, 9, 37, 95], [75, 46, 83, 18, 10, 2]], [[60, 6, 70, 86, 63, 90], [83, 58, 10, 29, 59, 95], [49, 13, 32, 51, 90, 0], [91, 13, 40, 89, 36, 89], [79, 65, 63, 4, 91, 4], [97, 56, 96, 35, 76, 49]], [[50, 86, 31, 88, 87, 57], [46, 53, 32, 38, 5, 38], [26, 94, 16, 17, 39, 72], [57, 66, 52, 11, 28, 8], [45, 92, 48, 46, 89, 16], [74, 24, 78, 83, 5, 67]], [[95, 62, 24, 0, 13, 64], [71, 45, 6, 97, 84, 7], [55, 75, 84, 40, 81, 76], [24, 4, 60, 8, 8, 51], [22, 4, 72, 94, 95, 77], [53, 36, 61, 71, 0, 52]], [[89, 75, 87, 50, 17, 47], [69, 86, 13, 17, 20, 67], [33, 14, 70, 30, 2, 49], [7, 94, 96, 21, 60, 23], [66, 30, 8, 78, 23, 99], [34, 40, 28, 69, 61, 56]]], 'objective': 29.0}","[[0, 1, 2], [1, 0, 3], [2, 2, 5], [3, 5, 4], [4, 4, 1], [5, 3, 0]]",29.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 76}, {'i': 0, 'j': 0, 'k': 1, 'cost': 19}, {'i': 0, 'j': 0, 'k': 2, 'cost': 93}, {'i': 0, 'j': 0, 'k': 3, 'cost': 55}, {'i': 0, 'j': 0, 'k': 4, 'cost': 3}, {'i': 0, 'j': 0, 'k': 5, 'cost': 61}, {'i': 0, 'j': 1, 'k': 0, 'cost': 65}, {'i': 0, 'j': 1, 'k': 1, 'cost': 14}, {'i': 0, 'j': 1, 'k': 2, 'cost': 10}, {'i': 0, 'j': 1, 'k': 3, 'cost': 51}, {'i': 0, 'j': 1, 'k': 4, 'cost': 56}, {'i': 0, 'j': 1, 'k': 5, 'cost': 17}, {'i': 0, 'j': 2, 'k': 0, 'cost': 65}, {'i': 0, 'j': 2, 'k': 1, 'cost': 82}, {'i': 0, 'j': 2, 'k': 2, 'cost': 27}, {'i': 0, 'j': 2, 'k': 3, 'cost': 58}, {'i': 0, 'j': 2, 'k': 4, 'cost': 93}, {'i': 0, 'j': 2, 'k': 5, 'cost': 87}, {'i': 0, 'j': 3, 'k': 0, 'cost': 11}, {'i': 0, 'j': 3, 'k': 1, 'cost': 84}, {'i': 0, 'j': 3, 'k': 2, 'cost': 36}, {'i': 0, 'j': 3, 'k': 3, 'cost': 41}, {'i': 0, 'j': 3, 'k': 4, 'cost': 88}, {'i': 0, 'j': 3, 'k': 5, 'cost': 76}, {'i': 0, 'j': 4, 'k': 0, 'cost': 71}, {'i': 0, 'j': 4, 'k': 1, 'cost': 75}, {'i': 0, 'j': 4, 'k': 2, 'cost': 16}, {'i': 0, 'j': 4, 'k': 3, 'cost': 40}, {'i': 0, 'j': 4, 'k': 4, 'cost': 69}, {'i': 0, 'j': 4, 'k': 5, 'cost': 54}, {'i': 0, 'j': 5, 'k': 0, 'cost': 25}, {'i': 0, 'j': 5, 'k': 1, 'cost': 32}, {'i': 0, 'j': 5, 'k': 2, 'cost': 27}, {'i': 0, 'j': 5, 'k': 3, 'cost': 52}, {'i': 0, 'j': 5, 'k': 4, 'cost': 49}, {'i': 0, 'j': 5, 'k': 5, 'cost': 66}, {'i': 1, 'j': 0, 'k': 0, 'cost': 21}, {'i': 1, 'j': 0, 'k': 1, 'cost': 88}, {'i': 1, 'j': 0, 'k': 2, 'cost': 16}, {'i': 1, 'j': 0, 'k': 3, 'cost': 3}, {'i': 1, 'j': 0, 'k': 4, 'cost': 65}, {'i': 1, 'j': 0, 'k': 5, 'cost': 32}, {'i': 1, 'j': 1, 'k': 0, 'cost': 5}, {'i': 1, 'j': 1, 'k': 1, 'cost': 24}, {'i': 1, 'j': 1, 'k': 2, 'cost': 89}, {'i': 1, 'j': 1, 'k': 3, 'cost': 28}, {'i': 1, 'j': 1, 'k': 4, 'cost': 81}, {'i': 1, 'j': 1, 'k': 5, 'cost': 36}, {'i': 1, 'j': 2, 'k': 0, 'cost': 82}, {'i': 1, 'j': 2, 'k': 1, 'cost': 95}, {'i': 1, 'j': 2, 'k': 2, 'cost': 51}, {'i': 1, 'j': 2, 'k': 3, 'cost': 69}, {'i': 1, 'j': 2, 'k': 4, 'cost': 12}, {'i': 1, 'j': 2, 'k': 5, 'cost': 73}, {'i': 1, 'j': 3, 'k': 0, 'cost': 52}, {'i': 1, 'j': 3, 'k': 1, 'cost': 46}, {'i': 1, 'j': 3, 'k': 2, 'cost': 77}, {'i': 1, 'j': 3, 'k': 3, 'cost': 18}, {'i': 1, 'j': 3, 'k': 4, 'cost': 47}, {'i': 1, 'j': 3, 'k': 5, 'cost': 71}, {'i': 1, 'j': 4, 'k': 0, 'cost': 28}, {'i': 1, 'j': 4, 'k': 1, 'cost': 54}, {'i': 1, 'j': 4, 'k': 2, 'cost': 37}, {'i': 1, 'j': 4, 'k': 3, 'cost': 9}, {'i': 1, 'j': 4, 'k': 4, 'cost': 37}, {'i': 1, 'j': 4, 'k': 5, 'cost': 95}, {'i': 1, 'j': 5, 'k': 0, 'cost': 75}, {'i': 1, 'j': 5, 'k': 1, 'cost': 46}, {'i': 1, 'j': 5, 'k': 2, 'cost': 83}, {'i': 1, 'j': 5, 'k': 3, 'cost': 18}, {'i': 1, 'j': 5, 'k': 4, 'cost': 10}, {'i': 1, 'j': 5, 'k': 5, 'cost': 2}, {'i': 2, 'j': 0, 'k': 0, 'cost': 60}, {'i': 2, 'j': 0, 'k': 1, 'cost': 6}, {'i': 2, 'j': 0, 'k': 2, 'cost': 70}, {'i': 2, 'j': 0, 'k': 3, 'cost': 86}, {'i': 2, 'j': 0, 'k': 4, 'cost': 63}, {'i': 2, 'j': 0, 'k': 5, 'cost': 90}, {'i': 2, 'j': 1, 'k': 0, 'cost': 83}, {'i': 2, 'j': 1, 'k': 1, 'cost': 58}, {'i': 2, 'j': 1, 'k': 2, 'cost': 10}, {'i': 2, 'j': 1, 'k': 3, 'cost': 29}, {'i': 2, 'j': 1, 'k': 4, 'cost': 59}, {'i': 2, 'j': 1, 'k': 5, 'cost': 95}, {'i': 2, 'j': 2, 'k': 0, 'cost': 49}, {'i': 2, 'j': 2, 'k': 1, 'cost': 13}, {'i': 2, 'j': 2, 'k': 2, 'cost': 32}, {'i': 2, 'j': 2, 'k': 3, 'cost': 51}, {'i': 2, 'j': 2, 'k': 4, 'cost': 90}, {'i': 2, 'j': 2, 'k': 5, 'cost': 0}, {'i': 2, 'j': 3, 'k': 0, 'cost': 91}, {'i': 2, 'j': 3, 'k': 1, 'cost': 13}, {'i': 2, 'j': 3, 'k': 2, 'cost': 40}, {'i': 2, 'j': 3, 'k': 3, 'cost': 89}, {'i': 2, 'j': 3, 'k': 4, 'cost': 36}, {'i': 2, 'j': 3, 'k': 5, 'cost': 89}, {'i': 2, 'j': 4, 'k': 0, 'cost': 79}, {'i': 2, 'j': 4, 'k': 1, 'cost': 65}, {'i': 2, 'j': 4, 'k': 2, 'cost': 63}, {'i': 2, 'j': 4, 'k': 3, 'cost': 4}, {'i': 2, 'j': 4, 'k': 4, 'cost': 91}, {'i': 2, 'j': 4, 'k': 5, 'cost': 4}, {'i': 2, 'j': 5, 'k': 0, 'cost': 97}, {'i': 2, 'j': 5, 'k': 1, 'cost': 56}, {'i': 2, 'j': 5, 'k': 2, 'cost': 96}, {'i': 2, 'j': 5, 'k': 3, 'cost': 35}, {'i': 2, 'j': 5, 'k': 4, 'cost': 76}, {'i': 2, 'j': 5, 'k': 5, 'cost': 49}, {'i': 3, 'j': 0, 'k': 0, 'cost': 50}, {'i': 3, 'j': 0, 'k': 1, 'cost': 86}, {'i': 3, 'j': 0, 'k': 2, 'cost': 31}, {'i': 3, 'j': 0, 'k': 3, 'cost': 88}, {'i': 3, 'j': 0, 'k': 4, 'cost': 87}, {'i': 3, 'j': 0, 'k': 5, 'cost': 57}, {'i': 3, 'j': 1, 'k': 0, 'cost': 46}, {'i': 3, 'j': 1, 'k': 1, 'cost': 53}, {'i': 3, 'j': 1, 'k': 2, 'cost': 32}, {'i': 3, 'j': 1, 'k': 3, 'cost': 38}, {'i': 3, 'j': 1, 'k': 4, 'cost': 5}, {'i': 3, 'j': 1, 'k': 5, 'cost': 38}, {'i': 3, 'j': 2, 'k': 0, 'cost': 26}, {'i': 3, 'j': 2, 'k': 1, 'cost': 94}, {'i': 3, 'j': 2, 'k': 2, 'cost': 16}, {'i': 3, 'j': 2, 'k': 3, 'cost': 17}, {'i': 3, 'j': 2, 'k': 4, 'cost': 39}, {'i': 3, 'j': 2, 'k': 5, 'cost': 72}, {'i': 3, 'j': 3, 'k': 0, 'cost': 57}, {'i': 3, 'j': 3, 'k': 1, 'cost': 66}, {'i': 3, 'j': 3, 'k': 2, 'cost': 52}, {'i': 3, 'j': 3, 'k': 3, 'cost': 11}, {'i': 3, 'j': 3, 'k': 4, 'cost': 28}, {'i': 3, 'j': 3, 'k': 5, 'cost': 8}, {'i': 3, 'j': 4, 'k': 0, 'cost': 45}, {'i': 3, 'j': 4, 'k': 1, 'cost': 92}, {'i': 3, 'j': 4, 'k': 2, 'cost': 48}, {'i': 3, 'j': 4, 'k': 3, 'cost': 46}, {'i': 3, 'j': 4, 'k': 4, 'cost': 89}, {'i': 3, 'j': 4, 'k': 5, 'cost': 16}, {'i': 3, 'j': 5, 'k': 0, 'cost': 74}, {'i': 3, 'j': 5, 'k': 1, 'cost': 24}, {'i': 3, 'j': 5, 'k': 2, 'cost': 78}, {'i': 3, 'j': 5, 'k': 3, 'cost': 83}, {'i': 3, 'j': 5, 'k': 4, 'cost': 5}, {'i': 3, 'j': 5, 'k': 5, 'cost': 67}, {'i': 4, 'j': 0, 'k': 0, 'cost': 95}, {'i': 4, 'j': 0, 'k': 1, 'cost': 62}, {'i': 4, 'j': 0, 'k': 2, 'cost': 24}, {'i': 4, 'j': 0, 'k': 3, 'cost': 0}, {'i': 4, 'j': 0, 'k': 4, 'cost': 13}, {'i': 4, 'j': 0, 'k': 5, 'cost': 64}, {'i': 4, 'j': 1, 'k': 0, 'cost': 71}, {'i': 4, 'j': 1, 'k': 1, 'cost': 45}, {'i': 4, 'j': 1, 'k': 2, 'cost': 6}, {'i': 4, 'j': 1, 'k': 3, 'cost': 97}, {'i': 4, 'j': 1, 'k': 4, 'cost': 84}, {'i': 4, 'j': 1, 'k': 5, 'cost': 7}, {'i': 4, 'j': 2, 'k': 0, 'cost': 55}, {'i': 4, 'j': 2, 'k': 1, 'cost': 75}, {'i': 4, 'j': 2, 'k': 2, 'cost': 84}, {'i': 4, 'j': 2, 'k': 3, 'cost': 40}, {'i': 4, 'j': 2, 'k': 4, 'cost': 81}, {'i': 4, 'j': 2, 'k': 5, 'cost': 76}, {'i': 4, 'j': 3, 'k': 0, 'cost': 24}, {'i': 4, 'j': 3, 'k': 1, 'cost': 4}, {'i': 4, 'j': 3, 'k': 2, 'cost': 60}, {'i': 4, 'j': 3, 'k': 3, 'cost': 8}, {'i': 4, 'j': 3, 'k': 4, 'cost': 8}, {'i': 4, 'j': 3, 'k': 5, 'cost': 51}, {'i': 4, 'j': 4, 'k': 0, 'cost': 22}, {'i': 4, 'j': 4, 'k': 1, 'cost': 4}, {'i': 4, 'j': 4, 'k': 2, 'cost': 72}, {'i': 4, 'j': 4, 'k': 3, 'cost': 94}, {'i': 4, 'j': 4, 'k': 4, 'cost': 95}, {'i': 4, 'j': 4, 'k': 5, 'cost': 77}, {'i': 4, 'j': 5, 'k': 0, 'cost': 53}, {'i': 4, 'j': 5, 'k': 1, 'cost': 36}, {'i': 4, 'j': 5, 'k': 2, 'cost': 61}, {'i': 4, 'j': 5, 'k': 3, 'cost': 71}, {'i': 4, 'j': 5, 'k': 4, 'cost': 0}, {'i': 4, 'j': 5, 'k': 5, 'cost': 52}, {'i': 5, 'j': 0, 'k': 0, 'cost': 89}, {'i': 5, 'j': 0, 'k': 1, 'cost': 75}, {'i': 5, 'j': 0, 'k': 2, 'cost': 87}, {'i': 5, 'j': 0, 'k': 3, 'cost': 50}, {'i': 5, 'j': 0, 'k': 4, 'cost': 17}, {'i': 5, 'j': 0, 'k': 5, 'cost': 47}, {'i': 5, 'j': 1, 'k': 0, 'cost': 69}, {'i': 5, 'j': 1, 'k': 1, 'cost': 86}, {'i': 5, 'j': 1, 'k': 2, 'cost': 13}, {'i': 5, 'j': 1, 'k': 3, 'cost': 17}, {'i': 5, 'j': 1, 'k': 4, 'cost': 20}, {'i': 5, 'j': 1, 'k': 5, 'cost': 67}, {'i': 5, 'j': 2, 'k': 0, 'cost': 33}, {'i': 5, 'j': 2, 'k': 1, 'cost': 14}, {'i': 5, 'j': 2, 'k': 2, 'cost': 70}, {'i': 5, 'j': 2, 'k': 3, 'cost': 30}, {'i': 5, 'j': 2, 'k': 4, 'cost': 2}, {'i': 5, 'j': 2, 'k': 5, 'cost': 49}, {'i': 5, 'j': 3, 'k': 0, 'cost': 7}, {'i': 5, 'j': 3, 'k': 1, 'cost': 94}, {'i': 5, 'j': 3, 'k': 2, 'cost': 96}, {'i': 5, 'j': 3, 'k': 3, 'cost': 21}, {'i': 5, 'j': 3, 'k': 4, 'cost': 60}, {'i': 5, 'j': 3, 'k': 5, 'cost': 23}, {'i': 5, 'j': 4, 'k': 0, 'cost': 66}, {'i': 5, 'j': 4, 'k': 1, 'cost': 30}, {'i': 5, 'j': 4, 'k': 2, 'cost': 8}, {'i': 5, 'j': 4, 'k': 3, 'cost': 78}, {'i': 5, 'j': 4, 'k': 4, 'cost': 23}, {'i': 5, 'j': 4, 'k': 5, 'cost': 99}, {'i': 5, 'j': 5, 'k': 0, 'cost': 34}, {'i': 5, 'j': 5, 'k': 1, 'cost': 40}, {'i': 5, 'j': 5, 'k': 2, 'cost': 28}, {'i': 5, 'j': 5, 'k': 3, 'cost': 69}, {'i': 5, 'j': 5, 'k': 4, 'cost': 61}, {'i': 5, 'j': 5, 'k': 5, 'cost': 56}]}","[[0, 1, 2], [1, 0, 3], [2, 2, 5], [3, 5, 4], [4, 4, 1], [5, 3, 0]]",23,csv,0
AP3,AP3,"I run a tiny shipping crew and every morning there’s a stack of packages waiting. The job is to pick one courier and one route for each package so that every courier and every route ends up handling exactly one package — nobody doubles up and nothing gets skipped. Each possible package–courier–route combination has a transit cost, and the plan that’s best is the one with the smallest total bill when all those individual costs are added together. The concrete details are shown below.

{
  ""num_packages"": 8,
  ""package_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H""
  ]
}

# Meaning: costs form a 3D tensor. For each fixed package_id=i, you are given a courier_id×route_id matrix whose entry at row courier_id=j and column route_id=k equals transit_cost(i,j,k). You must pick exactly one (j,k) for every i, with all courier_id and all route_id used exactly once.
# transit_cost_tensor (per-package_id markdown matrices)

## package_id=A
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 36 | 49 | 45 | 46 | 97 | 21 | 64 | 53 |
| B | 2 | 91 | 69 | 89 | 1 | 14 | 79 | 85 |
| C | 33 | 5 | 52 | 86 | 59 | 60 | 41 | 33 |
| D | 59 | 46 | 14 | 39 | 64 | 15 | 21 | 46 |
| E | 36 | 20 | 99 | 15 | 9 | 1 | 61 | 82 |
| F | 6 | 1 | 94 | 8 | 96 | 78 | 71 | 10 |
| G | 24 | 89 | 8 | 98 | 74 | 67 | 40 | 27 |
| H | 46 | 32 | 14 | 66 | 61 | 12 | 81 | 95 |

## package_id=B
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 37 | 36 | 21 | 67 | 50 | 63 | 65 | 73 |
| B | 1 | 8 | 50 | 86 | 34 | 81 | 1 | 35 |
| C | 72 | 65 | 30 | 78 | 1 | 27 | 31 | 13 |
| D | 93 | 2 | 62 | 5 | 84 | 25 | 68 | 37 |
| E | 31 | 6 | 72 | 41 | 89 | 36 | 86 | 50 |
| F | 22 | 20 | 68 | 5 | 45 | 95 | 68 | 99 |
| G | 82 | 46 | 36 | 82 | 58 | 15 | 78 | 72 |
| H | 98 | 43 | 84 | 96 | 21 | 58 | 86 | 81 |

## package_id=C
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 33 | 85 | 98 | 56 | 97 | 43 | 56 | 91 |
| B | 22 | 67 | 89 | 20 | 6 | 56 | 85 | 58 |
| C | 0 | 56 | 68 | 80 | 49 | 79 | 96 | 36 |
| D | 89 | 44 | 10 | 43 | 58 | 96 | 78 | 6 |
| E | 13 | 62 | 6 | 18 | 71 | 89 | 33 | 81 |
| F | 54 | 13 | 14 | 85 | 62 | 64 | 49 | 77 |
| G | 88 | 43 | 63 | 2 | 93 | 18 | 18 | 81 |
| H | 24 | 86 | 14 | 11 | 6 | 90 | 96 | 73 |

## package_id=D
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 5 | 79 | 47 | 8 | 96 | 48 | 7 | 77 |
| B | 54 | 41 | 14 | 75 | 11 | 47 | 90 | 10 |
| C | 31 | 18 | 46 | 73 | 95 | 0 | 27 | 45 |
| D | 47 | 96 | 70 | 15 | 11 | 84 | 33 | 14 |
| E | 58 | 88 | 27 | 13 | 43 | 7 | 96 | 98 |
| F | 60 | 56 | 31 | 63 | 75 | 76 | 17 | 54 |
| G | 41 | 49 | 67 | 97 | 2 | 86 | 25 | 81 |
| H | 60 | 63 | 34 | 31 | 38 | 49 | 68 | 61 |

## package_id=E
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 76 | 39 | 14 | 58 | 20 | 70 | 80 | 91 |
| B | 27 | 75 | 35 | 44 | 16 | 13 | 29 | 71 |
| C | 47 | 19 | 93 | 65 | 69 | 80 | 63 | 51 |
| D | 66 | 90 | 2 | 54 | 70 | 30 | 92 | 98 |
| E | 6 | 57 | 3 | 23 | 93 | 71 | 42 | 75 |
| F | 90 | 98 | 86 | 37 | 84 | 27 | 17 | 95 |
| G | 83 | 24 | 14 | 22 | 90 | 1 | 20 | 25 |
| H | 57 | 11 | 11 | 34 | 57 | 43 | 87 | 0 |

## package_id=F
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 21 | 78 | 18 | 64 | 96 | 86 | 38 | 81 |
| B | 31 | 96 | 28 | 75 | 8 | 13 | 9 | 2 |
| C | 59 | 23 | 24 | 55 | 60 | 60 | 33 | 23 |
| D | 2 | 54 | 89 | 92 | 50 | 96 | 69 | 41 |
| E | 11 | 66 | 41 | 94 | 39 | 80 | 76 | 70 |
| F | 72 | 59 | 13 | 51 | 96 | 25 | 23 | 14 |
| G | 51 | 29 | 85 | 20 | 52 | 38 | 16 | 46 |
| H | 10 | 96 | 38 | 5 | 54 | 38 | 25 | 94 |

## package_id=G
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 1 | 76 | 1 | 95 | 84 | 78 | 90 | 3 |
| B | 97 | 15 | 10 | 54 | 31 | 25 | 13 | 73 |
| C | 6 | 15 | 34 | 0 | 35 | 55 | 8 | 78 |
| D | 96 | 65 | 97 | 39 | 66 | 5 | 61 | 2 |
| E | 4 | 41 | 50 | 91 | 88 | 86 | 87 | 10 |
| F | 2 | 68 | 6 | 66 | 72 | 20 | 69 | 63 |
| G | 4 | 73 | 50 | 2 | 92 | 36 | 44 | 67 |
| H | 22 | 25 | 8 | 55 | 47 | 63 | 60 | 53 |

## package_id=H
| courier_id\route_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 58 | 0 | 85 | 22 | 58 | 10 | 7 | 42 |
| B | 51 | 8 | 30 | 27 | 8 | 81 | 78 | 83 |
| C | 43 | 63 | 70 | 57 | 19 | 3 | 71 | 39 |
| D | 70 | 19 | 41 | 58 | 28 | 83 | 48 | 95 |
| E | 42 | 84 | 39 | 9 | 64 | 2 | 11 | 25 |
| F | 45 | 10 | 26 | 69 | 40 | 47 | 51 | 91 |
| G | 71 | 34 | 34 | 36 | 89 | 97 | 73 | 14 |
| H | 3 | 20 | 14 | 49 | 72 | 25 | 52 | 5 |

If you want the plan in a simple, machine-readable form, just follow this little JSON shape — nothing fancy, just a list of triples showing which package goes with which courier and which route:

{
  ""solution"": [
    [<package_id>, <courier_id>, <route_id>],
    ...
  ]
}

Think of each inner triple as a single row on a form: the first entry is the package, the second is the courier assigned to it, and the third is the route they’ll take. This block is just a sketch of the shape I expect, not the actual assignment.

Please 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”.""","{'cost_tensor': [[[36, 49, 45, 46, 97, 21, 64, 53], [2, 91, 69, 89, 1, 14, 79, 85], [33, 5, 52, 86, 59, 60, 41, 33], [59, 46, 14, 39, 64, 15, 21, 46], [36, 20, 99, 15, 9, 1, 61, 82], [6, 1, 94, 8, 96, 78, 71, 10], [24, 89, 8, 98, 74, 67, 40, 27], [46, 32, 14, 66, 61, 12, 81, 95]], [[37, 36, 21, 67, 50, 63, 65, 73], [1, 8, 50, 86, 34, 81, 1, 35], [72, 65, 30, 78, 1, 27, 31, 13], [93, 2, 62, 5, 84, 25, 68, 37], [31, 6, 72, 41, 89, 36, 86, 50], [22, 20, 68, 5, 45, 95, 68, 99], [82, 46, 36, 82, 58, 15, 78, 72], [98, 43, 84, 96, 21, 58, 86, 81]], [[33, 85, 98, 56, 97, 43, 56, 91], [22, 67, 89, 20, 6, 56, 85, 58], [0, 56, 68, 80, 49, 79, 96, 36], [89, 44, 10, 43, 58, 96, 78, 6], [13, 62, 6, 18, 71, 89, 33, 81], [54, 13, 14, 85, 62, 64, 49, 77], [88, 43, 63, 2, 93, 18, 18, 81], [24, 86, 14, 11, 6, 90, 96, 73]], [[5, 79, 47, 8, 96, 48, 7, 77], [54, 41, 14, 75, 11, 47, 90, 10], [31, 18, 46, 73, 95, 0, 27, 45], [47, 96, 70, 15, 11, 84, 33, 14], [58, 88, 27, 13, 43, 7, 96, 98], [60, 56, 31, 63, 75, 76, 17, 54], [41, 49, 67, 97, 2, 86, 25, 81], [60, 63, 34, 31, 38, 49, 68, 61]], [[76, 39, 14, 58, 20, 70, 80, 91], [27, 75, 35, 44, 16, 13, 29, 71], [47, 19, 93, 65, 69, 80, 63, 51], [66, 90, 2, 54, 70, 30, 92, 98], [6, 57, 3, 23, 93, 71, 42, 75], [90, 98, 86, 37, 84, 27, 17, 95], [83, 24, 14, 22, 90, 1, 20, 25], [57, 11, 11, 34, 57, 43, 87, 0]], [[21, 78, 18, 64, 96, 86, 38, 81], [31, 96, 28, 75, 8, 13, 9, 2], [59, 23, 24, 55, 60, 60, 33, 23], [2, 54, 89, 92, 50, 96, 69, 41], [11, 66, 41, 94, 39, 80, 76, 70], [72, 59, 13, 51, 96, 25, 23, 14], [51, 29, 85, 20, 52, 38, 16, 46], [10, 96, 38, 5, 54, 38, 25, 94]], [[1, 76, 1, 95, 84, 78, 90, 3], [97, 15, 10, 54, 31, 25, 13, 73], [6, 15, 34, 0, 35, 55, 8, 78], [96, 65, 97, 39, 66, 5, 61, 2], [4, 41, 50, 91, 88, 86, 87, 10], [2, 68, 6, 66, 72, 20, 69, 63], [4, 73, 50, 2, 92, 36, 44, 67], [22, 25, 8, 55, 47, 63, 60, 53]], [[58, 0, 85, 22, 58, 10, 7, 42], [51, 8, 30, 27, 8, 81, 78, 83], [43, 63, 70, 57, 19, 3, 71, 39], [70, 19, 41, 58, 28, 83, 48, 95], [42, 84, 39, 9, 64, 2, 11, 25], [45, 10, 26, 69, 40, 47, 51, 91], [71, 34, 34, 36, 89, 97, 73, 14], [3, 20, 14, 49, 72, 25, 52, 5]]], 'objective': 16.0}","[[0, 5, 1], [1, 1, 6], [2, 2, 0], [3, 6, 4], [4, 3, 2], [5, 7, 3], [6, 0, 7], [7, 4, 5]]",16.0,"{'problem_type': 'AP3', 'n': 8, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 36}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 49}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 45}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 46}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 97}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 21}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 64}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 53}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 2}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 91}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 69}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 89}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 1}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 14}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 79}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 85}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 33}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 5}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 52}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 86}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 59}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 60}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 41}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 33}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 59}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 46}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 14}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 39}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 64}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 15}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 21}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 46}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 36}, {'i': 'A', 'j': 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'cost': 16}, {'i': 'F', 'j': 'G', 'k': 'H', 'cost': 46}, {'i': 'F', 'j': 'H', 'k': 'A', 'cost': 10}, {'i': 'F', 'j': 'H', 'k': 'B', 'cost': 96}, {'i': 'F', 'j': 'H', 'k': 'C', 'cost': 38}, {'i': 'F', 'j': 'H', 'k': 'D', 'cost': 5}, {'i': 'F', 'j': 'H', 'k': 'E', 'cost': 54}, {'i': 'F', 'j': 'H', 'k': 'F', 'cost': 38}, {'i': 'F', 'j': 'H', 'k': 'G', 'cost': 25}, {'i': 'F', 'j': 'H', 'k': 'H', 'cost': 94}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 1}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 76}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 1}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 95}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 84}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 78}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 90}, {'i': 'G', 'j': 'A', 'k': 'H', 'cost': 3}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 97}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 15}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 10}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 54}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 31}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 25}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 13}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 73}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 6}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 15}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 34}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 0}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 35}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 55}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 8}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 78}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 96}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 65}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 97}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 39}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 66}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 5}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 61}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 2}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 4}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 41}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 50}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 91}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 88}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 86}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 87}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 10}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 2}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 68}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 6}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 66}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 72}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 20}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 69}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 63}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 4}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 73}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 50}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 92}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 36}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 44}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 67}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 22}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 25}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 8}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 55}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 47}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 63}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 60}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 53}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 58}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 0}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 85}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 22}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 58}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 10}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 7}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 42}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 51}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 8}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 30}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 27}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 8}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 81}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 78}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 83}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 43}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 63}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 70}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 57}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 19}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 3}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 71}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 39}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 70}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 19}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 41}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 58}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 28}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 83}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 48}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 95}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 42}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 84}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 39}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 9}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 64}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 2}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 11}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 25}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 45}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 10}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 26}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 69}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 40}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 47}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 51}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 91}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 71}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 34}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 34}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 36}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 89}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 97}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 73}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 14}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 3}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 20}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 14}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 49}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 72}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 25}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 52}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 5}]}","[['A', 'F', 'B'], ['B', 'B', 'G'], ['C', 'C', 'A'], ['D', 'G', 'E'], ['E', 'D', 'C'], ['F', 'H', 'D'], ['G', 'A', 'H'], ['H', 'E', 'F']]",24,json,names
AP3,AP3,"There’s a busy day with as many repair jobs as there are technicians and kits, so the crew lead needs to match them up — one technician and one kit per job. Each possible match-up has a cost, every tech and every kit must be used exactly once, and the overall quality of a schedule is judged by adding all those match costs together: the smaller that grand total, the better the schedule. The exact options and numbers are shown below.

Below are the 7 repair request identifiers: 1, 2, 3, 4, 5, 6, 7.

*Meaning: costs form a 3D tensor. For each fixed request_id=i, you are given a technician_id×kit_id matrix whose entry at row technician_id=j and column kit_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all technician_id and all kit_id used exactly once.*

**assignment_cost_tensor (per-request_id markdown matrices)**

## request_id=1
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 55 | 19 | 41 | 48 | 67 | 97 | 40 |
| 2 | 64 | 23 | 78 | 74 | 24 | 31 | 84 |
| 3 | 38 | 58 | 97 | 2 | 62 | 46 | 83 |
| 4 | 66 | 12 | 49 | 52 | 56 | 58 | 60 |
| 5 | 32 | 68 | 26 | 7 | 88 | 34 | 42 |
| 6 | 86 | 75 | 75 | 75 | 13 | 36 | 92 |
| 7 | 25 | 30 | 64 | 65 | 52 | 96 | 56 |

## request_id=2
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 59 | 79 | 47 | 17 | 80 | 92 | 66 |
| 2 | 6 | 4 | 9 | 70 | 10 | 64 | 24 |
| 3 | 11 | 27 | 55 | 73 | 14 | 40 | 28 |
| 4 | 60 | 77 | 5 | 11 | 53 | 71 | 90 |
| 5 | 63 | 95 | 70 | 20 | 98 | 26 | 27 |
| 6 | 66 | 10 | 50 | 37 | 25 | 64 | 30 |
| 7 | 4 | 51 | 89 | 88 | 67 | 73 | 43 |

## request_id=3
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 59 | 34 | 30 | 76 | 49 | 44 | 79 |
| 2 | 2 | 21 | 58 | 6 | 69 | 6 | 81 |
| 3 | 91 | 69 | 17 | 34 | 90 | 41 | 47 |
| 4 | 37 | 91 | 56 | 45 | 9 | 91 | 65 |
| 5 | 58 | 17 | 3 | 66 | 41 | 20 | 70 |
| 6 | 29 | 65 | 87 | 19 | 20 | 8 | 33 |
| 7 | 76 | 45 | 26 | 84 | 35 | 83 | 20 |

## request_id=4
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 41 | 54 | 91 | 20 | 23 | 1 | 95 |
| 2 | 78 | 69 | 47 | 39 | 47 | 51 | 15 |
| 3 | 97 | 29 | 66 | 91 | 95 | 62 | 12 |
| 4 | 54 | 15 | 86 | 25 | 37 | 48 | 87 |
| 5 | 97 | 75 | 14 | 41 | 28 | 10 | 93 |
| 6 | 22 | 33 | 57 | 19 | 46 | 50 | 51 |
| 7 | 17 | 54 | 34 | 74 | 19 | 80 | 51 |

## request_id=5
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 18 | 36 | 37 | 92 | 20 | 96 | 52 |
| 2 | 6 | 1 | 76 | 94 | 45 | 90 | 79 |
| 3 | 61 | 23 | 76 | 60 | 81 | 24 | 58 |
| 4 | 32 | 51 | 91 | 66 | 61 | 88 | 1 |
| 5 | 61 | 89 | 51 | 29 | 81 | 71 | 43 |
| 6 | 46 | 46 | 17 | 59 | 37 | 73 | 31 |
| 7 | 10 | 13 | 83 | 87 | 73 | 64 | 53 |

## request_id=6
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 57 | 66 | 36 | 96 | 73 | 55 | 39 |
| 2 | 72 | 49 | 5 | 90 | 41 | 16 | 55 |
| 3 | 8 | 71 | 94 | 0 | 13 | 56 | 53 |
| 4 | 12 | 60 | 13 | 45 | 89 | 10 | 71 |
| 5 | 12 | 65 | 51 | 26 | 52 | 72 | 79 |
| 6 | 83 | 52 | 97 | 56 | 91 | 15 | 25 |
| 7 | 54 | 16 | 95 | 56 | 38 | 41 | 72 |

## request_id=7
| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 76 | 82 | 5 | 83 | 66 | 53 | 95 |
| 2 | 12 | 93 | 47 | 98 | 62 | 72 | 76 |
| 3 | 11 | 39 | 19 | 19 | 8 | 42 | 20 |
| 4 | 88 | 54 | 44 | 90 | 81 | 66 | 10 |
| 5 | 63 | 60 | 0 | 77 | 43 | 33 | 7 |
| 6 | 61 | 52 | 77 | 74 | 52 | 65 | 35 |
| 7 | 99 | 5 | 45 | 64 | 5 | 69 | 3 |

Aim to minimize the sum of these costs across all 7 requests.

When you’re ready to hand the chosen match-ups back, just send them in a little JSON snippet like this so it’s easy to read and reuse:

{
  ""solution"": [
    [<job_id>, <tech_id>, <kit_id>],
    ...
  ]
}

Each inner triple is one job with the technician and kit chosen for it (in that order: job, technician, kit). The outer list contains one triple per job. Think of this as a simple form to fill out — it’s just the shape I expect, not the actual answer.

Quick reminder: use the exact identifiers from the instance input — don’t rename them or 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"".","{'cost_tensor': [[[55, 19, 41, 48, 67, 97, 40], [64, 23, 78, 74, 24, 31, 84], [38, 58, 97, 2, 62, 46, 83], [66, 12, 49, 52, 56, 58, 60], [32, 68, 26, 7, 88, 34, 42], [86, 75, 75, 75, 13, 36, 92], [25, 30, 64, 65, 52, 96, 56]], [[59, 79, 47, 17, 80, 92, 66], [6, 4, 9, 70, 10, 64, 24], [11, 27, 55, 73, 14, 40, 28], [60, 77, 5, 11, 53, 71, 90], [63, 95, 70, 20, 98, 26, 27], [66, 10, 50, 37, 25, 64, 30], [4, 51, 89, 88, 67, 73, 43]], [[59, 34, 30, 76, 49, 44, 79], [2, 21, 58, 6, 69, 6, 81], [91, 69, 17, 34, 90, 41, 47], [37, 91, 56, 45, 9, 91, 65], [58, 17, 3, 66, 41, 20, 70], [29, 65, 87, 19, 20, 8, 33], [76, 45, 26, 84, 35, 83, 20]], [[41, 54, 91, 20, 23, 1, 95], [78, 69, 47, 39, 47, 51, 15], [97, 29, 66, 91, 95, 62, 12], [54, 15, 86, 25, 37, 48, 87], [97, 75, 14, 41, 28, 10, 93], [22, 33, 57, 19, 46, 50, 51], [17, 54, 34, 74, 19, 80, 51]], [[18, 36, 37, 92, 20, 96, 52], [6, 1, 76, 94, 45, 90, 79], [61, 23, 76, 60, 81, 24, 58], [32, 51, 91, 66, 61, 88, 1], [61, 89, 51, 29, 81, 71, 43], [46, 46, 17, 59, 37, 73, 31], [10, 13, 83, 87, 73, 64, 53]], [[57, 66, 36, 96, 73, 55, 39], [72, 49, 5, 90, 41, 16, 55], [8, 71, 94, 0, 13, 56, 53], [12, 60, 13, 45, 89, 10, 71], [12, 65, 51, 26, 52, 72, 79], [83, 52, 97, 56, 91, 15, 25], [54, 16, 95, 56, 38, 41, 72]], [[76, 82, 5, 83, 66, 53, 95], [12, 93, 47, 98, 62, 72, 76], [11, 39, 19, 19, 8, 42, 20], [88, 54, 44, 90, 81, 66, 10], [63, 60, 0, 77, 43, 33, 7], [61, 52, 77, 74, 52, 65, 35], [99, 5, 45, 64, 5, 69, 3]]], 'objective': 29.0}","[[0, 5, 4], [1, 1, 0], [2, 4, 2], [3, 0, 5], [4, 3, 6], [5, 2, 3], [6, 6, 1]]",29.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [1, 2, 3, 4, 5, 6, 7], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 55}, {'i': 1, 'j': 1, 'k': 2, 'cost': 19}, {'i': 1, 'j': 1, 'k': 3, 'cost': 41}, {'i': 1, 'j': 1, 'k': 4, 'cost': 48}, {'i': 1, 'j': 1, 'k': 5, 'cost': 67}, {'i': 1, 'j': 1, 'k': 6, 'cost': 97}, {'i': 1, 'j': 1, 'k': 7, 'cost': 40}, {'i': 1, 'j': 2, 'k': 1, 'cost': 64}, {'i': 1, 'j': 2, 'k': 2, 'cost': 23}, {'i': 1, 'j': 2, 'k': 3, 'cost': 78}, {'i': 1, 'j': 2, 'k': 4, 'cost': 74}, {'i': 1, 'j': 2, 'k': 5, 'cost': 24}, {'i': 1, 'j': 2, 'k': 6, 'cost': 31}, {'i': 1, 'j': 2, 'k': 7, 'cost': 84}, {'i': 1, 'j': 3, 'k': 1, 'cost': 38}, {'i': 1, 'j': 3, 'k': 2, 'cost': 58}, {'i': 1, 'j': 3, 'k': 3, 'cost': 97}, {'i': 1, 'j': 3, 'k': 4, 'cost': 2}, {'i': 1, 'j': 3, 'k': 5, 'cost': 62}, {'i': 1, 'j': 3, 'k': 6, 'cost': 46}, {'i': 1, 'j': 3, 'k': 7, 'cost': 83}, {'i': 1, 'j': 4, 'k': 1, 'cost': 66}, {'i': 1, 'j': 4, 'k': 2, 'cost': 12}, {'i': 1, 'j': 4, 'k': 3, 'cost': 49}, {'i': 1, 'j': 4, 'k': 4, 'cost': 52}, {'i': 1, 'j': 4, 'k': 5, 'cost': 56}, {'i': 1, 'j': 4, 'k': 6, 'cost': 58}, {'i': 1, 'j': 4, 'k': 7, 'cost': 60}, {'i': 1, 'j': 5, 'k': 1, 'cost': 32}, {'i': 1, 'j': 5, 'k': 2, 'cost': 68}, {'i': 1, 'j': 5, 'k': 3, 'cost': 26}, {'i': 1, 'j': 5, 'k': 4, 'cost': 7}, {'i': 1, 'j': 5, 'k': 5, 'cost': 88}, {'i': 1, 'j': 5, 'k': 6, 'cost': 34}, {'i': 1, 'j': 5, 'k': 7, 'cost': 42}, {'i': 1, 'j': 6, 'k': 1, 'cost': 86}, {'i': 1, 'j': 6, 'k': 2, 'cost': 75}, {'i': 1, 'j': 6, 'k': 3, 'cost': 75}, {'i': 1, 'j': 6, 'k': 4, 'cost': 75}, {'i': 1, 'j': 6, 'k': 5, 'cost': 13}, {'i': 1, 'j': 6, 'k': 6, 'cost': 36}, {'i': 1, 'j': 6, 'k': 7, 'cost': 92}, {'i': 1, 'j': 7, 'k': 1, 'cost': 25}, {'i': 1, 'j': 7, 'k': 2, 'cost': 30}, {'i': 1, 'j': 7, 'k': 3, 'cost': 64}, {'i': 1, 'j': 7, 'k': 4, 'cost': 65}, {'i': 1, 'j': 7, 'k': 5, 'cost': 52}, {'i': 1, 'j': 7, 'k': 6, 'cost': 96}, {'i': 1, 'j': 7, 'k': 7, 'cost': 56}, {'i': 2, 'j': 1, 'k': 1, 'cost': 59}, {'i': 2, 'j': 1, 'k': 2, 'cost': 79}, {'i': 2, 'j': 1, 'k': 3, 'cost': 47}, {'i': 2, 'j': 1, 'k': 4, 'cost': 17}, {'i': 2, 'j': 1, 'k': 5, 'cost': 80}, {'i': 2, 'j': 1, 'k': 6, 'cost': 92}, {'i': 2, 'j': 1, 'k': 7, 'cost': 66}, {'i': 2, 'j': 2, 'k': 1, 'cost': 6}, {'i': 2, 'j': 2, 'k': 2, 'cost': 4}, {'i': 2, 'j': 2, 'k': 3, 'cost': 9}, {'i': 2, 'j': 2, 'k': 4, 'cost': 70}, {'i': 2, 'j': 2, 'k': 5, 'cost': 10}, {'i': 2, 'j': 2, 'k': 6, 'cost': 64}, {'i': 2, 'j': 2, 'k': 7, 'cost': 24}, {'i': 2, 'j': 3, 'k': 1, 'cost': 11}, {'i': 2, 'j': 3, 'k': 2, 'cost': 27}, {'i': 2, 'j': 3, 'k': 3, 'cost': 55}, {'i': 2, 'j': 3, 'k': 4, 'cost': 73}, {'i': 2, 'j': 3, 'k': 5, 'cost': 14}, {'i': 2, 'j': 3, 'k': 6, 'cost': 40}, {'i': 2, 'j': 3, 'k': 7, 'cost': 28}, {'i': 2, 'j': 4, 'k': 1, 'cost': 60}, {'i': 2, 'j': 4, 'k': 2, 'cost': 77}, {'i': 2, 'j': 4, 'k': 3, 'cost': 5}, {'i': 2, 'j': 4, 'k': 4, 'cost': 11}, {'i': 2, 'j': 4, 'k': 5, 'cost': 53}, {'i': 2, 'j': 4, 'k': 6, 'cost': 71}, {'i': 2, 'j': 4, 'k': 7, 'cost': 90}, {'i': 2, 'j': 5, 'k': 1, 'cost': 63}, {'i': 2, 'j': 5, 'k': 2, 'cost': 95}, {'i': 2, 'j': 5, 'k': 3, 'cost': 70}, {'i': 2, 'j': 5, 'k': 4, 'cost': 20}, {'i': 2, 'j': 5, 'k': 5, 'cost': 98}, {'i': 2, 'j': 5, 'k': 6, 'cost': 26}, {'i': 2, 'j': 5, 'k': 7, 'cost': 27}, {'i': 2, 'j': 6, 'k': 1, 'cost': 66}, {'i': 2, 'j': 6, 'k': 2, 'cost': 10}, {'i': 2, 'j': 6, 'k': 3, 'cost': 50}, {'i': 2, 'j': 6, 'k': 4, 'cost': 37}, {'i': 2, 'j': 6, 'k': 5, 'cost': 25}, {'i': 2, 'j': 6, 'k': 6, 'cost': 64}, {'i': 2, 'j': 6, 'k': 7, 'cost': 30}, {'i': 2, 'j': 7, 'k': 1, 'cost': 4}, {'i': 2, 'j': 7, 'k': 2, 'cost': 51}, {'i': 2, 'j': 7, 'k': 3, 'cost': 89}, {'i': 2, 'j': 7, 'k': 4, 'cost': 88}, {'i': 2, 'j': 7, 'k': 5, 'cost': 67}, {'i': 2, 'j': 7, 'k': 6, 'cost': 73}, {'i': 2, 'j': 7, 'k': 7, 'cost': 43}, {'i': 3, 'j': 1, 'k': 1, 'cost': 59}, {'i': 3, 'j': 1, 'k': 2, 'cost': 34}, {'i': 3, 'j': 1, 'k': 3, 'cost': 30}, {'i': 3, 'j': 1, 'k': 4, 'cost': 76}, {'i': 3, 'j': 1, 'k': 5, 'cost': 49}, {'i': 3, 'j': 1, 'k': 6, 'cost': 44}, {'i': 3, 'j': 1, 'k': 7, 'cost': 79}, {'i': 3, 'j': 2, 'k': 1, 'cost': 2}, {'i': 3, 'j': 2, 'k': 2, 'cost': 21}, {'i': 3, 'j': 2, 'k': 3, 'cost': 58}, {'i': 3, 'j': 2, 'k': 4, 'cost': 6}, {'i': 3, 'j': 2, 'k': 5, 'cost': 69}, {'i': 3, 'j': 2, 'k': 6, 'cost': 6}, {'i': 3, 'j': 2, 'k': 7, 'cost': 81}, {'i': 3, 'j': 3, 'k': 1, 'cost': 91}, {'i': 3, 'j': 3, 'k': 2, 'cost': 69}, {'i': 3, 'j': 3, 'k': 3, 'cost': 17}, {'i': 3, 'j': 3, 'k': 4, 'cost': 34}, {'i': 3, 'j': 3, 'k': 5, 'cost': 90}, {'i': 3, 'j': 3, 'k': 6, 'cost': 41}, {'i': 3, 'j': 3, 'k': 7, 'cost': 47}, {'i': 3, 'j': 4, 'k': 1, 'cost': 37}, {'i': 3, 'j': 4, 'k': 2, 'cost': 91}, {'i': 3, 'j': 4, 'k': 3, 'cost': 56}, {'i': 3, 'j': 4, 'k': 4, 'cost': 45}, {'i': 3, 'j': 4, 'k': 5, 'cost': 9}, {'i': 3, 'j': 4, 'k': 6, 'cost': 91}, {'i': 3, 'j': 4, 'k': 7, 'cost': 65}, {'i': 3, 'j': 5, 'k': 1, 'cost': 58}, {'i': 3, 'j': 5, 'k': 2, 'cost': 17}, {'i': 3, 'j': 5, 'k': 3, 'cost': 3}, {'i': 3, 'j': 5, 'k': 4, 'cost': 66}, {'i': 3, 'j': 5, 'k': 5, 'cost': 41}, {'i': 3, 'j': 5, 'k': 6, 'cost': 20}, {'i': 3, 'j': 5, 'k': 7, 'cost': 70}, {'i': 3, 'j': 6, 'k': 1, 'cost': 29}, {'i': 3, 'j': 6, 'k': 2, 'cost': 65}, {'i': 3, 'j': 6, 'k': 3, 'cost': 87}, {'i': 3, 'j': 6, 'k': 4, 'cost': 19}, {'i': 3, 'j': 6, 'k': 5, 'cost': 20}, {'i': 3, 'j': 6, 'k': 6, 'cost': 8}, {'i': 3, 'j': 6, 'k': 7, 'cost': 33}, {'i': 3, 'j': 7, 'k': 1, 'cost': 76}, {'i': 3, 'j': 7, 'k': 2, 'cost': 45}, {'i': 3, 'j': 7, 'k': 3, 'cost': 26}, {'i': 3, 'j': 7, 'k': 4, 'cost': 84}, {'i': 3, 'j': 7, 'k': 5, 'cost': 35}, {'i': 3, 'j': 7, 'k': 6, 'cost': 83}, {'i': 3, 'j': 7, 'k': 7, 'cost': 20}, {'i': 4, 'j': 1, 'k': 1, 'cost': 41}, {'i': 4, 'j': 1, 'k': 2, 'cost': 54}, {'i': 4, 'j': 1, 'k': 3, 'cost': 91}, {'i': 4, 'j': 1, 'k': 4, 'cost': 20}, {'i': 4, 'j': 1, 'k': 5, 'cost': 23}, {'i': 4, 'j': 1, 'k': 6, 'cost': 1}, {'i': 4, 'j': 1, 'k': 7, 'cost': 95}, {'i': 4, 'j': 2, 'k': 1, 'cost': 78}, {'i': 4, 'j': 2, 'k': 2, 'cost': 69}, {'i': 4, 'j': 2, 'k': 3, 'cost': 47}, {'i': 4, 'j': 2, 'k': 4, 'cost': 39}, {'i': 4, 'j': 2, 'k': 5, 'cost': 47}, {'i': 4, 'j': 2, 'k': 6, 'cost': 51}, {'i': 4, 'j': 2, 'k': 7, 'cost': 15}, {'i': 4, 'j': 3, 'k': 1, 'cost': 97}, {'i': 4, 'j': 3, 'k': 2, 'cost': 29}, {'i': 4, 'j': 3, 'k': 3, 'cost': 66}, {'i': 4, 'j': 3, 'k': 4, 'cost': 91}, {'i': 4, 'j': 3, 'k': 5, 'cost': 95}, {'i': 4, 'j': 3, 'k': 6, 'cost': 62}, {'i': 4, 'j': 3, 'k': 7, 'cost': 12}, {'i': 4, 'j': 4, 'k': 1, 'cost': 54}, {'i': 4, 'j': 4, 'k': 2, 'cost': 15}, {'i': 4, 'j': 4, 'k': 3, 'cost': 86}, {'i': 4, 'j': 4, 'k': 4, 'cost': 25}, {'i': 4, 'j': 4, 'k': 5, 'cost': 37}, {'i': 4, 'j': 4, 'k': 6, 'cost': 48}, {'i': 4, 'j': 4, 'k': 7, 'cost': 87}, {'i': 4, 'j': 5, 'k': 1, 'cost': 97}, {'i': 4, 'j': 5, 'k': 2, 'cost': 75}, {'i': 4, 'j': 5, 'k': 3, 'cost': 14}, {'i': 4, 'j': 5, 'k': 4, 'cost': 41}, {'i': 4, 'j': 5, 'k': 5, 'cost': 28}, {'i': 4, 'j': 5, 'k': 6, 'cost': 10}, {'i': 4, 'j': 5, 'k': 7, 'cost': 93}, {'i': 4, 'j': 6, 'k': 1, 'cost': 22}, {'i': 4, 'j': 6, 'k': 2, 'cost': 33}, {'i': 4, 'j': 6, 'k': 3, 'cost': 57}, {'i': 4, 'j': 6, 'k': 4, 'cost': 19}, {'i': 4, 'j': 6, 'k': 5, 'cost': 46}, {'i': 4, 'j': 6, 'k': 6, 'cost': 50}, {'i': 4, 'j': 6, 'k': 7, 'cost': 51}, {'i': 4, 'j': 7, 'k': 1, 'cost': 17}, {'i': 4, 'j': 7, 'k': 2, 'cost': 54}, {'i': 4, 'j': 7, 'k': 3, 'cost': 34}, {'i': 4, 'j': 7, 'k': 4, 'cost': 74}, {'i': 4, 'j': 7, 'k': 5, 'cost': 19}, {'i': 4, 'j': 7, 'k': 6, 'cost': 80}, {'i': 4, 'j': 7, 'k': 7, 'cost': 51}, {'i': 5, 'j': 1, 'k': 1, 'cost': 18}, {'i': 5, 'j': 1, 'k': 2, 'cost': 36}, {'i': 5, 'j': 1, 'k': 3, 'cost': 37}, {'i': 5, 'j': 1, 'k': 4, 'cost': 92}, {'i': 5, 'j': 1, 'k': 5, 'cost': 20}, {'i': 5, 'j': 1, 'k': 6, 'cost': 96}, {'i': 5, 'j': 1, 'k': 7, 'cost': 52}, {'i': 5, 'j': 2, 'k': 1, 'cost': 6}, {'i': 5, 'j': 2, 'k': 2, 'cost': 1}, {'i': 5, 'j': 2, 'k': 3, 'cost': 76}, {'i': 5, 'j': 2, 'k': 4, 'cost': 94}, {'i': 5, 'j': 2, 'k': 5, 'cost': 45}, {'i': 5, 'j': 2, 'k': 6, 'cost': 90}, {'i': 5, 'j': 2, 'k': 7, 'cost': 79}, {'i': 5, 'j': 3, 'k': 1, 'cost': 61}, {'i': 5, 'j': 3, 'k': 2, 'cost': 23}, {'i': 5, 'j': 3, 'k': 3, 'cost': 76}, {'i': 5, 'j': 3, 'k': 4, 'cost': 60}, {'i': 5, 'j': 3, 'k': 5, 'cost': 81}, {'i': 5, 'j': 3, 'k': 6, 'cost': 24}, {'i': 5, 'j': 3, 'k': 7, 'cost': 58}, {'i': 5, 'j': 4, 'k': 1, 'cost': 32}, {'i': 5, 'j': 4, 'k': 2, 'cost': 51}, {'i': 5, 'j': 4, 'k': 3, 'cost': 91}, {'i': 5, 'j': 4, 'k': 4, 'cost': 66}, {'i': 5, 'j': 4, 'k': 5, 'cost': 61}, {'i': 5, 'j': 4, 'k': 6, 'cost': 88}, {'i': 5, 'j': 4, 'k': 7, 'cost': 1}, {'i': 5, 'j': 5, 'k': 1, 'cost': 61}, {'i': 5, 'j': 5, 'k': 2, 'cost': 89}, {'i': 5, 'j': 5, 'k': 3, 'cost': 51}, {'i': 5, 'j': 5, 'k': 4, 'cost': 29}, {'i': 5, 'j': 5, 'k': 5, 'cost': 81}, {'i': 5, 'j': 5, 'k': 6, 'cost': 71}, {'i': 5, 'j': 5, 'k': 7, 'cost': 43}, {'i': 5, 'j': 6, 'k': 1, 'cost': 46}, {'i': 5, 'j': 6, 'k': 2, 'cost': 46}, {'i': 5, 'j': 6, 'k': 3, 'cost': 17}, {'i': 5, 'j': 6, 'k': 4, 'cost': 59}, {'i': 5, 'j': 6, 'k': 5, 'cost': 37}, {'i': 5, 'j': 6, 'k': 6, 'cost': 73}, {'i': 5, 'j': 6, 'k': 7, 'cost': 31}, {'i': 5, 'j': 7, 'k': 1, 'cost': 10}, {'i': 5, 'j': 7, 'k': 2, 'cost': 13}, {'i': 5, 'j': 7, 'k': 3, 'cost': 83}, {'i': 5, 'j': 7, 'k': 4, 'cost': 87}, {'i': 5, 'j': 7, 'k': 5, 'cost': 73}, {'i': 5, 'j': 7, 'k': 6, 'cost': 64}, {'i': 5, 'j': 7, 'k': 7, 'cost': 53}, {'i': 6, 'j': 1, 'k': 1, 'cost': 57}, {'i': 6, 'j': 1, 'k': 2, 'cost': 66}, {'i': 6, 'j': 1, 'k': 3, 'cost': 36}, {'i': 6, 'j': 1, 'k': 4, 'cost': 96}, {'i': 6, 'j': 1, 'k': 5, 'cost': 73}, {'i': 6, 'j': 1, 'k': 6, 'cost': 55}, {'i': 6, 'j': 1, 'k': 7, 'cost': 39}, {'i': 6, 'j': 2, 'k': 1, 'cost': 72}, {'i': 6, 'j': 2, 'k': 2, 'cost': 49}, {'i': 6, 'j': 2, 'k': 3, 'cost': 5}, {'i': 6, 'j': 2, 'k': 4, 'cost': 90}, {'i': 6, 'j': 2, 'k': 5, 'cost': 41}, {'i': 6, 'j': 2, 'k': 6, 'cost': 16}, {'i': 6, 'j': 2, 'k': 7, 'cost': 55}, {'i': 6, 'j': 3, 'k': 1, 'cost': 8}, {'i': 6, 'j': 3, 'k': 2, 'cost': 71}, {'i': 6, 'j': 3, 'k': 3, 'cost': 94}, {'i': 6, 'j': 3, 'k': 4, 'cost': 0}, {'i': 6, 'j': 3, 'k': 5, 'cost': 13}, {'i': 6, 'j': 3, 'k': 6, 'cost': 56}, {'i': 6, 'j': 3, 'k': 7, 'cost': 53}, {'i': 6, 'j': 4, 'k': 1, 'cost': 12}, {'i': 6, 'j': 4, 'k': 2, 'cost': 60}, {'i': 6, 'j': 4, 'k': 3, 'cost': 13}, {'i': 6, 'j': 4, 'k': 4, 'cost': 45}, {'i': 6, 'j': 4, 'k': 5, 'cost': 89}, {'i': 6, 'j': 4, 'k': 6, 'cost': 10}, {'i': 6, 'j': 4, 'k': 7, 'cost': 71}, {'i': 6, 'j': 5, 'k': 1, 'cost': 12}, {'i': 6, 'j': 5, 'k': 2, 'cost': 65}, {'i': 6, 'j': 5, 'k': 3, 'cost': 51}, {'i': 6, 'j': 5, 'k': 4, 'cost': 26}, {'i': 6, 'j': 5, 'k': 5, 'cost': 52}, {'i': 6, 'j': 5, 'k': 6, 'cost': 72}, {'i': 6, 'j': 5, 'k': 7, 'cost': 79}, {'i': 6, 'j': 6, 'k': 1, 'cost': 83}, {'i': 6, 'j': 6, 'k': 2, 'cost': 52}, {'i': 6, 'j': 6, 'k': 3, 'cost': 97}, {'i': 6, 'j': 6, 'k': 4, 'cost': 56}, {'i': 6, 'j': 6, 'k': 5, 'cost': 91}, {'i': 6, 'j': 6, 'k': 6, 'cost': 15}, {'i': 6, 'j': 6, 'k': 7, 'cost': 25}, {'i': 6, 'j': 7, 'k': 1, 'cost': 54}, {'i': 6, 'j': 7, 'k': 2, 'cost': 16}, {'i': 6, 'j': 7, 'k': 3, 'cost': 95}, {'i': 6, 'j': 7, 'k': 4, 'cost': 56}, {'i': 6, 'j': 7, 'k': 5, 'cost': 38}, {'i': 6, 'j': 7, 'k': 6, 'cost': 41}, {'i': 6, 'j': 7, 'k': 7, 'cost': 72}, {'i': 7, 'j': 1, 'k': 1, 'cost': 76}, {'i': 7, 'j': 1, 'k': 2, 'cost': 82}, {'i': 7, 'j': 1, 'k': 3, 'cost': 5}, {'i': 7, 'j': 1, 'k': 4, 'cost': 83}, {'i': 7, 'j': 1, 'k': 5, 'cost': 66}, {'i': 7, 'j': 1, 'k': 6, 'cost': 53}, {'i': 7, 'j': 1, 'k': 7, 'cost': 95}, {'i': 7, 'j': 2, 'k': 1, 'cost': 12}, {'i': 7, 'j': 2, 'k': 2, 'cost': 93}, {'i': 7, 'j': 2, 'k': 3, 'cost': 47}, {'i': 7, 'j': 2, 'k': 4, 'cost': 98}, {'i': 7, 'j': 2, 'k': 5, 'cost': 62}, {'i': 7, 'j': 2, 'k': 6, 'cost': 72}, {'i': 7, 'j': 2, 'k': 7, 'cost': 76}, {'i': 7, 'j': 3, 'k': 1, 'cost': 11}, {'i': 7, 'j': 3, 'k': 2, 'cost': 39}, {'i': 7, 'j': 3, 'k': 3, 'cost': 19}, {'i': 7, 'j': 3, 'k': 4, 'cost': 19}, {'i': 7, 'j': 3, 'k': 5, 'cost': 8}, {'i': 7, 'j': 3, 'k': 6, 'cost': 42}, {'i': 7, 'j': 3, 'k': 7, 'cost': 20}, {'i': 7, 'j': 4, 'k': 1, 'cost': 88}, {'i': 7, 'j': 4, 'k': 2, 'cost': 54}, {'i': 7, 'j': 4, 'k': 3, 'cost': 44}, {'i': 7, 'j': 4, 'k': 4, 'cost': 90}, {'i': 7, 'j': 4, 'k': 5, 'cost': 81}, {'i': 7, 'j': 4, 'k': 6, 'cost': 66}, {'i': 7, 'j': 4, 'k': 7, 'cost': 10}, {'i': 7, 'j': 5, 'k': 1, 'cost': 63}, {'i': 7, 'j': 5, 'k': 2, 'cost': 60}, {'i': 7, 'j': 5, 'k': 3, 'cost': 0}, {'i': 7, 'j': 5, 'k': 4, 'cost': 77}, {'i': 7, 'j': 5, 'k': 5, 'cost': 43}, {'i': 7, 'j': 5, 'k': 6, 'cost': 33}, {'i': 7, 'j': 5, 'k': 7, 'cost': 7}, {'i': 7, 'j': 6, 'k': 1, 'cost': 61}, {'i': 7, 'j': 6, 'k': 2, 'cost': 52}, {'i': 7, 'j': 6, 'k': 3, 'cost': 77}, {'i': 7, 'j': 6, 'k': 4, 'cost': 74}, {'i': 7, 'j': 6, 'k': 5, 'cost': 52}, {'i': 7, 'j': 6, 'k': 6, 'cost': 65}, {'i': 7, 'j': 6, 'k': 7, 'cost': 35}, {'i': 7, 'j': 7, 'k': 1, 'cost': 99}, {'i': 7, 'j': 7, 'k': 2, 'cost': 5}, {'i': 7, 'j': 7, 'k': 3, 'cost': 45}, {'i': 7, 'j': 7, 'k': 4, 'cost': 64}, {'i': 7, 'j': 7, 'k': 5, 'cost': 5}, {'i': 7, 'j': 7, 'k': 6, 'cost': 69}, {'i': 7, 'j': 7, 'k': 7, 'cost': 3}]}","[[1, 6, 5], [2, 2, 1], [3, 5, 3], [4, 1, 6], [5, 4, 7], [6, 3, 4], [7, 7, 2]]",25,markdown_table,1
AP3,AP3,"Recently the planning team faced a neat challenge: match each meeting with a single presenter and a single room, using every presenter once and every room once. The smart schedule is the one that keeps the combined preparation and travel costs for everyone as small as possible — you figure that out by summing the prep+travel cost for each meeting in the plan and comparing totals. The full list of meetings, people, rooms, and costs is shown below.

# num_meetings=8
# meeting_ids=1, 2, 3, 4, 5, 6, 7, 8

# Meaning: costs form a 3D tensor. For each fixed meeting_id=i, you are given a presenter_id×room_id matrix whose entry at row presenter_id=j and column room_id=k equals prep_travel_cost(i,j,k). You must pick exactly one (j,k) for every i, with all presenter_id and all room_id used exactly once.
# prep_travel_cost_tensor (per-meeting_id markdown matrices)

## meeting_id=1
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 34 | 97 | 81 | 9 | 71 | 77 | 43 | 53 |
| 2 | 14 | 46 | 91 | 75 | 31 | 27 | 29 | 68 |
| 3 | 92 | 83 | 6 | 12 | 92 | 39 | 63 | 72 |
| 4 | 54 | 49 | 84 | 69 | 56 | 58 | 13 | 12 |
| 5 | 11 | 20 | 57 | 88 | 63 | 86 | 31 | 13 |
| 6 | 55 | 19 | 79 | 71 | 98 | 31 | 31 | 50 |
| 7 | 73 | 91 | 54 | 86 | 41 | 77 | 88 | 6 |
| 8 | 22 | 46 | 93 | 8 | 20 | 54 | 34 | 39 |

## meeting_id=2
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 65 | 8 | 7 | 71 | 50 | 69 | 37 | 22 |
| 2 | 62 | 7 | 66 | 4 | 34 | 47 | 54 | 49 |
| 3 | 91 | 54 | 7 | 16 | 18 | 32 | 79 | 40 |
| 4 | 94 | 34 | 38 | 72 | 55 | 13 | 88 | 12 |
| 5 | 76 | 27 | 85 | 35 | 57 | 11 | 21 | 8 |
| 6 | 96 | 19 | 16 | 47 | 14 | 19 | 42 | 80 |
| 7 | 9 | 84 | 16 | 63 | 73 | 14 | 73 | 61 |
| 8 | 69 | 58 | 50 | 21 | 36 | 40 | 91 | 18 |

## meeting_id=3
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 82 | 41 | 91 | 75 | 50 | 96 | 99 | 49 |
| 2 | 43 | 32 | 28 | 28 | 88 | 7 | 64 | 38 |
| 3 | 67 | 5 | 12 | 51 | 66 | 12 | 10 | 97 |
| 4 | 44 | 70 | 6 | 67 | 95 | 14 | 74 | 38 |
| 5 | 81 | 70 | 21 | 29 | 1 | 31 | 88 | 32 |
| 6 | 80 | 57 | 31 | 99 | 52 | 6 | 83 | 63 |
| 7 | 54 | 19 | 39 | 87 | 64 | 59 | 3 | 83 |
| 8 | 77 | 13 | 13 | 79 | 7 | 18 | 59 | 1 |

## meeting_id=4
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 7 | 16 | 2 | 48 | 21 | 20 | 81 | 52 |
| 2 | 16 | 43 | 16 | 27 | 38 | 62 | 97 | 4 |
| 3 | 83 | 37 | 54 | 35 | 92 | 80 | 27 | 12 |
| 4 | 24 | 94 | 82 | 22 | 16 | 29 | 39 | 21 |
| 5 | 85 | 84 | 67 | 20 | 36 | 22 | 3 | 75 |
| 6 | 26 | 40 | 95 | 2 | 0 | 73 | 17 | 49 |
| 7 | 52 | 29 | 55 | 50 | 86 | 63 | 27 | 69 |
| 8 | 99 | 21 | 26 | 28 | 29 | 4 | 15 | 20 |

## meeting_id=5
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 7 | 87 | 21 | 54 | 80 | 98 | 73 | 76 |
| 2 | 27 | 79 | 2 | 47 | 89 | 92 | 99 | 32 |
| 3 | 65 | 98 | 5 | 0 | 95 | 22 | 46 | 94 |
| 4 | 60 | 30 | 95 | 77 | 41 | 97 | 73 | 65 |
| 5 | 95 | 13 | 77 | 73 | 47 | 98 | 38 | 69 |
| 6 | 24 | 47 | 96 | 61 | 50 | 79 | 95 | 88 |
| 7 | 21 | 66 | 76 | 45 | 79 | 88 | 64 | 85 |
| 8 | 63 | 70 | 90 | 62 | 45 | 48 | 6 | 95 |

## meeting_id=6
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 92 | 48 | 60 | 79 | 65 | 62 | 25 | 97 |
| 2 | 36 | 80 | 0 | 13 | 35 | 51 | 29 | 54 |
| 3 | 62 | 34 | 55 | 64 | 20 | 95 | 24 | 42 |
| 4 | 79 | 96 | 38 | 33 | 20 | 90 | 10 | 17 |
| 5 | 90 | 76 | 18 | 40 | 52 | 51 | 94 | 56 |
| 6 | 88 | 90 | 14 | 55 | 75 | 35 | 65 | 21 |
| 7 | 2 | 32 | 57 | 27 | 14 | 42 | 76 | 63 |
| 8 | 96 | 29 | 75 | 64 | 28 | 95 | 4 | 12 |

## meeting_id=7
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 96 | 18 | 89 | 80 | 40 | 57 | 79 | 51 |
| 2 | 75 | 24 | 25 | 79 | 16 | 72 | 60 | 84 |
| 3 | 52 | 66 | 32 | 54 | 61 | 6 | 8 | 86 |
| 4 | 31 | 43 | 3 | 82 | 96 | 10 | 47 | 71 |
| 5 | 64 | 29 | 85 | 81 | 40 | 46 | 19 | 93 |
| 6 | 49 | 78 | 42 | 52 | 10 | 64 | 48 | 43 |
| 7 | 86 | 15 | 52 | 60 | 73 | 36 | 31 | 55 |
| 8 | 27 | 39 | 97 | 61 | 60 | 60 | 60 | 26 |

## meeting_id=8
| presenter_id\room_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 44 | 37 | 22 | 28 | 77 | 27 | 14 | 21 |
| 2 | 46 | 84 | 65 | 14 | 76 | 86 | 41 | 30 |
| 3 | 47 | 80 | 95 | 54 | 58 | 1 | 60 | 69 |
| 4 | 22 | 50 | 2 | 83 | 6 | 47 | 38 | 14 |
| 5 | 96 | 84 | 54 | 91 | 98 | 57 | 57 | 29 |
| 6 | 75 | 81 | 51 | 32 | 2 | 23 | 57 | 58 |
| 7 | 4 | 27 | 68 | 70 | 39 | 2 | 80 | 98 |
| 8 | 99 | 80 | 16 | 18 | 90 | 25 | 67 | 37 |

Oh, and when you’re ready to give the matching, please stick to this simple JSON layout so it’s easy to read and check:

{
  ""solution"": [
    [<meeting_id>, <presenter_id>, <room_id>],
    ...
  ]
}

Think of it like a little form: ""solution"" holds a list of triples, and each triple says which meeting goes with which presenter and which room. This is just the expected shape — not the actual assignment itself.

