diff --git "a/AP3/AP3_L_context.csv" "b/AP3/AP3_L_context.csv"
new file mode 100644--- /dev/null
+++ "b/AP3/AP3_L_context.csv"
@@ -0,0 +1,8887 @@
+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 9 couriers and corresponding restaurants and delivery zones with indices 0, 1, 2, 3, 4, 5, 6, 7, 8; 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=0
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 92 | 32 | 59 | 89 | 11 | 72 | 47 | 1 | 37 |
+| 1 | 32 | 41 | 62 | 25 | 12 | 85 | 7 | 96 | 35 |
+| 2 | 38 | 89 | 6 | 24 | 5 | 88 | 31 | 56 | 26 |
+| 3 | 46 | 62 | 30 | 42 | 98 | 53 | 9 | 72 | 83 |
+| 4 | 86 | 66 | 56 | 54 | 57 | 24 | 86 | 1 | 40 |
+| 5 | 23 | 82 | 53 | 70 | 25 | 7 | 30 | 68 | 73 |
+| 6 | 18 | 32 | 80 | 73 | 87 | 17 | 46 | 35 | 58 |
+| 7 | 24 | 35 | 94 | 0 | 97 | 2 | 40 | 79 | 42 |
+| 8 | 12 | 11 | 12 | 45 | 55 | 2 | 49 | 84 | 1 |
+
+## rider_id=1
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 93 | 53 | 4 | 43 | 96 | 70 | 85 | 38 | 53 |
+| 1 | 71 | 93 | 42 | 51 | 58 | 12 | 27 | 35 | 54 |
+| 2 | 72 | 67 | 6 | 12 | 87 | 51 | 89 | 62 | 44 |
+| 3 | 26 | 30 | 94 | 46 | 83 | 3 | 57 | 78 | 97 |
+| 4 | 21 | 53 | 21 | 11 | 82 | 46 | 96 | 12 | 14 |
+| 5 | 82 | 88 | 86 | 19 | 28 | 20 | 0 | 86 | 6 |
+| 6 | 31 | 14 | 20 | 38 | 62 | 15 | 92 | 14 | 40 |
+| 7 | 27 | 47 | 35 | 40 | 59 | 36 | 91 | 17 | 95 |
+| 8 | 34 | 70 | 22 | 88 | 52 | 63 | 28 | 30 | 44 |
+
+## rider_id=2
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 34 | 72 | 96 | 48 | 82 | 23 | 18 | 25 | 71 |
+| 1 | 94 | 40 | 60 | 35 | 33 | 37 | 87 | 40 | 65 |
+| 2 | 16 | 17 | 8 | 30 | 57 | 54 | 37 | 32 | 93 |
+| 3 | 76 | 83 | 41 | 70 | 14 | 11 | 11 | 10 | 37 |
+| 4 | 77 | 79 | 89 | 91 | 5 | 60 | 0 | 27 | 67 |
+| 5 | 57 | 23 | 80 | 95 | 62 | 72 | 21 | 28 | 58 |
+| 6 | 26 | 64 | 96 | 67 | 24 | 51 | 91 | 91 | 35 |
+| 7 | 94 | 15 | 58 | 30 | 6 | 25 | 40 | 57 | 78 |
+| 8 | 11 | 43 | 68 | 33 | 42 | 16 | 26 | 59 | 2 |
+
+## rider_id=3
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 20 | 44 | 29 | 56 | 55 | 22 | 67 | 62 | 51 |
+| 1 | 56 | 38 | 63 | 93 | 91 | 66 | 96 | 67 | 38 |
+| 2 | 67 | 74 | 7 | 72 | 27 | 87 | 47 | 52 | 86 |
+| 3 | 85 | 85 | 7 | 53 | 6 | 44 | 86 | 92 | 59 |
+| 4 | 13 | 89 | 13 | 38 | 69 | 96 | 41 | 66 | 37 |
+| 5 | 53 | 19 | 12 | 37 | 72 | 20 | 83 | 29 | 75 |
+| 6 | 66 | 33 | 70 | 76 | 70 | 12 | 5 | 81 | 17 |
+| 7 | 37 | 19 | 92 | 99 | 13 | 15 | 95 | 23 | 99 |
+| 8 | 93 | 11 | 92 | 47 | 50 | 19 | 38 | 11 | 3 |
+
+## rider_id=4
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 40 | 10 | 24 | 58 | 22 | 91 | 94 | 22 | 24 |
+| 1 | 0 | 18 | 42 | 54 | 64 | 49 | 51 | 99 | 4 |
+| 2 | 43 | 37 | 25 | 63 | 11 | 3 | 95 | 47 | 91 |
+| 3 | 96 | 17 | 23 | 51 | 80 | 57 | 76 | 92 | 14 |
+| 4 | 35 | 0 | 49 | 80 | 22 | 49 | 33 | 65 | 73 |
+| 5 | 43 | 22 | 51 | 21 | 98 | 35 | 68 | 10 | 76 |
+| 6 | 43 | 21 | 16 | 78 | 50 | 18 | 17 | 74 | 38 |
+| 7 | 55 | 8 | 20 | 23 | 62 | 44 | 69 | 61 | 8 |
+| 8 | 32 | 16 | 83 | 21 | 10 | 99 | 98 | 96 | 43 |
+
+## rider_id=5
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 86 | 89 | 74 | 84 | 94 | 93 | 94 | 24 | 46 |
+| 1 | 32 | 88 | 78 | 71 | 56 | 17 | 2 | 76 | 45 |
+| 2 | 53 | 66 | 36 | 56 | 30 | 51 | 2 | 8 | 2 |
+| 3 | 11 | 47 | 94 | 89 | 39 | 6 | 62 | 35 | 69 |
+| 4 | 75 | 67 | 13 | 70 | 54 | 70 | 14 | 6 | 0 |
+| 5 | 47 | 77 | 64 | 90 | 28 | 78 | 61 | 2 | 58 |
+| 6 | 75 | 35 | 91 | 81 | 85 | 37 | 49 | 67 | 5 |
+| 7 | 16 | 32 | 90 | 18 | 73 | 13 | 51 | 58 | 50 |
+| 8 | 1 | 7 | 57 | 25 | 99 | 71 | 59 | 54 | 91 |
+
+## rider_id=6
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 21 | 98 | 81 | 76 | 73 | 19 | 38 | 28 | 67 |
+| 1 | 9 | 37 | 88 | 2 | 99 | 57 | 20 | 80 | 16 |
+| 2 | 15 | 48 | 79 | 39 | 71 | 11 | 31 | 25 | 84 |
+| 3 | 92 | 33 | 91 | 16 | 38 | 84 | 8 | 38 | 1 |
+| 4 | 60 | 39 | 42 | 20 | 82 | 14 | 52 | 2 | 58 |
+| 5 | 27 | 26 | 34 | 33 | 96 | 51 | 91 | 20 | 54 |
+| 6 | 98 | 92 | 83 | 89 | 5 | 73 | 42 | 72 | 88 |
+| 7 | 77 | 10 | 36 | 4 | 28 | 75 | 99 | 53 | 74 |
+| 8 | 32 | 33 | 7 | 65 | 30 | 40 | 51 | 57 | 74 |
+
+## rider_id=7
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 58 | 7 | 43 | 85 | 61 | 97 | 25 | 40 | 14 |
+| 1 | 0 | 69 | 17 | 60 | 42 | 21 | 99 | 32 | 46 |
+| 2 | 59 | 15 | 42 | 13 | 79 | 4 | 66 | 51 | 1 |
+| 3 | 75 | 43 | 0 | 39 | 25 | 72 | 40 | 11 | 15 |
+| 4 | 24 | 25 | 99 | 30 | 92 | 88 | 19 | 74 | 2 |
+| 5 | 52 | 25 | 74 | 85 | 0 | 51 | 73 | 68 | 69 |
+| 6 | 72 | 78 | 48 | 11 | 37 | 38 | 33 | 44 | 48 |
+| 7 | 48 | 20 | 13 | 0 | 82 | 2 | 16 | 70 | 22 |
+| 8 | 76 | 58 | 37 | 82 | 63 | 43 | 42 | 5 | 51 |
+
+## rider_id=8
+| restaurant_id\delivery_zone_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 11 | 80 | 98 | 98 | 25 | 53 | 46 | 48 | 60 |
+| 1 | 12 | 45 | 71 | 4 | 22 | 63 | 76 | 85 | 39 |
+| 2 | 72 | 54 | 91 | 62 | 27 | 46 | 49 | 43 | 1 |
+| 3 | 17 | 31 | 88 | 78 | 90 | 38 | 47 | 99 | 61 |
+| 4 | 94 | 70 | 87 | 65 | 55 | 10 | 20 | 58 | 59 |
+| 5 | 87 | 6 | 43 | 94 | 52 | 94 | 35 | 20 | 82 |
+| 6 | 32 | 78 | 77 | 42 | 33 | 64 | 50 | 54 | 72 |
+| 7 | 37 | 45 | 86 | 60 | 5 | 75 | 29 | 62 | 95 |
+| 8 | 74 | 23 | 56 | 47 | 26 | 96 | 9 | 82 | 90 |
+
+Choose the assignment that minimizes the total sum of the listed trip lengths across all 9 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': [[[92, 32, 59, 89, 11, 72, 47, 1, 37], [32, 41, 62, 25, 12, 85, 7, 96, 35], [38, 89, 6, 24, 5, 88, 31, 56, 26], [46, 62, 30, 42, 98, 53, 9, 72, 83], [86, 66, 56, 54, 57, 24, 86, 1, 40], [23, 82, 53, 70, 25, 7, 30, 68, 73], [18, 32, 80, 73, 87, 17, 46, 35, 58], [24, 35, 94, 0, 97, 2, 40, 79, 42], [12, 11, 12, 45, 55, 2, 49, 84, 1]], [[93, 53, 4, 43, 96, 70, 85, 38, 53], [71, 93, 42, 51, 58, 12, 27, 35, 54], [72, 67, 6, 12, 87, 51, 89, 62, 44], [26, 30, 94, 46, 83, 3, 57, 78, 97], [21, 53, 21, 11, 82, 46, 96, 12, 14], [82, 88, 86, 19, 28, 20, 0, 86, 6], [31, 14, 20, 38, 62, 15, 92, 14, 40], [27, 47, 35, 40, 59, 36, 91, 17, 95], [34, 70, 22, 88, 52, 63, 28, 30, 44]], [[34, 72, 96, 48, 82, 23, 18, 25, 71], [94, 40, 60, 35, 33, 37, 87, 40, 65], [16, 17, 8, 30, 57, 54, 37, 32, 93], [76, 83, 41, 70, 14, 11, 11, 10, 37], [77, 79, 89, 91, 5, 60, 0, 27, 67], [57, 23, 80, 95, 62, 72, 21, 28, 58], [26, 64, 96, 67, 24, 51, 91, 91, 35], [94, 15, 58, 30, 6, 25, 40, 57, 78], [11, 43, 68, 33, 42, 16, 26, 59, 2]], [[20, 44, 29, 56, 55, 22, 67, 62, 51], [56, 38, 63, 93, 91, 66, 96, 67, 38], [67, 74, 7, 72, 27, 87, 47, 52, 86], [85, 85, 7, 53, 6, 44, 86, 92, 59], [13, 89, 13, 38, 69, 96, 41, 66, 37], [53, 19, 12, 37, 72, 20, 83, 29, 75], [66, 33, 70, 76, 70, 12, 5, 81, 17], [37, 19, 92, 99, 13, 15, 95, 23, 99], [93, 11, 92, 47, 50, 19, 38, 11, 3]], [[40, 10, 24, 58, 22, 91, 94, 22, 24], [0, 18, 42, 54, 64, 49, 51, 99, 4], [43, 37, 25, 63, 11, 3, 95, 47, 91], [96, 17, 23, 51, 80, 57, 76, 92, 14], [35, 0, 49, 80, 22, 49, 33, 65, 73], [43, 22, 51, 21, 98, 35, 68, 10, 76], [43, 21, 16, 78, 50, 18, 17, 74, 38], [55, 8, 20, 23, 62, 44, 69, 61, 8], [32, 16, 83, 21, 10, 99, 98, 96, 43]], [[86, 89, 74, 84, 94, 93, 94, 24, 46], [32, 88, 78, 71, 56, 17, 2, 76, 45], [53, 66, 36, 56, 30, 51, 2, 8, 2], [11, 47, 94, 89, 39, 6, 62, 35, 69], [75, 67, 13, 70, 54, 70, 14, 6, 0], [47, 77, 64, 90, 28, 78, 61, 2, 58], [75, 35, 91, 81, 85, 37, 49, 67, 5], [16, 32, 90, 18, 73, 13, 51, 58, 50], [1, 7, 57, 25, 99, 71, 59, 54, 91]], [[21, 98, 81, 76, 73, 19, 38, 28, 67], [9, 37, 88, 2, 99, 57, 20, 80, 16], [15, 48, 79, 39, 71, 11, 31, 25, 84], [92, 33, 91, 16, 38, 84, 8, 38, 1], [60, 39, 42, 20, 82, 14, 52, 2, 58], [27, 26, 34, 33, 96, 51, 91, 20, 54], [98, 92, 83, 89, 5, 73, 42, 72, 88], [77, 10, 36, 4, 28, 75, 99, 53, 74], [32, 33, 7, 65, 30, 40, 51, 57, 74]], [[58, 7, 43, 85, 61, 97, 25, 40, 14], [0, 69, 17, 60, 42, 21, 99, 32, 46], [59, 15, 42, 13, 79, 4, 66, 51, 1], [75, 43, 0, 39, 25, 72, 40, 11, 15], [24, 25, 99, 30, 92, 88, 19, 74, 2], [52, 25, 74, 85, 0, 51, 73, 68, 69], [72, 78, 48, 11, 37, 38, 33, 44, 48], [48, 20, 13, 0, 82, 2, 16, 70, 22], [76, 58, 37, 82, 63, 43, 42, 5, 51]], [[11, 80, 98, 98, 25, 53, 46, 48, 60], [12, 45, 71, 4, 22, 63, 76, 85, 39], [72, 54, 91, 62, 27, 46, 49, 43, 1], [17, 31, 88, 78, 90, 38, 47, 99, 61], [94, 70, 87, 65, 55, 10, 20, 58, 59], [87, 6, 43, 94, 52, 94, 35, 20, 82], [32, 78, 77, 42, 33, 64, 50, 54, 72], [37, 45, 86, 60, 5, 75, 29, 62, 95], [74, 23, 56, 47, 26, 96, 9, 82, 90]]], 'objective': 23.0}","[[0, 0, 7], [1, 5, 6], [2, 7, 4], [3, 6, 5], [4, 4, 1], [5, 8, 0], [6, 1, 3], [7, 3, 2], [8, 2, 8]]",23.