All identifiers must be used exactly as they appear in the instance input — no renaming and 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”.""","{'cost_tensor': [[[34, 97, 81, 9, 71, 77, 43, 53], [14, 46, 91, 75, 31, 27, 29, 68], [92, 83, 6, 12, 92, 39, 63, 72], [54, 49, 84, 69, 56, 58, 13, 12], [11, 20, 57, 88, 63, 86, 31, 13], [55, 19, 79, 71, 98, 31, 31, 50], [73, 91, 54, 86, 41, 77, 88, 6], [22, 46, 93, 8, 20, 54, 34, 39]], [[65, 8, 7, 71, 50, 69, 37, 22], [62, 7, 66, 4, 34, 47, 54, 49], [91, 54, 7, 16, 18, 32, 79, 40], [94, 34, 38, 72, 55, 13, 88, 12], [76, 27, 85, 35, 57, 11, 21, 8], [96, 19, 16, 47, 14, 19, 42, 80], [9, 84, 16, 63, 73, 14, 73, 61], [69, 58, 50, 21, 36, 40, 91, 18]], [[82, 41, 91, 75, 50, 96, 99, 49], [43, 32, 28, 28, 88, 7, 64, 38], [67, 5, 12, 51, 66, 12, 10, 97], [44, 70, 6, 67, 95, 14, 74, 38], [81, 70, 21, 29, 1, 31, 88, 32], [80, 57, 31, 99, 52, 6, 83, 63], [54, 19, 39, 87, 64, 59, 3, 83], [77, 13, 13, 79, 7, 18, 59, 1]], [[7, 16, 2, 48, 21, 20, 81, 52], [16, 43, 16, 27, 38, 62, 97, 4], [83, 37, 54, 35, 92, 80, 27, 12], [24, 94, 82, 22, 16, 29, 39, 21], [85, 84, 67, 20, 36, 22, 3, 75], [26, 40, 95, 2, 0, 73, 17, 49], [52, 29, 55, 50, 86, 63, 27, 69], [99, 21, 26, 28, 29, 4, 15, 20]], [[7, 87, 21, 54, 80, 98, 73, 76], [27, 79, 2, 47, 89, 92, 99, 32], [65, 98, 5, 0, 95, 22, 46, 94], [60, 30, 95, 77, 41, 97, 73, 65], [95, 13, 77, 73, 47, 98, 38, 69], [24, 47, 96, 61, 50, 79, 95, 88], [21, 66, 76, 45, 79, 88, 64, 85], [63, 70, 90, 62, 45, 48, 6, 95]], [[92, 48, 60, 79, 65, 62, 25, 97], [36, 80, 0, 13, 35, 51, 29, 54], [62, 34, 55, 64, 20, 95, 24, 42], [79, 96, 38, 33, 20, 90, 10, 17], [90, 76, 18, 40, 52, 51, 94, 56], [88, 90, 14, 55, 75, 35, 65, 21], [2, 32, 57, 27, 14, 42, 76, 63], [96, 29, 75, 64, 28, 95, 4, 12]], [[96, 18, 89, 80, 40, 57, 79, 51], [75, 24, 25, 79, 16, 72, 60, 84], [52, 66, 32, 54, 61, 6, 8, 86], [31, 43, 3, 82, 96, 10, 47, 71], [64, 29, 85, 81, 40, 46, 19, 93], [49, 78, 42, 52, 10, 64, 48, 43], [86, 15, 52, 60, 73, 36, 31, 55], [27, 39, 97, 61, 60, 60, 60, 26]], [[44, 37, 22, 28, 77, 27, 14, 21], [46, 84, 65, 14, 76, 86, 41, 30], [47, 80, 95, 54, 58, 1, 60, 69], [22, 50, 2, 83, 6, 47, 38, 14], [96, 84, 54, 91, 98, 57, 57, 29], [75, 81, 51, 32, 2, 23, 57, 58], [4, 27, 68, 70, 39, 2, 80, 98], [99, 80, 16, 18, 90, 25, 67, 37]]], 'objective': 31.0}","[[0, 6, 7], [1, 1, 1], [2, 4, 4], [3, 5, 3], [4, 0, 0], [5, 7, 6], [6, 3, 2], [7, 2, 5]]",31.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 34}, {'i': 1, 'j': 1, 'k': 2, 'cost': 97}, {'i': 1, 'j': 1, 'k': 3, 'cost': 81}, {'i': 1, 'j': 1, 'k': 4, 'cost': 9}, {'i': 1, 'j': 1, 'k': 5, 'cost': 71}, {'i': 1, 'j': 1, 'k': 6, 'cost': 77}, {'i': 1, 'j': 1, 'k': 7, 'cost': 43}, {'i': 1, 'j': 1, 'k': 8, 'cost': 53}, {'i': 1, 'j': 2, 'k': 1, 'cost': 14}, {'i': 1, 'j': 2, 'k': 2, 'cost': 46}, {'i': 1, 'j': 2, 'k': 3, 'cost': 91}, {'i': 1, 'j': 2, 'k': 4, 'cost': 75}, {'i': 1, 'j': 2, 'k': 5, 'cost': 31}, {'i': 1, 'j': 2, 'k': 6, 'cost': 27}, {'i': 1, 'j': 2, 'k': 7, 'cost': 29}, {'i': 1, 'j': 2, 'k': 8, 'cost': 68}, {'i': 1, 'j': 3, 'k': 1, 'cost': 92}, {'i': 1, 'j': 3, 'k': 2, 'cost': 83}, {'i': 1, 'j': 3, 'k': 3, 'cost': 6}, {'i': 1, 'j': 3, 'k': 4, 'cost': 12}, {'i': 1, 'j': 3, 'k': 5, 'cost': 92}, {'i': 1, 'j': 3, 'k': 6, 'cost': 39}, {'i': 1, 'j': 3, 'k': 7, 'cost': 63}, {'i': 1, 'j': 3, 'k': 8, 'cost': 72}, {'i': 1, 'j': 4, 'k': 1, 'cost': 54}, {'i': 1, 'j': 4, 'k': 2, 'cost': 49}, {'i': 1, 'j': 4, 'k': 3, 'cost': 84}, {'i': 1, 'j': 4, 'k': 4, 'cost': 69}, {'i': 1, 'j': 4, 'k': 5, 'cost': 56}, {'i': 1, 'j': 4, 'k': 6, 'cost': 58}, {'i': 1, 'j': 4, 'k': 7, 'cost': 13}, {'i': 1, 'j': 4, 'k': 8, 'cost': 12}, {'i': 1, 'j': 5, 'k': 1, 'cost': 11}, {'i': 1, 'j': 5, 'k': 2, 'cost': 20}, {'i': 1, 'j': 5, 'k': 3, 'cost': 57}, {'i': 1, 'j': 5, 'k': 4, 'cost': 88}, {'i': 1, 'j': 5, 'k': 5, 'cost': 63}, {'i': 1, 'j': 5, 'k': 6, 'cost': 86}, {'i': 1, 'j': 5, 'k': 7, 'cost': 31}, {'i': 1, 'j': 5, 'k': 8, 'cost': 13}, {'i': 1, 'j': 6, 'k': 1, 'cost': 55}, {'i': 1, 'j': 6, 'k': 2, 'cost': 19}, {'i': 1, 'j': 6, 'k': 3, 'cost': 79}, {'i': 1, 'j': 6, 'k': 4, 'cost': 71}, {'i': 1, 'j': 6, 'k': 5, 'cost': 98}, {'i': 1, 'j': 6, 'k': 6, 'cost': 31}, {'i': 1, 'j': 6, 'k': 7, 'cost': 31}, {'i': 1, 'j': 6, 'k': 8, 'cost': 50}, {'i': 1, 'j': 7, 'k': 1, 'cost': 73}, {'i': 1, 'j': 7, 'k': 2, 'cost': 91}, {'i': 1, 'j': 7, 'k': 3, 'cost': 54}, {'i': 1, 'j': 7, 'k': 4, 'cost': 86}, {'i': 1, 'j': 7, 'k': 5, 'cost': 41}, {'i': 1, 'j': 7, 'k': 6, 'cost': 77}, {'i': 1, 'j': 7, 'k': 7, 'cost': 88}, {'i': 1, 'j': 7, 'k': 8, 'cost': 6}, {'i': 1, 'j': 8, 'k': 1, 'cost': 22}, {'i': 1, 'j': 8, 'k': 2, 'cost': 46}, {'i': 1, 'j': 8, 'k': 3, 'cost': 93}, {'i': 1, 'j': 8, 'k': 4, 'cost': 8}, {'i': 1, 'j': 8, 'k': 5, 'cost': 20}, {'i': 1, 'j': 8, 'k': 6, 'cost': 54}, {'i': 1, 'j': 8, 'k': 7, 'cost': 34}, {'i': 1, 'j': 8, 'k': 8, 'cost': 39}, {'i': 2, 'j': 1, 'k': 1, 'cost': 65}, {'i': 2, 'j': 1, 'k': 2, 'cost': 8}, {'i': 2, 'j': 1, 'k': 3, 'cost': 7}, {'i': 2, 'j': 1, 'k': 4, 'cost': 71}, {'i': 2, 'j': 1, 'k': 5, 'cost': 50}, {'i': 2, 'j': 1, 'k': 6, 'cost': 69}, {'i': 2, 'j': 1, 'k': 7, 'cost': 37}, {'i': 2, 'j': 1, 'k': 8, 'cost': 22}, {'i': 2, 'j': 2, 'k': 1, 'cost': 62}, {'i': 2, 'j': 2, 'k': 2, 'cost': 7}, {'i': 2, 'j': 2, 'k': 3, 'cost': 66}, {'i': 2, 'j': 2, 'k': 4, 'cost': 4}, {'i': 2, 'j': 2, 'k': 5, 'cost': 34}, {'i': 2, 'j': 2, 'k': 6, 'cost': 47}, {'i': 2, 'j': 2, 'k': 7, 'cost': 54}, {'i': 2, 'j': 2, 'k': 8, 'cost': 49}, {'i': 2, 'j': 3, 'k': 1, 'cost': 91}, {'i': 2, 'j': 3, 'k': 2, 'cost': 54}, {'i': 2, 'j': 3, 'k': 3, 'cost': 7}, {'i': 2, 'j': 3, 'k': 4, 'cost': 16}, {'i': 2, 'j': 3, 'k': 5, 'cost': 18}, {'i': 2, 'j': 3, 'k': 6, 'cost': 32}, {'i': 2, 'j': 3, 'k': 7, 'cost': 79}, {'i': 2, 'j': 3, 'k': 8, 'cost': 40}, {'i': 2, 'j': 4, 'k': 1, 'cost': 94}, {'i': 2, 'j': 4, 'k': 2, 'cost': 34}, {'i': 2, 'j': 4, 'k': 3, 'cost': 38}, {'i': 2, 'j': 4, 'k': 4, 'cost': 72}, {'i': 2, 'j': 4, 'k': 5, 'cost': 55}, {'i': 2, 'j': 4, 'k': 6, 'cost': 13}, {'i': 2, 'j': 4, 'k': 7, 'cost': 88}, {'i': 2, 'j': 4, 'k': 8, 'cost': 12}, {'i': 2, 'j': 5, 'k': 1, 'cost': 76}, {'i': 2, 'j': 5, 'k': 2, 'cost': 27}, {'i': 2, 'j': 5, 'k': 3, 'cost': 85}, {'i': 2, 'j': 5, 'k': 4, 'cost': 35}, {'i': 2, 'j': 5, 'k': 5, 'cost': 57}, {'i': 2, 'j': 5, 'k': 6, 'cost': 11}, {'i': 2, 'j': 5, 'k': 7, 'cost': 21}, {'i': 2, 'j': 5, 'k': 8, 'cost': 8}, {'i': 2, 'j': 6, 'k': 1, 'cost': 96}, {'i': 2, 'j': 6, 'k': 2, 'cost': 19}, {'i': 2, 'j': 6, 'k': 3, 'cost': 16}, {'i': 2, 'j': 6, 'k': 4, 'cost': 47}, {'i': 2, 'j': 6, 'k': 5, 'cost': 14}, {'i': 2, 'j': 6, 'k': 6, 'cost': 19}, {'i': 2, 'j': 6, 'k': 7, 'cost': 42}, {'i': 2, 'j': 6, 'k': 8, 'cost': 80}, {'i': 2, 'j': 7, 'k': 1, 'cost': 9}, {'i': 2, 'j': 7, 'k': 2, 'cost': 84}, {'i': 2, 'j': 7, 'k': 3, 'cost': 16}, {'i': 2, 'j': 7, 'k': 4, 'cost': 63}, {'i': 2, 'j': 7, 'k': 5, 'cost': 73}, {'i': 2, 'j': 7, 'k': 6, 'cost': 14}, {'i': 2, 'j': 7, 'k': 7, 'cost': 73}, {'i': 2, 'j': 7, 'k': 8, 'cost': 61}, {'i': 2, 'j': 8, 'k': 1, 'cost': 69}, {'i': 2, 'j': 8, 'k': 2, 'cost': 58}, {'i': 2, 'j': 8, 'k': 3, 'cost': 50}, {'i': 2, 'j': 8, 'k': 4, 'cost': 21}, {'i': 2, 'j': 8, 'k': 5, 'cost': 36}, {'i': 2, 'j': 8, 'k': 6, 'cost': 40}, {'i': 2, 'j': 8, 'k': 7, 'cost': 91}, {'i': 2, 'j': 8, 'k': 8, 'cost': 18}, {'i': 3, 'j': 1, 'k': 1, 'cost': 82}, {'i': 3, 'j': 1, 'k': 2, 'cost': 41}, {'i': 3, 'j': 1, 'k': 3, 'cost': 91}, {'i': 3, 'j': 1, 'k': 4, 'cost': 75}, {'i': 3, 'j': 1, 'k': 5, 'cost': 50}, {'i': 3, 'j': 1, 'k': 6, 'cost': 96}, {'i': 3, 'j': 1, 'k': 7, 'cost': 99}, {'i': 3, 'j': 1, 'k': 8, 'cost': 49}, {'i': 3, 'j': 2, 'k': 1, 'cost': 43}, {'i': 3, 'j': 2, 'k': 2, 'cost': 32}, {'i': 3, 'j': 2, 'k': 3, 'cost': 28}, {'i': 3, 'j': 2, 'k': 4, 'cost': 28}, {'i': 3, 'j': 2, 'k': 5, 'cost': 88}, {'i': 3, 'j': 2, 'k': 6, 'cost': 7}, {'i': 3, 'j': 2, 'k': 7, 'cost': 64}, {'i': 3, 'j': 2, 'k': 8, 'cost': 38}, {'i': 3, 'j': 3, 'k': 1, 'cost': 67}, {'i': 3, 'j': 3, 'k': 2, 'cost': 5}, {'i': 3, 'j': 3, 'k': 3, 'cost': 12}, {'i': 3, 'j': 3, 'k': 4, 'cost': 51}, {'i': 3, 'j': 3, 'k': 5, 'cost': 66}, {'i': 3, 'j': 3, 'k': 6, 'cost': 12}, {'i': 3, 'j': 3, 'k': 7, 'cost': 10}, {'i': 3, 'j': 3, 'k': 8, 'cost': 97}, {'i': 3, 'j': 4, 'k': 1, 'cost': 44}, {'i': 3, 'j': 4, 'k': 2, 'cost': 70}, {'i': 3, 'j': 4, 'k': 3, 'cost': 6}, {'i': 3, 'j': 4, 'k': 4, 'cost': 67}, {'i': 3, 'j': 4, 'k': 5, 'cost': 95}, {'i': 3, 'j': 4, 'k': 6, 'cost': 14}, {'i': 3, 'j': 4, 'k': 7, 'cost': 74}, {'i': 3, 'j': 4, 'k': 8, 'cost': 38}, {'i': 3, 'j': 5, 'k': 1, 'cost': 81}, {'i': 3, 'j': 5, 'k': 2, 'cost': 70}, {'i': 3, 'j': 5, 'k': 3, 'cost': 21}, {'i': 3, 'j': 5, 'k': 4, 'cost': 29}, {'i': 3, 'j': 5, 'k': 5, 'cost': 1}, {'i': 3, 'j': 5, 'k': 6, 'cost': 31}, {'i': 3, 'j': 5, 'k': 7, 'cost': 88}, {'i': 3, 'j': 5, 'k': 8, 'cost': 32}, {'i': 3, 'j': 6, 'k': 1, 'cost': 80}, {'i': 3, 'j': 6, 'k': 2, 'cost': 57}, {'i': 3, 'j': 6, 'k': 3, 'cost': 31}, {'i': 3, 'j': 6, 'k': 4, 'cost': 99}, {'i': 3, 'j': 6, 'k': 5, 'cost': 52}, {'i': 3, 'j': 6, 'k': 6, 'cost': 6}, {'i': 3, 'j': 6, 'k': 7, 'cost': 83}, {'i': 3, 'j': 6, 'k': 8, 'cost': 63}, {'i': 3, 'j': 7, 'k': 1, 'cost': 54}, {'i': 3, 'j': 7, 'k': 2, 'cost': 19}, {'i': 3, 'j': 7, 'k': 3, 'cost': 39}, {'i': 3, 'j': 7, 'k': 4, 'cost': 87}, {'i': 3, 'j': 7, 'k': 5, 'cost': 64}, {'i': 3, 'j': 7, 'k': 6, 'cost': 59}, {'i': 3, 'j': 7, 'k': 7, 'cost': 3}, {'i': 3, 'j': 7, 'k': 8, 'cost': 83}, {'i': 3, 'j': 8, 'k': 1, 'cost': 77}, {'i': 3, 'j': 8, 'k': 2, 'cost': 13}, {'i': 3, 'j': 8, 'k': 3, 'cost': 13}, {'i': 3, 'j': 8, 'k': 4, 'cost': 79}, {'i': 3, 'j': 8, 'k': 5, 'cost': 7}, {'i': 3, 'j': 8, 'k': 6, 'cost': 18}, {'i': 3, 'j': 8, 'k': 7, 'cost': 59}, {'i': 3, 'j': 8, 'k': 8, 'cost': 1}, {'i': 4, 'j': 1, 'k': 1, 'cost': 7}, {'i': 4, 'j': 1, 'k': 2, 'cost': 16}, {'i': 4, 'j': 1, 'k': 3, 'cost': 2}, {'i': 4, 'j': 1, 'k': 4, 'cost': 48}, {'i': 4, 'j': 1, 'k': 5, 'cost': 21}, {'i': 4, 'j': 1, 'k': 6, 'cost': 20}, {'i': 4, 'j': 1, 'k': 7, 'cost': 81}, {'i': 4, 'j': 1, 'k': 8, 'cost': 52}, {'i': 4, 'j': 2, 'k': 1, 'cost': 16}, {'i': 4, 'j': 2, 'k': 2, 'cost': 43}, {'i': 4, 'j': 2, 'k': 3, 'cost': 16}, {'i': 4, 'j': 2, 'k': 4, 'cost': 27}, {'i': 4, 'j': 2, 'k': 5, 'cost': 38}, {'i': 4, 'j': 2, 'k': 6, 'cost': 62}, {'i': 4, 'j': 2, 'k': 7, 'cost': 97}, {'i': 4, 'j': 2, 'k': 8, 'cost': 4}, {'i': 4, 'j': 3, 'k': 1, 'cost': 83}, {'i': 4, 'j': 3, 'k': 2, 'cost': 37}, {'i': 4, 'j': 3, 'k': 3, 'cost': 54}, {'i': 4, 'j': 3, 'k': 4, 'cost': 35}, {'i': 4, 'j': 3, 'k': 5, 'cost': 92}, {'i': 4, 'j': 3, 'k': 6, 'cost': 80}, {'i': 4, 'j': 3, 'k': 7, 'cost': 27}, {'i': 4, 'j': 3, 'k': 8, 'cost': 12}, {'i': 4, 'j': 4, 'k': 1, 'cost': 24}, {'i': 4, 'j': 4, 'k': 2, 'cost': 94}, {'i': 4, 'j': 4, 'k': 3, 'cost': 82}, {'i': 4, 'j': 4, 'k': 4, 'cost': 22}, {'i': 4, 'j': 4, 'k': 5, 'cost': 16}, {'i': 4, 'j': 4, 'k': 6, 'cost': 29}, {'i': 4, 'j': 4, 'k': 7, 'cost': 39}, {'i': 4, 'j': 4, 'k': 8, 'cost': 21}, {'i': 4, 'j': 5, 'k': 1, 'cost': 85}, {'i': 4, 'j': 5, 'k': 2, 'cost': 84}, {'i': 4, 'j': 5, 'k': 3, 'cost': 67}, {'i': 4, 'j': 5, 'k': 4, 'cost': 20}, {'i': 4, 'j': 5, 'k': 5, 'cost': 36}, {'i': 4, 'j': 5, 'k': 6, 'cost': 22}, {'i': 4, 'j': 5, 'k': 7, 'cost': 3}, {'i': 4, 'j': 5, 'k': 8, 'cost': 75}, {'i': 4, 'j': 6, 'k': 1, 'cost': 26}, {'i': 4, 'j': 6, 'k': 2, 'cost': 40}, {'i': 4, 'j': 6, 'k': 3, 'cost': 95}, {'i': 4, 'j': 6, 'k': 4, 'cost': 2}, {'i': 4, 'j': 6, 'k': 5, 'cost': 0}, {'i': 4, 'j': 6, 'k': 6, 'cost': 73}, {'i': 4, 'j': 6, 'k': 7, 'cost': 17}, {'i': 4, 'j': 6, 'k': 8, 'cost': 49}, {'i': 4, 'j': 7, 'k': 1, 'cost': 52}, {'i': 4, 'j': 7, 'k': 2, 'cost': 29}, {'i': 4, 'j': 7, 'k': 3, 'cost': 55}, {'i': 4, 'j': 7, 'k': 4, 'cost': 50}, {'i': 4, 'j': 7, 'k': 5, 'cost': 86}, {'i': 4, 'j': 7, 'k': 6, 'cost': 63}, {'i': 4, 'j': 7, 'k': 7, 'cost': 27}, {'i': 4, 'j': 7, 'k': 8, 'cost': 69}, {'i': 4, 'j': 8, 'k': 1, 'cost': 99}, {'i': 4, 'j': 8, 'k': 2, 'cost': 21}, {'i': 4, 'j': 8, 'k': 3, 'cost': 26}, {'i': 4, 'j': 8, 'k': 4, 'cost': 28}, {'i': 4, 'j': 8, 'k': 5, 'cost': 29}, {'i': 4, 'j': 8, 'k': 6, 'cost': 4}, {'i': 4, 'j': 8, 'k': 7, 'cost': 15}, {'i': 4, 'j': 8, 'k': 8, 'cost': 20}, {'i': 5, 'j': 1, 'k': 1, 'cost': 7}, {'i': 5, 'j': 1, 'k': 2, 'cost': 87}, {'i': 5, 'j': 1, 'k': 3, 'cost': 21}, {'i': 5, 'j': 1, 'k': 4, 'cost': 54}, {'i': 5, 'j': 1, 'k': 5, 'cost': 80}, {'i': 5, 'j': 1, 'k': 6, 'cost': 98}, {'i': 5, 'j': 1, 'k': 7, 'cost': 73}, {'i': 5, 'j': 1, 'k': 8, 'cost': 76}, {'i': 5, 'j': 2, 'k': 1, 'cost': 27}, {'i': 5, 'j': 2, 'k': 2, 'cost': 79}, {'i': 5, 'j': 2, 'k': 3, 'cost': 2}, {'i': 5, 'j': 2, 'k': 4, 'cost': 47}, {'i': 5, 'j': 2, 'k': 5, 'cost': 89}, {'i': 5, 'j': 2, 'k': 6, 'cost': 92}, {'i': 5, 'j': 2, 'k': 7, 'cost': 99}, {'i': 5, 'j': 2, 'k': 8, 'cost': 32}, {'i': 5, 'j': 3, 'k': 1, 'cost': 65}, {'i': 5, 'j': 3, 'k': 2, 'cost': 98}, {'i': 5, 'j': 3, 'k': 3, 'cost': 5}, {'i': 5, 'j': 3, 'k': 4, 'cost': 0}, {'i': 5, 'j': 3, 'k': 5, 'cost': 95}, {'i': 5, 'j': 3, 'k': 6, 'cost': 22}, {'i': 5, 'j': 3, 'k': 7, 'cost': 46}, {'i': 5, 'j': 3, 'k': 8, 'cost': 94}, {'i': 5, 'j': 4, 'k': 1, 'cost': 60}, {'i': 5, 'j': 4, 'k': 2, 'cost': 30}, {'i': 5, 'j': 4, 'k': 3, 'cost': 95}, {'i': 5, 'j': 4, 'k': 4, 'cost': 77}, {'i': 5, 'j': 4, 'k': 5, 'cost': 41}, {'i': 5, 'j': 4, 'k': 6, 'cost': 97}, {'i': 5, 'j': 4, 'k': 7, 'cost': 73}, {'i': 5, 'j': 4, 'k': 8, 'cost': 65}, {'i': 5, 'j': 5, 'k': 1, 'cost': 95}, {'i': 5, 'j': 5, 'k': 2, 'cost': 13}, {'i': 5, 'j': 5, 'k': 3, 'cost': 77}, {'i': 5, 'j': 5, 'k': 4, 'cost': 73}, {'i': 5, 'j': 5, 'k': 5, 'cost': 47}, {'i': 5, 'j': 5, 'k': 6, 'cost': 98}, {'i': 5, 'j': 5, 'k': 7, 'cost': 38}, {'i': 5, 'j': 5, 'k': 8, 'cost': 69}, {'i': 5, 'j': 6, 'k': 1, 'cost': 24}, {'i': 5, 'j': 6, 'k': 2, 'cost': 47}, {'i': 5, 'j': 6, 'k': 3, 'cost': 96}, {'i': 5, 'j': 6, 'k': 4, 'cost': 61}, {'i': 5, 'j': 6, 'k': 5, 'cost': 50}, {'i': 5, 'j': 6, 'k': 6, 'cost': 79}, {'i': 5, 'j': 6, 'k': 7, 'cost': 95}, {'i': 5, 'j': 6, 'k': 8, 'cost': 88}, {'i': 5, 'j': 7, 'k': 1, 'cost': 21}, {'i': 5, 'j': 7, 'k': 2, 'cost': 66}, {'i': 5, 'j': 7, 'k': 3, 'cost': 76}, {'i': 5, 'j': 7, 'k': 4, 'cost': 45}, {'i': 5, 'j': 7, 'k': 5, 'cost': 79}, {'i': 5, 'j': 7, 'k': 6, 'cost': 88}, {'i': 5, 'j': 7, 'k': 7, 'cost': 64}, {'i': 5, 'j': 7, 'k': 8, 'cost': 85}, {'i': 5, 'j': 8, 'k': 1, 'cost': 63}, {'i': 5, 'j': 8, 'k': 2, 'cost': 70}, {'i': 5, 'j': 8, 'k': 3, 'cost': 90}, {'i': 5, 'j': 8, 'k': 4, 'cost': 62}, {'i': 5, 'j': 8, 'k': 5, 'cost': 45}, {'i': 5, 'j': 8, 'k': 6, 'cost': 48}, {'i': 5, 'j': 8, 'k': 7, 'cost': 6}, {'i': 5, 'j': 8, 'k': 8, 'cost': 95}, {'i': 6, 'j': 1, 'k': 1, 'cost': 92}, {'i': 6, 'j': 1, 'k': 2, 'cost': 48}, {'i': 6, 'j': 1, 'k': 3, 'cost': 60}, {'i': 6, 'j': 1, 'k': 4, 'cost': 79}, {'i': 6, 'j': 1, 'k': 5, 'cost': 65}, {'i': 6, 'j': 1, 'k': 6, 'cost': 62}, {'i': 6, 'j': 1, 'k': 7, 'cost': 25}, {'i': 6, 'j': 1, 'k': 8, 'cost': 97}, {'i': 6, 'j': 2, 'k': 1, 'cost': 36}, {'i': 6, 'j': 2, 'k': 2, 'cost': 80}, {'i': 6, 'j': 2, 'k': 3, 'cost': 0}, {'i': 6, 'j': 2, 'k': 4, 'cost': 13}, {'i': 6, 'j': 2, 'k': 5, 'cost': 35}, {'i': 6, 'j': 2, 'k': 6, 'cost': 51}, {'i': 6, 'j': 2, 'k': 7, 'cost': 29}, {'i': 6, 'j': 2, 'k': 8, 'cost': 54}, {'i': 6, 'j': 3, 'k': 1, 'cost': 62}, {'i': 6, 'j': 3, 'k': 2, 'cost': 34}, {'i': 6, 'j': 3, 'k': 3, 'cost': 55}, {'i': 6, 'j': 3, 'k': 4, 'cost': 64}, {'i': 6, 'j': 3, 'k': 5, 'cost': 20}, {'i': 6, 'j': 3, 'k': 6, 'cost': 95}, {'i': 6, 'j': 3, 'k': 7, 'cost': 24}, {'i': 6, 'j': 3, 'k': 8, 'cost': 42}, {'i': 6, 'j': 4, 'k': 1, 'cost': 79}, {'i': 6, 'j': 4, 'k': 2, 'cost': 96}, {'i': 6, 'j': 4, 'k': 3, 'cost': 38}, {'i': 6, 'j': 4, 'k': 4, 'cost': 33}, {'i': 6, 'j': 4, 'k': 5, 'cost': 20}, {'i': 6, 'j': 4, 'k': 6, 'cost': 90}, {'i': 6, 'j': 4, 'k': 7, 'cost': 10}, {'i': 6, 'j': 4, 'k': 8, 'cost': 17}, {'i': 6, 'j': 5, 'k': 1, 'cost': 90}, {'i': 6, 'j': 5, 'k': 2, 'cost': 76}, {'i': 6, 'j': 5, 'k': 3, 'cost': 18}, {'i': 6, 'j': 5, 'k': 4, 'cost': 40}, {'i': 6, 'j': 5, 'k': 5, 'cost': 52}, {'i': 6, 'j': 5, 'k': 6, 'cost': 51}, {'i': 6, 'j': 5, 'k': 7, 'cost': 94}, {'i': 6, 'j': 5, 'k': 8, 'cost': 56}, {'i': 6, 'j': 6, 'k': 1, 'cost': 88}, {'i': 6, 'j': 6, 'k': 2, 'cost': 90}, {'i': 6, 'j': 6, 'k': 3, 'cost': 14}, {'i': 6, 'j': 6, 'k': 4, 'cost': 55}, {'i': 6, 'j': 6, 'k': 5, 'cost': 75}, {'i': 6, 'j': 6, 'k': 6, 'cost': 35}, {'i': 6, 'j': 6, 'k': 7, 'cost': 65}, {'i': 6, 'j': 6, 'k': 8, 'cost': 21}, {'i': 6, 'j': 7, 'k': 1, 'cost': 2}, {'i': 6, 'j': 7, 'k': 2, 'cost': 32}, {'i': 6, 'j': 7, 'k': 3, 'cost': 57}, {'i': 6, 'j': 7, 'k': 4, 'cost': 27}, {'i': 6, 'j': 7, 'k': 5, 'cost': 14}, {'i': 6, 'j': 7, 'k': 6, 'cost': 42}, {'i': 6, 'j': 7, 'k': 7, 'cost': 76}, {'i': 6, 'j': 7, 'k': 8, 'cost': 63}, {'i': 6, 'j': 8, 'k': 1, 'cost': 96}, {'i': 6, 'j': 8, 'k': 2, 'cost': 29}, {'i': 6, 'j': 8, 'k': 3, 'cost': 75}, {'i': 6, 'j': 8, 'k': 4, 'cost': 64}, {'i': 6, 'j': 8, 'k': 5, 'cost': 28}, {'i': 6, 'j': 8, 'k': 6, 'cost': 95}, {'i': 6, 'j': 8, 'k': 7, 'cost': 4}, {'i': 6, 'j': 8, 'k': 8, 'cost': 12}, {'i': 7, 'j': 1, 'k': 1, 'cost': 96}, {'i': 7, 'j': 1, 'k': 2, 'cost': 18}, {'i': 7, 'j': 1, 'k': 3, 'cost': 89}, {'i': 7, 'j': 1, 'k': 4, 'cost': 80}, {'i': 7, 'j': 1, 'k': 5, 'cost': 40}, {'i': 7, 'j': 1, 'k': 6, 'cost': 57}, {'i': 7, 'j': 1, 'k': 7, 'cost': 79}, {'i': 7, 'j': 1, 'k': 8, 'cost': 51}, {'i': 7, 'j': 2, 'k': 1, 'cost': 75}, {'i': 7, 'j': 2, 'k': 2, 'cost': 24}, {'i': 7, 'j': 2, 'k': 3, 'cost': 25}, {'i': 7, 'j': 2, 'k': 4, 'cost': 79}, {'i': 7, 'j': 2, 'k': 5, 'cost': 16}, {'i': 7, 'j': 2, 'k': 6, 'cost': 72}, {'i': 7, 'j': 2, 'k': 7, 'cost': 60}, {'i': 7, 'j': 2, 'k': 8, 'cost': 84}, {'i': 7, 'j': 3, 'k': 1, 'cost': 52}, {'i': 7, 'j': 3, 'k': 2, 'cost': 66}, {'i': 7, 'j': 3, 'k': 3, 'cost': 32}, {'i': 7, 'j': 3, 'k': 4, 'cost': 54}, {'i': 7, 'j': 3, 'k': 5, 'cost': 61}, {'i': 7, 'j': 3, 'k': 6, 'cost': 6}, {'i': 7, 'j': 3, 'k': 7, 'cost': 8}, {'i': 7, 'j': 3, 'k': 8, 'cost': 86}, {'i': 7, 'j': 4, 'k': 1, 'cost': 31}, {'i': 7, 'j': 4, 'k': 2, 'cost': 43}, {'i': 7, 'j': 4, 'k': 3, 'cost': 3}, {'i': 7, 'j': 4, 'k': 4, 'cost': 82}, {'i': 7, 'j': 4, 'k': 5, 'cost': 96}, {'i': 7, 'j': 4, 'k': 6, 'cost': 10}, {'i': 7, 'j': 4, 'k': 7, 'cost': 47}, {'i': 7, 'j': 4, 'k': 8, 'cost': 71}, {'i': 7, 'j': 5, 'k': 1, 'cost': 64}, {'i': 7, 'j': 5, 'k': 2, 'cost': 29}, {'i': 7, 'j': 5, 'k': 3, 'cost': 85}, {'i': 7, 'j': 5, 'k': 4, 'cost': 81}, {'i': 7, 'j': 5, 'k': 5, 'cost': 40}, {'i': 7, 'j': 5, 'k': 6, 'cost': 46}, {'i': 7, 'j': 5, 'k': 7, 'cost': 19}, {'i': 7, 'j': 5, 'k': 8, 'cost': 93}, {'i': 7, 'j': 6, 'k': 1, 'cost': 49}, {'i': 7, 'j': 6, 'k': 2, 'cost': 78}, {'i': 7, 'j': 6, 'k': 3, 'cost': 42}, {'i': 7, 'j': 6, 'k': 4, 'cost': 52}, {'i': 7, 'j': 6, 'k': 5, 'cost': 10}, {'i': 7, 'j': 6, 'k': 6, 'cost': 64}, {'i': 7, 'j': 6, 'k': 7, 'cost': 48}, {'i': 7, 'j': 6, 'k': 8, 'cost': 43}, {'i': 7, 'j': 7, 'k': 1, 'cost': 86}, {'i': 7, 'j': 7, 'k': 2, 'cost': 15}, {'i': 7, 'j': 7, 'k': 3, 'cost': 52}, {'i': 7, 'j': 7, 'k': 4, 'cost': 60}, {'i': 7, 'j': 7, 'k': 5, 'cost': 73}, {'i': 7, 'j': 7, 'k': 6, 'cost': 36}, {'i': 7, 'j': 7, 'k': 7, 'cost': 31}, {'i': 7, 'j': 7, 'k': 8, 'cost': 55}, {'i': 7, 'j': 8, 'k': 1, 'cost': 27}, {'i': 7, 'j': 8, 'k': 2, 'cost': 39}, {'i': 7, 'j': 8, 'k': 3, 'cost': 97}, {'i': 7, 'j': 8, 'k': 4, 'cost': 61}, {'i': 7, 'j': 8, 'k': 5, 'cost': 60}, {'i': 7, 'j': 8, 'k': 6, 'cost': 60}, {'i': 7, 'j': 8, 'k': 7, 'cost': 60}, {'i': 7, 'j': 8, 'k': 8, 'cost': 26}, {'i': 8, 'j': 1, 'k': 1, 'cost': 44}, {'i': 8, 'j': 1, 'k': 2, 'cost': 37}, {'i': 8, 'j': 1, 'k': 3, 'cost': 22}, {'i': 8, 'j': 1, 'k': 4, 'cost': 28}, {'i': 8, 'j': 1, 'k': 5, 'cost': 77}, {'i': 8, 'j': 1, 'k': 6, 'cost': 27}, {'i': 8, 'j': 1, 'k': 7, 'cost': 14}, {'i': 8, 'j': 1, 'k': 8, 'cost': 21}, {'i': 8, 'j': 2, 'k': 1, 'cost': 46}, {'i': 8, 'j': 2, 'k': 2, 'cost': 84}, {'i': 8, 'j': 2, 'k': 3, 'cost': 65}, {'i': 8, 'j': 2, 'k': 4, 'cost': 14}, {'i': 8, 'j': 2, 'k': 5, 'cost': 76}, {'i': 8, 'j': 2, 'k': 6, 'cost': 86}, {'i': 8, 'j': 2, 'k': 7, 'cost': 41}, {'i': 8, 'j': 2, 'k': 8, 'cost': 30}, {'i': 8, 'j': 3, 'k': 1, 'cost': 47}, {'i': 8, 'j': 3, 'k': 2, 'cost': 80}, {'i': 8, 'j': 3, 'k': 3, 'cost': 95}, {'i': 8, 'j': 3, 'k': 4, 'cost': 54}, {'i': 8, 'j': 3, 'k': 5, 'cost': 58}, {'i': 8, 'j': 3, 'k': 6, 'cost': 1}, {'i': 8, 'j': 3, 'k': 7, 'cost': 60}, {'i': 8, 'j': 3, 'k': 8, 'cost': 69}, {'i': 8, 'j': 4, 'k': 1, 'cost': 22}, {'i': 8, 'j': 4, 'k': 2, 'cost': 50}, {'i': 8, 'j': 4, 'k': 3, 'cost': 2}, {'i': 8, 'j': 4, 'k': 4, 'cost': 83}, {'i': 8, 'j': 4, 'k': 5, 'cost': 6}, {'i': 8, 'j': 4, 'k': 6, 'cost': 47}, {'i': 8, 'j': 4, 'k': 7, 'cost': 38}, {'i': 8, 'j': 4, 'k': 8, 'cost': 14}, {'i': 8, 'j': 5, 'k': 1, 'cost': 96}, {'i': 8, 'j': 5, 'k': 2, 'cost': 84}, {'i': 8, 'j': 5, 'k': 3, 'cost': 54}, {'i': 8, 'j': 5, 'k': 4, 'cost': 91}, {'i': 8, 'j': 5, 'k': 5, 'cost': 98}, {'i': 8, 'j': 5, 'k': 6, 'cost': 57}, {'i': 8, 'j': 5, 'k': 7, 'cost': 57}, {'i': 8, 'j': 5, 'k': 8, 'cost': 29}, {'i': 8, 'j': 6, 'k': 1, 'cost': 75}, {'i': 8, 'j': 6, 'k': 2, 'cost': 81}, {'i': 8, 'j': 6, 'k': 3, 'cost': 51}, {'i': 8, 'j': 6, 'k': 4, 'cost': 32}, {'i': 8, 'j': 6, 'k': 5, 'cost': 2}, {'i': 8, 'j': 6, 'k': 6, 'cost': 23}, {'i': 8, 'j': 6, 'k': 7, 'cost': 57}, {'i': 8, 'j': 6, 'k': 8, 'cost': 58}, {'i': 8, 'j': 7, 'k': 1, 'cost': 4}, {'i': 8, 'j': 7, 'k': 2, 'cost': 27}, {'i': 8, 'j': 7, 'k': 3, 'cost': 68}, {'i': 8, 'j': 7, 'k': 4, 'cost': 70}, {'i': 8, 'j': 7, 'k': 5, 'cost': 39}, {'i': 8, 'j': 7, 'k': 6, 'cost': 2}, {'i': 8, 'j': 7, 'k': 7, 'cost': 80}, {'i': 8, 'j': 7, 'k': 8, 'cost': 98}, {'i': 8, 'j': 8, 'k': 1, 'cost': 99}, {'i': 8, 'j': 8, 'k': 2, 'cost': 80}, {'i': 8, 'j': 8, 'k': 3, 'cost': 16}, {'i': 8, 'j': 8, 'k': 4, 'cost': 18}, {'i': 8, 'j': 8, 'k': 5, 'cost': 90}, {'i': 8, 'j': 8, 'k': 6, 'cost': 25}, {'i': 8, 'j': 8, 'k': 7, 'cost': 67}, {'i': 8, 'j': 8, 'k': 8, 'cost': 37}]}","[[1, 7, 8], [2, 2, 2], [3, 5, 5], [4, 6, 4], [5, 1, 1], [6, 8, 7], [7, 4, 3], [8, 3, 6]]",26,csv,1
AP3,AP3,"Imagine the wardrobe and casting teams spread out on a big table of name tags: each scene needs a single actor tag and a single costume tag, and every tag must be placed exactly once. The trick is to choose which actor goes with which costume in which scene so the overall tab (each scene’s actor fee plus costume charge, added up for all scenes) comes out minimal. The specific costs and scene details are listed below.

Now list the 6 scene→(actor,costume) assignments using these identifiers 0, 1, 2, 3, 4, 5:

*Meaning: costs form a 3D tensor. For each fixed scene_id=i, you are given a actor_id×costume_id matrix whose entry at row actor_id=j and column costume_id=k equals total_assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all actor_id and all costume_id used exactly once.*

**total_assignment_cost_tensor (per-scene_id markdown matrices)**

## scene_id=0
| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 20 | 35 | 83 | 68 | 45 | 33 |
| 1 | 60 | 82 | 33 | 8 | 30 | 42 |
| 2 | 67 | 19 | 57 | 4 | 72 | 62 |
| 3 | 70 | 11 | 92 | 7 | 47 | 9 |
| 4 | 43 | 45 | 41 | 90 | 20 | 58 |
| 5 | 51 | 72 | 12 | 44 | 59 | 74 |

## scene_id=1
| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 78 | 78 | 32 | 33 | 47 | 81 |
| 1 | 2 | 28 | 81 | 71 | 34 | 52 |
| 2 | 74 | 82 | 91 | 40 | 24 | 42 |
| 3 | 22 | 45 | 56 | 79 | 68 | 98 |
| 4 | 50 | 94 | 39 | 68 | 93 | 17 |
| 5 | 89 | 14 | 19 | 32 | 13 | 84 |

## scene_id=2
| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 44 | 24 | 76 | 11 | 36 | 2 |
| 1 | 51 | 68 | 38 | 20 | 62 | 0 |
| 2 | 29 | 73 | 35 | 47 | 13 | 59 |
| 3 | 76 | 61 | 87 | 93 | 92 | 25 |
| 4 | 4 | 71 | 95 | 24 | 62 | 96 |
| 5 | 84 | 97 | 84 | 69 | 58 | 53 |

## scene_id=3
| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 34 | 9 | 80 | 18 | 66 | 79 |
| 1 | 44 | 83 | 39 | 66 | 85 | 15 |
| 2 | 87 | 19 | 91 | 31 | 28 | 83 |
| 3 | 7 | 27 | 57 | 50 | 27 | 5 |
| 4 | 98 | 87 | 50 | 49 | 53 | 55 |
| 5 | 47 | 78 | 18 | 40 | 39 | 84 |

## scene_id=4
| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 17 | 22 | 59 | 22 | 38 | 48 |
| 1 | 68 | 5 | 70 | 69 | 24 | 76 |
| 2 | 52 | 93 | 13 | 44 | 10 | 36 |
| 3 | 38 | 63 | 88 | 97 | 31 | 5 |
| 4 | 74 | 5 | 96 | 86 | 44 | 4 |
| 5 | 40 | 62 | 80 | 79 | 53 | 30 |

## scene_id=5
| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 10 | 99 | 82 | 39 | 5 | 92 |
| 1 | 58 | 15 | 65 | 41 | 49 | 9 |
| 2 | 81 | 20 | 5 | 93 | 48 | 90 |
| 3 | 43 | 35 | 54 | 32 | 13 | 39 |
| 4 | 26 | 38 | 74 | 26 | 62 | 1 |
| 5 | 75 | 5 | 80 | 74 | 45 | 95 |

Arrange the pairings so the overall tab (sum of each scene’s listed costs) is as small as possible.

Oh — and when you send the picks back, a little JSON like this is perfect:

{
  ""solution"": [
    [<scene_id>, <actor_id>, <costume_id>],
    ...
  ]
}

This just says ""solution"" is a list of triples. Each triple picks the scene, the actor tag, and the costume tag for that scene. The angle-bracket placeholders show the shape you should follow — fill them with the actual ids from the instance. This is only a sketch of the expected shape, not the actual assignment.

Please use the identifiers exactly as they appear in the instance input — do not rename or invent new labels. Valid identifiers look like:
- ""1"" or ""23""
- ""A"" or ""B""
- ""A1"" or ""X7""

No renaming, no extra labels — just the ids exactly as given.","{'cost_tensor': [[[20, 35, 83, 68, 45, 33], [60, 82, 33, 8, 30, 42], [67, 19, 57, 4, 72, 62], [70, 11, 92, 7, 47, 9], [43, 45, 41, 90, 20, 58], [51, 72, 12, 44, 59, 74]], [[78, 78, 32, 33, 47, 81], [2, 28, 81, 71, 34, 52], [74, 82, 91, 40, 24, 42], [22, 45, 56, 79, 68, 98], [50, 94, 39, 68, 93, 17], [89, 14, 19, 32, 13, 84]], [[44, 24, 76, 11, 36, 2], [51, 68, 38, 20, 62, 0], [29, 73, 35, 47, 13, 59], [76, 61, 87, 93, 92, 25], [4, 71, 95, 24, 62, 96], [84, 97, 84, 69, 58, 53]], [[34, 9, 80, 18, 66, 79], [44, 83, 39, 66, 85, 15], [87, 19, 91, 31, 28, 83], [7, 27, 57, 50, 27, 5], [98, 87, 50, 49, 53, 55], [47, 78, 18, 40, 39, 84]], [[17, 22, 59, 22, 38, 48], [68, 5, 70, 69, 24, 76], [52, 93, 13, 44, 10, 36], [38, 63, 88, 97, 31, 5], [74, 5, 96, 86, 44, 4], [40, 62, 80, 79, 53, 30]], [[10, 99, 82, 39, 5, 92], [58, 15, 65, 41, 49, 9], [81, 20, 5, 93, 48, 90], [43, 35, 54, 32, 13, 39], [26, 38, 74, 26, 62, 1], [75, 5, 80, 74, 45, 95]]], 'objective': 40.0}","[[0, 1, 3], [1, 5, 4], [2, 0, 5], [3, 3, 0], [4, 4, 1], [5, 2, 2]]",40.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 20}, {'i': 0, 'j': 0, 'k': 1, 'cost': 35}, {'i': 0, 'j': 0, 'k': 2, 'cost': 83}, {'i': 0, 'j': 0, 'k': 3, 'cost': 68}, {'i': 0, 'j': 0, 'k': 4, 'cost': 45}, {'i': 0, 'j': 0, 'k': 5, 'cost': 33}, {'i': 0, 'j': 1, 'k': 0, 'cost': 60}, {'i': 0, 'j': 1, 'k': 1, 'cost': 82}, {'i': 0, 'j': 1, 'k': 2, 'cost': 33}, {'i': 0, 'j': 1, 'k': 3, 'cost': 8}, {'i': 0, 'j': 1, 'k': 4, 'cost': 30}, {'i': 0, 'j': 1, 'k': 5, 'cost': 42}, {'i': 0, 'j': 2, 'k': 0, 'cost': 67}, {'i': 0, 'j': 2, 'k': 1, 'cost': 19}, {'i': 0, 'j': 2, 'k': 2, 'cost': 57}, {'i': 0, 'j': 2, 'k': 3, 'cost': 4}, {'i': 0, 'j': 2, 'k': 4, 'cost': 72}, {'i': 0, 'j': 2, 'k': 5, 'cost': 62}, {'i': 0, 'j': 3, 'k': 0, 'cost': 70}, {'i': 0, 'j': 3, 'k': 1, 'cost': 11}, {'i': 0, 'j': 3, 'k': 2, 'cost': 92}, {'i': 0, 'j': 3, 'k': 3, 'cost': 7}, {'i': 0, 'j': 3, 'k': 4, 'cost': 47}, {'i': 0, 'j': 3, 'k': 5, 'cost': 9}, {'i': 0, 'j': 4, 'k': 0, 'cost': 43}, {'i': 0, 'j': 4, 'k': 1, 'cost': 45}, {'i': 0, 'j': 4, 'k': 2, 'cost': 41}, {'i': 0, 'j': 4, 'k': 3, 'cost': 90}, {'i': 0, 'j': 4, 'k': 4, 'cost': 20}, {'i': 0, 'j': 4, 'k': 5, 'cost': 58}, {'i': 0, 'j': 5, 'k': 0, 'cost': 51}, {'i': 0, 'j': 5, 'k': 1, 'cost': 72}, {'i': 0, 'j': 5, 'k': 2, 'cost': 12}, {'i': 0, 'j': 5, 'k': 3, 'cost': 44}, {'i': 0, 'j': 5, 'k': 4, 'cost': 59}, {'i': 0, 'j': 5, 'k': 5, 'cost': 74}, {'i': 1, 'j': 0, 'k': 0, 'cost': 78}, {'i': 1, 'j': 0, 'k': 1, 'cost': 78}, {'i': 1, 'j': 0, 'k': 2, 'cost': 32}, {'i': 1, 'j': 0, 'k': 3, 'cost': 33}, {'i': 1, 'j': 0, 'k': 4, 'cost': 47}, {'i': 1, 'j': 0, 'k': 5, 'cost': 81}, {'i': 1, 'j': 1, 'k': 0, 'cost': 2}, {'i': 1, 'j': 1, 'k': 1, 'cost': 28}, {'i': 1, 'j': 1, 'k': 2, 'cost': 81}, {'i': 1, 'j': 1, 'k': 3, 'cost': 71}, {'i': 1, 'j': 1, 'k': 4, 'cost': 34}, {'i': 1, 'j': 1, 'k': 5, 'cost': 52}, {'i': 1, 'j': 2, 'k': 0, 'cost': 74}, {'i': 1, 'j': 2, 'k': 1, 'cost': 82}, {'i': 1, 'j': 2, 'k': 2, 'cost': 91}, {'i': 1, 'j': 2, 'k': 3, 'cost': 40}, {'i': 1, 'j': 2, 'k': 4, 'cost': 24}, {'i': 1, 'j': 2, 'k': 5, 'cost': 42}, {'i': 1, 'j': 3, 'k': 0, 'cost': 22}, {'i': 1, 'j': 3, 'k': 1, 'cost': 45}, {'i': 1, 'j': 3, 'k': 2, 'cost': 56}, {'i': 1, 'j': 3, 'k': 3, 'cost': 79}, {'i': 1, 'j': 3, 'k': 4, 'cost': 68}, {'i': 1, 'j': 3, 'k': 5, 'cost': 98}, {'i': 1, 'j': 4, 'k': 0, 'cost': 50}, {'i': 1, 'j': 4, 'k': 1, 'cost': 94}, {'i': 1, 'j': 4, 'k': 2, 'cost': 39}, {'i': 1, 'j': 4, 'k': 3, 'cost': 68}, {'i': 1, 'j': 4, 'k': 4, 'cost': 93}, {'i': 1, 'j': 4, 'k': 5, 'cost': 17}, {'i': 1, 'j': 5, 'k': 0, 'cost': 89}, {'i': 1, 'j': 5, 'k': 1, 'cost': 14}, {'i': 1, 'j': 5, 'k': 2, 'cost': 19}, {'i': 1, 'j': 5, 'k': 3, 'cost': 32}, {'i': 1, 'j': 5, 'k': 4, 'cost': 13}, {'i': 1, 'j': 5, 'k': 5, 'cost': 84}, {'i': 2, 'j': 0, 'k': 0, 'cost': 44}, {'i': 2, 'j': 0, 'k': 1, 'cost': 24}, {'i': 2, 'j': 0, 'k': 2, 'cost': 76}, {'i': 2, 'j': 0, 'k': 3, 'cost': 11}, {'i': 2, 'j': 0, 'k': 4, 'cost': 36}, {'i': 2, 'j': 0, 'k': 5, 'cost': 2}, {'i': 2, 'j': 1, 'k': 0, 'cost': 51}, {'i': 2, 'j': 1, 'k': 1, 'cost': 68}, {'i': 2, 'j': 1, 'k': 2, 'cost': 38}, {'i': 2, 'j': 1, 'k': 3, 'cost': 20}, {'i': 2, 'j': 1, 'k': 4, 'cost': 62}, {'i': 2, 'j': 1, 'k': 5, 'cost': 0}, {'i': 2, 'j': 2, 'k': 0, 'cost': 29}, {'i': 2, 'j': 2, 'k': 1, 'cost': 73}, {'i': 2, 'j': 2, 'k': 2, 'cost': 35}, {'i': 2, 'j': 2, 'k': 3, 'cost': 47}, {'i': 2, 'j': 2, 'k': 4, 'cost': 13}, {'i': 2, 'j': 2, 'k': 5, 'cost': 59}, {'i': 2, 'j': 3, 'k': 0, 'cost': 76}, {'i': 2, 'j': 3, 'k': 1, 'cost': 61}, {'i': 2, 'j': 3, 'k': 2, 'cost': 87}, {'i': 2, 'j': 3, 'k': 3, 'cost': 93}, {'i': 2, 'j': 3, 'k': 4, 'cost': 92}, {'i': 2, 'j': 3, 'k': 5, 'cost': 25}, {'i': 2, 'j': 4, 'k': 0, 'cost': 4}, {'i': 2, 'j': 4, 'k': 1, 'cost': 71}, {'i': 2, 'j': 4, 'k': 2, 'cost': 95}, {'i': 2, 'j': 4, 'k': 3, 'cost': 24}, {'i': 2, 'j': 4, 'k': 4, 'cost': 62}, {'i': 2, 'j': 4, 'k': 5, 'cost': 96}, {'i': 2, 'j': 5, 'k': 0, 'cost': 84}, {'i': 2, 'j': 5, 'k': 1, 'cost': 97}, {'i': 2, 'j': 5, 'k': 2, 'cost': 84}, {'i': 2, 'j': 5, 'k': 3, 'cost': 69}, {'i': 2, 'j': 5, 'k': 4, 'cost': 58}, {'i': 2, 'j': 5, 'k': 5, 'cost': 53}, {'i': 3, 'j': 0, 'k': 0, 'cost': 34}, {'i': 3, 'j': 0, 'k': 1, 'cost': 9}, {'i': 3, 'j': 0, 'k': 2, 'cost': 80}, {'i': 3, 'j': 0, 'k': 3, 'cost': 18}, {'i': 3, 'j': 0, 'k': 4, 'cost': 66}, {'i': 3, 'j': 0, 'k': 5, 'cost': 79}, {'i': 3, 'j': 1, 'k': 0, 'cost': 44}, {'i': 3, 'j': 1, 'k': 1, 'cost': 83}, {'i': 3, 'j': 1, 'k': 2, 'cost': 39}, {'i': 3, 'j': 1, 'k': 3, 'cost': 66}, {'i': 3, 'j': 1, 'k': 4, 'cost': 85}, {'i': 3, 'j': 1, 'k': 5, 'cost': 15}, {'i': 3, 'j': 2, 'k': 0, 'cost': 87}, {'i': 3, 'j': 2, 'k': 1, 'cost': 19}, {'i': 3, 'j': 2, 'k': 2, 'cost': 91}, {'i': 3, 'j': 2, 'k': 3, 'cost': 31}, {'i': 3, 'j': 2, 'k': 4, 'cost': 28}, {'i': 3, 'j': 2, 'k': 5, 'cost': 83}, {'i': 3, 'j': 3, 'k': 0, 'cost': 7}, {'i': 3, 'j': 3, 'k': 1, 'cost': 27}, {'i': 3, 'j': 3, 'k': 2, 'cost': 57}, {'i': 3, 'j': 3, 'k': 3, 'cost': 50}, {'i': 3, 'j': 3, 'k': 4, 'cost': 27}, {'i': 3, 'j': 3, 'k': 5, 'cost': 5}, {'i': 3, 'j': 4, 'k': 0, 'cost': 98}, {'i': 3, 'j': 4, 'k': 1, 'cost': 87}, {'i': 3, 'j': 4, 'k': 2, 'cost': 50}, {'i': 3, 'j': 4, 'k': 3, 'cost': 49}, {'i': 3, 'j': 4, 'k': 4, 'cost': 53}, {'i': 3, 'j': 4, 'k': 5, 'cost': 55}, {'i': 3, 'j': 5, 'k': 0, 'cost': 47}, {'i': 3, 'j': 5, 'k': 1, 'cost': 78}, {'i': 3, 'j': 5, 'k': 2, 'cost': 18}, {'i': 3, 'j': 5, 'k': 3, 'cost': 40}, {'i': 3, 'j': 5, 'k': 4, 'cost': 39}, {'i': 3, 'j': 5, 'k': 5, 'cost': 84}, {'i': 4, 'j': 0, 'k': 0, 'cost': 17}, {'i': 4, 'j': 0, 'k': 1, 'cost': 22}, {'i': 4, 'j': 0, 'k': 2, 'cost': 59}, {'i': 4, 'j': 0, 'k': 3, 'cost': 22}, {'i': 4, 'j': 0, 'k': 4, 'cost': 38}, {'i': 4, 'j': 0, 'k': 5, 'cost': 48}, {'i': 4, 'j': 1, 'k': 0, 'cost': 68}, {'i': 4, 'j': 1, 'k': 1, 'cost': 5}, {'i': 4, 'j': 1, 'k': 2, 'cost': 70}, {'i': 4, 'j': 1, 'k': 3, 'cost': 69}, {'i': 4, 'j': 1, 'k': 4, 'cost': 24}, {'i': 4, 'j': 1, 'k': 5, 'cost': 76}, {'i': 4, 'j': 2, 'k': 0, 'cost': 52}, {'i': 4, 'j': 2, 'k': 1, 'cost': 93}, {'i': 4, 'j': 2, 'k': 2, 'cost': 13}, {'i': 4, 'j': 2, 'k': 3, 'cost': 44}, {'i': 4, 'j': 2, 'k': 4, 'cost': 10}, {'i': 4, 'j': 2, 'k': 5, 'cost': 36}, {'i': 4, 'j': 3, 'k': 0, 'cost': 38}, {'i': 4, 'j': 3, 'k': 1, 'cost': 63}, {'i': 4, 'j': 3, 'k': 2, 'cost': 88}, {'i': 4, 'j': 3, 'k': 3, 'cost': 97}, {'i': 4, 'j': 3, 'k': 4, 'cost': 31}, {'i': 4, 'j': 3, 'k': 5, 'cost': 5}, {'i': 4, 'j': 4, 'k': 0, 'cost': 74}, {'i': 4, 'j': 4, 'k': 1, 'cost': 5}, {'i': 4, 'j': 4, 'k': 2, 'cost': 96}, {'i': 4, 'j': 4, 'k': 3, 'cost': 86}, {'i': 4, 'j': 4, 'k': 4, 'cost': 44}, {'i': 4, 'j': 4, 'k': 5, 'cost': 4}, {'i': 4, 'j': 5, 'k': 0, 'cost': 40}, {'i': 4, 'j': 5, 'k': 1, 'cost': 62}, {'i': 4, 'j': 5, 'k': 2, 'cost': 80}, {'i': 4, 'j': 5, 'k': 3, 'cost': 79}, {'i': 4, 'j': 5, 'k': 4, 'cost': 53}, {'i': 4, 'j': 5, 'k': 5, 'cost': 30}, {'i': 5, 'j': 0, 'k': 0, 'cost': 10}, {'i': 5, 'j': 0, 'k': 1, 'cost': 99}, {'i': 5, 'j': 0, 'k': 2, 'cost': 82}, {'i': 5, 'j': 0, 'k': 3, 'cost': 39}, {'i': 5, 'j': 0, 'k': 4, 'cost': 5}, {'i': 5, 'j': 0, 'k': 5, 'cost': 92}, {'i': 5, 'j': 1, 'k': 0, 'cost': 58}, {'i': 5, 'j': 1, 'k': 1, 'cost': 15}, {'i': 5, 'j': 1, 'k': 2, 'cost': 65}, {'i': 5, 'j': 1, 'k': 3, 'cost': 41}, {'i': 5, 'j': 1, 'k': 4, 'cost': 49}, {'i': 5, 'j': 1, 'k': 5, 'cost': 9}, {'i': 5, 'j': 2, 'k': 0, 'cost': 81}, {'i': 5, 'j': 2, 'k': 1, 'cost': 20}, {'i': 5, 'j': 2, 'k': 2, 'cost': 5}, {'i': 5, 'j': 2, 'k': 3, 'cost': 93}, {'i': 5, 'j': 2, 'k': 4, 'cost': 48}, {'i': 5, 'j': 2, 'k': 5, 'cost': 90}, {'i': 5, 'j': 3, 'k': 0, 'cost': 43}, {'i': 5, 'j': 3, 'k': 1, 'cost': 35}, {'i': 5, 'j': 3, 'k': 2, 'cost': 54}, {'i': 5, 'j': 3, 'k': 3, 'cost': 32}, {'i': 5, 'j': 3, 'k': 4, 'cost': 13}, {'i': 5, 'j': 3, 'k': 5, 'cost': 39}, {'i': 5, 'j': 4, 'k': 0, 'cost': 26}, {'i': 5, 'j': 4, 'k': 1, 'cost': 38}, {'i': 5, 'j': 4, 'k': 2, 'cost': 74}, {'i': 5, 'j': 4, 'k': 3, 'cost': 26}, {'i': 5, 'j': 4, 'k': 4, 'cost': 62}, {'i': 5, 'j': 4, 'k': 5, 'cost': 1}, {'i': 5, 'j': 5, 'k': 0, 'cost': 75}, {'i': 5, 'j': 5, 'k': 1, 'cost': 5}, {'i': 5, 'j': 5, 'k': 2, 'cost': 80}, {'i': 5, 'j': 5, 'k': 3, 'cost': 74}, {'i': 5, 'j': 5, 'k': 4, 'cost': 45}, {'i': 5, 'j': 5, 'k': 5, 'cost': 95}]}","[[0, 1, 3], [1, 5, 4], [2, 0, 5], [3, 3, 0], [4, 4, 1], [5, 2, 2]]",27,markdown_table,0
AP3,AP3,"There's a little scheduling puzzle at the community center: a set of clients, a set of interpreters, and a set of available time slots, and each client needs one interpreter at one slot. The aim is to choose those matches so that no interpreter or time appears twice and every client gets exactly one session, and then you add up the cost of each chosen session — the schedule with the lowest total cost is the goal. The full list of who’s available and how much each possible session costs is shown below.

{
  ""num_clients"": 7,
  ""index_ids"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7
  ]
}

# Meaning: costs form a 3D tensor. For each fixed client_id=i, you are given a interpreter_id×timeslot_id matrix whose entry at row interpreter_id=j and column timeslot_id=k equals session_cost(i,j,k). You must pick exactly one (j,k) for every i, with all interpreter_id and all timeslot_id used exactly once.
# session_cost_tensor (per-client_id markdown matrices)

## client_id=1
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 70 | 87 | 0 | 20 | 80 | 51 | 1 |
| 2 | 6 | 52 | 18 | 90 | 88 | 86 | 82 |
| 3 | 17 | 47 | 54 | 34 | 3 | 74 | 27 |
| 4 | 45 | 32 | 9 | 98 | 4 | 4 | 97 |
| 5 | 86 | 4 | 58 | 53 | 53 | 61 | 97 |
| 6 | 12 | 8 | 3 | 34 | 64 | 55 | 87 |
| 7 | 31 | 35 | 69 | 47 | 33 | 22 | 20 |

## client_id=2
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 81 | 37 | 26 | 64 | 11 | 24 | 72 |
| 2 | 74 | 14 | 50 | 83 | 45 | 67 | 45 |
| 3 | 7 | 81 | 53 | 91 | 5 | 1 | 27 |
| 4 | 10 | 64 | 3 | 76 | 84 | 9 | 66 |
| 5 | 59 | 66 | 33 | 31 | 14 | 54 | 72 |
| 6 | 54 | 80 | 4 | 53 | 27 | 80 | 78 |
| 7 | 47 | 70 | 45 | 55 | 80 | 37 | 87 |

## client_id=3
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 17 | 14 | 36 | 19 | 35 | 73 | 51 |
| 2 | 5 | 34 | 41 | 23 | 68 | 2 | 72 |
| 3 | 80 | 68 | 23 | 47 | 63 | 80 | 25 |
| 4 | 42 | 94 | 23 | 25 | 7 | 21 | 12 |
| 5 | 26 | 93 | 86 | 5 | 79 | 24 | 14 |
| 6 | 74 | 14 | 13 | 29 | 75 | 28 | 84 |
| 7 | 71 | 72 | 75 | 72 | 65 | 94 | 43 |

## client_id=4
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 94 | 47 | 24 | 78 | 46 | 62 | 50 |
| 2 | 53 | 53 | 35 | 30 | 6 | 35 | 81 |
| 3 | 82 | 54 | 18 | 15 | 50 | 8 | 45 |
| 4 | 97 | 73 | 66 | 10 | 69 | 14 | 59 |
| 5 | 0 | 31 | 19 | 30 | 16 | 26 | 53 |
| 6 | 38 | 30 | 85 | 69 | 41 | 39 | 44 |
| 7 | 6 | 14 | 39 | 92 | 2 | 17 | 13 |

## client_id=5
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 59 | 67 | 7 | 54 | 54 | 89 | 41 |
| 2 | 45 | 25 | 77 | 57 | 32 | 57 | 49 |
| 3 | 80 | 15 | 42 | 62 | 89 | 41 | 81 |
| 4 | 83 | 69 | 6 | 20 | 24 | 89 | 91 |
| 5 | 99 | 31 | 13 | 2 | 98 | 49 | 92 |
| 6 | 94 | 37 | 10 | 74 | 1 | 75 | 60 |
| 7 | 64 | 40 | 78 | 40 | 3 | 54 | 86 |

## client_id=6
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 3 | 80 | 39 | 24 | 97 | 2 | 87 |
| 2 | 36 | 87 | 29 | 35 | 97 | 48 | 98 |
| 3 | 38 | 23 | 37 | 63 | 19 | 2 | 87 |
| 4 | 85 | 21 | 31 | 89 | 63 | 28 | 98 |
| 5 | 84 | 78 | 79 | 86 | 53 | 66 | 1 |
| 6 | 93 | 79 | 40 | 72 | 9 | 64 | 44 |
| 7 | 67 | 9 | 13 | 68 | 73 | 63 | 92 |

## client_id=7
| interpreter_id\timeslot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 92 | 40 | 60 | 8 | 40 | 39 | 25 |
| 2 | 28 | 59 | 52 | 46 | 85 | 21 | 30 |
| 3 | 61 | 13 | 46 | 10 | 48 | 80 | 82 |
| 4 | 92 | 57 | 78 | 80 | 41 | 62 | 66 |
| 5 | 77 | 3 | 88 | 36 | 51 | 10 | 50 |
| 6 | 40 | 29 | 23 | 36 | 62 | 83 | 29 |
| 7 | 95 | 32 | 80 | 6 | 92 | 96 | 8 |

You can hand me the final matching in a tiny JSON snippet like this — super simple and just the shape I need:

{
  ""solution"": [
    [<client_id>, <interpreter_id>, <slot_id>],
    ...
  ]
}

Think of each inner array as one chosen session: the client, the interpreter, and the time slot, in that order. The whole ""solution"" list is just the set of sessions that together make the schedule. This is just a sketch of the required format, not the actual schedule — I just need the same shape when you give the answer.

Please use the exact identifiers from the instance input — no renaming, no 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”.","{'cost_tensor': [[[70, 87, 0, 20, 80, 51, 1], [6, 52, 18, 90, 88, 86, 82], [17, 47, 54, 34, 3, 74, 27], [45, 32, 9, 98, 4, 4, 97], [86, 4, 58, 53, 53, 61, 97], [12, 8, 3, 34, 64, 55, 87], [31, 35, 69, 47, 33, 22, 20]], [[81, 37, 26, 64, 11, 24, 72], [74, 14, 50, 83, 45, 67, 45], [7, 81, 53, 91, 5, 1, 27], [10, 64, 3, 76, 84, 9, 66], [59, 66, 33, 31, 14, 54, 72], [54, 80, 4, 53, 27, 80, 78], [47, 70, 45, 55, 80, 37, 87]], [[17, 14, 36, 19, 35, 73, 51], [5, 34, 41, 23, 68, 2, 72], [80, 68, 23, 47, 63, 80, 25], [42, 94, 23, 25, 7, 21, 12], [26, 93, 86, 5, 79, 24, 14], [74, 14, 13, 29, 75, 28, 84], [71, 72, 75, 72, 65, 94, 43]], [[94, 47, 24, 78, 46, 62, 50], [53, 53, 35, 30, 6, 35, 81], [82, 54, 18, 15, 50, 8, 45], [97, 73, 66, 10, 69, 14, 59], [0, 31, 19, 30, 16, 26, 53], [38, 30, 85, 69, 41, 39, 44], [6, 14, 39, 92, 2, 17, 13]], [[59, 67, 7, 54, 54, 89, 41], [45, 25, 77, 57, 32, 57, 49], [80, 15, 42, 62, 89, 41, 81], [83, 69, 6, 20, 24, 89, 91], [99, 31, 13, 2, 98, 49, 92], [94, 37, 10, 74, 1, 75, 60], [64, 40, 78, 40, 3, 54, 86]], [[3, 80, 39, 24, 97, 2, 87], [36, 87, 29, 35, 97, 48, 98], [38, 23, 37, 63, 19, 2, 87], [85, 21, 31, 89, 63, 28, 98], [84, 78, 79, 86, 53, 66, 1], [93, 79, 40, 72, 9, 64, 44], [67, 9, 13, 68, 73, 63, 92]], [[92, 40, 60, 8, 40, 39, 25], [28, 59, 52, 46, 85, 21, 30], [61, 13, 46, 10, 48, 80, 82], [92, 57, 78, 80, 41, 62, 66], [77, 3, 88, 36, 51, 10, 50], [40, 29, 23, 36, 62, 83, 29], [95, 32, 80, 6, 92, 96, 8]]], 'objective': 26.0}","[[0, 0, 6], [1, 3, 2], [2, 1, 5], [3, 4, 0], [4, 5, 4], [5, 6, 1], [6, 2, 3]]",26.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [1, 2, 3, 4, 5, 6, 7], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 70}, {'i': 1, 'j': 1, 'k': 2, 'cost': 87}, {'i': 1, 'j': 1, 'k': 3, 'cost': 0}, {'i': 1, 'j': 1, 'k': 4, 'cost': 20}, {'i': 1, 'j': 1, 'k': 5, 'cost': 80}, {'i': 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4, 'k': 7, 'cost': 66}, {'i': 7, 'j': 5, 'k': 1, 'cost': 77}, {'i': 7, 'j': 5, 'k': 2, 'cost': 3}, {'i': 7, 'j': 5, 'k': 3, 'cost': 88}, {'i': 7, 'j': 5, 'k': 4, 'cost': 36}, {'i': 7, 'j': 5, 'k': 5, 'cost': 51}, {'i': 7, 'j': 5, 'k': 6, 'cost': 10}, {'i': 7, 'j': 5, 'k': 7, 'cost': 50}, {'i': 7, 'j': 6, 'k': 1, 'cost': 40}, {'i': 7, 'j': 6, 'k': 2, 'cost': 29}, {'i': 7, 'j': 6, 'k': 3, 'cost': 23}, {'i': 7, 'j': 6, 'k': 4, 'cost': 36}, {'i': 7, 'j': 6, 'k': 5, 'cost': 62}, {'i': 7, 'j': 6, 'k': 6, 'cost': 83}, {'i': 7, 'j': 6, 'k': 7, 'cost': 29}, {'i': 7, 'j': 7, 'k': 1, 'cost': 95}, {'i': 7, 'j': 7, 'k': 2, 'cost': 32}, {'i': 7, 'j': 7, 'k': 3, 'cost': 80}, {'i': 7, 'j': 7, 'k': 4, 'cost': 6}, {'i': 7, 'j': 7, 'k': 5, 'cost': 92}, {'i': 7, 'j': 7, 'k': 6, 'cost': 96}, {'i': 7, 'j': 7, 'k': 7, 'cost': 8}]}","[[1, 1, 7], [2, 4, 3], [3, 2, 6], [4, 5, 1], [5, 6, 5], [6, 7, 2], [7, 3, 4]]",28,json,1
AP3,AP3,"At the university there’s a little matching task every term: assign a single proctor and a single hall to each exam, with every proctor and every hall used for only one exam. Each possible exam–proctor–hall choice comes with a cost, and once a choice is made for every exam the costs are summed — the better plan is the one with the smallest sum. Nothing can be skipped or duplicated. The full list of exams, proctors, halls, and their costs follows below.

There are 7 exams, 7 proctors and 7 halls, identified by 0, 1, 2, 3, 4, 5, 6.

*Meaning: costs form a 3D tensor. For each fixed exam_id=i, you are given a proctor_id×hall_id matrix whose entry at row proctor_id=j and column hall_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all proctor_id and all hall_id used exactly once.*

**assignment_cost_tensor (per-exam_id markdown matrices)**

## exam_id=0
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 20 | 17 | 57 | 9 | 4 | 69 | 55 |
| 1 | 11 | 16 | 88 | 92 | 11 | 3 | 44 |
| 2 | 16 | 66 | 16 | 87 | 30 | 89 | 37 |
| 3 | 48 | 67 | 97 | 87 | 37 | 6 | 66 |
| 4 | 58 | 95 | 55 | 12 | 53 | 37 | 30 |
| 5 | 26 | 64 | 63 | 94 | 42 | 19 | 64 |
| 6 | 42 | 7 | 46 | 29 | 97 | 86 | 43 |

## exam_id=1
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 37 | 61 | 74 | 97 | 56 | 40 | 86 |
| 1 | 17 | 15 | 39 | 19 | 86 | 65 | 18 |
| 2 | 13 | 34 | 78 | 56 | 95 | 37 | 22 |
| 3 | 52 | 35 | 4 | 10 | 82 | 40 | 65 |
| 4 | 31 | 31 | 24 | 44 | 43 | 40 | 69 |
| 5 | 36 | 66 | 62 | 33 | 90 | 77 | 57 |
| 6 | 85 | 19 | 90 | 35 | 78 | 68 | 97 |

## exam_id=2
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 80 | 95 | 41 | 85 | 18 | 6 | 99 |
| 1 | 64 | 72 | 63 | 99 | 50 | 76 | 57 |
| 2 | 71 | 87 | 2 | 95 | 70 | 77 | 66 |
| 3 | 99 | 4 | 15 | 84 | 20 | 19 | 38 |
| 4 | 11 | 66 | 40 | 83 | 72 | 65 | 18 |
| 5 | 96 | 45 | 38 | 39 | 46 | 83 | 48 |
| 6 | 44 | 19 | 32 | 62 | 96 | 45 | 84 |

## exam_id=3
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 73 | 40 | 86 | 37 | 69 | 98 | 41 |
| 1 | 73 | 59 | 90 | 57 | 62 | 20 | 79 |
| 2 | 64 | 75 | 31 | 94 | 87 | 61 | 62 |
| 3 | 59 | 72 | 66 | 38 | 62 | 68 | 0 |
| 4 | 96 | 65 | 77 | 96 | 56 | 29 | 52 |
| 5 | 30 | 66 | 61 | 61 | 53 | 60 | 68 |
| 6 | 82 | 59 | 16 | 23 | 60 | 84 | 91 |

## exam_id=4
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 11 | 54 | 49 | 19 | 13 | 80 | 18 |
| 1 | 7 | 31 | 5 | 78 | 99 | 64 | 13 |
| 2 | 74 | 42 | 20 | 65 | 80 | 45 | 79 |
| 3 | 50 | 14 | 19 | 83 | 43 | 81 | 80 |
| 4 | 63 | 74 | 62 | 64 | 19 | 29 | 22 |
| 5 | 58 | 22 | 7 | 67 | 29 | 58 | 72 |
| 6 | 7 | 4 | 57 | 93 | 46 | 99 | 95 |

## exam_id=5
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 80 | 50 | 76 | 21 | 66 | 71 | 38 |
| 1 | 84 | 62 | 2 | 3 | 46 | 0 | 45 |
| 2 | 88 | 19 | 70 | 59 | 94 | 25 | 52 |
| 3 | 2 | 21 | 62 | 41 | 73 | 56 | 54 |
| 4 | 36 | 58 | 53 | 38 | 66 | 50 | 43 |
| 5 | 48 | 21 | 7 | 31 | 38 | 86 | 35 |
| 6 | 13 | 2 | 10 | 20 | 22 | 79 | 71 |

## exam_id=6
| proctor_id\hall_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 40 | 60 | 79 | 79 | 22 | 70 | 52 |
| 1 | 80 | 28 | 11 | 60 | 41 | 51 | 97 |
| 2 | 21 | 99 | 18 | 37 | 91 | 48 | 46 |
| 3 | 79 | 62 | 34 | 41 | 66 | 36 | 72 |
| 4 | 56 | 16 | 11 | 22 | 28 | 30 | 78 |
| 5 | 1 | 25 | 84 | 58 | 82 | 37 | 14 |
| 6 | 69 | 78 | 71 | 70 | 8 | 50 | 22 |

Select one triple for each of the 7 exams so that every proctor and every hall in 0, 1, 2, 3, 4, 5, 6 is used exactly once and the summed cost is minimized.