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 92}, {'i': 0, 'j': 0, 'k': 1, 'cost': 32}, {'i': 0, 'j': 0, 'k': 2, 'cost': 59}, {'i': 0, 'j': 0, 'k': 3, 'cost': 89}, {'i': 0, 'j': 0, 'k': 4, 'cost': 11}, {'i': 0, 'j': 0, 'k': 5, 'cost': 72}, {'i': 0, 'j': 0, 'k': 6, 'cost': 47}, {'i': 0, 'j': 0, 'k': 7, 'cost': 1}, {'i': 0, 'j': 0, 'k': 8, 'cost': 37}, {'i': 0, 'j': 1, 'k': 0, 'cost': 32}, {'i': 0, 'j': 1, 'k': 1, 'cost': 41}, {'i': 0, 'j': 1, 'k': 2, 'cost': 62}, {'i': 0, 'j': 1, 'k': 3, 'cost': 25}, {'i': 0, 'j': 1, 'k': 4, 'cost': 12}, {'i': 0, 'j': 1, 'k': 5, 'cost': 85}, {'i': 0, 'j': 1, 'k': 6, 'cost': 7}, {'i': 0, 'j': 1, 'k': 7, 'cost': 96}, {'i': 0, 'j': 1, 'k': 8, 'cost': 35}, {'i': 0, 'j': 2, 'k': 0, 'cost': 38}, {'i': 0, 'j': 2, 'k': 1, 'cost': 89}, {'i': 0, 'j': 2, 'k': 2, 'cost': 6}, {'i': 0, 'j': 2, 'k': 3, 'cost': 24}, {'i': 0, 'j': 2, 'k': 4, 'cost': 5}, {'i': 0, 'j': 2, 'k': 5, 'cost': 88}, {'i': 0, 'j': 2, 'k': 6, 'cost': 31}, {'i': 0, 'j': 2, 'k': 7, 'cost': 56}, {'i': 0, 'j': 2, 'k': 8, 'cost': 26}, {'i': 0, 'j': 3, 'k': 0, 'cost': 46}, {'i': 0, 'j': 3, 'k': 1, 'cost': 62}, {'i': 0, 'j': 3, 'k': 2, 'cost': 30}, {'i': 0, 'j': 3, 'k': 3, 'cost': 42}, {'i': 0, 'j': 3, 'k': 4, 'cost': 98}, {'i': 0, 'j': 3, 'k': 5, 'cost': 53}, {'i': 0, 'j': 3, 'k': 6, 'cost': 9}, {'i': 0, 'j': 3, 'k': 7, 'cost': 72}, {'i': 0, 'j': 3, 'k': 8, 'cost': 83}, {'i': 0, 'j': 4, 'k': 0, 'cost': 86}, {'i': 0, 'j': 4, 'k': 1, 'cost': 66}, {'i': 0, 'j': 4, 'k': 2, 'cost': 56}, {'i': 0, 'j': 4, 'k': 3, 'cost': 54}, {'i': 0, 'j': 4, 'k': 4, 'cost': 57}, {'i': 0, 'j': 4, 'k': 5, 'cost': 24}, {'i': 0, 'j': 4, 'k': 6, 'cost': 86}, {'i': 0, 'j': 4, 'k': 7, 'cost': 1}, {'i': 0, 'j': 4, 'k': 8, 'cost': 40}, {'i': 0, 'j': 5, 'k': 0, 'cost': 23}, {'i': 0, 'j': 5, 'k': 1, 'cost': 82}, {'i': 0, 'j': 5, 'k': 2, 'cost': 53}, {'i': 0, 'j': 5, 'k': 3, 'cost': 70}, {'i': 0, 'j': 5, 'k': 4, 'cost': 25}, {'i': 0, 'j': 5, 'k': 5, 'cost': 7}, {'i': 0, 'j': 5, 'k': 6, 'cost': 30}, {'i': 0, 'j': 5, 'k': 7, 'cost': 68}, {'i': 0, 'j': 5, 'k': 8, 'cost': 73}, {'i': 0, 'j': 6, 'k': 0, 'cost': 18}, {'i': 0, 'j': 6, 'k': 1, 'cost': 32}, {'i': 0, 'j': 6, 'k': 2, 'cost': 80}, {'i': 0, 'j': 6, 'k': 3, 'cost': 73}, {'i': 0, 'j': 6, 'k': 4, 'cost': 87}, {'i': 0, 'j': 6, 'k': 5, 'cost': 17}, {'i': 0, 'j': 6, 'k': 6, 'cost': 46}, {'i': 0, 'j': 6, 'k': 7, 'cost': 35}, {'i': 0, 'j': 6, 'k': 8, 'cost': 58}, {'i': 0, 'j': 7, 'k': 0, 'cost': 24}, {'i': 0, 'j': 7, 'k': 1, 'cost': 35}, {'i': 0, 'j': 7, 'k': 2, 'cost': 94}, {'i': 0, 'j': 7, 'k': 3, 'cost': 0}, {'i': 0, 'j': 7, 'k': 4, 'cost': 97}, {'i': 0, 'j': 7, 'k': 5, 'cost': 2}, {'i': 0, 'j': 7, 'k': 6, 'cost': 40}, {'i': 0, 'j': 7, 'k': 7, 'cost': 79}, {'i': 0, 'j': 7, 'k': 8, 'cost': 42}, {'i': 0, 'j': 8, 'k': 0, 'cost': 12}, {'i': 0, 'j': 8, 'k': 1, 'cost': 11}, {'i': 0, 'j': 8, 'k': 2, 'cost': 12}, {'i': 0, 'j': 8, 'k': 3, 'cost': 45}, {'i': 0, 'j': 8, 'k': 4, 'cost': 55}, {'i': 0, 'j': 8, 'k': 5, 'cost': 2}, {'i': 0, 'j': 8, 'k': 6, 'cost': 49}, {'i': 0, 'j': 8, 'k': 7, 'cost': 84}, {'i': 0, 'j': 8, 'k': 8, 'cost': 1}, {'i': 1, 'j': 0, 'k': 0, 'cost': 93}, {'i': 1, 'j': 0, 'k': 1, 'cost': 53}, {'i': 1, 'j': 0, 'k': 2, 'cost': 4}, {'i': 1, 'j': 0, 'k': 3, 'cost': 43}, {'i': 1, 'j': 0, 'k': 4, 'cost': 96}, {'i': 1, 'j': 0, 'k': 5, 'cost': 70}, {'i': 1, 'j': 0, 'k': 6, 'cost': 85}, {'i': 1, 'j': 0, 'k': 7, 'cost': 38}, {'i': 1, 'j': 0, 'k': 8, 'cost': 53}, {'i': 1, 'j': 1, 'k': 0, 'cost': 71}, {'i': 1, 'j': 1, 'k': 1, 'cost': 93}, {'i': 1, 'j': 1, 'k': 2, 'cost': 42}, {'i': 1, 'j': 1, 'k': 3, 'cost': 51}, {'i': 1, 'j': 1, 'k': 4, 'cost': 58}, {'i': 1, 'j': 1, 'k': 5, 'cost': 12}, {'i': 1, 'j': 1, 'k': 6, 'cost': 27}, {'i': 1, 'j': 1, 'k': 7, 'cost': 35}, {'i': 1, 'j': 1, 'k': 8, 'cost': 54}, {'i': 1, 'j': 2, 'k': 0, 'cost': 72}, {'i': 1, 'j': 2, 'k': 1, 'cost': 67}, {'i': 1, 'j': 2, 'k': 2, 'cost': 6}, {'i': 1, 'j': 2, 'k': 3, 'cost': 12}, {'i': 1, 'j': 2, 'k': 4, 'cost': 87}, {'i': 1, 'j': 2, 'k': 5, 'cost': 51}, {'i': 1, 'j': 2, 'k': 6, 'cost': 89}, {'i': 1, 'j': 2, 'k': 7, 'cost': 62}, {'i': 1, 'j': 2, 'k': 8, 'cost': 44}, {'i': 1, 'j': 3, 'k': 0, 'cost': 26}, {'i': 1, 'j': 3, 'k': 1, 'cost': 30}, {'i': 1, 'j': 3, 'k': 2, 'cost': 94}, {'i': 1, 'j': 3, 'k': 3, 'cost': 46}, {'i': 1, 'j': 3, 'k': 4, 'cost': 83}, {'i': 1, 'j': 3, 'k': 5, 'cost': 3}, {'i': 1, 'j': 3, 'k': 6, 'cost': 57}, {'i': 1, 'j': 3, 'k': 7, 'cost': 78}, {'i': 1, 'j': 3, 'k': 8, 'cost': 97}, {'i': 1, 'j': 4, 'k': 0, 'cost': 21}, {'i': 1, 'j': 4, 'k': 1, 'cost': 53}, {'i': 1, 'j': 4, 'k': 2, 'cost': 21}, {'i': 1, 'j': 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81}, {'i': 5, 'j': 6, 'k': 4, 'cost': 85}, {'i': 5, 'j': 6, 'k': 5, 'cost': 37}, {'i': 5, 'j': 6, 'k': 6, 'cost': 49}, {'i': 5, 'j': 6, 'k': 7, 'cost': 67}, {'i': 5, 'j': 6, 'k': 8, 'cost': 5}, {'i': 5, 'j': 7, 'k': 0, 'cost': 16}, {'i': 5, 'j': 7, 'k': 1, 'cost': 32}, {'i': 5, 'j': 7, 'k': 2, 'cost': 90}, {'i': 5, 'j': 7, 'k': 3, 'cost': 18}, {'i': 5, 'j': 7, 'k': 4, 'cost': 73}, {'i': 5, 'j': 7, 'k': 5, 'cost': 13}, {'i': 5, 'j': 7, 'k': 6, 'cost': 51}, {'i': 5, 'j': 7, 'k': 7, 'cost': 58}, {'i': 5, 'j': 7, 'k': 8, 'cost': 50}, {'i': 5, 'j': 8, 'k': 0, 'cost': 1}, {'i': 5, 'j': 8, 'k': 1, 'cost': 7}, {'i': 5, 'j': 8, 'k': 2, 'cost': 57}, {'i': 5, 'j': 8, 'k': 3, 'cost': 25}, {'i': 5, 'j': 8, 'k': 4, 'cost': 99}, {'i': 5, 'j': 8, 'k': 5, 'cost': 71}, {'i': 5, 'j': 8, 'k': 6, 'cost': 59}, {'i': 5, 'j': 8, 'k': 7, 'cost': 54}, {'i': 5, 'j': 8, 'k': 8, 'cost': 91}, {'i': 6, 'j': 0, 'k': 0, 'cost': 21}, {'i': 6, 'j': 0, 'k': 1, 'cost': 98}, {'i': 6, 'j': 0, 'k': 2, 'cost': 81}, {'i': 6, 'j': 0, 'k': 3, 'cost': 76}, {'i': 6, 'j': 0, 'k': 4, 'cost': 73}, {'i': 6, 'j': 0, 'k': 5, 'cost': 19}, {'i': 6, 'j': 0, 'k': 6, 'cost': 38}, {'i': 6, 'j': 0, 'k': 7, 'cost': 28}, {'i': 6, 'j': 0, 'k': 8, 'cost': 67}, {'i': 6, 'j': 1, 'k': 0, 'cost': 9}, {'i': 6, 'j': 1, 'k': 1, 'cost': 37}, {'i': 6, 'j': 1, 'k': 2, 'cost': 88}, {'i': 6, 'j': 1, 'k': 3, 'cost': 2}, {'i': 6, 'j': 1, 'k': 4, 'cost': 99}, {'i': 6, 'j': 1, 'k': 5, 'cost': 57}, {'i': 6, 'j': 1, 'k': 6, 'cost': 20}, {'i': 6, 'j': 1, 'k': 7, 'cost': 80}, {'i': 6, 'j': 1, 'k': 8, 'cost': 16}, {'i': 6, 'j': 2, 'k': 0, 'cost': 15}, {'i': 6, 'j': 2, 'k': 1, 'cost': 48}, {'i': 6, 'j': 2, 'k': 2, 'cost': 79}, {'i': 6, 'j': 2, 'k': 3, 'cost': 39}, {'i': 6, 'j': 2, 'k': 4, 'cost': 71}, {'i': 6, 'j': 2, 'k': 5, 'cost': 11}, {'i': 6, 'j': 2, 'k': 6, 'cost': 31}, {'i': 6, 'j': 2, 'k': 7, 'cost': 25}, {'i': 6, 'j': 2, 'k': 8, 'cost': 84}, {'i': 6, 'j': 3, 'k': 0, 'cost': 92}, {'i': 6, 'j': 3, 'k': 1, 'cost': 33}, {'i': 6, 'j': 3, 'k': 2, 'cost': 91}, {'i': 6, 'j': 3, 'k': 3, 'cost': 16}, {'i': 6, 'j': 3, 'k': 4, 'cost': 38}, {'i': 6, 'j': 3, 'k': 5, 'cost': 84}, {'i': 6, 'j': 3, 'k': 6, 'cost': 8}, {'i': 6, 'j': 3, 'k': 7, 'cost': 38}, {'i': 6, 'j': 3, 'k': 8, 'cost': 1}, {'i': 6, 'j': 4, 'k': 0, 'cost': 60}, {'i': 6, 'j': 4, 'k': 1, 'cost': 39}, {'i': 6, 'j': 4, 'k': 2, 'cost': 42}, {'i': 6, 'j': 4, 'k': 3, 'cost': 20}, {'i': 6, 'j': 4, 'k': 4, 'cost': 82}, {'i': 6, 'j': 4, 'k': 5, 'cost': 14}, {'i': 6, 'j': 4, 'k': 6, 'cost': 52}, {'i': 6, 'j': 4, 'k': 7, 'cost': 2}, {'i': 6, 'j': 4, 'k': 8, 'cost': 58}, {'i': 6, 'j': 5, 'k': 0, 'cost': 27}, {'i': 6, 'j': 5, 'k': 1, 'cost': 26}, {'i': 6, 'j': 5, 'k': 2, 'cost': 34}, {'i': 6, 'j': 5, 'k': 3, 'cost': 33}, {'i': 6, 'j': 5, 'k': 4, 'cost': 96}, {'i': 6, 'j': 5, 'k': 5, 'cost': 51}, {'i': 6, 'j': 5, 'k': 6, 'cost': 91}, {'i': 6, 'j': 5, 'k': 7, 'cost': 20}, {'i': 6, 'j': 5, 'k': 8, 'cost': 54}, {'i': 6, 'j': 6, 'k': 0, 'cost': 98}, {'i': 6, 'j': 6, 'k': 1, 'cost': 92}, {'i': 6, 'j': 6, 'k': 2, 'cost': 83}, {'i': 6, 'j': 6, 'k': 3, 'cost': 89}, {'i': 6, 'j': 6, 'k': 4, 'cost': 5}, {'i': 6, 'j': 6, 'k': 5, 'cost': 73}, {'i': 6, 'j': 6, 'k': 6, 'cost': 42}, {'i': 6, 'j': 6, 'k': 7, 'cost': 72}, {'i': 6, 'j': 6, 'k': 8, 'cost': 88}, {'i': 6, 'j': 7, 'k': 0, 'cost': 77}, {'i': 6, 'j': 7, 'k': 1, 'cost': 10}, {'i': 6, 'j': 7, 'k': 2, 'cost': 36}, {'i': 6, 'j': 7, 'k': 3, 'cost': 4}, {'i': 6, 'j': 7, 'k': 4, 'cost': 28}, {'i': 6, 'j': 7, 'k': 5, 'cost': 75}, {'i': 6, 'j': 7, 'k': 6, 'cost': 99}, {'i': 6, 'j': 7, 'k': 7, 'cost': 53}, {'i': 6, 'j': 7, 'k': 8, 'cost': 74}, {'i': 6, 'j': 8, 'k': 0, 'cost': 32}, {'i': 6, 'j': 8, 'k': 1, 'cost': 33}, {'i': 6, 'j': 8, 'k': 2, 'cost': 7}, {'i': 6, 'j': 8, 'k': 3, 'cost': 65}, {'i': 6, 'j': 8, 'k': 4, 'cost': 30}, {'i': 6, 'j': 8, 'k': 5, 'cost': 40}, {'i': 6, 'j': 8, 'k': 6, 'cost': 51}, {'i': 6, 'j': 8, 'k': 7, 'cost': 57}, {'i': 6, 'j': 8, 'k': 8, 'cost': 74}, {'i': 7, 'j': 0, 'k': 0, 'cost': 58}, {'i': 7, 'j': 0, 'k': 1, 'cost': 7}, {'i': 7, 'j': 0, 'k': 2, 'cost': 43}, {'i': 7, 'j': 0, 'k': 3, 'cost': 85}, {'i': 7, 'j': 0, 'k': 4, 'cost': 61}, {'i': 7, 'j': 0, 'k': 5, 'cost': 97}, {'i': 7, 'j': 0, 'k': 6, 'cost': 25}, {'i': 7, 'j': 0, 'k': 7, 'cost': 40}, {'i': 7, 'j': 0, 'k': 8, 'cost': 14}, {'i': 7, 'j': 1, 'k': 0, 'cost': 0}, {'i': 7, 'j': 1, 'k': 1, 'cost': 69}, {'i': 7, 'j': 1, 'k': 2, 'cost': 17}, {'i': 7, 'j': 1, 'k': 3, 'cost': 60}, {'i': 7, 'j': 1, 'k': 4, 'cost': 42}, {'i': 7, 'j': 1, 'k': 5, 'cost': 21}, {'i': 7, 'j': 1, 'k': 6, 'cost': 99}, {'i': 7, 'j': 1, 'k': 7, 'cost': 32}, {'i': 7, 'j': 1, 'k': 8, 'cost': 46}, {'i': 7, 'j': 2, 'k': 0, 'cost': 59}, {'i': 7, 'j': 2, 'k': 1, 'cost': 15}, {'i': 7, 'j': 2, 'k': 2, 'cost': 42}, {'i': 7, 'j': 2, 'k': 3, 'cost': 13}, {'i': 7, 'j': 2, 'k': 4, 'cost': 79}, {'i': 7, 'j': 2, 'k': 5, 'cost': 4}, {'i': 7, 'j': 2, 'k': 6, 'cost': 66}, {'i': 7, 'j': 2, 'k': 7, 'cost': 51}, {'i': 7, 'j': 2, 'k': 8, 'cost': 1}, {'i': 7, 'j': 3, 'k': 0, 'cost': 75}, {'i': 7, 'j': 3, 'k': 1, 'cost': 43}, {'i': 7, 'j': 3, 'k': 2, 'cost': 0}, {'i': 7, 'j': 3, 'k': 3, 'cost': 39}, {'i': 7, 'j': 3, 'k': 4, 'cost': 25}, {'i': 7, 'j': 3, 'k': 5, 'cost': 72}, {'i': 7, 'j': 3, 'k': 6, 'cost': 40}, {'i': 7, 'j': 3, 'k': 7, 'cost': 11}, {'i': 7, 'j': 3, 'k': 8, 'cost': 15}, {'i': 7, 'j': 4, 'k': 0, 'cost': 24}, {'i': 7, 'j': 4, 'k': 1, 'cost': 25}, {'i': 7, 'j': 4, 'k': 2, 'cost': 99}, {'i': 7, 'j': 4, 'k': 3, 'cost': 30}, {'i': 7, 'j': 4, 'k': 4, 'cost': 92}, {'i': 7, 'j': 4, 'k': 5, 'cost': 88}, {'i': 7, 'j': 4, 'k': 6, 'cost': 19}, {'i': 7, 'j': 4, 'k': 7, 'cost': 74}, {'i': 7, 'j': 4, 'k': 8, 'cost': 2}, {'i': 7, 'j': 5, 'k': 0, 'cost': 52}, {'i': 7, 'j': 5, 'k': 1, 'cost': 25}, {'i': 7, 'j': 5, 'k': 2, 'cost': 74}, {'i': 7, 'j': 5, 'k': 3, 'cost': 85}, {'i': 7, 'j': 5, 'k': 4, 'cost': 0}, {'i': 7, 'j': 5, 'k': 5, 'cost': 51}, {'i': 7, 'j': 5, 'k': 6, 'cost': 73}, {'i': 7, 'j': 5, 'k': 7, 'cost': 68}, {'i': 7, 'j': 5, 'k': 8, 'cost': 69}, {'i': 7, 'j': 6, 'k': 0, 'cost': 72}, {'i': 7, 'j': 6, 'k': 1, 'cost': 78}, {'i': 7, 'j': 6, 'k': 2, 'cost': 48}, {'i': 7, 'j': 6, 'k': 3, 'cost': 11}, {'i': 7, 'j': 6, 'k': 4, 'cost': 37}, {'i': 7, 'j': 6, 'k': 5, 'cost': 38}, {'i': 7, 'j': 6, 'k': 6, 'cost': 33}, {'i': 7, 'j': 6, 'k': 7, 'cost': 44}, {'i': 7, 'j': 6, 'k': 8, 'cost': 48}, {'i': 7, 'j': 7, 'k': 0, 'cost': 48}, {'i': 7, 'j': 7, 'k': 1, 'cost': 20}, {'i': 7, 'j': 7, 'k': 2, 'cost': 13}, {'i': 7, 'j': 7, 'k': 3, 'cost': 0}, {'i': 7, 'j': 7, 'k': 4, 'cost': 82}, {'i': 7, 'j': 7, 'k': 5, 'cost': 2}, {'i': 7, 'j': 7, 'k': 6, 'cost': 16}, {'i': 7, 'j': 7, 'k': 7, 'cost': 70}, {'i': 7, 'j': 7, 'k': 8, 'cost': 22}, {'i': 7, 'j': 8, 'k': 0, 'cost': 76}, {'i': 7, 'j': 8, 'k': 1, 'cost': 58}, {'i': 7, 'j': 8, 'k': 2, 'cost': 37}, {'i': 7, 'j': 8, 'k': 3, 'cost': 82}, {'i': 7, 'j': 8, 'k': 4, 'cost': 63}, {'i': 7, 'j': 8, 'k': 5, 'cost': 43}, {'i': 7, 'j': 8, 'k': 6, 'cost': 42}, {'i': 7, 'j': 8, 'k': 7, 'cost': 5}, {'i': 7, 'j': 8, 'k': 8, 'cost': 51}, {'i': 8, 'j': 0, 'k': 0, 'cost': 11}, {'i': 8, 'j': 0, 'k': 1, 'cost': 80}, {'i': 8, 'j': 0, 'k': 2, 'cost': 98}, {'i': 8, 'j': 0, 'k': 3, 'cost': 98}, {'i': 8, 'j': 0, 'k': 4, 'cost': 25}, {'i': 8, 'j': 0, 'k': 5, 'cost': 53}, {'i': 8, 'j': 0, 'k': 6, 'cost': 46}, {'i': 8, 'j': 0, 'k': 7, 'cost': 48}, {'i': 8, 'j': 0, 'k': 8, 'cost': 60}, {'i': 8, 'j': 1, 'k': 0, 'cost': 12}, {'i': 8, 'j': 1, 'k': 1, 'cost': 45}, {'i': 8, 'j': 1, 'k': 2, 'cost': 71}, {'i': 8, 'j': 1, 'k': 3, 'cost': 4}, {'i': 8, 'j': 1, 'k': 4, 'cost': 22}, {'i': 8, 'j': 1, 'k': 5, 'cost': 63}, {'i': 8, 'j': 1, 'k': 6, 'cost': 76}, {'i': 8, 'j': 1, 'k': 7, 'cost': 85}, {'i': 8, 'j': 1, 'k': 8, 'cost': 39}, {'i': 8, 'j': 2, 'k': 0, 'cost': 72}, {'i': 8, 'j': 2, 'k': 1, 'cost': 54}, {'i': 8, 'j': 2, 'k': 2, 'cost': 91}, {'i': 8, 'j': 2, 'k': 3, 'cost': 62}, {'i': 8, 'j': 2, 'k': 4, 'cost': 27}, {'i': 8, 'j': 2, 'k': 5, 'cost': 46}, {'i': 8, 'j': 2, 'k': 6, 'cost': 49}, {'i': 8, 'j': 2, 'k': 7, 'cost': 43}, {'i': 8, 'j': 2, 'k': 8, 'cost': 1}, {'i': 8, 'j': 3, 'k': 0, 'cost': 17}, {'i': 8, 'j': 3, 'k': 1, 'cost': 31}, {'i': 8, 'j': 3, 'k': 2, 'cost': 88}, {'i': 8, 'j': 3, 'k': 3, 'cost': 78}, {'i': 8, 'j': 3, 'k': 4, 'cost': 90}, {'i': 8, 'j': 3, 'k': 5, 'cost': 38}, {'i': 8, 'j': 3, 'k': 6, 'cost': 47}, {'i': 8, 'j': 3, 'k': 7, 'cost': 99}, {'i': 8, 'j': 3, 'k': 8, 'cost': 61}, {'i': 8, 'j': 4, 'k': 0, 'cost': 94}, {'i': 8, 'j': 4, 'k': 1, 'cost': 70}, {'i': 8, 'j': 4, 'k': 2, 'cost': 87}, {'i': 8, 'j': 4, 'k': 3, 'cost': 65}, {'i': 8, 'j': 4, 'k': 4, 'cost': 55}, {'i': 8, 'j': 4, 'k': 5, 'cost': 10}, {'i': 8, 'j': 4, 'k': 6, 'cost': 20}, {'i': 8, 'j': 4, 'k': 7, 'cost': 58}, {'i': 8, 'j': 4, 'k': 8, 'cost': 59}, {'i': 8, 'j': 5, 'k': 0, 'cost': 87}, {'i': 8, 'j': 5, 'k': 1, 'cost': 6}, {'i': 8, 'j': 5, 'k': 2, 'cost': 43}, {'i': 8, 'j': 5, 'k': 3, 'cost': 94}, {'i': 8, 'j': 5, 'k': 4, 'cost': 52}, {'i': 8, 'j': 5, 'k': 5, 'cost': 94}, {'i': 8, 'j': 5, 'k': 6, 'cost': 35}, {'i': 8, 'j': 5, 'k': 7, 'cost': 20}, {'i': 8, 'j': 5, 'k': 8, 'cost': 82}, {'i': 8, 'j': 6, 'k': 0, 'cost': 32}, {'i': 8, 'j': 6, 'k': 1, 'cost': 78}, {'i': 8, 'j': 6, 'k': 2, 'cost': 77}, {'i': 8, 'j': 6, 'k': 3, 'cost': 42}, {'i': 8, 'j': 6, 'k': 4, 'cost': 33}, {'i': 8, 'j': 6, 'k': 5, 'cost': 64}, {'i': 8, 'j': 6, 'k': 6, 'cost': 50}, {'i': 8, 'j': 6, 'k': 7, 'cost': 54}, {'i': 8, 'j': 6, 'k': 8, 'cost': 72}, {'i': 8, 'j': 7, 'k': 0, 'cost': 37}, {'i': 8, 'j': 7, 'k': 1, 'cost': 45}, {'i': 8, 'j': 7, 'k': 2, 'cost': 86}, {'i': 8, 'j': 7, 'k': 3, 'cost': 60}, {'i': 8, 'j': 7, 'k': 4, 'cost': 5}, {'i': 8, 'j': 7, 'k': 5, 'cost': 75}, {'i': 8, 'j': 7, 'k': 6, 'cost': 29}, {'i': 8, 'j': 7, 'k': 7, 'cost': 62}, {'i': 8, 'j': 7, 'k': 8, 'cost': 95}, {'i': 8, 'j': 8, 'k': 0, 'cost': 74}, {'i': 8, 'j': 8, 'k': 1, 'cost': 23}, {'i': 8, 'j': 8, 'k': 2, 'cost': 56}, {'i': 8, 'j': 8, 'k': 3, 'cost': 47}, {'i': 8, 'j': 8, 'k': 4, 'cost': 26}, {'i': 8, 'j': 8, 'k': 5, 'cost': 96}, {'i': 8, 'j': 8, 'k': 6, 'cost': 9}, {'i': 8, 'j': 8, 'k': 7, 'cost': 82}, {'i': 8, 'j': 8, 'k': 8, 'cost': 90}]}","[[0, 0, 7], [1, 5, 6], [2, 7, 4], [3, 6, 5], [4, 4, 1], [5, 8, 0], [6, 1, 3], [7, 3, 2], [8, 2, 8]]",1,markdown_table,0
+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.