Also, if you could send your choices back in a simple JSON layout, that makes it easy to check — nothing fancy, just a single key with a list of triples, like this:

{
  ""solution"": [
    [<exam_id>, <proctor_id>, <hall_id>],
    ...
  ]
}

Each inner array is one exam paired with the proctor and the hall you picked for it. Think of it like a little form: exam, proctor, hall. This block is just the shape I expect — don’t fill it in yet here, use the actual IDs from the instance when you submit your plan.

Please make sure to use the exact identifiers given in the input — no renaming and no 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”.","{'cost_tensor': [[[20, 17, 57, 9, 4, 69, 55], [11, 16, 88, 92, 11, 3, 44], [16, 66, 16, 87, 30, 89, 37], [48, 67, 97, 87, 37, 6, 66], [58, 95, 55, 12, 53, 37, 30], [26, 64, 63, 94, 42, 19, 64], [42, 7, 46, 29, 97, 86, 43]], [[37, 61, 74, 97, 56, 40, 86], [17, 15, 39, 19, 86, 65, 18], [13, 34, 78, 56, 95, 37, 22], [52, 35, 4, 10, 82, 40, 65], [31, 31, 24, 44, 43, 40, 69], [36, 66, 62, 33, 90, 77, 57], [85, 19, 90, 35, 78, 68, 97]], [[80, 95, 41, 85, 18, 6, 99], [64, 72, 63, 99, 50, 76, 57], [71, 87, 2, 95, 70, 77, 66], [99, 4, 15, 84, 20, 19, 38], [11, 66, 40, 83, 72, 65, 18], [96, 45, 38, 39, 46, 83, 48], [44, 19, 32, 62, 96, 45, 84]], [[73, 40, 86, 37, 69, 98, 41], [73, 59, 90, 57, 62, 20, 79], [64, 75, 31, 94, 87, 61, 62], [59, 72, 66, 38, 62, 68, 0], [96, 65, 77, 96, 56, 29, 52], [30, 66, 61, 61, 53, 60, 68], [82, 59, 16, 23, 60, 84, 91]], [[11, 54, 49, 19, 13, 80, 18], [7, 31, 5, 78, 99, 64, 13], [74, 42, 20, 65, 80, 45, 79], [50, 14, 19, 83, 43, 81, 80], [63, 74, 62, 64, 19, 29, 22], [58, 22, 7, 67, 29, 58, 72], [7, 4, 57, 93, 46, 99, 95]], [[80, 50, 76, 21, 66, 71, 38], [84, 62, 2, 3, 46, 0, 45], [88, 19, 70, 59, 94, 25, 52], [2, 21, 62, 41, 73, 56, 54], [36, 58, 53, 38, 66, 50, 43], [48, 21, 7, 31, 38, 86, 35], [13, 2, 10, 20, 22, 79, 71]], [[40, 60, 79, 79, 22, 70, 52], [80, 28, 11, 60, 41, 51, 97], [21, 99, 18, 37, 91, 48, 46], [79, 62, 34, 41, 66, 36, 72], [56, 16, 11, 22, 28, 30, 78], [1, 25, 84, 58, 82, 37, 14], [69, 78, 71, 70, 8, 50, 22]]], 'objective': 47.0}","[[0, 4, 3], [1, 6, 1], [2, 2, 2], [3, 3, 6], [4, 0, 4], [5, 1, 5], [6, 5, 0]]",47.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [0, 1, 2, 3, 4, 5, 6], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 20}, {'i': 0, 'j': 0, 'k': 1, 'cost': 17}, {'i': 0, 'j': 0, 'k': 2, 'cost': 57}, {'i': 0, 'j': 0, 'k': 3, 'cost': 9}, {'i': 0, 'j': 0, 'k': 4, 'cost': 4}, {'i': 0, 'j': 0, 'k': 5, 'cost': 69}, {'i': 0, 'j': 0, 'k': 6, 'cost': 55}, {'i': 0, 'j': 1, 'k': 0, 'cost': 11}, {'i': 0, 'j': 1, 'k': 1, 'cost': 16}, {'i': 0, 'j': 1, 'k': 2, 'cost': 88}, {'i': 0, 'j': 1, 'k': 3, 'cost': 92}, {'i': 0, 'j': 1, 'k': 4, 'cost': 11}, {'i': 0, 'j': 1, 'k': 5, 'cost': 3}, {'i': 0, 'j': 1, 'k': 6, 'cost': 44}, {'i': 0, 'j': 2, 'k': 0, 'cost': 16}, {'i': 0, 'j': 2, 'k': 1, 'cost': 66}, {'i': 0, 'j': 2, 'k': 2, 'cost': 16}, {'i': 0, 'j': 2, 'k': 3, 'cost': 87}, {'i': 0, 'j': 2, 'k': 4, 'cost': 30}, {'i': 0, 'j': 2, 'k': 5, 'cost': 89}, {'i': 0, 'j': 2, 'k': 6, 'cost': 37}, {'i': 0, 'j': 3, 'k': 0, 'cost': 48}, {'i': 0, 'j': 3, 'k': 1, 'cost': 67}, {'i': 0, 'j': 3, 'k': 2, 'cost': 97}, {'i': 0, 'j': 3, 'k': 3, 'cost': 87}, {'i': 0, 'j': 3, 'k': 4, 'cost': 37}, {'i': 0, 'j': 3, 'k': 5, 'cost': 6}, {'i': 0, 'j': 3, 'k': 6, 'cost': 66}, {'i': 0, 'j': 4, 'k': 0, 'cost': 58}, {'i': 0, 'j': 4, 'k': 1, 'cost': 95}, {'i': 0, 'j': 4, 'k': 2, 'cost': 55}, {'i': 0, 'j': 4, 'k': 3, 'cost': 12}, {'i': 0, 'j': 4, 'k': 4, 'cost': 53}, {'i': 0, 'j': 4, 'k': 5, 'cost': 37}, {'i': 0, 'j': 4, 'k': 6, 'cost': 30}, {'i': 0, 'j': 5, 'k': 0, 'cost': 26}, {'i': 0, 'j': 5, 'k': 1, 'cost': 64}, {'i': 0, 'j': 5, 'k': 2, 'cost': 63}, {'i': 0, 'j': 5, 'k': 3, 'cost': 94}, {'i': 0, 'j': 5, 'k': 4, 'cost': 42}, {'i': 0, 'j': 5, 'k': 5, 'cost': 19}, {'i': 0, 'j': 5, 'k': 6, 'cost': 64}, {'i': 0, 'j': 6, 'k': 0, 'cost': 42}, {'i': 0, 'j': 6, 'k': 1, 'cost': 7}, {'i': 0, 'j': 6, 'k': 2, 'cost': 46}, {'i': 0, 'j': 6, 'k': 3, 'cost': 29}, {'i': 0, 'j': 6, 'k': 4, 'cost': 97}, {'i': 0, 'j': 6, 'k': 5, 'cost': 86}, {'i': 0, 'j': 6, 'k': 6, 'cost': 43}, {'i': 1, 'j': 0, 'k': 0, 'cost': 37}, {'i': 1, 'j': 0, 'k': 1, 'cost': 61}, {'i': 1, 'j': 0, 'k': 2, 'cost': 74}, {'i': 1, 'j': 0, 'k': 3, 'cost': 97}, {'i': 1, 'j': 0, 'k': 4, 'cost': 56}, {'i': 1, 'j': 0, 'k': 5, 'cost': 40}, {'i': 1, 'j': 0, 'k': 6, 'cost': 86}, {'i': 1, 'j': 1, 'k': 0, 'cost': 17}, {'i': 1, 'j': 1, 'k': 1, 'cost': 15}, {'i': 1, 'j': 1, 'k': 2, 'cost': 39}, {'i': 1, 'j': 1, 'k': 3, 'cost': 19}, {'i': 1, 'j': 1, 'k': 4, 'cost': 86}, {'i': 1, 'j': 1, 'k': 5, 'cost': 65}, {'i': 1, 'j': 1, 'k': 6, 'cost': 18}, {'i': 1, 'j': 2, 'k': 0, 'cost': 13}, {'i': 1, 'j': 2, 'k': 1, 'cost': 34}, {'i': 1, 'j': 2, 'k': 2, 'cost': 78}, {'i': 1, 'j': 2, 'k': 3, 'cost': 56}, {'i': 1, 'j': 2, 'k': 4, 'cost': 95}, {'i': 1, 'j': 2, 'k': 5, 'cost': 37}, {'i': 1, 'j': 2, 'k': 6, 'cost': 22}, {'i': 1, 'j': 3, 'k': 0, 'cost': 52}, {'i': 1, 'j': 3, 'k': 1, 'cost': 35}, {'i': 1, 'j': 3, 'k': 2, 'cost': 4}, {'i': 1, 'j': 3, 'k': 3, 'cost': 10}, {'i': 1, 'j': 3, 'k': 4, 'cost': 82}, {'i': 1, 'j': 3, 'k': 5, 'cost': 40}, {'i': 1, 'j': 3, 'k': 6, 'cost': 65}, {'i': 1, 'j': 4, 'k': 0, 'cost': 31}, {'i': 1, 'j': 4, 'k': 1, 'cost': 31}, {'i': 1, 'j': 4, 'k': 2, 'cost': 24}, {'i': 1, 'j': 4, 'k': 3, 'cost': 44}, {'i': 1, 'j': 4, 'k': 4, 'cost': 43}, {'i': 1, 'j': 4, 'k': 5, 'cost': 40}, {'i': 1, 'j': 4, 'k': 6, 'cost': 69}, {'i': 1, 'j': 5, 'k': 0, 'cost': 36}, {'i': 1, 'j': 5, 'k': 1, 'cost': 66}, {'i': 1, 'j': 5, 'k': 2, 'cost': 62}, {'i': 1, 'j': 5, 'k': 3, 'cost': 33}, {'i': 1, 'j': 5, 'k': 4, 'cost': 90}, {'i': 1, 'j': 5, 'k': 5, 'cost': 77}, {'i': 1, 'j': 5, 'k': 6, 'cost': 57}, {'i': 1, 'j': 6, 'k': 0, 'cost': 85}, {'i': 1, 'j': 6, 'k': 1, 'cost': 19}, {'i': 1, 'j': 6, 'k': 2, 'cost': 90}, {'i': 1, 'j': 6, 'k': 3, 'cost': 35}, {'i': 1, 'j': 6, 'k': 4, 'cost': 78}, {'i': 1, 'j': 6, 'k': 5, 'cost': 68}, {'i': 1, 'j': 6, 'k': 6, 'cost': 97}, {'i': 2, 'j': 0, 'k': 0, 'cost': 80}, {'i': 2, 'j': 0, 'k': 1, 'cost': 95}, {'i': 2, 'j': 0, 'k': 2, 'cost': 41}, {'i': 2, 'j': 0, 'k': 3, 'cost': 85}, {'i': 2, 'j': 0, 'k': 4, 'cost': 18}, {'i': 2, 'j': 0, 'k': 5, 'cost': 6}, {'i': 2, 'j': 0, 'k': 6, 'cost': 99}, {'i': 2, 'j': 1, 'k': 0, 'cost': 64}, {'i': 2, 'j': 1, 'k': 1, 'cost': 72}, {'i': 2, 'j': 1, 'k': 2, 'cost': 63}, {'i': 2, 'j': 1, 'k': 3, 'cost': 99}, {'i': 2, 'j': 1, 'k': 4, 'cost': 50}, {'i': 2, 'j': 1, 'k': 5, 'cost': 76}, {'i': 2, 'j': 1, 'k': 6, 'cost': 57}, {'i': 2, 'j': 2, 'k': 0, 'cost': 71}, {'i': 2, 'j': 2, 'k': 1, 'cost': 87}, {'i': 2, 'j': 2, 'k': 2, 'cost': 2}, {'i': 2, 'j': 2, 'k': 3, 'cost': 95}, {'i': 2, 'j': 2, 'k': 4, 'cost': 70}, {'i': 2, 'j': 2, 'k': 5, 'cost': 77}, {'i': 2, 'j': 2, 'k': 6, 'cost': 66}, {'i': 2, 'j': 3, 'k': 0, 'cost': 99}, {'i': 2, 'j': 3, 'k': 1, 'cost': 4}, {'i': 2, 'j': 3, 'k': 2, 'cost': 15}, {'i': 2, 'j': 3, 'k': 3, 'cost': 84}, {'i': 2, 'j': 3, 'k': 4, 'cost': 20}, {'i': 2, 'j': 3, 'k': 5, 'cost': 19}, {'i': 2, 'j': 3, 'k': 6, 'cost': 38}, {'i': 2, 'j': 4, 'k': 0, 'cost': 11}, {'i': 2, 'j': 4, 'k': 1, 'cost': 66}, {'i': 2, 'j': 4, 'k': 2, 'cost': 40}, {'i': 2, 'j': 4, 'k': 3, 'cost': 83}, {'i': 2, 'j': 4, 'k': 4, 'cost': 72}, {'i': 2, 'j': 4, 'k': 5, 'cost': 65}, {'i': 2, 'j': 4, 'k': 6, 'cost': 18}, {'i': 2, 'j': 5, 'k': 0, 'cost': 96}, {'i': 2, 'j': 5, 'k': 1, 'cost': 45}, {'i': 2, 'j': 5, 'k': 2, 'cost': 38}, {'i': 2, 'j': 5, 'k': 3, 'cost': 39}, {'i': 2, 'j': 5, 'k': 4, 'cost': 46}, {'i': 2, 'j': 5, 'k': 5, 'cost': 83}, {'i': 2, 'j': 5, 'k': 6, 'cost': 48}, {'i': 2, 'j': 6, 'k': 0, 'cost': 44}, {'i': 2, 'j': 6, 'k': 1, 'cost': 19}, {'i': 2, 'j': 6, 'k': 2, 'cost': 32}, {'i': 2, 'j': 6, 'k': 3, 'cost': 62}, {'i': 2, 'j': 6, 'k': 4, 'cost': 96}, {'i': 2, 'j': 6, 'k': 5, 'cost': 45}, {'i': 2, 'j': 6, 'k': 6, 'cost': 84}, {'i': 3, 'j': 0, 'k': 0, 'cost': 73}, {'i': 3, 'j': 0, 'k': 1, 'cost': 40}, {'i': 3, 'j': 0, 'k': 2, 'cost': 86}, {'i': 3, 'j': 0, 'k': 3, 'cost': 37}, {'i': 3, 'j': 0, 'k': 4, 'cost': 69}, {'i': 3, 'j': 0, 'k': 5, 'cost': 98}, {'i': 3, 'j': 0, 'k': 6, 'cost': 41}, {'i': 3, 'j': 1, 'k': 0, 'cost': 73}, {'i': 3, 'j': 1, 'k': 1, 'cost': 59}, {'i': 3, 'j': 1, 'k': 2, 'cost': 90}, {'i': 3, 'j': 1, 'k': 3, 'cost': 57}, {'i': 3, 'j': 1, 'k': 4, 'cost': 62}, {'i': 3, 'j': 1, 'k': 5, 'cost': 20}, {'i': 3, 'j': 1, 'k': 6, 'cost': 79}, {'i': 3, 'j': 2, 'k': 0, 'cost': 64}, {'i': 3, 'j': 2, 'k': 1, 'cost': 75}, {'i': 3, 'j': 2, 'k': 2, 'cost': 31}, {'i': 3, 'j': 2, 'k': 3, 'cost': 94}, {'i': 3, 'j': 2, 'k': 4, 'cost': 87}, {'i': 3, 'j': 2, 'k': 5, 'cost': 61}, {'i': 3, 'j': 2, 'k': 6, 'cost': 62}, {'i': 3, 'j': 3, 'k': 0, 'cost': 59}, {'i': 3, 'j': 3, 'k': 1, 'cost': 72}, {'i': 3, 'j': 3, 'k': 2, 'cost': 66}, {'i': 3, 'j': 3, 'k': 3, 'cost': 38}, {'i': 3, 'j': 3, 'k': 4, 'cost': 62}, {'i': 3, 'j': 3, 'k': 5, 'cost': 68}, {'i': 3, 'j': 3, 'k': 6, 'cost': 0}, {'i': 3, 'j': 4, 'k': 0, 'cost': 96}, {'i': 3, 'j': 4, 'k': 1, 'cost': 65}, {'i': 3, 'j': 4, 'k': 2, 'cost': 77}, {'i': 3, 'j': 4, 'k': 3, 'cost': 96}, {'i': 3, 'j': 4, 'k': 4, 'cost': 56}, {'i': 3, 'j': 4, 'k': 5, 'cost': 29}, {'i': 3, 'j': 4, 'k': 6, 'cost': 52}, {'i': 3, 'j': 5, 'k': 0, 'cost': 30}, {'i': 3, 'j': 5, 'k': 1, 'cost': 66}, {'i': 3, 'j': 5, 'k': 2, 'cost': 61}, {'i': 3, 'j': 5, 'k': 3, 'cost': 61}, {'i': 3, 'j': 5, 'k': 4, 'cost': 53}, {'i': 3, 'j': 5, 'k': 5, 'cost': 60}, {'i': 3, 'j': 5, 'k': 6, 'cost': 68}, {'i': 3, 'j': 6, 'k': 0, 'cost': 82}, {'i': 3, 'j': 6, 'k': 1, 'cost': 59}, {'i': 3, 'j': 6, 'k': 2, 'cost': 16}, {'i': 3, 'j': 6, 'k': 3, 'cost': 23}, {'i': 3, 'j': 6, 'k': 4, 'cost': 60}, {'i': 3, 'j': 6, 'k': 5, 'cost': 84}, {'i': 3, 'j': 6, 'k': 6, 'cost': 91}, {'i': 4, 'j': 0, 'k': 0, 'cost': 11}, {'i': 4, 'j': 0, 'k': 1, 'cost': 54}, {'i': 4, 'j': 0, 'k': 2, 'cost': 49}, {'i': 4, 'j': 0, 'k': 3, 'cost': 19}, {'i': 4, 'j': 0, 'k': 4, 'cost': 13}, {'i': 4, 'j': 0, 'k': 5, 'cost': 80}, {'i': 4, 'j': 0, 'k': 6, 'cost': 18}, {'i': 4, 'j': 1, 'k': 0, 'cost': 7}, {'i': 4, 'j': 1, 'k': 1, 'cost': 31}, {'i': 4, 'j': 1, 'k': 2, 'cost': 5}, {'i': 4, 'j': 1, 'k': 3, 'cost': 78}, {'i': 4, 'j': 1, 'k': 4, 'cost': 99}, {'i': 4, 'j': 1, 'k': 5, 'cost': 64}, {'i': 4, 'j': 1, 'k': 6, 'cost': 13}, {'i': 4, 'j': 2, 'k': 0, 'cost': 74}, {'i': 4, 'j': 2, 'k': 1, 'cost': 42}, {'i': 4, 'j': 2, 'k': 2, 'cost': 20}, {'i': 4, 'j': 2, 'k': 3, 'cost': 65}, {'i': 4, 'j': 2, 'k': 4, 'cost': 80}, {'i': 4, 'j': 2, 'k': 5, 'cost': 45}, {'i': 4, 'j': 2, 'k': 6, 'cost': 79}, {'i': 4, 'j': 3, 'k': 0, 'cost': 50}, {'i': 4, 'j': 3, 'k': 1, 'cost': 14}, {'i': 4, 'j': 3, 'k': 2, 'cost': 19}, {'i': 4, 'j': 3, 'k': 3, 'cost': 83}, {'i': 4, 'j': 3, 'k': 4, 'cost': 43}, {'i': 4, 'j': 3, 'k': 5, 'cost': 81}, {'i': 4, 'j': 3, 'k': 6, 'cost': 80}, {'i': 4, 'j': 4, 'k': 0, 'cost': 63}, {'i': 4, 'j': 4, 'k': 1, 'cost': 74}, {'i': 4, 'j': 4, 'k': 2, 'cost': 62}, {'i': 4, 'j': 4, 'k': 3, 'cost': 64}, {'i': 4, 'j': 4, 'k': 4, 'cost': 19}, {'i': 4, 'j': 4, 'k': 5, 'cost': 29}, {'i': 4, 'j': 4, 'k': 6, 'cost': 22}, {'i': 4, 'j': 5, 'k': 0, 'cost': 58}, {'i': 4, 'j': 5, 'k': 1, 'cost': 22}, {'i': 4, 'j': 5, 'k': 2, 'cost': 7}, {'i': 4, 'j': 5, 'k': 3, 'cost': 67}, {'i': 4, 'j': 5, 'k': 4, 'cost': 29}, {'i': 4, 'j': 5, 'k': 5, 'cost': 58}, {'i': 4, 'j': 5, 'k': 6, 'cost': 72}, {'i': 4, 'j': 6, 'k': 0, 'cost': 7}, {'i': 4, 'j': 6, 'k': 1, 'cost': 4}, {'i': 4, 'j': 6, 'k': 2, 'cost': 57}, {'i': 4, 'j': 6, 'k': 3, 'cost': 93}, {'i': 4, 'j': 6, 'k': 4, 'cost': 46}, {'i': 4, 'j': 6, 'k': 5, 'cost': 99}, {'i': 4, 'j': 6, 'k': 6, 'cost': 95}, {'i': 5, 'j': 0, 'k': 0, 'cost': 80}, {'i': 5, 'j': 0, 'k': 1, 'cost': 50}, {'i': 5, 'j': 0, 'k': 2, 'cost': 76}, {'i': 5, 'j': 0, 'k': 3, 'cost': 21}, {'i': 5, 'j': 0, 'k': 4, 'cost': 66}, {'i': 5, 'j': 0, 'k': 5, 'cost': 71}, {'i': 5, 'j': 0, 'k': 6, 'cost': 38}, {'i': 5, 'j': 1, 'k': 0, 'cost': 84}, {'i': 5, 'j': 1, 'k': 1, 'cost': 62}, {'i': 5, 'j': 1, 'k': 2, 'cost': 2}, {'i': 5, 'j': 1, 'k': 3, 'cost': 3}, {'i': 5, 'j': 1, 'k': 4, 'cost': 46}, {'i': 5, 'j': 1, 'k': 5, 'cost': 0}, {'i': 5, 'j': 1, 'k': 6, 'cost': 45}, {'i': 5, 'j': 2, 'k': 0, 'cost': 88}, {'i': 5, 'j': 2, 'k': 1, 'cost': 19}, {'i': 5, 'j': 2, 'k': 2, 'cost': 70}, {'i': 5, 'j': 2, 'k': 3, 'cost': 59}, {'i': 5, 'j': 2, 'k': 4, 'cost': 94}, {'i': 5, 'j': 2, 'k': 5, 'cost': 25}, {'i': 5, 'j': 2, 'k': 6, 'cost': 52}, {'i': 5, 'j': 3, 'k': 0, 'cost': 2}, {'i': 5, 'j': 3, 'k': 1, 'cost': 21}, {'i': 5, 'j': 3, 'k': 2, 'cost': 62}, {'i': 5, 'j': 3, 'k': 3, 'cost': 41}, {'i': 5, 'j': 3, 'k': 4, 'cost': 73}, {'i': 5, 'j': 3, 'k': 5, 'cost': 56}, {'i': 5, 'j': 3, 'k': 6, 'cost': 54}, {'i': 5, 'j': 4, 'k': 0, 'cost': 36}, {'i': 5, 'j': 4, 'k': 1, 'cost': 58}, {'i': 5, 'j': 4, 'k': 2, 'cost': 53}, {'i': 5, 'j': 4, 'k': 3, 'cost': 38}, {'i': 5, 'j': 4, 'k': 4, 'cost': 66}, {'i': 5, 'j': 4, 'k': 5, 'cost': 50}, {'i': 5, 'j': 4, 'k': 6, 'cost': 43}, {'i': 5, 'j': 5, 'k': 0, 'cost': 48}, {'i': 5, 'j': 5, 'k': 1, 'cost': 21}, {'i': 5, 'j': 5, 'k': 2, 'cost': 7}, {'i': 5, 'j': 5, 'k': 3, 'cost': 31}, {'i': 5, 'j': 5, 'k': 4, 'cost': 38}, {'i': 5, 'j': 5, 'k': 5, 'cost': 86}, {'i': 5, 'j': 5, 'k': 6, 'cost': 35}, {'i': 5, 'j': 6, 'k': 0, 'cost': 13}, {'i': 5, 'j': 6, 'k': 1, 'cost': 2}, {'i': 5, 'j': 6, 'k': 2, 'cost': 10}, {'i': 5, 'j': 6, 'k': 3, 'cost': 20}, {'i': 5, 'j': 6, 'k': 4, 'cost': 22}, {'i': 5, 'j': 6, 'k': 5, 'cost': 79}, {'i': 5, 'j': 6, 'k': 6, 'cost': 71}, {'i': 6, 'j': 0, 'k': 0, 'cost': 40}, {'i': 6, 'j': 0, 'k': 1, 'cost': 60}, {'i': 6, 'j': 0, 'k': 2, 'cost': 79}, {'i': 6, 'j': 0, 'k': 3, 'cost': 79}, {'i': 6, 'j': 0, 'k': 4, 'cost': 22}, {'i': 6, 'j': 0, 'k': 5, 'cost': 70}, {'i': 6, 'j': 0, 'k': 6, 'cost': 52}, {'i': 6, 'j': 1, 'k': 0, 'cost': 80}, {'i': 6, 'j': 1, 'k': 1, 'cost': 28}, {'i': 6, 'j': 1, 'k': 2, 'cost': 11}, {'i': 6, 'j': 1, 'k': 3, 'cost': 60}, {'i': 6, 'j': 1, 'k': 4, 'cost': 41}, {'i': 6, 'j': 1, 'k': 5, 'cost': 51}, {'i': 6, 'j': 1, 'k': 6, 'cost': 97}, {'i': 6, 'j': 2, 'k': 0, 'cost': 21}, {'i': 6, 'j': 2, 'k': 1, 'cost': 99}, {'i': 6, 'j': 2, 'k': 2, 'cost': 18}, {'i': 6, 'j': 2, 'k': 3, 'cost': 37}, {'i': 6, 'j': 2, 'k': 4, 'cost': 91}, {'i': 6, 'j': 2, 'k': 5, 'cost': 48}, {'i': 6, 'j': 2, 'k': 6, 'cost': 46}, {'i': 6, 'j': 3, 'k': 0, 'cost': 79}, {'i': 6, 'j': 3, 'k': 1, 'cost': 62}, {'i': 6, 'j': 3, 'k': 2, 'cost': 34}, {'i': 6, 'j': 3, 'k': 3, 'cost': 41}, {'i': 6, 'j': 3, 'k': 4, 'cost': 66}, {'i': 6, 'j': 3, 'k': 5, 'cost': 36}, {'i': 6, 'j': 3, 'k': 6, 'cost': 72}, {'i': 6, 'j': 4, 'k': 0, 'cost': 56}, {'i': 6, 'j': 4, 'k': 1, 'cost': 16}, {'i': 6, 'j': 4, 'k': 2, 'cost': 11}, {'i': 6, 'j': 4, 'k': 3, 'cost': 22}, {'i': 6, 'j': 4, 'k': 4, 'cost': 28}, {'i': 6, 'j': 4, 'k': 5, 'cost': 30}, {'i': 6, 'j': 4, 'k': 6, 'cost': 78}, {'i': 6, 'j': 5, 'k': 0, 'cost': 1}, {'i': 6, 'j': 5, 'k': 1, 'cost': 25}, {'i': 6, 'j': 5, 'k': 2, 'cost': 84}, {'i': 6, 'j': 5, 'k': 3, 'cost': 58}, {'i': 6, 'j': 5, 'k': 4, 'cost': 82}, {'i': 6, 'j': 5, 'k': 5, 'cost': 37}, {'i': 6, 'j': 5, 'k': 6, 'cost': 14}, {'i': 6, 'j': 6, 'k': 0, 'cost': 69}, {'i': 6, 'j': 6, 'k': 1, 'cost': 78}, {'i': 6, 'j': 6, 'k': 2, 'cost': 71}, {'i': 6, 'j': 6, 'k': 3, 'cost': 70}, {'i': 6, 'j': 6, 'k': 4, 'cost': 8}, {'i': 6, 'j': 6, 'k': 5, 'cost': 50}, {'i': 6, 'j': 6, 'k': 6, 'cost': 22}]}","[[0, 4, 3], [1, 6, 1], [2, 2, 2], [3, 3, 6], [4, 0, 4], [5, 1, 5], [6, 5, 0]]",29,markdown_table,0
AP3,AP3,"A nurse manager described it like a game of musical chairs: equal numbers of patients, nurses, and rooms, and when the music stops each patient must have one nurse and one room, with no nurse or room sitting with two people. Each possible patient–nurse–room setup has a cost sticker, so the idea is to select one stickered setup per patient and tally those stickers — the winning arrangement is the one with the lowest total sum. The exact pairings and costs are shown below.

Below are the 7 stickered patient–nurse–room triples, shown with the instance IDs A, B, C, D, E, F, G.
Meaning: costs form a 3D tensor. For each fixed patient_id=i, you are given a nurse_id×room_id matrix whose entry at row nurse_id=j and column room_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all nurse_id and all room_id used exactly once.
assignment_cost_tensor (per-patient_id markdown matrices):
## patient_id=A
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 20 | 35 | 83 | 45 | 33 | 58 | 53 |
| B | 60 | 82 | 33 | 30 | 42 | 22 | 11 |
| C | 67 | 19 | 57 | 72 | 62 | 25 | 87 |
| D | 43 | 45 | 41 | 20 | 58 | 18 | 97 |
| E | 51 | 72 | 12 | 59 | 74 | 52 | 94 |
| F | 37 | 29 | 2 | 93 | 26 | 76 | 1 |
| G | 45 | 52 | 17 | 2 | 98 | 4 | 91 |

## patient_id=B
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 78 | 78 | 32 | 47 | 81 | 49 | 71 |
| B | 2 | 28 | 81 | 34 | 52 | 32 | 72 |
| C | 74 | 82 | 91 | 24 | 42 | 36 | 25 |
| D | 50 | 94 | 39 | 93 | 17 | 22 | 9 |
| E | 89 | 14 | 19 | 13 | 84 | 65 | 40 |
| F | 83 | 24 | 75 | 86 | 87 | 17 | 91 |
| G | 10 | 91 | 3 | 8 | 26 | 50 | 33 |

## patient_id=C
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 44 | 24 | 76 | 36 | 2 | 92 | 43 |
| B | 51 | 68 | 38 | 62 | 0 | 41 | 93 |
| C | 29 | 73 | 35 | 13 | 59 | 17 | 30 |
| D | 4 | 71 | 95 | 62 | 96 | 98 | 0 |
| E | 84 | 97 | 84 | 58 | 53 | 32 | 20 |
| F | 36 | 18 | 89 | 43 | 77 | 15 | 68 |
| G | 46 | 1 | 72 | 2 | 56 | 52 | 90 |

## patient_id=D
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 17 | 22 | 59 | 38 | 48 | 86 | 49 |
| B | 68 | 5 | 70 | 24 | 76 | 88 | 97 |
| C | 52 | 93 | 13 | 10 | 36 | 89 | 97 |
| D | 74 | 5 | 96 | 44 | 4 | 14 | 22 |
| E | 40 | 62 | 80 | 53 | 30 | 54 | 57 |
| F | 31 | 47 | 10 | 55 | 76 | 86 | 37 |
| G | 77 | 64 | 3 | 37 | 35 | 5 | 76 |

## patient_id=E
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 10 | 99 | 82 | 5 | 92 | 39 | 12 |
| B | 58 | 15 | 65 | 49 | 9 | 64 | 95 |
| C | 81 | 20 | 5 | 48 | 90 | 56 | 62 |
| D | 26 | 38 | 74 | 62 | 1 | 7 | 30 |
| E | 75 | 5 | 80 | 45 | 95 | 98 | 81 |
| F | 84 | 33 | 23 | 89 | 30 | 85 | 81 |
| G | 19 | 53 | 10 | 95 | 14 | 20 | 46 |

## patient_id=F
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 82 | 28 | 63 | 69 | 45 | 47 | 83 |
| B | 2 | 43 | 10 | 82 | 93 | 18 | 83 |
| C | 78 | 76 | 21 | 82 | 67 | 46 | 99 |
| D | 96 | 47 | 75 | 85 | 57 | 73 | 73 |
| E | 12 | 13 | 78 | 11 | 30 | 73 | 67 |
| F | 64 | 15 | 92 | 45 | 98 | 94 | 17 |
| G | 28 | 88 | 91 | 75 | 57 | 18 | 11 |

## patient_id=G
| nurse_id\room_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 49 | 46 | 69 | 81 | 92 | 84 | 1 |
| B | 36 | 70 | 39 | 93 | 56 | 94 | 95 |
| C | 99 | 85 | 64 | 1 | 39 | 70 | 35 |
| D | 78 | 45 | 40 | 38 | 29 | 63 | 63 |
| E | 64 | 43 | 84 | 98 | 40 | 98 | 25 |
| F | 2 | 94 | 97 | 87 | 28 | 0 | 47 |
| G | 53 | 13 | 93 | 60 | 55 | 58 | 66 |
Exactly one sticker per patient must be chosen so no nurse or room is used more than once; the winning arrangement minimizes the total cost.

If you want to hand me a result, a handy way to shape it is this little JSON sketch — just shows how I expect the triples to be listed back to you.

{
  ""solution"": [
    [<patient_id>, <nurse_id>, <room_id>],
    ...
  ]
}

Think of each inner triple [<patient_id>, <nurse_id>, <room_id>] as saying “this patient goes with this nurse and this room,” and the outer list just collects one triple per patient. This is only the shape I’m expecting, not the actual answer — fill in the real identifiers from the instance when you reply.

Please use the identifiers exactly as they appear in the instance input — don’t rename them or make up 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”.""","{'cost_tensor': [[[20, 35, 83, 45, 33, 58, 53], [60, 82, 33, 30, 42, 22, 11], [67, 19, 57, 72, 62, 25, 87], [43, 45, 41, 20, 58, 18, 97], [51, 72, 12, 59, 74, 52, 94], [37, 29, 2, 93, 26, 76, 1], [45, 52, 17, 2, 98, 4, 91]], [[78, 78, 32, 47, 81, 49, 71], [2, 28, 81, 34, 52, 32, 72], [74, 82, 91, 24, 42, 36, 25], [50, 94, 39, 93, 17, 22, 9], [89, 14, 19, 13, 84, 65, 40], [83, 24, 75, 86, 87, 17, 91], [10, 91, 3, 8, 26, 50, 33]], [[44, 24, 76, 36, 2, 92, 43], [51, 68, 38, 62, 0, 41, 93], [29, 73, 35, 13, 59, 17, 30], [4, 71, 95, 62, 96, 98, 0], [84, 97, 84, 58, 53, 32, 20], [36, 18, 89, 43, 77, 15, 68], [46, 1, 72, 2, 56, 52, 90]], [[17, 22, 59, 38, 48, 86, 49], [68, 5, 70, 24, 76, 88, 97], [52, 93, 13, 10, 36, 89, 97], [74, 5, 96, 44, 4, 14, 22], [40, 62, 80, 53, 30, 54, 57], [31, 47, 10, 55, 76, 86, 37], [77, 64, 3, 37, 35, 5, 76]], [[10, 99, 82, 5, 92, 39, 12], [58, 15, 65, 49, 9, 64, 95], [81, 20, 5, 48, 90, 56, 62], [26, 38, 74, 62, 1, 7, 30], [75, 5, 80, 45, 95, 98, 81], [84, 33, 23, 89, 30, 85, 81], [19, 53, 10, 95, 14, 20, 46]], [[82, 28, 63, 69, 45, 47, 83], [2, 43, 10, 82, 93, 18, 83], [78, 76, 21, 82, 67, 46, 99], [96, 47, 75, 85, 57, 73, 73], [12, 13, 78, 11, 30, 73, 67], [64, 15, 92, 45, 98, 94, 17], [28, 88, 91, 75, 57, 18, 11]], [[49, 46, 69, 81, 92, 84, 1], [36, 70, 39, 93, 56, 94, 95], [99, 85, 64, 1, 39, 70, 35], [78, 45, 40, 38, 29, 63, 63], [64, 43, 84, 98, 40, 98, 25], [2, 94, 97, 87, 28, 0, 47], [53, 13, 93, 60, 55, 58, 66]]], 'objective': 26.0}","[[0, 5, 2], [1, 3, 6], [2, 0, 4], [3, 6, 5], [4, 4, 1], [5, 1, 0], [6, 2, 3]]",26.0,"{'problem_type': 'AP3', 'n': 7, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 20}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 35}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 83}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 45}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 33}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 58}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 53}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 60}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 82}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 33}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 30}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 42}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 22}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 11}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 67}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 19}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 57}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 72}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 62}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 25}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 87}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 43}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 45}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 41}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 20}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 58}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 18}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 97}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 51}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 72}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 12}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 59}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 74}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 52}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 94}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 37}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 29}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 2}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 93}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 26}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 76}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 1}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 45}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 52}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 17}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 98}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 4}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 91}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 78}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 78}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 32}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 47}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 81}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 49}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 71}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 2}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 28}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 81}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 34}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 52}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 32}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 72}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 74}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 82}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 91}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 24}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 42}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 36}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 25}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 50}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 94}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 39}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 93}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 17}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 22}, {'i': 'B', 'j': 'D', 'k': 'G', 'cost': 9}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 89}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 14}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 19}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 13}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 84}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 65}, {'i': 'B', 'j': 'E', 'k': 'G', 'cost': 40}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 83}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 24}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 75}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 86}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 87}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 17}, {'i': 'B', 'j': 'F', 'k': 'G', 'cost': 91}, {'i': 'B', 'j': 'G', 'k': 'A', 'cost': 10}, {'i': 'B', 'j': 'G', 'k': 'B', 'cost': 91}, {'i': 'B', 'j': 'G', 'k': 'C', 'cost': 3}, {'i': 'B', 'j': 'G', 'k': 'D', 'cost': 8}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 26}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 50}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 33}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 44}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 24}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 76}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 36}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 2}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 92}, {'i': 'C', 'j': 'A', 'k': 'G', 'cost': 43}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 51}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 68}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 38}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 62}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 0}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 41}, {'i': 'C', 'j': 'B', 'k': 'G', 'cost': 93}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 29}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 73}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 35}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 13}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 59}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 17}, {'i': 'C', 'j': 'C', 'k': 'G', 'cost': 30}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 4}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 71}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 95}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 62}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 96}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 98}, {'i': 'C', 'j': 'D', 'k': 'G', 'cost': 0}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 84}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 97}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 84}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 58}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 53}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 32}, {'i': 'C', 'j': 'E', 'k': 'G', 'cost': 20}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 36}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 18}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 89}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 43}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 77}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 15}, {'i': 'C', 'j': 'F', 'k': 'G', 'cost': 68}, {'i': 'C', 'j': 'G', 'k': 'A', 'cost': 46}, {'i': 'C', 'j': 'G', 'k': 'B', 'cost': 1}, {'i': 'C', 'j': 'G', 'k': 'C', 'cost': 72}, {'i': 'C', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'C', 'j': 'G', 'k': 'E', 'cost': 56}, {'i': 'C', 'j': 'G', 'k': 'F', 'cost': 52}, {'i': 'C', 'j': 'G', 'k': 'G', 'cost': 90}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 17}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 22}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 59}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 38}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 48}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 86}, {'i': 'D', 'j': 'A', 'k': 'G', 'cost': 49}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 68}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 5}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 70}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 24}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 76}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 88}, {'i': 'D', 'j': 'B', 'k': 'G', 'cost': 97}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 52}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 93}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 13}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 10}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 36}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 89}, {'i': 'D', 'j': 'C', 'k': 'G', 'cost': 97}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 74}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 5}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 96}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 44}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 4}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 14}, {'i': 'D', 'j': 'D', 'k': 'G', 'cost': 22}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 40}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 62}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 80}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 53}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 30}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 54}, {'i': 'D', 'j': 'E', 'k': 'G', 'cost': 57}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 31}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 47}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 10}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 55}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 76}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 86}, {'i': 'D', 'j': 'F', 'k': 'G', 'cost': 37}, {'i': 'D', 'j': 'G', 'k': 'A', 'cost': 77}, {'i': 'D', 'j': 'G', 'k': 'B', 'cost': 64}, {'i': 'D', 'j': 'G', 'k': 'C', 'cost': 3}, {'i': 'D', 'j': 'G', 'k': 'D', 'cost': 37}, {'i': 'D', 'j': 'G', 'k': 'E', 'cost': 35}, {'i': 'D', 'j': 'G', 'k': 'F', 'cost': 5}, {'i': 'D', 'j': 'G', 'k': 'G', 'cost': 76}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 10}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 99}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 82}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 5}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 92}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 39}, {'i': 'E', 'j': 'A', 'k': 'G', 'cost': 12}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 58}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 15}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 65}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 49}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 9}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 64}, {'i': 'E', 'j': 'B', 'k': 'G', 'cost': 95}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 81}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 20}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 5}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 48}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 90}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 56}, {'i': 'E', 'j': 'C', 'k': 'G', 'cost': 62}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 26}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 38}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 74}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 62}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 1}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 7}, {'i': 'E', 'j': 'D', 'k': 'G', 'cost': 30}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 75}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 5}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 80}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 45}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 95}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 98}, {'i': 'E', 'j': 'E', 'k': 'G', 'cost': 81}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 84}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 33}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 23}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 89}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 30}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 85}, {'i': 'E', 'j': 'F', 'k': 'G', 'cost': 81}, {'i': 'E', 'j': 'G', 'k': 'A', 'cost': 19}, {'i': 'E', 'j': 'G', 'k': 'B', 'cost': 53}, {'i': 'E', 'j': 'G', 'k': 'C', 'cost': 10}, {'i': 'E', 'j': 'G', 'k': 'D', 'cost': 95}, {'i': 'E', 'j': 'G', 'k': 'E', 'cost': 14}, {'i': 'E', 'j': 'G', 'k': 'F', 'cost': 20}, {'i': 'E', 'j': 'G', 'k': 'G', 'cost': 46}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 82}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 28}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 63}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 69}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 45}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 47}, {'i': 'F', 'j': 'A', 'k': 'G', 'cost': 83}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 2}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 43}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 10}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 82}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 93}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 18}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 83}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 78}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 76}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 21}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 82}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 67}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 46}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 99}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 96}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 47}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 75}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 85}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 57}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 73}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 73}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 12}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 13}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 78}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 11}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 30}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 73}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 67}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 64}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 15}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 92}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 45}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 98}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 94}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 17}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 28}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 88}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 91}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 75}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 57}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 18}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 11}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 49}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 46}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 69}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 81}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 92}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 84}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 1}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 36}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 70}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 39}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 93}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 56}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 94}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 95}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 99}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 85}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 64}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 1}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 39}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 70}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 35}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 78}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 45}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 40}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 38}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 29}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 63}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 63}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 64}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 43}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 84}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 98}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 40}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 98}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 25}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 2}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 94}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 97}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 87}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 28}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 0}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 47}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 53}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 13}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 93}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 60}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 55}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 58}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 66}]}","[['A', 'F', 'C'], ['B', 'D', 'G'], ['C', 'A', 'E'], ['D', 'G', 'F'], ['E', 'E', 'B'], ['F', 'B', 'A'], ['G', 'C', 'D']]",30,nl,names
AP3,AP3,"Picture this: a rehearsal studio, a stack of song sheets, and a roster of musicians and instruments to assign — each song needs one musician and one instrument, and each musician and instrument must be used once and only once. Every possible assignment has a rehearsal cost and an instrument rental cost attached, and the task is to arrange the whole set so the total of those costs (sum rehearsal plus rental for each chosen trio) is as low as it can get. The exact data and costs appear below.

There are 6 songs, 6 musicians, and 6 instruments labeled 1, 2, 3, 4, 5, 6.
Meaning: costs form a 3D tensor. For each fixed song_id=i, you are given a musician_id×instrument_id matrix whose entry at row musician_id=j and column instrument_id=k equals rehearsal_plus_rental_cost(i,j,k). You must pick exactly one (j,k) for every i, with all musician_id and all instrument_id used exactly once.
rehearsal_plus_rental_cost_tensor (per-song_id markdown matrices):
## song_id=1
| musician_id\instrument_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 29 | 3 | 85 | 14 | 24 | 47 |
| 2 | 91 | 17 | 13 | 9 | 89 | 6 |
| 3 | 21 | 74 | 34 | 89 | 53 | 17 |
| 4 | 67 | 37 | 30 | 92 | 29 | 32 |
| 5 | 7 | 52 | 16 | 9 | 20 | 97 |
| 6 | 73 | 67 | 70 | 67 | 32 | 56 |

## song_id=2
| musician_id\instrument_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 19 | 20 | 18 | 1 | 63 | 81 |
| 2 | 60 | 35 | 69 | 63 | 93 | 43 |
| 3 | 80 | 3 | 77 | 29 | 62 | 97 |
| 4 | 90 | 28 | 89 | 81 | 9 | 92 |
| 5 | 1 | 12 | 77 | 85 | 20 | 99 |
| 6 | 49 | 57 | 93 | 45 | 52 | 2 |

## song_id=3
| musician_id\instrument_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 41 | 54 | 70 | 88 | 78 | 37 |
| 2 | 56 | 30 | 52 | 30 | 30 | 44 |
| 3 | 66 | 3 | 12 | 7 | 95 | 23 |
| 4 | 6 | 73 | 38 | 87 | 78 | 92 |
| 5 | 67 | 23 | 93 | 33 | 75 | 56 |
| 6 | 37 | 61 | 45 | 78 | 52 | 24 |

## song_id=4
| musician_id\instrument_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 23 | 17 | 29 | 83 | 74 | 66 |
| 2 | 76 | 67 | 43 | 13 | 75 | 99 |
| 3 | 56 | 67 | 17 | 44 | 99 | 85 |
| 4 | 18 | 70 | 70 | 94 | 37 | 56 |
| 5 | 9 | 61 | 35 | 48 | 38 | 84 |
| 6 | 77 | 33 | 16 | 48 | 25 | 49 |

## song_id=5
| musician_id\instrument_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 22 | 86 | 88 | 75 | 78 | 12 |
| 2 | 52 | 52 | 11 | 23 | 49 | 76 |
| 3 | 21 | 7 | 32 | 98 | 95 | 86 |
| 4 | 46 | 87 | 88 | 49 | 8 | 65 |
| 5 | 57 | 13 | 92 | 92 | 85 | 12 |
| 6 | 52 | 68 | 92 | 10 | 79 | 64 |

## song_id=6
| musician_id\instrument_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 34 | 73 | 56 | 51 | 73 | 69 |
| 2 | 24 | 56 | 8 | 80 | 27 | 5 |
| 3 | 59 | 6 | 54 | 25 | 98 | 44 |
| 4 | 38 | 27 | 0 | 36 | 31 | 30 |
| 5 | 4 | 95 | 34 | 52 | 25 | 63 |
| 6 | 99 | 59 | 31 | 70 | 10 | 90 |
List each triple and its combined cost so the total can be minimized.

Also, when you want to give me the matching, just drop it in this little JSON shape so it's easy to parse and double-check:

{
  ""solution"": [
    [<song_id>, <musician_id>, <instrument_id>],
    ...
  ]
}

Here ""solution"" is a list of triples. Each triple picks one song, one musician, and one instrument — in that order. Think of each inner array as the form you'd fill out for a single song: [which song, which musician, which instrument]. This block is just a sketch of the expected shape, not the actual answer — fill it with the actual identifiers from the instance.

Please be sure to use the exact identifiers from the instance input with no renaming and no 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”.","{'cost_tensor': [[[29, 3, 85, 14, 24, 47], [91, 17, 13, 9, 89, 6], [21, 74, 34, 89, 53, 17], [67, 37, 30, 92, 29, 32], [7, 52, 16, 9, 20, 97], [73, 67, 70, 67, 32, 56]], [[19, 20, 18, 1, 63, 81], [60, 35, 69, 63, 93, 43], [80, 3, 77, 29, 62, 97], [90, 28, 89, 81, 9, 92], [1, 12, 77, 85, 20, 99], [49, 57, 93, 45, 52, 2]], [[41, 54, 70, 88, 78, 37], [56, 30, 52, 30, 30, 44], [66, 3, 12, 7, 95, 23], [6, 73, 38, 87, 78, 92], [67, 23, 93, 33, 75, 56], [37, 61, 45, 78, 52, 24]], [[23, 17, 29, 83, 74, 66], [76, 67, 43, 13, 75, 99], [56, 67, 17, 44, 99, 85], [18, 70, 70, 94, 37, 56], [9, 61, 35, 48, 38, 84], [77, 33, 16, 48, 25, 49]], [[22, 86, 88, 75, 78, 12], [52, 52, 11, 23, 49, 76], [21, 7, 32, 98, 95, 86], [46, 87, 88, 49, 8, 65], [57, 13, 92, 92, 85, 12], [52, 68, 92, 10, 79, 64]], [[34, 73, 56, 51, 73, 69], [24, 56, 8, 80, 27, 5], [59, 6, 54, 25, 98, 44], [38, 27, 0, 36, 31, 30], [4, 95, 34, 52, 25, 63], [99, 59, 31, 70, 10, 90]]], 'objective': 37.0}","[[0, 0, 1], [1, 5, 5], [2, 2, 3], [3, 4, 0], [4, 3, 4], [5, 1, 2]]",37.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 29}, {'i': 1, 'j': 1, 'k': 2, 'cost': 3}, {'i': 1, 'j': 1, 'k': 3, 'cost': 85}, {'i': 1, 'j': 1, 'k': 4, 'cost': 14}, {'i': 1, 'j': 1, 'k': 5, 'cost': 24}, {'i': 1, 'j': 1, 'k': 6, 'cost': 47}, {'i': 1, 'j': 2, 'k': 1, 'cost': 91}, {'i': 1, 'j': 2, 'k': 2, 'cost': 17}, {'i': 1, 'j': 2, 'k': 3, 'cost': 13}, {'i': 1, 'j': 2, 'k': 4, 'cost': 9}, {'i': 1, 'j': 2, 'k': 5, 'cost': 89}, {'i': 1, 'j': 2, 'k': 6, 'cost': 6}, {'i': 1, 'j': 3, 'k': 1, 'cost': 21}, {'i': 1, 'j': 3, 'k': 2, 'cost': 74}, {'i': 1, 'j': 3, 'k': 3, 'cost': 34}, {'i': 1, 'j': 3, 'k': 4, 'cost': 89}, {'i': 1, 'j': 3, 'k': 5, 'cost': 53}, {'i': 1, 'j': 3, 'k': 6, 'cost': 17}, {'i': 1, 'j': 4, 'k': 1, 'cost': 67}, {'i': 1, 'j': 4, 'k': 2, 'cost': 37}, {'i': 1, 'j': 4, 'k': 3, 'cost': 30}, {'i': 1, 'j': 4, 'k': 4, 'cost': 92}, {'i': 1, 'j': 4, 'k': 5, 'cost': 29}, {'i': 1, 'j': 4, 'k': 6, 'cost': 32}, {'i': 1, 'j': 5, 'k': 1, 'cost': 7}, {'i': 1, 'j': 5, 'k': 2, 'cost': 52}, {'i': 1, 'j': 5, 'k': 3, 'cost': 16}, {'i': 1, 'j': 5, 'k': 4, 'cost': 9}, {'i': 1, 'j': 5, 'k': 5, 'cost': 20}, {'i': 1, 'j': 5, 'k': 6, 'cost': 97}, {'i': 1, 'j': 6, 'k': 1, 'cost': 73}, {'i': 1, 'j': 6, 'k': 2, 'cost': 67}, {'i': 1, 'j': 6, 'k': 3, 'cost': 70}, {'i': 1, 'j': 6, 'k': 4, 'cost': 67}, {'i': 1, 'j': 6, 'k': 5, 'cost': 32}, {'i': 1, 'j': 6, 'k': 6, 'cost': 56}, {'i': 2, 'j': 1, 'k': 1, 'cost': 19}, {'i': 2, 'j': 1, 'k': 2, 'cost': 20}, {'i': 2, 'j': 1, 'k': 3, 'cost': 18}, {'i': 2, 'j': 1, 'k': 4, 'cost': 1}, {'i': 2, 'j': 1, 'k': 5, 'cost': 63}, {'i': 2, 'j': 1, 'k': 6, 'cost': 81}, {'i': 2, 'j': 2, 'k': 1, 'cost': 60}, {'i': 2, 'j': 2, 'k': 2, 'cost': 35}, {'i': 2, 'j': 2, 'k': 3, 'cost': 69}, {'i': 2, 'j': 2, 'k': 4, 'cost': 63}, {'i': 2, 'j': 2, 'k': 5, 'cost': 93}, {'i': 2, 'j': 2, 'k': 6, 'cost': 43}, {'i': 2, 'j': 3, 'k': 1, 'cost': 80}, {'i': 2, 'j': 3, 'k': 2, 'cost': 3}, {'i': 2, 'j': 3, 'k': 3, 'cost': 77}, {'i': 2, 'j': 3, 'k': 4, 'cost': 29}, {'i': 2, 'j': 3, 'k': 5, 'cost': 62}, {'i': 2, 'j': 3, 'k': 6, 'cost': 97}, {'i': 2, 'j': 4, 'k': 1, 'cost': 90}, {'i': 2, 'j': 4, 'k': 2, 'cost': 28}, {'i': 2, 'j': 4, 'k': 3, 'cost': 89}, {'i': 2, 'j': 4, 'k': 4, 'cost': 81}, {'i': 2, 'j': 4, 'k': 5, 'cost': 9}, {'i': 2, 'j': 4, 'k': 6, 'cost': 92}, {'i': 2, 'j': 5, 'k': 1, 'cost': 1}, {'i': 2, 'j': 5, 'k': 2, 'cost': 12}, {'i': 2, 'j': 5, 'k': 3, 'cost': 77}, {'i': 2, 'j': 5, 'k': 4, 'cost': 85}, {'i': 2, 'j': 5, 'k': 5, 'cost': 20}, {'i': 2, 'j': 5, 'k': 6, 'cost': 99}, {'i': 2, 'j': 6, 'k': 1, 'cost': 49}, {'i': 2, 'j': 6, 'k': 2, 'cost': 57}, {'i': 2, 'j': 6, 'k': 3, 'cost': 93}, {'i': 2, 'j': 6, 'k': 4, 'cost': 45}, {'i': 2, 'j': 6, 'k': 5, 'cost': 52}, {'i': 2, 'j': 6, 'k': 6, 'cost': 2}, {'i': 3, 'j': 1, 'k': 1, 'cost': 41}, {'i': 3, 'j': 1, 'k': 2, 'cost': 54}, {'i': 3, 'j': 1, 'k': 3, 'cost': 70}, {'i': 3, 'j': 1, 'k': 4, 'cost': 88}, {'i': 3, 'j': 1, 'k': 5, 'cost': 78}, {'i': 3, 'j': 1, 'k': 6, 'cost': 37}, {'i': 3, 'j': 2, 'k': 1, 'cost': 56}, {'i': 3, 'j': 2, 'k': 2, 'cost': 30}, {'i': 3, 'j': 2, 'k': 3, 'cost': 52}, {'i': 3, 'j': 2, 'k': 4, 'cost': 30}, {'i': 3, 'j': 2, 'k': 5, 'cost': 30}, {'i': 3, 'j': 2, 'k': 6, 'cost': 44}, {'i': 3, 'j': 3, 'k': 1, 'cost': 66}, {'i': 3, 'j': 3, 'k': 2, 'cost': 3}, {'i': 3, 'j': 3, 'k': 3, 'cost': 12}, {'i': 3, 'j': 3, 'k': 4, 'cost': 7}, {'i': 3, 'j': 3, 'k': 5, 'cost': 95}, {'i': 3, 'j': 3, 'k': 6, 'cost': 23}, {'i': 3, 'j': 4, 'k': 1, 'cost': 6}, {'i': 3, 'j': 4, 'k': 2, 'cost': 73}, {'i': 3, 'j': 4, 'k': 3, 'cost': 38}, {'i': 3, 'j': 4, 'k': 4, 'cost': 87}, {'i': 3, 'j': 4, 'k': 5, 'cost': 78}, {'i': 3, 'j': 4, 'k': 6, 'cost': 92}, {'i': 3, 'j': 5, 'k': 1, 'cost': 67}, {'i': 3, 'j': 5, 'k': 2, 'cost': 23}, {'i': 3, 'j': 5, 'k': 3, 'cost': 93}, {'i': 3, 'j': 5, 'k': 4, 'cost': 33}, {'i': 3, 'j': 5, 'k': 5, 'cost': 75}, {'i': 3, 'j': 5, 'k': 6, 'cost': 56}, {'i': 3, 'j': 6, 'k': 1, 'cost': 37}, {'i': 3, 'j': 6, 'k': 2, 'cost': 61}, {'i': 3, 'j': 6, 'k': 3, 'cost': 45}, {'i': 3, 'j': 6, 'k': 4, 'cost': 78}, {'i': 3, 'j': 6, 'k': 5, 'cost': 52}, {'i': 3, 'j': 6, 'k': 6, 'cost': 24}, {'i': 4, 'j': 1, 'k': 1, 'cost': 23}, {'i': 4, 'j': 1, 'k': 2, 'cost': 17}, {'i': 4, 'j': 1, 'k': 3, 'cost': 29}, {'i': 4, 'j': 1, 'k': 4, 'cost': 83}, {'i': 4, 'j': 1, 'k': 5, 'cost': 74}, {'i': 4, 'j': 1, 'k': 6, 'cost': 66}, {'i': 4, 'j': 2, 'k': 1, 'cost': 76}, {'i': 4, 'j': 2, 'k': 2, 'cost': 67}, {'i': 4, 'j': 2, 'k': 3, 'cost': 43}, {'i': 4, 'j': 2, 'k': 4, 'cost': 13}, {'i': 4, 'j': 2, 'k': 5, 'cost': 75}, {'i': 4, 'j': 2, 'k': 6, 'cost': 99}, {'i': 4, 'j': 3, 'k': 1, 'cost': 56}, {'i': 4, 'j': 3, 'k': 2, 'cost': 67}, {'i': 4, 'j': 3, 'k': 3, 'cost': 17}, {'i': 4, 'j': 3, 'k': 4, 'cost': 44}, {'i': 4, 'j': 3, 'k': 5, 'cost': 99}, {'i': 4, 'j': 3, 'k': 6, 'cost': 85}, {'i': 4, 'j': 4, 'k': 1, 'cost': 18}, {'i': 4, 'j': 4, 'k': 2, 'cost': 70}, {'i': 4, 'j': 4, 'k': 3, 'cost': 70}, {'i': 4, 'j': 4, 'k': 4, 'cost': 94}, {'i': 4, 'j': 4, 'k': 5, 'cost': 37}, {'i': 4, 'j': 4, 'k': 6, 'cost': 56}, {'i': 4, 'j': 5, 'k': 1, 'cost': 9}, {'i': 4, 'j': 5, 'k': 2, 'cost': 61}, {'i': 4, 'j': 5, 'k': 3, 'cost': 35}, {'i': 4, 'j': 5, 'k': 4, 'cost': 48}, {'i': 4, 'j': 5, 'k': 5, 'cost': 38}, {'i': 4, 'j': 5, 'k': 6, 'cost': 84}, {'i': 4, 'j': 6, 'k': 1, 'cost': 77}, {'i': 4, 'j': 6, 'k': 2, 'cost': 33}, {'i': 4, 'j': 6, 'k': 3, 'cost': 16}, {'i': 4, 'j': 6, 'k': 4, 'cost': 48}, {'i': 4, 'j': 6, 'k': 5, 'cost': 25}, {'i': 4, 'j': 6, 'k': 6, 'cost': 49}, {'i': 5, 'j': 1, 'k': 1, 'cost': 22}, {'i': 5, 'j': 1, 'k': 2, 'cost': 86}, {'i': 5, 'j': 1, 'k': 3, 'cost': 88}, {'i': 5, 'j': 1, 'k': 4, 'cost': 75}, {'i': 5, 'j': 1, 'k': 5, 'cost': 78}, {'i': 5, 'j': 1, 'k': 6, 'cost': 12}, {'i': 5, 'j': 2, 'k': 1, 'cost': 52}, {'i': 5, 'j': 2, 'k': 2, 'cost': 52}, {'i': 5, 'j': 2, 'k': 3, 'cost': 11}, {'i': 5, 'j': 2, 'k': 4, 'cost': 23}, {'i': 5, 'j': 2, 'k': 5, 'cost': 49}, {'i': 5, 'j': 2, 'k': 6, 'cost': 76}, {'i': 5, 'j': 3, 'k': 1, 'cost': 21}, {'i': 5, 'j': 3, 'k': 2, 'cost': 7}, {'i': 5, 'j': 3, 'k': 3, 'cost': 32}, {'i': 5, 'j': 3, 'k': 4, 'cost': 98}, {'i': 5, 'j': 3, 'k': 5, 'cost': 95}, {'i': 5, 'j': 3, 'k': 6, 'cost': 86}, {'i': 5, 'j': 4, 'k': 1, 'cost': 46}, {'i': 5, 'j': 4, 'k': 2, 'cost': 87}, {'i': 5, 'j': 4, 'k': 3, 'cost': 88}, {'i': 5, 'j': 4, 'k': 4, 'cost': 49}, {'i': 5, 'j': 4, 'k': 5, 'cost': 8}, {'i': 5, 'j': 4, 'k': 6, 'cost': 65}, {'i': 5, 'j': 5, 'k': 1, 'cost': 57}, {'i': 5, 'j': 5, 'k': 2, 'cost': 13}, {'i': 5, 'j': 5, 'k': 3, 'cost': 92}, {'i': 5, 'j': 5, 'k': 4, 'cost': 92}, {'i': 5, 'j': 5, 'k': 5, 'cost': 85}, {'i': 5, 'j': 5, 'k': 6, 'cost': 12}, {'i': 5, 'j': 6, 'k': 1, 'cost': 52}, {'i': 5, 'j': 6, 'k': 2, 'cost': 68}, {'i': 5, 'j': 6, 'k': 3, 'cost': 92}, {'i': 5, 'j': 6, 'k': 4, 'cost': 10}, {'i': 5, 'j': 6, 'k': 5, 'cost': 79}, {'i': 5, 'j': 6, 'k': 6, 'cost': 64}, {'i': 6, 'j': 1, 'k': 1, 'cost': 34}, {'i': 6, 'j': 1, 'k': 2, 'cost': 73}, {'i': 6, 'j': 1, 'k': 3, 'cost': 56}, {'i': 6, 'j': 1, 'k': 4, 'cost': 51}, {'i': 6, 'j': 1, 'k': 5, 'cost': 73}, {'i': 6, 'j': 1, 'k': 6, 'cost': 69}, {'i': 6, 'j': 2, 'k': 1, 'cost': 24}, {'i': 6, 'j': 2, 'k': 2, 'cost': 56}, {'i': 6, 'j': 2, 'k': 3, 'cost': 8}, {'i': 6, 'j': 2, 'k': 4, 'cost': 80}, {'i': 6, 'j': 2, 'k': 5, 'cost': 27}, {'i': 6, 'j': 2, 'k': 6, 'cost': 5}, {'i': 6, 'j': 3, 'k': 1, 'cost': 59}, {'i': 6, 'j': 3, 'k': 2, 'cost': 6}, {'i': 6, 'j': 3, 'k': 3, 'cost': 54}, {'i': 6, 'j': 3, 'k': 4, 'cost': 25}, {'i': 6, 'j': 3, 'k': 5, 'cost': 98}, {'i': 6, 'j': 3, 'k': 6, 'cost': 44}, {'i': 6, 'j': 4, 'k': 1, 'cost': 38}, {'i': 6, 'j': 4, 'k': 2, 'cost': 27}, {'i': 6, 'j': 4, 'k': 3, 'cost': 0}, {'i': 6, 'j': 4, 'k': 4, 'cost': 36}, {'i': 6, 'j': 4, 'k': 5, 'cost': 31}, {'i': 6, 'j': 4, 'k': 6, 'cost': 30}, {'i': 6, 'j': 5, 'k': 1, 'cost': 4}, {'i': 6, 'j': 5, 'k': 2, 'cost': 95}, {'i': 6, 'j': 5, 'k': 3, 'cost': 34}, {'i': 6, 'j': 5, 'k': 4, 'cost': 52}, {'i': 6, 'j': 5, 'k': 5, 'cost': 25}, {'i': 6, 'j': 5, 'k': 6, 'cost': 63}, {'i': 6, 'j': 6, 'k': 1, 'cost': 99}, {'i': 6, 'j': 6, 'k': 2, 'cost': 59}, {'i': 6, 'j': 6, 'k': 3, 'cost': 31}, {'i': 6, 'j': 6, 'k': 4, 'cost': 70}, {'i': 6, 'j': 6, 'k': 5, 'cost': 10}, {'i': 6, 'j': 6, 'k': 6, 'cost': 90}]}","[[1, 1, 2], [2, 6, 6], [3, 3, 4], [4, 5, 1], [5, 4, 5], [6, 2, 3]]",31,nl,1
AP3,AP3,"Recently the team had to assign one artist and one frame to each commission, and there happened to be exactly as many artists and frames as jobs, so each artist and each frame is assigned exactly once. Every possible artist+frame choice for a commission carries a specific price; the idea is to decide the pairing for each commission so the sum of those chosen prices (the total cost) ends up as small as possible. The concrete details — who, which frame, and how much — are laid out below.

# num_commissions=6
# commission_ids=1, 2, 3, 4, 5, 6

# Meaning: costs form a 3D tensor. For each fixed commission_id=i, you are given a artist_id×frame_id matrix whose entry at row artist_id=j and column frame_id=k equals commission_price(i,j,k). You must pick exactly one (j,k) for every i, with all artist_id and all frame_id used exactly once.
# commission_price_tensor (per-commission_id markdown matrices)

## commission_id=1
| artist_id\frame_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 85 | 43 | 53 | 99 | 31 | 27 |
| 2 | 64 | 61 | 72 | 92 | 23 | 96 |
| 3 | 12 | 55 | 40 | 10 | 33 | 73 |
| 4 | 81 | 52 | 53 | 75 | 0 | 14 |
| 5 | 85 | 35 | 8 | 32 | 3 | 78 |
| 6 | 24 | 8 | 48 | 75 | 27 | 62 |

## commission_id=2
| artist_id\frame_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 4 | 44 | 12 | 57 | 55 | 86 |
| 2 | 60 | 85 | 76 | 11 | 57 | 31 |
| 3 | 10 | 53 | 93 | 96 | 81 | 53 |
| 4 | 8 | 46 | 49 | 80 | 67 | 67 |
| 5 | 58 | 61 | 82 | 29 | 2 | 4 |
| 6 | 93 | 87 | 88 | 82 | 85 | 25 |

## commission_id=3
| artist_id\frame_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 74 | 97 | 13 | 14 | 7 | 16 |
| 2 | 64 | 16 | 1 | 97 | 11 | 72 |
| 3 | 80 | 93 | 80 | 28 | 24 | 95 |
| 4 | 25 | 93 | 86 | 2 | 90 | 84 |
| 5 | 21 | 49 | 3 | 1 | 92 | 4 |
| 6 | 40 | 98 | 5 | 26 | 34 | 27 |

## commission_id=4
| artist_id\frame_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 84 | 73 | 83 | 26 | 19 | 99 |
| 2 | 53 | 51 | 54 | 97 | 58 | 44 |
| 3 | 2 | 60 | 79 | 26 | 85 | 92 |
| 4 | 70 | 70 | 48 | 50 | 62 | 29 |
| 5 | 6 | 73 | 92 | 75 | 65 | 75 |
| 6 | 81 | 59 | 19 | 96 | 89 | 30 |

## commission_id=5
| artist_id\frame_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 56 | 1 | 28 | 52 | 99 | 42 |
| 2 | 0 | 14 | 78 | 45 | 59 | 54 |
| 3 | 71 | 62 | 57 | 26 | 61 | 62 |
| 4 | 64 | 12 | 52 | 69 | 48 | 81 |
| 5 | 12 | 76 | 16 | 6 | 58 | 80 |
| 6 | 83 | 46 | 75 | 71 | 41 | 27 |

## commission_id=6
| artist_id\frame_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 68 | 89 | 28 | 73 | 51 | 19 |
| 2 | 83 | 77 | 27 | 6 | 86 | 48 |
| 3 | 69 | 88 | 82 | 91 | 84 | 36 |
| 4 | 29 | 5 | 24 | 10 | 3 | 19 |
| 5 | 43 | 5 | 29 | 7 | 15 | 13 |
| 6 | 16 | 71 | 96 | 94 | 0 | 6 |

If you want the result in a predictable, machine-friendly shape, just hand it over like this:

{
  ""solution"": [
    [<commission_id>, <artist_id>, <frame_id>],
    ...
  ]
}

This just means ""solution"" is a list of triples, and each triple says which commission gets which artist and which frame. It's just a sketch of the shape I expect — replace each placeholder with the actual identifier from the instance to show your chosen assignments.

Please use the identifiers exactly as they appear in the instance input — don't 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"".","{'cost_tensor': [[[85, 43, 53, 99, 31, 27], [64, 61, 72, 92, 23, 96], [12, 55, 40, 10, 33, 73], [81, 52, 53, 75, 0, 14], [85, 35, 8, 32, 3, 78], [24, 8, 48, 75, 27, 62]], [[4, 44, 12, 57, 55, 86], [60, 85, 76, 11, 57, 31], [10, 53, 93, 96, 81, 53], [8, 46, 49, 80, 67, 67], [58, 61, 82, 29, 2, 4], [93, 87, 88, 82, 85, 25]], [[74, 97, 13, 14, 7, 16], [64, 16, 1, 97, 11, 72], [80, 93, 80, 28, 24, 95], [25, 93, 86, 2, 90, 84], [21, 49, 3, 1, 92, 4], [40, 98, 5, 26, 34, 27]], [[84, 73, 83, 26, 19, 99], [53, 51, 54, 97, 58, 44], [2, 60, 79, 26, 85, 92], [70, 70, 48, 50, 62, 29], [6, 73, 92, 75, 65, 75], [81, 59, 19, 96, 89, 30]], [[56, 1, 28, 52, 99, 42], [0, 14, 78, 45, 59, 54], [71, 62, 57, 26, 61, 62], [64, 12, 52, 69, 48, 81], [12, 76, 16, 6, 58, 80], [83, 46, 75, 71, 41, 27]], [[68, 89, 28, 73, 51, 19], [83, 77, 27, 6, 86, 48], [69, 88, 82, 91, 84, 36], [29, 5, 24, 10, 3, 19], [43, 5, 29, 7, 15, 13], [16, 71, 96, 94, 0, 6]]], 'objective': 18.0}","[[0, 3, 4], [1, 4, 5], [2, 5, 2], [3, 2, 0], [4, 0, 1], [5, 1, 3]]",18.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 85}, {'i': 1, 'j': 1, 'k': 2, 'cost': 43}, {'i': 1, 'j': 1, 'k': 3, 'cost': 53}, {'i': 1, 'j': 1, 'k': 4, 'cost': 99}, {'i': 1, 'j': 1, 'k': 5, 'cost': 31}, {'i': 1, 'j': 1, 'k': 6, 'cost': 27}, {'i': 1, 'j': 2, 'k': 1, 'cost': 64}, {'i': 1, 'j': 2, 'k': 2, 'cost': 61}, {'i': 1, 'j': 2, 'k': 3, 'cost': 72}, {'i': 1, 'j': 2, 'k': 4, 'cost': 92}, {'i': 1, 'j': 2, 'k': 5, 'cost': 23}, {'i': 1, 'j': 2, 'k': 6, 'cost': 96}, {'i': 1, 'j': 3, 'k': 1, 'cost': 12}, {'i': 1, 'j': 3, 'k': 2, 'cost': 55}, {'i': 1, 'j': 3, 'k': 3, 'cost': 40}, {'i': 1, 'j': 3, 'k': 4, 'cost': 10}, {'i': 1, 'j': 3, 'k': 5, 'cost': 33}, {'i': 1, 'j': 3, 'k': 6, 'cost': 73}, {'i': 1, 'j': 4, 'k': 1, 'cost': 81}, {'i': 1, 'j': 4, 'k': 2, 'cost': 52}, {'i': 1, 'j': 4, 'k': 3, 'cost': 53}, {'i': 1, 'j': 4, 'k': 4, 'cost': 75}, {'i': 1, 'j': 4, 'k': 5, 'cost': 0}, {'i': 1, 'j': 4, 'k': 6, 'cost': 14}, {'i': 1, 'j': 5, 'k': 1, 'cost': 85}, {'i': 1, 'j': 5, 'k': 2, 'cost': 35}, {'i': 1, 'j': 5, 'k': 3, 'cost': 8}, {'i': 1, 'j': 5, 'k': 4, 'cost': 32}, {'i': 1, 'j': 5, 'k': 5, 'cost': 3}, {'i': 1, 'j': 5, 'k': 6, 'cost': 78}, {'i': 1, 'j': 6, 'k': 1, 'cost': 24}, {'i': 1, 'j': 6, 'k': 2, 'cost': 8}, {'i': 1, 'j': 6, 'k': 3, 'cost': 48}, {'i': 1, 'j': 6, 'k': 4, 'cost': 75}, {'i': 1, 'j': 6, 'k': 5, 'cost': 27}, {'i': 1, 'j': 6, 'k': 6, 'cost': 62}, {'i': 2, 'j': 1, 'k': 1, 'cost': 4}, {'i': 2, 'j': 1, 'k': 2, 'cost': 44}, {'i': 2, 'j': 1, 'k': 3, 'cost': 12}, {'i': 2, 'j': 1, 'k': 4, 'cost': 57}, {'i': 2, 'j': 1, 'k': 5, 'cost': 55}, {'i': 2, 'j': 1, 'k': 6, 'cost': 86}, {'i': 2, 'j': 2, 'k': 1, 'cost': 60}, {'i': 2, 'j': 2, 'k': 2, 'cost': 85}, {'i': 2, 'j': 2, 'k': 3, 'cost': 76}, {'i': 2, 'j': 2, 'k': 4, 'cost': 11}, {'i': 2, 'j': 2, 'k': 5, 'cost': 57}, {'i': 2, 'j': 2, 'k': 6, 'cost': 31}, {'i': 2, 'j': 3, 'k': 1, 'cost': 10}, {'i': 2, 'j': 3, 'k': 2, 'cost': 53}, {'i': 2, 'j': 3, 'k': 3, 'cost': 93}, {'i': 2, 'j': 3, 'k': 4, 'cost': 96}, {'i': 2, 'j': 3, 'k': 5, 'cost': 81}, {'i': 2, 'j': 3, 'k': 6, 'cost': 53}, {'i': 2, 'j': 4, 'k': 1, 'cost': 8}, {'i': 2, 'j': 4, 'k': 2, 'cost': 46}, {'i': 2, 'j': 4, 'k': 3, 'cost': 49}, {'i': 2, 'j': 4, 'k': 4, 'cost': 80}, {'i': 2, 'j': 4, 'k': 5, 'cost': 67}, {'i': 2, 'j': 4, 'k': 6, 'cost': 67}, {'i': 2, 'j': 5, 'k': 1, 'cost': 58}, {'i': 2, 'j': 5, 'k': 2, 'cost': 61}, {'i': 2, 'j': 5, 'k': 3, 'cost': 82}, {'i': 2, 'j': 5, 'k': 4, 'cost': 29}, {'i': 2, 'j': 5, 'k': 5, 'cost': 2}, {'i': 2, 'j': 5, 'k': 6, 'cost': 4}, {'i': 2, 'j': 6, 'k': 1, 'cost': 93}, {'i': 2, 'j': 6, 'k': 2, 'cost': 87}, {'i': 2, 'j': 6, 'k': 3, 'cost': 88}, {'i': 2, 'j': 6, 'k': 4, 'cost': 82}, {'i': 2, 'j': 6, 'k': 5, 'cost': 85}, {'i': 2, 'j': 6, 'k': 6, 'cost': 25}, {'i': 3, 'j': 1, 'k': 1, 'cost': 74}, {'i': 3, 'j': 1, 'k': 2, 'cost': 97}, {'i': 3, 'j': 1, 'k': 3, 'cost': 13}, {'i': 3, 'j': 1, 'k': 4, 'cost': 14}, {'i': 3, 'j': 1, 'k': 5, 'cost': 7}, {'i': 3, 'j': 1, 'k': 6, 'cost': 16}, {'i': 3, 'j': 2, 'k': 1, 'cost': 64}, {'i': 3, 'j': 2, 'k': 2, 'cost': 16}, {'i': 3, 'j': 2, 'k': 3, 'cost': 1}, {'i': 3, 'j': 2, 'k': 4, 'cost': 97}, {'i': 3, 'j': 2, 'k': 5, 'cost': 11}, {'i': 3, 'j': 2, 'k': 6, 'cost': 72}, {'i': 3, 'j': 3, 'k': 1, 'cost': 80}, {'i': 3, 'j': 3, 'k': 2, 'cost': 93}, {'i': 3, 'j': 3, 'k': 3, 'cost': 80}, {'i': 3, 'j': 3, 'k': 4, 'cost': 28}, {'i': 3, 'j': 3, 'k': 5, 'cost': 24}, {'i': 3, 'j': 3, 'k': 6, 'cost': 95}, {'i': 3, 'j': 4, 'k': 1, 'cost': 25}, {'i': 3, 'j': 4, 'k': 2, 'cost': 93}, {'i': 3, 'j': 4, 'k': 3, 'cost': 86}, {'i': 3, 'j': 4, 'k': 4, 'cost': 2}, {'i': 3, 'j': 4, 'k': 5, 'cost': 90}, {'i': 3, 'j': 4, 'k': 6, 'cost': 84}, {'i': 3, 'j': 5, 'k': 1, 'cost': 21}, {'i': 3, 'j': 5, 'k': 2, 'cost': 49}, {'i': 3, 'j': 5, 'k': 3, 'cost': 3}, {'i': 3, 'j': 5, 'k': 4, 'cost': 1}, {'i': 3, 'j': 5, 'k': 5, 'cost': 92}, {'i': 3, 'j': 5, 'k': 6, 'cost': 4}, {'i': 3, 'j': 6, 'k': 1, 'cost': 40}, {'i': 3, 'j': 6, 'k': 2, 'cost': 98}, {'i': 3, 'j': 6, 'k': 3, 'cost': 5}, {'i': 3, 'j': 6, 'k': 4, 'cost': 26}, {'i': 3, 'j': 6, 'k': 5, 'cost': 34}, {'i': 3, 'j': 6, 'k': 6, 'cost': 27}, {'i': 4, 'j': 1, 'k': 1, 'cost': 84}, {'i': 4, 'j': 1, 'k': 2, 'cost': 73}, {'i': 4, 'j': 1, 'k': 3, 'cost': 83}, {'i': 4, 'j': 1, 'k': 4, 'cost': 26}, {'i': 4, 'j': 1, 'k': 5, 'cost': 19}, {'i': 4, 'j': 1, 'k': 6, 'cost': 99}, {'i': 4, 'j': 2, 'k': 1, 'cost': 53}, {'i': 4, 'j': 2, 'k': 2, 'cost': 51}, {'i': 4, 'j': 2, 'k': 3, 'cost': 54}, {'i': 4, 'j': 2, 'k': 4, 'cost': 97}, {'i': 4, 'j': 2, 'k': 5, 'cost': 58}, {'i': 4, 'j': 2, 'k': 6, 'cost': 44}, {'i': 4, 'j': 3, 'k': 1, 'cost': 2}, {'i': 4, 'j': 3, 'k': 2, 'cost': 60}, {'i': 4, 'j': 3, 'k': 3, 'cost': 79}, {'i': 4, 'j': 3, 'k': 4, 'cost': 26}, {'i': 4, 'j': 3, 'k': 5, 'cost': 85}, {'i': 4, 'j': 3, 'k': 6, 'cost': 92}, {'i': 4, 'j': 4, 'k': 1, 'cost': 70}, {'i': 4, 'j': 4, 'k': 2, 'cost': 70}, {'i': 4, 'j': 4, 'k': 3, 'cost': 48}, {'i': 4, 'j': 4, 'k': 4, 'cost': 50}, {'i': 4, 'j': 4, 'k': 5, 'cost': 62}, {'i': 4, 'j': 4, 'k': 6, 'cost': 29}, {'i': 4, 'j': 5, 'k': 1, 'cost': 6}, {'i': 4, 'j': 5, 'k': 2, 'cost': 73}, {'i': 4, 'j': 5, 'k': 3, 'cost': 92}, {'i': 4, 'j': 5, 'k': 4, 'cost': 75}, {'i': 4, 'j': 5, 'k': 5, 'cost': 65}, {'i': 4, 'j': 5, 'k': 6, 'cost': 75}, {'i': 4, 'j': 6, 'k': 1, 'cost': 81}, {'i': 4, 'j': 6, 'k': 2, 'cost': 59}, {'i': 4, 'j': 6, 'k': 3, 'cost': 19}, {'i': 4, 'j': 6, 'k': 4, 'cost': 96}, {'i': 4, 'j': 6, 'k': 5, 'cost': 89}, {'i': 4, 'j': 6, 'k': 6, 'cost': 30}, {'i': 5, 'j': 1, 'k': 1, 'cost': 56}, {'i': 5, 'j': 1, 'k': 2, 'cost': 1}, {'i': 5, 'j': 1, 'k': 3, 'cost': 28}, {'i': 5, 'j': 1, 'k': 4, 'cost': 52}, {'i': 5, 'j': 1, 'k': 5, 'cost': 99}, {'i': 5, 'j': 1, 'k': 6, 'cost': 42}, {'i': 5, 'j': 2, 'k': 1, 'cost': 0}, {'i': 5, 'j': 2, 'k': 2, 'cost': 14}, {'i': 5, 'j': 2, 'k': 3, 'cost': 78}, {'i': 5, 'j': 2, 'k': 4, 'cost': 45}, {'i': 5, 'j': 2, 'k': 5, 'cost': 59}, {'i': 5, 'j': 2, 'k': 6, 'cost': 54}, {'i': 5, 'j': 3, 'k': 1, 'cost': 71}, {'i': 5, 'j': 3, 'k': 2, 'cost': 62}, {'i': 5, 'j': 3, 'k': 3, 'cost': 57}, {'i': 5, 'j': 3, 'k': 4, 'cost': 26}, {'i': 5, 'j': 3, 'k': 5, 'cost': 61}, {'i': 5, 'j': 3, 'k': 6, 'cost': 62}, {'i': 5, 'j': 4, 'k': 1, 'cost': 64}, {'i': 5, 'j': 4, 'k': 2, 'cost': 12}, {'i': 5, 'j': 4, 'k': 3, 'cost': 52}, {'i': 5, 'j': 4, 'k': 4, 'cost': 69}, {'i': 5, 'j': 4, 'k': 5, 'cost': 48}, {'i': 5, 'j': 4, 'k': 6, 'cost': 81}, {'i': 5, 'j': 5, 'k': 1, 'cost': 12}, {'i': 5, 'j': 5, 'k': 2, 'cost': 76}, {'i': 5, 'j': 5, 'k': 3, 'cost': 16}, {'i': 5, 'j': 5, 'k': 4, 'cost': 6}, {'i': 5, 'j': 5, 'k': 5, 'cost': 58}, {'i': 5, 'j': 5, 'k': 6, 'cost': 80}, {'i': 5, 'j': 6, 'k': 1, 'cost': 83}, {'i': 5, 'j': 6, 'k': 2, 'cost': 46}, {'i': 5, 'j': 6, 'k': 3, 'cost': 75}, {'i': 5, 'j': 6, 'k': 4, 'cost': 71}, {'i': 5, 'j': 6, 'k': 5, 'cost': 41}, {'i': 5, 'j': 6, 'k': 6, 'cost': 27}, {'i': 6, 'j': 1, 'k': 1, 'cost': 68}, {'i': 6, 'j': 1, 'k': 2, 'cost': 89}, {'i': 6, 'j': 1, 'k': 3, 'cost': 28}, {'i': 6, 'j': 1, 'k': 4, 'cost': 73}, {'i': 6, 'j': 1, 'k': 5, 'cost': 51}, {'i': 6, 'j': 1, 'k': 6, 'cost': 19}, {'i': 6, 'j': 2, 'k': 1, 'cost': 83}, {'i': 6, 'j': 2, 'k': 2, 'cost': 77}, {'i': 6, 'j': 2, 'k': 3, 'cost': 27}, {'i': 6, 'j': 2, 'k': 4, 'cost': 6}, {'i': 6, 'j': 2, 'k': 5, 'cost': 86}, {'i': 6, 'j': 2, 'k': 6, 'cost': 48}, {'i': 6, 'j': 3, 'k': 1, 'cost': 69}, {'i': 6, 'j': 3, 'k': 2, 'cost': 88}, {'i': 6, 'j': 3, 'k': 3, 'cost': 82}, {'i': 6, 'j': 3, 'k': 4, 'cost': 91}, {'i': 6, 'j': 3, 'k': 5, 'cost': 84}, {'i': 6, 'j': 3, 'k': 6, 'cost': 36}, {'i': 6, 'j': 4, 'k': 1, 'cost': 29}, {'i': 6, 'j': 4, 'k': 2, 'cost': 5}, {'i': 6, 'j': 4, 'k': 3, 'cost': 24}, {'i': 6, 'j': 4, 'k': 4, 'cost': 10}, {'i': 6, 'j': 4, 'k': 5, 'cost': 3}, {'i': 6, 'j': 4, 'k': 6, 'cost': 19}, {'i': 6, 'j': 5, 'k': 1, 'cost': 43}, {'i': 6, 'j': 5, 'k': 2, 'cost': 5}, {'i': 6, 'j': 5, 'k': 3, 'cost': 29}, {'i': 6, 'j': 5, 'k': 4, 'cost': 7}, {'i': 6, 'j': 5, 'k': 5, 'cost': 15}, {'i': 6, 'j': 5, 'k': 6, 'cost': 13}, {'i': 6, 'j': 6, 'k': 1, 'cost': 16}, {'i': 6, 'j': 6, 'k': 2, 'cost': 71}, {'i': 6, 'j': 6, 'k': 3, 'cost': 96}, {'i': 6, 'j': 6, 'k': 4, 'cost': 94}, {'i': 6, 'j': 6, 'k': 5, 'cost': 0}, {'i': 6, 'j': 6, 'k': 6, 'cost': 6}]}","[[1, 4, 5], [2, 5, 6], [3, 6, 3], [4, 3, 1], [5, 1, 2], [6, 2, 4]]",32,csv,1
AP3,AP3,"Many people on the floor talk about it like a matching game: each shipment needs one container and one loading bay, and there are exactly as many containers and bays as there are shipments. One container and one bay per shipment, no sharing, no leftovers. Each combination of shipment, container, and bay has a price, and the whole day’s expense is the sum of those prices — the aim is to keep that sum as low as possible. The concrete details are shown below.

Concretely, there are 6 shipments listed as A, B, C, D, E, F.
Meaning: costs form a 3D tensor. For each fixed shipment_id=i, you are given a container_id×loading_dock_id matrix whose entry at row container_id=j and column loading_dock_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all container_id and all loading_dock_id used exactly once.
assignment_cost_tensor (per-shipment_id markdown matrices):
## shipment_id=A
| container_id\loading_dock_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 26 | 46 | 17 | 21 | 0 | 57 |
| B | 43 | 37 | 22 | 37 | 93 | 49 |
| C | 81 | 39 | 70 | 81 | 94 | 7 |
| D | 93 | 80 | 56 | 46 | 53 | 72 |
| E | 29 | 91 | 5 | 94 | 19 | 82 |
| F | 3 | 18 | 93 | 19 | 31 | 82 |

## shipment_id=B
| container_id\loading_dock_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 5 | 40 | 62 | 4 | 92 | 71 |
| B | 85 | 22 | 83 | 89 | 34 | 90 |
| C | 56 | 94 | 50 | 41 | 69 | 54 |
| D | 65 | 58 | 29 | 91 | 0 | 60 |
| E | 87 | 20 | 3 | 72 | 71 | 74 |
| F | 2 | 25 | 31 | 84 | 67 | 83 |

## shipment_id=C
| container_id\loading_dock_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 58 | 24 | 52 | 71 | 24 | 84 |
| B | 81 | 55 | 53 | 15 | 81 | 55 |
| C | 81 | 31 | 78 | 48 | 55 | 27 |
| D | 34 | 60 | 94 | 18 | 80 | 47 |
| E | 84 | 91 | 46 | 64 | 1 | 54 |
| F | 69 | 22 | 52 | 80 | 29 | 23 |

## shipment_id=D
| container_id\loading_dock_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 49 | 86 | 52 | 74 | 46 | 13 |
| B | 36 | 99 | 94 | 31 | 76 | 68 |
| C | 62 | 3 | 50 | 20 | 36 | 62 |
| D | 38 | 72 | 11 | 57 | 25 | 15 |
| E | 96 | 73 | 90 | 28 | 52 | 0 |
| F | 55 | 57 | 25 | 13 | 85 | 14 |

## shipment_id=E
| container_id\loading_dock_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 68 | 49 | 66 | 49 | 50 | 46 |
| B | 53 | 43 | 6 | 85 | 75 | 21 |
| C | 25 | 63 | 67 | 24 | 25 | 60 |
| D | 82 | 11 | 2 | 62 | 52 | 35 |
| E | 67 | 32 | 97 | 81 | 86 | 87 |
| F | 64 | 9 | 31 | 6 | 37 | 71 |

## shipment_id=F
| container_id\loading_dock_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 59 | 65 | 73 | 22 | 26 | 56 |
| B | 3 | 30 | 27 | 28 | 21 | 87 |
| C | 48 | 55 | 22 | 68 | 61 | 86 |
| D | 26 | 5 | 82 | 60 | 57 | 84 |
| E | 91 | 47 | 91 | 32 | 52 | 11 |
| F | 17 | 8 | 87 | 67 | 42 | 73 |
The aim is to keep the total of these costs across all 6 shipments as low as possible.

If you want to hand the matching back in a tidy way, just follow this little JSON sketch below — it's an easy, predictable shape that makes it clear which shipment goes with which container and which bay.

{
  ""solution"": [
    [<shipment_id>, <container_id>, <bay_id>],
    ...
  ]
}

Each inner array is one chosen triple: [shipment_id, container_id, bay_id]. Think of each line as ""this shipment gets this container and this bay."" It's just an example of the expected shape — not the actual answer.

Please 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"".","{'cost_tensor': [[[26, 46, 17, 21, 0, 57], [43, 37, 22, 37, 93, 49], [81, 39, 70, 81, 94, 7], [93, 80, 56, 46, 53, 72], [29, 91, 5, 94, 19, 82], [3, 18, 93, 19, 31, 82]], [[5, 40, 62, 4, 92, 71], [85, 22, 83, 89, 34, 90], [56, 94, 50, 41, 69, 54], [65, 58, 29, 91, 0, 60], [87, 20, 3, 72, 71, 74], [2, 25, 31, 84, 67, 83]], [[58, 24, 52, 71, 24, 84], [81, 55, 53, 15, 81, 55], [81, 31, 78, 48, 55, 27], [34, 60, 94, 18, 80, 47], [84, 91, 46, 64, 1, 54], [69, 22, 52, 80, 29, 23]], [[49, 86, 52, 74, 46, 13], [36, 99, 94, 31, 76, 68], [62, 3, 50, 20, 36, 62], [38, 72, 11, 57, 25, 15], [96, 73, 90, 28, 52, 0], [55, 57, 25, 13, 85, 14]], [[68, 49, 66, 49, 50, 46], [53, 43, 6, 85, 75, 21], [25, 63, 67, 24, 25, 60], [82, 11, 2, 62, 52, 35], [67, 32, 97, 81, 86, 87], [64, 9, 31, 6, 37, 71]], [[59, 65, 73, 22, 26, 56], [3, 30, 27, 28, 21, 87], [48, 55, 22, 68, 61, 86], [26, 5, 82, 60, 57, 84], [91, 47, 91, 32, 52, 11], [17, 8, 87, 67, 42, 73]]], 'objective': 33.0}","[[0, 0, 4], [1, 5, 0], [2, 1, 3], [3, 2, 1], [4, 3, 2], [5, 4, 5]]",33.0,"{'problem_type': 'AP3', 'n': 6, 'ids': ['A', 'B', 'C', 'D', 'E', 'F'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 26}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 46}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 17}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 21}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 0}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 57}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 43}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 37}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 22}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 37}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 93}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 49}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 81}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 39}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 70}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 81}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 94}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 7}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 93}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 80}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 56}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 46}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 53}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 72}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 29}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 91}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 5}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 94}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 19}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 82}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 3}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 18}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 93}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 19}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 31}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 82}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 5}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 40}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 62}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 4}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 92}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 71}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 85}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 22}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 83}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 89}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 34}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 90}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 56}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 94}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 50}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 41}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 69}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 54}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 65}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 58}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 29}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 91}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 0}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 60}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 87}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 20}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 3}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 72}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 71}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 74}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 2}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 25}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 31}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 84}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 67}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 83}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 58}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 24}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 52}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 71}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 24}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 84}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 81}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 55}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 53}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 15}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 81}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 55}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 81}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 31}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 78}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 48}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 55}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 27}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 34}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 60}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 94}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 18}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 80}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 47}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 84}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 91}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 46}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 64}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 1}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 54}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 69}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 22}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 52}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 80}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 29}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 23}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 49}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 86}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 52}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 74}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 46}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 13}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 36}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 99}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 94}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 31}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 76}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 68}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 62}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 3}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 50}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 20}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 36}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 62}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 38}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 72}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 11}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 57}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 25}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 15}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 96}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 73}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 90}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 28}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 52}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 0}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 55}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 57}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 25}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 13}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 85}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 14}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 68}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 49}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 66}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 49}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 50}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 46}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 53}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 43}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 6}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 85}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 75}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 21}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 25}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 63}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 67}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 24}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 25}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 60}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 82}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 11}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 2}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 62}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 52}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 35}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 67}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 32}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 97}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 81}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 86}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 87}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 64}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 9}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 31}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 6}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 37}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 71}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 59}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 65}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 73}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 22}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 26}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 56}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 3}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 30}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 27}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 28}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 21}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 87}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 48}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 55}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 22}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 68}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 61}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 86}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 26}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 5}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 82}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 60}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 57}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 84}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 91}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 47}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 91}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 32}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 52}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 11}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 17}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 8}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 87}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 67}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 42}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 73}]}","[['A', 'A', 'E'], ['B', 'F', 'A'], ['C', 'B', 'D'], ['D', 'C', 'B'], ['E', 'D', 'C'], ['F', 'E', 'F']]",33,nl,names
AP3,AP3,"There’s a day with a set of tutoring slots that all need a single tutor and a single textbook, and the catch is each tutor and each textbook can be used only once so nothing is repeated or left unused. The best plan is simply the one with the least total expense — get the cost for each session (tutor plus book), add them up, and choose the arrangement with the smallest sum. The concrete numbers are shown below.

# num_sessions=7
# index_labels=A, B, C, D, E, F, G

# Meaning: costs form a 3D tensor. For each fixed session_id=i, you are given a tutor_id×textbook_id matrix whose entry at row tutor_id=j and column textbook_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all tutor_id and all textbook_id used exactly once.
# assignment_cost_tensor (per-session_id markdown matrices)

## session_id=A
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 94 | 94 | 77 | 73 | 81 | 3 | 1 |
| B | 27 | 5 | 92 | 73 | 84 | 84 | 37 |
| C | 50 | 28 | 56 | 95 | 13 | 6 | 29 |
| D | 31 | 1 | 23 | 10 | 57 | 78 | 88 |
| E | 18 | 42 | 28 | 79 | 40 | 10 | 45 |
| F | 86 | 16 | 42 | 43 | 29 | 55 | 18 |
| G | 2 | 60 | 90 | 92 | 17 | 52 | 57 |

## session_id=B
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 89 | 84 | 42 | 26 | 97 | 14 | 69 |
| B | 33 | 6 | 61 | 1 | 2 | 11 | 46 |
| C | 43 | 81 | 94 | 32 | 41 | 19 | 94 |
| D | 43 | 14 | 6 | 21 | 82 | 8 | 74 |
| E | 94 | 58 | 36 | 95 | 2 | 62 | 95 |
| F | 24 | 37 | 86 | 31 | 94 | 98 | 85 |
| G | 54 | 69 | 88 | 26 | 78 | 83 | 67 |

## session_id=C
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 20 | 96 | 47 | 38 | 41 | 0 | 90 |
| B | 56 | 66 | 15 | 76 | 54 | 91 | 13 |
| C | 44 | 10 | 1 | 20 | 98 | 97 | 31 |
| D | 98 | 96 | 82 | 44 | 89 | 94 | 35 |
| E | 77 | 12 | 19 | 64 | 98 | 11 | 59 |
| F | 68 | 40 | 27 | 35 | 81 | 33 | 20 |
| G | 68 | 88 | 66 | 60 | 16 | 38 | 5 |

## session_id=D
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 33 | 57 | 88 | 33 | 16 | 73 | 82 |
| B | 67 | 71 | 93 | 50 | 63 | 63 | 84 |
| C | 43 | 84 | 79 | 55 | 50 | 59 | 65 |
| D | 18 | 6 | 84 | 33 | 36 | 91 | 52 |
| E | 61 | 46 | 49 | 82 | 15 | 90 | 57 |
| F | 59 | 8 | 72 | 57 | 47 | 94 | 7 |
| G | 95 | 67 | 84 | 68 | 44 | 31 | 47 |

## session_id=E
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 47 | 19 | 44 | 42 | 83 | 18 | 0 |
| B | 54 | 29 | 7 | 49 | 24 | 96 | 54 |
| C | 72 | 12 | 84 | 97 | 8 | 32 | 40 |
| D | 0 | 17 | 25 | 3 | 73 | 80 | 46 |
| E | 31 | 69 | 99 | 32 | 88 | 62 | 27 |
| F | 58 | 50 | 32 | 55 | 76 | 16 | 25 |
| G | 93 | 40 | 93 | 39 | 56 | 88 | 38 |

## session_id=F
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 67 | 96 | 22 | 85 | 78 | 47 | 68 |
| B | 54 | 44 | 10 | 11 | 41 | 50 | 6 |
| C | 98 | 80 | 85 | 12 | 84 | 76 | 54 |
| D | 44 | 98 | 12 | 91 | 16 | 55 | 63 |
| E | 80 | 49 | 65 | 57 | 50 | 52 | 63 |
| F | 51 | 25 | 36 | 47 | 97 | 7 | 24 |
| G | 58 | 29 | 84 | 7 | 33 | 50 | 97 |

## session_id=G
| tutor_id\textbook_id | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| A | 32 | 30 | 42 | 20 | 0 | 93 | 69 |
| B | 15 | 65 | 10 | 28 | 69 | 13 | 18 |
| C | 65 | 81 | 83 | 68 | 93 | 18 | 71 |
| D | 70 | 46 | 90 | 29 | 63 | 13 | 89 |
| E | 33 | 83 | 70 | 0 | 73 | 27 | 70 |
| F | 55 | 47 | 22 | 42 | 98 | 52 | 88 |
| G | 71 | 51 | 48 | 0 | 94 | 31 | 55 |

If you prefer to get the plan in a tidy, machine-friendly snippet, I usually show it in a little JSON object like this.

{
  ""solution"": [
    [<slot_id>, <tutor_id>, <textbook_id>],
    ...
  ]
}

Each inner triple is one tutoring session: the first placeholder is the slot, the second is the tutor assigned to that slot, and the third is the textbook used. Think of it as a simple form where each row says ""slot X gets tutor Y and book Z."" This is just a sketch of the shape the answer should take, not the actual assignment.

Please make sure to use the exact identifiers from the instance input — no renaming and 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”.""","{'cost_tensor': [[[94, 94, 77, 73, 81, 3, 1], [27, 5, 92, 73, 84, 84, 37], [50, 28, 56, 95, 13, 6, 29], [31, 1, 23, 10, 57, 78, 88], [18, 42, 28, 79, 40, 10, 45], [86, 16, 42, 43, 29, 55, 18], [2, 60, 90, 92, 17, 52, 57]], [[89, 84, 42, 26, 97, 14, 69], [33, 6, 61, 1, 2, 11, 46], [43, 81, 94, 32, 41, 19, 94], [43, 14, 6, 21, 82, 8, 74], [94, 58, 36, 95, 2, 62, 95], [24, 37, 86, 31, 94, 98, 85], [54, 69, 88, 26, 78, 83, 67]], [[20, 96, 47, 38, 41, 0, 90], [56, 66, 15, 76, 54, 91, 13], [44, 10, 1, 20, 98, 97, 31], [98, 96, 82, 44, 89, 94, 35], [77, 12, 19, 64, 98, 11, 59], [68, 40, 27, 35, 81, 33, 20], [68, 88, 66, 60, 16, 38, 5]], [[33, 57, 88, 33, 16, 73, 82], [67, 71, 93, 50, 63, 63, 84], [43, 84, 79, 55, 50, 59, 65], [18, 6, 84, 33, 36, 91, 52], [61, 46, 49, 82, 15, 90, 57], [59, 8, 72, 57, 47, 94, 7], [95, 67, 84, 68, 44, 31, 47]], [[47, 19, 44, 42, 83, 18, 0], [54, 29, 7, 49, 24, 96, 54], [72, 12, 84, 97, 8, 32, 40], [0, 17, 25, 3, 73, 80, 46], [31, 69, 99, 32, 88, 62, 27], [58, 50, 32, 55, 76, 16, 25], [93, 40, 93, 39, 56, 88, 38]], [[67, 96, 22, 85, 78, 47, 68], [54, 44, 10, 11, 41, 50, 6], [98, 80, 85, 12, 84, 76, 54], [44, 98, 12, 91, 16, 55, 63], [80, 49, 65, 57, 50, 52, 63], [51, 25, 36, 47, 97, 7, 24], [58, 29, 84, 7, 33, 50, 97]], [[32, 30, 42, 20, 0, 93, 69], [15, 65, 10, 28, 69, 13, 18], [65, 81, 83, 68, 93, 18, 71], [70, 46, 90, 29, 63, 13, 89], [33, 83, 70, 0, 73, 27, 70], [55, 47, 22, 42, 98, 52, 88], [71, 51, 48, 0, 94, 31, 55]]], 'objective': 18.0}","[[0, 6, 0], [1, 1, 4], [2, 2, 2], [3, 3, 1], [4, 0, 6], [5, 5, 5], [6, 4, 3]]",18.0,"{'problem_type': 'AP3', 'n': 7, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 94}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 94}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 77}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 73}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 81}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 3}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 1}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 27}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 5}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 92}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 73}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 84}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 84}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 37}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 50}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 28}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 56}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 95}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 13}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 6}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 29}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 31}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 1}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 23}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 10}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 57}, {'i': 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{'i': 'G', 'j': 'E', 'k': 'A', 'cost': 33}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 83}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 70}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 0}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 73}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 27}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 70}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 55}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 47}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 22}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 42}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 98}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 52}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 88}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 71}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 51}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 48}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 0}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 94}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 31}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 55}]}","[['A', 'G', 'A'], ['B', 'B', 'E'], ['C', 'C', 'C'], ['D', 'D', 'B'], ['E', 'A', 'G'], ['F', 'F', 'F'], ['G', 'E', 'D']]",34,csv,names
AP3,AP3,"Someone working the yard-of-records had to match crews and paint cans to houses so that each crew works once and each color shows up on only one house. The idea was to keep the total expenditure as low as it can be: for each house add up that team’s labor charge and the cost of the chosen paint, and then sum those amounts for every house to get the final cost. Every crew must be used exactly once and every color must be used exactly once, and the detailed instance information follows below.

# problem_size=7
# index_identifiers=1, 2, 3, 4, 5, 6, 7

# Meaning: costs form a 3D tensor. For each fixed house_id=i, you are given a crew_id×paint_color_id matrix whose entry at row crew_id=j and column paint_color_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all crew_id and all paint_color_id used exactly once.
# assignment_cost_tensor (per-house_id markdown matrices)

## house_id=1
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 28 | 15 | 69 | 24 | 48 | 50 | 15 |
| 2 | 10 | 5 | 84 | 89 | 18 | 6 | 71 |
| 3 | 75 | 35 | 23 | 54 | 83 | 41 | 54 |
| 4 | 61 | 26 | 7 | 80 | 20 | 46 | 50 |
| 5 | 53 | 19 | 91 | 77 | 78 | 29 | 68 |
| 6 | 87 | 63 | 98 | 52 | 29 | 56 | 18 |
| 7 | 93 | 91 | 70 | 36 | 7 | 36 | 86 |

## house_id=2
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 17 | 44 | 60 | 88 | 40 | 61 | 92 |
| 2 | 74 | 42 | 22 | 20 | 20 | 17 | 79 |
| 3 | 1 | 67 | 85 | 7 | 94 | 64 | 21 |
| 4 | 55 | 72 | 19 | 2 | 3 | 49 | 29 |
| 5 | 84 | 10 | 46 | 95 | 82 | 57 | 90 |
| 6 | 3 | 31 | 43 | 26 | 87 | 17 | 54 |
| 7 | 2 | 72 | 73 | 70 | 60 | 65 | 8 |

## house_id=3
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 89 | 90 | 91 | 95 | 15 | 29 | 92 |
| 2 | 10 | 0 | 43 | 0 | 78 | 85 | 78 |
| 3 | 92 | 88 | 64 | 78 | 84 | 26 | 77 |
| 4 | 31 | 42 | 94 | 15 | 81 | 14 | 95 |
| 5 | 80 | 74 | 3 | 25 | 26 | 74 | 38 |
| 6 | 92 | 26 | 16 | 90 | 11 | 63 | 62 |
| 7 | 13 | 30 | 42 | 3 | 60 | 45 | 42 |

## house_id=4
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 29 | 42 | 29 | 3 | 59 | 87 | 17 |
| 2 | 30 | 67 | 81 | 71 | 92 | 12 | 55 |
| 3 | 52 | 96 | 91 | 62 | 47 | 6 | 65 |
| 4 | 9 | 25 | 97 | 13 | 99 | 4 | 94 |
| 5 | 79 | 35 | 31 | 53 | 15 | 41 | 27 |
| 6 | 17 | 44 | 40 | 24 | 47 | 69 | 13 |
| 7 | 78 | 16 | 72 | 97 | 59 | 52 | 73 |

## house_id=5
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 33 | 0 | 58 | 99 | 81 | 85 | 16 |
| 2 | 80 | 1 | 78 | 14 | 38 | 17 | 40 |
| 3 | 22 | 17 | 35 | 71 | 50 | 21 | 94 |
| 4 | 35 | 36 | 53 | 86 | 77 | 4 | 73 |
| 5 | 71 | 70 | 9 | 99 | 26 | 27 | 17 |
| 6 | 91 | 14 | 90 | 13 | 9 | 21 | 4 |
| 7 | 73 | 19 | 6 | 20 | 24 | 12 | 32 |

## house_id=6
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 21 | 46 | 98 | 81 | 77 | 84 | 15 |
| 2 | 17 | 81 | 62 | 29 | 47 | 52 | 11 |
| 3 | 33 | 47 | 30 | 84 | 81 | 43 | 84 |
| 4 | 99 | 52 | 46 | 96 | 34 | 72 | 84 |
| 5 | 58 | 90 | 92 | 92 | 69 | 75 | 46 |
| 6 | 40 | 1 | 91 | 97 | 72 | 42 | 5 |
| 7 | 29 | 93 | 57 | 33 | 93 | 3 | 31 |

## house_id=7
| crew_id\paint_color_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 52 | 98 | 46 | 75 | 55 | 88 |
| 2 | 47 | 70 | 84 | 37 | 29 | 98 | 90 |
| 3 | 63 | 69 | 64 | 49 | 60 | 39 | 59 |
| 4 | 35 | 25 | 17 | 69 | 73 | 84 | 9 |
| 5 | 43 | 20 | 68 | 73 | 91 | 26 | 26 |
| 6 | 47 | 46 | 45 | 71 | 36 | 63 | 36 |
| 7 | 5 | 26 | 44 | 42 | 28 | 67 | 24 |

If you want to hand me the matching in a tidy, machine-friendly way, just follow this simple shape — nothing fancy, just a list of triples that say which house gets which crew and which color:

{
  ""solution"": [
    [<house_id>, <crew_id>, <color_id>],
    ...
  ]
}

This is just a quick template: each inner array is one triple — the house, the crew assigned to that house, and the paint color used there. It's only the form I expect, not the actual assignment.

Please make sure to use the exact identifiers from the instance input — no renaming and no invented 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”.","{'cost_tensor': [[[28, 15, 69, 24, 48, 50, 15], [10, 5, 84, 89, 18, 6, 71], [75, 35, 23, 54, 83, 41, 54], [61, 26, 7, 80, 20, 46, 50], [53, 19, 91, 77, 78, 29, 68], [87, 63, 98, 52, 29, 56, 18], [93, 91, 70, 36, 7, 36, 86]], [[17, 44, 60, 88, 40, 61, 92], [74, 42, 22, 20, 20, 17, 79], [1, 67, 85, 7, 94, 64, 21], [55, 72, 19, 2, 3, 49, 29], [84, 10, 46, 95, 82, 57, 90], [3, 31, 43, 26, 87, 17, 54], [2, 72, 73, 70, 60, 65, 8]], [[89, 90, 91, 95, 15, 29, 92], [10, 0, 43, 0, 78, 85, 78], [92, 88, 64, 78, 84, 26, 77], [31, 42, 94, 15, 81, 14, 95], [80, 74, 3, 25, 26, 74, 38], [92, 26, 16, 90, 11, 63, 62], [13, 30, 42, 3, 60, 45, 42]], [[29, 42, 29, 3, 59, 87, 17], [30, 67, 81, 71, 92, 12, 55], [52, 96, 91, 62, 47, 6, 65], [9, 25, 97, 13, 99, 4, 94], [79, 35, 31, 53, 15, 41, 27], [17, 44, 40, 24, 47, 69, 13], [78, 16, 72, 97, 59, 52, 73]], [[33, 0, 58, 99, 81, 85, 16], [80, 1, 78, 14, 38, 17, 40], [22, 17, 35, 71, 50, 21, 94], [35, 36, 53, 86, 77, 4, 73], [71, 70, 9, 99, 26, 27, 17], [91, 14, 90, 13, 9, 21, 4], [73, 19, 6, 20, 24, 12, 32]], [[21, 46, 98, 81, 77, 84, 15], [17, 81, 62, 29, 47, 52, 11], [33, 47, 30, 84, 81, 43, 84], [99, 52, 46, 96, 34, 72, 84], [58, 90, 92, 92, 69, 75, 46], [40, 1, 91, 97, 72, 42, 5], [29, 93, 57, 33, 93, 3, 31]], [[1, 52, 98, 46, 75, 55, 88], [47, 70, 84, 37, 29, 98, 90], [63, 69, 64, 49, 60, 39, 59], [35, 25, 17, 69, 73, 84, 9], [43, 20, 68, 73, 91, 26, 26], [47, 46, 45, 71, 36, 63, 36], [5, 26, 44, 42, 28, 67, 24]]], 'objective': 25.0}","[[0, 6, 4], [1, 3, 3], [2, 4, 2], [3, 2, 5], [4, 1, 1], [5, 5, 6], [6, 0, 0]]",25.0,"{'problem_type': 'AP3', 'n': 7, 'ids': [1, 2, 3, 4, 5, 6, 7], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 28}, {'i': 1, 'j': 1, 'k': 2, 'cost': 15}, {'i': 1, 'j': 1, 'k': 3, 'cost': 69}, {'i': 1, 'j': 1, 'k': 4, 'cost': 24}, {'i': 1, 'j': 1, 'k': 5, 'cost': 48}, {'i': 1, 'j': 1, 'k': 6, 'cost': 50}, {'i': 1, 'j': 1, 'k': 7, 'cost': 15}, {'i': 1, 'j': 2, 'k': 1, 'cost': 10}, {'i': 1, 'j': 2, 'k': 2, 'cost': 5}, {'i': 1, 'j': 2, 'k': 3, 'cost': 84}, {'i': 1, 'j': 2, 'k': 4, 'cost': 89}, {'i': 1, 'j': 2, 'k': 5, 'cost': 18}, {'i': 1, 'j': 2, 'k': 6, 'cost': 6}, {'i': 1, 'j': 2, 'k': 7, 'cost': 71}, {'i': 1, 'j': 3, 'k': 1, 'cost': 75}, {'i': 1, 'j': 3, 'k': 2, 'cost': 35}, {'i': 1, 'j': 3, 'k': 3, 'cost': 23}, {'i': 1, 'j': 3, 'k': 4, 'cost': 54}, {'i': 1, 'j': 3, 'k': 5, 'cost': 83}, {'i': 1, 'j': 3, 'k': 6, 'cost': 41}, {'i': 1, 'j': 3, 'k': 7, 'cost': 54}, {'i': 1, 'j': 4, 'k': 1, 'cost': 61}, {'i': 1, 'j': 4, 'k': 2, 'cost': 26}, {'i': 1, 'j': 4, 'k': 3, 'cost': 7}, {'i': 1, 'j': 4, 'k': 4, 'cost': 80}, {'i': 1, 'j': 4, 'k': 5, 'cost': 20}, {'i': 1, 'j': 4, 'k': 6, 'cost': 46}, {'i': 1, 'j': 4, 'k': 7, 'cost': 50}, {'i': 1, 'j': 5, 'k': 1, 'cost': 53}, {'i': 1, 'j': 5, 'k': 2, 'cost': 19}, {'i': 1, 'j': 5, 'k': 3, 'cost': 91}, {'i': 1, 'j': 5, 'k': 4, 'cost': 77}, {'i': 1, 'j': 5, 'k': 5, 'cost': 78}, {'i': 1, 'j': 5, 'k': 6, 'cost': 29}, {'i': 1, 'j': 5, 'k': 7, 'cost': 68}, {'i': 1, 'j': 6, 'k': 1, 'cost': 87}, {'i': 1, 'j': 6, 'k': 2, 'cost': 63}, {'i': 1, 'j': 6, 'k': 3, 'cost': 98}, {'i': 1, 'j': 6, 'k': 4, 'cost': 52}, {'i': 1, 'j': 6, 'k': 5, 'cost': 29}, {'i': 1, 'j': 6, 'k': 6, 'cost': 56}, {'i': 1, 'j': 6, 'k': 7, 'cost': 18}, {'i': 1, 'j': 7, 'k': 1, 'cost': 93}, {'i': 1, 'j': 7, 'k': 2, 'cost': 91}, {'i': 1, 'j': 7, 'k': 3, 'cost': 70}, {'i': 1, 'j': 7, 'k': 4, 'cost': 36}, {'i': 1, 'j': 7, 'k': 5, 'cost': 7}, {'i': 1, 'j': 7, 'k': 6, 'cost': 36}, {'i': 1, 'j': 7, 'k': 7, 'cost': 86}, {'i': 2, 'j': 1, 'k': 1, 'cost': 17}, {'i': 2, 'j': 1, 'k': 2, 'cost': 44}, {'i': 2, 'j': 1, 'k': 3, 'cost': 60}, {'i': 2, 'j': 1, 'k': 4, 'cost': 88}, {'i': 2, 'j': 1, 'k': 5, 'cost': 40}, {'i': 2, 'j': 1, 'k': 6, 'cost': 61}, {'i': 2, 'j': 1, 'k': 7, 'cost': 92}, {'i': 2, 'j': 2, 'k': 1, 'cost': 74}, {'i': 2, 'j': 2, 'k': 2, 'cost': 42}, {'i': 2, 'j': 2, 'k': 3, 'cost': 22}, {'i': 2, 'j': 2, 'k': 4, 'cost': 20}, {'i': 2, 'j': 2, 'k': 5, 'cost': 20}, {'i': 2, 'j': 2, 'k': 6, 'cost': 17}, {'i': 2, 'j': 2, 'k': 7, 'cost': 79}, {'i': 2, 'j': 3, 'k': 1, 'cost': 1}, {'i': 2, 'j': 3, 'k': 2, 'cost': 67}, {'i': 2, 'j': 3, 'k': 3, 'cost': 85}, {'i': 2, 'j': 3, 'k': 4, 'cost': 7}, {'i': 2, 'j': 3, 'k': 5, 'cost': 94}, {'i': 2, 'j': 3, 'k': 6, 'cost': 64}, {'i': 2, 'j': 3, 'k': 7, 'cost': 21}, {'i': 2, 'j': 4, 'k': 1, 'cost': 55}, {'i': 2, 'j': 4, 'k': 2, 'cost': 72}, {'i': 2, 'j': 4, 'k': 3, 'cost': 19}, {'i': 2, 'j': 4, 'k': 4, 'cost': 2}, {'i': 2, 'j': 4, 'k': 5, 'cost': 3}, {'i': 2, 'j': 4, 'k': 6, 'cost': 49}, {'i': 2, 'j': 4, 'k': 7, 'cost': 29}, {'i': 2, 'j': 5, 'k': 1, 'cost': 84}, {'i': 2, 'j': 5, 'k': 2, 'cost': 10}, {'i': 2, 'j': 5, 'k': 3, 'cost': 46}, {'i': 2, 'j': 5, 'k': 4, 'cost': 95}, {'i': 2, 'j': 5, 'k': 5, 'cost': 82}, {'i': 2, 'j': 5, 'k': 6, 'cost': 57}, {'i': 2, 'j': 5, 'k': 7, 'cost': 90}, {'i': 2, 'j': 6, 'k': 1, 'cost': 3}, {'i': 2, 'j': 6, 'k': 2, 'cost': 31}, {'i': 2, 'j': 6, 'k': 3, 'cost': 43}, {'i': 2, 'j': 6, 'k': 4, 'cost': 26}, {'i': 2, 'j': 6, 'k': 5, 'cost': 87}, {'i': 2, 'j': 6, 'k': 6, 'cost': 17}, {'i': 2, 'j': 6, 'k': 7, 'cost': 54}, {'i': 2, 'j': 7, 'k': 1, 'cost': 2}, {'i': 2, 'j': 7, 'k': 2, 'cost': 72}, {'i': 2, 'j': 7, 'k': 3, 'cost': 73}, {'i': 2, 'j': 7, 'k': 4, 'cost': 70}, {'i': 2, 'j': 7, 'k': 5, 'cost': 60}, {'i': 2, 'j': 7, 'k': 6, 'cost': 65}, {'i': 2, 'j': 7, 'k': 7, 'cost': 8}, {'i': 3, 'j': 1, 'k': 1, 'cost': 89}, {'i': 3, 'j': 1, 'k': 2, 'cost': 90}, {'i': 3, 'j': 1, 'k': 3, 'cost': 91}, {'i': 3, 'j': 1, 'k': 4, 'cost': 95}, {'i': 3, 'j': 1, 'k': 5, 'cost': 15}, {'i': 3, 'j': 1, 'k': 6, 'cost': 29}, {'i': 3, 'j': 1, 'k': 7, 'cost': 92}, {'i': 3, 'j': 2, 'k': 1, 'cost': 10}, {'i': 3, 'j': 2, 'k': 2, 'cost': 0}, {'i': 3, 'j': 2, 'k': 3, 'cost': 43}, {'i': 3, 'j': 2, 'k': 4, 'cost': 0}, {'i': 3, 'j': 2, 'k': 5, 'cost': 78}, {'i': 3, 'j': 2, 'k': 6, 'cost': 85}, {'i': 3, 'j': 2, 'k': 7, 'cost': 78}, {'i': 3, 'j': 3, 'k': 1, 'cost': 92}, {'i': 3, 'j': 3, 'k': 2, 'cost': 88}, {'i': 3, 'j': 3, 'k': 3, 'cost': 64}, {'i': 3, 'j': 3, 'k': 4, 'cost': 78}, {'i': 3, 'j': 3, 'k': 5, 'cost': 84}, {'i': 3, 'j': 3, 'k': 6, 'cost': 26}, {'i': 3, 'j': 3, 'k': 7, 'cost': 77}, {'i': 3, 'j': 4, 'k': 1, 'cost': 31}, {'i': 3, 'j': 4, 'k': 2, 'cost': 42}, {'i': 3, 'j': 4, 'k': 3, 'cost': 94}, {'i': 3, 'j': 4, 'k': 4, 'cost': 15}, {'i': 3, 'j': 4, 'k': 5, 'cost': 81}, {'i': 3, 'j': 4, 'k': 6, 'cost': 14}, {'i': 3, 'j': 4, 'k': 7, 'cost': 95}, {'i': 3, 'j': 5, 'k': 1, 'cost': 80}, {'i': 3, 'j': 5, 'k': 2, 'cost': 74}, {'i': 3, 'j': 5, 'k': 3, 'cost': 3}, {'i': 3, 'j': 5, 'k': 4, 'cost': 25}, {'i': 3, 'j': 5, 'k': 5, 'cost': 26}, {'i': 3, 'j': 5, 'k': 6, 'cost': 74}, {'i': 3, 'j': 5, 'k': 7, 'cost': 38}, {'i': 3, 'j': 6, 'k': 1, 'cost': 92}, {'i': 3, 'j': 6, 'k': 2, 'cost': 26}, {'i': 3, 'j': 6, 'k': 3, 'cost': 16}, {'i': 3, 'j': 6, 'k': 4, 'cost': 90}, {'i': 3, 'j': 6, 'k': 5, 'cost': 11}, {'i': 3, 'j': 6, 'k': 6, 'cost': 63}, {'i': 3, 'j': 6, 'k': 7, 'cost': 62}, {'i': 3, 'j': 7, 'k': 1, 'cost': 13}, {'i': 3, 'j': 7, 'k': 2, 'cost': 30}, {'i': 3, 'j': 7, 'k': 3, 'cost': 42}, {'i': 3, 'j': 7, 'k': 4, 'cost': 3}, {'i': 3, 'j': 7, 'k': 5, 'cost': 60}, {'i': 3, 'j': 7, 'k': 6, 'cost': 45}, {'i': 3, 'j': 7, 'k': 7, 'cost': 42}, {'i': 4, 'j': 1, 'k': 1, 'cost': 29}, {'i': 4, 'j': 1, 'k': 2, 'cost': 42}, {'i': 4, 'j': 1, 'k': 3, 'cost': 29}, {'i': 4, 'j': 1, 'k': 4, 'cost': 3}, {'i': 4, 'j': 1, 'k': 5, 'cost': 59}, {'i': 4, 'j': 1, 'k': 6, 'cost': 87}, {'i': 4, 'j': 1, 'k': 7, 'cost': 17}, {'i': 4, 'j': 2, 'k': 1, 'cost': 30}, {'i': 4, 'j': 2, 'k': 2, 'cost': 67}, {'i': 4, 'j': 2, 'k': 3, 'cost': 81}, {'i': 4, 'j': 2, 'k': 4, 'cost': 71}, {'i': 4, 'j': 2, 'k': 5, 'cost': 92}, {'i': 4, 'j': 2, 'k': 6, 'cost': 12}, {'i': 4, 'j': 2, 'k': 7, 'cost': 55}, {'i': 4, 'j': 3, 'k': 1, 'cost': 52}, {'i': 4, 'j': 3, 'k': 2, 'cost': 96}, {'i': 4, 'j': 3, 'k': 3, 'cost': 91}, {'i': 4, 'j': 3, 'k': 4, 'cost': 62}, {'i': 4, 'j': 3, 'k': 5, 'cost': 47}, {'i': 4, 'j': 3, 'k': 6, 'cost': 6}, {'i': 4, 'j': 3, 'k': 7, 'cost': 65}, {'i': 4, 'j': 4, 'k': 1, 'cost': 9}, {'i': 4, 'j': 4, 'k': 2, 'cost': 25}, {'i': 4, 'j': 4, 'k': 3, 'cost': 97}, {'i': 4, 'j': 4, 'k': 4, 'cost': 13}, {'i': 4, 'j': 4, 'k': 5, 'cost': 99}, {'i': 4, 'j': 4, 'k': 6, 'cost': 4}, {'i': 4, 'j': 4, 'k': 7, 'cost': 94}, {'i': 4, 'j': 5, 'k': 1, 'cost': 79}, {'i': 4, 'j': 5, 'k': 2, 'cost': 35}, {'i': 4, 'j': 5, 'k': 3, 'cost': 31}, {'i': 4, 'j': 5, 'k': 4, 'cost': 53}, {'i': 4, 'j': 5, 'k': 5, 'cost': 15}, {'i': 4, 'j': 5, 'k': 6, 'cost': 41}, {'i': 4, 'j': 5, 'k': 7, 'cost': 27}, {'i': 4, 'j': 6, 'k': 1, 'cost': 17}, {'i': 4, 'j': 6, 'k': 2, 'cost': 44}, {'i': 4, 'j': 6, 'k': 3, 'cost': 40}, {'i': 4, 'j': 6, 'k': 4, 'cost': 24}, {'i': 4, 'j': 6, 'k': 5, 'cost': 47}, {'i': 4, 'j': 6, 'k': 6, 'cost': 69}, {'i': 4, 'j': 6, 'k': 7, 'cost': 13}, {'i': 4, 'j': 7, 'k': 1, 'cost': 78}, {'i': 4, 'j': 7, 'k': 2, 'cost': 16}, {'i': 4, 'j': 7, 'k': 3, 'cost': 72}, {'i': 4, 'j': 7, 'k': 4, 'cost': 97}, {'i': 4, 'j': 7, 'k': 5, 'cost': 59}, {'i': 4, 'j': 7, 'k': 6, 'cost': 52}, {'i': 4, 'j': 7, 'k': 7, 'cost': 73}, {'i': 5, 'j': 1, 'k': 1, 'cost': 33}, {'i': 5, 'j': 1, 'k': 2, 'cost': 0}, {'i': 5, 'j': 1, 'k': 3, 'cost': 58}, {'i': 5, 'j': 1, 'k': 4, 'cost': 99}, {'i': 5, 'j': 1, 'k': 5, 'cost': 81}, {'i': 5, 'j': 1, 'k': 6, 'cost': 85}, {'i': 5, 'j': 1, 'k': 7, 'cost': 16}, {'i': 5, 'j': 2, 'k': 1, 'cost': 80}, {'i': 5, 'j': 2, 'k': 2, 'cost': 1}, {'i': 5, 'j': 2, 'k': 3, 'cost': 78}, {'i': 5, 'j': 2, 'k': 4, 'cost': 14}, {'i': 5, 'j': 2, 'k': 5, 'cost': 38}, {'i': 5, 'j': 2, 'k': 6, 'cost': 17}, {'i': 5, 'j': 2, 'k': 7, 'cost': 40}, {'i': 5, 'j': 3, 'k': 1, 'cost': 22}, {'i': 5, 'j': 3, 'k': 2, 'cost': 17}, {'i': 5, 'j': 3, 'k': 3, 'cost': 35}, {'i': 5, 'j': 3, 'k': 4, 'cost': 71}, {'i': 5, 'j': 3, 'k': 5, 'cost': 50}, {'i': 5, 'j': 3, 'k': 6, 'cost': 21}, {'i': 5, 'j': 3, 'k': 7, 'cost': 94}, {'i': 5, 'j': 4, 'k': 1, 'cost': 35}, {'i': 5, 'j': 4, 'k': 2, 'cost': 36}, {'i': 5, 'j': 4, 'k': 3, 'cost': 53}, {'i': 5, 'j': 4, 'k': 4, 'cost': 86}, {'i': 5, 'j': 4, 'k': 5, 'cost': 77}, {'i': 5, 'j': 4, 'k': 6, 'cost': 4}, {'i': 5, 'j': 4, 'k': 7, 'cost': 73}, {'i': 5, 'j': 5, 'k': 1, 'cost': 71}, {'i': 5, 'j': 5, 'k': 2, 'cost': 70}, {'i': 5, 'j': 5, 'k': 3, 'cost': 9}, {'i': 5, 'j': 5, 'k': 4, 'cost': 99}, {'i': 5, 'j': 5, 'k': 5, 'cost': 26}, {'i': 5, 'j': 5, 'k': 6, 'cost': 27}, {'i': 5, 'j': 5, 'k': 7, 'cost': 17}, {'i': 5, 'j': 6, 'k': 1, 'cost': 91}, {'i': 5, 'j': 6, 'k': 2, 'cost': 14}, {'i': 5, 'j': 6, 'k': 3, 'cost': 90}, {'i': 5, 'j': 6, 'k': 4, 'cost': 13}, {'i': 5, 'j': 6, 'k': 5, 'cost': 9}, {'i': 5, 'j': 6, 'k': 6, 'cost': 21}, {'i': 5, 'j': 6, 'k': 7, 'cost': 4}, {'i': 5, 'j': 7, 'k': 1, 'cost': 73}, {'i': 5, 'j': 7, 'k': 2, 'cost': 19}, {'i': 5, 'j': 7, 'k': 3, 'cost': 6}, {'i': 5, 'j': 7, 'k': 4, 'cost': 20}, {'i': 5, 'j': 7, 'k': 5, 'cost': 24}, {'i': 5, 'j': 7, 'k': 6, 'cost': 12}, {'i': 5, 'j': 7, 'k': 7, 'cost': 32}, {'i': 6, 'j': 1, 'k': 1, 'cost': 21}, {'i': 6, 'j': 1, 'k': 2, 'cost': 46}, {'i': 6, 'j': 1, 'k': 3, 'cost': 98}, {'i': 6, 'j': 1, 'k': 4, 'cost': 81}, {'i': 6, 'j': 1, 'k': 5, 'cost': 77}, {'i': 6, 'j': 1, 'k': 6, 'cost': 84}, {'i': 6, 'j': 1, 'k': 7, 'cost': 15}, {'i': 6, 'j': 2, 'k': 1, 'cost': 17}, {'i': 6, 'j': 2, 'k': 2, 'cost': 81}, {'i': 6, 'j': 2, 'k': 3, 'cost': 62}, {'i': 6, 'j': 2, 'k': 4, 'cost': 29}, {'i': 6, 'j': 2, 'k': 5, 'cost': 47}, {'i': 6, 'j': 2, 'k': 6, 'cost': 52}, {'i': 6, 'j': 2, 'k': 7, 'cost': 11}, {'i': 6, 'j': 3, 'k': 1, 'cost': 33}, {'i': 6, 'j': 3, 'k': 2, 'cost': 47}, {'i': 6, 'j': 3, 'k': 3, 'cost': 30}, {'i': 6, 'j': 3, 'k': 4, 'cost': 84}, {'i': 6, 'j': 3, 'k': 5, 'cost': 81}, {'i': 6, 'j': 3, 'k': 6, 'cost': 43}, {'i': 6, 'j': 3, 'k': 7, 'cost': 84}, {'i': 6, 'j': 4, 'k': 1, 'cost': 99}, {'i': 6, 'j': 4, 'k': 2, 'cost': 52}, {'i': 6, 'j': 4, 'k': 3, 'cost': 46}, {'i': 6, 'j': 4, 'k': 4, 'cost': 96}, {'i': 6, 'j': 4, 'k': 5, 'cost': 34}, {'i': 6, 'j': 4, 'k': 6, 'cost': 72}, {'i': 6, 'j': 4, 'k': 7, 'cost': 84}, {'i': 6, 'j': 5, 'k': 1, 'cost': 58}, {'i': 6, 'j': 5, 'k': 2, 'cost': 90}, {'i': 6, 'j': 5, 'k': 3, 'cost': 92}, {'i': 6, 'j': 5, 'k': 4, 'cost': 92}, {'i': 6, 'j': 5, 'k': 5, 'cost': 69}, {'i': 6, 'j': 5, 'k': 6, 'cost': 75}, {'i': 6, 'j': 5, 'k': 7, 'cost': 46}, {'i': 6, 'j': 6, 'k': 1, 'cost': 40}, {'i': 6, 'j': 6, 'k': 2, 'cost': 1}, {'i': 6, 'j': 6, 'k': 3, 'cost': 91}, {'i': 6, 'j': 6, 'k': 4, 'cost': 97}, {'i': 6, 'j': 6, 'k': 5, 'cost': 72}, {'i': 6, 'j': 6, 'k': 6, 'cost': 42}, {'i': 6, 'j': 6, 'k': 7, 'cost': 5}, {'i': 6, 'j': 7, 'k': 1, 'cost': 29}, {'i': 6, 'j': 7, 'k': 2, 'cost': 93}, {'i': 6, 'j': 7, 'k': 3, 'cost': 57}, {'i': 6, 'j': 7, 'k': 4, 'cost': 33}, {'i': 6, 'j': 7, 'k': 5, 'cost': 93}, {'i': 6, 'j': 7, 'k': 6, 'cost': 3}, {'i': 6, 'j': 7, 'k': 7, 'cost': 31}, {'i': 7, 'j': 1, 'k': 1, 'cost': 1}, {'i': 7, 'j': 1, 'k': 2, 'cost': 52}, {'i': 7, 'j': 1, 'k': 3, 'cost': 98}, {'i': 7, 'j': 1, 'k': 4, 'cost': 46}, {'i': 7, 'j': 1, 'k': 5, 'cost': 75}, {'i': 7, 'j': 1, 'k': 6, 'cost': 55}, {'i': 7, 'j': 1, 'k': 7, 'cost': 88}, {'i': 7, 'j': 2, 'k': 1, 'cost': 47}, {'i': 7, 'j': 2, 'k': 2, 'cost': 70}, {'i': 7, 'j': 2, 'k': 3, 'cost': 84}, {'i': 7, 'j': 2, 'k': 4, 'cost': 37}, {'i': 7, 'j': 2, 'k': 5, 'cost': 29}, {'i': 7, 'j': 2, 'k': 6, 'cost': 98}, {'i': 7, 'j': 2, 'k': 7, 'cost': 90}, {'i': 7, 'j': 3, 'k': 1, 'cost': 63}, {'i': 7, 'j': 3, 'k': 2, 'cost': 69}, {'i': 7, 'j': 3, 'k': 3, 'cost': 64}, {'i': 7, 'j': 3, 'k': 4, 'cost': 49}, {'i': 7, 'j': 3, 'k': 5, 'cost': 60}, {'i': 7, 'j': 3, 'k': 6, 'cost': 39}, {'i': 7, 'j': 3, 'k': 7, 'cost': 59}, {'i': 7, 'j': 4, 'k': 1, 'cost': 35}, {'i': 7, 'j': 4, 'k': 2, 'cost': 25}, {'i': 7, 'j': 4, 'k': 3, 'cost': 17}, {'i': 7, 'j': 4, 'k': 4, 'cost': 69}, {'i': 7, 'j': 4, 'k': 5, 'cost': 73}, {'i': 7, 'j': 4, 'k': 6, 'cost': 84}, {'i': 7, 'j': 4, 'k': 7, 'cost': 9}, {'i': 7, 'j': 5, 'k': 1, 'cost': 43}, {'i': 7, 'j': 5, 'k': 2, 'cost': 20}, {'i': 7, 'j': 5, 'k': 3, 'cost': 68}, {'i': 7, 'j': 5, 'k': 4, 'cost': 73}, {'i': 7, 'j': 5, 'k': 5, 'cost': 91}, {'i': 7, 'j': 5, 'k': 6, 'cost': 26}, {'i': 7, 'j': 5, 'k': 7, 'cost': 26}, {'i': 7, 'j': 6, 'k': 1, 'cost': 47}, {'i': 7, 'j': 6, 'k': 2, 'cost': 46}, {'i': 7, 'j': 6, 'k': 3, 'cost': 45}, {'i': 7, 'j': 6, 'k': 4, 'cost': 71}, {'i': 7, 'j': 6, 'k': 5, 'cost': 36}, {'i': 7, 'j': 6, 'k': 6, 'cost': 63}, {'i': 7, 'j': 6, 'k': 7, 'cost': 36}, {'i': 7, 'j': 7, 'k': 1, 'cost': 5}, {'i': 7, 'j': 7, 'k': 2, 'cost': 26}, {'i': 7, 'j': 7, 'k': 3, 'cost': 44}, {'i': 7, 'j': 7, 'k': 4, 'cost': 42}, {'i': 7, 'j': 7, 'k': 5, 'cost': 28}, {'i': 7, 'j': 7, 'k': 6, 'cost': 67}, {'i': 7, 'j': 7, 'k': 7, 'cost': 24}]}","[[1, 7, 5], [2, 4, 4], [3, 5, 3], [4, 3, 6], [5, 2, 2], [6, 6, 7], [7, 1, 1]]",35,csv,1
AP3,AP3,"I’m juggling the neighborhood grocery deliveries: for every online order there’s a need to pick one courier and one dropoff window. The trick is to choose those pairs so the total delivery bill — the sum of each order’s chosen courier+window cost — ends up as small as possible, and nobody gets left out or double-booked: every courier does exactly one order and every time window is used exactly once. The exact orders, couriers, windows and their costs are listed below.

I'm looking at 6 orders, identified as 1, 2, 3, 4, 5, 6.
Meaning: costs form a 3D tensor. For each fixed order_id=i, you are given a courier_id×window_id matrix whose entry at row courier_id=j and column window_id=k equals delivery_cost(i,j,k). You must pick exactly one (j,k) for every i, with all courier_id and all window_id used exactly once.
delivery_cost_tensor (per-order_id markdown matrices):
## order_id=1
| courier_id\window_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 19 | 16 | 25 | 96 | 93 | 56 |
| 2 | 18 | 85 | 65 | 39 | 3 | 24 |
| 3 | 61 | 93 | 16 | 35 | 40 | 99 |
| 4 | 6 | 73 | 62 | 28 | 41 | 90 |
| 5 | 10 | 47 | 31 | 48 | 69 | 77 |
| 6 | 37 | 14 | 51 | 89 | 30 | 15 |

## order_id=2
| courier_id\window_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 36 | 65 | 55 | 57 | 83 | 91 |
| 2 | 28 | 32 | 40 | 74 | 60 | 75 |
| 3 | 7 | 69 | 2 | 75 | 63 | 86 |
| 4 | 68 | 48 | 48 | 82 | 65 | 57 |
| 5 | 89 | 1 | 17 | 53 | 60 | 41 |
| 6 | 33 | 85 | 55 | 62 | 17 | 32 |

## order_id=3
| courier_id\window_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 92 | 56 | 74 | 38 | 3 | 8 |
| 2 | 85 | 14 | 2 | 38 | 73 | 54 |
| 3 | 57 | 64 | 51 | 30 | 58 | 7 |
| 4 | 60 | 5 | 58 | 82 | 7 | 91 |
| 5 | 44 | 51 | 72 | 17 | 87 | 57 |
| 6 | 33 | 71 | 97 | 38 | 75 | 94 |

## order_id=4
| courier_id\window_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 49 | 94 | 5 | 27 | 99 | 97 |
| 2 | 98 | 99 | 27 | 0 | 12 | 6 |
| 3 | 25 | 99 | 8 | 5 | 80 | 15 |
| 4 | 46 | 70 | 76 | 38 | 74 | 68 |
| 5 | 96 | 94 | 74 | 47 | 6 | 3 |
| 6 | 38 | 50 | 68 | 61 | 37 | 60 |

## order_id=5
| courier_id\window_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 64 | 76 | 78 | 20 | 83 | 85 |
| 2 | 50 | 14 | 47 | 75 | 71 | 45 |
| 3 | 85 | 79 | 20 | 7 | 80 | 60 |
| 4 | 90 | 98 | 53 | 7 | 81 | 45 |
| 5 | 31 | 69 | 67 | 77 | 81 | 4 |
| 6 | 48 | 88 | 34 | 71 | 57 | 56 |

## order_id=6
| courier_id\window_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 69 | 65 | 71 | 4 | 30 | 88 |
| 2 | 12 | 82 | 48 | 71 | 11 | 29 |
| 3 | 12 | 36 | 13 | 96 | 44 | 58 |
| 4 | 54 | 0 | 74 | 41 | 86 | 56 |
| 5 | 27 | 45 | 20 | 75 | 66 | 18 |
| 6 | 82 | 43 | 9 | 31 | 76 | 86 |
That's the full list — time for me to pick the one-to-one courier/window pairings that minimize the total delivery bill.

Oh, and when you send back the picks, a little JSON like this makes it super easy to read:

{
  ""solution"": [
    [""<order_id>"", ""<courier_id>"", ""<window_id>""],
    [""<order_id>"", ""<courier_id>"", ""<window_id>""],
    [""<order_id>"", ""<courier_id>"", ""<window_id>""]
  ]
}

Each inner triple is just one assignment: which order goes with which courier and which dropoff window. Think of the block above as a form — the shape I expect, not the actual filled-in answer.