+
+# num_speakers=9
+# index_identifiers=1, 2, 3, 4, 5, 6, 7, 8, 9
+
+# 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=1
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 92 | 32 | 59 | 89 | 11 | 47 | 6 | 1 | 37 |
+| 2 | 32 | 41 | 62 | 25 | 12 | 7 | 77 | 96 | 35 |
+| 3 | 38 | 89 | 6 | 24 | 5 | 31 | 2 | 56 | 26 |
+| 4 | 46 | 62 | 30 | 42 | 98 | 9 | 9 | 72 | 83 |
+| 5 | 86 | 66 | 56 | 54 | 57 | 86 | 30 | 1 | 40 |
+| 6 | 18 | 32 | 80 | 73 | 87 | 46 | 57 | 35 | 58 |
+| 7 | 43 | 15 | 21 | 58 | 64 | 1 | 9 | 96 | 15 |
+| 8 | 24 | 35 | 94 | 0 | 97 | 40 | 5 | 79 | 42 |
+| 9 | 12 | 11 | 12 | 45 | 55 | 49 | 60 | 84 | 1 |
+
+## speaker_id=2
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 93 | 53 | 4 | 43 | 96 | 85 | 35 | 38 | 53 |
+| 2 | 71 | 93 | 42 | 51 | 58 | 27 | 78 | 35 | 54 |
+| 3 | 72 | 67 | 6 | 12 | 87 | 89 | 48 | 62 | 44 |
+| 4 | 26 | 30 | 94 | 46 | 83 | 57 | 30 | 78 | 97 |
+| 5 | 21 | 53 | 21 | 11 | 82 | 96 | 88 | 12 | 14 |
+| 6 | 31 | 14 | 20 | 38 | 62 | 92 | 26 | 14 | 40 |
+| 7 | 39 | 80 | 12 | 30 | 43 | 28 | 51 | 25 | 43 |
+| 8 | 27 | 47 | 35 | 40 | 59 | 91 | 25 | 17 | 95 |
+| 9 | 34 | 70 | 22 | 88 | 52 | 28 | 58 | 30 | 44 |
+
+## speaker_id=3
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 72 | 96 | 48 | 82 | 18 | 43 | 25 | 71 |
+| 2 | 94 | 40 | 60 | 35 | 33 | 87 | 25 | 40 | 65 |
+| 3 | 16 | 17 | 8 | 30 | 57 | 37 | 92 | 32 | 93 |
+| 4 | 76 | 83 | 41 | 70 | 14 | 11 | 97 | 10 | 37 |
+| 5 | 77 | 79 | 89 | 91 | 5 | 0 | 5 | 27 | 67 |
+| 6 | 26 | 64 | 96 | 67 | 24 | 91 | 28 | 91 | 35 |
+| 7 | 69 | 30 | 46 | 24 | 29 | 68 | 24 | 43 | 66 |
+| 8 | 94 | 15 | 58 | 30 | 6 | 40 | 81 | 57 | 78 |
+| 9 | 11 | 43 | 68 | 33 | 42 | 26 | 3 | 59 | 2 |
+
+## speaker_id=4
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 20 | 44 | 29 | 56 | 55 | 67 | 23 | 62 | 51 |
+| 2 | 56 | 38 | 63 | 93 | 91 | 96 | 26 | 67 | 38 |
+| 3 | 67 | 74 | 7 | 72 | 27 | 47 | 47 | 52 | 86 |
+| 4 | 85 | 85 | 7 | 53 | 6 | 86 | 66 | 92 | 59 |
+| 5 | 13 | 89 | 13 | 38 | 69 | 41 | 53 | 66 | 37 |
+| 6 | 66 | 33 | 70 | 76 | 70 | 5 | 18 | 81 | 17 |
+| 7 | 25 | 56 | 52 | 6 | 78 | 4 | 93 | 27 | 64 |
+| 8 | 37 | 19 | 92 | 99 | 13 | 95 | 9 | 23 | 99 |
+| 9 | 93 | 11 | 92 | 47 | 50 | 38 | 93 | 11 | 3 |
+
+## speaker_id=5
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 40 | 10 | 24 | 58 | 22 | 94 | 68 | 22 | 24 |
+| 2 | 0 | 18 | 42 | 54 | 64 | 51 | 30 | 99 | 4 |
+| 3 | 43 | 37 | 25 | 63 | 11 | 95 | 6 | 47 | 91 |
+| 4 | 96 | 17 | 23 | 51 | 80 | 76 | 57 | 92 | 14 |
+| 5 | 35 | 0 | 49 | 80 | 22 | 33 | 38 | 65 | 73 |
+| 6 | 43 | 21 | 16 | 78 | 50 | 17 | 90 | 74 | 38 |
+| 7 | 86 | 19 | 16 | 4 | 95 | 29 | 30 | 45 | 30 |
+| 8 | 55 | 8 | 20 | 23 | 62 | 69 | 30 | 61 | 8 |
+| 9 | 32 | 16 | 83 | 21 | 10 | 98 | 61 | 96 | 43 |
+
+## speaker_id=6
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 21 | 98 | 81 | 76 | 73 | 38 | 25 | 28 | 67 |
+| 2 | 9 | 37 | 88 | 2 | 99 | 20 | 43 | 80 | 16 |
+| 3 | 15 | 48 | 79 | 39 | 71 | 31 | 89 | 25 | 84 |
+| 4 | 92 | 33 | 91 | 16 | 38 | 8 | 0 | 38 | 1 |
+| 5 | 60 | 39 | 42 | 20 | 82 | 52 | 80 | 2 | 58 |
+| 6 | 98 | 92 | 83 | 89 | 5 | 42 | 69 | 72 | 88 |
+| 7 | 40 | 5 | 9 | 97 | 85 | 73 | 96 | 12 | 71 |
+| 8 | 77 | 10 | 36 | 4 | 28 | 99 | 39 | 53 | 74 |
+| 9 | 32 | 33 | 7 | 65 | 30 | 51 | 57 | 57 | 74 |
+
+## speaker_id=7
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 63 | 82 | 80 | 89 | 72 | 86 | 40 | 94 |
+| 2 | 26 | 8 | 62 | 21 | 87 | 18 | 65 | 18 | 92 |
+| 3 | 51 | 87 | 67 | 38 | 87 | 24 | 65 | 76 | 25 |
+| 4 | 79 | 84 | 65 | 27 | 88 | 75 | 10 | 70 | 96 |
+| 5 | 76 | 78 | 25 | 69 | 34 | 94 | 64 | 35 | 16 |
+| 6 | 85 | 9 | 38 | 34 | 57 | 63 | 99 | 1 | 16 |
+| 7 | 82 | 52 | 79 | 42 | 24 | 28 | 71 | 4 | 14 |
+| 8 | 18 | 62 | 48 | 49 | 31 | 81 | 14 | 53 | 73 |
+| 9 | 30 | 30 | 45 | 10 | 1 | 0 | 40 | 0 | 15 |
+
+## speaker_id=8
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 58 | 7 | 43 | 85 | 61 | 25 | 54 | 40 | 14 |
+| 2 | 0 | 69 | 17 | 60 | 42 | 99 | 67 | 32 | 46 |
+| 3 | 59 | 15 | 42 | 13 | 79 | 66 | 25 | 51 | 1 |
+| 4 | 75 | 43 | 0 | 39 | 25 | 40 | 80 | 11 | 15 |
+| 5 | 24 | 25 | 99 | 30 | 92 | 19 | 94 | 74 | 2 |
+| 6 | 72 | 78 | 48 | 11 | 37 | 33 | 37 | 44 | 48 |
+| 7 | 51 | 76 | 95 | 87 | 52 | 9 | 48 | 30 | 44 |
+| 8 | 48 | 20 | 13 | 0 | 82 | 16 | 6 | 70 | 22 |
+| 9 | 76 | 58 | 37 | 82 | 63 | 42 | 2 | 5 | 51 |
+
+## speaker_id=9
+| room_id\time_slot_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 11 | 80 | 98 | 98 | 25 | 46 | 7 | 48 | 60 |
+| 2 | 12 | 45 | 71 | 4 | 22 | 76 | 6 | 85 | 39 |
+| 3 | 72 | 54 | 91 | 62 | 27 | 49 | 61 | 43 | 1 |
+| 4 | 17 | 31 | 88 | 78 | 90 | 47 | 49 | 99 | 61 |
+| 5 | 94 | 70 | 87 | 65 | 55 | 20 | 57 | 58 | 59 |
+| 6 | 32 | 78 | 77 | 42 | 33 | 50 | 51 | 54 | 72 |
+| 7 | 66 | 94 | 45 | 44 | 60 | 67 | 68 | 83 | 70 |
+| 8 | 37 | 45 | 86 | 60 | 5 | 29 | 19 | 62 | 95 |
+| 9 | 74 | 23 | 56 | 47 | 26 | 9 | 83 | 82 | 90 |
+
+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': [[[92, 32, 59, 89, 11, 47, 6, 1, 37], [32, 41, 62, 25, 12, 7, 77, 96, 35], [38, 89, 6, 24, 5, 31, 2, 56, 26], [46, 62, 30, 42, 98, 9, 9, 72, 83], [86, 66, 56, 54, 57, 86, 30, 1, 40], [18, 32, 80, 73, 87, 46, 57, 35, 58], [43, 15, 21, 58, 64, 1, 9, 96, 15], [24, 35, 94, 0, 97, 40, 5, 79, 42], [12, 11, 12, 45, 55, 49, 60, 84, 1]], [[93, 53, 4, 43, 96, 85, 35, 38, 53], [71, 93, 42, 51, 58, 27, 78, 35, 54], [72, 67, 6, 12, 87, 89, 48, 62, 44], [26, 30, 94, 46, 83, 57, 30, 78, 97], [21, 53, 21, 11, 82, 96, 88, 12, 14], [31, 14, 20, 38, 62, 92, 26, 14, 40], [39, 80, 12, 30, 43, 28, 51, 25, 43], [27, 47, 35, 40, 59, 91, 25, 17, 95], [34, 70, 22, 88, 52, 28, 58, 30, 44]], [[34, 72, 96, 48, 82, 18, 43, 25, 71], [94, 40, 60, 35, 33, 87, 25, 40, 65], [16, 17, 8, 30, 57, 37, 92, 32, 93], [76, 83, 41, 70, 14, 11, 97, 10, 37], [77, 79, 89, 91, 5, 0, 5, 27, 67], [26, 64, 96, 67, 24, 91, 28, 91, 35], [69, 30, 46, 24, 29, 68, 24, 43, 66], [94, 15, 58, 30, 6, 40, 81, 57, 78], [11, 43, 68, 33, 42, 26, 3, 59, 2]], [[20, 44, 29, 56, 55, 67, 23, 62, 51], [56, 38, 63, 93, 91, 96, 26, 67, 38], [67, 74, 7, 72, 27, 47, 47, 52, 86], [85, 85, 7, 53, 6, 86, 66, 92, 59], [13, 89, 13, 38, 69, 41, 53, 66, 37], [66, 33, 70, 76, 70, 5, 18, 81, 17], [25, 56, 52, 6, 78, 4, 93, 27, 64], [37, 19, 92, 99, 13, 95, 9, 23, 99], [93, 11, 92, 47, 50, 38, 93, 11, 3]], [[40, 10, 24, 58, 22, 94, 68, 22, 24], [0, 18, 42, 54, 64, 51, 30, 99, 4], [43, 37, 25, 63, 11, 95, 6, 47, 91], [96, 17, 23, 51, 80, 76, 57, 92, 14], [35, 0, 49, 80, 22, 33, 38, 65, 73], [43, 21, 16, 78, 50, 17, 90, 74, 38], [86, 19, 16, 4, 95, 29, 30, 45, 30], [55, 8, 20, 23, 62, 69, 30, 61, 8], [32, 16, 83, 21, 10, 98, 61, 96, 43]], [[21, 98, 81, 76, 73, 38, 25, 28, 67], [9, 37, 88, 2, 99, 20, 43, 80, 16], [15, 48, 79, 39, 71, 31, 89, 25, 84], [92, 33, 91, 16, 38, 