Please make sure you use the exact identifiers from the instance input — no renaming and no 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"".","{'cost_tensor': [[[19, 16, 25, 96, 93, 56], [18, 85, 65, 39, 3, 24], [61, 93, 16, 35, 40, 99], [6, 73, 62, 28, 41, 90], [10, 47, 31, 48, 69, 77], [37, 14, 51, 89, 30, 15]], [[36, 65, 55, 57, 83, 91], [28, 32, 40, 74, 60, 75], [7, 69, 2, 75, 63, 86], [68, 48, 48, 82, 65, 57], [89, 1, 17, 53, 60, 41], [33, 85, 55, 62, 17, 32]], [[92, 56, 74, 38, 3, 8], [85, 14, 2, 38, 73, 54], [57, 64, 51, 30, 58, 7], [60, 5, 58, 82, 7, 91], [44, 51, 72, 17, 87, 57], [33, 71, 97, 38, 75, 94]], [[49, 94, 5, 27, 99, 97], [98, 99, 27, 0, 12, 6], [25, 99, 8, 5, 80, 15], [46, 70, 76, 38, 74, 68], [96, 94, 74, 47, 6, 3], [38, 50, 68, 61, 37, 60]], [[64, 76, 78, 20, 83, 85], [50, 14, 47, 75, 71, 45], [85, 79, 20, 7, 80, 60], [90, 98, 53, 7, 81, 45], [31, 69, 67, 77, 81, 4], [48, 88, 34, 71, 57, 56]], [[69, 65, 71, 4, 30, 88], [12, 82, 48, 71, 11, 29], [12, 36, 13, 96, 44, 58], [54, 0, 74, 41, 86, 56], [27, 45, 20, 75, 66, 18], [82, 43, 9, 31, 76, 86]]], 'objective': 32.0}","[[0, 3, 0], [1, 4, 1], [2, 0, 4], [3, 1, 5], [4, 2, 3], [5, 5, 2]]",32.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 19}, {'i': 1, 'j': 1, 'k': 2, 'cost': 16}, {'i': 1, 'j': 1, 'k': 3, 'cost': 25}, {'i': 1, 'j': 1, 'k': 4, 'cost': 96}, {'i': 1, 'j': 1, 'k': 5, 'cost': 93}, {'i': 1, 'j': 1, 'k': 6, 'cost': 56}, {'i': 1, 'j': 2, 'k': 1, 'cost': 18}, {'i': 1, 'j': 2, 'k': 2, 'cost': 85}, {'i': 1, 'j': 2, 'k': 3, 'cost': 65}, {'i': 1, 'j': 2, 'k': 4, 'cost': 39}, {'i': 1, 'j': 2, 'k': 5, 'cost': 3}, {'i': 1, 'j': 2, 'k': 6, 'cost': 24}, {'i': 1, 'j': 3, 'k': 1, 'cost': 61}, {'i': 1, 'j': 3, 'k': 2, 'cost': 93}, {'i': 1, 'j': 3, 'k': 3, 'cost': 16}, {'i': 1, 'j': 3, 'k': 4, 'cost': 35}, {'i': 1, 'j': 3, 'k': 5, 'cost': 40}, {'i': 1, 'j': 3, 'k': 6, 'cost': 99}, {'i': 1, 'j': 4, 'k': 1, 'cost': 6}, {'i': 1, 'j': 4, 'k': 2, 'cost': 73}, {'i': 1, 'j': 4, 'k': 3, 'cost': 62}, {'i': 1, 'j': 4, 'k': 4, 'cost': 28}, {'i': 1, 'j': 4, 'k': 5, 'cost': 41}, {'i': 1, 'j': 4, 'k': 6, 'cost': 90}, {'i': 1, 'j': 5, 'k': 1, 'cost': 10}, {'i': 1, 'j': 5, 'k': 2, 'cost': 47}, {'i': 1, 'j': 5, 'k': 3, 'cost': 31}, {'i': 1, 'j': 5, 'k': 4, 'cost': 48}, {'i': 1, 'j': 5, 'k': 5, 'cost': 69}, {'i': 1, 'j': 5, 'k': 6, 'cost': 77}, {'i': 1, 'j': 6, 'k': 1, 'cost': 37}, {'i': 1, 'j': 6, 'k': 2, 'cost': 14}, {'i': 1, 'j': 6, 'k': 3, 'cost': 51}, {'i': 1, 'j': 6, 'k': 4, 'cost': 89}, {'i': 1, 'j': 6, 'k': 5, 'cost': 30}, {'i': 1, 'j': 6, 'k': 6, 'cost': 15}, {'i': 2, 'j': 1, 'k': 1, 'cost': 36}, {'i': 2, 'j': 1, 'k': 2, 'cost': 65}, {'i': 2, 'j': 1, 'k': 3, 'cost': 55}, {'i': 2, 'j': 1, 'k': 4, 'cost': 57}, {'i': 2, 'j': 1, 'k': 5, 'cost': 83}, {'i': 2, 'j': 1, 'k': 6, 'cost': 91}, {'i': 2, 'j': 2, 'k': 1, 'cost': 28}, {'i': 2, 'j': 2, 'k': 2, 'cost': 32}, {'i': 2, 'j': 2, 'k': 3, 'cost': 40}, {'i': 2, 'j': 2, 'k': 4, 'cost': 74}, {'i': 2, 'j': 2, 'k': 5, 'cost': 60}, {'i': 2, 'j': 2, 'k': 6, 'cost': 75}, {'i': 2, 'j': 3, 'k': 1, 'cost': 7}, {'i': 2, 'j': 3, 'k': 2, 'cost': 69}, {'i': 2, 'j': 3, 'k': 3, 'cost': 2}, {'i': 2, 'j': 3, 'k': 4, 'cost': 75}, {'i': 2, 'j': 3, 'k': 5, 'cost': 63}, {'i': 2, 'j': 3, 'k': 6, 'cost': 86}, {'i': 2, 'j': 4, 'k': 1, 'cost': 68}, {'i': 2, 'j': 4, 'k': 2, 'cost': 48}, {'i': 2, 'j': 4, 'k': 3, 'cost': 48}, {'i': 2, 'j': 4, 'k': 4, 'cost': 82}, {'i': 2, 'j': 4, 'k': 5, 'cost': 65}, {'i': 2, 'j': 4, 'k': 6, 'cost': 57}, {'i': 2, 'j': 5, 'k': 1, 'cost': 89}, {'i': 2, 'j': 5, 'k': 2, 'cost': 1}, {'i': 2, 'j': 5, 'k': 3, 'cost': 17}, {'i': 2, 'j': 5, 'k': 4, 'cost': 53}, {'i': 2, 'j': 5, 'k': 5, 'cost': 60}, {'i': 2, 'j': 5, 'k': 6, 'cost': 41}, {'i': 2, 'j': 6, 'k': 1, 'cost': 33}, {'i': 2, 'j': 6, 'k': 2, 'cost': 85}, {'i': 2, 'j': 6, 'k': 3, 'cost': 55}, {'i': 2, 'j': 6, 'k': 4, 'cost': 62}, {'i': 2, 'j': 6, 'k': 5, 'cost': 17}, {'i': 2, 'j': 6, 'k': 6, 'cost': 32}, {'i': 3, 'j': 1, 'k': 1, 'cost': 92}, {'i': 3, 'j': 1, 'k': 2, 'cost': 56}, {'i': 3, 'j': 1, 'k': 3, 'cost': 74}, {'i': 3, 'j': 1, 'k': 4, 'cost': 38}, {'i': 3, 'j': 1, 'k': 5, 'cost': 3}, {'i': 3, 'j': 1, 'k': 6, 'cost': 8}, {'i': 3, 'j': 2, 'k': 1, 'cost': 85}, {'i': 3, 'j': 2, 'k': 2, 'cost': 14}, {'i': 3, 'j': 2, 'k': 3, 'cost': 2}, {'i': 3, 'j': 2, 'k': 4, 'cost': 38}, {'i': 3, 'j': 2, 'k': 5, 'cost': 73}, {'i': 3, 'j': 2, 'k': 6, 'cost': 54}, {'i': 3, 'j': 3, 'k': 1, 'cost': 57}, {'i': 3, 'j': 3, 'k': 2, 'cost': 64}, {'i': 3, 'j': 3, 'k': 3, 'cost': 51}, {'i': 3, 'j': 3, 'k': 4, 'cost': 30}, {'i': 3, 'j': 3, 'k': 5, 'cost': 58}, {'i': 3, 'j': 3, 'k': 6, 'cost': 7}, {'i': 3, 'j': 4, 'k': 1, 'cost': 60}, {'i': 3, 'j': 4, 'k': 2, 'cost': 5}, {'i': 3, 'j': 4, 'k': 3, 'cost': 58}, {'i': 3, 'j': 4, 'k': 4, 'cost': 82}, {'i': 3, 'j': 4, 'k': 5, 'cost': 7}, {'i': 3, 'j': 4, 'k': 6, 'cost': 91}, {'i': 3, 'j': 5, 'k': 1, 'cost': 44}, {'i': 3, 'j': 5, 'k': 2, 'cost': 51}, {'i': 3, 'j': 5, 'k': 3, 'cost': 72}, {'i': 3, 'j': 5, 'k': 4, 'cost': 17}, {'i': 3, 'j': 5, 'k': 5, 'cost': 87}, {'i': 3, 'j': 5, 'k': 6, 'cost': 57}, {'i': 3, 'j': 6, 'k': 1, 'cost': 33}, {'i': 3, 'j': 6, 'k': 2, 'cost': 71}, {'i': 3, 'j': 6, 'k': 3, 'cost': 97}, {'i': 3, 'j': 6, 'k': 4, 'cost': 38}, {'i': 3, 'j': 6, 'k': 5, 'cost': 75}, {'i': 3, 'j': 6, 'k': 6, 'cost': 94}, {'i': 4, 'j': 1, 'k': 1, 'cost': 49}, {'i': 4, 'j': 1, 'k': 2, 'cost': 94}, {'i': 4, 'j': 1, 'k': 3, 'cost': 5}, {'i': 4, 'j': 1, 'k': 4, 'cost': 27}, {'i': 4, 'j': 1, 'k': 5, 'cost': 99}, {'i': 4, 'j': 1, 'k': 6, 'cost': 97}, {'i': 4, 'j': 2, 'k': 1, 'cost': 98}, {'i': 4, 'j': 2, 'k': 2, 'cost': 99}, {'i': 4, 'j': 2, 'k': 3, 'cost': 27}, {'i': 4, 'j': 2, 'k': 4, 'cost': 0}, {'i': 4, 'j': 2, 'k': 5, 'cost': 12}, {'i': 4, 'j': 2, 'k': 6, 'cost': 6}, {'i': 4, 'j': 3, 'k': 1, 'cost': 25}, {'i': 4, 'j': 3, 'k': 2, 'cost': 99}, {'i': 4, 'j': 3, 'k': 3, 'cost': 8}, {'i': 4, 'j': 3, 'k': 4, 'cost': 5}, {'i': 4, 'j': 3, 'k': 5, 'cost': 80}, {'i': 4, 'j': 3, 'k': 6, 'cost': 15}, {'i': 4, 'j': 4, 'k': 1, 'cost': 46}, {'i': 4, 'j': 4, 'k': 2, 'cost': 70}, {'i': 4, 'j': 4, 'k': 3, 'cost': 76}, {'i': 4, 'j': 4, 'k': 4, 'cost': 38}, {'i': 4, 'j': 4, 'k': 5, 'cost': 74}, {'i': 4, 'j': 4, 'k': 6, 'cost': 68}, {'i': 4, 'j': 5, 'k': 1, 'cost': 96}, {'i': 4, 'j': 5, 'k': 2, 'cost': 94}, {'i': 4, 'j': 5, 'k': 3, 'cost': 74}, {'i': 4, 'j': 5, 'k': 4, 'cost': 47}, {'i': 4, 'j': 5, 'k': 5, 'cost': 6}, {'i': 4, 'j': 5, 'k': 6, 'cost': 3}, {'i': 4, 'j': 6, 'k': 1, 'cost': 38}, {'i': 4, 'j': 6, 'k': 2, 'cost': 50}, {'i': 4, 'j': 6, 'k': 3, 'cost': 68}, {'i': 4, 'j': 6, 'k': 4, 'cost': 61}, {'i': 4, 'j': 6, 'k': 5, 'cost': 37}, {'i': 4, 'j': 6, 'k': 6, 'cost': 60}, {'i': 5, 'j': 1, 'k': 1, 'cost': 64}, {'i': 5, 'j': 1, 'k': 2, 'cost': 76}, {'i': 5, 'j': 1, 'k': 3, 'cost': 78}, {'i': 5, 'j': 1, 'k': 4, 'cost': 20}, {'i': 5, 'j': 1, 'k': 5, 'cost': 83}, {'i': 5, 'j': 1, 'k': 6, 'cost': 85}, {'i': 5, 'j': 2, 'k': 1, 'cost': 50}, {'i': 5, 'j': 2, 'k': 2, 'cost': 14}, {'i': 5, 'j': 2, 'k': 3, 'cost': 47}, {'i': 5, 'j': 2, 'k': 4, 'cost': 75}, {'i': 5, 'j': 2, 'k': 5, 'cost': 71}, {'i': 5, 'j': 2, 'k': 6, 'cost': 45}, {'i': 5, 'j': 3, 'k': 1, 'cost': 85}, {'i': 5, 'j': 3, 'k': 2, 'cost': 79}, {'i': 5, 'j': 3, 'k': 3, 'cost': 20}, {'i': 5, 'j': 3, 'k': 4, 'cost': 7}, {'i': 5, 'j': 3, 'k': 5, 'cost': 80}, {'i': 5, 'j': 3, 'k': 6, 'cost': 60}, {'i': 5, 'j': 4, 'k': 1, 'cost': 90}, {'i': 5, 'j': 4, 'k': 2, 'cost': 98}, {'i': 5, 'j': 4, 'k': 3, 'cost': 53}, {'i': 5, 'j': 4, 'k': 4, 'cost': 7}, {'i': 5, 'j': 4, 'k': 5, 'cost': 81}, {'i': 5, 'j': 4, 'k': 6, 'cost': 45}, {'i': 5, 'j': 5, 'k': 1, 'cost': 31}, {'i': 5, 'j': 5, 'k': 2, 'cost': 69}, {'i': 5, 'j': 5, 'k': 3, 'cost': 67}, {'i': 5, 'j': 5, 'k': 4, 'cost': 77}, {'i': 5, 'j': 5, 'k': 5, 'cost': 81}, {'i': 5, 'j': 5, 'k': 6, 'cost': 4}, {'i': 5, 'j': 6, 'k': 1, 'cost': 48}, {'i': 5, 'j': 6, 'k': 2, 'cost': 88}, {'i': 5, 'j': 6, 'k': 3, 'cost': 34}, {'i': 5, 'j': 6, 'k': 4, 'cost': 71}, {'i': 5, 'j': 6, 'k': 5, 'cost': 57}, {'i': 5, 'j': 6, 'k': 6, 'cost': 56}, {'i': 6, 'j': 1, 'k': 1, 'cost': 69}, {'i': 6, 'j': 1, 'k': 2, 'cost': 65}, {'i': 6, 'j': 1, 'k': 3, 'cost': 71}, {'i': 6, 'j': 1, 'k': 4, 'cost': 4}, {'i': 6, 'j': 1, 'k': 5, 'cost': 30}, {'i': 6, 'j': 1, 'k': 6, 'cost': 88}, {'i': 6, 'j': 2, 'k': 1, 'cost': 12}, {'i': 6, 'j': 2, 'k': 2, 'cost': 82}, {'i': 6, 'j': 2, 'k': 3, 'cost': 48}, {'i': 6, 'j': 2, 'k': 4, 'cost': 71}, {'i': 6, 'j': 2, 'k': 5, 'cost': 11}, {'i': 6, 'j': 2, 'k': 6, 'cost': 29}, {'i': 6, 'j': 3, 'k': 1, 'cost': 12}, {'i': 6, 'j': 3, 'k': 2, 'cost': 36}, {'i': 6, 'j': 3, 'k': 3, 'cost': 13}, {'i': 6, 'j': 3, 'k': 4, 'cost': 96}, {'i': 6, 'j': 3, 'k': 5, 'cost': 44}, {'i': 6, 'j': 3, 'k': 6, 'cost': 58}, {'i': 6, 'j': 4, 'k': 1, 'cost': 54}, {'i': 6, 'j': 4, 'k': 2, 'cost': 0}, {'i': 6, 'j': 4, 'k': 3, 'cost': 74}, {'i': 6, 'j': 4, 'k': 4, 'cost': 41}, {'i': 6, 'j': 4, 'k': 5, 'cost': 86}, {'i': 6, 'j': 4, 'k': 6, 'cost': 56}, {'i': 6, 'j': 5, 'k': 1, 'cost': 27}, {'i': 6, 'j': 5, 'k': 2, 'cost': 45}, {'i': 6, 'j': 5, 'k': 3, 'cost': 20}, {'i': 6, 'j': 5, 'k': 4, 'cost': 75}, {'i': 6, 'j': 5, 'k': 5, 'cost': 66}, {'i': 6, 'j': 5, 'k': 6, 'cost': 18}, {'i': 6, 'j': 6, 'k': 1, 'cost': 82}, {'i': 6, 'j': 6, 'k': 2, 'cost': 43}, {'i': 6, 'j': 6, 'k': 3, 'cost': 9}, {'i': 6, 'j': 6, 'k': 4, 'cost': 31}, {'i': 6, 'j': 6, 'k': 5, 'cost': 76}, {'i': 6, 'j': 6, 'k': 6, 'cost': 86}]}","[[1, 4, 1], [2, 5, 2], [3, 1, 5], [4, 2, 6], [5, 3, 4], [6, 6, 3]]",36,nl,1
AP3,AP3,"On a busy week the theater must pair up rehearsals, rooms, and techs so that each rehearsal gets one room and one technician and each room and technician is used once and only once. Every pairing carries a setup-plus-staff cost, and the aim is to choose the combination of pairings that makes the total of all those costs as small as it can be. The specific entries and cost figures are shown below.

There are 8 rehearsals, identified as 0, 1, 2, 3, 4, 5, 6, 7.

*Meaning: costs form a 3D tensor. For each fixed rehearsal_id=i, you are given a room_id×technician_id matrix whose entry at row room_id=j and column technician_id=k equals setup_and_staff_cost(i,j,k). You must pick exactly one (j,k) for every i, with all room_id and all technician_id used exactly once.*

**setup_and_staff_cost_tensor (per-rehearsal_id markdown matrices)**

## rehearsal_id=0
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 53 | 16 | 20 | 92 | 84 | 30 | 99 | 2 |
| 1 | 79 | 84 | 96 | 83 | 69 | 16 | 98 | 76 |
| 2 | 98 | 74 | 74 | 76 | 84 | 71 | 83 | 77 |
| 3 | 74 | 96 | 33 | 21 | 61 | 75 | 7 | 1 |
| 4 | 84 | 84 | 83 | 88 | 97 | 42 | 3 | 62 |
| 5 | 25 | 93 | 97 | 87 | 79 | 86 | 97 | 87 |
| 6 | 20 | 97 | 38 | 14 | 32 | 11 | 84 | 74 |
| 7 | 64 | 48 | 54 | 33 | 42 | 37 | 42 | 66 |

## rehearsal_id=1
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 81 | 6 | 66 | 89 | 33 | 78 | 96 | 85 |
| 1 | 15 | 76 | 22 | 60 | 30 | 31 | 57 | 56 |
| 2 | 43 | 95 | 7 | 41 | 21 | 55 | 45 | 68 |
| 3 | 99 | 41 | 19 | 40 | 46 | 64 | 55 | 97 |
| 4 | 25 | 88 | 52 | 75 | 70 | 45 | 59 | 79 |
| 5 | 56 | 8 | 32 | 91 | 65 | 96 | 94 | 49 |
| 6 | 54 | 85 | 41 | 61 | 18 | 80 | 21 | 60 |
| 7 | 63 | 60 | 49 | 70 | 90 | 59 | 30 | 20 |

## rehearsal_id=2
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 92 | 48 | 39 | 35 | 65 | 31 | 97 | 2 |
| 1 | 14 | 90 | 69 | 74 | 14 | 59 | 36 | 96 |
| 2 | 73 | 71 | 63 | 23 | 17 | 21 | 45 | 27 |
| 3 | 81 | 74 | 65 | 43 | 22 | 57 | 73 | 78 |
| 4 | 83 | 62 | 3 | 81 | 51 | 2 | 8 | 59 |
| 5 | 52 | 2 | 33 | 13 | 8 | 1 | 9 | 96 |
| 6 | 16 | 37 | 73 | 81 | 85 | 13 | 59 | 96 |
| 7 | 57 | 47 | 36 | 3 | 80 | 50 | 57 | 18 |

## rehearsal_id=3
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 15 | 99 | 70 | 59 | 74 | 21 | 63 | 75 |
| 1 | 43 | 88 | 55 | 99 | 82 | 17 | 67 | 9 |
| 2 | 80 | 56 | 49 | 65 | 84 | 17 | 91 | 77 |
| 3 | 92 | 87 | 61 | 46 | 11 | 59 | 70 | 35 |
| 4 | 90 | 31 | 56 | 73 | 57 | 90 | 32 | 52 |
| 5 | 33 | 68 | 15 | 1 | 78 | 7 | 68 | 25 |
| 6 | 83 | 49 | 13 | 99 | 72 | 58 | 61 | 9 |
| 7 | 44 | 41 | 86 | 18 | 21 | 1 | 59 | 50 |

## rehearsal_id=4
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 12 | 46 | 56 | 1 | 40 | 40 | 84 | 16 |
| 1 | 92 | 7 | 38 | 61 | 10 | 58 | 54 | 21 |
| 2 | 75 | 61 | 92 | 45 | 49 | 98 | 70 | 40 |
| 3 | 17 | 28 | 26 | 65 | 39 | 58 | 26 | 91 |
| 4 | 97 | 13 | 77 | 81 | 10 | 82 | 75 | 78 |
| 5 | 8 | 48 | 21 | 4 | 80 | 85 | 50 | 39 |
| 6 | 58 | 59 | 16 | 50 | 11 | 17 | 49 | 1 |
| 7 | 30 | 39 | 49 | 52 | 38 | 21 | 36 | 20 |

## rehearsal_id=5
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 74 | 68 | 42 | 94 | 36 | 12 | 51 | 52 |
| 1 | 21 | 95 | 59 | 43 | 33 | 53 | 87 | 46 |
| 2 | 81 | 89 | 20 | 71 | 46 | 76 | 23 | 39 |
| 3 | 58 | 41 | 33 | 13 | 26 | 78 | 24 | 11 |
| 4 | 35 | 48 | 61 | 28 | 20 | 75 | 83 | 4 |
| 5 | 18 | 64 | 42 | 60 | 90 | 28 | 77 | 63 |
| 6 | 13 | 85 | 61 | 96 | 77 | 25 | 67 | 24 |
| 7 | 15 | 18 | 83 | 80 | 46 | 47 | 41 | 81 |

## rehearsal_id=6
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 45 | 33 | 20 | 25 | 27 | 54 | 1 | 97 |
| 1 | 21 | 8 | 16 | 95 | 67 | 68 | 61 | 76 |
| 2 | 54 | 7 | 18 | 84 | 68 | 32 | 96 | 78 |
| 3 | 58 | 57 | 7 | 87 | 61 | 86 | 57 | 18 |
| 4 | 12 | 56 | 17 | 28 | 82 | 55 | 41 | 56 |
| 5 | 84 | 51 | 75 | 17 | 43 | 0 | 98 | 73 |
| 6 | 66 | 43 | 41 | 39 | 2 | 43 | 72 | 82 |
| 7 | 69 | 35 | 97 | 90 | 67 | 23 | 4 | 82 |

## rehearsal_id=7
| room_id\technician_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 12 | 97 | 12 | 8 | 94 | 8 | 84 | 62 |
| 1 | 7 | 62 | 2 | 14 | 63 | 4 | 90 | 57 |
| 2 | 59 | 51 | 63 | 57 | 74 | 30 | 23 | 58 |
| 3 | 91 | 48 | 84 | 55 | 70 | 97 | 87 | 70 |
| 4 | 8 | 35 | 17 | 39 | 16 | 13 | 55 | 32 |
| 5 | 53 | 26 | 74 | 97 | 75 | 4 | 54 | 17 |
| 6 | 92 | 22 | 78 | 78 | 25 | 37 | 16 | 70 |
| 7 | 81 | 61 | 16 | 31 | 22 | 49 | 37 | 45 |

One triple must be selected for each of the 8 rehearsals (0, 1, 2, 3, 4, 5, 6, 7) so that the total setup-plus-staff cost is minimized.

If you send the final matching back, a nice compact way to show it is in a little JSON snippet like this:

{
  ""solution"": [
    [<rehearsal_id>, <room_id>, <tech_id>],
    ...
  ]
}

This just says ""solution"" is a list of triples — each triple picks one rehearsal, one room, and one technician. Think of each inner array as one complete booking (which rehearsal goes with which room and which tech). This is just the expected shape of the answer, not the actual matching — fill in the real IDs from the instance when you reply.

Please be sure to use the exact identifiers from the instance input — no renaming and 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”.""","{'cost_tensor': [[[53, 16, 20, 92, 84, 30, 99, 2], [79, 84, 96, 83, 69, 16, 98, 76], [98, 74, 74, 76, 84, 71, 83, 77], [74, 96, 33, 21, 61, 75, 7, 1], [84, 84, 83, 88, 97, 42, 3, 62], [25, 93, 97, 87, 79, 86, 97, 87], [20, 97, 38, 14, 32, 11, 84, 74], [64, 48, 54, 33, 42, 37, 42, 66]], [[81, 6, 66, 89, 33, 78, 96, 85], [15, 76, 22, 60, 30, 31, 57, 56], [43, 95, 7, 41, 21, 55, 45, 68], [99, 41, 19, 40, 46, 64, 55, 97], [25, 88, 52, 75, 70, 45, 59, 79], [56, 8, 32, 91, 65, 96, 94, 49], [54, 85, 41, 61, 18, 80, 21, 60], [63, 60, 49, 70, 90, 59, 30, 20]], [[92, 48, 39, 35, 65, 31, 97, 2], [14, 90, 69, 74, 14, 59, 36, 96], [73, 71, 63, 23, 17, 21, 45, 27], [81, 74, 65, 43, 22, 57, 73, 78], [83, 62, 3, 81, 51, 2, 8, 59], [52, 2, 33, 13, 8, 1, 9, 96], [16, 37, 73, 81, 85, 13, 59, 96], [57, 47, 36, 3, 80, 50, 57, 18]], [[15, 99, 70, 59, 74, 21, 63, 75], [43, 88, 55, 99, 82, 17, 67, 9], [80, 56, 49, 65, 84, 17, 91, 77], [92, 87, 61, 46, 11, 59, 70, 35], [90, 31, 56, 73, 57, 90, 32, 52], [33, 68, 15, 1, 78, 7, 68, 25], [83, 49, 13, 99, 72, 58, 61, 9], [44, 41, 86, 18, 21, 1, 59, 50]], [[12, 46, 56, 1, 40, 40, 84, 16], [92, 7, 38, 61, 10, 58, 54, 21], [75, 61, 92, 45, 49, 98, 70, 40], [17, 28, 26, 65, 39, 58, 26, 91], [97, 13, 77, 81, 10, 82, 75, 78], [8, 48, 21, 4, 80, 85, 50, 39], [58, 59, 16, 50, 11, 17, 49, 1], [30, 39, 49, 52, 38, 21, 36, 20]], [[74, 68, 42, 94, 36, 12, 51, 52], [21, 95, 59, 43, 33, 53, 87, 46], [81, 89, 20, 71, 46, 76, 23, 39], [58, 41, 33, 13, 26, 78, 24, 11], [35, 48, 61, 28, 20, 75, 83, 4], [18, 64, 42, 60, 90, 28, 77, 63], [13, 85, 61, 96, 77, 25, 67, 24], [15, 18, 83, 80, 46, 47, 41, 81]], [[45, 33, 20, 25, 27, 54, 1, 97], [21, 8, 16, 95, 67, 68, 61, 76], [54, 7, 18, 84, 68, 32, 96, 78], [58, 57, 7, 87, 61, 86, 57, 18], [12, 56, 17, 28, 82, 55, 41, 56], [84, 51, 75, 17, 43, 0, 98, 73], [66, 43, 41, 39, 2, 43, 72, 82], [69, 35, 97, 90, 67, 23, 4, 82]], [[12, 97, 12, 8, 94, 8, 84, 62], [7, 62, 2, 14, 63, 4, 90, 57], [59, 51, 63, 57, 74, 30, 23, 58], [91, 48, 84, 55, 70, 97, 87, 70], [8, 35, 17, 39, 16, 13, 55, 32], [53, 26, 74, 97, 75, 4, 54, 17], [92, 22, 78, 78, 25, 37, 16, 70], [81, 61, 16, 31, 22, 49, 37, 45]]], 'objective': 31.0}","[[0, 3, 6], [1, 2, 2], [2, 5, 1], [3, 7, 5], [4, 0, 3], [5, 4, 7], [6, 6, 4], [7, 1, 0]]",31.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [0, 1, 2, 3, 4, 5, 6, 7], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 53}, {'i': 0, 'j': 0, 'k': 1, 'cost': 16}, {'i': 0, 'j': 0, 'k': 2, 'cost': 20}, {'i': 0, 'j': 0, 'k': 3, 'cost': 92}, {'i': 0, 'j': 0, 'k': 4, 'cost': 84}, {'i': 0, 'j': 0, 'k': 5, 'cost': 30}, {'i': 0, 'j': 0, 'k': 6, 'cost': 99}, {'i': 0, 'j': 0, 'k': 7, 'cost': 2}, {'i': 0, 'j': 1, 'k': 0, 'cost': 79}, {'i': 0, 'j': 1, 'k': 1, 'cost': 84}, {'i': 0, 'j': 1, 'k': 2, 'cost': 96}, {'i': 0, 'j': 1, 'k': 3, 'cost': 83}, {'i': 0, 'j': 1, 'k': 4, 'cost': 69}, {'i': 0, 'j': 1, 'k': 5, 'cost': 16}, {'i': 0, 'j': 1, 'k': 6, 'cost': 98}, {'i': 0, 'j': 1, 'k': 7, 'cost': 76}, {'i': 0, 'j': 2, 'k': 0, 'cost': 98}, {'i': 0, 'j': 2, 'k': 1, 'cost': 74}, {'i': 0, 'j': 2, 'k': 2, 'cost': 74}, {'i': 0, 'j': 2, 'k': 3, 'cost': 76}, {'i': 0, 'j': 2, 'k': 4, 'cost': 84}, {'i': 0, 'j': 2, 'k': 5, 'cost': 71}, {'i': 0, 'j': 2, 'k': 6, 'cost': 83}, {'i': 0, 'j': 2, 'k': 7, 'cost': 77}, {'i': 0, 'j': 3, 'k': 0, 'cost': 74}, {'i': 0, 'j': 3, 'k': 1, 'cost': 96}, {'i': 0, 'j': 3, 'k': 2, 'cost': 33}, {'i': 0, 'j': 3, 'k': 3, 'cost': 21}, {'i': 0, 'j': 3, 'k': 4, 'cost': 61}, {'i': 0, 'j': 3, 'k': 5, 'cost': 75}, {'i': 0, 'j': 3, 'k': 6, 'cost': 7}, {'i': 0, 'j': 3, 'k': 7, 'cost': 1}, {'i': 0, 'j': 4, 'k': 0, 'cost': 84}, {'i': 0, 'j': 4, 'k': 1, 'cost': 84}, {'i': 0, 'j': 4, 'k': 2, 'cost': 83}, {'i': 0, 'j': 4, 'k': 3, 'cost': 88}, {'i': 0, 'j': 4, 'k': 4, 'cost': 97}, {'i': 0, 'j': 4, 'k': 5, 'cost': 42}, {'i': 0, 'j': 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4, 'cost': 46}, {'i': 5, 'j': 7, 'k': 5, 'cost': 47}, {'i': 5, 'j': 7, 'k': 6, 'cost': 41}, {'i': 5, 'j': 7, 'k': 7, 'cost': 81}, {'i': 6, 'j': 0, 'k': 0, 'cost': 45}, {'i': 6, 'j': 0, 'k': 1, 'cost': 33}, {'i': 6, 'j': 0, 'k': 2, 'cost': 20}, {'i': 6, 'j': 0, 'k': 3, 'cost': 25}, {'i': 6, 'j': 0, 'k': 4, 'cost': 27}, {'i': 6, 'j': 0, 'k': 5, 'cost': 54}, {'i': 6, 'j': 0, 'k': 6, 'cost': 1}, {'i': 6, 'j': 0, 'k': 7, 'cost': 97}, {'i': 6, 'j': 1, 'k': 0, 'cost': 21}, {'i': 6, 'j': 1, 'k': 1, 'cost': 8}, {'i': 6, 'j': 1, 'k': 2, 'cost': 16}, {'i': 6, 'j': 1, 'k': 3, 'cost': 95}, {'i': 6, 'j': 1, 'k': 4, 'cost': 67}, {'i': 6, 'j': 1, 'k': 5, 'cost': 68}, {'i': 6, 'j': 1, 'k': 6, 'cost': 61}, {'i': 6, 'j': 1, 'k': 7, 'cost': 76}, {'i': 6, 'j': 2, 'k': 0, 'cost': 54}, {'i': 6, 'j': 2, 'k': 1, 'cost': 7}, {'i': 6, 'j': 2, 'k': 2, 'cost': 18}, {'i': 6, 'j': 2, 'k': 3, 'cost': 84}, {'i': 6, 'j': 2, 'k': 4, 'cost': 68}, {'i': 6, 'j': 2, 'k': 5, 'cost': 32}, {'i': 6, 'j': 2, 'k': 6, 'cost': 96}, {'i': 6, 'j': 2, 'k': 7, 'cost': 78}, {'i': 6, 'j': 3, 'k': 0, 'cost': 58}, {'i': 6, 'j': 3, 'k': 1, 'cost': 57}, {'i': 6, 'j': 3, 'k': 2, 'cost': 7}, {'i': 6, 'j': 3, 'k': 3, 'cost': 87}, {'i': 6, 'j': 3, 'k': 4, 'cost': 61}, {'i': 6, 'j': 3, 'k': 5, 'cost': 86}, {'i': 6, 'j': 3, 'k': 6, 'cost': 57}, {'i': 6, 'j': 3, 'k': 7, 'cost': 18}, {'i': 6, 'j': 4, 'k': 0, 'cost': 12}, {'i': 6, 'j': 4, 'k': 1, 'cost': 56}, {'i': 6, 'j': 4, 'k': 2, 'cost': 17}, {'i': 6, 'j': 4, 'k': 3, 'cost': 28}, {'i': 6, 'j': 4, 'k': 4, 'cost': 82}, {'i': 6, 'j': 4, 'k': 5, 'cost': 55}, {'i': 6, 'j': 4, 'k': 6, 'cost': 41}, {'i': 6, 'j': 4, 'k': 7, 'cost': 56}, {'i': 6, 'j': 5, 'k': 0, 'cost': 84}, {'i': 6, 'j': 5, 'k': 1, 'cost': 51}, {'i': 6, 'j': 5, 'k': 2, 'cost': 75}, {'i': 6, 'j': 5, 'k': 3, 'cost': 17}, {'i': 6, 'j': 5, 'k': 4, 'cost': 43}, {'i': 6, 'j': 5, 'k': 5, 'cost': 0}, {'i': 6, 'j': 5, 'k': 6, 'cost': 98}, {'i': 6, 'j': 5, 'k': 7, 'cost': 73}, {'i': 6, 'j': 6, 'k': 0, 'cost': 66}, {'i': 6, 'j': 6, 'k': 1, 'cost': 43}, {'i': 6, 'j': 6, 'k': 2, 'cost': 41}, {'i': 6, 'j': 6, 'k': 3, 'cost': 39}, {'i': 6, 'j': 6, 'k': 4, 'cost': 2}, {'i': 6, 'j': 6, 'k': 5, 'cost': 43}, {'i': 6, 'j': 6, 'k': 6, 'cost': 72}, {'i': 6, 'j': 6, 'k': 7, 'cost': 82}, {'i': 6, 'j': 7, 'k': 0, 'cost': 69}, {'i': 6, 'j': 7, 'k': 1, 'cost': 35}, {'i': 6, 'j': 7, 'k': 2, 'cost': 97}, {'i': 6, 'j': 7, 'k': 3, 'cost': 90}, {'i': 6, 'j': 7, 'k': 4, 'cost': 67}, {'i': 6, 'j': 7, 'k': 5, 'cost': 23}, {'i': 6, 'j': 7, 'k': 6, 'cost': 4}, {'i': 6, 'j': 7, 'k': 7, 'cost': 82}, {'i': 7, 'j': 0, 'k': 0, 'cost': 12}, {'i': 7, 'j': 0, 'k': 1, 'cost': 97}, {'i': 7, 'j': 0, 'k': 2, 'cost': 12}, {'i': 7, 'j': 0, 'k': 3, 'cost': 8}, {'i': 7, 'j': 0, 'k': 4, 'cost': 94}, {'i': 7, 'j': 0, 'k': 5, 'cost': 8}, {'i': 7, 'j': 0, 'k': 6, 'cost': 84}, {'i': 7, 'j': 0, 'k': 7, 'cost': 62}, {'i': 7, 'j': 1, 'k': 0, 'cost': 7}, {'i': 7, 'j': 1, 'k': 1, 'cost': 62}, {'i': 7, 'j': 1, 'k': 2, 'cost': 2}, {'i': 7, 'j': 1, 'k': 3, 'cost': 14}, {'i': 7, 'j': 1, 'k': 4, 'cost': 63}, {'i': 7, 'j': 1, 'k': 5, 'cost': 4}, {'i': 7, 'j': 1, 'k': 6, 'cost': 90}, {'i': 7, 'j': 1, 'k': 7, 'cost': 57}, {'i': 7, 'j': 2, 'k': 0, 'cost': 59}, {'i': 7, 'j': 2, 'k': 1, 'cost': 51}, {'i': 7, 'j': 2, 'k': 2, 'cost': 63}, {'i': 7, 'j': 2, 'k': 3, 'cost': 57}, {'i': 7, 'j': 2, 'k': 4, 'cost': 74}, {'i': 7, 'j': 2, 'k': 5, 'cost': 30}, {'i': 7, 'j': 2, 'k': 6, 'cost': 23}, {'i': 7, 'j': 2, 'k': 7, 'cost': 58}, {'i': 7, 'j': 3, 'k': 0, 'cost': 91}, {'i': 7, 'j': 3, 'k': 1, 'cost': 48}, {'i': 7, 'j': 3, 'k': 2, 'cost': 84}, {'i': 7, 'j': 3, 'k': 3, 'cost': 55}, {'i': 7, 'j': 3, 'k': 4, 'cost': 70}, {'i': 7, 'j': 3, 'k': 5, 'cost': 97}, {'i': 7, 'j': 3, 'k': 6, 'cost': 87}, {'i': 7, 'j': 3, 'k': 7, 'cost': 70}, {'i': 7, 'j': 4, 'k': 0, 'cost': 8}, {'i': 7, 'j': 4, 'k': 1, 'cost': 35}, {'i': 7, 'j': 4, 'k': 2, 'cost': 17}, {'i': 7, 'j': 4, 'k': 3, 'cost': 39}, {'i': 7, 'j': 4, 'k': 4, 'cost': 16}, {'i': 7, 'j': 4, 'k': 5, 'cost': 13}, {'i': 7, 'j': 4, 'k': 6, 'cost': 55}, {'i': 7, 'j': 4, 'k': 7, 'cost': 32}, {'i': 7, 'j': 5, 'k': 0, 'cost': 53}, {'i': 7, 'j': 5, 'k': 1, 'cost': 26}, {'i': 7, 'j': 5, 'k': 2, 'cost': 74}, {'i': 7, 'j': 5, 'k': 3, 'cost': 97}, {'i': 7, 'j': 5, 'k': 4, 'cost': 75}, {'i': 7, 'j': 5, 'k': 5, 'cost': 4}, {'i': 7, 'j': 5, 'k': 6, 'cost': 54}, {'i': 7, 'j': 5, 'k': 7, 'cost': 17}, {'i': 7, 'j': 6, 'k': 0, 'cost': 92}, {'i': 7, 'j': 6, 'k': 1, 'cost': 22}, {'i': 7, 'j': 6, 'k': 2, 'cost': 78}, {'i': 7, 'j': 6, 'k': 3, 'cost': 78}, {'i': 7, 'j': 6, 'k': 4, 'cost': 25}, {'i': 7, 'j': 6, 'k': 5, 'cost': 37}, {'i': 7, 'j': 6, 'k': 6, 'cost': 16}, {'i': 7, 'j': 6, 'k': 7, 'cost': 70}, {'i': 7, 'j': 7, 'k': 0, 'cost': 81}, {'i': 7, 'j': 7, 'k': 1, 'cost': 61}, {'i': 7, 'j': 7, 'k': 2, 'cost': 16}, {'i': 7, 'j': 7, 'k': 3, 'cost': 31}, {'i': 7, 'j': 7, 'k': 4, 'cost': 22}, {'i': 7, 'j': 7, 'k': 5, 'cost': 49}, {'i': 7, 'j': 7, 'k': 6, 'cost': 37}, {'i': 7, 'j': 7, 'k': 7, 'cost': 45}]}","[[0, 3, 6], [1, 2, 2], [2, 5, 1], [3, 7, 5], [4, 0, 3], [5, 4, 7], [6, 6, 4], [7, 1, 0]]",37,markdown_table,0
AP3,AP3,"I was the one arranging the reception and had to pick, for every table, exactly one caterer and exactly one dessert so nobody doubles up and nothing gets left out. For each table the caterer-plus-dessert combo has a price, and the trick is to make choices so that when all those table bills are added together the whole catering tab is as small as possible. Every caterer can only be assigned to one table and every dessert choice can only be used once. The exact list of tables, caterers, desserts and their prices is shown below.

{
  ""num_tables"": 8,
  ""table_identifiers"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8
  ]
}

# Meaning: costs form a 3D tensor. For each fixed table_id=i, you are given a caterer_id×dessert_id matrix whose entry at row caterer_id=j and column dessert_id=k equals price(i,j,k). You must pick exactly one (j,k) for every i, with all caterer_id and all dessert_id used exactly once.
# price_tensor (per-table_id markdown matrices)

## table_id=1
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 21 | 55 | 20 | 85 | 90 | 80 | 88 | 71 |
| 2 | 20 | 99 | 13 | 48 | 72 | 79 | 57 | 72 |
| 3 | 96 | 13 | 48 | 95 | 59 | 33 | 28 | 59 |
| 4 | 38 | 5 | 87 | 23 | 5 | 53 | 54 | 51 |
| 5 | 66 | 84 | 55 | 88 | 87 | 47 | 14 | 1 |
| 6 | 12 | 32 | 40 | 73 | 46 | 76 | 7 | 48 |
| 7 | 82 | 26 | 49 | 25 | 14 | 28 | 75 | 27 |
| 8 | 5 | 46 | 90 | 73 | 15 | 52 | 92 | 14 |

## table_id=2
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 80 | 69 | 70 | 26 | 86 | 40 | 0 | 30 |
| 2 | 10 | 98 | 67 | 79 | 2 | 5 | 25 | 95 |
| 3 | 38 | 13 | 74 | 24 | 18 | 78 | 14 | 68 |
| 4 | 24 | 43 | 4 | 50 | 60 | 18 | 24 | 49 |
| 5 | 35 | 91 | 45 | 80 | 53 | 86 | 7 | 15 |
| 6 | 65 | 28 | 73 | 25 | 66 | 19 | 35 | 57 |
| 7 | 21 | 21 | 93 | 88 | 76 | 40 | 85 | 67 |
| 8 | 72 | 84 | 90 | 13 | 52 | 37 | 39 | 74 |

## table_id=3
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 30 | 23 | 19 | 15 | 4 | 82 | 36 | 38 |
| 2 | 60 | 16 | 94 | 60 | 25 | 88 | 66 | 65 |
| 3 | 19 | 45 | 57 | 48 | 57 | 53 | 51 | 48 |
| 4 | 5 | 74 | 11 | 40 | 17 | 79 | 98 | 16 |
| 5 | 10 | 34 | 32 | 1 | 61 | 19 | 0 | 95 |
| 6 | 67 | 50 | 14 | 46 | 10 | 18 | 74 | 59 |
| 7 | 62 | 69 | 98 | 2 | 50 | 69 | 49 | 58 |
| 8 | 56 | 26 | 17 | 72 | 82 | 35 | 54 | 51 |

## table_id=4
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 87 | 64 | 29 | 38 | 81 | 53 | 11 | 23 |
| 2 | 53 | 48 | 82 | 70 | 18 | 53 | 62 | 48 |
| 3 | 35 | 74 | 51 | 81 | 73 | 89 | 86 | 21 |
| 4 | 48 | 19 | 81 | 44 | 91 | 65 | 51 | 53 |
| 5 | 2 | 42 | 71 | 7 | 52 | 29 | 21 | 67 |
| 6 | 14 | 66 | 80 | 46 | 69 | 76 | 77 | 9 |
| 7 | 38 | 56 | 43 | 68 | 70 | 91 | 4 | 69 |
| 8 | 26 | 73 | 84 | 79 | 78 | 20 | 83 | 37 |

## table_id=5
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 69 | 45 | 54 | 56 | 73 | 69 | 40 | 16 |
| 2 | 55 | 7 | 13 | 0 | 0 | 83 | 7 | 21 |
| 3 | 93 | 49 | 56 | 38 | 84 | 15 | 46 | 69 |
| 4 | 12 | 1 | 35 | 58 | 44 | 94 | 52 | 31 |
| 5 | 42 | 11 | 20 | 91 | 92 | 31 | 57 | 76 |
| 6 | 1 | 7 | 51 | 44 | 97 | 53 | 54 | 40 |
| 7 | 89 | 13 | 25 | 20 | 36 | 66 | 24 | 5 |
| 8 | 81 | 37 | 77 | 88 | 57 | 94 | 76 | 14 |

## table_id=6
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 11 | 49 | 65 | 90 | 47 | 28 | 79 | 8 |
| 2 | 81 | 30 | 54 | 41 | 68 | 12 | 42 | 7 |
| 3 | 28 | 82 | 17 | 78 | 38 | 69 | 74 | 80 |
| 4 | 12 | 59 | 37 | 88 | 2 | 36 | 14 | 11 |
| 5 | 66 | 76 | 17 | 81 | 29 | 35 | 74 | 74 |
| 6 | 50 | 1 | 96 | 24 | 13 | 0 | 29 | 58 |
| 7 | 90 | 36 | 22 | 65 | 94 | 5 | 51 | 55 |
| 8 | 85 | 45 | 11 | 23 | 30 | 55 | 56 | 47 |

## table_id=7
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 38 | 1 | 17 | 4 | 41 | 50 | 21 | 30 |
| 2 | 32 | 42 | 73 | 16 | 96 | 68 | 14 | 55 |
| 3 | 86 | 13 | 94 | 22 | 49 | 57 | 46 | 81 |
| 4 | 45 | 98 | 68 | 40 | 27 | 39 | 24 | 48 |
| 5 | 25 | 12 | 89 | 17 | 35 | 24 | 90 | 36 |
| 6 | 33 | 13 | 86 | 49 | 53 | 61 | 53 | 67 |
| 7 | 98 | 42 | 72 | 11 | 24 | 43 | 88 | 37 |
| 8 | 58 | 92 | 89 | 37 | 63 | 57 | 24 | 43 |

## table_id=8
| caterer_id\dessert_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 17 | 89 | 70 | 86 | 90 | 58 | 62 | 89 |
| 2 | 63 | 14 | 89 | 88 | 31 | 66 | 60 | 53 |
| 3 | 28 | 51 | 66 | 21 | 2 | 65 | 94 | 16 |
| 4 | 98 | 90 | 44 | 56 | 48 | 31 | 38 | 60 |
| 5 | 90 | 20 | 44 | 39 | 5 | 46 | 74 | 7 |
| 6 | 16 | 81 | 22 | 59 | 94 | 50 | 33 | 29 |
| 7 | 61 | 37 | 43 | 69 | 3 | 31 | 84 | 10 |
| 8 | 35 | 27 | 16 | 86 | 26 | 81 | 43 | 38 |

Oh, and when you give the actual matching, just drop it into a tiny JSON object so it's easy to read and reuse. For example:

{
  ""solution"": [
    [<table_id>, <caterer_id>, <dessert_id>],
    ...
  ]
}

This means ""solution"" is a list of triples. Each triple is one table with the caterer and dessert assigned to it — [table, caterer, dessert]. It's just a sketch of the shape I expect, not the real assignment.

Please be sure to use the identifiers exactly as they appear in 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”.""","{'cost_tensor': [[[21, 55, 20, 85, 90, 80, 88, 71], [20, 99, 13, 48, 72, 79, 57, 72], [96, 13, 48, 95, 59, 33, 28, 59], [38, 5, 87, 23, 5, 53, 54, 51], [66, 84, 55, 88, 87, 47, 14, 1], [12, 32, 40, 73, 46, 76, 7, 48], [82, 26, 49, 25, 14, 28, 75, 27], [5, 46, 90, 73, 15, 52, 92, 14]], [[80, 69, 70, 26, 86, 40, 0, 30], [10, 98, 67, 79, 2, 5, 25, 95], [38, 13, 74, 24, 18, 78, 14, 68], [24, 43, 4, 50, 60, 18, 24, 49], [35, 91, 45, 80, 53, 86, 7, 15], [65, 28, 73, 25, 66, 19, 35, 57], [21, 21, 93, 88, 76, 40, 85, 67], [72, 84, 90, 13, 52, 37, 39, 74]], [[30, 23, 19, 15, 4, 82, 36, 38], [60, 16, 94, 60, 25, 88, 66, 65], [19, 45, 57, 48, 57, 53, 51, 48], [5, 74, 11, 40, 17, 79, 98, 16], [10, 34, 32, 1, 61, 19, 0, 95], [67, 50, 14, 46, 10, 18, 74, 59], [62, 69, 98, 2, 50, 69, 49, 58], [56, 26, 17, 72, 82, 35, 54, 51]], [[87, 64, 29, 38, 81, 53, 11, 23], [53, 48, 82, 70, 18, 53, 62, 48], [35, 74, 51, 81, 73, 89, 86, 21], [48, 19, 81, 44, 91, 65, 51, 53], [2, 42, 71, 7, 52, 29, 21, 67], [14, 66, 80, 46, 69, 76, 77, 9], [38, 56, 43, 68, 70, 91, 4, 69], [26, 73, 84, 79, 78, 20, 83, 37]], [[69, 45, 54, 56, 73, 69, 40, 16], [55, 7, 13, 0, 0, 83, 7, 21], [93, 49, 56, 38, 84, 15, 46, 69], [12, 1, 35, 58, 44, 94, 52, 31], [42, 11, 20, 91, 92, 31, 57, 76], [1, 7, 51, 44, 97, 53, 54, 40], [89, 13, 25, 20, 36, 66, 24, 5], [81, 37, 77, 88, 57, 94, 76, 14]], [[11, 49, 65, 90, 47, 28, 79, 8], [81, 30, 54, 41, 68, 12, 42, 7], [28, 82, 17, 78, 38, 69, 74, 80], [12, 59, 37, 88, 2, 36, 14, 11], [66, 76, 17, 81, 29, 35, 74, 74], [50, 1, 96, 24, 13, 0, 29, 58], [90, 36, 22, 65, 94, 5, 51, 55], [85, 45, 11, 23, 30, 55, 56, 47]], [[38, 1, 17, 4, 41, 50, 21, 30], [32, 42, 73, 16, 96, 68, 14, 55], [86, 13, 94, 22, 49, 57, 46, 81], [45, 98, 68, 40, 27, 39, 24, 48], [25, 12, 89, 17, 35, 24, 90, 36], [33, 13, 86, 49, 53, 61, 53, 67], [98, 42, 72, 11, 24, 43, 88, 37], [58, 92, 89, 37, 63, 57, 24, 43]], [[17, 89, 70, 86, 90, 58, 62, 89], [63, 14, 89, 88, 31, 66, 60, 53], [28, 51, 66, 21, 2, 65, 94, 16], [98, 90, 44, 56, 48, 31, 38, 60], [90, 20, 44, 39, 5, 46, 74, 7], [16, 81, 22, 59, 94, 50, 33, 29], [61, 37, 43, 69, 3, 31, 84, 10], [35, 27, 16, 86, 26, 81, 43, 38]]], 'objective': 26.0}","[[0, 7, 0], [1, 3, 2], [2, 4, 6], [3, 5, 7], [4, 1, 3], [5, 6, 5], [6, 0, 1], [7, 2, 4]]",26.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 21}, {'i': 1, 'j': 1, 'k': 2, 'cost': 55}, {'i': 1, 'j': 1, 'k': 3, 'cost': 20}, {'i': 1, 'j': 1, 'k': 4, 'cost': 85}, {'i': 1, 'j': 1, 'k': 5, 'cost': 90}, {'i': 1, 'j': 1, 'k': 6, 'cost': 80}, {'i': 1, 'j': 1, 'k': 7, 'cost': 88}, {'i': 1, 'j': 1, 'k': 8, 'cost': 71}, {'i': 1, 'j': 2, 'k': 1, 'cost': 20}, {'i': 1, 'j': 2, 'k': 2, 'cost': 99}, {'i': 1, 'j': 2, 'k': 3, 'cost': 13}, {'i': 1, 'j': 2, 'k': 4, 'cost': 48}, 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{'i': 6, 'j': 8, 'k': 6, 'cost': 55}, {'i': 6, 'j': 8, 'k': 7, 'cost': 56}, {'i': 6, 'j': 8, 'k': 8, 'cost': 47}, {'i': 7, 'j': 1, 'k': 1, 'cost': 38}, {'i': 7, 'j': 1, 'k': 2, 'cost': 1}, {'i': 7, 'j': 1, 'k': 3, 'cost': 17}, {'i': 7, 'j': 1, 'k': 4, 'cost': 4}, {'i': 7, 'j': 1, 'k': 5, 'cost': 41}, {'i': 7, 'j': 1, 'k': 6, 'cost': 50}, {'i': 7, 'j': 1, 'k': 7, 'cost': 21}, {'i': 7, 'j': 1, 'k': 8, 'cost': 30}, {'i': 7, 'j': 2, 'k': 1, 'cost': 32}, {'i': 7, 'j': 2, 'k': 2, 'cost': 42}, {'i': 7, 'j': 2, 'k': 3, 'cost': 73}, {'i': 7, 'j': 2, 'k': 4, 'cost': 16}, {'i': 7, 'j': 2, 'k': 5, 'cost': 96}, {'i': 7, 'j': 2, 'k': 6, 'cost': 68}, {'i': 7, 'j': 2, 'k': 7, 'cost': 14}, {'i': 7, 'j': 2, 'k': 8, 'cost': 55}, {'i': 7, 'j': 3, 'k': 1, 'cost': 86}, {'i': 7, 'j': 3, 'k': 2, 'cost': 13}, {'i': 7, 'j': 3, 'k': 3, 'cost': 94}, {'i': 7, 'j': 3, 'k': 4, 'cost': 22}, {'i': 7, 'j': 3, 'k': 5, 'cost': 49}, {'i': 7, 'j': 3, 'k': 6, 'cost': 57}, {'i': 7, 'j': 3, 'k': 7, 'cost': 46}, {'i': 7, 'j': 3, 'k': 8, 'cost': 81}, {'i': 7, 'j': 4, 'k': 1, 'cost': 45}, {'i': 7, 'j': 4, 'k': 2, 'cost': 98}, {'i': 7, 'j': 4, 'k': 3, 'cost': 68}, {'i': 7, 'j': 4, 'k': 4, 'cost': 40}, {'i': 7, 'j': 4, 'k': 5, 'cost': 27}, {'i': 7, 'j': 4, 'k': 6, 'cost': 39}, {'i': 7, 'j': 4, 'k': 7, 'cost': 24}, {'i': 7, 'j': 4, 'k': 8, 'cost': 48}, {'i': 7, 'j': 5, 'k': 1, 'cost': 25}, {'i': 7, 'j': 5, 'k': 2, 'cost': 12}, {'i': 7, 'j': 5, 'k': 3, 'cost': 89}, {'i': 7, 'j': 5, 'k': 4, 'cost': 17}, {'i': 7, 'j': 5, 'k': 5, 'cost': 35}, {'i': 7, 'j': 5, 'k': 6, 'cost': 24}, {'i': 7, 'j': 5, 'k': 7, 'cost': 90}, {'i': 7, 'j': 5, 'k': 8, 'cost': 36}, {'i': 7, 'j': 6, 'k': 1, 'cost': 33}, {'i': 7, 'j': 6, 'k': 2, 'cost': 13}, {'i': 7, 'j': 6, 'k': 3, 'cost': 86}, {'i': 7, 'j': 6, 'k': 4, 'cost': 49}, {'i': 7, 'j': 6, 'k': 5, 'cost': 53}, {'i': 7, 'j': 6, 'k': 6, 'cost': 61}, {'i': 7, 'j': 6, 'k': 7, 'cost': 53}, {'i': 7, 'j': 6, 'k': 8, 'cost': 67}, {'i': 7, 'j': 7, 'k': 1, 'cost': 98}, {'i': 7, 'j': 7, 'k': 2, 'cost': 42}, {'i': 7, 'j': 7, 'k': 3, 'cost': 72}, {'i': 7, 'j': 7, 'k': 4, 'cost': 11}, {'i': 7, 'j': 7, 'k': 5, 'cost': 24}, {'i': 7, 'j': 7, 'k': 6, 'cost': 43}, {'i': 7, 'j': 7, 'k': 7, 'cost': 88}, {'i': 7, 'j': 7, 'k': 8, 'cost': 37}, {'i': 7, 'j': 8, 'k': 1, 'cost': 58}, {'i': 7, 'j': 8, 'k': 2, 'cost': 92}, {'i': 7, 'j': 8, 'k': 3, 'cost': 89}, {'i': 7, 'j': 8, 'k': 4, 'cost': 37}, {'i': 7, 'j': 8, 'k': 5, 'cost': 63}, {'i': 7, 'j': 8, 'k': 6, 'cost': 57}, {'i': 7, 'j': 8, 'k': 7, 'cost': 24}, {'i': 7, 'j': 8, 'k': 8, 'cost': 43}, {'i': 8, 'j': 1, 'k': 1, 'cost': 17}, {'i': 8, 'j': 1, 'k': 2, 'cost': 89}, {'i': 8, 'j': 1, 'k': 3, 'cost': 70}, {'i': 8, 'j': 1, 'k': 4, 'cost': 86}, {'i': 8, 'j': 1, 'k': 5, 'cost': 90}, {'i': 8, 'j': 1, 'k': 6, 'cost': 58}, {'i': 8, 'j': 1, 'k': 7, 'cost': 62}, {'i': 8, 'j': 1, 'k': 8, 'cost': 89}, {'i': 8, 'j': 2, 'k': 1, 'cost': 63}, {'i': 8, 'j': 2, 'k': 2, 'cost': 14}, {'i': 8, 'j': 2, 'k': 3, 'cost': 89}, {'i': 8, 'j': 2, 'k': 4, 'cost': 88}, {'i': 8, 'j': 2, 'k': 5, 'cost': 31}, {'i': 8, 'j': 2, 'k': 6, 'cost': 66}, {'i': 8, 'j': 2, 'k': 7, 'cost': 60}, {'i': 8, 'j': 2, 'k': 8, 'cost': 53}, {'i': 8, 'j': 3, 'k': 1, 'cost': 28}, {'i': 8, 'j': 3, 'k': 2, 'cost': 51}, {'i': 8, 'j': 3, 'k': 3, 'cost': 66}, {'i': 8, 'j': 3, 'k': 4, 'cost': 21}, {'i': 8, 'j': 3, 'k': 5, 'cost': 2}, {'i': 8, 'j': 3, 'k': 6, 'cost': 65}, {'i': 8, 'j': 3, 'k': 7, 'cost': 94}, {'i': 8, 'j': 3, 'k': 8, 'cost': 16}, {'i': 8, 'j': 4, 'k': 1, 'cost': 98}, {'i': 8, 'j': 4, 'k': 2, 'cost': 90}, {'i': 8, 'j': 4, 'k': 3, 'cost': 44}, {'i': 8, 'j': 4, 'k': 4, 'cost': 56}, {'i': 8, 'j': 4, 'k': 5, 'cost': 48}, {'i': 8, 'j': 4, 'k': 6, 'cost': 31}, {'i': 8, 'j': 4, 'k': 7, 'cost': 38}, {'i': 8, 'j': 4, 'k': 8, 'cost': 60}, {'i': 8, 'j': 5, 'k': 1, 'cost': 90}, {'i': 8, 'j': 5, 'k': 2, 'cost': 20}, {'i': 8, 'j': 5, 'k': 3, 'cost': 44}, {'i': 8, 'j': 5, 'k': 4, 'cost': 39}, {'i': 8, 'j': 5, 'k': 5, 'cost': 5}, {'i': 8, 'j': 5, 'k': 6, 'cost': 46}, {'i': 8, 'j': 5, 'k': 7, 'cost': 74}, {'i': 8, 'j': 5, 'k': 8, 'cost': 7}, {'i': 8, 'j': 6, 'k': 1, 'cost': 16}, {'i': 8, 'j': 6, 'k': 2, 'cost': 81}, {'i': 8, 'j': 6, 'k': 3, 'cost': 22}, {'i': 8, 'j': 6, 'k': 4, 'cost': 59}, {'i': 8, 'j': 6, 'k': 5, 'cost': 94}, {'i': 8, 'j': 6, 'k': 6, 'cost': 50}, {'i': 8, 'j': 6, 'k': 7, 'cost': 33}, {'i': 8, 'j': 6, 'k': 8, 'cost': 29}, {'i': 8, 'j': 7, 'k': 1, 'cost': 61}, {'i': 8, 'j': 7, 'k': 2, 'cost': 37}, {'i': 8, 'j': 7, 'k': 3, 'cost': 43}, {'i': 8, 'j': 7, 'k': 4, 'cost': 69}, {'i': 8, 'j': 7, 'k': 5, 'cost': 3}, {'i': 8, 'j': 7, 'k': 6, 'cost': 31}, {'i': 8, 'j': 7, 'k': 7, 'cost': 84}, {'i': 8, 'j': 7, 'k': 8, 'cost': 10}, {'i': 8, 'j': 8, 'k': 1, 'cost': 35}, {'i': 8, 'j': 8, 'k': 2, 'cost': 27}, {'i': 8, 'j': 8, 'k': 3, 'cost': 16}, {'i': 8, 'j': 8, 'k': 4, 'cost': 86}, {'i': 8, 'j': 8, 'k': 5, 'cost': 26}, {'i': 8, 'j': 8, 'k': 6, 'cost': 81}, {'i': 8, 'j': 8, 'k': 7, 'cost': 43}, {'i': 8, 'j': 8, 'k': 8, 'cost': 38}]}","[[1, 8, 1], [2, 4, 3], [3, 5, 7], [4, 6, 8], [5, 2, 4], [6, 7, 6], [7, 1, 2], [8, 3, 5]]",38,json,1
AP3,AP3,"There’s a stack of class schedules and a roster of classrooms and TAs on the desk, and the task is simple in words: give every class exactly one classroom and exactly one teaching assistant. No classroom or assistant can be assigned twice and nothing should be left unassigned. Each possible triple (class, room, assistant) has a cost, and the goal is to pick triples that lead to the smallest overall running cost — you just add up the cost for each chosen triple to see the total. The detailed options and their costs are shown below.

There are 6 classes, 6 classrooms, and 6 teaching assistants identified as 1, 2, 3, 4, 5, 6.

*Meaning: costs form a 3D tensor. For each fixed class_id=i, you are given a room_id×ta_id matrix whose entry at row room_id=j and column ta_id=k equals running_cost(i,j,k). You must pick exactly one (j,k) for every i, with all room_id and all ta_id used exactly once.*

**running_cost_tensor (per-class_id markdown matrices)**

## class_id=1
| room_id\ta_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 16 | 52 | 57 | 54 | 51 | 67 |
| 2 | 8 | 10 | 16 | 13 | 61 | 22 |
| 3 | 73 | 21 | 27 | 87 | 49 | 52 |
| 4 | 90 | 13 | 97 | 32 | 18 | 17 |
| 5 | 70 | 19 | 39 | 25 | 31 | 49 |
| 6 | 73 | 75 | 1 | 46 | 51 | 45 |

## class_id=2
| room_id\ta_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 30 | 89 | 18 | 41 | 33 | 83 |
| 2 | 83 | 95 | 88 | 73 | 6 | 43 |
| 3 | 71 | 15 | 96 | 2 | 89 | 40 |
| 4 | 0 | 97 | 27 | 57 | 97 | 99 |
| 5 | 72 | 0 | 97 | 35 | 83 | 89 |
| 6 | 3 | 96 | 80 | 82 | 42 | 9 |

## class_id=3
| room_id\ta_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 49 | 98 | 37 | 62 | 6 | 55 |
| 2 | 83 | 93 | 81 | 60 | 72 | 54 |
| 3 | 99 | 53 | 45 | 81 | 62 | 16 |
| 4 | 20 | 18 | 92 | 40 | 77 | 85 |
| 5 | 46 | 94 | 77 | 80 | 10 | 29 |
| 6 | 22 | 97 | 54 | 91 | 68 | 90 |

## class_id=4
| room_id\ta_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 34 | 1 | 47 | 92 | 89 | 39 |
| 2 | 76 | 94 | 28 | 22 | 81 | 96 |
| 3 | 65 | 17 | 49 | 45 | 35 | 2 |
| 4 | 44 | 61 | 52 | 22 | 29 | 92 |
| 5 | 7 | 39 | 8 | 22 | 14 | 65 |
| 6 | 80 | 24 | 13 | 82 | 6 | 28 |

## class_id=5
| room_id\ta_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 40 | 78 | 94 | 74 | 11 | 79 |
| 2 | 52 | 27 | 22 | 62 | 60 | 99 |
| 3 | 86 | 11 | 92 | 34 | 97 | 46 |
| 4 | 90 | 53 | 85 | 11 | 81 | 27 |
| 5 | 28 | 26 | 42 | 23 | 75 | 46 |
| 6 | 29 | 69 | 54 | 33 | 7 | 16 |

## class_id=6
| room_id\ta_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 21 | 90 | 82 | 89 | 1 | 33 |
| 2 | 11 | 32 | 40 | 91 | 95 | 53 |
| 3 | 19 | 74 | 85 | 52 | 93 | 90 |
| 4 | 86 | 28 | 48 | 25 | 91 | 2 |
| 5 | 93 | 69 | 43 | 84 | 90 | 82 |
| 6 | 98 | 85 | 85 | 99 | 58 | 35 |

Pick 6 triples so every class, room, and TA is used exactly once and the sum of the listed costs is minimized.

If you want the final assignment as a tidy little package, just hand it back in this JSON shape:

{
  ""solution"": [
    [<class_id>, <room_id>, <ta_id>],
    ...
  ]
}

This ""solution"" array should list one triple per class: each triple is the class identifier, the room identifier, and the TA identifier (in that order). Think of it like a simple form: one line per class saying which room and which TA it gets. This JSON is just a sketch of the expected shape — not the actual filled-in answer.

Please use the exact identifiers that appear in the instance input — no renaming and 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”.","{'cost_tensor': [[[16, 52, 57, 54, 51, 67], [8, 10, 16, 13, 61, 22], [73, 21, 27, 87, 49, 52], [90, 13, 97, 32, 18, 17], [70, 19, 39, 25, 31, 49], [73, 75, 1, 46, 51, 45]], [[30, 89, 18, 41, 33, 83], [83, 95, 88, 73, 6, 43], [71, 15, 96, 2, 89, 40], [0, 97, 27, 57, 97, 99], [72, 0, 97, 35, 83, 89], [3, 96, 80, 82, 42, 9]], [[49, 98, 37, 62, 6, 55], [83, 93, 81, 60, 72, 54], [99, 53, 45, 81, 62, 16], [20, 18, 92, 40, 77, 85], [46, 94, 77, 80, 10, 29], [22, 97, 54, 91, 68, 90]], [[34, 1, 47, 92, 89, 39], [76, 94, 28, 22, 81, 96], [65, 17, 49, 45, 35, 2], [44, 61, 52, 22, 29, 92], [7, 39, 8, 22, 14, 65], [80, 24, 13, 82, 6, 28]], [[40, 78, 94, 74, 11, 79], [52, 27, 22, 62, 60, 99], [86, 11, 92, 34, 97, 46], [90, 53, 85, 11, 81, 27], [28, 26, 42, 23, 75, 46], [29, 69, 54, 33, 7, 16]], [[21, 90, 82, 89, 1, 33], [11, 32, 40, 91, 95, 53], [19, 74, 85, 52, 93, 90], [86, 28, 48, 25, 91, 2], [93, 69, 43, 84, 90, 82], [98, 85, 85, 99, 58, 35]]], 'objective': 31.0}","[[0, 5, 2], [1, 4, 1], [2, 0, 4], [3, 2, 5], [4, 3, 3], [5, 1, 0]]",31.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 16}, {'i': 1, 'j': 1, 'k': 2, 'cost': 52}, {'i': 1, 'j': 1, 'k': 3, 'cost': 57}, {'i': 1, 'j': 1, 'k': 4, 'cost': 54}, {'i': 1, 'j': 1, 'k': 5, 'cost': 51}, {'i': 1, 'j': 1, 'k': 6, 'cost': 67}, {'i': 1, 'j': 2, 'k': 1, 'cost': 8}, {'i': 1, 'j': 2, 'k': 2, 'cost': 10}, {'i': 1, 'j': 2, 'k': 3, 'cost': 16}, {'i': 1, 'j': 2, 'k': 4, 'cost': 13}, {'i': 1, 'j': 2, 'k': 5, 'cost': 61}, {'i': 1, 'j': 2, 'k': 6, 'cost': 22}, {'i': 1, 'j': 3, 'k': 1, 'cost': 73}, {'i': 1, 'j': 3, 'k': 2, 'cost': 21}, {'i': 1, 'j': 3, 'k': 3, 'cost': 27}, {'i': 1, 'j': 3, 'k': 4, 'cost': 87}, {'i': 1, 'j': 3, 'k': 5, 'cost': 49}, {'i': 1, 'j': 3, 'k': 6, 'cost': 52}, {'i': 1, 'j': 4, 'k': 1, 'cost': 90}, {'i': 1, 'j': 4, 'k': 2, 'cost': 13}, {'i': 1, 'j': 4, 'k': 3, 'cost': 97}, {'i': 1, 'j': 4, 'k': 4, 'cost': 32}, {'i': 1, 'j': 4, 'k': 5, 'cost': 18}, {'i': 1, 'j': 4, 'k': 6, 'cost': 17}, {'i': 1, 'j': 5, 'k': 1, 'cost': 70}, {'i': 1, 'j': 5, 'k': 2, 'cost': 19}, {'i': 1, 'j': 5, 'k': 3, 'cost': 39}, {'i': 1, 'j': 5, 'k': 4, 'cost': 25}, {'i': 1, 'j': 5, 'k': 5, 'cost': 31}, {'i': 1, 'j': 5, 'k': 6, 'cost': 49}, {'i': 1, 'j': 6, 'k': 1, 'cost': 73}, {'i': 1, 'j': 6, 'k': 2, 'cost': 75}, {'i': 1, 'j': 6, 'k': 3, 'cost': 1}, {'i': 1, 'j': 6, 'k': 4, 'cost': 46}, {'i': 1, 'j': 6, 'k': 5, 'cost': 51}, {'i': 1, 'j': 6, 'k': 6, 'cost': 45}, {'i': 2, 'j': 1, 'k': 1, 'cost': 30}, {'i': 2, 'j': 1, 'k': 2, 'cost': 89}, {'i': 2, 'j': 1, 'k': 3, 'cost': 18}, {'i': 2, 'j': 1, 'k': 4, 'cost': 41}, {'i': 2, 'j': 1, 'k': 5, 'cost': 33}, {'i': 2, 'j': 1, 'k': 6, 'cost': 83}, {'i': 2, 'j': 2, 'k': 1, 'cost': 83}, {'i': 2, 'j': 2, 'k': 2, 'cost': 95}, {'i': 2, 'j': 2, 'k': 3, 'cost': 88}, {'i': 2, 'j': 2, 'k': 4, 'cost': 73}, {'i': 2, 'j': 2, 'k': 5, 'cost': 6}, {'i': 2, 'j': 2, 'k': 6, 'cost': 43}, {'i': 2, 'j': 3, 'k': 1, 'cost': 71}, {'i': 2, 'j': 3, 'k': 2, 'cost': 15}, {'i': 2, 'j': 3, 'k': 3, 'cost': 96}, {'i': 2, 'j': 3, 'k': 4, 'cost': 2}, {'i': 2, 'j': 3, 'k': 5, 'cost': 89}, {'i': 2, 'j': 3, 'k': 6, 'cost': 40}, {'i': 2, 'j': 4, 'k': 1, 'cost': 0}, {'i': 2, 'j': 4, 'k': 2, 'cost': 97}, {'i': 2, 'j': 4, 'k': 3, 'cost': 27}, {'i': 2, 'j': 4, 'k': 4, 'cost': 57}, {'i': 2, 'j': 4, 'k': 5, 'cost': 97}, {'i': 2, 'j': 4, 'k': 6, 'cost': 99}, {'i': 2, 'j': 5, 'k': 1, 'cost': 72}, {'i': 2, 'j': 5, 'k': 2, 'cost': 0}, {'i': 2, 'j': 5, 'k': 3, 'cost': 97}, {'i': 2, 'j': 5, 'k': 4, 'cost': 35}, {'i': 2, 'j': 5, 'k': 5, 'cost': 83}, {'i': 2, 'j': 5, 'k': 6, 'cost': 89}, {'i': 2, 'j': 6, 'k': 1, 'cost': 3}, {'i': 2, 'j': 6, 'k': 2, 'cost': 96}, {'i': 2, 'j': 6, 'k': 3, 'cost': 80}, {'i': 2, 'j': 6, 'k': 4, 'cost': 82}, {'i': 2, 'j': 6, 'k': 5, 'cost': 42}, {'i': 2, 'j': 6, 'k': 6, 'cost': 9}, {'i': 3, 'j': 1, 'k': 1, 'cost': 49}, {'i': 3, 'j': 1, 'k': 2, 'cost': 98}, {'i': 3, 'j': 1, 'k': 3, 'cost': 37}, {'i': 3, 'j': 1, 'k': 4, 'cost': 62}, {'i': 3, 'j': 1, 'k': 5, 'cost': 6}, {'i': 3, 'j': 1, 'k': 6, 'cost': 55}, {'i': 3, 'j': 2, 'k': 1, 'cost': 83}, {'i': 3, 'j': 2, 'k': 2, 'cost': 93}, {'i': 3, 'j': 2, 'k': 3, 'cost': 81}, {'i': 3, 'j': 2, 'k': 4, 'cost': 60}, {'i': 3, 'j': 2, 'k': 5, 'cost': 72}, {'i': 3, 'j': 2, 'k': 6, 'cost': 54}, {'i': 3, 'j': 3, 'k': 1, 'cost': 99}, {'i': 3, 'j': 3, 'k': 2, 'cost': 53}, {'i': 3, 'j': 3, 'k': 3, 'cost': 45}, {'i': 3, 'j': 3, 'k': 4, 'cost': 81}, {'i': 3, 'j': 3, 'k': 5, 'cost': 62}, {'i': 3, 'j': 3, 'k': 6, 'cost': 16}, {'i': 3, 'j': 4, 'k': 1, 'cost': 20}, {'i': 3, 'j': 4, 'k': 2, 'cost': 18}, {'i': 3, 'j': 4, 'k': 3, 'cost': 92}, {'i': 3, 'j': 4, 'k': 4, 'cost': 40}, {'i': 3, 'j': 4, 'k': 5, 'cost': 77}, {'i': 3, 'j': 4, 'k': 6, 'cost': 85}, {'i': 3, 'j': 5, 'k': 1, 'cost': 46}, {'i': 3, 'j': 5, 'k': 2, 'cost': 94}, {'i': 3, 'j': 5, 'k': 3, 'cost': 77}, {'i': 3, 'j': 5, 'k': 4, 'cost': 80}, {'i': 3, 'j': 5, 'k': 5, 'cost': 10}, {'i': 3, 'j': 5, 'k': 6, 'cost': 29}, {'i': 3, 'j': 6, 'k': 1, 'cost': 22}, {'i': 3, 'j': 6, 'k': 2, 'cost': 97}, {'i': 3, 'j': 6, 'k': 3, 'cost': 54}, {'i': 3, 'j': 6, 'k': 4, 'cost': 91}, {'i': 3, 'j': 6, 'k': 5, 'cost': 68}, {'i': 3, 'j': 6, 'k': 6, 'cost': 90}, {'i': 4, 'j': 1, 'k': 1, 'cost': 34}, {'i': 4, 'j': 1, 'k': 2, 'cost': 1}, {'i': 4, 'j': 1, 'k': 3, 'cost': 47}, {'i': 4, 'j': 1, 'k': 4, 'cost': 92}, {'i': 4, 'j': 1, 'k': 5, 'cost': 89}, {'i': 4, 'j': 1, 'k': 6, 'cost': 39}, {'i': 4, 'j': 2, 'k': 1, 'cost': 76}, {'i': 4, 'j': 2, 'k': 2, 'cost': 94}, {'i': 4, 'j': 2, 'k': 3, 'cost': 28}, {'i': 4, 'j': 2, 'k': 4, 'cost': 22}, {'i': 4, 'j': 2, 'k': 5, 'cost': 81}, {'i': 4, 'j': 2, 'k': 6, 'cost': 96}, {'i': 4, 'j': 3, 'k': 1, 'cost': 65}, {'i': 4, 'j': 3, 'k': 2, 'cost': 17}, {'i': 4, 'j': 3, 'k': 3, 'cost': 49}, {'i': 4, 'j': 3, 'k': 4, 'cost': 45}, {'i': 4, 'j': 3, 'k': 5, 'cost': 35}, {'i': 4, 'j': 3, 'k': 6, 'cost': 2}, {'i': 4, 'j': 4, 'k': 1, 'cost': 44}, {'i': 4, 'j': 4, 'k': 2, 'cost': 61}, {'i': 4, 'j': 4, 'k': 3, 'cost': 52}, {'i': 4, 'j': 4, 'k': 4, 'cost': 22}, {'i': 4, 'j': 4, 'k': 5, 'cost': 29}, {'i': 4, 'j': 4, 'k': 6, 'cost': 92}, {'i': 4, 'j': 5, 'k': 1, 'cost': 7}, {'i': 4, 'j': 5, 'k': 2, 'cost': 39}, {'i': 4, 'j': 5, 'k': 3, 'cost': 8}, {'i': 4, 'j': 5, 'k': 4, 'cost': 22}, {'i': 4, 'j': 5, 'k': 5, 'cost': 14}, {'i': 4, 'j': 5, 'k': 6, 'cost': 65}, {'i': 4, 'j': 6, 'k': 1, 'cost': 80}, {'i': 4, 'j': 6, 'k': 2, 'cost': 24}, {'i': 4, 'j': 6, 'k': 3, 'cost': 13}, {'i': 4, 'j': 6, 'k': 4, 'cost': 82}, {'i': 4, 'j': 6, 'k': 5, 'cost': 6}, {'i': 4, 'j': 6, 'k': 6, 'cost': 28}, {'i': 5, 'j': 1, 'k': 1, 'cost': 40}, {'i': 5, 'j': 1, 'k': 2, 'cost': 78}, {'i': 5, 'j': 1, 'k': 3, 'cost': 94}, {'i': 5, 'j': 1, 'k': 4, 'cost': 74}, {'i': 5, 'j': 1, 'k': 5, 'cost': 11}, {'i': 5, 'j': 1, 'k': 6, 'cost': 79}, {'i': 5, 'j': 2, 'k': 1, 'cost': 52}, {'i': 5, 'j': 2, 'k': 2, 'cost': 27}, {'i': 5, 'j': 2, 'k': 3, 'cost': 22}, {'i': 5, 'j': 2, 'k': 4, 'cost': 62}, {'i': 5, 'j': 2, 'k': 5, 'cost': 60}, {'i': 5, 'j': 2, 'k': 6, 'cost': 99}, {'i': 5, 'j': 3, 'k': 1, 'cost': 86}, {'i': 5, 'j': 3, 'k': 2, 'cost': 11}, {'i': 5, 'j': 3, 'k': 3, 'cost': 92}, {'i': 5, 'j': 3, 'k': 4, 'cost': 34}, {'i': 5, 'j': 3, 'k': 5, 'cost': 97}, {'i': 5, 'j': 3, 'k': 6, 'cost': 46}, {'i': 5, 'j': 4, 'k': 1, 'cost': 90}, {'i': 5, 'j': 4, 'k': 2, 'cost': 53}, {'i': 5, 'j': 4, 'k': 3, 'cost': 85}, {'i': 5, 'j': 4, 'k': 4, 'cost': 11}, {'i': 5, 'j': 4, 'k': 5, 'cost': 81}, {'i': 5, 'j': 4, 'k': 6, 'cost': 27}, {'i': 5, 'j': 5, 'k': 1, 'cost': 28}, {'i': 5, 'j': 5, 'k': 2, 'cost': 26}, {'i': 5, 'j': 5, 'k': 3, 'cost': 42}, {'i': 5, 'j': 5, 'k': 4, 'cost': 23}, {'i': 5, 'j': 5, 'k': 5, 'cost': 75}, {'i': 5, 'j': 5, 'k': 6, 'cost': 46}, {'i': 5, 'j': 6, 'k': 1, 'cost': 29}, {'i': 5, 'j': 6, 'k': 2, 'cost': 69}, {'i': 5, 'j': 6, 'k': 3, 'cost': 54}, {'i': 5, 'j': 6, 'k': 4, 'cost': 33}, {'i': 5, 'j': 6, 'k': 5, 'cost': 7}, {'i': 5, 'j': 6, 'k': 6, 'cost': 16}, {'i': 6, 'j': 1, 'k': 1, 'cost': 21}, {'i': 6, 'j': 1, 'k': 2, 'cost': 90}, {'i': 6, 'j': 1, 'k': 3, 'cost': 82}, {'i': 6, 'j': 1, 'k': 4, 'cost': 89}, {'i': 6, 'j': 1, 'k': 5, 'cost': 1}, {'i': 6, 'j': 1, 'k': 6, 'cost': 33}, {'i': 6, 'j': 2, 'k': 1, 'cost': 11}, {'i': 6, 'j': 2, 'k': 2, 'cost': 32}, {'i': 6, 'j': 2, 'k': 3, 'cost': 40}, {'i': 6, 'j': 2, 'k': 4, 'cost': 91}, {'i': 6, 'j': 2, 'k': 5, 'cost': 95}, {'i': 6, 'j': 2, 'k': 6, 'cost': 53}, {'i': 6, 'j': 3, 'k': 1, 'cost': 19}, {'i': 6, 'j': 3, 'k': 2, 'cost': 74}, {'i': 6, 'j': 3, 'k': 3, 'cost': 85}, {'i': 6, 'j': 3, 'k': 4, 'cost': 52}, {'i': 6, 'j': 3, 'k': 5, 'cost': 93}, {'i': 6, 'j': 3, 'k': 6, 'cost': 90}, {'i': 6, 'j': 4, 'k': 1, 'cost': 86}, {'i': 6, 'j': 4, 'k': 2, 'cost': 28}, {'i': 6, 'j': 4, 'k': 3, 'cost': 48}, {'i': 6, 'j': 4, 'k': 4, 'cost': 25}, {'i': 6, 'j': 4, 'k': 5, 'cost': 91}, {'i': 6, 'j': 4, 'k': 6, 'cost': 2}, {'i': 6, 'j': 5, 'k': 1, 'cost': 93}, {'i': 6, 'j': 5, 'k': 2, 'cost': 69}, {'i': 6, 'j': 5, 'k': 3, 'cost': 43}, {'i': 6, 'j': 5, 'k': 4, 'cost': 84}, {'i': 6, 'j': 5, 'k': 5, 'cost': 90}, {'i': 6, 'j': 5, 'k': 6, 'cost': 82}, {'i': 6, 'j': 6, 'k': 1, 'cost': 98}, {'i': 6, 'j': 6, 'k': 2, 'cost': 85}, {'i': 6, 'j': 6, 'k': 3, 'cost': 85}, {'i': 6, 'j': 6, 'k': 4, 'cost': 99}, {'i': 6, 'j': 6, 'k': 5, 'cost': 58}, {'i': 6, 'j': 6, 'k': 6, 'cost': 35}]}","[[1, 6, 3], [2, 5, 2], [3, 1, 5], [4, 3, 6], [5, 4, 4], [6, 2, 1]]",39,markdown_table,1
AP3,AP3,"On a busy morning the task is to assign a single nurse and a single equipment kit to each scheduled home visit, ensuring every nurse gets exactly one assignment and every kit is sent out one time only. Because pairings vary in cost, the aim is to arrange the assignments so the total spending — calculated by adding up the cost for each visit’s chosen nurse-and-kit — ends up as small as possible. The concrete list of visits, nurses, kits and their costs is shown below.

There are 8 scheduled home visits, listed as A, B, C, D, E, F, G, H.

*Meaning: costs form a 3D tensor. For each fixed visit_id=i, you are given a nurse_id×kit_id matrix whose entry at row nurse_id=j and column kit_id=k equals operational_cost(i,j,k). You must pick exactly one (j,k) for every i, with all nurse_id and all kit_id used exactly once.*

**operational_cost_tensor (per-visit_id markdown matrices)**

## visit_id=A
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 22 | 40 | 89 | 33 | 18 | 16 | 7 | 13 |
| B | 57 | 17 | 15 | 51 | 33 | 79 | 35 | 78 |
| C | 6 | 24 | 0 | 5 | 20 | 91 | 78 | 58 |
| D | 16 | 97 | 45 | 60 | 10 | 77 | 52 | 62 |
| E | 23 | 10 | 12 | 94 | 20 | 16 | 88 | 2 |
| F | 49 | 63 | 43 | 86 | 70 | 95 | 62 | 7 |
| G | 58 | 76 | 83 | 56 | 64 | 35 | 34 | 53 |
| H | 86 | 62 | 22 | 9 | 21 | 47 | 76 | 76 |

## visit_id=B
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 62 | 72 | 62 | 75 | 4 | 27 | 24 | 51 |
| B | 95 | 38 | 35 | 97 | 91 | 56 | 46 | 23 |
| C | 4 | 11 | 30 | 39 | 44 | 13 | 31 | 20 |
| D | 62 | 5 | 27 | 27 | 58 | 24 | 22 | 14 |
| E | 70 | 85 | 64 | 38 | 10 | 6 | 14 | 38 |
| F | 29 | 28 | 60 | 79 | 62 | 39 | 86 | 65 |
| G | 92 | 61 | 10 | 42 | 76 | 62 | 39 | 81 |
| H | 62 | 51 | 34 | 16 | 71 | 15 | 71 | 99 |

## visit_id=C
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 51 | 27 | 0 | 72 | 56 | 9 | 28 | 32 |
| B | 52 | 13 | 82 | 69 | 55 | 64 | 23 | 97 |
| C | 60 | 81 | 60 | 89 | 38 | 95 | 58 | 47 |
| D | 26 | 74 | 84 | 84 | 18 | 96 | 58 | 33 |
| E | 91 | 19 | 14 | 10 | 99 | 4 | 57 | 86 |
| F | 93 | 9 | 44 | 75 | 68 | 81 | 55 | 69 |
| G | 82 | 9 | 53 | 91 | 58 | 76 | 79 | 69 |
| H | 10 | 53 | 37 | 88 | 55 | 13 | 42 | 57 |

## visit_id=D
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 24 | 56 | 14 | 7 | 17 | 15 | 63 | 49 |
| B | 61 | 22 | 50 | 77 | 69 | 83 | 87 | 53 |
| C | 91 | 88 | 32 | 58 | 82 | 86 | 31 | 74 |
| D | 2 | 67 | 31 | 63 | 22 | 59 | 3 | 22 |
| E | 52 | 27 | 84 | 74 | 21 | 48 | 56 | 29 |
| F | 8 | 5 | 14 | 19 | 88 | 64 | 88 | 75 |
| G | 40 | 39 | 29 | 88 | 72 | 50 | 23 | 42 |
| H | 26 | 69 | 49 | 93 | 37 | 39 | 22 | 79 |

## visit_id=E
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 55 | 35 | 23 | 6 | 96 | 75 | 2 | 84 |
| B | 90 | 7 | 60 | 34 | 87 | 30 | 45 | 45 |
| C | 55 | 78 | 9 | 22 | 4 | 18 | 83 | 28 |
| D | 10 | 38 | 11 | 71 | 66 | 15 | 0 | 91 |
| E | 80 | 76 | 99 | 79 | 11 | 91 | 75 | 89 |
| F | 48 | 80 | 24 | 74 | 9 | 21 | 67 | 98 |
| G | 60 | 72 | 48 | 43 | 53 | 17 | 17 | 18 |
| H | 16 | 75 | 29 | 90 | 2 | 95 | 94 | 38 |

## visit_id=F
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 83 | 51 | 87 | 0 | 50 | 42 | 20 | 70 |
| B | 35 | 32 | 95 | 86 | 72 | 38 | 76 | 87 |
| C | 26 | 46 | 36 | 14 | 46 | 67 | 84 | 91 |
| D | 59 | 66 | 81 | 82 | 55 | 9 | 66 | 96 |
| E | 22 | 74 | 84 | 43 | 51 | 34 | 89 | 0 |
| F | 73 | 75 | 75 | 90 | 88 | 86 | 9 | 4 |
| G | 13 | 20 | 15 | 39 | 30 | 20 | 54 | 88 |
| H | 48 | 17 | 0 | 35 | 42 | 15 | 10 | 35 |

## visit_id=G
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 48 | 64 | 91 | 83 | 46 | 82 | 63 | 32 |
| B | 49 | 94 | 60 | 61 | 62 | 63 | 9 | 1 |
| C | 80 | 80 | 14 | 69 | 29 | 62 | 2 | 72 |
| D | 52 | 98 | 98 | 61 | 40 | 65 | 70 | 79 |
| E | 2 | 59 | 9 | 53 | 73 | 31 | 1 | 15 |
| F | 35 | 74 | 68 | 68 | 62 | 17 | 92 | 55 |
| G | 28 | 85 | 39 | 7 | 21 | 35 | 7 | 38 |
| H | 18 | 24 | 3 | 6 | 15 | 55 | 86 | 13 |

## visit_id=H
| nurse_id\kit_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 14 | 14 | 94 | 13 | 84 | 22 | 70 | 58 |
| B | 39 | 19 | 36 | 26 | 94 | 30 | 46 | 91 |
| C | 38 | 13 | 59 | 32 | 70 | 16 | 92 | 84 |
| D | 69 | 54 | 19 | 74 | 56 | 27 | 93 | 88 |
| E | 6 | 23 | 27 | 98 | 12 | 5 | 38 | 9 |
| F | 36 | 66 | 93 | 9 | 65 | 0 | 53 | 36 |
| G | 81 | 43 | 20 | 45 | 90 | 87 | 92 | 72 |
| H | 66 | 59 | 30 | 85 | 31 | 28 | 85 | 62 |

Assign exactly one nurse and one kit to each visit so every nurse and every kit is used once and the total operational cost is minimized.

To keep things simple, the final reply should just be a small JSON object showing the chosen triples — one triple per visit, listing the visit, the nurse, and the kit.

{
  ""solution"": [
    [<visit_id>, <nurse_id>, <kit_id>],
    ...
  ]
}

Each inner list is a single assignment: the visit identifier, the nurse identifier assigned to that visit, and the equipment kit identifier sent along. Think of it like filling out a form where each row says ""Visit X gets Nurse Y and Kit Z."" This JSON is just the shape I expect — a sketch, not the actual solved assignments.

Please use the exact identifiers from the instance input — no renaming and 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”.""","{'cost_tensor': [[[22, 40, 89, 33, 18, 16, 7, 13], [57, 17, 15, 51, 33, 79, 35, 78], [6, 24, 0, 5, 20, 91, 78, 58], [16, 97, 45, 60, 10, 77, 52, 62], [23, 10, 12, 94, 20, 16, 88, 2], [49, 63, 43, 86, 70, 95, 62, 7], [58, 76, 83, 56, 64, 35, 34, 53], [86, 62, 22, 9, 21, 47, 76, 76]], [[62, 72, 62, 75, 4, 27, 24, 51], [95, 38, 35, 97, 91, 56, 46, 23], [4, 11, 30, 39, 44, 13, 31, 20], [62, 5, 27, 27, 58, 24, 22, 14], [70, 85, 64, 38, 10, 6, 14, 38], [29, 28, 60, 79, 62, 39, 86, 65], [92, 61, 10, 42, 76, 62, 39, 81], [62, 51, 34, 16, 71, 15, 71, 99]], [[51, 27, 0, 72, 56, 9, 28, 32], [52, 13, 82, 69, 55, 64, 23, 97], [60, 81, 60, 89, 38, 95, 58, 47], [26, 74, 84, 84, 18, 96, 58, 33], [91, 19, 14, 10, 99, 4, 57, 86], [93, 9, 44, 75, 68, 81, 55, 69], [82, 9, 53, 91, 58, 76, 79, 69], [10, 53, 37, 88, 55, 13, 42, 57]], [[24, 56, 14, 7, 17, 15, 63, 49], [61, 22, 50, 77, 69, 83, 87, 53], [91, 88, 32, 58, 82, 86, 31, 74], [2, 67, 31, 63, 22, 59, 3, 22], [52, 27, 84, 74, 21, 48, 56, 29], [8, 5, 14, 19, 88, 64, 88, 75], [40, 39, 29, 88, 72, 50, 23, 42], [26, 69, 49, 93, 37, 39, 22, 79]], [[55, 35, 23, 6, 96, 75, 2, 84], [90, 7, 60, 34, 87, 30, 45, 45], [55, 78, 9, 22, 4, 18, 83, 28], [10, 38, 11, 71, 66, 15, 0, 91], [80, 76, 99, 79, 11, 91, 75, 89], [48, 80, 24, 74, 9, 21, 67, 98], [60, 72, 48, 43, 53, 17, 17, 18], [16, 75, 29, 90, 2, 95, 94, 38]], [[83, 51, 87, 0, 50, 42, 20, 70], [35, 32, 95, 86, 72, 38, 76, 87], [26, 46, 36, 14, 46, 67, 84, 91], [59, 66, 81, 82, 55, 9, 66, 96], [22, 74, 84, 43, 51, 34, 89, 0], [73, 75, 75, 90, 88, 86, 9, 4], [13, 20, 15, 39, 30, 20, 54, 88], [48, 17, 0, 35, 42, 15, 10, 35]], [[48, 64, 91, 83, 46, 82, 63, 32], [49, 94, 60, 61, 62, 63, 9, 1], [80, 80, 14, 69, 29, 62, 2, 72], [52, 98, 98, 61, 40, 65, 70, 79], [2, 59, 9, 53, 73, 31, 1, 15], [35, 74, 68, 68, 62, 17, 92, 55], [28, 85, 39, 7, 21, 35, 7, 38], [18, 24, 3, 6, 15, 55, 86, 13]], [[14, 14, 94, 13, 84, 22, 70, 58], [39, 19, 36, 26, 94, 30, 46, 91], [38, 13, 59, 32, 70, 16, 92, 84], [69, 54, 19, 74, 56, 27, 93, 88], [6, 23, 27, 98, 12, 5, 38, 9], [36, 66, 93, 9, 65, 0, 53, 36], [81, 43, 20, 45, 90, 87, 92, 72], [66, 59, 30, 85, 31, 28, 85, 62]]], 'objective': 28.0}","[[0, 2, 2], [1, 4, 6], [2, 6, 1], [3, 3, 0], [4, 7, 4], [5, 0, 3], [6, 1, 7], [7, 5, 5]]",28.0,"{'problem_type': 'AP3', 'n': 8, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 22}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 40}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 89}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 33}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 18}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 16}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 7}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 13}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 57}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 17}, {'i': 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'k': 'H', 'cost': 96}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 22}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 74}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 84}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 43}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 51}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 34}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 89}, {'i': 'F', 'j': 'E', 'k': 'H', 'cost': 0}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 73}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 75}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 75}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 90}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 88}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 86}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 9}, {'i': 'F', 'j': 'F', 'k': 'H', 'cost': 4}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 13}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 20}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 15}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 39}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 30}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 20}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 54}, {'i': 'F', 'j': 'G', 'k': 'H', 'cost': 88}, {'i': 'F', 'j': 'H', 'k': 'A', 'cost': 48}, {'i': 'F', 'j': 'H', 'k': 'B', 'cost': 17}, {'i': 'F', 'j': 'H', 'k': 'C', 'cost': 0}, {'i': 'F', 'j': 'H', 'k': 'D', 'cost': 35}, {'i': 'F', 'j': 'H', 'k': 'E', 'cost': 42}, {'i': 'F', 'j': 'H', 'k': 'F', 'cost': 15}, {'i': 'F', 'j': 'H', 'k': 'G', 'cost': 10}, {'i': 'F', 'j': 'H', 'k': 'H', 'cost': 35}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 48}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 64}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 91}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 83}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 46}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 82}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 63}, {'i': 'G', 'j': 'A', 'k': 'H', 'cost': 32}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 49}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 94}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 60}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 61}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 62}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 63}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 9}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 1}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 80}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 80}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 14}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 69}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 29}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 62}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 2}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 72}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 52}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 98}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 98}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 61}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 40}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 65}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 70}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 79}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 2}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 59}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 9}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 53}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 73}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 31}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 1}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 15}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 35}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 74}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 68}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 68}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 62}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 17}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 92}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 55}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 28}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 85}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 39}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 7}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 21}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 35}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 7}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 38}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 18}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 24}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 3}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 6}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 15}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 55}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 86}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 13}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 14}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 14}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 94}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 13}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 84}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 22}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 70}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 58}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 39}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 19}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 36}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 26}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 94}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 30}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 46}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 91}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 38}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 13}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 59}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 32}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 70}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 16}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 92}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 84}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 69}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 54}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 19}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 74}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 56}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 27}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 93}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 88}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 6}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 23}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 27}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 98}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 12}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 5}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 38}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 9}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 36}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 66}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 93}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 9}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 65}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 0}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 53}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 36}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 81}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 43}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 20}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 45}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 90}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 87}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 92}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 72}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 66}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 59}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 30}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 85}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 31}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 28}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 85}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 62}]}","[['A', 'C', 'C'], ['B', 'E', 'G'], ['C', 'G', 'B'], ['D', 'D', 'A'], ['E', 'H', 'E'], ['F', 'A', 'D'], ['G', 'B', 'H'], ['H', 'F', 'F']]",40,markdown_table,names
AP3,AP3,"Many museums handle exhibit installs like a matching game: each exhibit space gets one artwork and one lighting configuration, and there are exactly as many artworks and lighting options as there are spaces. That means every artwork and every light ends up in exactly one spot — nothing duplicated, nothing omitted. Each possible assignment of space, art, and light has an installation cost, and the preferred arrangement is the one whose costs add up to the least amount. Look below for the concrete list of spaces, artworks, lights, and prices.

Below are the 8 candidate triples for the identifiers A, B, C, D, E, F, G, H.
Meaning: costs form a 3D tensor. For each fixed space_id=i, you are given a artwork_id×lighting_setup_id matrix whose entry at row artwork_id=j and column lighting_setup_id=k equals installation_cost(i,j,k). You must pick exactly one (j,k) for every i, with all artwork_id and all lighting_setup_id used exactly once.
installation_cost_tensor (per-space_id markdown matrices):
## space_id=A
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 87 | 75 | 42 | 90 | 74 | 76 | 54 | 6 |
| B | 74 | 49 | 92 | 60 | 92 | 27 | 12 | 29 |
| C | 38 | 75 | 53 | 67 | 30 | 67 | 17 | 70 |
| D | 70 | 52 | 95 | 23 | 23 | 88 | 22 | 24 |
| E | 40 | 18 | 11 | 25 | 97 | 92 | 25 | 86 |
| F | 13 | 74 | 1 | 39 | 13 | 80 | 32 | 1 |
| G | 10 | 69 | 83 | 93 | 62 | 82 | 10 | 73 |
| H | 3 | 60 | 25 | 70 | 37 | 58 | 82 | 6 |

## space_id=B
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 35 | 80 | 55 | 0 | 96 | 61 | 24 | 79 |
| B | 23 | 13 | 12 | 1 | 46 | 26 | 52 | 57 |
| C | 64 | 18 | 95 | 96 | 32 | 7 | 57 | 36 |
| D | 17 | 14 | 30 | 84 | 76 | 31 | 39 | 51 |
| E | 30 | 70 | 12 | 79 | 97 | 17 | 69 | 46 |
| F | 13 | 70 | 17 | 99 | 76 | 70 | 85 | 1 |
| G | 69 | 41 | 93 | 47 | 10 | 93 | 19 | 30 |
| H | 69 | 97 | 15 | 30 | 75 | 28 | 47 | 67 |

## space_id=C
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 38 | 31 | 7 | 75 | 57 | 75 | 86 | 14 |
| B | 29 | 53 | 7 | 1 | 19 | 35 | 14 | 60 |
| C | 51 | 29 | 60 | 50 | 35 | 50 | 74 | 30 |
| D | 89 | 92 | 91 | 64 | 95 | 80 | 31 | 15 |
| E | 30 | 61 | 77 | 76 | 50 | 92 | 17 | 50 |
| F | 89 | 87 | 81 | 66 | 8 | 33 | 14 | 14 |
| G | 77 | 31 | 86 | 78 | 56 | 23 | 26 | 91 |
| H | 4 | 94 | 31 | 21 | 80 | 54 | 97 | 76 |

## space_id=D
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 61 | 74 | 81 | 78 | 14 | 94 | 25 | 84 |
| B | 90 | 41 | 27 | 82 | 39 | 7 | 64 | 7 |
| C | 26 | 93 | 26 | 34 | 47 | 20 | 42 | 50 |
| D | 50 | 14 | 29 | 52 | 69 | 82 | 82 | 68 |
| E | 51 | 8 | 76 | 37 | 39 | 50 | 48 | 49 |
| F | 78 | 66 | 76 | 27 | 9 | 31 | 87 | 20 |
| G | 53 | 2 | 33 | 41 | 64 | 92 | 66 | 72 |
| H | 10 | 9 | 22 | 6 | 75 | 49 | 47 | 91 |

## space_id=E
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 57 | 40 | 50 | 5 | 72 | 93 | 98 | 5 |
| B | 70 | 91 | 43 | 19 | 42 | 8 | 3 | 1 |
| C | 54 | 17 | 13 | 93 | 84 | 4 | 51 | 37 |
| D | 5 | 18 | 7 | 45 | 84 | 58 | 82 | 38 |
| E | 48 | 82 | 94 | 37 | 76 | 70 | 51 | 49 |
| F | 43 | 72 | 73 | 2 | 87 | 96 | 27 | 72 |
| G | 18 | 94 | 32 | 6 | 14 | 16 | 15 | 42 |
| H | 98 | 48 | 79 | 7 | 74 | 1 | 64 | 69 |

## space_id=F
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 6 | 90 | 27 | 76 | 8 | 60 | 6 | 21 |
| B | 16 | 36 | 52 | 54 | 24 | 59 | 86 | 53 |
| C | 93 | 49 | 89 | 97 | 14 | 6 | 89 | 93 |
| D | 77 | 91 | 47 | 32 | 38 | 24 | 85 | 62 |
| E | 9 | 12 | 67 | 54 | 78 | 26 | 88 | 30 |
| F | 29 | 99 | 27 | 14 | 68 | 6 | 56 | 82 |
| G | 58 | 23 | 36 | 2 | 90 | 77 | 65 | 58 |
| H | 83 | 51 | 38 | 17 | 16 | 83 | 88 | 53 |

## space_id=G
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 93 | 76 | 63 | 36 | 8 | 7 | 37 | 25 |
| B | 27 | 18 | 80 | 61 | 85 | 35 | 35 | 66 |
| C | 79 | 57 | 61 | 75 | 71 | 93 | 61 | 61 |
| D | 85 | 87 | 57 | 16 | 47 | 56 | 96 | 85 |
| E | 60 | 25 | 19 | 86 | 77 | 61 | 78 | 56 |
| F | 84 | 80 | 10 | 90 | 76 | 50 | 77 | 62 |
| G | 80 | 97 | 79 | 81 | 79 | 43 | 32 | 58 |
| H | 82 | 16 | 53 | 6 | 9 | 33 | 63 | 38 |

## space_id=H
| artwork_id\lighting_setup_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 4 | 59 | 78 | 16 | 83 | 11 | 27 | 36 |
| B | 22 | 52 | 56 | 85 | 35 | 5 | 23 | 54 |
| C | 86 | 75 | 49 | 32 | 33 | 43 | 64 | 22 |
| D | 62 | 37 | 37 | 16 | 51 | 71 | 80 | 28 |
| E | 80 | 76 | 29 | 37 | 35 | 59 | 92 | 88 |
| F | 18 | 17 | 48 | 42 | 60 | 31 | 26 | 70 |
| G | 57 | 13 | 64 | 3 | 83 | 90 | 49 | 12 |
| H | 31 | 14 | 31 | 12 | 5 | 71 | 48 | 80 |
The solver will select 8 non-overlapping triples that minimize the total installation cost.

If you want to give me the final plan, a simple JSON sketch like this is perfect — just list the chosen triples (one per space) in the same shape shown below.

{
  ""solution"": [
    [<space_id>, <art_id>, <light_id>],
    ...
  ]
}

Each inner triple is one installation: which space gets which artwork and which lighting setup. Think of each row as a short form of “space, artwork, light.” This is just the shape I expect — don’t treat the placeholders as the actual choices.

Please be sure to use the exact identifiers from the instance input, with no renaming and 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”.""","{'cost_tensor': [[[87, 75, 42, 90, 74, 76, 54, 6], [74, 49, 92, 60, 92, 27, 12, 29], [38, 75, 53, 67, 30, 67, 17, 70], [70, 52, 95, 23, 23, 88, 22, 24], [40, 18, 11, 25, 97, 92, 25, 86], [13, 74, 1, 39, 13, 80, 32, 1], [10, 69, 83, 93, 62, 82, 10, 73], [3, 60, 25, 70, 37, 58, 82, 6]], [[35, 80, 55, 0, 96, 61, 24, 79], [23, 13, 12, 1, 46, 26, 52, 57], [64, 18, 95, 96, 32, 7, 57, 36], [17, 14, 30, 84, 76, 31, 39, 51], [30, 70, 12, 79, 97, 17, 69, 46], [13, 70, 17, 99, 76, 70, 85, 1], [69, 41, 93, 47, 10, 93, 19, 30], [69, 97, 15, 30, 75, 28, 47, 67]], [[38, 31, 7, 75, 57, 75, 86, 14], [29, 53, 7, 1, 19, 35, 14, 60], [51, 29, 60, 50, 35, 50, 74, 30], [89, 92, 91, 64, 95, 80, 31, 15], [30, 61, 77, 76, 50, 92, 17, 50], [89, 87, 81, 66, 8, 33, 14, 14], [77, 31, 86, 78, 56, 23, 26, 91], [4, 94, 31, 21, 80, 54, 97, 76]], [[61, 74, 81, 78, 14, 94, 25, 84], [90, 41, 27, 82, 39, 7, 64, 7], [26, 93, 26, 34, 47, 20, 42, 50], [50, 14, 29, 52, 69, 82, 82, 68], [51, 8, 76, 37, 39, 50, 48, 49], [78, 66, 76, 27, 9, 31, 87, 20], [53, 2, 33, 41, 64, 92, 66, 72], [10, 9, 22, 6, 75, 49, 47, 91]], [[57, 40, 50, 5, 72, 93, 98, 5], [70, 91, 43, 19, 42, 8, 3, 1], [54, 17, 13, 93, 84, 4, 51, 37], [5, 18, 7, 45, 84, 58, 82, 38], [48, 82, 94, 37, 76, 70, 51, 49], [43, 72, 73, 2, 87, 96, 27, 72], [18, 94, 32, 6, 14, 16, 15, 42], [98, 48, 79, 7, 74, 1, 64, 69]], [[6, 90, 27, 76, 8, 60, 6, 21], [16, 36, 52, 54, 24, 59, 86, 53], [93, 49, 89, 97, 14, 6, 89, 93], [77, 91, 47, 32, 38, 24, 85, 62], [9, 12, 67, 54, 78, 26, 88, 30], [29, 99, 27, 14, 68, 6, 56, 82], [58, 23, 36, 2, 90, 77, 65, 58], [83, 51, 38, 17, 16, 83, 88, 53]], [[93, 76, 63, 36, 8, 7, 37, 25], [27, 18, 80, 61, 85, 35, 35, 66], [79, 57, 61, 75, 71, 93, 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5}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 18}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 7}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 45}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 84}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 58}, {'i': 'E', 'j': 'D', 'k': 'G', 'cost': 82}, {'i': 'E', 'j': 'D', 'k': 'H', 'cost': 38}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 48}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 82}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 94}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 37}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 76}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 70}, {'i': 'E', 'j': 'E', 'k': 'G', 'cost': 51}, {'i': 'E', 'j': 'E', 'k': 'H', 'cost': 49}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 43}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 72}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 73}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 2}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 87}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 96}, {'i': 'E', 'j': 'F', 'k': 'G', 'cost': 27}, {'i': 'E', 'j': 'F', 'k': 'H', 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'k': 'G', 'cost': 6}, {'i': 'F', 'j': 'A', 'k': 'H', 'cost': 21}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 16}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 36}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 52}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 54}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 24}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 59}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 86}, {'i': 'F', 'j': 'B', 'k': 'H', 'cost': 53}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 93}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 49}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 89}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 97}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 14}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 6}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 89}, {'i': 'F', 'j': 'C', 'k': 'H', 'cost': 93}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 77}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 91}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 47}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 32}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 38}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 24}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 85}, {'i': 'F', 'j': 'D', 'k': 'H', 'cost': 62}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 9}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 12}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 67}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 54}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 78}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 26}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 88}, {'i': 'F', 'j': 'E', 'k': 'H', 'cost': 30}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 29}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 99}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 27}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 14}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 68}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 6}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 56}, {'i': 'F', 'j': 'F', 'k': 'H', 'cost': 82}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 58}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 23}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 36}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 90}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 77}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 65}, {'i': 'F', 'j': 'G', 'k': 'H', 'cost': 58}, {'i': 'F', 'j': 'H', 'k': 'A', 'cost': 83}, {'i': 'F', 'j': 'H', 'k': 'B', 'cost': 51}, {'i': 'F', 'j': 'H', 'k': 'C', 'cost': 38}, {'i': 'F', 'j': 'H', 'k': 'D', 'cost': 17}, {'i': 'F', 'j': 'H', 'k': 'E', 'cost': 16}, {'i': 'F', 'j': 'H', 'k': 'F', 'cost': 83}, {'i': 'F', 'j': 'H', 'k': 'G', 'cost': 88}, {'i': 'F', 'j': 'H', 'k': 'H', 'cost': 53}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 93}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 76}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 63}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 36}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 8}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 7}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 37}, {'i': 'G', 'j': 'A', 'k': 'H', 'cost': 25}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 27}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 18}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 80}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 61}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 85}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 35}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 35}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 66}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 79}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 57}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 61}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 75}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 71}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 93}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 61}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 61}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 85}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 87}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 57}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 16}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 47}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 56}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 96}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 85}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 60}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 25}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 19}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 86}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 77}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 61}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 78}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 56}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 84}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 80}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 10}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 90}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 76}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 50}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 77}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 62}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 80}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 97}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 79}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 81}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 79}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 43}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 32}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 58}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 82}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 16}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 53}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 6}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 9}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 33}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 63}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 38}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 4}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 59}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 78}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 16}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 83}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 11}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 27}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 36}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 22}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 52}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 56}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 85}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 35}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 5}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 23}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 54}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 86}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 75}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 49}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 32}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 33}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 43}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 64}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 22}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 62}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 37}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 37}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 16}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 51}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 71}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 80}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 28}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 80}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 76}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 29}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 37}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 35}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 59}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 92}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 88}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 18}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 17}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 48}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 42}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 60}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 31}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 26}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 70}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 57}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 13}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 64}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 3}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 83}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 90}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 49}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 12}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 31}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 14}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 31}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 12}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 5}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 71}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 48}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 80}]}","[['A', 'F', 'H'], ['B', 'C', 'F'], ['C', 'B', 'C'], ['D', 'E', 'B'], ['E', 'D', 'A'], ['F', 'A', 'G'], ['G', 'H', 'E'], ['H', 'G', 'D']]",41,nl,names
AP3,AP3,"My friend runs a compact assembly line where each incoming order needs to be matched with one machine and one operator, and nothing can be reused: every machine and every operator can only be assigned to a single order. Each possible trio of order, machine and operator has a known processing cost, so they look for the set of assignments that, when adding up the costs of all chosen trios, gives the lowest total. The actual orders, machines, operators and the cost details are listed below.

There are 6 production orders identified as 0, 1, 2, 3, 4, 5.
Meaning: costs form a 3D tensor. For each fixed order_id=i, you are given a machine_id×operator_id matrix whose entry at row machine_id=j and column operator_id=k equals processing_cost(i,j,k). You must pick exactly one (j,k) for every i, with all machine_id and all operator_id used exactly once.
processing_cost_tensor (per-order_id markdown matrices):
## order_id=0
| machine_id\operator_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 8 | 87 | 29 | 88 | 33 | 17 |
| 1 | 57 | 14 | 63 | 65 | 13 | 49 |
| 2 | 19 | 56 | 0 | 52 | 91 | 55 |
| 3 | 24 | 7 | 80 | 40 | 51 | 89 |
| 4 | 66 | 64 | 18 | 61 | 93 | 28 |
| 5 | 59 | 20 | 25 | 33 | 6 | 70 |

## order_id=1
| machine_id\operator_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 67 | 30 | 42 | 76 | 40 | 79 |
| 1 | 75 | 87 | 85 | 36 | 50 | 68 |
| 2 | 12 | 90 | 44 | 81 | 29 | 90 |
| 3 | 38 | 22 | 20 | 25 | 92 | 90 |
| 4 | 87 | 26 | 88 | 92 | 74 | 28 |
| 5 | 79 | 89 | 82 | 17 | 85 | 31 |

## order_id=2
| machine_id\operator_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 14 | 61 | 68 | 34 | 16 | 43 |
| 1 | 5 | 59 | 21 | 37 | 46 | 40 |
| 2 | 19 | 3 | 84 | 26 | 18 | 39 |
| 3 | 15 | 76 | 0 | 77 | 62 | 82 |
| 4 | 94 | 75 | 8 | 42 | 19 | 36 |
| 5 | 6 | 18 | 8 | 60 | 5 | 99 |

## order_id=3
| machine_id\operator_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 56 | 58 | 54 | 88 | 26 | 21 |
| 1 | 33 | 84 | 39 | 52 | 74 | 5 |
| 2 | 55 | 92 | 45 | 80 | 7 | 46 |
| 3 | 47 | 48 | 92 | 89 | 65 | 20 |
| 4 | 77 | 47 | 13 | 30 | 83 | 20 |
| 5 | 97 | 87 | 91 | 92 | 21 | 9 |

## order_id=4
| machine_id\operator_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 32 | 7 | 34 | 59 | 16 | 76 |
| 1 | 92 | 58 | 70 | 34 | 52 | 32 |
| 2 | 37 | 40 | 34 | 42 | 16 | 88 |
| 3 | 80 | 39 | 24 | 4 | 90 | 13 |
| 4 | 22 | 5 | 46 | 18 | 88 | 51 |
| 5 | 62 | 93 | 23 | 75 | 2 | 6 |

## order_id=5
| machine_id\operator_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 33 | 66 | 63 | 2 | 93 | 99 |
| 1 | 99 | 65 | 47 | 57 | 9 | 95 |
| 2 | 71 | 13 | 11 | 62 | 15 | 96 |
| 3 | 20 | 97 | 77 | 47 | 46 | 37 |
| 4 | 55 | 11 | 16 | 30 | 11 | 3 |
| 5 | 46 | 69 | 58 | 39 | 97 | 31 |
They must select a one-to-one assignment of orders to machines and operators that minimizes the total processing cost.

Oh, and when you send back the chosen assignments, a simple JSON sketch like this is handy — nothing fancy, just a list of the triples we pick:

{
  ""solution"": [
    [<order_id>, <machine_id>, <operator_id>],
    ...
  ]
}

This just means ""solution"" contains a list of triples, and each triple is one order together with the machine and operator assigned to it. It's just a template to show the shape I expect — not the actual answer.

Please make sure to use the exact identifiers from the instance input — don't 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”.""","{'cost_tensor': [[[8, 87, 29, 88, 33, 17], [57, 14, 63, 65, 13, 49], [19, 56, 0, 52, 91, 55], [24, 7, 80, 40, 51, 89], [66, 64, 18, 61, 93, 28], [59, 20, 25, 33, 6, 70]], [[67, 30, 42, 76, 40, 79], [75, 87, 85, 36, 50, 68], [12, 90, 44, 81, 29, 90], [38, 22, 20, 25, 92, 90], [87, 26, 88, 92, 74, 28], [79, 89, 82, 17, 85, 31]], [[14, 61, 68, 34, 16, 43], [5, 59, 21, 37, 46, 40], [19, 3, 84, 26, 18, 39], [15, 76, 0, 77, 62, 82], [94, 75, 8, 42, 19, 36], [6, 18, 8, 60, 5, 99]], [[56, 58, 54, 88, 26, 21], [33, 84, 39, 52, 74, 5], [55, 92, 45, 80, 7, 46], [47, 48, 92, 89, 65, 20], [77, 47, 13, 30, 83, 20], [97, 87, 91, 92, 21, 9]], [[32, 7, 34, 59, 16, 76], [92, 58, 70, 34, 52, 32], [37, 40, 34, 42, 16, 88], [80, 39, 24, 4, 90, 13], [22, 5, 46, 18, 88, 51], [62, 93, 23, 75, 2, 6]], [[33, 66, 63, 2, 93, 99], [99, 65, 47, 57, 9, 95], [71, 13, 11, 62, 15, 96], [20, 97, 77, 47, 46, 37], [55, 11, 16, 30, 11, 3], [46, 69, 58, 39, 97, 31]]], 'objective': 30.0}","[[0, 5, 4], [1, 2, 0], [2, 3, 2], [3, 1, 5], [4, 4, 1], [5, 0, 3]]",30.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 8}, {'i': 0, 'j': 0, 'k': 1, 'cost': 87}, {'i': 0, 'j': 0, 'k': 2, 'cost': 29}, {'i': 0, 'j': 0, 'k': 3, 'cost': 88}, {'i': 0, 'j': 0, 'k': 4, 'cost': 33}, {'i': 0, 'j': 0, 'k': 5, 'cost': 17}, {'i': 0, 'j': 1, 'k': 0, 'cost': 57}, {'i': 0, 'j': 1, 'k': 1, 'cost': 14}, {'i': 0, 'j': 1, 'k': 2, 'cost': 63}, {'i': 0, 'j': 1, 'k': 3, 'cost': 65}, {'i': 0, 'j': 1, 'k': 4, 'cost': 13}, {'i': 0, 'j': 1, 'k': 5, 'cost': 49}, {'i': 0, 'j': 2, 'k': 0, 'cost': 19}, {'i': 0, 'j': 2, 'k': 1, 'cost': 56}, {'i': 0, 'j': 2, 'k': 2, 'cost': 0}, {'i': 0, 'j': 2, 'k': 3, 'cost': 52}, {'i': 0, 'j': 2, 'k': 4, 'cost': 91}, {'i': 0, 'j': 2, 'k': 5, 'cost': 55}, {'i': 0, 'j': 3, 'k': 0, 'cost': 24}, {'i': 0, 'j': 3, 'k': 1, 'cost': 7}, {'i': 0, 'j': 3, 'k': 2, 'cost': 80}, {'i': 0, 'j': 3, 'k': 3, 'cost': 40}, {'i': 0, 'j': 3, 'k': 4, 'cost': 51}, {'i': 0, 'j': 3, 'k': 5, 'cost': 89}, {'i': 0, 'j': 4, 'k': 0, 'cost': 66}, {'i': 0, 'j': 4, 'k': 1, 'cost': 64}, {'i': 0, 'j': 4, 'k': 2, 'cost': 18}, {'i': 0, 'j': 4, 'k': 3, 'cost': 61}, {'i': 0, 'j': 4, 'k': 4, 'cost': 93}, {'i': 0, 'j': 4, 'k': 5, 'cost': 28}, {'i': 0, 'j': 5, 'k': 0, 'cost': 59}, {'i': 0, 'j': 5, 'k': 1, 'cost': 20}, {'i': 0, 'j': 5, 'k': 2, 'cost': 25}, {'i': 0, 'j': 5, 'k': 3, 'cost': 33}, {'i': 0, 'j': 5, 'k': 4, 'cost': 6}, {'i': 0, 'j': 5, 'k': 5, 'cost': 70}, {'i': 1, 'j': 0, 'k': 0, 'cost': 67}, {'i': 1, 'j': 0, 'k': 1, 'cost': 30}, {'i': 1, 'j': 0, 'k': 2, 'cost': 42}, {'i': 1, 'j': 0, 'k': 3, 'cost': 76}, {'i': 1, 'j': 0, 'k': 4, 'cost': 40}, {'i': 1, 'j': 0, 'k': 5, 'cost': 79}, {'i': 1, 'j': 1, 'k': 0, 'cost': 75}, {'i': 1, 'j': 1, 'k': 1, 'cost': 87}, {'i': 1, 'j': 1, 'k': 2, 'cost': 85}, {'i': 1, 'j': 1, 'k': 3, 'cost': 36}, {'i': 1, 'j': 1, 'k': 4, 'cost': 50}, {'i': 1, 'j': 1, 'k': 5, 'cost': 68}, {'i': 1, 'j': 2, 'k': 0, 'cost': 12}, {'i': 1, 'j': 2, 'k': 1, 'cost': 90}, {'i': 1, 'j': 2, 'k': 2, 'cost': 44}, {'i': 1, 'j': 2, 'k': 3, 'cost': 81}, {'i': 1, 'j': 2, 'k': 4, 'cost': 29}, {'i': 1, 'j': 2, 'k': 5, 'cost': 90}, {'i': 1, 'j': 3, 'k': 0, 'cost': 38}, {'i': 1, 'j': 3, 'k': 1, 'cost': 22}, {'i': 1, 'j': 3, 'k': 2, 'cost': 20}, {'i': 1, 'j': 3, 'k': 3, 'cost': 25}, {'i': 1, 'j': 3, 'k': 4, 'cost': 92}, {'i': 1, 'j': 3, 'k': 5, 'cost': 90}, {'i': 1, 'j': 4, 'k': 0, 'cost': 87}, {'i': 1, 'j': 4, 'k': 1, 'cost': 26}, {'i': 1, 'j': 4, 'k': 2, 'cost': 88}, {'i': 1, 'j': 4, 'k': 3, 'cost': 92}, {'i': 1, 'j': 4, 'k': 4, 'cost': 74}, {'i': 1, 'j': 4, 'k': 5, 'cost': 28}, {'i': 1, 'j': 5, 'k': 0, 'cost': 79}, {'i': 1, 'j': 5, 'k': 1, 'cost': 89}, {'i': 1, 'j': 5, 'k': 2, 'cost': 82}, {'i': 1, 'j': 5, 'k': 3, 'cost': 17}, {'i': 1, 'j': 5, 'k': 4, 'cost': 85}, {'i': 1, 'j': 5, 'k': 5, 'cost': 31}, {'i': 2, 'j': 0, 'k': 0, 'cost': 14}, {'i': 2, 'j': 0, 'k': 1, 'cost': 61}, {'i': 2, 'j': 0, 'k': 2, 'cost': 68}, {'i': 2, 'j': 0, 'k': 3, 'cost': 34}, {'i': 2, 'j': 0, 'k': 4, 'cost': 16}, {'i': 2, 'j': 0, 'k': 5, 'cost': 43}, {'i': 2, 'j': 1, 'k': 0, 'cost': 5}, {'i': 2, 'j': 1, 'k': 1, 'cost': 59}, {'i': 2, 'j': 1, 'k': 2, 'cost': 21}, {'i': 2, 'j': 1, 'k': 3, 'cost': 37}, {'i': 2, 'j': 1, 'k': 4, 'cost': 46}, {'i': 2, 'j': 1, 'k': 5, 'cost': 40}, {'i': 2, 'j': 2, 'k': 0, 'cost': 19}, {'i': 2, 'j': 2, 'k': 1, 'cost': 3}, {'i': 2, 'j': 2, 'k': 2, 'cost': 84}, {'i': 2, 'j': 2, 'k': 3, 'cost': 26}, {'i': 2, 'j': 2, 'k': 4, 'cost': 18}, {'i': 2, 'j': 2, 'k': 5, 'cost': 39}, {'i': 2, 'j': 3, 'k': 0, 'cost': 15}, {'i': 2, 'j': 3, 'k': 1, 'cost': 76}, {'i': 2, 'j': 3, 'k': 2, 'cost': 0}, {'i': 2, 'j': 3, 'k': 3, 'cost': 77}, {'i': 2, 'j': 3, 'k': 4, 'cost': 62}, {'i': 2, 'j': 3, 'k': 5, 'cost': 82}, {'i': 2, 'j': 4, 'k': 0, 'cost': 94}, {'i': 2, 'j': 4, 'k': 1, 'cost': 75}, {'i': 2, 'j': 4, 'k': 2, 'cost': 8}, {'i': 2, 'j': 4, 'k': 3, 'cost': 42}, {'i': 2, 'j': 4, 'k': 4, 'cost': 19}, {'i': 2, 'j': 4, 'k': 5, 'cost': 36}, {'i': 2, 'j': 5, 'k': 0, 'cost': 6}, {'i': 2, 'j': 5, 'k': 1, 'cost': 18}, {'i': 2, 'j': 5, 'k': 2, 'cost': 8}, {'i': 2, 'j': 5, 'k': 3, 'cost': 60}, {'i': 2, 'j': 5, 'k': 4, 'cost': 5}, {'i': 2, 'j': 5, 'k': 5, 'cost': 99}, {'i': 3, 'j': 0, 'k': 0, 'cost': 56}, {'i': 3, 'j': 0, 'k': 1, 'cost': 58}, {'i': 3, 'j': 0, 'k': 2, 'cost': 54}, {'i': 3, 'j': 0, 'k': 3, 'cost': 88}, {'i': 3, 'j': 0, 'k': 4, 'cost': 26}, {'i': 3, 'j': 0, 'k': 5, 'cost': 21}, {'i': 3, 'j': 1, 'k': 0, 'cost': 33}, {'i': 3, 'j': 1, 'k': 1, 'cost': 84}, {'i': 3, 'j': 1, 'k': 2, 'cost': 39}, {'i': 3, 'j': 1, 'k': 3, 'cost': 52}, {'i': 3, 'j': 1, 'k': 4, 'cost': 74}, {'i': 3, 'j': 1, 'k': 5, 'cost': 5}, {'i': 3, 'j': 2, 'k': 0, 'cost': 55}, {'i': 3, 'j': 2, 'k': 1, 'cost': 92}, {'i': 3, 'j': 2, 'k': 2, 'cost': 45}, {'i': 3, 'j': 2, 'k': 3, 'cost': 80}, {'i': 3, 'j': 2, 'k': 4, 'cost': 7}, {'i': 3, 'j': 2, 'k': 5, 'cost': 46}, {'i': 3, 'j': 3, 'k': 0, 'cost': 47}, {'i': 3, 'j': 3, 'k': 1, 'cost': 48}, {'i': 3, 'j': 3, 'k': 2, 'cost': 92}, {'i': 3, 'j': 3, 'k': 3, 'cost': 89}, {'i': 3, 'j': 3, 'k': 4, 'cost': 65}, {'i': 3, 'j': 3, 'k': 5, 'cost': 20}, {'i': 3, 'j': 4, 'k': 0, 'cost': 77}, {'i': 3, 'j': 4, 'k': 1, 'cost': 47}, {'i': 3, 'j': 4, 'k': 2, 'cost': 13}, {'i': 3, 'j': 4, 'k': 3, 'cost': 30}, {'i': 3, 'j': 4, 'k': 4, 'cost': 83}, {'i': 3, 'j': 4, 'k': 5, 'cost': 20}, {'i': 3, 'j': 5, 'k': 0, 'cost': 97}, {'i': 3, 'j': 5, 'k': 1, 'cost': 87}, {'i': 3, 'j': 5, 'k': 2, 'cost': 91}, {'i': 3, 'j': 5, 'k': 3, 'cost': 92}, {'i': 3, 'j': 5, 'k': 4, 'cost': 21}, {'i': 3, 'j': 5, 'k': 5, 'cost': 9}, {'i': 4, 'j': 0, 'k': 0, 'cost': 32}, {'i': 4, 'j': 0, 'k': 1, 'cost': 7}, {'i': 4, 'j': 0, 'k': 2, 'cost': 34}, {'i': 4, 'j': 0, 'k': 3, 'cost': 59}, {'i': 4, 'j': 0, 'k': 4, 'cost': 16}, {'i': 4, 'j': 0, 'k': 5, 'cost': 76}, {'i': 4, 'j': 1, 'k': 0, 'cost': 92}, {'i': 4, 'j': 1, 'k': 1, 'cost': 58}, {'i': 4, 'j': 1, 'k': 2, 'cost': 70}, {'i': 4, 'j': 1, 'k': 3, 'cost': 34}, {'i': 4, 'j': 1, 'k': 4, 'cost': 52}, {'i': 4, 'j': 1, 'k': 5, 'cost': 32}, {'i': 4, 'j': 2, 'k': 0, 'cost': 37}, {'i': 4, 'j': 2, 'k': 1, 'cost': 40}, {'i': 4, 'j': 2, 'k': 2, 'cost': 34}, {'i': 4, 'j': 2, 'k': 3, 'cost': 42}, {'i': 4, 'j': 2, 'k': 4, 'cost': 16}, {'i': 4, 'j': 2, 'k': 5, 'cost': 88}, {'i': 4, 'j': 3, 'k': 0, 'cost': 80}, {'i': 4, 'j': 3, 'k': 1, 'cost': 39}, {'i': 4, 'j': 3, 'k': 2, 'cost': 24}, {'i': 4, 'j': 3, 'k': 3, 'cost': 4}, {'i': 4, 'j': 3, 'k': 4, 'cost': 90}, {'i': 4, 'j': 3, 'k': 5, 'cost': 13}, {'i': 4, 'j': 4, 'k': 0, 'cost': 22}, {'i': 4, 'j': 4, 'k': 1, 'cost': 5}, {'i': 4, 'j': 4, 'k': 2, 'cost': 46}, {'i': 4, 'j': 4, 'k': 3, 'cost': 18}, {'i': 4, 'j': 4, 'k': 4, 'cost': 88}, {'i': 4, 'j': 4, 'k': 5, 'cost': 51}, {'i': 4, 'j': 5, 'k': 0, 'cost': 62}, {'i': 4, 'j': 5, 'k': 1, 'cost': 93}, {'i': 4, 'j': 5, 'k': 2, 'cost': 23}, {'i': 4, 'j': 5, 'k': 3, 'cost': 75}, {'i': 4, 'j': 5, 'k': 4, 'cost': 2}, {'i': 4, 'j': 5, 'k': 5, 'cost': 6}, {'i': 5, 'j': 0, 'k': 0, 'cost': 33}, {'i': 5, 'j': 0, 'k': 1, 'cost': 66}, {'i': 5, 'j': 0, 'k': 2, 'cost': 63}, {'i': 5, 'j': 0, 'k': 3, 'cost': 2}, {'i': 5, 'j': 0, 'k': 4, 'cost': 93}, {'i': 5, 'j': 0, 'k': 5, 'cost': 99}, {'i': 5, 'j': 1, 'k': 0, 'cost': 99}, {'i': 5, 'j': 1, 'k': 1, 'cost': 65}, {'i': 5, 'j': 1, 'k': 2, 'cost': 47}, {'i': 5, 'j': 1, 'k': 3, 'cost': 57}, {'i': 5, 'j': 1, 'k': 4, 'cost': 9}, {'i': 5, 'j': 1, 'k': 5, 'cost': 95}, {'i': 5, 'j': 2, 'k': 0, 'cost': 71}, {'i': 5, 'j': 2, 'k': 1, 'cost': 13}, {'i': 5, 'j': 2, 'k': 2, 'cost': 11}, {'i': 5, 'j': 2, 'k': 3, 'cost': 62}, {'i': 5, 'j': 2, 'k': 4, 'cost': 15}, {'i': 5, 'j': 2, 'k': 5, 'cost': 96}, {'i': 5, 'j': 3, 'k': 0, 'cost': 20}, {'i': 5, 'j': 3, 'k': 1, 'cost': 97}, {'i': 5, 'j': 3, 'k': 2, 'cost': 77}, {'i': 5, 'j': 3, 'k': 3, 'cost': 47}, {'i': 5, 'j': 3, 'k': 4, 'cost': 46}, {'i': 5, 'j': 3, 'k': 5, 'cost': 37}, {'i': 5, 'j': 4, 'k': 0, 'cost': 55}, {'i': 5, 'j': 4, 'k': 1, 'cost': 11}, {'i': 5, 'j': 4, 'k': 2, 'cost': 16}, {'i': 5, 'j': 4, 'k': 3, 'cost': 30}, {'i': 5, 'j': 4, 'k': 4, 'cost': 11}, {'i': 5, 'j': 4, 'k': 5, 'cost': 3}, {'i': 5, 'j': 5, 'k': 0, 'cost': 46}, {'i': 5, 'j': 5, 'k': 1, 'cost': 69}, {'i': 5, 'j': 5, 'k': 2, 'cost': 58}, {'i': 5, 'j': 5, 'k': 3, 'cost': 39}, {'i': 5, 'j': 5, 'k': 4, 'cost': 97}, {'i': 5, 'j': 5, 'k': 5, 'cost': 31}]}","[[0, 5, 4], [1, 2, 0], [2, 3, 2], [3, 1, 5], [4, 4, 1], [5, 0, 3]]",42,nl,0
AP3,AP3,"Someone is organizing a one-day outreach effort and has to pair volunteers and cars with sites. For each site there are different volunteer+vehicle choices, each with a specific travel plus coordination cost; the plan that wins is the one where those costs, summed over every site, come out smallest. It’s crucial that every site gets one volunteer and one vehicle, and no volunteer or vehicle goes to more than one site or gets left out. The specific details and cost table follow below.

{
  ""number_of_sites"": 6,
  ""index_identifiers"": [
    1,
    2,
    3,
    4,
    5,
    6
  ]
}

# Meaning: costs form a 3D tensor. For each fixed site_id=i, you are given a volunteer_id×vehicle_id matrix whose entry at row volunteer_id=j and column vehicle_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all volunteer_id and all vehicle_id used exactly once.
# assignment_cost_tensor (per-site_id markdown matrices)

## site_id=1
| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 98 | 39 | 80 | 80 | 39 | 69 |
| 2 | 11 | 97 | 80 | 1 | 26 | 59 |
| 3 | 20 | 57 | 71 | 81 | 54 | 40 |
| 4 | 40 | 10 | 69 | 43 | 28 | 33 |
| 5 | 91 | 79 | 23 | 9 | 7 | 42 |
| 6 | 58 | 2 | 16 | 25 | 39 | 77 |

## site_id=2
| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 11 | 31 | 6 | 46 | 47 | 47 |
| 2 | 28 | 45 | 21 | 86 | 33 | 50 |
| 3 | 58 | 29 | 71 | 70 | 30 | 58 |
| 4 | 70 | 0 | 76 | 92 | 20 | 50 |
| 5 | 59 | 63 | 11 | 3 | 35 | 60 |
| 6 | 15 | 53 | 97 | 28 | 43 | 73 |

## site_id=3
| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 47 | 47 | 14 | 3 | 54 | 78 |
| 2 | 97 | 34 | 75 | 51 | 28 | 46 |
| 3 | 95 | 21 | 0 | 36 | 77 | 5 |
| 4 | 46 | 38 | 2 | 27 | 40 | 67 |
| 5 | 23 | 97 | 44 | 45 | 13 | 77 |
| 6 | 36 | 16 | 35 | 48 | 16 | 39 |

## site_id=4
| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 66 | 41 | 73 | 51 | 93 | 83 |
| 2 | 41 | 5 | 86 | 63 | 82 | 5 |
| 3 | 88 | 1 | 83 | 10 | 62 | 18 |
| 4 | 7 | 47 | 6 | 15 | 91 | 87 |
| 5 | 88 | 81 | 15 | 11 | 21 | 63 |
| 6 | 95 | 15 | 30 | 47 | 44 | 13 |

## site_id=5
| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 60 | 39 | 95 | 47 | 64 | 72 |
| 2 | 16 | 44 | 3 | 1 | 18 | 72 |
| 3 | 33 | 84 | 84 | 0 | 14 | 73 |
| 4 | 56 | 88 | 5 | 24 | 11 | 54 |
| 5 | 39 | 38 | 61 | 78 | 78 | 84 |
| 6 | 70 | 97 | 82 | 57 | 63 | 62 |

## site_id=6
| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 1 | 43 | 45 | 12 | 45 |
| 2 | 42 | 40 | 49 | 8 | 92 | 49 |
| 3 | 50 | 76 | 6 | 29 | 65 | 38 |
| 4 | 74 | 18 | 66 | 31 | 35 | 53 |
| 5 | 84 | 60 | 72 | 80 | 37 | 10 |
| 6 | 84 | 80 | 86 | 46 | 78 | 61 |

Also, when you send back the final plan, please stick to a simple JSON layout so it's easy to check automatically and by eye.

{
  ""solution"": [
    [<site_id>, <volunteer_id>, <car_id>],
    ...
  ]
}

Each inner array is one chosen triple: the site, the volunteer who'll go there, and the car they'll use. Think of it like filling out a short form where each row lists a site and the pair (person + vehicle) assigned to it. This JSON is just a sketch of the shape I need — not the actual assignments.

Please make sure to 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”.","{'cost_tensor': [[[98, 39, 80, 80, 39, 69], [11, 97, 80, 1, 26, 59], [20, 57, 71, 81, 54, 40], [40, 10, 69, 43, 28, 33], [91, 79, 23, 9, 7, 42], [58, 2, 16, 25, 39, 77]], [[11, 31, 6, 46, 47, 47], [28, 45, 21, 86, 33, 50], [58, 29, 71, 70, 30, 58], [70, 0, 76, 92, 20, 50], [59, 63, 11, 3, 35, 60], [15, 53, 97, 28, 43, 73]], [[47, 47, 14, 3, 54, 78], [97, 34, 75, 51, 28, 46], [95, 21, 0, 36, 77, 5], [46, 38, 2, 27, 40, 67], [23, 97, 44, 45, 13, 77], [36, 16, 35, 48, 16, 39]], [[66, 41, 73, 51, 93, 83], [41, 5, 86, 63, 82, 5], [88, 1, 83, 10, 62, 18], [7, 47, 6, 15, 91, 87], [88, 81, 15, 11, 21, 63], [95, 15, 30, 47, 44, 13]], [[60, 39, 95, 47, 64, 72], [16, 44, 3, 1, 18, 72], [33, 84, 84, 0, 14, 73], [56, 88, 5, 24, 11, 54], [39, 38, 61, 78, 78, 84], [70, 97, 82, 57, 63, 62]], [[2, 1, 43, 45, 12, 45], [42, 40, 49, 8, 92, 49], [50, 76, 6, 29, 65, 38], [74, 18, 66, 31, 35, 53], [84, 60, 72, 80, 37, 10], [84, 80, 86, 46, 78, 61]]], 'objective': 23.0}","[[0, 4, 4], [1, 3, 1], [2, 2, 2], [3, 5, 5], [4, 1, 3], [5, 0, 0]]",23.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 98}, {'i': 1, 'j': 1, 'k': 2, 'cost': 39}, {'i': 1, 'j': 1, 'k': 3, 'cost': 80}, {'i': 1, 'j': 1, 'k': 4, 'cost': 80}, {'i': 1, 'j': 1, 'k': 5, 'cost': 39}, {'i': 1, 'j': 1, 'k': 6, 'cost': 69}, {'i': 1, 'j': 2, 'k': 1, 'cost': 11}, {'i': 1, 'j': 2, 'k': 2, 'cost': 97}, {'i': 1, 'j': 2, 'k': 3, 'cost': 80}, {'i': 1, 'j': 2, 'k': 4, 'cost': 1}, {'i': 1, 'j': 2, 'k': 5, 'cost': 26}, {'i': 1, 'j': 2, 'k': 6, 'cost': 59}, {'i': 1, 'j': 3, 'k': 1, 'cost': 20}, {'i': 1, 'j': 3, 'k': 2, 'cost': 57}, {'i': 1, 'j': 3, 'k': 3, 'cost': 71}, {'i': 1, 'j': 3, 'k': 4, 'cost': 81}, {'i': 1, 'j': 3, 'k': 5, 'cost': 54}, {'i': 1, 'j': 3, 'k': 6, 'cost': 40}, {'i': 1, 'j': 4, 'k': 1, 'cost': 40}, {'i': 1, 'j': 4, 'k': 2, 'cost': 10}, {'i': 1, 'j': 4, 'k': 3, 'cost': 69}, {'i': 1, 'j': 4, 'k': 4, 'cost': 43}, {'i': 1, 'j': 4, 'k': 5, 'cost': 28}, {'i': 1, 'j': 4, 'k': 6, 'cost': 33}, {'i': 1, 'j': 5, 'k': 1, 'cost': 91}, {'i': 1, 'j': 5, 'k': 2, 'cost': 79}, {'i': 1, 'j': 5, 'k': 3, 'cost': 23}, {'i': 1, 'j': 5, 'k': 4, 'cost': 9}, {'i': 1, 'j': 5, 'k': 5, 'cost': 7}, {'i': 1, 'j': 5, 'k': 6, 'cost': 42}, {'i': 1, 'j': 6, 'k': 1, 'cost': 58}, {'i': 1, 'j': 6, 'k': 2, 'cost': 2}, {'i': 1, 'j': 6, 'k': 3, 'cost': 16}, {'i': 1, 'j': 6, 'k': 4, 'cost': 25}, {'i': 1, 'j': 6, 'k': 5, 'cost': 39}, {'i': 1, 'j': 6, 'k': 6, 'cost': 77}, {'i': 2, 'j': 1, 'k': 1, 'cost': 11}, {'i': 2, 'j': 1, 'k': 2, 'cost': 31}, {'i': 2, 'j': 1, 'k': 3, 'cost': 6}, {'i': 2, 'j': 1, 'k': 4, 'cost': 46}, {'i': 2, 'j': 1, 'k': 5, 'cost': 47}, {'i': 2, 'j': 1, 'k': 6, 'cost': 47}, {'i': 2, 'j': 2, 'k': 1, 'cost': 28}, {'i': 2, 'j': 2, 'k': 2, 'cost': 45}, {'i': 2, 'j': 2, 'k': 3, 'cost': 21}, {'i': 2, 'j': 2, 'k': 4, 'cost': 86}, {'i': 2, 'j': 2, 'k': 5, 'cost': 33}, {'i': 2, 'j': 2, 'k': 6, 'cost': 50}, {'i': 2, 'j': 3, 'k': 1, 'cost': 58}, {'i': 2, 'j': 3, 'k': 2, 'cost': 29}, {'i': 2, 'j': 3, 'k': 3, 'cost': 71}, {'i': 2, 'j': 3, 'k': 4, 'cost': 70}, {'i': 2, 'j': 3, 'k': 5, 'cost': 30}, {'i': 2, 'j': 3, 'k': 6, 'cost': 58}, {'i': 2, 'j': 4, 'k': 1, 'cost': 70}, {'i': 2, 'j': 4, 'k': 2, 'cost': 0}, {'i': 2, 'j': 4, 'k': 3, 'cost': 76}, {'i': 2, 'j': 4, 'k': 4, 'cost': 92}, {'i': 2, 'j': 4, 'k': 5, 'cost': 20}, {'i': 2, 'j': 4, 'k': 6, 'cost': 50}, {'i': 2, 'j': 5, 'k': 1, 'cost': 59}, {'i': 2, 'j': 5, 'k': 2, 'cost': 63}, {'i': 2, 'j': 5, 'k': 3, 'cost': 11}, {'i': 2, 'j': 5, 'k': 4, 'cost': 3}, {'i': 2, 'j': 5, 'k': 5, 'cost': 35}, {'i': 2, 'j': 5, 'k': 6, 'cost': 60}, {'i': 2, 'j': 6, 'k': 1, 'cost': 15}, {'i': 2, 'j': 6, 'k': 2, 'cost': 53}, {'i': 2, 'j': 6, 'k': 3, 'cost': 97}, {'i': 2, 'j': 6, 'k': 4, 'cost': 28}, {'i': 2, 'j': 6, 'k': 5, 'cost': 43}, {'i': 2, 'j': 6, 'k': 6, 'cost': 73}, {'i': 3, 'j': 1, 'k': 1, 'cost': 47}, {'i': 3, 'j': 1, 'k': 2, 'cost': 47}, {'i': 3, 'j': 1, 'k': 3, 'cost': 14}, {'i': 3, 'j': 1, 'k': 4, 'cost': 3}, {'i': 3, 'j': 1, 'k': 5, 'cost': 54}, {'i': 3, 'j': 1, 'k': 6, 'cost': 78}, {'i': 3, 'j': 2, 'k': 1, 'cost': 97}, {'i': 3, 'j': 2, 'k': 2, 'cost': 34}, {'i': 3, 'j': 2, 'k': 3, 'cost': 75}, {'i': 3, 'j': 2, 'k': 4, 'cost': 51}, {'i': 3, 'j': 2, 'k': 5, 'cost': 28}, {'i': 3, 'j': 2, 'k': 6, 'cost': 46}, {'i': 3, 'j': 3, 'k': 1, 'cost': 95}, {'i': 3, 'j': 3, 'k': 2, 'cost': 21}, {'i': 3, 'j': 3, 'k': 3, 'cost': 0}, {'i': 3, 'j': 3, 'k': 4, 'cost': 36}, {'i': 3, 'j': 3, 'k': 5, 'cost': 77}, {'i': 3, 'j': 3, 'k': 6, 'cost': 5}, {'i': 3, 'j': 4, 'k': 1, 'cost': 46}, {'i': 3, 'j': 4, 'k': 2, 'cost': 38}, {'i': 3, 'j': 4, 'k': 3, 'cost': 2}, {'i': 3, 'j': 4, 'k': 4, 'cost': 27}, {'i': 3, 'j': 4, 'k': 5, 'cost': 40}, {'i': 3, 'j': 4, 'k': 6, 'cost': 67}, {'i': 3, 'j': 5, 'k': 1, 'cost': 23}, {'i': 3, 'j': 5, 'k': 2, 'cost': 97}, {'i': 3, 'j': 5, 'k': 3, 'cost': 44}, {'i': 3, 'j': 5, 'k': 4, 'cost': 45}, {'i': 3, 'j': 5, 'k': 5, 'cost': 13}, {'i': 3, 'j': 5, 'k': 6, 'cost': 77}, {'i': 3, 'j': 6, 'k': 1, 'cost': 36}, {'i': 3, 'j': 6, 'k': 2, 'cost': 16}, {'i': 3, 'j': 6, 'k': 3, 'cost': 35}, {'i': 3, 'j': 6, 'k': 4, 'cost': 48}, {'i': 3, 'j': 6, 'k': 5, 'cost': 16}, {'i': 3, 'j': 6, 'k': 6, 'cost': 39}, {'i': 4, 'j': 1, 'k': 1, 'cost': 66}, {'i': 4, 'j': 1, 'k': 2, 'cost': 41}, {'i': 4, 'j': 1, 'k': 3, 'cost': 73}, {'i': 4, 'j': 1, 'k': 4, 'cost': 51}, {'i': 4, 'j': 1, 'k': 5, 'cost': 93}, {'i': 4, 'j': 1, 'k': 6, 'cost': 83}, {'i': 4, 'j': 2, 'k': 1, 'cost': 41}, {'i': 4, 'j': 2, 'k': 2, 'cost': 5}, {'i': 4, 'j': 2, 'k': 3, 'cost': 86}, {'i': 4, 'j': 2, 'k': 4, 'cost': 63}, {'i': 4, 'j': 2, 'k': 5, 'cost': 82}, {'i': 4, 'j': 2, 'k': 6, 'cost': 5}, {'i': 4, 'j': 3, 'k': 1, 'cost': 88}, {'i': 4, 'j': 3, 'k': 2, 'cost': 1}, {'i': 4, 'j': 3, 'k': 3, 'cost': 83}, {'i': 4, 'j': 3, 'k': 4, 'cost': 10}, {'i': 4, 'j': 3, 'k': 5, 'cost': 62}, {'i': 4, 'j': 3, 'k': 6, 'cost': 18}, {'i': 4, 'j': 4, 'k': 1, 'cost': 7}, {'i': 4, 'j': 4, 'k': 2, 'cost': 47}, {'i': 4, 'j': 4, 'k': 3, 'cost': 6}, {'i': 4, 'j': 4, 'k': 4, 'cost': 15}, {'i': 4, 'j': 4, 'k': 5, 'cost': 91}, {'i': 4, 'j': 4, 'k': 6, 'cost': 87}, {'i': 4, 'j': 5, 'k': 1, 'cost': 88}, {'i': 4, 'j': 5, 'k': 2, 'cost': 81}, {'i': 4, 'j': 5, 'k': 3, 'cost': 15}, {'i': 4, 'j': 5, 'k': 4, 'cost': 11}, {'i': 4, 'j': 5, 'k': 5, 'cost': 21}, {'i': 4, 'j': 5, 'k': 6, 'cost': 63}, {'i': 4, 'j': 6, 'k': 1, 'cost': 95}, {'i': 4, 'j': 6, 'k': 2, 'cost': 15}, {'i': 4, 'j': 6, 'k': 3, 'cost': 30}, {'i': 4, 'j': 6, 'k': 4, 'cost': 47}, {'i': 4, 'j': 6, 'k': 5, 'cost': 44}, {'i': 4, 'j': 6, 'k': 6, 'cost': 13}, {'i': 5, 'j': 1, 'k': 1, 'cost': 60}, {'i': 5, 'j': 1, 'k': 2, 'cost': 39}, {'i': 5, 'j': 1, 'k': 3, 'cost': 95}, {'i': 5, 'j': 1, 'k': 4, 'cost': 47}, {'i': 5, 'j': 1, 'k': 5, 'cost': 64}, {'i': 5, 'j': 1, 'k': 6, 'cost': 72}, {'i': 5, 'j': 2, 'k': 1, 'cost': 16}, {'i': 5, 'j': 2, 'k': 2, 'cost': 44}, {'i': 5, 'j': 2, 'k': 3, 'cost': 3}, {'i': 5, 'j': 2, 'k': 4, 'cost': 1}, {'i': 5, 'j': 2, 'k': 5, 'cost': 18}, {'i': 5, 'j': 2, 'k': 6, 'cost': 72}, {'i': 5, 'j': 3, 'k': 1, 'cost': 33}, {'i': 5, 'j': 3, 'k': 2, 'cost': 84}, {'i': 5, 'j': 3, 'k': 3, 'cost': 84}, {'i': 5, 'j': 3, 'k': 4, 'cost': 0}, {'i': 5, 'j': 3, 'k': 5, 'cost': 14}, {'i': 5, 'j': 3, 'k': 6, 'cost': 73}, {'i': 5, 'j': 4, 'k': 1, 'cost': 56}, {'i': 5, 'j': 4, 'k': 2, 'cost': 88}, {'i': 5, 'j': 4, 'k': 3, 'cost': 5}, {'i': 5, 'j': 4, 'k': 4, 'cost': 24}, {'i': 5, 'j': 4, 'k': 5, 'cost': 11}, {'i': 5, 'j': 4, 'k': 6, 'cost': 54}, {'i': 5, 'j': 5, 'k': 1, 'cost': 39}, {'i': 5, 'j': 5, 'k': 2, 'cost': 38}, {'i': 5, 'j': 5, 'k': 3, 'cost': 61}, {'i': 5, 'j': 5, 'k': 4, 'cost': 78}, {'i': 5, 'j': 5, 'k': 5, 'cost': 78}, {'i': 5, 'j': 5, 'k': 6, 'cost': 84}, {'i': 5, 'j': 6, 'k': 1, 'cost': 70}, {'i': 5, 'j': 6, 'k': 2, 'cost': 97}, {'i': 5, 'j': 6, 'k': 3, 'cost': 82}, {'i': 5, 'j': 6, 'k': 4, 'cost': 57}, {'i': 5, 'j': 6, 'k': 5, 'cost': 63}, {'i': 5, 'j': 6, 'k': 6, 'cost': 62}, {'i': 6, 'j': 1, 'k': 1, 'cost': 2}, {'i': 6, 'j': 1, 'k': 2, 'cost': 1}, {'i': 6, 'j': 1, 'k': 3, 'cost': 43}, {'i': 6, 'j': 1, 'k': 4, 'cost': 45}, {'i': 6, 'j': 1, 'k': 5, 'cost': 12}, {'i': 6, 'j': 1, 'k': 6, 'cost': 45}, {'i': 6, 'j': 2, 'k': 1, 'cost': 42}, {'i': 6, 'j': 2, 'k': 2, 'cost': 40}, {'i': 6, 'j': 2, 'k': 3, 'cost': 49}, {'i': 6, 'j': 2, 'k': 4, 'cost': 8}, {'i': 6, 'j': 2, 'k': 5, 'cost': 92}, {'i': 6, 'j': 2, 'k': 6, 'cost': 49}, {'i': 6, 'j': 3, 'k': 1, 'cost': 50}, {'i': 6, 'j': 3, 'k': 2, 'cost': 76}, {'i': 6, 'j': 3, 'k': 3, 'cost': 6}, {'i': 6, 'j': 3, 'k': 4, 'cost': 29}, {'i': 6, 'j': 3, 'k': 5, 'cost': 65}, {'i': 6, 'j': 3, 'k': 6, 'cost': 38}, {'i': 6, 'j': 4, 'k': 1, 'cost': 74}, {'i': 6, 'j': 4, 'k': 2, 'cost': 18}, {'i': 6, 'j': 4, 'k': 3, 'cost': 66}, {'i': 6, 'j': 4, 'k': 4, 'cost': 31}, {'i': 6, 'j': 4, 'k': 5, 'cost': 35}, {'i': 6, 'j': 4, 'k': 6, 'cost': 53}, {'i': 6, 'j': 5, 'k': 1, 'cost': 84}, {'i': 6, 'j': 5, 'k': 2, 'cost': 60}, {'i': 6, 'j': 5, 'k': 3, 'cost': 72}, {'i': 6, 'j': 5, 'k': 4, 'cost': 80}, {'i': 6, 'j': 5, 'k': 5, 'cost': 37}, {'i': 6, 'j': 5, 'k': 6, 'cost': 10}, {'i': 6, 'j': 6, 'k': 1, 'cost': 84}, {'i': 6, 'j': 6, 'k': 2, 'cost': 80}, {'i': 6, 'j': 6, 'k': 3, 'cost': 86}, {'i': 6, 'j': 6, 'k': 4, 'cost': 46}, {'i': 6, 'j': 6, 'k': 5, 'cost': 78}, {'i': 6, 'j': 6, 'k': 6, 'cost': 61}]}","[[1, 5, 5], [2, 4, 2], [3, 3, 3], [4, 6, 6], [5, 2, 4], [6, 1, 1]]",43,json,1
AP3,AP3,"We’re juggling appointments at the shop: every customer must be matched with one stylist and one fitting room, and each stylist and each room can only serve one customer that day. Every possible trio comes with a cost, so the idea is to choose a trio for each customer so the sum of all those trio-costs is as low as it can be. The specific numbers and options follow below.