8, 0, 38, 1], [60, 39, 42, 20, 82, 52, 80, 2, 58], [98, 92, 83, 89, 5, 42, 69, 72, 88], [40, 5, 9, 97, 85, 73, 96, 12, 71], [77, 10, 36, 4, 28, 99, 39, 53, 74], [32, 33, 7, 65, 30, 51, 57, 57, 74]], [[82, 63, 82, 80, 89, 72, 86, 40, 94], [26, 8, 62, 21, 87, 18, 65, 18, 92], [51, 87, 67, 38, 87, 24, 65, 76, 25], [79, 84, 65, 27, 88, 75, 10, 70, 96], [76, 78, 25, 69, 34, 94, 64, 35, 16], [85, 9, 38, 34, 57, 63, 99, 1, 16], [82, 52, 79, 42, 24, 28, 71, 4, 14], [18, 62, 48, 49, 31, 81, 14, 53, 73], [30, 30, 45, 10, 1, 0, 40, 0, 15]], [[58, 7, 43, 85, 61, 25, 54, 40, 14], [0, 69, 17, 60, 42, 99, 67, 32, 46], [59, 15, 42, 13, 79, 66, 25, 51, 1], [75, 43, 0, 39, 25, 40, 80, 11, 15], [24, 25, 99, 30, 92, 19, 94, 74, 2], [72, 78, 48, 11, 37, 33, 37, 44, 48], [51, 76, 95, 87, 52, 9, 48, 30, 44], [48, 20, 13, 0, 82, 16, 6, 70, 22], [76, 58, 37, 82, 63, 42, 2, 5, 51]], [[11, 80, 98, 98, 25, 46, 7, 48, 60], [12, 45, 71, 4, 22, 76, 6, 85, 39], [72, 54, 91, 62, 27, 49, 61, 43, 1], [17, 31, 88, 78, 90, 47, 49, 99, 61], [94, 70, 87, 65, 55, 20, 57, 58, 59], [32, 78, 77, 42, 33, 50, 51, 54, 72], [66, 94, 45, 44, 60, 67, 68, 83, 70], [37, 45, 86, 60, 5, 29, 19, 62, 95], [74, 23, 56, 47, 26, 9, 83, 82, 90]]], 'objective': 19.0}","[[0, 7, 3], [1, 0, 2], [2, 4, 5], [3, 3, 4], [4, 1, 0], [5, 6, 1], [6, 5, 7], [7, 8, 6], [8, 2, 8]]",19.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 92}, {'i': 1, 'j': 1, 'k': 2, 'cost': 32}, {'i': 1, 'j': 1, 'k': 3, 'cost': 59}, {'i': 1, 'j': 1, 'k': 4, 'cost': 89}, {'i': 1, 'j': 1, 'k': 5, 'cost': 11}, {'i': 1, 'j': 1, 'k': 6, 'cost': 47}, {'i': 1, 'j': 1, 'k': 7, 'cost': 6}, {'i': 1, 'j': 1, 'k': 8, 'cost': 1}, {'i': 1, 'j': 1, 'k': 9, 'cost': 37}, {'i': 1, 'j': 2, 'k': 1, 'cost': 32}, {'i': 1, 'j': 2, 'k': 2, 'cost': 41}, {'i': 1, 'j': 2, 'k': 3, 'cost': 62}, {'i': 1, 'j': 2, 'k': 4, 'cost': 25}, {'i': 1, 'j': 2, 'k': 5, 'cost': 12}, {'i': 1, 'j': 2, 'k': 6, 'cost': 7}, {'i': 1, 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75}, {'i': 8, 'j': 4, 'k': 2, 'cost': 43}, {'i': 8, 'j': 4, 'k': 3, 'cost': 0}, {'i': 8, 'j': 4, 'k': 4, 'cost': 39}, {'i': 8, 'j': 4, 'k': 5, 'cost': 25}, {'i': 8, 'j': 4, 'k': 6, 'cost': 40}, {'i': 8, 'j': 4, 'k': 7, 'cost': 80}, {'i': 8, 'j': 4, 'k': 8, 'cost': 11}, {'i': 8, 'j': 4, 'k': 9, 'cost': 15}, {'i': 8, 'j': 5, 'k': 1, 'cost': 24}, {'i': 8, 'j': 5, 'k': 2, 'cost': 25}, {'i': 8, 'j': 5, 'k': 3, 'cost': 99}, {'i': 8, 'j': 5, 'k': 4, 'cost': 30}, {'i': 8, 'j': 5, 'k': 5, 'cost': 92}, {'i': 8, 'j': 5, 'k': 6, 'cost': 19}, {'i': 8, 'j': 5, 'k': 7, 'cost': 94}, {'i': 8, 'j': 5, 'k': 8, 'cost': 74}, {'i': 8, 'j': 5, 'k': 9, 'cost': 2}, {'i': 8, 'j': 6, 'k': 1, 'cost': 72}, {'i': 8, 'j': 6, 'k': 2, 'cost': 78}, {'i': 8, 'j': 6, 'k': 3, 'cost': 48}, {'i': 8, 'j': 6, 'k': 4, 'cost': 11}, {'i': 8, 'j': 6, 'k': 5, 'cost': 37}, {'i': 8, 'j': 6, 'k': 6, 'cost': 33}, {'i': 8, 'j': 6, 'k': 7, 'cost': 37}, {'i': 8, 'j': 6, 'k': 8, 'cost': 44}, {'i': 8, 'j': 6, 'k': 9, 'cost': 48}, {'i': 8, 'j': 7, 'k': 1, 'cost': 51}, {'i': 8, 'j': 7, 'k': 2, 'cost': 76}, {'i': 8, 'j': 7, 'k': 3, 'cost': 95}, {'i': 8, 'j': 7, 'k': 4, 'cost': 87}, {'i': 8, 'j': 7, 'k': 5, 'cost': 52}, {'i': 8, 'j': 7, 'k': 6, 'cost': 9}, {'i': 8, 'j': 7, 'k': 7, 'cost': 48}, {'i': 8, 'j': 7, 'k': 8, 'cost': 30}, {'i': 8, 'j': 7, 'k': 9, 'cost': 44}, {'i': 8, 'j': 8, 'k': 1, 'cost': 48}, {'i': 8, 'j': 8, 'k': 2, 'cost': 20}, {'i': 8, 'j': 8, 'k': 3, 'cost': 13}, {'i': 8, 'j': 8, 'k': 4, 'cost': 0}, {'i': 8, 'j': 8, 'k': 5, 'cost': 82}, {'i': 8, 'j': 8, 'k': 6, 'cost': 16}, {'i': 8, 'j': 8, 'k': 7, 'cost': 6}, {'i': 8, 'j': 8, 'k': 8, 'cost': 70}, {'i': 8, 'j': 8, 'k': 9, 'cost': 22}, {'i': 8, 'j': 9, 'k': 1, 'cost': 76}, {'i': 8, 'j': 9, 'k': 2, 'cost': 58}, {'i': 8, 'j': 9, 'k': 3, 'cost': 37}, {'i': 8, 'j': 9, 'k': 4, 'cost': 82}, {'i': 8, 'j': 9, 'k': 5, 'cost': 63}, {'i': 8, 'j': 9, 'k': 6, 'cost': 42}, {'i': 8, 'j': 9, 'k': 7, 'cost': 2}, {'i': 8, 'j': 9, 'k': 8, 'cost': 5}, {'i': 8, 'j': 9, 'k': 9, 'cost': 51}, {'i': 9, 'j': 1, 'k': 1, 'cost': 11}, {'i': 9, 'j': 1, 'k': 2, 'cost': 80}, {'i': 9, 'j': 1, 'k': 3, 'cost': 98}, {'i': 9, 'j': 1, 'k': 4, 'cost': 98}, {'i': 9, 'j': 1, 'k': 5, 'cost': 25}, {'i': 9, 'j': 1, 'k': 6, 'cost': 46}, {'i': 9, 'j': 1, 'k': 7, 'cost': 7}, {'i': 9, 'j': 1, 'k': 8, 'cost': 48}, {'i': 9, 'j': 1, 'k': 9, 'cost': 60}, {'i': 9, 'j': 2, 'k': 1, 'cost': 12}, {'i': 9, 'j': 2, 'k': 2, 'cost': 45}, {'i': 9, 'j': 2, 'k': 3, 'cost': 71}, {'i': 9, 'j': 2, 'k': 4, 'cost': 4}, {'i': 9, 'j': 2, 'k': 5, 'cost': 22}, {'i': 9, 'j': 2, 'k': 6, 'cost': 76}, {'i': 9, 'j': 2, 'k': 7, 'cost': 6}, {'i': 9, 'j': 2, 'k': 8, 'cost': 85}, {'i': 9, 'j': 2, 'k': 9, 'cost': 39}, {'i': 9, 'j': 3, 'k': 1, 'cost': 72}, {'i': 9, 'j': 3, 'k': 2, 'cost': 54}, {'i': 9, 'j': 3, 'k': 3, 'cost': 91}, {'i': 9, 'j': 3, 'k': 4, 'cost': 62}, {'i': 9, 'j': 3, 'k': 5, 'cost': 27}, {'i': 9, 'j': 3, 'k': 6, 'cost': 49}, {'i': 9, 'j': 3, 'k': 7, 'cost': 61}, {'i': 9, 'j': 3, 'k': 8, 'cost': 43}, {'i': 9, 'j': 3, 'k': 9, 'cost': 1}, {'i': 9, 'j': 4, 'k': 1, 'cost': 17}, {'i': 9, 'j': 4, 'k': 2, 'cost': 31}, {'i': 9, 'j': 4, 'k': 3, 'cost': 88}, {'i': 9, 'j': 4, 'k': 4, 'cost': 78}, {'i': 9, 'j': 4, 'k': 5, 'cost': 90}, {'i': 9, 'j': 4, 'k': 6, 'cost': 47}, {'i': 9, 'j': 4, 'k': 7, 'cost': 49}, {'i': 9, 'j': 4, 'k': 8, 'cost': 99}, {'i': 9, 'j': 4, 'k': 9, 'cost': 61}, {'i': 9, 'j': 5, 'k': 1, 'cost': 94}, {'i': 9, 'j': 5, 'k': 2, 'cost': 70}, {'i': 9, 'j': 5, 'k': 3, 'cost': 87}, {'i': 9, 'j': 5, 'k': 4, 'cost': 65}, {'i': 9, 'j': 5, 'k': 5, 'cost': 55}, {'i': 9, 'j': 5, 'k': 6, 'cost': 20}, {'i': 9, 'j': 5, 'k': 7, 'cost': 57}, {'i': 9, 'j': 5, 'k': 8, 'cost': 58}, {'i': 9, 'j': 5, 'k': 9, 'cost': 59}, {'i': 9, 'j': 6, 'k': 1, 'cost': 32}, {'i': 9, 'j': 6, 'k': 2, 'cost': 78}, {'i': 9, 'j': 6, 'k': 3, 'cost': 77}, {'i': 9, 'j': 6, 'k': 4, 'cost': 42}, {'i': 9, 'j': 6, 'k': 5, 'cost': 33}, {'i': 9, 'j': 6, 'k': 6, 'cost': 50}, {'i': 9, 'j': 6, 'k': 7, 'cost': 51}, {'i': 9, 'j': 6, 'k': 8, 'cost': 54}, {'i': 9, 'j': 6, 'k': 9, 'cost': 72}, {'i': 9, 'j': 7, 'k': 1, 'cost': 66}, {'i': 9, 'j': 7, 'k': 2, 'cost': 94}, {'i': 9, 'j': 7, 'k': 3, 'cost': 45}, {'i': 9, 'j': 7, 'k': 4, 'cost': 44}, {'i': 9, 'j': 7, 'k': 5, 'cost': 60}, {'i': 9, 'j': 7, 'k': 6, 'cost': 67}, {'i': 9, 'j': 7, 'k': 7, 'cost': 68}, {'i': 9, 'j': 7, 'k': 8, 'cost': 83}, {'i': 9, 'j': 7, 'k': 9, 'cost': 70}, {'i': 9, 'j': 8, 'k': 1, 'cost': 37}, {'i': 9, 'j': 8, 'k': 2, 'cost': 45}, {'i': 9, 'j': 8, 'k': 3, 'cost': 86}, {'i': 9, 'j': 8, 'k': 4, 'cost': 60}, {'i': 9, 'j': 8, 'k': 5, 'cost': 5}, {'i': 9, 'j': 8, 'k': 6, 'cost': 29}, {'i': 9, 'j': 8, 'k': 7, 'cost': 19}, {'i': 9, 'j': 8, 'k': 8, 'cost': 62}, {'i': 9, 'j': 8, 'k': 9, 'cost': 95}, {'i': 9, 'j': 9, 'k': 1, 'cost': 74}, {'i': 9, 'j': 9, 'k': 2, 'cost': 23}, {'i': 9, 'j': 9, 'k': 3, 'cost': 56}, {'i': 9, 'j': 9, 'k': 4, 'cost': 47}, {'i': 9, 'j': 9, 'k': 5, 'cost': 26}, {'i': 9, 'j': 9, 'k': 6, 'cost': 9}, {'i': 9, 'j': 9, 'k': 7, 'cost': 83}, {'i': 9, 'j': 9, 'k': 8, 'cost': 82}, {'i': 9, 'j': 9, 'k': 9, 'cost': 90}]}","[[1, 8, 4], [2, 1, 3], [3, 5, 6], [4, 4, 5], [5, 2, 1], [6, 7, 2], [7, 6, 8], [8, 9, 7], [9, 3, 9]]",2,csv,1
+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=12
+# index_identifiers=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
+
+# 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 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 74 | 21 | 32 | 81 | 78 | 77 | 6 | 25 | 52 | 70 | 76 | 9 |
+| 2 | 81 | 86 | 65 | 9 | 86 | 24 | 47 | 68 | 12 | 9 | 4 | 95 |
+| 3 | 15 | 44 | 55 | 42 | 66 | 11 | 98 | 78 | 72 | 44 | 80 | 97 |
+| 4 | 49 | 29 | 83 | 31 | 11 | 64 | 30 | 62 | 71 | 48 | 18 | 21 |
+| 5 | 65 | 72 | 53 | 70 | 59 | 70 | 12 | 23 | 29 | 51 | 8 | 42 |
+| 6 | 0 | 49 | 25 | 12 | 75 | 18 | 3 | 76 | 60 | 92 | 80 | 96 |
+| 7 | 47 | 8 | 18 | 15 | 91 | 37 | 15 | 4 | 52 | 14 | 39 | 46 |
+| 8 | 90 | 19 | 84 | 46 | 91 | 94 | 44 | 64 | 91 | 70 | 42 | 9 |
+| 9 | 18 | 62 | 82 | 88 | 13 | 75 | 36 | 84 | 22 | 16 | 10 | 5 |
+| 10 | 63 | 31 | 5 | 46 | 77 | 63 | 1 | 13 | 12 | 78 | 6 | 7 |
+| 11 | 50 | 15 | 33 | 15 | 80 | 89 | 79 | 74 | 45 | 41 | 43 | 55 |
+| 12 | 74 | 44 | 19 | 49 | 53 | 80 | 55 | 37 | 60 | 67 | 2 | 50 |
+
+## product_id=2
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 4 | 4 | 38 | 83 | 52 | 61 | 9 | 30 | 4 | 20 | 8 | 4 |
+| 2 | 62 | 83 | 5 | 10 | 8 | 89 | 45 | 5 | 72 | 55 | 30 | 65 |
+| 3 | 97 | 95 | 98 | 30 | 47 | 55 | 40 | 18 | 46 | 54 | 29 | 39 |
+| 4 | 45 | 82 | 51 | 51 | 12 | 8 | 37 | 31 | 0 | 90 | 52 | 25 |
+| 5 | 41 | 26 | 95 | 9 | 20 | 90 | 35 | 15 | 29 | 19 | 57 | 59 |
+| 6 | 49 | 6 | 53 | 60 | 52 | 13 | 49 | 62 | 20 | 33 | 30 | 44 |
+| 7 | 13 | 28 | 18 | 93 | 77 | 26 | 61 | 33 | 84 | 30 | 43 | 1 |
+| 8 | 70 | 9 | 90 | 56 | 7 | 56 | 45 | 3 | 8 | 31 | 76 | 95 |
+| 9 | 47 | 11 | 38 | 11 | 76 | 67 | 96 | 77 | 98 | 55 | 70 | 54 |
+| 10 | 76 | 56 | 9 | 64 | 97 | 38 | 97 | 22 | 87 | 42 | 18 | 51 |
+| 11 | 39 | 51 | 97 | 77 | 55 | 95 | 69 | 45 | 94 | 9 | 46 | 77 |
+| 12 | 95 | 17 | 72 | 9 | 94 | 16 | 57 | 38 | 99 | 9 | 29 | 82 |
+
+## product_id=3
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 16 | 7 | 21 | 86 | 45 | 38 | 42 | 79 | 75 | 68 | 86 |
+| 2 | 6 | 24 | 97 | 15 | 15 | 63 | 45 | 29 | 99 | 52 | 89 | 65 |
+| 3 | 88 | 76 | 27 | 20 | 58 | 28 | 34 | 92 | 84 | 82 | 32 | 13 |
+| 4 | 71 | 82 | 62 | 66 | 85 | 30 | 26 | 20 | 64 | 64 | 37 | 92 |
+| 5 | 37 | 62 | 83 | 17 | 99 | 77 | 99 | 97 | 97 | 36 | 1 | 57 |
+| 6 | 93 | 77 | 89 | 59 | 10 | 36 | 35 | 22 | 17 | 52 | 93 | 68 |
+| 7 | 8 | 29 | 19 | 93 | 2 | 41 | 42 | 54 | 15 | 41 | 19 | 72 |
+| 8 | 71 | 36 | 81 | 96 | 58 | 42 | 23 | 77 | 48 | 99 | 37 | 19 |
+| 9 | 64 | 5 | 10 | 78 | 55 | 39 | 73 | 72 | 40 | 20 | 19 | 34 |
+| 10 | 30 | 28 | 55 | 84 | 0 | 69 | 77 | 46 | 58 | 37 | 4 | 42 |
+| 11 | 51 | 6 | 8 | 14 | 40 | 45 | 37 | 24 | 38 | 10 | 21 | 27 |
+| 12 | 95 | 82 | 17 | 71 | 97 | 82 | 10 | 50 | 67 | 1 | 9 | 7 |
+
+## product_id=4
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 53 | 39 | 17 | 31 | 23 | 32 | 71 | 69 | 86 | 47 | 83 | 28 |
+| 2 | 95 | 39 | 30 | 52 | 98 | 74 | 74 | 98 | 85 | 22 | 39 | 64 |
+| 3 | 96 | 15 | 33 | 91 | 32 | 41 | 58 | 73 | 90 | 64 | 67 | 81 |
+| 4 | 47 | 3 | 15 | 8 | 8 | 30 | 95 | 71 | 41 | 82 | 46 | 51 |
+| 5 | 83 | 69 | 46 | 46 | 25 | 53 | 76 | 57 | 11 | 31 | 85 | 56 |
+| 6 | 33 | 45 | 9 | 60 | 28 | 48 | 32 | 15 | 7 | 54 | 6 | 65 |
+| 7 | 75 | 74 | 70 | 10 | 79 | 85 | 34 | 44 | 58 | 7 | 44 | 70 |
+| 8 | 47 | 29 | 55 | 40 | 46 | 81 | 99 | 65 | 96 | 94 | 88 | 7 |
+| 9 | 4 | 1 | 92 | 68 | 61 | 96 | 44 | 38 | 9 | 73 | 97 | 4 |
+| 10 | 4 | 29 | 80 | 45 | 96 | 12 | 41 | 85 | 3 | 78 | 13 | 36 |
+| 11 | 28 | 14 | 0 | 59 | 2 | 59 | 18 | 75 | 34 | 68 | 84 | 95 |
+| 12 | 13 | 99 | 77 | 0 | 63 | 60 | 48 | 95 | 69 | 61 | 89 | 32 |
+
+## product_id=5
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 57 | 39 | 24 | 91 | 43 | 55 | 42 | 62 | 62 | 93 | 64 | 80 |
+| 2 | 33 | 35 | 30 | 28 | 42 | 56 | 55 | 87 | 84 | 58 | 96 | 84 |
+| 3 | 85 | 49 | 26 | 5 | 50 | 23 | 86 | 46 | 9 | 1 | 8 | 77 |
+| 4 | 21 | 88 | 97 | 18 | 28 | 0 | 59 | 80 | 52 | 59 | 79 | 14 |
+| 5 | 82 | 9 | 91 | 37 | 55 | 49 | 60 | 78 | 35 | 4 | 39 | 0 |
+| 6 | 21 | 82 | 66 | 3 | 41 | 47 | 1 | 57 | 39 | 24 | 49 | 8 |
+| 7 | 66 | 79 | 60 | 18 | 93 | 66 | 32 | 67 | 33 | 6 | 17 | 83 |
+| 8 | 22 | 68 | 65 | 94 | 85 | 77 | 68 | 4 | 71 | 27 | 52 | 66 |
+| 9 | 65 | 41 | 75 | 32 | 12 | 82 | 8 | 55 | 43 | 49 | 59 | 64 |
+| 10 | 57 | 95 | 93 | 21 | 20 | 34 | 35 | 5 | 71 | 42 | 69 | 87 |
+| 11 | 65 | 23 | 83 | 81 | 7 | 84 | 23 | 60 | 64 | 67 | 92 | 25 |
+| 12 | 87 | 54 | 57 | 29 | 52 | 89 | 29 | 69 | 24 | 87 | 64 | 32 |
+
+## product_id=6
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 27 | 43 | 45 | 95 | 55 | 21 | 26 | 15 | 97 | 11 | 56 | 38 |
+| 2 | 48 | 27 | 61 | 85 | 3 | 69 | 47 | 66 | 48 | 14 | 71 | 78 |
+| 3 | 78 | 47 | 0 | 11 | 28 | 53 | 34 | 32 | 65 | 7 | 95 | 7 |
+| 4 | 52 | 17 | 56 | 63 | 69 | 18 | 97 | 70 | 78 | 26 | 33 | 22 |
+| 5 | 60 | 68 | 2 | 43 | 58 | 65 | 38 | 3 | 20 | 71 | 30 | 55 |
+| 6 | 52 | 93 | 4 | 48 | 59 | 10 | 35 | 48 | 64 | 87 | 59 | 4 |
+| 7 | 59 | 88 | 89 | 43 | 86 | 27 | 0 | 60 | 37 | 22 | 58 | 39 |
+| 8 | 66 | 90 | 77 | 12 | 5 | 9 | 8 | 5 | 87 | 85 | 69 | 81 |
+| 9 | 30 | 79 | 10 | 62 | 58 | 91 | 18 | 83 | 27 | 78 | 76 | 67 |
+| 10 | 91 | 10 | 51 | 64 | 72 | 93 | 62 | 24 | 14 | 79 | 62 | 15 |
+| 11 | 87 | 71 | 0 | 73 | 72 | 96 | 41 | 87 | 65 | 69 | 9 | 59 |
+| 12 | 96 | 59 | 53 | 80 | 9 | 35 | 17 | 49 | 33 | 69 | 99 | 91 |
+
+## product_id=7
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 75 | 18 | 50 | 14 | 75 | 44 | 24 | 55 | 96 | 31 | 5 | 40 |
+| 2 | 62 | 34 | 90 | 9 | 52 | 7 | 54 | 31 | 67 | 58 | 37 | 98 |
+| 3 | 32 | 59 | 15 | 43 | 49 | 42 | 55 | 55 | 3 | 82 | 13 | 78 |
+| 4 | 8 | 15 | 12 | 9 | 11 | 67 | 8 | 94 | 77 | 52 | 30 | 29 |
+| 5 | 62 | 14 | 79 | 48 | 84 | 83 | 5 | 90 | 88 | 49 | 28 | 63 |
+| 6 | 92 | 93 | 63 | 27 | 18 | 88 | 34 | 16 | 22 | 59 | 48 | 77 |
+| 7 | 7 | 0 | 11 | 67 | 21 | 49 | 20 | 46 | 6 | 19 | 99 | 79 |
+| 8 | 38 | 61 | 47 | 32 | 30 | 64 | 51 | 84 | 19 | 55 | 64 | 86 |
+| 9 | 31 | 70 | 1 | 14 | 53 | 19 | 58 | 61 | 4 | 24 | 11 | 1 |
+| 10 | 4 | 70 | 0 | 94 | 5 | 23 | 72 | 36 | 84 | 34 | 3 | 71 |
+| 11 | 55 | 14 | 92 | 85 | 95 | 8 | 34 | 10 | 98 | 73 | 67 | 3 |
+| 12 | 99 | 73 | 69 | 2 | 30 | 4 | 8 | 54 | 91 | 98 | 40 | 87 |
+
+## product_id=8
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 91 | 70 | 34 | 39 | 53 | 48 | 10 | 59 | 51 | 29 | 18 | 98 |