# num_customers=8
# index_ids=A, B, C, D, E, F, G, H

# Meaning: costs form a 3D tensor. For each fixed customer_id=i, you are given a stylist_id×fitting_room_id matrix whose entry at row stylist_id=j and column fitting_room_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all stylist_id and all fitting_room_id used exactly once.
# assignment_cost_tensor (per-customer_id markdown matrices)

## customer_id=A
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 79 | 90 | 60 | 37 | 68 | 64 | 32 | 59 |
| B | 24 | 34 | 52 | 25 | 40 | 63 | 85 | 78 |
| C | 1 | 71 | 18 | 11 | 40 | 71 | 49 | 28 |
| D | 17 | 62 | 69 | 54 | 32 | 53 | 10 | 30 |
| E | 64 | 85 | 14 | 1 | 77 | 65 | 80 | 5 |
| F | 91 | 92 | 71 | 85 | 66 | 36 | 59 | 43 |
| G | 8 | 65 | 87 | 1 | 96 | 53 | 82 | 3 |
| H | 75 | 87 | 19 | 41 | 14 | 50 | 98 | 20 |

## customer_id=B
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 76 | 35 | 93 | 13 | 0 | 39 | 83 | 69 |
| B | 43 | 31 | 83 | 95 | 15 | 75 | 85 | 99 |
| C | 93 | 86 | 30 | 0 | 57 | 0 | 98 | 82 |
| D | 58 | 43 | 44 | 86 | 19 | 40 | 44 | 35 |
| E | 64 | 4 | 43 | 81 | 96 | 42 | 38 | 73 |
| F | 41 | 59 | 62 | 1 | 40 | 51 | 46 | 69 |
| G | 48 | 49 | 55 | 43 | 96 | 90 | 66 | 41 |
| H | 54 | 47 | 29 | 1 | 21 | 96 | 16 | 24 |

## customer_id=C
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 75 | 27 | 64 | 87 | 25 | 7 | 25 | 64 |
| B | 2 | 94 | 4 | 56 | 54 | 81 | 18 | 60 |
| C | 69 | 74 | 59 | 46 | 73 | 29 | 73 | 45 |
| D | 18 | 80 | 5 | 67 | 64 | 94 | 8 | 15 |
| E | 74 | 75 | 30 | 24 | 23 | 54 | 67 | 68 |
| F | 55 | 45 | 88 | 77 | 33 | 43 | 22 | 51 |
| G | 47 | 81 | 74 | 77 | 53 | 81 | 34 | 74 |
| H | 47 | 21 | 91 | 60 | 38 | 19 | 3 | 3 |

## customer_id=D
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 68 | 4 | 53 | 32 | 37 | 4 | 25 | 95 |
| B | 73 | 37 | 38 | 16 | 37 | 32 | 6 | 86 |
| C | 32 | 35 | 49 | 54 | 34 | 46 | 46 | 78 |
| D | 29 | 48 | 91 | 34 | 69 | 94 | 98 | 1 |
| E | 60 | 14 | 70 | 26 | 9 | 45 | 32 | 79 |
| F | 78 | 28 | 12 | 96 | 55 | 12 | 44 | 25 |
| G | 79 | 58 | 11 | 17 | 65 | 88 | 21 | 59 |
| H | 70 | 60 | 9 | 41 | 31 | 72 | 28 | 88 |

## customer_id=E
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 84 | 88 | 81 | 80 | 40 | 20 | 39 | 71 |
| B | 54 | 85 | 8 | 70 | 3 | 47 | 4 | 88 |
| C | 82 | 30 | 58 | 64 | 86 | 44 | 73 | 41 |
| D | 79 | 11 | 43 | 3 | 94 | 5 | 30 | 21 |
| E | 1 | 25 | 38 | 3 | 13 | 93 | 16 | 22 |
| F | 3 | 67 | 13 | 62 | 26 | 68 | 79 | 92 |
| G | 34 | 60 | 69 | 20 | 62 | 81 | 3 | 20 |
| H | 91 | 47 | 85 | 44 | 72 | 42 | 81 | 87 |

## customer_id=F
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 0 | 32 | 22 | 5 | 50 | 81 | 45 | 85 |
| B | 17 | 73 | 37 | 17 | 7 | 19 | 14 | 91 |
| C | 95 | 44 | 78 | 1 | 88 | 37 | 2 | 64 |
| D | 8 | 91 | 20 | 67 | 8 | 36 | 43 | 33 |
| E | 95 | 79 | 80 | 69 | 86 | 21 | 37 | 79 |
| F | 3 | 9 | 46 | 42 | 48 | 52 | 88 | 51 |
| G | 52 | 93 | 33 | 82 | 47 | 37 | 35 | 42 |
| H | 55 | 60 | 93 | 43 | 87 | 84 | 80 | 12 |

## customer_id=G
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 28 | 89 | 32 | 48 | 22 | 31 | 20 | 36 |
| B | 88 | 48 | 61 | 34 | 86 | 80 | 84 | 38 |
| C | 60 | 77 | 87 | 99 | 85 | 22 | 57 | 94 |
| D | 48 | 19 | 14 | 7 | 27 | 62 | 78 | 87 |
| E | 69 | 79 | 10 | 93 | 46 | 78 | 61 | 57 |
| F | 83 | 37 | 20 | 99 | 35 | 25 | 49 | 90 |
| G | 14 | 6 | 53 | 85 | 40 | 55 | 3 | 77 |
| H | 95 | 52 | 44 | 50 | 31 | 36 | 10 | 33 |

## customer_id=H
| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| A | 18 | 7 | 92 | 85 | 2 | 94 | 55 | 36 |
| B | 48 | 1 | 77 | 77 | 89 | 86 | 60 | 36 |
| C | 81 | 3 | 54 | 79 | 63 | 28 | 4 | 55 |
| D | 77 | 84 | 67 | 66 | 73 | 27 | 85 | 15 |
| E | 45 | 88 | 97 | 45 | 74 | 90 | 75 | 49 |
| F | 92 | 95 | 12 | 14 | 94 | 23 | 69 | 38 |
| G | 43 | 82 | 43 | 7 | 32 | 64 | 21 | 72 |
| H | 22 | 65 | 74 | 23 | 80 | 76 | 63 | 10 |

If you want to send back the matching, a simple JSON sketch like this is perfect — one triple per customer showing which stylist and which room they get:

{
  ""solution"": [
    [<customer_id>, <stylist_id>, <room_id>],
    ...
  ]
}

This just means: the ""solution"" field is a list of triples, each triple being the customer, the stylist and the fitting room chosen for that customer. Think of it as a little form: one row per customer, three columns (customer, stylist, room). It's just the expected shape — not the actual answer.

Please use the exact identifiers given 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”.","{'cost_tensor': [[[79, 90, 60, 37, 68, 64, 32, 59], [24, 34, 52, 25, 40, 63, 85, 78], [1, 71, 18, 11, 40, 71, 49, 28], [17, 62, 69, 54, 32, 53, 10, 30], [64, 85, 14, 1, 77, 65, 80, 5], [91, 92, 71, 85, 66, 36, 59, 43], [8, 65, 87, 1, 96, 53, 82, 3], [75, 87, 19, 41, 14, 50, 98, 20]], [[76, 35, 93, 13, 0, 39, 83, 69], [43, 31, 83, 95, 15, 75, 85, 99], [93, 86, 30, 0, 57, 0, 98, 82], [58, 43, 44, 86, 19, 40, 44, 35], [64, 4, 43, 81, 96, 42, 38, 73], [41, 59, 62, 1, 40, 51, 46, 69], [48, 49, 55, 43, 96, 90, 66, 41], [54, 47, 29, 1, 21, 96, 16, 24]], [[75, 27, 64, 87, 25, 7, 25, 64], [2, 94, 4, 56, 54, 81, 18, 60], [69, 74, 59, 46, 73, 29, 73, 45], [18, 80, 5, 67, 64, 94, 8, 15], [74, 75, 30, 24, 23, 54, 67, 68], [55, 45, 88, 77, 33, 43, 22, 51], [47, 81, 74, 77, 53, 81, 34, 74], [47, 21, 91, 60, 38, 19, 3, 3]], [[68, 4, 53, 32, 37, 4, 25, 95], [73, 37, 38, 16, 37, 32, 6, 86], [32, 35, 49, 54, 34, 46, 46, 78], [29, 48, 91, 34, 69, 94, 98, 1], [60, 14, 70, 26, 9, 45, 32, 79], [78, 28, 12, 96, 55, 12, 44, 25], [79, 58, 11, 17, 65, 88, 21, 59], [70, 60, 9, 41, 31, 72, 28, 88]], [[84, 88, 81, 80, 40, 20, 39, 71], [54, 85, 8, 70, 3, 47, 4, 88], [82, 30, 58, 64, 86, 44, 73, 41], [79, 11, 43, 3, 94, 5, 30, 21], [1, 25, 38, 3, 13, 93, 16, 22], [3, 67, 13, 62, 26, 68, 79, 92], [34, 60, 69, 20, 62, 81, 3, 20], [91, 47, 85, 44, 72, 42, 81, 87]], [[0, 32, 22, 5, 50, 81, 45, 85], [17, 73, 37, 17, 7, 19, 14, 91], [95, 44, 78, 1, 88, 37, 2, 64], [8, 91, 20, 67, 8, 36, 43, 33], [95, 79, 80, 69, 86, 21, 37, 79], [3, 9, 46, 42, 48, 52, 88, 51], [52, 93, 33, 82, 47, 37, 35, 42], [55, 60, 93, 43, 87, 84, 80, 12]], [[28, 89, 32, 48, 22, 31, 20, 36], [88, 48, 61, 34, 86, 80, 84, 38], [60, 77, 87, 99, 85, 22, 57, 94], [48, 19, 14, 7, 27, 62, 78, 87], [69, 79, 10, 93, 46, 78, 61, 57], [83, 37, 20, 99, 35, 25, 49, 90], [14, 6, 53, 85, 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'cost': 3}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 94}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 5}, {'i': 'E', 'j': 'D', 'k': 'G', 'cost': 30}, {'i': 'E', 'j': 'D', 'k': 'H', 'cost': 21}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 1}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 25}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 38}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 3}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 13}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 93}, {'i': 'E', 'j': 'E', 'k': 'G', 'cost': 16}, {'i': 'E', 'j': 'E', 'k': 'H', 'cost': 22}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 3}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 67}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 13}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 62}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 26}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 68}, {'i': 'E', 'j': 'F', 'k': 'G', 'cost': 79}, {'i': 'E', 'j': 'F', 'k': 'H', 'cost': 92}, {'i': 'E', 'j': 'G', 'k': 'A', 'cost': 34}, {'i': 'E', 'j': 'G', 'k': 'B', 'cost': 60}, {'i': 'E', 'j': 'G', 'k': 'C', 'cost': 69}, {'i': 'E', 'j': 'G', 'k': 'D', 'cost': 20}, {'i': 'E', 'j': 'G', 'k': 'E', 'cost': 62}, {'i': 'E', 'j': 'G', 'k': 'F', 'cost': 81}, {'i': 'E', 'j': 'G', 'k': 'G', 'cost': 3}, {'i': 'E', 'j': 'G', 'k': 'H', 'cost': 20}, {'i': 'E', 'j': 'H', 'k': 'A', 'cost': 91}, {'i': 'E', 'j': 'H', 'k': 'B', 'cost': 47}, {'i': 'E', 'j': 'H', 'k': 'C', 'cost': 85}, {'i': 'E', 'j': 'H', 'k': 'D', 'cost': 44}, {'i': 'E', 'j': 'H', 'k': 'E', 'cost': 72}, {'i': 'E', 'j': 'H', 'k': 'F', 'cost': 42}, {'i': 'E', 'j': 'H', 'k': 'G', 'cost': 81}, {'i': 'E', 'j': 'H', 'k': 'H', 'cost': 87}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 0}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 32}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 22}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 5}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 50}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 81}, {'i': 'F', 'j': 'A', 'k': 'G', 'cost': 45}, {'i': 'F', 'j': 'A', 'k': 'H', 'cost': 85}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 17}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 73}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 37}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 17}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 7}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 19}, {'i': 'F', 'j': 'B', 'k': 'G', 'cost': 14}, {'i': 'F', 'j': 'B', 'k': 'H', 'cost': 91}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 95}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 44}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 78}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 1}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 88}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 37}, {'i': 'F', 'j': 'C', 'k': 'G', 'cost': 2}, {'i': 'F', 'j': 'C', 'k': 'H', 'cost': 64}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 8}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 91}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 20}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 67}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 8}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 36}, {'i': 'F', 'j': 'D', 'k': 'G', 'cost': 43}, {'i': 'F', 'j': 'D', 'k': 'H', 'cost': 33}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 95}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 79}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 80}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 69}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 86}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 21}, {'i': 'F', 'j': 'E', 'k': 'G', 'cost': 37}, {'i': 'F', 'j': 'E', 'k': 'H', 'cost': 79}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 3}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 9}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 46}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 42}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 48}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 52}, {'i': 'F', 'j': 'F', 'k': 'G', 'cost': 88}, {'i': 'F', 'j': 'F', 'k': 'H', 'cost': 51}, {'i': 'F', 'j': 'G', 'k': 'A', 'cost': 52}, {'i': 'F', 'j': 'G', 'k': 'B', 'cost': 93}, {'i': 'F', 'j': 'G', 'k': 'C', 'cost': 33}, {'i': 'F', 'j': 'G', 'k': 'D', 'cost': 82}, {'i': 'F', 'j': 'G', 'k': 'E', 'cost': 47}, {'i': 'F', 'j': 'G', 'k': 'F', 'cost': 37}, {'i': 'F', 'j': 'G', 'k': 'G', 'cost': 35}, {'i': 'F', 'j': 'G', 'k': 'H', 'cost': 42}, {'i': 'F', 'j': 'H', 'k': 'A', 'cost': 55}, {'i': 'F', 'j': 'H', 'k': 'B', 'cost': 60}, {'i': 'F', 'j': 'H', 'k': 'C', 'cost': 93}, {'i': 'F', 'j': 'H', 'k': 'D', 'cost': 43}, {'i': 'F', 'j': 'H', 'k': 'E', 'cost': 87}, {'i': 'F', 'j': 'H', 'k': 'F', 'cost': 84}, {'i': 'F', 'j': 'H', 'k': 'G', 'cost': 80}, {'i': 'F', 'j': 'H', 'k': 'H', 'cost': 12}, {'i': 'G', 'j': 'A', 'k': 'A', 'cost': 28}, {'i': 'G', 'j': 'A', 'k': 'B', 'cost': 89}, {'i': 'G', 'j': 'A', 'k': 'C', 'cost': 32}, {'i': 'G', 'j': 'A', 'k': 'D', 'cost': 48}, {'i': 'G', 'j': 'A', 'k': 'E', 'cost': 22}, {'i': 'G', 'j': 'A', 'k': 'F', 'cost': 31}, {'i': 'G', 'j': 'A', 'k': 'G', 'cost': 20}, {'i': 'G', 'j': 'A', 'k': 'H', 'cost': 36}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 88}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 48}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 61}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 34}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 86}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 80}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 84}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 38}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 60}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 77}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 87}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 99}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 85}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 22}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 57}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 94}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 48}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 19}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 14}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 7}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 27}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 62}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 78}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 87}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 69}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 79}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 10}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 93}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 46}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 78}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 61}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 57}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 83}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 37}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 20}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 99}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 35}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 25}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 49}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 90}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 14}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 6}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 53}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 85}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 40}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 55}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 3}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 77}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 95}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 52}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 44}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 50}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 31}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 36}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 10}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 33}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 18}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 7}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 92}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 85}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 2}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 94}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 55}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 36}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 48}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 1}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 77}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 77}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 89}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 86}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 60}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 36}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 81}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 3}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 54}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 79}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 63}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 28}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 4}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 55}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 77}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 84}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 67}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 66}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 73}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 27}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 85}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 15}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 45}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 88}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 97}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 45}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 74}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 90}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 75}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 49}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 92}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 95}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 12}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 14}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 94}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 23}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 69}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 38}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 43}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 82}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 43}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 7}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 32}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 64}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 21}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 72}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 22}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 65}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 74}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 23}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 80}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 76}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 63}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 10}]}","[['A', 'E', 'D'], ['B', 'C', 'F'], ['C', 'H', 'G'], ['D', 'D', 'H'], ['E', 'B', 'C'], ['F', 'F', 'A'], ['G', 'G', 'B'], ['H', 'A', 'E']]",44,csv,names
AP3,AP3,"Many people think staffing a festival is just picking people and gear, but here the director needs to match each screening with one technician and one projector model, making sure nobody or no model gets assigned twice. Every possible triple of screening, technician, and projector carries a cost, and the aim is to pick the set of triples whose prices, when added up across all screenings, give the lowest possible total. The exact match-up options and their costs are shown below.

# num_screenings=6
# index_identifiers=0, 1, 2, 3, 4, 5

# Meaning: costs form a 3D tensor. For each fixed screening_id=i, you are given a technician_id×projector_model_id matrix whose entry at row technician_id=j and column projector_model_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all technician_id and all projector_model_id used exactly once.
# assignment_cost_tensor (per-screening_id markdown matrices)

## screening_id=0
| technician_id\projector_model_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 98 | 39 | 85 | 80 | 39 | 69 |
| 1 | 11 | 97 | 4 | 1 | 26 | 59 |
| 2 | 8 | 77 | 97 | 11 | 68 | 92 |
| 3 | 40 | 10 | 65 | 43 | 28 | 33 |
| 4 | 91 | 79 | 40 | 9 | 7 | 42 |
| 5 | 58 | 2 | 29 | 25 | 39 | 77 |

## screening_id=1
| technician_id\projector_model_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 11 | 31 | 57 | 46 | 47 | 47 |
| 1 | 28 | 45 | 17 | 86 | 33 | 50 |
| 2 | 47 | 82 | 7 | 89 | 34 | 9 |
| 3 | 70 | 0 | 87 | 92 | 20 | 50 |
| 4 | 59 | 63 | 29 | 3 | 35 | 60 |
| 5 | 15 | 53 | 30 | 28 | 43 | 73 |

## screening_id=2
| technician_id\projector_model_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 39 | 72 | 8 | 29 | 55 | 46 |
| 1 | 93 | 20 | 15 | 20 | 74 | 22 |
| 2 | 1 | 71 | 23 | 15 | 47 | 16 |
| 3 | 73 | 83 | 39 | 0 | 58 | 43 |
| 4 | 33 | 10 | 58 | 33 | 79 | 44 |
| 5 | 15 | 88 | 81 | 24 | 64 | 21 |

## screening_id=3
| technician_id\projector_model_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 66 | 41 | 79 | 51 | 93 | 83 |
| 1 | 41 | 5 | 29 | 63 | 82 | 5 |
| 2 | 92 | 86 | 34 | 32 | 44 | 83 |
| 3 | 7 | 47 | 11 | 15 | 91 | 87 |
| 4 | 88 | 81 | 77 | 11 | 21 | 63 |
| 5 | 95 | 15 | 48 | 47 | 44 | 13 |

## screening_id=4
| technician_id\projector_model_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 60 | 39 | 25 | 47 | 64 | 72 |
| 1 | 16 | 44 | 56 | 1 | 18 | 72 |
| 2 | 57 | 55 | 66 | 80 | 20 | 96 |
| 3 | 56 | 88 | 24 | 24 | 11 | 54 |
| 4 | 39 | 38 | 34 | 78 | 78 | 84 |
| 5 | 70 | 97 | 3 | 57 | 63 | 62 |

## screening_id=5
| technician_id\projector_model_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 2 | 1 | 17 | 45 | 12 | 45 |
| 1 | 42 | 40 | 86 | 8 | 92 | 49 |
| 2 | 10 | 17 | 46 | 18 | 24 | 67 |
| 3 | 74 | 18 | 24 | 31 | 35 | 53 |
| 4 | 84 | 60 | 95 | 80 | 37 | 10 |
| 5 | 84 | 80 | 31 | 46 | 78 | 61 |

When you send the final matching back, just use this simple JSON shape so it's easy to parse:

{
  ""solution"": [
    [<screening_id>, <technician_id>, <projector_id>],
    ...
  ]
}

Think of the ""solution"" list as a set of triples: each inner list picks one screening, the technician who runs it, and the projector model used. It's just a lightweight way to say ""screening X goes with tech Y and projector Z"" for every screening. This is just the shape I expect — not the actual answer.

Please 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"".","{'cost_tensor': [[[98, 39, 85, 80, 39, 69], [11, 97, 4, 1, 26, 59], [8, 77, 97, 11, 68, 92], [40, 10, 65, 43, 28, 33], [91, 79, 40, 9, 7, 42], [58, 2, 29, 25, 39, 77]], [[11, 31, 57, 46, 47, 47], [28, 45, 17, 86, 33, 50], [47, 82, 7, 89, 34, 9], [70, 0, 87, 92, 20, 50], [59, 63, 29, 3, 35, 60], [15, 53, 30, 28, 43, 73]], [[39, 72, 8, 29, 55, 46], [93, 20, 15, 20, 74, 22], [1, 71, 23, 15, 47, 16], [73, 83, 39, 0, 58, 43], [33, 10, 58, 33, 79, 44], [15, 88, 81, 24, 64, 21]], [[66, 41, 79, 51, 93, 83], [41, 5, 29, 63, 82, 5], [92, 86, 34, 32, 44, 83], [7, 47, 11, 15, 91, 87], [88, 81, 77, 11, 21, 63], [95, 15, 48, 47, 44, 13]], [[60, 39, 25, 47, 64, 72], [16, 44, 56, 1, 18, 72], [57, 55, 66, 80, 20, 96], [56, 88, 24, 24, 11, 54], [39, 38, 34, 78, 78, 84], [70, 97, 3, 57, 63, 62]], [[2, 1, 17, 45, 12, 45], [42, 40, 86, 8, 92, 49], [10, 17, 46, 18, 24, 67], [74, 18, 24, 31, 35, 53], [84, 60, 95, 80, 37, 10], [84, 80, 31, 46, 78, 61]]], 'objective': 26.0}","[[0, 4, 4], [1, 2, 5], [2, 3, 3], [3, 1, 1], [4, 5, 2], [5, 0, 0]]",26.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [0, 1, 2, 3, 4, 5], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 98}, {'i': 0, 'j': 0, 'k': 1, 'cost': 39}, {'i': 0, 'j': 0, 'k': 2, 'cost': 85}, {'i': 0, 'j': 0, 'k': 3, 'cost': 80}, {'i': 0, 'j': 0, 'k': 4, 'cost': 39}, {'i': 0, 'j': 0, 'k': 5, 'cost': 69}, {'i': 0, 'j': 1, 'k': 0, 'cost': 11}, {'i': 0, 'j': 1, 'k': 1, 'cost': 97}, {'i': 0, 'j': 1, 'k': 2, 'cost': 4}, {'i': 0, 'j': 1, 'k': 3, 'cost': 1}, {'i': 0, 'j': 1, 'k': 4, 'cost': 26}, {'i': 0, 'j': 1, 'k': 5, 'cost': 59}, {'i': 0, 'j': 2, 'k': 0, 'cost': 8}, {'i': 0, 'j': 2, 'k': 1, 'cost': 77}, {'i': 0, 'j': 2, 'k': 2, 'cost': 97}, {'i': 0, 'j': 2, 'k': 3, 'cost': 11}, {'i': 0, 'j': 2, 'k': 4, 'cost': 68}, {'i': 0, 'j': 2, 'k': 5, 'cost': 92}, {'i': 0, 'j': 3, 'k': 0, 'cost': 40}, {'i': 0, 'j': 3, 'k': 1, 'cost': 10}, {'i': 0, 'j': 3, 'k': 2, 'cost': 65}, {'i': 0, 'j': 3, 'k': 3, 'cost': 43}, {'i': 0, 'j': 3, 'k': 4, 'cost': 28}, {'i': 0, 'j': 3, 'k': 5, 'cost': 33}, {'i': 0, 'j': 4, 'k': 0, 'cost': 91}, {'i': 0, 'j': 4, 'k': 1, 'cost': 79}, {'i': 0, 'j': 4, 'k': 2, 'cost': 40}, {'i': 0, 'j': 4, 'k': 3, 'cost': 9}, {'i': 0, 'j': 4, 'k': 4, 'cost': 7}, {'i': 0, 'j': 4, 'k': 5, 'cost': 42}, {'i': 0, 'j': 5, 'k': 0, 'cost': 58}, {'i': 0, 'j': 5, 'k': 1, 'cost': 2}, {'i': 0, 'j': 5, 'k': 2, 'cost': 29}, {'i': 0, 'j': 5, 'k': 3, 'cost': 25}, {'i': 0, 'j': 5, 'k': 4, 'cost': 39}, {'i': 0, 'j': 5, 'k': 5, 'cost': 77}, {'i': 1, 'j': 0, 'k': 0, 'cost': 11}, {'i': 1, 'j': 0, 'k': 1, 'cost': 31}, {'i': 1, 'j': 0, 'k': 2, 'cost': 57}, {'i': 1, 'j': 0, 'k': 3, 'cost': 46}, {'i': 1, 'j': 0, 'k': 4, 'cost': 47}, {'i': 1, 'j': 0, 'k': 5, 'cost': 47}, {'i': 1, 'j': 1, 'k': 0, 'cost': 28}, {'i': 1, 'j': 1, 'k': 1, 'cost': 45}, {'i': 1, 'j': 1, 'k': 2, 'cost': 17}, {'i': 1, 'j': 1, 'k': 3, 'cost': 86}, {'i': 1, 'j': 1, 'k': 4, 'cost': 33}, {'i': 1, 'j': 1, 'k': 5, 'cost': 50}, {'i': 1, 'j': 2, 'k': 0, 'cost': 47}, {'i': 1, 'j': 2, 'k': 1, 'cost': 82}, {'i': 1, 'j': 2, 'k': 2, 'cost': 7}, {'i': 1, 'j': 2, 'k': 3, 'cost': 89}, {'i': 1, 'j': 2, 'k': 4, 'cost': 34}, {'i': 1, 'j': 2, 'k': 5, 'cost': 9}, {'i': 1, 'j': 3, 'k': 0, 'cost': 70}, {'i': 1, 'j': 3, 'k': 1, 'cost': 0}, {'i': 1, 'j': 3, 'k': 2, 'cost': 87}, {'i': 1, 'j': 3, 'k': 3, 'cost': 92}, {'i': 1, 'j': 3, 'k': 4, 'cost': 20}, {'i': 1, 'j': 3, 'k': 5, 'cost': 50}, {'i': 1, 'j': 4, 'k': 0, 'cost': 59}, {'i': 1, 'j': 4, 'k': 1, 'cost': 63}, {'i': 1, 'j': 4, 'k': 2, 'cost': 29}, {'i': 1, 'j': 4, 'k': 3, 'cost': 3}, {'i': 1, 'j': 4, 'k': 4, 'cost': 35}, {'i': 1, 'j': 4, 'k': 5, 'cost': 60}, {'i': 1, 'j': 5, 'k': 0, 'cost': 15}, {'i': 1, 'j': 5, 'k': 1, 'cost': 53}, {'i': 1, 'j': 5, 'k': 2, 'cost': 30}, {'i': 1, 'j': 5, 'k': 3, 'cost': 28}, {'i': 1, 'j': 5, 'k': 4, 'cost': 43}, {'i': 1, 'j': 5, 'k': 5, 'cost': 73}, {'i': 2, 'j': 0, 'k': 0, 'cost': 39}, {'i': 2, 'j': 0, 'k': 1, 'cost': 72}, {'i': 2, 'j': 0, 'k': 2, 'cost': 8}, {'i': 2, 'j': 0, 'k': 3, 'cost': 29}, {'i': 2, 'j': 0, 'k': 4, 'cost': 55}, {'i': 2, 'j': 0, 'k': 5, 'cost': 46}, {'i': 2, 'j': 1, 'k': 0, 'cost': 93}, {'i': 2, 'j': 1, 'k': 1, 'cost': 20}, {'i': 2, 'j': 1, 'k': 2, 'cost': 15}, {'i': 2, 'j': 1, 'k': 3, 'cost': 20}, {'i': 2, 'j': 1, 'k': 4, 'cost': 74}, {'i': 2, 'j': 1, 'k': 5, 'cost': 22}, {'i': 2, 'j': 2, 'k': 0, 'cost': 1}, {'i': 2, 'j': 2, 'k': 1, 'cost': 71}, {'i': 2, 'j': 2, 'k': 2, 'cost': 23}, {'i': 2, 'j': 2, 'k': 3, 'cost': 15}, {'i': 2, 'j': 2, 'k': 4, 'cost': 47}, {'i': 2, 'j': 2, 'k': 5, 'cost': 16}, {'i': 2, 'j': 3, 'k': 0, 'cost': 73}, {'i': 2, 'j': 3, 'k': 1, 'cost': 83}, {'i': 2, 'j': 3, 'k': 2, 'cost': 39}, {'i': 2, 'j': 3, 'k': 3, 'cost': 0}, {'i': 2, 'j': 3, 'k': 4, 'cost': 58}, {'i': 2, 'j': 3, 'k': 5, 'cost': 43}, {'i': 2, 'j': 4, 'k': 0, 'cost': 33}, {'i': 2, 'j': 4, 'k': 1, 'cost': 10}, {'i': 2, 'j': 4, 'k': 2, 'cost': 58}, {'i': 2, 'j': 4, 'k': 3, 'cost': 33}, {'i': 2, 'j': 4, 'k': 4, 'cost': 79}, {'i': 2, 'j': 4, 'k': 5, 'cost': 44}, {'i': 2, 'j': 5, 'k': 0, 'cost': 15}, {'i': 2, 'j': 5, 'k': 1, 'cost': 88}, {'i': 2, 'j': 5, 'k': 2, 'cost': 81}, {'i': 2, 'j': 5, 'k': 3, 'cost': 24}, {'i': 2, 'j': 5, 'k': 4, 'cost': 64}, {'i': 2, 'j': 5, 'k': 5, 'cost': 21}, {'i': 3, 'j': 0, 'k': 0, 'cost': 66}, {'i': 3, 'j': 0, 'k': 1, 'cost': 41}, {'i': 3, 'j': 0, 'k': 2, 'cost': 79}, {'i': 3, 'j': 0, 'k': 3, 'cost': 51}, {'i': 3, 'j': 0, 'k': 4, 'cost': 93}, {'i': 3, 'j': 0, 'k': 5, 'cost': 83}, {'i': 3, 'j': 1, 'k': 0, 'cost': 41}, {'i': 3, 'j': 1, 'k': 1, 'cost': 5}, {'i': 3, 'j': 1, 'k': 2, 'cost': 29}, {'i': 3, 'j': 1, 'k': 3, 'cost': 63}, {'i': 3, 'j': 1, 'k': 4, 'cost': 82}, {'i': 3, 'j': 1, 'k': 5, 'cost': 5}, {'i': 3, 'j': 2, 'k': 0, 'cost': 92}, {'i': 3, 'j': 2, 'k': 1, 'cost': 86}, {'i': 3, 'j': 2, 'k': 2, 'cost': 34}, {'i': 3, 'j': 2, 'k': 3, 'cost': 32}, {'i': 3, 'j': 2, 'k': 4, 'cost': 44}, {'i': 3, 'j': 2, 'k': 5, 'cost': 83}, {'i': 3, 'j': 3, 'k': 0, 'cost': 7}, {'i': 3, 'j': 3, 'k': 1, 'cost': 47}, {'i': 3, 'j': 3, 'k': 2, 'cost': 11}, {'i': 3, 'j': 3, 'k': 3, 'cost': 15}, {'i': 3, 'j': 3, 'k': 4, 'cost': 91}, {'i': 3, 'j': 3, 'k': 5, 'cost': 87}, {'i': 3, 'j': 4, 'k': 0, 'cost': 88}, {'i': 3, 'j': 4, 'k': 1, 'cost': 81}, {'i': 3, 'j': 4, 'k': 2, 'cost': 77}, {'i': 3, 'j': 4, 'k': 3, 'cost': 11}, {'i': 3, 'j': 4, 'k': 4, 'cost': 21}, {'i': 3, 'j': 4, 'k': 5, 'cost': 63}, {'i': 3, 'j': 5, 'k': 0, 'cost': 95}, {'i': 3, 'j': 5, 'k': 1, 'cost': 15}, {'i': 3, 'j': 5, 'k': 2, 'cost': 48}, {'i': 3, 'j': 5, 'k': 3, 'cost': 47}, {'i': 3, 'j': 5, 'k': 4, 'cost': 44}, {'i': 3, 'j': 5, 'k': 5, 'cost': 13}, {'i': 4, 'j': 0, 'k': 0, 'cost': 60}, {'i': 4, 'j': 0, 'k': 1, 'cost': 39}, {'i': 4, 'j': 0, 'k': 2, 'cost': 25}, {'i': 4, 'j': 0, 'k': 3, 'cost': 47}, {'i': 4, 'j': 0, 'k': 4, 'cost': 64}, {'i': 4, 'j': 0, 'k': 5, 'cost': 72}, {'i': 4, 'j': 1, 'k': 0, 'cost': 16}, {'i': 4, 'j': 1, 'k': 1, 'cost': 44}, {'i': 4, 'j': 1, 'k': 2, 'cost': 56}, {'i': 4, 'j': 1, 'k': 3, 'cost': 1}, {'i': 4, 'j': 1, 'k': 4, 'cost': 18}, {'i': 4, 'j': 1, 'k': 5, 'cost': 72}, {'i': 4, 'j': 2, 'k': 0, 'cost': 57}, {'i': 4, 'j': 2, 'k': 1, 'cost': 55}, {'i': 4, 'j': 2, 'k': 2, 'cost': 66}, {'i': 4, 'j': 2, 'k': 3, 'cost': 80}, {'i': 4, 'j': 2, 'k': 4, 'cost': 20}, {'i': 4, 'j': 2, 'k': 5, 'cost': 96}, {'i': 4, 'j': 3, 'k': 0, 'cost': 56}, {'i': 4, 'j': 3, 'k': 1, 'cost': 88}, {'i': 4, 'j': 3, 'k': 2, 'cost': 24}, {'i': 4, 'j': 3, 'k': 3, 'cost': 24}, {'i': 4, 'j': 3, 'k': 4, 'cost': 11}, {'i': 4, 'j': 3, 'k': 5, 'cost': 54}, {'i': 4, 'j': 4, 'k': 0, 'cost': 39}, {'i': 4, 'j': 4, 'k': 1, 'cost': 38}, {'i': 4, 'j': 4, 'k': 2, 'cost': 34}, {'i': 4, 'j': 4, 'k': 3, 'cost': 78}, {'i': 4, 'j': 4, 'k': 4, 'cost': 78}, {'i': 4, 'j': 4, 'k': 5, 'cost': 84}, {'i': 4, 'j': 5, 'k': 0, 'cost': 70}, {'i': 4, 'j': 5, 'k': 1, 'cost': 97}, {'i': 4, 'j': 5, 'k': 2, 'cost': 3}, {'i': 4, 'j': 5, 'k': 3, 'cost': 57}, {'i': 4, 'j': 5, 'k': 4, 'cost': 63}, {'i': 4, 'j': 5, 'k': 5, 'cost': 62}, {'i': 5, 'j': 0, 'k': 0, 'cost': 2}, {'i': 5, 'j': 0, 'k': 1, 'cost': 1}, {'i': 5, 'j': 0, 'k': 2, 'cost': 17}, {'i': 5, 'j': 0, 'k': 3, 'cost': 45}, {'i': 5, 'j': 0, 'k': 4, 'cost': 12}, {'i': 5, 'j': 0, 'k': 5, 'cost': 45}, {'i': 5, 'j': 1, 'k': 0, 'cost': 42}, {'i': 5, 'j': 1, 'k': 1, 'cost': 40}, {'i': 5, 'j': 1, 'k': 2, 'cost': 86}, {'i': 5, 'j': 1, 'k': 3, 'cost': 8}, {'i': 5, 'j': 1, 'k': 4, 'cost': 92}, {'i': 5, 'j': 1, 'k': 5, 'cost': 49}, {'i': 5, 'j': 2, 'k': 0, 'cost': 10}, {'i': 5, 'j': 2, 'k': 1, 'cost': 17}, {'i': 5, 'j': 2, 'k': 2, 'cost': 46}, {'i': 5, 'j': 2, 'k': 3, 'cost': 18}, {'i': 5, 'j': 2, 'k': 4, 'cost': 24}, {'i': 5, 'j': 2, 'k': 5, 'cost': 67}, {'i': 5, 'j': 3, 'k': 0, 'cost': 74}, {'i': 5, 'j': 3, 'k': 1, 'cost': 18}, {'i': 5, 'j': 3, 'k': 2, 'cost': 24}, {'i': 5, 'j': 3, 'k': 3, 'cost': 31}, {'i': 5, 'j': 3, 'k': 4, 'cost': 35}, {'i': 5, 'j': 3, 'k': 5, 'cost': 53}, {'i': 5, 'j': 4, 'k': 0, 'cost': 84}, {'i': 5, 'j': 4, 'k': 1, 'cost': 60}, {'i': 5, 'j': 4, 'k': 2, 'cost': 95}, {'i': 5, 'j': 4, 'k': 3, 'cost': 80}, {'i': 5, 'j': 4, 'k': 4, 'cost': 37}, {'i': 5, 'j': 4, 'k': 5, 'cost': 10}, {'i': 5, 'j': 5, 'k': 0, 'cost': 84}, {'i': 5, 'j': 5, 'k': 1, 'cost': 80}, {'i': 5, 'j': 5, 'k': 2, 'cost': 31}, {'i': 5, 'j': 5, 'k': 3, 'cost': 46}, {'i': 5, 'j': 5, 'k': 4, 'cost': 78}, {'i': 5, 'j': 5, 'k': 5, 'cost': 61}]}","[[0, 4, 4], [1, 2, 5], [2, 3, 3], [3, 1, 1], [4, 5, 2], [5, 0, 0]]",45,csv,0
AP3,AP3,"Back at the office, the problem was simple to explain over coffee: assign one developer and one test environment to each task, make sure each developer and each environment shows up exactly once across all tasks, and pick combinations that don’t overlap. Each possible grouping has a cost, and the preferred assignment is the one whose total cost (found by adding every task’s chosen grouping cost) is the lowest. Concrete details are shown below.

There are 8 tasks (and 8 developers and 8 test environments), identified by 1, 2, 3, 4, 5, 6, 7, 8.

*Meaning: costs form a 3D tensor. For each fixed task_id=i, you are given a developer_id×test_environment_id matrix whose entry at row developer_id=j and column test_environment_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all developer_id and all test_environment_id used exactly once.*

**assignment_cost_tensor (per-task_id markdown matrices)**

## task_id=1
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 70 | 87 | 43 | 25 | 0 | 20 | 51 | 1 |
| 2 | 6 | 52 | 49 | 10 | 18 | 90 | 86 | 82 |
| 3 | 65 | 59 | 96 | 90 | 5 | 19 | 11 | 31 |
| 4 | 69 | 51 | 40 | 34 | 53 | 42 | 1 | 62 |
| 5 | 17 | 47 | 66 | 14 | 54 | 34 | 74 | 27 |
| 6 | 45 | 32 | 74 | 64 | 9 | 98 | 4 | 97 |
| 7 | 12 | 8 | 3 | 9 | 3 | 34 | 55 | 87 |
| 8 | 31 | 35 | 58 | 65 | 69 | 47 | 22 | 20 |

## task_id=2
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 81 | 37 | 76 | 21 | 26 | 64 | 24 | 72 |
| 2 | 74 | 14 | 69 | 83 | 50 | 83 | 67 | 45 |
| 3 | 36 | 90 | 86 | 18 | 9 | 43 | 7 | 68 |
| 4 | 85 | 43 | 5 | 18 | 99 | 42 | 63 | 3 |
| 5 | 7 | 81 | 27 | 2 | 53 | 91 | 1 | 27 |
| 6 | 10 | 64 | 77 | 33 | 3 | 76 | 9 | 66 |
| 7 | 54 | 80 | 7 | 80 | 4 | 53 | 80 | 78 |
| 8 | 47 | 70 | 61 | 42 | 45 | 55 | 37 | 87 |

## task_id=3
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 75 | 8 | 28 | 97 | 96 | 9 | 91 | 55 |
| 2 | 46 | 70 | 28 | 23 | 78 | 78 | 68 | 38 |
| 3 | 77 | 15 | 15 | 77 | 51 | 16 | 27 | 88 |
| 4 | 63 | 35 | 41 | 44 | 71 | 74 | 25 | 50 |
| 5 | 83 | 30 | 66 | 33 | 80 | 70 | 67 | 14 |
| 6 | 47 | 26 | 69 | 59 | 39 | 48 | 68 | 33 |
| 7 | 61 | 12 | 57 | 21 | 78 | 66 | 9 | 0 |
| 8 | 52 | 8 | 39 | 47 | 57 | 63 | 64 | 34 |

## task_id=4
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 16 | 41 | 8 | 61 | 93 | 21 | 6 | 55 |
| 2 | 46 | 3 | 41 | 5 | 2 | 22 | 95 | 8 |
| 3 | 38 | 79 | 89 | 72 | 56 | 7 | 96 | 34 |
| 4 | 1 | 12 | 23 | 63 | 37 | 15 | 70 | 5 |
| 5 | 52 | 89 | 9 | 71 | 89 | 82 | 24 | 55 |
| 6 | 30 | 17 | 10 | 21 | 49 | 87 | 74 | 22 |
| 7 | 10 | 76 | 40 | 54 | 58 | 94 | 61 | 52 |
| 8 | 76 | 19 | 85 | 71 | 96 | 58 | 8 | 44 |

## task_id=5
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 17 | 14 | 32 | 69 | 36 | 19 | 73 | 51 |
| 2 | 5 | 34 | 28 | 16 | 41 | 23 | 2 | 72 |
| 3 | 55 | 56 | 80 | 57 | 59 | 74 | 55 | 1 |
| 4 | 2 | 99 | 92 | 95 | 70 | 49 | 86 | 62 |
| 5 | 80 | 68 | 85 | 94 | 23 | 47 | 80 | 25 |
| 6 | 42 | 94 | 5 | 79 | 23 | 25 | 21 | 12 |
| 7 | 74 | 14 | 75 | 33 | 13 | 29 | 28 | 84 |
| 8 | 71 | 72 | 53 | 43 | 75 | 72 | 94 | 43 |

## task_id=6
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 94 | 47 | 75 | 18 | 24 | 78 | 62 | 50 |
| 2 | 53 | 53 | 37 | 53 | 35 | 30 | 35 | 81 |
| 3 | 12 | 29 | 26 | 45 | 53 | 9 | 22 | 82 |
| 4 | 47 | 67 | 42 | 36 | 58 | 43 | 80 | 47 |
| 5 | 82 | 54 | 27 | 91 | 18 | 15 | 8 | 45 |
| 6 | 97 | 73 | 99 | 84 | 66 | 10 | 14 | 59 |
| 7 | 38 | 30 | 89 | 21 | 85 | 69 | 39 | 44 |
| 8 | 6 | 14 | 76 | 64 | 39 | 92 | 17 | 13 |

## task_id=7
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 3 | 80 | 6 | 68 | 39 | 24 | 2 | 87 |
| 2 | 36 | 87 | 67 | 78 | 29 | 35 | 48 | 98 |
| 3 | 48 | 99 | 91 | 82 | 35 | 5 | 53 | 9 |
| 4 | 23 | 2 | 71 | 32 | 16 | 18 | 3 | 36 |
| 5 | 38 | 23 | 93 | 80 | 37 | 63 | 2 | 87 |
| 6 | 85 | 21 | 59 | 69 | 31 | 89 | 28 | 98 |
| 7 | 93 | 79 | 72 | 14 | 40 | 72 | 64 | 44 |
| 8 | 67 | 9 | 30 | 83 | 13 | 68 | 63 | 92 |

## task_id=8
| developer_id\test_environment_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 92 | 40 | 14 | 2 | 60 | 8 | 39 | 25 |
| 2 | 28 | 59 | 19 | 61 | 52 | 46 | 21 | 30 |
| 3 | 89 | 47 | 27 | 54 | 59 | 57 | 19 | 82 |
| 4 | 23 | 22 | 17 | 94 | 3 | 75 | 1 | 44 |
| 5 | 61 | 13 | 45 | 19 | 46 | 10 | 80 | 82 |
| 6 | 92 | 57 | 33 | 76 | 78 | 80 | 62 | 66 |
| 7 | 40 | 29 | 71 | 10 | 23 | 36 | 83 | 29 |
| 8 | 95 | 32 | 18 | 68 | 80 | 6 | 96 | 8 |

Choose exactly one triple per task so every developer and every test environment appears once and the sum of the 8 chosen costs is minimal.

Also, when you send the final assignment back, just use this simple JSON layout so it's easy to parse:

{
  ""solution"": [
    [<task_id>, <dev_id>, <env_id>],
    ...
  ]
}

It's just a list called ""solution"" where each item is a triple: the first entry is the task, the second is the developer assigned to that task, and the third is the test environment assigned to that task. Super informal: think of each triple as ""task → developer + environment.""

This JSON is only a sketch of the expected shape — not the actual answer.

- Please use the exact identifiers that appear in the instance input, with no renaming and no 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”.","{'cost_tensor': [[[70, 87, 43, 25, 0, 20, 51, 1], [6, 52, 49, 10, 18, 90, 86, 82], [65, 59, 96, 90, 5, 19, 11, 31], [69, 51, 40, 34, 53, 42, 1, 62], [17, 47, 66, 14, 54, 34, 74, 27], [45, 32, 74, 64, 9, 98, 4, 97], [12, 8, 3, 9, 3, 34, 55, 87], [31, 35, 58, 65, 69, 47, 22, 20]], [[81, 37, 76, 21, 26, 64, 24, 72], [74, 14, 69, 83, 50, 83, 67, 45], [36, 90, 86, 18, 9, 43, 7, 68], [85, 43, 5, 18, 99, 42, 63, 3], [7, 81, 27, 2, 53, 91, 1, 27], [10, 64, 77, 33, 3, 76, 9, 66], [54, 80, 7, 80, 4, 53, 80, 78], [47, 70, 61, 42, 45, 55, 37, 87]], [[75, 8, 28, 97, 96, 9, 91, 55], [46, 70, 28, 23, 78, 78, 68, 38], [77, 15, 15, 77, 51, 16, 27, 88], [63, 35, 41, 44, 71, 74, 25, 50], [83, 30, 66, 33, 80, 70, 67, 14], [47, 26, 69, 59, 39, 48, 68, 33], [61, 12, 57, 21, 78, 66, 9, 0], [52, 8, 39, 47, 57, 63, 64, 34]], [[16, 41, 8, 61, 93, 21, 6, 55], [46, 3, 41, 5, 2, 22, 95, 8], [38, 79, 89, 72, 56, 7, 96, 34], [1, 12, 23, 63, 37, 15, 70, 5], [52, 89, 9, 71, 89, 82, 24, 55], [30, 17, 10, 21, 49, 87, 74, 22], [10, 76, 40, 54, 58, 94, 61, 52], [76, 19, 85, 71, 96, 58, 8, 44]], [[17, 14, 32, 69, 36, 19, 73, 51], [5, 34, 28, 16, 41, 23, 2, 72], [55, 56, 80, 57, 59, 74, 55, 1], [2, 99, 92, 95, 70, 49, 86, 62], [80, 68, 85, 94, 23, 47, 80, 25], [42, 94, 5, 79, 23, 25, 21, 12], [74, 14, 75, 33, 13, 29, 28, 84], [71, 72, 53, 43, 75, 72, 94, 43]], [[94, 47, 75, 18, 24, 78, 62, 50], [53, 53, 37, 53, 35, 30, 35, 81], [12, 29, 26, 45, 53, 9, 22, 82], [47, 67, 42, 36, 58, 43, 80, 47], [82, 54, 27, 91, 18, 15, 8, 45], [97, 73, 99, 84, 66, 10, 14, 59], [38, 30, 89, 21, 85, 69, 39, 44], [6, 14, 76, 64, 39, 92, 17, 13]], [[3, 80, 6, 68, 39, 24, 2, 87], [36, 87, 67, 78, 29, 35, 48, 98], [48, 99, 91, 82, 35, 5, 53, 9], [23, 2, 71, 32, 16, 18, 3, 36], [38, 23, 93, 80, 37, 63, 2, 87], [85, 21, 59, 69, 31, 89, 28, 98], [93, 79, 72, 14, 40, 72, 64, 44], [67, 9, 30, 83, 13, 68, 63, 92]], [[92, 40, 14, 2, 60, 8, 39, 25], [28, 59, 19, 61, 52, 46, 21, 30], [89, 47, 27, 54, 59, 57, 19, 82], [23, 22, 17, 94, 3, 75, 1, 44], [61, 13, 45, 19, 46, 10, 80, 82], [92, 57, 33, 76, 78, 80, 62, 66], [40, 29, 71, 10, 23, 36, 83, 29], [95, 32, 18, 68, 80, 6, 96, 8]]], 'objective': 22.0}","[[0, 0, 4], [1, 4, 3], [2, 6, 7], [3, 1, 1], [4, 5, 2], [5, 7, 0], [6, 2, 5], [7, 3, 6]]",22.0,"{'problem_type': 'AP3', 'n': 8, 'ids': [1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 70}, {'i': 1, 'j': 1, 'k': 2, 'cost': 87}, {'i': 1, 'j': 1, 'k': 3, 'cost': 43}, {'i': 1, 'j': 1, 'k': 4, 'cost': 25}, {'i': 1, 'j': 1, 'k': 5, 'cost': 0}, {'i': 1, 'j': 1, 'k': 6, 'cost': 20}, {'i': 1, 'j': 1, 'k': 7, 'cost': 51}, {'i': 1, 'j': 1, 'k': 8, 'cost': 1}, {'i': 1, 'j': 2, 'k': 1, 'cost': 6}, {'i': 1, 'j': 2, 'k': 2, 'cost': 52}, {'i': 1, 'j': 2, 'k': 3, 'cost': 49}, {'i': 1, 'j': 2, 'k': 4, 'cost': 10}, {'i': 1, 'j': 2, 'k': 5, 'cost': 18}, {'i': 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59}, {'i': 5, 'j': 3, 'k': 6, 'cost': 74}, {'i': 5, 'j': 3, 'k': 7, 'cost': 55}, {'i': 5, 'j': 3, 'k': 8, 'cost': 1}, {'i': 5, 'j': 4, 'k': 1, 'cost': 2}, {'i': 5, 'j': 4, 'k': 2, 'cost': 99}, {'i': 5, 'j': 4, 'k': 3, 'cost': 92}, {'i': 5, 'j': 4, 'k': 4, 'cost': 95}, {'i': 5, 'j': 4, 'k': 5, 'cost': 70}, {'i': 5, 'j': 4, 'k': 6, 'cost': 49}, {'i': 5, 'j': 4, 'k': 7, 'cost': 86}, {'i': 5, 'j': 4, 'k': 8, 'cost': 62}, {'i': 5, 'j': 5, 'k': 1, 'cost': 80}, {'i': 5, 'j': 5, 'k': 2, 'cost': 68}, {'i': 5, 'j': 5, 'k': 3, 'cost': 85}, {'i': 5, 'j': 5, 'k': 4, 'cost': 94}, {'i': 5, 'j': 5, 'k': 5, 'cost': 23}, {'i': 5, 'j': 5, 'k': 6, 'cost': 47}, {'i': 5, 'j': 5, 'k': 7, 'cost': 80}, {'i': 5, 'j': 5, 'k': 8, 'cost': 25}, {'i': 5, 'j': 6, 'k': 1, 'cost': 42}, {'i': 5, 'j': 6, 'k': 2, 'cost': 94}, {'i': 5, 'j': 6, 'k': 3, 'cost': 5}, {'i': 5, 'j': 6, 'k': 4, 'cost': 79}, {'i': 5, 'j': 6, 'k': 5, 'cost': 23}, {'i': 5, 'j': 6, 'k': 6, 'cost': 25}, {'i': 5, 'j': 6, 'k': 7, 'cost': 21}, {'i': 5, 'j': 6, 'k': 8, 'cost': 12}, {'i': 5, 'j': 7, 'k': 1, 'cost': 74}, {'i': 5, 'j': 7, 'k': 2, 'cost': 14}, {'i': 5, 'j': 7, 'k': 3, 'cost': 75}, {'i': 5, 'j': 7, 'k': 4, 'cost': 33}, {'i': 5, 'j': 7, 'k': 5, 'cost': 13}, {'i': 5, 'j': 7, 'k': 6, 'cost': 29}, {'i': 5, 'j': 7, 'k': 7, 'cost': 28}, {'i': 5, 'j': 7, 'k': 8, 'cost': 84}, {'i': 5, 'j': 8, 'k': 1, 'cost': 71}, {'i': 5, 'j': 8, 'k': 2, 'cost': 72}, {'i': 5, 'j': 8, 'k': 3, 'cost': 53}, {'i': 5, 'j': 8, 'k': 4, 'cost': 43}, {'i': 5, 'j': 8, 'k': 5, 'cost': 75}, {'i': 5, 'j': 8, 'k': 6, 'cost': 72}, {'i': 5, 'j': 8, 'k': 7, 'cost': 94}, {'i': 5, 'j': 8, 'k': 8, 'cost': 43}, {'i': 6, 'j': 1, 'k': 1, 'cost': 94}, {'i': 6, 'j': 1, 'k': 2, 'cost': 47}, {'i': 6, 'j': 1, 'k': 3, 'cost': 75}, {'i': 6, 'j': 1, 'k': 4, 'cost': 18}, {'i': 6, 'j': 1, 'k': 5, 'cost': 24}, {'i': 6, 'j': 1, 'k': 6, 'cost': 78}, {'i': 6, 'j': 1, 'k': 7, 'cost': 62}, {'i': 6, 'j': 1, 'k': 8, 'cost': 50}, {'i': 6, 'j': 2, 'k': 1, 'cost': 53}, {'i': 6, 'j': 2, 'k': 2, 'cost': 53}, {'i': 6, 'j': 2, 'k': 3, 'cost': 37}, {'i': 6, 'j': 2, 'k': 4, 'cost': 53}, {'i': 6, 'j': 2, 'k': 5, 'cost': 35}, {'i': 6, 'j': 2, 'k': 6, 'cost': 30}, {'i': 6, 'j': 2, 'k': 7, 'cost': 35}, {'i': 6, 'j': 2, 'k': 8, 'cost': 81}, {'i': 6, 'j': 3, 'k': 1, 'cost': 12}, {'i': 6, 'j': 3, 'k': 2, 'cost': 29}, {'i': 6, 'j': 3, 'k': 3, 'cost': 26}, {'i': 6, 'j': 3, 'k': 4, 'cost': 45}, {'i': 6, 'j': 3, 'k': 5, 'cost': 53}, {'i': 6, 'j': 3, 'k': 6, 'cost': 9}, {'i': 6, 'j': 3, 'k': 7, 'cost': 22}, {'i': 6, 'j': 3, 'k': 8, 'cost': 82}, {'i': 6, 'j': 4, 'k': 1, 'cost': 47}, {'i': 6, 'j': 4, 'k': 2, 'cost': 67}, {'i': 6, 'j': 4, 'k': 3, 'cost': 42}, {'i': 6, 'j': 4, 'k': 4, 'cost': 36}, {'i': 6, 'j': 4, 'k': 5, 'cost': 58}, {'i': 6, 'j': 4, 'k': 6, 'cost': 43}, {'i': 6, 'j': 4, 'k': 7, 'cost': 80}, {'i': 6, 'j': 4, 'k': 8, 'cost': 47}, {'i': 6, 'j': 5, 'k': 1, 'cost': 82}, {'i': 6, 'j': 5, 'k': 2, 'cost': 54}, {'i': 6, 'j': 5, 'k': 3, 'cost': 27}, {'i': 6, 'j': 5, 'k': 4, 'cost': 91}, {'i': 6, 'j': 5, 'k': 5, 'cost': 18}, {'i': 6, 'j': 5, 'k': 6, 'cost': 15}, {'i': 6, 'j': 5, 'k': 7, 'cost': 8}, {'i': 6, 'j': 5, 'k': 8, 'cost': 45}, {'i': 6, 'j': 6, 'k': 1, 'cost': 97}, {'i': 6, 'j': 6, 'k': 2, 'cost': 73}, {'i': 6, 'j': 6, 'k': 3, 'cost': 99}, {'i': 6, 'j': 6, 'k': 4, 'cost': 84}, {'i': 6, 'j': 6, 'k': 5, 'cost': 66}, {'i': 6, 'j': 6, 'k': 6, 'cost': 10}, {'i': 6, 'j': 6, 'k': 7, 'cost': 14}, {'i': 6, 'j': 6, 'k': 8, 'cost': 59}, {'i': 6, 'j': 7, 'k': 1, 'cost': 38}, {'i': 6, 'j': 7, 'k': 2, 'cost': 30}, {'i': 6, 'j': 7, 'k': 3, 'cost': 89}, {'i': 6, 'j': 7, 'k': 4, 'cost': 21}, {'i': 6, 'j': 7, 'k': 5, 'cost': 85}, {'i': 6, 'j': 7, 'k': 6, 'cost': 69}, {'i': 6, 'j': 7, 'k': 7, 'cost': 39}, {'i': 6, 'j': 7, 'k': 8, 'cost': 44}, {'i': 6, 'j': 8, 'k': 1, 'cost': 6}, {'i': 6, 'j': 8, 'k': 2, 'cost': 14}, {'i': 6, 'j': 8, 'k': 3, 'cost': 76}, {'i': 6, 'j': 8, 'k': 4, 'cost': 64}, {'i': 6, 'j': 8, 'k': 5, 'cost': 39}, {'i': 6, 'j': 8, 'k': 6, 'cost': 92}, {'i': 6, 'j': 8, 'k': 7, 'cost': 17}, {'i': 6, 'j': 8, 'k': 8, 'cost': 13}, {'i': 7, 'j': 1, 'k': 1, 'cost': 3}, {'i': 7, 'j': 1, 'k': 2, 'cost': 80}, {'i': 7, 'j': 1, 'k': 3, 'cost': 6}, {'i': 7, 'j': 1, 'k': 4, 'cost': 68}, {'i': 7, 'j': 1, 'k': 5, 'cost': 39}, {'i': 7, 'j': 1, 'k': 6, 'cost': 24}, {'i': 7, 'j': 1, 'k': 7, 'cost': 2}, {'i': 7, 'j': 1, 'k': 8, 'cost': 87}, {'i': 7, 'j': 2, 'k': 1, 'cost': 36}, {'i': 7, 'j': 2, 'k': 2, 'cost': 87}, {'i': 7, 'j': 2, 'k': 3, 'cost': 67}, {'i': 7, 'j': 2, 'k': 4, 'cost': 78}, {'i': 7, 'j': 2, 'k': 5, 'cost': 29}, {'i': 7, 'j': 2, 'k': 6, 'cost': 35}, {'i': 7, 'j': 2, 'k': 7, 'cost': 48}, {'i': 7, 'j': 2, 'k': 8, 'cost': 98}, {'i': 7, 'j': 3, 'k': 1, 'cost': 48}, {'i': 7, 'j': 3, 'k': 2, 'cost': 99}, {'i': 7, 'j': 3, 'k': 3, 'cost': 91}, {'i': 7, 'j': 3, 'k': 4, 'cost': 82}, {'i': 7, 'j': 3, 'k': 5, 'cost': 35}, {'i': 7, 'j': 3, 'k': 6, 'cost': 5}, {'i': 7, 'j': 3, 'k': 7, 'cost': 53}, {'i': 7, 'j': 3, 'k': 8, 'cost': 9}, {'i': 7, 'j': 4, 'k': 1, 'cost': 23}, {'i': 7, 'j': 4, 'k': 2, 'cost': 2}, {'i': 7, 'j': 4, 'k': 3, 'cost': 71}, {'i': 7, 'j': 4, 'k': 4, 'cost': 32}, {'i': 7, 'j': 4, 'k': 5, 'cost': 16}, {'i': 7, 'j': 4, 'k': 6, 'cost': 18}, {'i': 7, 'j': 4, 'k': 7, 'cost': 3}, {'i': 7, 'j': 4, 'k': 8, 'cost': 36}, {'i': 7, 'j': 5, 'k': 1, 'cost': 38}, {'i': 7, 'j': 5, 'k': 2, 'cost': 23}, {'i': 7, 'j': 5, 'k': 3, 'cost': 93}, {'i': 7, 'j': 5, 'k': 4, 'cost': 80}, {'i': 7, 'j': 5, 'k': 5, 'cost': 37}, {'i': 7, 'j': 5, 'k': 6, 'cost': 63}, {'i': 7, 'j': 5, 'k': 7, 'cost': 2}, {'i': 7, 'j': 5, 'k': 8, 'cost': 87}, {'i': 7, 'j': 6, 'k': 1, 'cost': 85}, {'i': 7, 'j': 6, 'k': 2, 'cost': 21}, {'i': 7, 'j': 6, 'k': 3, 'cost': 59}, {'i': 7, 'j': 6, 'k': 4, 'cost': 69}, {'i': 7, 'j': 6, 'k': 5, 'cost': 31}, {'i': 7, 'j': 6, 'k': 6, 'cost': 89}, {'i': 7, 'j': 6, 'k': 7, 'cost': 28}, {'i': 7, 'j': 6, 'k': 8, 'cost': 98}, {'i': 7, 'j': 7, 'k': 1, 'cost': 93}, {'i': 7, 'j': 7, 'k': 2, 'cost': 79}, {'i': 7, 'j': 7, 'k': 3, 'cost': 72}, {'i': 7, 'j': 7, 'k': 4, 'cost': 14}, {'i': 7, 'j': 7, 'k': 5, 'cost': 40}, {'i': 7, 'j': 7, 'k': 6, 'cost': 72}, {'i': 7, 'j': 7, 'k': 7, 'cost': 64}, {'i': 7, 'j': 7, 'k': 8, 'cost': 44}, {'i': 7, 'j': 8, 'k': 1, 'cost': 67}, {'i': 7, 'j': 8, 'k': 2, 'cost': 9}, {'i': 7, 'j': 8, 'k': 3, 'cost': 30}, {'i': 7, 'j': 8, 'k': 4, 'cost': 83}, {'i': 7, 'j': 8, 'k': 5, 'cost': 13}, {'i': 7, 'j': 8, 'k': 6, 'cost': 68}, {'i': 7, 'j': 8, 'k': 7, 'cost': 63}, {'i': 7, 'j': 8, 'k': 8, 'cost': 92}, {'i': 8, 'j': 1, 'k': 1, 'cost': 92}, {'i': 8, 'j': 1, 'k': 2, 'cost': 40}, {'i': 8, 'j': 1, 'k': 3, 'cost': 14}, {'i': 8, 'j': 1, 'k': 4, 'cost': 2}, {'i': 8, 'j': 1, 'k': 5, 'cost': 60}, {'i': 8, 'j': 1, 'k': 6, 'cost': 8}, {'i': 8, 'j': 1, 'k': 7, 'cost': 39}, {'i': 8, 'j': 1, 'k': 8, 'cost': 25}, {'i': 8, 'j': 2, 'k': 1, 'cost': 28}, {'i': 8, 'j': 2, 'k': 2, 'cost': 59}, {'i': 8, 'j': 2, 'k': 3, 'cost': 19}, {'i': 8, 'j': 2, 'k': 4, 'cost': 61}, {'i': 8, 'j': 2, 'k': 5, 'cost': 52}, {'i': 8, 'j': 2, 'k': 6, 'cost': 46}, {'i': 8, 'j': 2, 'k': 7, 'cost': 21}, {'i': 8, 'j': 2, 'k': 8, 'cost': 30}, {'i': 8, 'j': 3, 'k': 1, 'cost': 89}, {'i': 8, 'j': 3, 'k': 2, 'cost': 47}, {'i': 8, 'j': 3, 'k': 3, 'cost': 27}, {'i': 8, 'j': 3, 'k': 4, 'cost': 54}, {'i': 8, 'j': 3, 'k': 5, 'cost': 59}, {'i': 8, 'j': 3, 'k': 6, 'cost': 57}, {'i': 8, 'j': 3, 'k': 7, 'cost': 19}, {'i': 8, 'j': 3, 'k': 8, 'cost': 82}, {'i': 8, 'j': 4, 'k': 1, 'cost': 23}, {'i': 8, 'j': 4, 'k': 2, 'cost': 22}, {'i': 8, 'j': 4, 'k': 3, 'cost': 17}, {'i': 8, 'j': 4, 'k': 4, 'cost': 94}, {'i': 8, 'j': 4, 'k': 5, 'cost': 3}, {'i': 8, 'j': 4, 'k': 6, 'cost': 75}, {'i': 8, 'j': 4, 'k': 7, 'cost': 1}, {'i': 8, 'j': 4, 'k': 8, 'cost': 44}, {'i': 8, 'j': 5, 'k': 1, 'cost': 61}, {'i': 8, 'j': 5, 'k': 2, 'cost': 13}, {'i': 8, 'j': 5, 'k': 3, 'cost': 45}, {'i': 8, 'j': 5, 'k': 4, 'cost': 19}, {'i': 8, 'j': 5, 'k': 5, 'cost': 46}, {'i': 8, 'j': 5, 'k': 6, 'cost': 10}, {'i': 8, 'j': 5, 'k': 7, 'cost': 80}, {'i': 8, 'j': 5, 'k': 8, 'cost': 82}, {'i': 8, 'j': 6, 'k': 1, 'cost': 92}, {'i': 8, 'j': 6, 'k': 2, 'cost': 57}, {'i': 8, 'j': 6, 'k': 3, 'cost': 33}, {'i': 8, 'j': 6, 'k': 4, 'cost': 76}, {'i': 8, 'j': 6, 'k': 5, 'cost': 78}, {'i': 8, 'j': 6, 'k': 6, 'cost': 80}, {'i': 8, 'j': 6, 'k': 7, 'cost': 62}, {'i': 8, 'j': 6, 'k': 8, 'cost': 66}, {'i': 8, 'j': 7, 'k': 1, 'cost': 40}, {'i': 8, 'j': 7, 'k': 2, 'cost': 29}, {'i': 8, 'j': 7, 'k': 3, 'cost': 71}, {'i': 8, 'j': 7, 'k': 4, 'cost': 10}, {'i': 8, 'j': 7, 'k': 5, 'cost': 23}, {'i': 8, 'j': 7, 'k': 6, 'cost': 36}, {'i': 8, 'j': 7, 'k': 7, 'cost': 83}, {'i': 8, 'j': 7, 'k': 8, 'cost': 29}, {'i': 8, 'j': 8, 'k': 1, 'cost': 95}, {'i': 8, 'j': 8, 'k': 2, 'cost': 32}, {'i': 8, 'j': 8, 'k': 3, 'cost': 18}, {'i': 8, 'j': 8, 'k': 4, 'cost': 68}, {'i': 8, 'j': 8, 'k': 5, 'cost': 80}, {'i': 8, 'j': 8, 'k': 6, 'cost': 6}, {'i': 8, 'j': 8, 'k': 7, 'cost': 96}, {'i': 8, 'j': 8, 'k': 8, 'cost': 8}]}","[[1, 1, 5], [2, 5, 4], [3, 7, 8], [4, 2, 2], [5, 6, 3], [6, 8, 1], [7, 3, 6], [8, 4, 7]]",46,markdown_table,1
AP3,AP3,"I worked with the housing crew to picture a simple scene: every incoming student needs to be handed one dorm room and one choice of a roommate setup, and the rule is strict — each room can go to only one student and each roommate option can only be used once. The trick is to pick those room-plus-roommate pairings so the whole semester’s housing bill is as small as possible — that total comes from adding the cost attached to each student’s chosen room-and-roommate combo. The better plan is the one with the lowest combined cost, and no student, room, or pairing can be skipped or doubled up. Concrete details for the specific students, rooms, roommate options, and costs are shown below.

I list the 6 students, rooms, and roommate options by their identifiers 1, 2, 3, 4, 5, 6.

*Meaning: costs form a 3D tensor. For each fixed student_id=i, you are given a room_id×roommate_option_id matrix whose entry at row room_id=j and column roommate_option_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all room_id and all roommate_option_id used exactly once.*

**assignment_cost_tensor (per-student_id markdown matrices)**

## student_id=1
| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 21 | 20 | 90 | 71 | 46 | 71 |
| 2 | 96 | 48 | 59 | 31 | 12 | 59 |
| 3 | 66 | 55 | 87 | 93 | 60 | 1 |
| 4 | 80 | 84 | 22 | 53 | 55 | 29 |
| 5 | 89 | 42 | 3 | 89 | 45 | 62 |
| 6 | 5 | 90 | 15 | 14 | 28 | 14 |

## student_id=2
| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 30 | 19 | 4 | 42 | 58 | 38 |
| 2 | 19 | 57 | 57 | 71 | 37 | 48 |
| 3 | 10 | 32 | 61 | 41 | 93 | 95 |
| 4 | 95 | 98 | 44 | 20 | 14 | 60 |
| 5 | 56 | 41 | 76 | 7 | 3 | 29 |
| 6 | 56 | 17 | 82 | 18 | 89 | 51 |

## student_id=3
| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 69 | 54 | 73 | 96 | 10 | 16 |
| 2 | 93 | 56 | 84 | 88 | 54 | 69 |
| 3 | 42 | 20 | 92 | 34 | 8 | 76 |
| 4 | 12 | 17 | 56 | 85 | 39 | 74 |
| 5 | 66 | 17 | 38 | 59 | 58 | 25 |
| 6 | 81 | 77 | 57 | 90 | 83 | 14 |

## student_id=4
| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 34 | 26 | 1 | 17 | 28 | 35 |
| 2 | 39 | 55 | 82 | 84 | 43 | 84 |
| 3 | 85 | 12 | 31 | 69 | 11 | 14 |
| 4 | 29 | 90 | 0 | 11 | 35 | 24 |
| 5 | 69 | 51 | 95 | 56 | 92 | 56 |
| 6 | 54 | 60 | 86 | 60 | 45 | 44 |

## student_id=5
| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 78 | 74 | 0 | 70 | 2 | 60 |
| 2 | 37 | 99 | 2 | 44 | 43 | 89 |
| 3 | 21 | 33 | 45 | 27 | 67 | 11 |
| 4 | 1 | 0 | 29 | 49 | 69 | 95 |
| 5 | 73 | 58 | 63 | 94 | 47 | 67 |
| 6 | 7 | 87 | 22 | 43 | 66 | 16 |

## student_id=6
| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 17 | 70 | 90 | 7 | 80 | 89 |
| 2 | 28 | 66 | 2 | 40 | 52 | 16 |
| 3 | 90 | 44 | 5 | 73 | 99 | 7 |
| 4 | 47 | 65 | 4 | 35 | 64 | 7 |
| 5 | 45 | 89 | 65 | 51 | 23 | 35 |
| 6 | 35 | 16 | 26 | 36 | 99 | 38 |

I will pick one triple per student so the sum of these costs is minimized.