+| 2 | 64 | 52 | 2 | 32 | 35 | 82 | 25 | 96 | 96 | 28 | 99 | 98 |
+| 3 | 80 | 3 | 26 | 83 | 79 | 92 | 75 | 32 | 77 | 90 | 35 | 83 |
+| 4 | 66 | 61 | 50 | 67 | 43 | 48 | 45 | 25 | 38 | 67 | 74 | 10 |
+| 5 | 73 | 20 | 90 | 99 | 47 | 12 | 69 | 15 | 56 | 73 | 11 | 62 |
+| 6 | 12 | 44 | 99 | 40 | 57 | 60 | 17 | 36 | 81 | 31 | 75 | 44 |
+| 7 | 7 | 63 | 13 | 33 | 89 | 60 | 96 | 59 | 41 | 24 | 1 | 22 |
+| 8 | 7 | 64 | 30 | 44 | 98 | 38 | 85 | 74 | 5 | 95 | 67 | 45 |
+| 9 | 78 | 53 | 22 | 99 | 50 | 98 | 51 | 3 | 53 | 68 | 56 | 41 |
+| 10 | 7 | 82 | 53 | 58 | 74 | 97 | 77 | 56 | 22 | 88 | 51 | 27 |
+| 11 | 19 | 8 | 73 | 85 | 52 | 37 | 17 | 59 | 10 | 10 | 3 | 40 |
+| 12 | 20 | 84 | 38 | 61 | 29 | 8 | 5 | 20 | 80 | 89 | 23 | 5 |
+
+## product_id=9
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 71 | 99 | 8 | 62 | 76 | 74 | 76 | 16 | 34 | 98 | 34 | 68 |
+| 2 | 99 | 94 | 24 | 7 | 6 | 41 | 41 | 53 | 25 | 90 | 51 | 65 |
+| 3 | 58 | 66 | 44 | 59 | 72 | 42 | 35 | 94 | 30 | 26 | 8 | 85 |
+| 4 | 35 | 39 | 96 | 75 | 65 | 27 | 51 | 21 | 70 | 79 | 16 | 86 |
+| 5 | 80 | 31 | 50 | 63 | 7 | 63 | 80 | 6 | 88 | 76 | 20 | 58 |
+| 6 | 57 | 67 | 31 | 48 | 29 | 7 | 81 | 8 | 60 | 62 | 69 | 75 |
+| 7 | 46 | 34 | 2 | 68 | 4 | 27 | 16 | 10 | 10 | 17 | 73 | 52 |
+| 8 | 57 | 94 | 43 | 50 | 92 | 80 | 22 | 44 | 37 | 36 | 0 | 8 |
+| 9 | 49 | 41 | 91 | 64 | 92 | 45 | 58 | 32 | 1 | 39 | 57 | 2 |
+| 10 | 83 | 49 | 2 | 62 | 51 | 62 | 25 | 89 | 0 | 46 | 82 | 51 |
+| 11 | 87 | 27 | 75 | 33 | 75 | 47 | 61 | 66 | 62 | 13 | 68 | 42 |
+| 12 | 92 | 91 | 72 | 61 | 87 | 33 | 32 | 6 | 24 | 81 | 74 | 27 |
+
+## product_id=10
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 73 | 30 | 93 | 79 | 55 | 36 | 64 | 4 | 12 | 14 | 87 | 66 |
+| 2 | 83 | 58 | 57 | 50 | 64 | 83 | 7 | 82 | 89 | 30 | 25 | 68 |
+| 3 | 53 | 72 | 76 | 43 | 18 | 92 | 9 | 9 | 47 | 47 | 89 | 30 |
+| 4 | 15 | 40 | 43 | 61 | 82 | 28 | 80 | 56 | 29 | 63 | 87 | 59 |
+| 5 | 32 | 15 | 10 | 19 | 39 | 30 | 45 | 11 | 29 | 35 | 41 | 77 |
+| 6 | 58 | 45 | 78 | 2 | 6 | 31 | 17 | 2 | 47 | 51 | 87 | 24 |
+| 7 | 44 | 89 | 47 | 71 | 76 | 53 | 93 | 9 | 78 | 58 | 52 | 37 |
+| 8 | 41 | 44 | 62 | 83 | 3 | 14 | 24 | 31 | 75 | 26 | 93 | 60 |
+| 9 | 90 | 71 | 91 | 17 | 93 | 33 | 11 | 84 | 32 | 3 | 33 | 54 |
+| 10 | 8 | 28 | 50 | 70 | 7 | 45 | 1 | 29 | 25 | 75 | 81 | 5 |
+| 11 | 22 | 1 | 70 | 88 | 42 | 92 | 51 | 55 | 93 | 10 | 81 | 46 |
+| 12 | 5 | 87 | 85 | 28 | 96 | 10 | 38 | 77 | 48 | 51 | 56 | 40 |
+
+## product_id=11
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 5 | 4 | 79 | 90 | 94 | 51 | 46 | 34 | 97 | 80 | 70 | 32 |
+| 2 | 59 | 94 | 93 | 6 | 11 | 16 | 71 | 91 | 69 | 32 | 69 | 78 |
+| 3 | 1 | 76 | 80 | 85 | 78 | 96 | 8 | 17 | 81 | 21 | 8 | 95 |
+| 4 | 74 | 13 | 94 | 79 | 83 | 67 | 13 | 37 | 77 | 5 | 12 | 50 |
+| 5 | 30 | 8 | 56 | 73 | 99 | 54 | 59 | 13 | 98 | 55 | 20 | 3 |
+| 6 | 51 | 84 | 98 | 76 | 53 | 40 | 96 | 59 | 76 | 77 | 41 | 49 |
+| 7 | 69 | 95 | 52 | 7 | 8 | 46 | 59 | 39 | 31 | 63 | 97 | 74 |
+| 8 | 71 | 88 | 63 | 25 | 87 | 2 | 75 | 24 | 33 | 38 | 56 | 91 |
+| 9 | 59 | 96 | 55 | 56 | 4 | 32 | 45 | 47 | 0 | 85 | 35 | 75 |
+| 10 | 88 | 75 | 77 | 28 | 48 | 69 | 38 | 74 | 44 | 16 | 48 | 76 |
+| 11 | 76 | 51 | 86 | 52 | 53 | 71 | 68 | 67 | 7 | 91 | 28 | 75 |
+| 12 | 66 | 40 | 0 | 86 | 92 | 94 | 25 | 37 | 52 | 86 | 54 | 55 |
+
+## product_id=12
+| machine_id\shift_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 93 | 45 | 13 | 26 | 14 | 63 | 89 | 61 | 3 | 97 | 81 | 43 |
+| 2 | 36 | 83 | 87 | 2 | 40 | 40 | 13 | 31 | 16 | 34 | 13 | 83 |
+| 3 | 59 | 80 | 54 | 3 | 30 | 85 | 50 | 32 | 6 | 41 | 84 | 90 |
+| 4 | 82 | 18 | 60 | 22 | 84 | 48 | 47 | 87 | 21 | 76 | 61 | 76 |
+| 5 | 57 | 98 | 6 | 36 | 26 | 23 | 46 | 59 | 70 | 26 | 92 | 43 |
+| 6 | 84 | 31 | 31 | 23 | 11 | 22 | 33 | 29 | 3 | 2 | 39 | 21 |
+| 7 | 38 | 28 | 69 | 61 | 60 | 5 | 77 | 80 | 60 | 49 | 11 | 0 |
+| 8 | 62 | 39 | 70 | 31 | 95 | 41 | 58 | 4 | 45 | 49 | 38 | 27 |
+| 9 | 89 | 17 | 3 | 98 | 61 | 89 | 39 | 43 | 63 | 23 | 88 | 14 |
+| 10 | 2 | 21 | 99 | 15 | 11 | 0 | 72 | 62 | 45 | 2 | 7 | 76 |
+| 11 | 51 | 78 | 39 | 5 | 91 | 94 | 21 | 69 | 94 | 27 | 26 | 91 |
+| 12 | 9 | 31 | 56 | 47 | 21 | 34 | 24 | 23 | 73 | 74 | 13 | 84 |
+
+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': [[[74, 21, 32, 81, 78, 77, 6, 25, 52, 70, 76, 9], [81, 86, 65, 9, 86, 24, 47, 68, 12, 9, 4, 95], [15, 44, 55, 42, 66, 11, 98, 78, 72, 44, 80, 97], [49, 29, 83, 31, 11, 64, 30, 62, 71, 48, 18, 21], [65, 72, 53, 70, 59, 70, 12, 23, 29, 51, 8, 42], [0, 49, 25, 12, 75, 18, 3, 76, 60, 92, 80, 96], [47, 8, 18, 15, 91, 37, 15, 4, 52, 14, 39, 46], [90, 19, 84, 46, 91, 94, 44, 64, 91, 70, 42, 9], [18, 62, 82, 88, 13, 75, 36, 84, 22, 16, 10, 5], [63, 31, 5, 46, 77, 63, 1, 13, 12, 78, 6, 7], [50, 15, 33, 15, 80, 89, 79, 74, 45, 41, 43, 55], [74, 44, 19, 49, 53, 80, 55, 37, 60, 67, 2, 50]], [[4, 4, 38, 83, 52, 61, 9, 30, 4, 20, 8, 4], [62, 83, 5, 10, 8, 89, 45, 5, 72, 55, 30, 65], [97, 95, 98, 30, 47, 55, 40, 18, 46, 54, 29, 39], [45, 82, 51, 51, 12, 8, 37, 31, 0, 90, 52, 25], [41, 26, 95, 9, 20, 90, 35, 15, 29, 19, 57, 59], [49, 6, 53, 60, 52, 13, 49, 62, 20, 33, 30, 44], [13, 28, 18, 93, 77, 26, 61, 33, 84, 30, 43, 1], [70, 9, 90, 56, 7, 56, 45, 3, 8, 31, 76, 95], [47, 11, 38, 11, 76, 67, 96, 77, 98, 55, 70, 54], [76, 56, 9, 64, 97, 38, 97, 22, 87, 42, 18, 51], [39, 51, 97, 77, 55, 95, 69, 45, 94, 9, 46, 77], [95, 17, 72, 9, 94, 16, 57, 38, 99, 9, 29, 82]], [[34, 16, 7, 21, 86, 45, 38, 42, 79, 75, 68, 86], [6, 24, 97, 15, 15, 63, 45, 29, 99, 52, 89, 65], [88, 76, 27, 20, 58, 28, 34, 92, 84, 82, 32, 13], [71, 82, 62, 66, 85, 30, 26, 20, 64, 64, 37, 92], [37, 62, 83, 17, 99, 77, 99, 97, 97, 36, 1, 57], [93, 77, 89, 59, 10, 36, 35, 22, 17, 52, 93, 68], [8, 29, 19, 93, 2, 41, 42, 54, 15, 41, 19, 72], [71, 36, 81, 96, 58, 42, 23, 77, 48, 99, 37, 19], [64, 5, 10, 78, 55, 39, 73, 72, 40, 20, 19, 34], [30, 28, 55, 84, 0, 69, 77, 46, 58, 37, 4, 42], [51, 6, 8, 14, 40, 45, 37, 24, 38, 10, 21, 27], [95, 82, 17, 71, 97, 82, 10, 50, 67, 1, 9, 7]], [[53, 39, 17, 31, 23, 32, 71, 69, 86, 47, 83, 28], [95, 39, 30, 52, 98, 74, 74, 98, 85, 22, 39, 64], [96, 15, 33, 91, 32, 41, 58, 73, 90, 64, 67, 81], [47, 3, 15, 8, 8, 30, 95, 71, 41, 82, 46, 51], [83, 69, 46, 46, 25, 53, 76, 57, 11, 31, 85, 56], [33, 45, 9, 60, 28, 48, 32, 15, 7, 54, 6, 65], [75, 74, 70, 10, 79, 85, 34, 44, 58, 7, 44, 70], [47, 29, 55, 40, 46, 81, 99, 65, 96, 94, 88, 7], [4, 1, 92, 68, 61, 96, 44, 38, 9, 73, 97, 4], [4, 29, 80, 45, 96, 12, 41, 85, 3, 78, 13, 36], [28, 14, 0, 59, 2, 59, 18, 75, 34, 68, 84, 95], [13, 99, 77, 0, 63, 60, 48, 95, 69, 61, 89, 32]], [[57, 39, 24, 91, 43, 55, 42, 62, 62, 93, 64, 80], [33, 35, 30, 28, 42, 56, 55, 87, 84, 58, 96, 84], [85, 49, 26, 5, 50, 23, 86, 46, 9, 1, 8, 