I'll sketch the shape of the reply I need in case it helps — just a simple JSON list showing which student gets which room and which roommate option.

{
  ""solution"": [
    [<student_id>, <room_id>, <roommate_option_id>]
  ]
}

This is just a lightweight example: ""solution"" is an array of triples, and each triple is one student's final pick — first the student, then the room they get, then the roommate option chosen. Think of it like filling out a form for each incoming student: one line per student with those three labels.

The JSON above is only a sketch of the expected shape, not the actual answer. Also, please use the identifiers exactly as they appear in the instance input — don't rename them or invent new ones.  
- 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”.""","{'cost_tensor': [[[21, 20, 90, 71, 46, 71], [96, 48, 59, 31, 12, 59], [66, 55, 87, 93, 60, 1], [80, 84, 22, 53, 55, 29], [89, 42, 3, 89, 45, 62], [5, 90, 15, 14, 28, 14]], [[30, 19, 4, 42, 58, 38], [19, 57, 57, 71, 37, 48], [10, 32, 61, 41, 93, 95], [95, 98, 44, 20, 14, 60], [56, 41, 76, 7, 3, 29], [56, 17, 82, 18, 89, 51]], [[69, 54, 73, 96, 10, 16], [93, 56, 84, 88, 54, 69], [42, 20, 92, 34, 8, 76], [12, 17, 56, 85, 39, 74], [66, 17, 38, 59, 58, 25], [81, 77, 57, 90, 83, 14]], [[34, 26, 1, 17, 28, 35], [39, 55, 82, 84, 43, 84], [85, 12, 31, 69, 11, 14], [29, 90, 0, 11, 35, 24], [69, 51, 95, 56, 92, 56], [54, 60, 86, 60, 45, 44]], [[78, 74, 0, 70, 2, 60], [37, 99, 2, 44, 43, 89], [21, 33, 45, 27, 67, 11], [1, 0, 29, 49, 69, 95], [73, 58, 63, 94, 47, 67], [7, 87, 22, 43, 66, 16]], [[17, 70, 90, 7, 80, 89], [28, 66, 2, 40, 52, 16], [90, 44, 5, 73, 99, 7], [47, 65, 4, 35, 64, 7], [45, 89, 65, 51, 23, 35], [35, 16, 26, 36, 99, 38]]], 'objective': 37.0}","[[0, 5, 0], [1, 4, 3], [2, 2, 4], [3, 0, 2], [4, 3, 1], [5, 1, 5]]",37.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 21}, {'i': 1, 'j': 1, 'k': 2, 'cost': 20}, {'i': 1, 'j': 1, 'k': 3, 'cost': 90}, {'i': 1, 'j': 1, 'k': 4, 'cost': 71}, {'i': 1, 'j': 1, 'k': 5, 'cost': 46}, {'i': 1, 'j': 1, 'k': 6, 'cost': 71}, {'i': 1, 'j': 2, 'k': 1, 'cost': 96}, {'i': 1, 'j': 2, 'k': 2, 'cost': 48}, {'i': 1, 'j': 2, 'k': 3, 'cost': 59}, {'i': 1, 'j': 2, 'k': 4, 'cost': 31}, {'i': 1, 'j': 2, 'k': 5, 'cost': 12}, {'i': 1, 'j': 2, 'k': 6, 'cost': 59}, {'i': 1, 'j': 3, 'k': 1, 'cost': 66}, {'i': 1, 'j': 3, 'k': 2, 'cost': 55}, {'i': 1, 'j': 3, 'k': 3, 'cost': 87}, {'i': 1, 'j': 3, 'k': 4, 'cost': 93}, {'i': 1, 'j': 3, 'k': 5, 'cost': 60}, {'i': 1, 'j': 3, 'k': 6, 'cost': 1}, {'i': 1, 'j': 4, 'k': 1, 'cost': 80}, {'i': 1, 'j': 4, 'k': 2, 'cost': 84}, {'i': 1, 'j': 4, 'k': 3, 'cost': 22}, {'i': 1, 'j': 4, 'k': 4, 'cost': 53}, {'i': 1, 'j': 4, 'k': 5, 'cost': 55}, {'i': 1, 'j': 4, 'k': 6, 'cost': 29}, {'i': 1, 'j': 5, 'k': 1, 'cost': 89}, {'i': 1, 'j': 5, 'k': 2, 'cost': 42}, {'i': 1, 'j': 5, 'k': 3, 'cost': 3}, {'i': 1, 'j': 5, 'k': 4, 'cost': 89}, {'i': 1, 'j': 5, 'k': 5, 'cost': 45}, {'i': 1, 'j': 5, 'k': 6, 'cost': 62}, {'i': 1, 'j': 6, 'k': 1, 'cost': 5}, {'i': 1, 'j': 6, 'k': 2, 'cost': 90}, {'i': 1, 'j': 6, 'k': 3, 'cost': 15}, {'i': 1, 'j': 6, 'k': 4, 'cost': 14}, {'i': 1, 'j': 6, 'k': 5, 'cost': 28}, {'i': 1, 'j': 6, 'k': 6, 'cost': 14}, {'i': 2, 'j': 1, 'k': 1, 'cost': 30}, {'i': 2, 'j': 1, 'k': 2, 'cost': 19}, {'i': 2, 'j': 1, 'k': 3, 'cost': 4}, {'i': 2, 'j': 1, 'k': 4, 'cost': 42}, {'i': 2, 'j': 1, 'k': 5, 'cost': 58}, {'i': 2, 'j': 1, 'k': 6, 'cost': 38}, {'i': 2, 'j': 2, 'k': 1, 'cost': 19}, {'i': 2, 'j': 2, 'k': 2, 'cost': 57}, {'i': 2, 'j': 2, 'k': 3, 'cost': 57}, {'i': 2, 'j': 2, 'k': 4, 'cost': 71}, {'i': 2, 'j': 2, 'k': 5, 'cost': 37}, {'i': 2, 'j': 2, 'k': 6, 'cost': 48}, {'i': 2, 'j': 3, 'k': 1, 'cost': 10}, {'i': 2, 'j': 3, 'k': 2, 'cost': 32}, {'i': 2, 'j': 3, 'k': 3, 'cost': 61}, {'i': 2, 'j': 3, 'k': 4, 'cost': 41}, {'i': 2, 'j': 3, 'k': 5, 'cost': 93}, {'i': 2, 'j': 3, 'k': 6, 'cost': 95}, {'i': 2, 'j': 4, 'k': 1, 'cost': 95}, {'i': 2, 'j': 4, 'k': 2, 'cost': 98}, {'i': 2, 'j': 4, 'k': 3, 'cost': 44}, {'i': 2, 'j': 4, 'k': 4, 'cost': 20}, {'i': 2, 'j': 4, 'k': 5, 'cost': 14}, {'i': 2, 'j': 4, 'k': 6, 'cost': 60}, {'i': 2, 'j': 5, 'k': 1, 'cost': 56}, {'i': 2, 'j': 5, 'k': 2, 'cost': 41}, {'i': 2, 'j': 5, 'k': 3, 'cost': 76}, {'i': 2, 'j': 5, 'k': 4, 'cost': 7}, {'i': 2, 'j': 5, 'k': 5, 'cost': 3}, {'i': 2, 'j': 5, 'k': 6, 'cost': 29}, {'i': 2, 'j': 6, 'k': 1, 'cost': 56}, {'i': 2, 'j': 6, 'k': 2, 'cost': 17}, {'i': 2, 'j': 6, 'k': 3, 'cost': 82}, {'i': 2, 'j': 6, 'k': 4, 'cost': 18}, {'i': 2, 'j': 6, 'k': 5, 'cost': 89}, {'i': 2, 'j': 6, 'k': 6, 'cost': 51}, {'i': 3, 'j': 1, 'k': 1, 'cost': 69}, {'i': 3, 'j': 1, 'k': 2, 'cost': 54}, {'i': 3, 'j': 1, 'k': 3, 'cost': 73}, {'i': 3, 'j': 1, 'k': 4, 'cost': 96}, {'i': 3, 'j': 1, 'k': 5, 'cost': 10}, {'i': 3, 'j': 1, 'k': 6, 'cost': 16}, {'i': 3, 'j': 2, 'k': 1, 'cost': 93}, {'i': 3, 'j': 2, 'k': 2, 'cost': 56}, {'i': 3, 'j': 2, 'k': 3, 'cost': 84}, {'i': 3, 'j': 2, 'k': 4, 'cost': 88}, {'i': 3, 'j': 2, 'k': 5, 'cost': 54}, {'i': 3, 'j': 2, 'k': 6, 'cost': 69}, {'i': 3, 'j': 3, 'k': 1, 'cost': 42}, {'i': 3, 'j': 3, 'k': 2, 'cost': 20}, {'i': 3, 'j': 3, 'k': 3, 'cost': 92}, {'i': 3, 'j': 3, 'k': 4, 'cost': 34}, {'i': 3, 'j': 3, 'k': 5, 'cost': 8}, {'i': 3, 'j': 3, 'k': 6, 'cost': 76}, {'i': 3, 'j': 4, 'k': 1, 'cost': 12}, {'i': 3, 'j': 4, 'k': 2, 'cost': 17}, {'i': 3, 'j': 4, 'k': 3, 'cost': 56}, {'i': 3, 'j': 4, 'k': 4, 'cost': 85}, {'i': 3, 'j': 4, 'k': 5, 'cost': 39}, {'i': 3, 'j': 4, 'k': 6, 'cost': 74}, {'i': 3, 'j': 5, 'k': 1, 'cost': 66}, {'i': 3, 'j': 5, 'k': 2, 'cost': 17}, {'i': 3, 'j': 5, 'k': 3, 'cost': 38}, {'i': 3, 'j': 5, 'k': 4, 'cost': 59}, {'i': 3, 'j': 5, 'k': 5, 'cost': 58}, {'i': 3, 'j': 5, 'k': 6, 'cost': 25}, {'i': 3, 'j': 6, 'k': 1, 'cost': 81}, {'i': 3, 'j': 6, 'k': 2, 'cost': 77}, {'i': 3, 'j': 6, 'k': 3, 'cost': 57}, {'i': 3, 'j': 6, 'k': 4, 'cost': 90}, {'i': 3, 'j': 6, 'k': 5, 'cost': 83}, {'i': 3, 'j': 6, 'k': 6, 'cost': 14}, {'i': 4, 'j': 1, 'k': 1, 'cost': 34}, {'i': 4, 'j': 1, 'k': 2, 'cost': 26}, {'i': 4, 'j': 1, 'k': 3, 'cost': 1}, {'i': 4, 'j': 1, 'k': 4, 'cost': 17}, {'i': 4, 'j': 1, 'k': 5, 'cost': 28}, {'i': 4, 'j': 1, 'k': 6, 'cost': 35}, {'i': 4, 'j': 2, 'k': 1, 'cost': 39}, {'i': 4, 'j': 2, 'k': 2, 'cost': 55}, {'i': 4, 'j': 2, 'k': 3, 'cost': 82}, {'i': 4, 'j': 2, 'k': 4, 'cost': 84}, {'i': 4, 'j': 2, 'k': 5, 'cost': 43}, {'i': 4, 'j': 2, 'k': 6, 'cost': 84}, {'i': 4, 'j': 3, 'k': 1, 'cost': 85}, {'i': 4, 'j': 3, 'k': 2, 'cost': 12}, {'i': 4, 'j': 3, 'k': 3, 'cost': 31}, {'i': 4, 'j': 3, 'k': 4, 'cost': 69}, {'i': 4, 'j': 3, 'k': 5, 'cost': 11}, {'i': 4, 'j': 3, 'k': 6, 'cost': 14}, {'i': 4, 'j': 4, 'k': 1, 'cost': 29}, {'i': 4, 'j': 4, 'k': 2, 'cost': 90}, {'i': 4, 'j': 4, 'k': 3, 'cost': 0}, {'i': 4, 'j': 4, 'k': 4, 'cost': 11}, {'i': 4, 'j': 4, 'k': 5, 'cost': 35}, {'i': 4, 'j': 4, 'k': 6, 'cost': 24}, {'i': 4, 'j': 5, 'k': 1, 'cost': 69}, {'i': 4, 'j': 5, 'k': 2, 'cost': 51}, {'i': 4, 'j': 5, 'k': 3, 'cost': 95}, {'i': 4, 'j': 5, 'k': 4, 'cost': 56}, {'i': 4, 'j': 5, 'k': 5, 'cost': 92}, {'i': 4, 'j': 5, 'k': 6, 'cost': 56}, {'i': 4, 'j': 6, 'k': 1, 'cost': 54}, {'i': 4, 'j': 6, 'k': 2, 'cost': 60}, {'i': 4, 'j': 6, 'k': 3, 'cost': 86}, {'i': 4, 'j': 6, 'k': 4, 'cost': 60}, {'i': 4, 'j': 6, 'k': 5, 'cost': 45}, {'i': 4, 'j': 6, 'k': 6, 'cost': 44}, {'i': 5, 'j': 1, 'k': 1, 'cost': 78}, {'i': 5, 'j': 1, 'k': 2, 'cost': 74}, {'i': 5, 'j': 1, 'k': 3, 'cost': 0}, {'i': 5, 'j': 1, 'k': 4, 'cost': 70}, {'i': 5, 'j': 1, 'k': 5, 'cost': 2}, {'i': 5, 'j': 1, 'k': 6, 'cost': 60}, {'i': 5, 'j': 2, 'k': 1, 'cost': 37}, {'i': 5, 'j': 2, 'k': 2, 'cost': 99}, {'i': 5, 'j': 2, 'k': 3, 'cost': 2}, {'i': 5, 'j': 2, 'k': 4, 'cost': 44}, {'i': 5, 'j': 2, 'k': 5, 'cost': 43}, {'i': 5, 'j': 2, 'k': 6, 'cost': 89}, {'i': 5, 'j': 3, 'k': 1, 'cost': 21}, {'i': 5, 'j': 3, 'k': 2, 'cost': 33}, {'i': 5, 'j': 3, 'k': 3, 'cost': 45}, {'i': 5, 'j': 3, 'k': 4, 'cost': 27}, {'i': 5, 'j': 3, 'k': 5, 'cost': 67}, {'i': 5, 'j': 3, 'k': 6, 'cost': 11}, {'i': 5, 'j': 4, 'k': 1, 'cost': 1}, {'i': 5, 'j': 4, 'k': 2, 'cost': 0}, {'i': 5, 'j': 4, 'k': 3, 'cost': 29}, {'i': 5, 'j': 4, 'k': 4, 'cost': 49}, {'i': 5, 'j': 4, 'k': 5, 'cost': 69}, {'i': 5, 'j': 4, 'k': 6, 'cost': 95}, {'i': 5, 'j': 5, 'k': 1, 'cost': 73}, {'i': 5, 'j': 5, 'k': 2, 'cost': 58}, {'i': 5, 'j': 5, 'k': 3, 'cost': 63}, {'i': 5, 'j': 5, 'k': 4, 'cost': 94}, {'i': 5, 'j': 5, 'k': 5, 'cost': 47}, {'i': 5, 'j': 5, 'k': 6, 'cost': 67}, {'i': 5, 'j': 6, 'k': 1, 'cost': 7}, {'i': 5, 'j': 6, 'k': 2, 'cost': 87}, {'i': 5, 'j': 6, 'k': 3, 'cost': 22}, {'i': 5, 'j': 6, 'k': 4, 'cost': 43}, {'i': 5, 'j': 6, 'k': 5, 'cost': 66}, {'i': 5, 'j': 6, 'k': 6, 'cost': 16}, {'i': 6, 'j': 1, 'k': 1, 'cost': 17}, {'i': 6, 'j': 1, 'k': 2, 'cost': 70}, {'i': 6, 'j': 1, 'k': 3, 'cost': 90}, {'i': 6, 'j': 1, 'k': 4, 'cost': 7}, {'i': 6, 'j': 1, 'k': 5, 'cost': 80}, {'i': 6, 'j': 1, 'k': 6, 'cost': 89}, {'i': 6, 'j': 2, 'k': 1, 'cost': 28}, {'i': 6, 'j': 2, 'k': 2, 'cost': 66}, {'i': 6, 'j': 2, 'k': 3, 'cost': 2}, {'i': 6, 'j': 2, 'k': 4, 'cost': 40}, {'i': 6, 'j': 2, 'k': 5, 'cost': 52}, {'i': 6, 'j': 2, 'k': 6, 'cost': 16}, {'i': 6, 'j': 3, 'k': 1, 'cost': 90}, {'i': 6, 'j': 3, 'k': 2, 'cost': 44}, {'i': 6, 'j': 3, 'k': 3, 'cost': 5}, {'i': 6, 'j': 3, 'k': 4, 'cost': 73}, {'i': 6, 'j': 3, 'k': 5, 'cost': 99}, {'i': 6, 'j': 3, 'k': 6, 'cost': 7}, {'i': 6, 'j': 4, 'k': 1, 'cost': 47}, {'i': 6, 'j': 4, 'k': 2, 'cost': 65}, {'i': 6, 'j': 4, 'k': 3, 'cost': 4}, {'i': 6, 'j': 4, 'k': 4, 'cost': 35}, {'i': 6, 'j': 4, 'k': 5, 'cost': 64}, {'i': 6, 'j': 4, 'k': 6, 'cost': 7}, {'i': 6, 'j': 5, 'k': 1, 'cost': 45}, {'i': 6, 'j': 5, 'k': 2, 'cost': 89}, {'i': 6, 'j': 5, 'k': 3, 'cost': 65}, {'i': 6, 'j': 5, 'k': 4, 'cost': 51}, {'i': 6, 'j': 5, 'k': 5, 'cost': 23}, {'i': 6, 'j': 5, 'k': 6, 'cost': 35}, {'i': 6, 'j': 6, 'k': 1, 'cost': 35}, {'i': 6, 'j': 6, 'k': 2, 'cost': 16}, {'i': 6, 'j': 6, 'k': 3, 'cost': 26}, {'i': 6, 'j': 6, 'k': 4, 'cost': 36}, {'i': 6, 'j': 6, 'k': 5, 'cost': 99}, {'i': 6, 'j': 6, 'k': 6, 'cost': 38}]}","[[1, 6, 1], [2, 5, 4], [3, 3, 5], [4, 1, 3], [5, 4, 2], [6, 2, 6]]",47,markdown_table,1
AP3,AP3,"There's a busy week at the garden center where each landscaping project needs a single plant source and a single delivery slot. No supplier or delivery slot can be stretched across multiple projects, and every project must get exactly one supplier and one delivery date. Each possible pairing of project, supplier, and date carries a cost, so better choices are the ones that make the overall bill — calculated by adding up the cost for each project's chosen pairing — smaller. The specific jobs, suppliers, dates, and their costs follow below.

{
  ""job_count"": 6,
  ""index_identifiers"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F""
  ]
}

# Meaning: costs form a 3D tensor. For each fixed job_id=i, you are given a supplier_id×delivery_date_id matrix whose entry at row supplier_id=j and column delivery_date_id=k equals procurement_and_delivery_cost(i,j,k). You must pick exactly one (j,k) for every i, with all supplier_id and all delivery_date_id used exactly once.
# procurement_and_delivery_cost_tensor (per-job_id markdown matrices)

## job_id=A
| supplier_id\delivery_date_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 69 | 83 | 86 | 38 | 59 | 3 |
| B | 79 | 85 | 61 | 29 | 55 | 72 |
| C | 60 | 4 | 23 | 70 | 62 | 35 |
| D | 89 | 62 | 26 | 6 | 48 | 70 |
| E | 18 | 42 | 24 | 45 | 60 | 59 |
| F | 1 | 32 | 14 | 76 | 29 | 51 |

## job_id=B
| supplier_id\delivery_date_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 46 | 22 | 48 | 89 | 51 | 70 |
| B | 13 | 61 | 66 | 35 | 24 | 69 |
| C | 71 | 76 | 67 | 8 | 77 | 36 |
| D | 97 | 90 | 52 | 89 | 67 | 71 |
| E | 67 | 34 | 97 | 47 | 58 | 87 |
| F | 74 | 86 | 54 | 45 | 28 | 8 |

## job_id=C
| supplier_id\delivery_date_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 82 | 28 | 91 | 86 | 72 | 79 |
| B | 65 | 98 | 53 | 77 | 10 | 1 |
| C | 23 | 69 | 97 | 75 | 82 | 84 |
| D | 1 | 13 | 91 | 54 | 42 | 70 |
| E | 50 | 11 | 89 | 92 | 37 | 53 |
| F | 39 | 8 | 99 | 94 | 27 | 38 |

## job_id=D
| supplier_id\delivery_date_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 22 | 40 | 99 | 4 | 83 | 5 |
| B | 41 | 89 | 95 | 43 | 30 | 25 |
| C | 95 | 62 | 5 | 80 | 35 | 52 |
| D | 9 | 54 | 77 | 20 | 94 | 47 |
| E | 29 | 15 | 47 | 20 | 5 | 75 |
| F | 40 | 20 | 81 | 12 | 18 | 77 |

## job_id=E
| supplier_id\delivery_date_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 69 | 47 | 36 | 11 | 97 | 5 |
| B | 90 | 84 | 86 | 38 | 94 | 85 |
| C | 94 | 94 | 18 | 22 | 34 | 61 |
| D | 74 | 45 | 90 | 16 | 78 | 93 |
| E | 35 | 90 | 13 | 9 | 91 | 85 |
| F | 77 | 87 | 70 | 90 | 72 | 96 |

## job_id=F
| supplier_id\delivery_date_id | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| A | 21 | 61 | 91 | 89 | 58 | 73 |
| B | 66 | 64 | 43 | 52 | 44 | 64 |
| C | 61 | 37 | 92 | 5 | 29 | 8 |
| D | 93 | 58 | 7 | 40 | 12 | 41 |
| E | 66 | 89 | 29 | 69 | 14 | 78 |
| F | 97 | 97 | 37 | 58 | 8 | 32 |

Also, when you send the final matching, a relaxed little JSON snippet like this is perfect — a single list of triples, each triple saying which project gets which supplier and which delivery slot:

{
  ""solution"": [
    [<project_id>, <supplier_id>, <date_id>],
    ...
  ]
}

Each inner array is one assignment: the first entry is the project, the second is the chosen plant supplier, and the third is the delivery date/slot. Think of it like filling out a tiny form for each job. This JSON is just the shape I expect, not the actual solution — replace the placeholders with the actual identifiers from the instance when you submit your answer.

Please use the exact identifiers from the instance input — no renaming and no 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”.","{'cost_tensor': [[[69, 83, 86, 38, 59, 3], [79, 85, 61, 29, 55, 72], [60, 4, 23, 70, 62, 35], [89, 62, 26, 6, 48, 70], [18, 42, 24, 45, 60, 59], [1, 32, 14, 76, 29, 51]], [[46, 22, 48, 89, 51, 70], [13, 61, 66, 35, 24, 69], [71, 76, 67, 8, 77, 36], [97, 90, 52, 89, 67, 71], [67, 34, 97, 47, 58, 87], [74, 86, 54, 45, 28, 8]], [[82, 28, 91, 86, 72, 79], [65, 98, 53, 77, 10, 1], [23, 69, 97, 75, 82, 84], [1, 13, 91, 54, 42, 70], [50, 11, 89, 92, 37, 53], [39, 8, 99, 94, 27, 38]], [[22, 40, 99, 4, 83, 5], [41, 89, 95, 43, 30, 25], [95, 62, 5, 80, 35, 52], [9, 54, 77, 20, 94, 47], [29, 15, 47, 20, 5, 75], [40, 20, 81, 12, 18, 77]], [[69, 47, 36, 11, 97, 5], [90, 84, 86, 38, 94, 85], [94, 94, 18, 22, 34, 61], [74, 45, 90, 16, 78, 93], [35, 90, 13, 9, 91, 85], [77, 87, 70, 90, 72, 96]], [[21, 61, 91, 89, 58, 73], [66, 64, 43, 52, 44, 64], [61, 37, 92, 5, 29, 8], [93, 58, 7, 40, 12, 41], [66, 89, 29, 69, 14, 78], [97, 97, 37, 58, 8, 32]]], 'objective': 46.0}","[[0, 5, 0], [1, 2, 3], [2, 1, 4], [3, 4, 1], [4, 0, 5], [5, 3, 2]]",46.0,"{'problem_type': 'AP3', 'n': 6, 'ids': ['A', 'B', 'C', 'D', 'E', 'F'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 69}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 83}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 86}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 38}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 59}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 3}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 79}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 85}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 61}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 29}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 55}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 72}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 60}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 4}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 23}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 70}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 62}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 35}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 89}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 62}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 26}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 6}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 48}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 70}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 42}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 24}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 45}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 60}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 59}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 1}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 32}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 14}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 76}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 29}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 51}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 46}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 22}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 48}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 89}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 51}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 70}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 13}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 61}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 66}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 35}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 24}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 69}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 71}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 76}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 67}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 8}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 77}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 36}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 97}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 90}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 52}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 89}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 67}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 71}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 67}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 34}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 97}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 47}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 58}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 87}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 74}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 86}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 54}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 45}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 28}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 8}, {'i': 'C', 'j': 'A', 'k': 'A', 'cost': 82}, {'i': 'C', 'j': 'A', 'k': 'B', 'cost': 28}, {'i': 'C', 'j': 'A', 'k': 'C', 'cost': 91}, {'i': 'C', 'j': 'A', 'k': 'D', 'cost': 86}, {'i': 'C', 'j': 'A', 'k': 'E', 'cost': 72}, {'i': 'C', 'j': 'A', 'k': 'F', 'cost': 79}, {'i': 'C', 'j': 'B', 'k': 'A', 'cost': 65}, {'i': 'C', 'j': 'B', 'k': 'B', 'cost': 98}, {'i': 'C', 'j': 'B', 'k': 'C', 'cost': 53}, {'i': 'C', 'j': 'B', 'k': 'D', 'cost': 77}, {'i': 'C', 'j': 'B', 'k': 'E', 'cost': 10}, {'i': 'C', 'j': 'B', 'k': 'F', 'cost': 1}, {'i': 'C', 'j': 'C', 'k': 'A', 'cost': 23}, {'i': 'C', 'j': 'C', 'k': 'B', 'cost': 69}, {'i': 'C', 'j': 'C', 'k': 'C', 'cost': 97}, {'i': 'C', 'j': 'C', 'k': 'D', 'cost': 75}, {'i': 'C', 'j': 'C', 'k': 'E', 'cost': 82}, {'i': 'C', 'j': 'C', 'k': 'F', 'cost': 84}, {'i': 'C', 'j': 'D', 'k': 'A', 'cost': 1}, {'i': 'C', 'j': 'D', 'k': 'B', 'cost': 13}, {'i': 'C', 'j': 'D', 'k': 'C', 'cost': 91}, {'i': 'C', 'j': 'D', 'k': 'D', 'cost': 54}, {'i': 'C', 'j': 'D', 'k': 'E', 'cost': 42}, {'i': 'C', 'j': 'D', 'k': 'F', 'cost': 70}, {'i': 'C', 'j': 'E', 'k': 'A', 'cost': 50}, {'i': 'C', 'j': 'E', 'k': 'B', 'cost': 11}, {'i': 'C', 'j': 'E', 'k': 'C', 'cost': 89}, {'i': 'C', 'j': 'E', 'k': 'D', 'cost': 92}, {'i': 'C', 'j': 'E', 'k': 'E', 'cost': 37}, {'i': 'C', 'j': 'E', 'k': 'F', 'cost': 53}, {'i': 'C', 'j': 'F', 'k': 'A', 'cost': 39}, {'i': 'C', 'j': 'F', 'k': 'B', 'cost': 8}, {'i': 'C', 'j': 'F', 'k': 'C', 'cost': 99}, {'i': 'C', 'j': 'F', 'k': 'D', 'cost': 94}, {'i': 'C', 'j': 'F', 'k': 'E', 'cost': 27}, {'i': 'C', 'j': 'F', 'k': 'F', 'cost': 38}, {'i': 'D', 'j': 'A', 'k': 'A', 'cost': 22}, {'i': 'D', 'j': 'A', 'k': 'B', 'cost': 40}, {'i': 'D', 'j': 'A', 'k': 'C', 'cost': 99}, {'i': 'D', 'j': 'A', 'k': 'D', 'cost': 4}, {'i': 'D', 'j': 'A', 'k': 'E', 'cost': 83}, {'i': 'D', 'j': 'A', 'k': 'F', 'cost': 5}, {'i': 'D', 'j': 'B', 'k': 'A', 'cost': 41}, {'i': 'D', 'j': 'B', 'k': 'B', 'cost': 89}, {'i': 'D', 'j': 'B', 'k': 'C', 'cost': 95}, {'i': 'D', 'j': 'B', 'k': 'D', 'cost': 43}, {'i': 'D', 'j': 'B', 'k': 'E', 'cost': 30}, {'i': 'D', 'j': 'B', 'k': 'F', 'cost': 25}, {'i': 'D', 'j': 'C', 'k': 'A', 'cost': 95}, {'i': 'D', 'j': 'C', 'k': 'B', 'cost': 62}, {'i': 'D', 'j': 'C', 'k': 'C', 'cost': 5}, {'i': 'D', 'j': 'C', 'k': 'D', 'cost': 80}, {'i': 'D', 'j': 'C', 'k': 'E', 'cost': 35}, {'i': 'D', 'j': 'C', 'k': 'F', 'cost': 52}, {'i': 'D', 'j': 'D', 'k': 'A', 'cost': 9}, {'i': 'D', 'j': 'D', 'k': 'B', 'cost': 54}, {'i': 'D', 'j': 'D', 'k': 'C', 'cost': 77}, {'i': 'D', 'j': 'D', 'k': 'D', 'cost': 20}, {'i': 'D', 'j': 'D', 'k': 'E', 'cost': 94}, {'i': 'D', 'j': 'D', 'k': 'F', 'cost': 47}, {'i': 'D', 'j': 'E', 'k': 'A', 'cost': 29}, {'i': 'D', 'j': 'E', 'k': 'B', 'cost': 15}, {'i': 'D', 'j': 'E', 'k': 'C', 'cost': 47}, {'i': 'D', 'j': 'E', 'k': 'D', 'cost': 20}, {'i': 'D', 'j': 'E', 'k': 'E', 'cost': 5}, {'i': 'D', 'j': 'E', 'k': 'F', 'cost': 75}, {'i': 'D', 'j': 'F', 'k': 'A', 'cost': 40}, {'i': 'D', 'j': 'F', 'k': 'B', 'cost': 20}, {'i': 'D', 'j': 'F', 'k': 'C', 'cost': 81}, {'i': 'D', 'j': 'F', 'k': 'D', 'cost': 12}, {'i': 'D', 'j': 'F', 'k': 'E', 'cost': 18}, {'i': 'D', 'j': 'F', 'k': 'F', 'cost': 77}, {'i': 'E', 'j': 'A', 'k': 'A', 'cost': 69}, {'i': 'E', 'j': 'A', 'k': 'B', 'cost': 47}, {'i': 'E', 'j': 'A', 'k': 'C', 'cost': 36}, {'i': 'E', 'j': 'A', 'k': 'D', 'cost': 11}, {'i': 'E', 'j': 'A', 'k': 'E', 'cost': 97}, {'i': 'E', 'j': 'A', 'k': 'F', 'cost': 5}, {'i': 'E', 'j': 'B', 'k': 'A', 'cost': 90}, {'i': 'E', 'j': 'B', 'k': 'B', 'cost': 84}, {'i': 'E', 'j': 'B', 'k': 'C', 'cost': 86}, {'i': 'E', 'j': 'B', 'k': 'D', 'cost': 38}, {'i': 'E', 'j': 'B', 'k': 'E', 'cost': 94}, {'i': 'E', 'j': 'B', 'k': 'F', 'cost': 85}, {'i': 'E', 'j': 'C', 'k': 'A', 'cost': 94}, {'i': 'E', 'j': 'C', 'k': 'B', 'cost': 94}, {'i': 'E', 'j': 'C', 'k': 'C', 'cost': 18}, {'i': 'E', 'j': 'C', 'k': 'D', 'cost': 22}, {'i': 'E', 'j': 'C', 'k': 'E', 'cost': 34}, {'i': 'E', 'j': 'C', 'k': 'F', 'cost': 61}, {'i': 'E', 'j': 'D', 'k': 'A', 'cost': 74}, {'i': 'E', 'j': 'D', 'k': 'B', 'cost': 45}, {'i': 'E', 'j': 'D', 'k': 'C', 'cost': 90}, {'i': 'E', 'j': 'D', 'k': 'D', 'cost': 16}, {'i': 'E', 'j': 'D', 'k': 'E', 'cost': 78}, {'i': 'E', 'j': 'D', 'k': 'F', 'cost': 93}, {'i': 'E', 'j': 'E', 'k': 'A', 'cost': 35}, {'i': 'E', 'j': 'E', 'k': 'B', 'cost': 90}, {'i': 'E', 'j': 'E', 'k': 'C', 'cost': 13}, {'i': 'E', 'j': 'E', 'k': 'D', 'cost': 9}, {'i': 'E', 'j': 'E', 'k': 'E', 'cost': 91}, {'i': 'E', 'j': 'E', 'k': 'F', 'cost': 85}, {'i': 'E', 'j': 'F', 'k': 'A', 'cost': 77}, {'i': 'E', 'j': 'F', 'k': 'B', 'cost': 87}, {'i': 'E', 'j': 'F', 'k': 'C', 'cost': 70}, {'i': 'E', 'j': 'F', 'k': 'D', 'cost': 90}, {'i': 'E', 'j': 'F', 'k': 'E', 'cost': 72}, {'i': 'E', 'j': 'F', 'k': 'F', 'cost': 96}, {'i': 'F', 'j': 'A', 'k': 'A', 'cost': 21}, {'i': 'F', 'j': 'A', 'k': 'B', 'cost': 61}, {'i': 'F', 'j': 'A', 'k': 'C', 'cost': 91}, {'i': 'F', 'j': 'A', 'k': 'D', 'cost': 89}, {'i': 'F', 'j': 'A', 'k': 'E', 'cost': 58}, {'i': 'F', 'j': 'A', 'k': 'F', 'cost': 73}, {'i': 'F', 'j': 'B', 'k': 'A', 'cost': 66}, {'i': 'F', 'j': 'B', 'k': 'B', 'cost': 64}, {'i': 'F', 'j': 'B', 'k': 'C', 'cost': 43}, {'i': 'F', 'j': 'B', 'k': 'D', 'cost': 52}, {'i': 'F', 'j': 'B', 'k': 'E', 'cost': 44}, {'i': 'F', 'j': 'B', 'k': 'F', 'cost': 64}, {'i': 'F', 'j': 'C', 'k': 'A', 'cost': 61}, {'i': 'F', 'j': 'C', 'k': 'B', 'cost': 37}, {'i': 'F', 'j': 'C', 'k': 'C', 'cost': 92}, {'i': 'F', 'j': 'C', 'k': 'D', 'cost': 5}, {'i': 'F', 'j': 'C', 'k': 'E', 'cost': 29}, {'i': 'F', 'j': 'C', 'k': 'F', 'cost': 8}, {'i': 'F', 'j': 'D', 'k': 'A', 'cost': 93}, {'i': 'F', 'j': 'D', 'k': 'B', 'cost': 58}, {'i': 'F', 'j': 'D', 'k': 'C', 'cost': 7}, {'i': 'F', 'j': 'D', 'k': 'D', 'cost': 40}, {'i': 'F', 'j': 'D', 'k': 'E', 'cost': 12}, {'i': 'F', 'j': 'D', 'k': 'F', 'cost': 41}, {'i': 'F', 'j': 'E', 'k': 'A', 'cost': 66}, {'i': 'F', 'j': 'E', 'k': 'B', 'cost': 89}, {'i': 'F', 'j': 'E', 'k': 'C', 'cost': 29}, {'i': 'F', 'j': 'E', 'k': 'D', 'cost': 69}, {'i': 'F', 'j': 'E', 'k': 'E', 'cost': 14}, {'i': 'F', 'j': 'E', 'k': 'F', 'cost': 78}, {'i': 'F', 'j': 'F', 'k': 'A', 'cost': 97}, {'i': 'F', 'j': 'F', 'k': 'B', 'cost': 97}, {'i': 'F', 'j': 'F', 'k': 'C', 'cost': 37}, {'i': 'F', 'j': 'F', 'k': 'D', 'cost': 58}, {'i': 'F', 'j': 'F', 'k': 'E', 'cost': 8}, {'i': 'F', 'j': 'F', 'k': 'F', 'cost': 32}]}","[['A', 'F', 'A'], ['B', 'C', 'D'], ['C', 'B', 'E'], ['D', 'E', 'B'], ['E', 'A', 'F'], ['F', 'D', 'C']]",48,json,names
AP3,AP3,"We were tasked with sorting the dressing-room chaos: assign one outfit and one helper to each model, with each outfit and helper going to only one model. The goal is simple in plain terms — pick the pairings so that when you add every model’s outfit cost and assistant cost together, the sum is as small as it can be. Everything must be used exactly once, so no duplicates and no model left without something. The concrete lineup and cost numbers are listed below.

# num_models=8
# model_outfit_assistant_ids=1, 2, 3, 4, 5, 6, 7, 8

# Meaning: costs form a 3D tensor. For each fixed model_id=i, you are given a outfit_id×assistant_id matrix whose entry at row outfit_id=j and column assistant_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all outfit_id and all assistant_id used exactly once.
# assignment_cost_tensor (per-model_id markdown matrices)

## model_id=1
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 80 | 36 | 82 | 34 | 2 | 23 | 73 | 15 |
| 2 | 88 | 93 | 26 | 87 | 96 | 71 | 48 | 87 |
| 3 | 34 | 92 | 66 | 16 | 95 | 47 | 2 | 35 |
| 4 | 80 | 17 | 49 | 72 | 30 | 69 | 10 | 66 |
| 5 | 41 | 94 | 41 | 57 | 89 | 26 | 64 | 82 |
| 6 | 85 | 96 | 92 | 41 | 68 | 77 | 0 | 63 |
| 7 | 1 | 39 | 45 | 18 | 83 | 7 | 41 | 15 |
| 8 | 25 | 86 | 58 | 28 | 35 | 74 | 70 | 30 |

## model_id=2
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 46 | 60 | 43 | 12 | 74 | 96 | 46 | 14 |
| 2 | 87 | 26 | 29 | 70 | 87 | 42 | 52 | 68 |
| 3 | 26 | 3 | 18 | 14 | 70 | 30 | 61 | 97 |
| 4 | 83 | 14 | 63 | 85 | 87 | 5 | 39 | 9 |
| 5 | 75 | 39 | 52 | 48 | 56 | 39 | 90 | 69 |
| 6 | 14 | 22 | 43 | 51 | 92 | 30 | 33 | 56 |
| 7 | 26 | 51 | 13 | 44 | 47 | 68 | 48 | 87 |
| 8 | 33 | 89 | 36 | 72 | 59 | 47 | 70 | 23 |

## model_id=3
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 48 | 58 | 29 | 21 | 92 | 85 | 36 | 76 |
| 2 | 30 | 76 | 88 | 52 | 46 | 19 | 85 | 66 |
| 3 | 96 | 39 | 62 | 79 | 43 | 87 | 54 | 9 |
| 4 | 39 | 14 | 96 | 85 | 35 | 37 | 8 | 50 |
| 5 | 0 | 30 | 96 | 55 | 66 | 54 | 61 | 59 |
| 6 | 99 | 75 | 88 | 82 | 64 | 68 | 63 | 20 |
| 7 | 60 | 4 | 89 | 91 | 32 | 90 | 76 | 63 |
| 8 | 6 | 95 | 26 | 73 | 41 | 4 | 1 | 3 |

## model_id=4
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 67 | 93 | 98 | 77 | 4 | 60 | 79 | 19 |
| 2 | 0 | 68 | 11 | 45 | 79 | 30 | 48 | 45 |
| 3 | 11 | 92 | 9 | 0 | 98 | 24 | 12 | 78 |
| 4 | 36 | 49 | 33 | 74 | 21 | 89 | 5 | 35 |
| 5 | 41 | 58 | 30 | 22 | 53 | 46 | 66 | 27 |
| 6 | 15 | 69 | 73 | 57 | 40 | 36 | 47 | 57 |
| 7 | 96 | 56 | 31 | 20 | 84 | 73 | 28 | 11 |
| 8 | 54 | 77 | 30 | 94 | 59 | 91 | 43 | 72 |

## model_id=5
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 56 | 39 | 0 | 55 | 13 | 39 | 78 | 27 |
| 2 | 74 | 96 | 0 | 29 | 77 | 27 | 35 | 24 |
| 3 | 60 | 19 | 73 | 32 | 2 | 37 | 78 | 51 |
| 4 | 1 | 93 | 18 | 14 | 65 | 37 | 71 | 38 |
| 5 | 39 | 95 | 17 | 2 | 40 | 94 | 14 | 61 |
| 6 | 87 | 16 | 51 | 89 | 38 | 65 | 48 | 37 |
| 7 | 91 | 54 | 25 | 16 | 14 | 23 | 67 | 76 |
| 8 | 50 | 67 | 22 | 46 | 90 | 64 | 23 | 42 |

## model_id=6
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 80 | 93 | 36 | 12 | 74 | 98 | 6 | 90 |
| 2 | 2 | 82 | 81 | 36 | 23 | 90 | 30 | 22 |
| 3 | 9 | 66 | 60 | 82 | 62 | 83 | 40 | 31 |
| 4 | 97 | 36 | 42 | 85 | 75 | 35 | 61 | 7 |
| 5 | 13 | 63 | 55 | 77 | 53 | 21 | 23 | 62 |
| 6 | 18 | 95 | 89 | 83 | 92 | 75 | 36 | 0 |
| 7 | 94 | 40 | 0 | 90 | 8 | 45 | 34 | 47 |
| 8 | 36 | 90 | 75 | 1 | 20 | 5 | 20 | 97 |

## model_id=7
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 29 | 79 | 38 | 89 | 88 | 52 | 82 | 29 |
| 2 | 66 | 16 | 3 | 58 | 42 | 42 | 52 | 95 |
| 3 | 3 | 30 | 33 | 35 | 32 | 8 | 74 | 4 |
| 4 | 96 | 3 | 15 | 48 | 55 | 55 | 7 | 90 |
| 5 | 3 | 50 | 7 | 91 | 79 | 73 | 71 | 67 |
| 6 | 89 | 61 | 70 | 38 | 97 | 69 | 85 | 67 |
| 7 | 62 | 22 | 73 | 73 | 47 | 90 | 79 | 21 |
| 8 | 99 | 56 | 29 | 74 | 9 | 72 | 88 | 89 |

## model_id=8
| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 8 | 9 | 66 | 88 | 13 | 52 | 92 | 42 |
| 2 | 76 | 74 | 48 | 33 | 29 | 5 | 1 | 42 |
| 3 | 31 | 89 | 31 | 3 | 23 | 30 | 84 | 77 |
| 4 | 44 | 23 | 30 | 14 | 50 | 64 | 61 | 20 |
| 5 | 33 | 16 | 82 | 49 | 22 | 89 | 97 | 85 |
| 6 | 84 | 13 | 48 | 38 | 9 | 85 | 3 | 62 |
| 7 | 84 | 55 | 32 | 27 | 36 | 84 | 3 | 87 |
| 8 | 79 | 13 | 46 | 44 | 92 | 63 | 16 | 64 |

Also, when you give the final answer, just stick to a simple JSON layout so it's easy to check automatically. Something like this will do:

{
  ""solution"": [
    [<model_id>, <outfit_id>, <helper_id>],
    ...
  ]
}

Here the ""solution"" list is just a rundown of every assignment. Each inner triple [<model_id>, <outfit_id>, <helper_id>] means: that model gets that outfit and that helper. It's just a sketch of the shape we expect — you'll replace those placeholders with the actual identifiers from the instance when you submit the real solution.

Please make sure you use the exact identifiers from the instance input, with no renaming and no invented 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”.""","{'cost_tensor': [[[80, 36, 82, 34, 2, 23, 73, 15], [88, 93, 26, 87, 96, 71, 48, 87], [34, 92, 66, 16, 95, 47, 2, 35], [80, 17, 49, 72, 30, 69, 10, 66], [41, 94, 41, 57, 89, 26, 64, 82], [85, 96, 92, 41, 68, 77, 0, 63], [1, 39, 45, 18, 83, 7, 41, 15], [25, 86, 58, 28, 35, 74, 70, 30]], [[46, 60, 43, 12, 74, 96, 46, 14], [87, 26, 29, 70, 87, 42, 52, 68], [26, 3, 18, 14, 70, 30, 61, 97], [83, 14, 63, 85, 87, 5, 39, 9], [75, 39, 52, 48, 56, 39, 90, 69], [14, 22, 43, 51, 92, 30, 33, 56], [26, 51, 13, 44, 47, 68, 48, 87], [33, 89, 36, 72, 59, 47, 70, 23]], [[48, 58, 29, 21, 92, 85, 36, 76], [30, 76, 88, 52, 46, 19, 85, 66], [96, 39, 62, 79, 43, 87, 54, 9], [39, 14, 96, 85, 35, 37, 8, 50], [0, 30, 96, 55, 66, 54, 61, 59], [99, 75, 88, 82, 64, 68, 63, 20], [60, 4, 89, 91, 32, 90, 76, 63], [6, 95, 26, 73, 41, 4, 1, 3]], [[67, 93, 98, 77, 4, 60, 79, 19], [0, 68, 11, 45, 79, 30, 48, 45], [11, 92, 9, 0, 98, 24, 12, 78], [36, 49, 33, 74, 21, 89, 5, 35], [41, 58, 30, 22, 53, 46, 66, 27], [15, 69, 73, 57, 40, 36, 47, 57], [96, 56, 31, 20, 84, 73, 28, 11], [54, 77, 30, 94, 59, 91, 43, 72]], [[56, 39, 0, 55, 13, 39, 78, 27], [74, 96, 0, 29, 77, 27, 35, 24], [60, 19, 73, 32, 2, 37, 78, 51], [1, 93, 18, 14, 65, 37, 71, 38], [39, 95, 17, 2, 40, 94, 14, 61], [87, 16, 51, 89, 38, 65, 48, 37], [91, 54, 25, 16, 14, 23, 67, 76], [50, 67, 22, 46, 90, 64, 23, 42]], [[80, 93, 36, 12, 74, 98, 6, 90], [2, 82, 81, 36, 23, 90, 30, 22], [9, 66, 60, 82, 62, 83, 40, 31], [97, 36, 42, 85, 75, 35, 61, 7], [13, 63, 55, 77, 53, 21, 23, 62], [18, 95, 89, 83, 92, 75, 36, 0], [94, 40, 0, 90, 8, 45, 34, 47], [36, 90, 75, 1, 20, 5, 20, 97]], [[29, 79, 38, 89, 88, 52, 82, 29], [66, 16, 3, 58, 42, 42, 52, 95], [3, 30, 33, 35, 32, 8, 74, 4], [96, 3, 15, 48, 55, 55, 7, 90], [3, 50, 7, 91, 79, 73, 71, 67], [89, 61, 70, 38, 97, 69, 85, 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4, 'cost': 32}, {'i': 5, 'j': 3, 'k': 5, 'cost': 2}, {'i': 5, 'j': 3, 'k': 6, 'cost': 37}, {'i': 5, 'j': 3, 'k': 7, 'cost': 78}, {'i': 5, 'j': 3, 'k': 8, 'cost': 51}, {'i': 5, 'j': 4, 'k': 1, 'cost': 1}, {'i': 5, 'j': 4, 'k': 2, 'cost': 93}, {'i': 5, 'j': 4, 'k': 3, 'cost': 18}, {'i': 5, 'j': 4, 'k': 4, 'cost': 14}, {'i': 5, 'j': 4, 'k': 5, 'cost': 65}, {'i': 5, 'j': 4, 'k': 6, 'cost': 37}, {'i': 5, 'j': 4, 'k': 7, 'cost': 71}, {'i': 5, 'j': 4, 'k': 8, 'cost': 38}, {'i': 5, 'j': 5, 'k': 1, 'cost': 39}, {'i': 5, 'j': 5, 'k': 2, 'cost': 95}, {'i': 5, 'j': 5, 'k': 3, 'cost': 17}, {'i': 5, 'j': 5, 'k': 4, 'cost': 2}, {'i': 5, 'j': 5, 'k': 5, 'cost': 40}, {'i': 5, 'j': 5, 'k': 6, 'cost': 94}, {'i': 5, 'j': 5, 'k': 7, 'cost': 14}, {'i': 5, 'j': 5, 'k': 8, 'cost': 61}, {'i': 5, 'j': 6, 'k': 1, 'cost': 87}, {'i': 5, 'j': 6, 'k': 2, 'cost': 16}, {'i': 5, 'j': 6, 'k': 3, 'cost': 51}, {'i': 5, 'j': 6, 'k': 4, 'cost': 89}, {'i': 5, 'j': 6, 'k': 5, 'cost': 38}, {'i': 5, 'j': 6, 'k': 6, 'cost': 65}, {'i': 5, 'j': 6, 'k': 7, 'cost': 48}, {'i': 5, 'j': 6, 'k': 8, 'cost': 37}, {'i': 5, 'j': 7, 'k': 1, 'cost': 91}, {'i': 5, 'j': 7, 'k': 2, 'cost': 54}, {'i': 5, 'j': 7, 'k': 3, 'cost': 25}, {'i': 5, 'j': 7, 'k': 4, 'cost': 16}, {'i': 5, 'j': 7, 'k': 5, 'cost': 14}, {'i': 5, 'j': 7, 'k': 6, 'cost': 23}, {'i': 5, 'j': 7, 'k': 7, 'cost': 67}, {'i': 5, 'j': 7, 'k': 8, 'cost': 76}, {'i': 5, 'j': 8, 'k': 1, 'cost': 50}, {'i': 5, 'j': 8, 'k': 2, 'cost': 67}, {'i': 5, 'j': 8, 'k': 3, 'cost': 22}, {'i': 5, 'j': 8, 'k': 4, 'cost': 46}, {'i': 5, 'j': 8, 'k': 5, 'cost': 90}, {'i': 5, 'j': 8, 'k': 6, 'cost': 64}, {'i': 5, 'j': 8, 'k': 7, 'cost': 23}, {'i': 5, 'j': 8, 'k': 8, 'cost': 42}, {'i': 6, 'j': 1, 'k': 1, 'cost': 80}, {'i': 6, 'j': 1, 'k': 2, 'cost': 93}, {'i': 6, 'j': 1, 'k': 3, 'cost': 36}, {'i': 6, 'j': 1, 'k': 4, 'cost': 12}, {'i': 6, 'j': 1, 'k': 5, 'cost': 74}, {'i': 6, 'j': 1, 'k': 6, 'cost': 98}, {'i': 6, 'j': 1, 'k': 7, 'cost': 6}, {'i': 6, 'j': 1, 'k': 8, 'cost': 90}, {'i': 6, 'j': 2, 'k': 1, 'cost': 2}, {'i': 6, 'j': 2, 'k': 2, 'cost': 82}, {'i': 6, 'j': 2, 'k': 3, 'cost': 81}, {'i': 6, 'j': 2, 'k': 4, 'cost': 36}, {'i': 6, 'j': 2, 'k': 5, 'cost': 23}, {'i': 6, 'j': 2, 'k': 6, 'cost': 90}, {'i': 6, 'j': 2, 'k': 7, 'cost': 30}, {'i': 6, 'j': 2, 'k': 8, 'cost': 22}, {'i': 6, 'j': 3, 'k': 1, 'cost': 9}, {'i': 6, 'j': 3, 'k': 2, 'cost': 66}, {'i': 6, 'j': 3, 'k': 3, 'cost': 60}, {'i': 6, 'j': 3, 'k': 4, 'cost': 82}, {'i': 6, 'j': 3, 'k': 5, 'cost': 62}, {'i': 6, 'j': 3, 'k': 6, 'cost': 83}, {'i': 6, 'j': 3, 'k': 7, 'cost': 40}, {'i': 6, 'j': 3, 'k': 8, 'cost': 31}, {'i': 6, 'j': 4, 'k': 1, 'cost': 97}, {'i': 6, 'j': 4, 'k': 2, 'cost': 36}, {'i': 6, 'j': 4, 'k': 3, 'cost': 42}, {'i': 6, 'j': 4, 'k': 4, 'cost': 85}, {'i': 6, 'j': 4, 'k': 5, 'cost': 75}, {'i': 6, 'j': 4, 'k': 6, 'cost': 35}, {'i': 6, 'j': 4, 'k': 7, 'cost': 61}, {'i': 6, 'j': 4, 'k': 8, 'cost': 7}, {'i': 6, 'j': 5, 'k': 1, 'cost': 13}, {'i': 6, 'j': 5, 'k': 2, 'cost': 63}, {'i': 6, 'j': 5, 'k': 3, 'cost': 55}, {'i': 6, 'j': 5, 'k': 4, 'cost': 77}, {'i': 6, 'j': 5, 'k': 5, 'cost': 53}, {'i': 6, 'j': 5, 'k': 6, 'cost': 21}, {'i': 6, 'j': 5, 'k': 7, 'cost': 23}, {'i': 6, 'j': 5, 'k': 8, 'cost': 62}, {'i': 6, 'j': 6, 'k': 1, 'cost': 18}, {'i': 6, 'j': 6, 'k': 2, 'cost': 95}, {'i': 6, 'j': 6, 'k': 3, 'cost': 89}, {'i': 6, 'j': 6, 'k': 4, 'cost': 83}, {'i': 6, 'j': 6, 'k': 5, 'cost': 92}, {'i': 6, 'j': 6, 'k': 6, 'cost': 75}, {'i': 6, 'j': 6, 'k': 7, 'cost': 36}, {'i': 6, 'j': 6, 'k': 8, 'cost': 0}, {'i': 6, 'j': 7, 'k': 1, 'cost': 94}, {'i': 6, 'j': 7, 'k': 2, 'cost': 40}, {'i': 6, 'j': 7, 'k': 3, 'cost': 0}, {'i': 6, 'j': 7, 'k': 4, 'cost': 90}, {'i': 6, 'j': 7, 'k': 5, 'cost': 8}, {'i': 6, 'j': 7, 'k': 6, 'cost': 45}, {'i': 6, 'j': 7, 'k': 7, 'cost': 34}, {'i': 6, 'j': 7, 'k': 8, 'cost': 47}, {'i': 6, 'j': 8, 'k': 1, 'cost': 36}, {'i': 6, 'j': 8, 'k': 2, 'cost': 90}, {'i': 6, 'j': 8, 'k': 3, 'cost': 75}, {'i': 6, 'j': 8, 'k': 4, 'cost': 1}, {'i': 6, 'j': 8, 'k': 5, 'cost': 20}, {'i': 6, 'j': 8, 'k': 6, 'cost': 5}, {'i': 6, 'j': 8, 'k': 7, 'cost': 20}, {'i': 6, 'j': 8, 'k': 8, 'cost': 97}, {'i': 7, 'j': 1, 'k': 1, 'cost': 29}, {'i': 7, 'j': 1, 'k': 2, 'cost': 79}, {'i': 7, 'j': 1, 'k': 3, 'cost': 38}, {'i': 7, 'j': 1, 'k': 4, 'cost': 89}, {'i': 7, 'j': 1, 'k': 5, 'cost': 88}, {'i': 7, 'j': 1, 'k': 6, 'cost': 52}, {'i': 7, 'j': 1, 'k': 7, 'cost': 82}, {'i': 7, 'j': 1, 'k': 8, 'cost': 29}, {'i': 7, 'j': 2, 'k': 1, 'cost': 66}, {'i': 7, 'j': 2, 'k': 2, 'cost': 16}, {'i': 7, 'j': 2, 'k': 3, 'cost': 3}, {'i': 7, 'j': 2, 'k': 4, 'cost': 58}, {'i': 7, 'j': 2, 'k': 5, 'cost': 42}, {'i': 7, 'j': 2, 'k': 6, 'cost': 42}, {'i': 7, 'j': 2, 'k': 7, 'cost': 52}, {'i': 7, 'j': 2, 'k': 8, 'cost': 95}, {'i': 7, 'j': 3, 'k': 1, 'cost': 3}, {'i': 7, 'j': 3, 'k': 2, 'cost': 30}, {'i': 7, 'j': 3, 'k': 3, 'cost': 33}, {'i': 7, 'j': 3, 'k': 4, 'cost': 35}, {'i': 7, 'j': 3, 'k': 5, 'cost': 32}, {'i': 7, 'j': 3, 'k': 6, 'cost': 8}, {'i': 7, 'j': 3, 'k': 7, 'cost': 74}, {'i': 7, 'j': 3, 'k': 8, 'cost': 4}, {'i': 7, 'j': 4, 'k': 1, 'cost': 96}, {'i': 7, 'j': 4, 'k': 2, 'cost': 3}, {'i': 7, 'j': 4, 'k': 3, 'cost': 15}, {'i': 7, 'j': 4, 'k': 4, 'cost': 48}, {'i': 7, 'j': 4, 'k': 5, 'cost': 55}, {'i': 7, 'j': 4, 'k': 6, 'cost': 55}, {'i': 7, 'j': 4, 'k': 7, 'cost': 7}, {'i': 7, 'j': 4, 'k': 8, 'cost': 90}, {'i': 7, 'j': 5, 'k': 1, 'cost': 3}, {'i': 7, 'j': 5, 'k': 2, 'cost': 50}, {'i': 7, 'j': 5, 'k': 3, 'cost': 7}, {'i': 7, 'j': 5, 'k': 4, 'cost': 91}, {'i': 7, 'j': 5, 'k': 5, 'cost': 79}, {'i': 7, 'j': 5, 'k': 6, 'cost': 73}, {'i': 7, 'j': 5, 'k': 7, 'cost': 71}, {'i': 7, 'j': 5, 'k': 8, 'cost': 67}, {'i': 7, 'j': 6, 'k': 1, 'cost': 89}, {'i': 7, 'j': 6, 'k': 2, 'cost': 61}, {'i': 7, 'j': 6, 'k': 3, 'cost': 70}, {'i': 7, 'j': 6, 'k': 4, 'cost': 38}, {'i': 7, 'j': 6, 'k': 5, 'cost': 97}, {'i': 7, 'j': 6, 'k': 6, 'cost': 69}, {'i': 7, 'j': 6, 'k': 7, 'cost': 85}, {'i': 7, 'j': 6, 'k': 8, 'cost': 67}, {'i': 7, 'j': 7, 'k': 1, 'cost': 62}, {'i': 7, 'j': 7, 'k': 2, 'cost': 22}, {'i': 7, 'j': 7, 'k': 3, 'cost': 73}, {'i': 7, 'j': 7, 'k': 4, 'cost': 73}, {'i': 7, 'j': 7, 'k': 5, 'cost': 47}, {'i': 7, 'j': 7, 'k': 6, 'cost': 90}, {'i': 7, 'j': 7, 'k': 7, 'cost': 79}, {'i': 7, 'j': 7, 'k': 8, 'cost': 21}, {'i': 7, 'j': 8, 'k': 1, 'cost': 99}, {'i': 7, 'j': 8, 'k': 2, 'cost': 56}, {'i': 7, 'j': 8, 'k': 3, 'cost': 29}, {'i': 7, 'j': 8, 'k': 4, 'cost': 74}, {'i': 7, 'j': 8, 'k': 5, 'cost': 9}, {'i': 7, 'j': 8, 'k': 6, 'cost': 72}, {'i': 7, 'j': 8, 'k': 7, 'cost': 88}, {'i': 7, 'j': 8, 'k': 8, 'cost': 89}, {'i': 8, 'j': 1, 'k': 1, 'cost': 8}, {'i': 8, 'j': 1, 'k': 2, 'cost': 9}, {'i': 8, 'j': 1, 'k': 3, 'cost': 66}, {'i': 8, 'j': 1, 'k': 4, 'cost': 88}, {'i': 8, 'j': 1, 'k': 5, 'cost': 13}, {'i': 8, 'j': 1, 'k': 6, 'cost': 52}, {'i': 8, 'j': 1, 'k': 7, 'cost': 92}, {'i': 8, 'j': 1, 'k': 8, 'cost': 42}, {'i': 8, 'j': 2, 'k': 1, 'cost': 76}, {'i': 8, 'j': 2, 'k': 2, 'cost': 74}, {'i': 8, 'j': 2, 'k': 3, 'cost': 48}, {'i': 8, 'j': 2, 'k': 4, 'cost': 33}, {'i': 8, 'j': 2, 'k': 5, 'cost': 29}, {'i': 8, 'j': 2, 'k': 6, 'cost': 5}, {'i': 8, 'j': 2, 'k': 7, 'cost': 1}, {'i': 8, 'j': 2, 'k': 8, 'cost': 42}, {'i': 8, 'j': 3, 'k': 1, 'cost': 31}, {'i': 8, 'j': 3, 'k': 2, 'cost': 89}, {'i': 8, 'j': 3, 'k': 3, 'cost': 31}, {'i': 8, 'j': 3, 'k': 4, 'cost': 3}, {'i': 8, 'j': 3, 'k': 5, 'cost': 23}, {'i': 8, 'j': 3, 'k': 6, 'cost': 30}, {'i': 8, 'j': 3, 'k': 7, 'cost': 84}, {'i': 8, 'j': 3, 'k': 8, 'cost': 77}, {'i': 8, 'j': 4, 'k': 1, 'cost': 44}, {'i': 8, 'j': 4, 'k': 2, 'cost': 23}, {'i': 8, 'j': 4, 'k': 3, 'cost': 30}, {'i': 8, 'j': 4, 'k': 4, 'cost': 14}, {'i': 8, 'j': 4, 'k': 5, 'cost': 50}, {'i': 8, 'j': 4, 'k': 6, 'cost': 64}, {'i': 8, 'j': 4, 'k': 7, 'cost': 61}, {'i': 8, 'j': 4, 'k': 8, 'cost': 20}, {'i': 8, 'j': 5, 'k': 1, 'cost': 33}, {'i': 8, 'j': 5, 'k': 2, 'cost': 16}, {'i': 8, 'j': 5, 'k': 3, 'cost': 82}, {'i': 8, 'j': 5, 'k': 4, 'cost': 49}, {'i': 8, 'j': 5, 'k': 5, 'cost': 22}, {'i': 8, 'j': 5, 'k': 6, 'cost': 89}, {'i': 8, 'j': 5, 'k': 7, 'cost': 97}, {'i': 8, 'j': 5, 'k': 8, 'cost': 85}, {'i': 8, 'j': 6, 'k': 1, 'cost': 84}, {'i': 8, 'j': 6, 'k': 2, 'cost': 13}, {'i': 8, 'j': 6, 'k': 3, 'cost': 48}, {'i': 8, 'j': 6, 'k': 4, 'cost': 38}, {'i': 8, 'j': 6, 'k': 5, 'cost': 9}, {'i': 8, 'j': 6, 'k': 6, 'cost': 85}, {'i': 8, 'j': 6, 'k': 7, 'cost': 3}, {'i': 8, 'j': 6, 'k': 8, 'cost': 62}, {'i': 8, 'j': 7, 'k': 1, 'cost': 84}, {'i': 8, 'j': 7, 'k': 2, 'cost': 55}, {'i': 8, 'j': 7, 'k': 3, 'cost': 32}, {'i': 8, 'j': 7, 'k': 4, 'cost': 27}, {'i': 8, 'j': 7, 'k': 5, 'cost': 36}, {'i': 8, 'j': 7, 'k': 6, 'cost': 84}, {'i': 8, 'j': 7, 'k': 7, 'cost': 3}, {'i': 8, 'j': 7, 'k': 8, 'cost': 87}, {'i': 8, 'j': 8, 'k': 1, 'cost': 79}, {'i': 8, 'j': 8, 'k': 2, 'cost': 13}, {'i': 8, 'j': 8, 'k': 3, 'cost': 46}, {'i': 8, 'j': 8, 'k': 4, 'cost': 44}, {'i': 8, 'j': 8, 'k': 5, 'cost': 92}, {'i': 8, 'j': 8, 'k': 6, 'cost': 63}, {'i': 8, 'j': 8, 'k': 7, 'cost': 16}, {'i': 8, 'j': 8, 'k': 8, 'cost': 64}]}","[[1, 1, 5], [2, 4, 2], [3, 8, 6], [4, 3, 4], [5, 2, 3], [6, 6, 8], [7, 5, 1], [8, 7, 7]]",49,csv,1
AP3,AP3,"I run the community library’s events, and for each reading session I need to pick exactly one storyteller and one seating layout. Every storyteller should lead just one session and every seating plan should be used for exactly one session, so nothing gets repeated or left out. Each possible pairing of session, storyteller, and seating has a price, and the plan that’s best is the one where, when the price for every session is added up, that total is as small as possible. The exact lists and costs are shown below.

{
  ""num_reading_sessions"": 6,
  ""index_identifiers"": [
    1,
    2,
    3,
    4,
    5,
    6
  ]
}

# Meaning: costs form a 3D tensor. For each fixed session_id=i, you are given a storyteller_id×seating_layout_id matrix whose entry at row storyteller_id=j and column seating_layout_id=k equals assignment_cost(i,j,k). You must pick exactly one (j,k) for every i, with all storyteller_id and all seating_layout_id used exactly once.
# assignment_cost_tensor (per-session_id markdown matrices)

## session_id=1
| storyteller_id\seating_layout_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 96 | 93 | 36 | 6 | 68 | 37 |
| 2 | 20 | 36 | 36 | 31 | 52 | 29 |
| 3 | 17 | 57 | 92 | 26 | 94 | 94 |
| 4 | 54 | 7 | 75 | 84 | 63 | 81 |
| 5 | 92 | 25 | 20 | 41 | 4 | 37 |
| 6 | 36 | 77 | 93 | 2 | 57 | 28 |

## session_id=2
| storyteller_id\seating_layout_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 45 | 54 | 96 | 74 | 83 | 94 |
| 2 | 88 | 5 | 63 | 41 | 18 | 20 |
| 3 | 75 | 37 | 80 | 89 | 58 | 29 |
| 4 | 63 | 45 | 87 | 78 | 99 | 62 |
| 5 | 5 | 12 | 95 | 22 | 90 | 69 |
| 6 | 46 | 15 | 31 | 91 | 31 | 28 |

## session_id=3
| storyteller_id\seating_layout_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 66 | 46 | 82 | 66 | 25 | 50 |
| 2 | 70 | 29 | 19 | 85 | 34 | 94 |
| 3 | 66 | 18 | 7 | 81 | 90 | 60 |
| 4 | 39 | 41 | 83 | 55 | 22 | 36 |
| 5 | 24 | 13 | 1 | 77 | 79 | 97 |
| 6 | 91 | 93 | 75 | 84 | 95 | 61 |

## session_id=4
| storyteller_id\seating_layout_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 54 | 35 | 83 | 21 | 98 | 57 |
| 2 | 30 | 24 | 25 | 1 | 28 | 59 |
| 3 | 76 | 27 | 91 | 73 | 3 | 91 |
| 4 | 91 | 74 | 68 | 28 | 63 | 55 |
| 5 | 39 | 1 | 28 | 74 | 86 | 53 |
| 6 | 80 | 63 | 78 | 2 | 53 | 93 |

## session_id=5
| storyteller_id\seating_layout_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 84 | 94 | 27 | 51 | 76 | 89 |
| 2 | 49 | 24 | 40 | 15 | 43 | 66 |
| 3 | 53 | 78 | 72 | 53 | 31 | 73 |
| 4 | 87 | 7 | 52 | 94 | 95 | 46 |
| 5 | 39 | 10 | 45 | 86 | 6 | 51 |
| 6 | 54 | 36 | 46 | 66 | 47 | 61 |

## session_id=6
| storyteller_id\seating_layout_id | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 21 | 31 | 59 | 1 | 89 | 89 |
| 2 | 79 | 26 | 81 | 98 | 29 | 95 |
| 3 | 22 | 82 | 55 | 99 | 47 | 7 |
| 4 | 79 | 27 | 12 | 13 | 92 | 55 |
| 5 | 81 | 92 | 99 | 83 | 12 | 90 |
| 6 | 32 | 85 | 43 | 31 | 37 | 40 |

Also, when you send the final plan back, just follow this simple JSON layout.

{
  ""solution"": [
    [<session_id>, <storyteller_id>, <layout_id>],
    ...
  ]
}

Each inner array is a triple: [session, storyteller, seating layout] — so one triple per reading session showing which storyteller and which seating plan you picked. This is just a sketch of the shape I expect, not the actual answer.

Please make sure you use the exact identifiers from the instance input — no renaming and 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”.""","{'cost_tensor': [[[96, 93, 36, 6, 68, 37], [20, 36, 36, 31, 52, 29], [17, 57, 92, 26, 94, 94], [54, 7, 75, 84, 63, 81], [92, 25, 20, 41, 4, 37], [36, 77, 93, 2, 57, 28]], [[45, 54, 96, 74, 83, 94], [88, 5, 63, 41, 18, 20], [75, 37, 80, 89, 58, 29], [63, 45, 87, 78, 99, 62], [5, 12, 95, 22, 90, 69], [46, 15, 31, 91, 31, 28]], [[66, 46, 82, 66, 25, 50], [70, 29, 19, 85, 34, 94], [66, 18, 7, 81, 90, 60], [39, 41, 83, 55, 22, 36], [24, 13, 1, 77, 79, 97], [91, 93, 75, 84, 95, 61]], [[54, 35, 83, 21, 98, 57], [30, 24, 25, 1, 28, 59], [76, 27, 91, 73, 3, 91], [91, 74, 68, 28, 63, 55], [39, 1, 28, 74, 86, 53], [80, 63, 78, 2, 53, 93]], [[84, 94, 27, 51, 76, 89], [49, 24, 40, 15, 43, 66], [53, 78, 72, 53, 31, 73], [87, 7, 52, 94, 95, 46], [39, 10, 45, 86, 6, 51], [54, 36, 46, 66, 47, 61]], [[21, 31, 59, 1, 89, 89], [79, 26, 81, 98, 29, 95], [22, 82, 55, 99, 47, 7], [79, 27, 12, 13, 92, 55], [81, 92, 99, 83, 12, 90], [32, 85, 43, 31, 37, 40]]], 'objective': 54.0}","[[0, 5, 3], [1, 1, 5], [2, 4, 2], [3, 2, 4], [4, 3, 1], [5, 0, 0]]",54.0,"{'problem_type': 'AP3', 'n': 6, 'ids': [1, 2, 3, 4, 5, 6], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 96}, {'i': 1, 'j': 1, 'k': 2, 'cost': 93}, {'i': 1, 'j': 1, 'k': 3, 'cost': 36}, {'i': 1, 'j': 1, 'k': 4, 'cost': 6}, {'i': 1, 'j': 1, 'k': 5, 'cost': 68}, {'i': 1, 'j': 1, 'k': 6, 'cost': 37}, {'i': 1, 'j': 2, 'k': 1, 'cost': 20}, {'i': 1, 'j': 2, 'k': 2, 'cost': 36}, {'i': 1, 'j': 2, 'k': 3, 'cost': 36}, {'i': 1, 'j': 2, 'k': 4, 'cost': 31}, {'i': 1, 'j': 2, 'k': 5, 'cost': 52}, {'i': 1, 'j': 2, 'k': 6, 'cost': 29}, {'i': 1, 'j': 3, 'k': 1, 'cost': 17}, {'i': 1, 'j': 3, 'k': 2, 'cost': 57}, {'i': 1, 'j': 3, 'k': 3, 'cost': 92}, {'i': 1, 'j': 3, 'k': 4, 'cost': 26}, {'i': 1, 'j': 3, 'k': 5, 'cost': 94}, {'i': 1, 'j': 3, 'k': 6, 'cost': 94}, {'i': 1, 'j': 4, 'k': 1, 'cost': 54}, {'i': 1, 'j': 4, 'k': 2, 'cost': 7}, {'i': 1, 'j': 4, 'k': 3, 'cost': 75}, {'i': 1, 'j': 4, 'k': 4, 'cost': 84}, {'i': 1, 'j': 4, 'k': 5, 'cost': 63}, {'i': 1, 'j': 4, 'k': 6, 'cost': 81}, {'i': 1, 'j': 5, 'k': 1, 'cost': 92}, {'i': 1, 'j': 5, 'k': 2, 'cost': 25}, {'i': 1, 'j': 5, 'k': 3, 'cost': 20}, {'i': 1, 'j': 5, 'k': 4, 'cost': 41}, {'i': 1, 'j': 5, 'k': 5, 'cost': 4}, {'i': 1, 'j': 5, 'k': 6, 'cost': 37}, {'i': 1, 'j': 6, 'k': 1, 'cost': 36}, {'i': 1, 'j': 6, 'k': 2, 'cost': 77}, {'i': 1, 'j': 6, 'k': 3, 'cost': 93}, {'i': 1, 'j': 6, 'k': 4, 'cost': 2}, {'i': 1, 'j': 6, 'k': 5, 'cost': 57}, {'i': 1, 'j': 6, 'k': 6, 'cost': 28}, {'i': 2, 'j': 1, 'k': 1, 'cost': 45}, {'i': 2, 'j': 1, 'k': 2, 'cost': 54}, {'i': 2, 'j': 1, 'k': 3, 'cost': 96}, {'i': 2, 'j': 1, 'k': 4, 'cost': 74}, {'i': 2, 'j': 1, 'k': 5, 'cost': 83}, {'i': 2, 'j': 1, 'k': 6, 'cost': 94}, {'i': 2, 'j': 2, 'k': 1, 'cost': 88}, {'i': 2, 'j': 2, 'k': 2, 'cost': 5}, {'i': 2, 'j': 2, 'k': 3, 'cost': 63}, 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