77], [21, 88, 97, 18, 28, 0, 59, 80, 52, 59, 79, 14], [82, 9, 91, 37, 55, 49, 60, 78, 35, 4, 39, 0], [21, 82, 66, 3, 41, 47, 1, 57, 39, 24, 49, 8], [66, 79, 60, 18, 93, 66, 32, 67, 33, 6, 17, 83], [22, 68, 65, 94, 85, 77, 68, 4, 71, 27, 52, 66], [65, 41, 75, 32, 12, 82, 8, 55, 43, 49, 59, 64], [57, 95, 93, 21, 20, 34, 35, 5, 71, 42, 69, 87], [65, 23, 83, 81, 7, 84, 23, 60, 64, 67, 92, 25], [87, 54, 57, 29, 52, 89, 29, 69, 24, 87, 64, 32]], [[27, 43, 45, 95, 55, 21, 26, 15, 97, 11, 56, 38], [48, 27, 61, 85, 3, 69, 47, 66, 48, 14, 71, 78], [78, 47, 0, 11, 28, 53, 34, 32, 65, 7, 95, 7], [52, 17, 56, 63, 69, 18, 97, 70, 78, 26, 33, 22], [60, 68, 2, 43, 58, 65, 38, 3, 20, 71, 30, 55], [52, 93, 4, 48, 59, 10, 35, 48, 64, 87, 59, 4], [59, 88, 89, 43, 86, 27, 0, 60, 37, 22, 58, 39], [66, 90, 77, 12, 5, 9, 8, 5, 87, 85, 69, 81], [30, 79, 10, 62, 58, 91, 18, 83, 27, 78, 76, 67], [91, 10, 51, 64, 72, 93, 62, 24, 14, 79, 62, 15], [87, 71, 0, 73, 72, 96, 41, 87, 65, 69, 9, 59], [96, 59, 53, 80, 9, 35, 17, 49, 33, 69, 99, 91]], [[75, 18, 50, 14, 75, 44, 24, 55, 96, 31, 5, 40], [62, 34, 90, 9, 52, 7, 54, 31, 67, 58, 37, 98], [32, 59, 15, 43, 49, 42, 55, 55, 3, 82, 13, 78], [8, 15, 12, 9, 11, 67, 8, 94, 77, 52, 30, 29], [62, 14, 79, 48, 84, 83, 5, 90, 88, 49, 28, 63], [92, 93, 63, 27, 18, 88, 34, 16, 22, 59, 48, 77], [7, 0, 11, 67, 21, 49, 20, 46, 6, 19, 99, 79], [38, 61, 47, 32, 30, 64, 51, 84, 19, 55, 64, 86], [31, 70, 1, 14, 53, 19, 58, 61, 4, 24, 11, 1], [4, 70, 0, 94, 5, 23, 72, 36, 84, 34, 3, 71], [55, 14, 92, 85, 95, 8, 34, 10, 98, 73, 67, 3], [99, 73, 69, 2, 30, 4, 8, 54, 91, 98, 40, 87]], [[91, 70, 34, 39, 53, 48, 10, 59, 51, 29, 18, 98], [64, 52, 2, 32, 35, 82, 25, 96, 96, 28, 99, 98], [80, 3, 26, 83, 79, 92, 75, 32, 77, 90, 35, 83], [66, 61, 50, 67, 43, 48, 45, 25, 38, 67, 74, 10], [73, 20, 90, 99, 47, 12, 69, 15, 56, 73, 11, 62], [12, 44, 99, 40, 57, 60, 17, 36, 81, 31, 75, 44], [7, 63, 13, 33, 89, 60, 96, 59, 41, 24, 1, 22], [7, 64, 30, 44, 98, 38, 85, 74, 5, 95, 67, 45], [78, 53, 22, 99, 50, 98, 51, 3, 53, 68, 56, 41], [7, 82, 53, 58, 74, 97, 77, 56, 22, 88, 51, 27], [19, 8, 73, 85, 52, 37, 17, 59, 10, 10, 3, 40], [20, 84, 38, 61, 29, 8, 5, 20, 80, 89, 23, 5]], [[71, 99, 8, 62, 76, 74, 76, 16, 34, 98, 34, 68], [99, 94, 24, 7, 6, 41, 41, 53, 25, 90, 51, 65], [58, 66, 44, 59, 72, 42, 35, 94, 30, 26, 8, 85], [35, 39, 96, 75, 65, 27, 51, 21, 70, 79, 16, 86], [80, 31, 50, 63, 7, 63, 80, 6, 88, 76, 20, 58], [57, 67, 31, 48, 29, 7, 81, 8, 60, 62, 69, 75], [46, 34, 2, 68, 4, 27, 16, 10, 10, 17, 73, 52], [57, 94, 43, 50, 92, 80, 22, 44, 37, 36, 0, 8], [49, 41, 91, 64, 92, 45, 58, 32, 1, 39, 57, 2], [83, 49, 2, 62, 51, 62, 25, 89, 0, 46, 82, 51], [87, 27, 75, 33, 75, 47, 61, 66, 62, 13, 68, 42], [92, 91, 72, 61, 87, 33, 32, 6, 24, 81, 74, 27]], [[73, 30, 93, 79, 55, 36, 64, 4, 12, 14, 87, 66], [83, 58, 57, 50, 64, 83, 7, 82, 89, 30, 25, 68], [53, 72, 76, 43, 18, 92, 9, 9, 47, 47, 89, 30], [15, 40, 43, 61, 82, 28, 80, 56, 29, 63, 87, 59], [32, 15, 10, 19, 39, 30, 45, 11, 29, 35, 41, 77], [58, 45, 78, 2, 6, 31, 17, 2, 47, 51, 87, 24], [44, 89, 47, 71, 76, 53, 93, 9, 78, 58, 52, 37], [41, 44, 62, 83, 3, 14, 24, 31, 75, 26, 93, 60], [90, 71, 91, 17, 93, 33, 11, 84, 32, 3, 33, 54], [8, 28, 50, 70, 7, 45, 1, 29, 25, 75, 81, 5], [22, 1, 70, 88, 42, 92, 51, 55, 93, 10, 81, 46], [5, 87, 85, 28, 96, 10, 38, 77, 48, 51, 56, 40]], [[5, 4, 79, 90, 94, 51, 46, 34, 97, 80, 70, 32], [59, 94, 93, 6, 11, 16, 71, 91, 69, 32, 69, 78], [1, 76, 80, 85, 78, 96, 8, 17, 81, 21, 8, 95], [74, 13, 94, 79, 83, 67, 13, 37, 77, 5, 12, 50], [30, 8, 56, 73, 99, 54, 59, 13, 98, 55, 20, 3], [51, 84, 98, 76, 53, 40, 96, 59, 76, 77, 41, 49], [69, 95, 52, 7, 8, 46, 59, 39, 31, 63, 97, 74], [71, 88, 63, 25, 87, 2, 75, 24, 33, 38, 56, 91], [59, 96, 55, 56, 4, 32, 45, 47, 0, 85, 35, 75], [88, 75, 77, 28, 48, 69, 38, 74, 44, 16, 48, 76], [76, 51, 86, 52, 53, 71, 68, 67, 7, 91, 28, 75], [66, 40, 0, 86, 92, 94, 25, 37, 52, 86, 54, 55]], [[93, 45, 13, 26, 14, 63, 89, 61, 3, 97, 81, 43], [36, 83, 87, 2, 40, 40, 13, 31, 16, 34, 13, 83], [59, 80, 54, 3, 30, 85, 50, 32, 6, 41, 84, 90], [82, 18, 60, 22, 84, 48, 47, 87, 21, 76, 61, 76], [57, 98, 6, 36, 26, 23, 46, 59, 70, 26, 92, 43], [84, 31, 31, 23, 11, 22, 33, 29, 3, 2, 39, 21], [38, 28, 69, 61, 60, 5, 77, 80, 60, 49, 11, 0], [62, 39, 70, 31, 95, 41, 58, 4, 45, 49, 38, 27], [89, 17, 3, 98, 61, 89, 39, 43, 63, 23, 88, 14], [2, 21, 99, 15, 11, 0, 72, 62, 45, 2, 7, 76], [51, 78, 39, 5, 91, 94, 21, 69, 94, 27, 26, 91], [9, 31, 56, 47, 21, 34, 24, 23, 73, 74, 13, 84]]], 'objective': 16.0}","[[0, 5, 0], [1, 0, 11], [2, 11, 9], [3, 10, 4], [4, 3, 5], [5, 4, 7], [6, 6, 1], [7, 1, 2], [8, 7, 10], [9, 9, 6], [10, 8, 8], [11, 2, 3]]",16.0,"{'problem_type': 'AP3', 'n': 12, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 74}, {'i': 1, 'j': 1, 'k': 2, 'cost': 21}, {'i': 1, 'j': 1, 'k': 3, 'cost': 32}, {'i': 1, 'j': 1, 'k': 4, 'cost': 81}, {'i': 1, 'j': 1, 'k': 5, 'cost': 78}, {'i': 1, 'j': 1, 'k': 6, 'cost': 77}, {'i': 1, 'j': 1, 'k': 7, 'cost': 6}, {'i': 1, 'j': 1, 'k': 8, 'cost': 25}, {'i': 1, 'j': 1, 'k': 9, 'cost': 52}, {'i': 1, 'j': 1, 'k': 10, 'cost': 70}, {'i': 1, 'j': 1, 'k': 11, 'cost': 76}, {'i': 1, 'j': 1, 'k': 12, 'cost': 9}, {'i': 1, 'j': 2, 'k': 1, 'cost': 81}, {'i': 1, 'j': 2, 'k': 2, 'cost': 86}, {'i': 1, 'j': 2, 'k': 3, 'cost': 65}, {'i': 1, 'j': 2, 'k': 4, 'cost': 9}, {'i': 1, 'j': 2, 'k': 5, 'cost': 86}, {'i': 1, 'j': 2, 'k': 6, 'cost': 24}, {'i': 1, 'j': 2, 'k': 7, 'cost': 47}, {'i': 1, 'j': 2, 'k': 8, 'cost': 68}, {'i': 1, 'j': 2, 'k': 9, 'cost': 12}, {'i': 1, 'j': 2, 'k': 10, 'cost': 9}, {'i': 1, 'j': 2, 'k': 11, 'cost': 4}, {'i': 1, 'j': 2, 'k': 12, 'cost': 95}, {'i': 1, 'j': 3, 'k': 1, 'cost': 15}, {'i': 1, 'j': 3, 'k': 2, 'cost': 44}, {'i': 1, 'j': 3, 'k': 3, 'cost': 55}, {'i': 1, 'j': 3, 'k': 4, 'cost': 42}, {'i': 1, 'j': 3, 'k': 5, 'cost': 66}, {'i': 1, 'j': 3, 'k': 6, 'cost': 11}, {'i': 1, 'j': 3, 'k': 7, 'cost': 98}, {'i': 1, 'j': 3, 'k': 8, 'cost': 78}, {'i': 1, 'j': 3, 'k': 9, 'cost': 72}, {'i': 1, 'j': 3, 'k': 10, 'cost': 44}, {'i': 1, 'j': 3, 'k': 11, 'cost': 80}, {'i': 1, 'j': 3, 'k': 12, 'cost': 97}, {'i': 1, 'j': 4, 'k': 1, 'cost': 49}, {'i': 1, 'j': 4, 'k': 2, 'cost': 29}, {'i': 1, 'j': 4, 'k': 3, 'cost': 83}, {'i': 1, 'j': 4, 'k': 4, 'cost': 31}, {'i': 1, 'j': 4, 'k': 5, 'cost': 11}, {'i': 1, 'j': 4, 'k': 6, 'cost': 64}, {'i': 1, 'j': 4, 'k': 7, 'cost': 30}, {'i': 1, 'j': 4, 'k': 8, 'cost': 62}, {'i': 1, 'j': 4, 'k': 9, 'cost': 71}, {'i': 1, 'j': 4, 'k': 10, 'cost': 48}, {'i': 1, 'j': 4, 'k': 11, 'cost': 18}, {'i': 1, 'j': 4, 'k': 12, 'cost': 21}, {'i': 1, 'j': 5, 'k': 1, 'cost': 65}, {'i': 1, 'j': 5, 'k': 2, 'cost': 72}, {'i': 1, 'j': 5, 'k': 3, 'cost': 53}, {'i': 1, 'j': 5, 'k': 4, 'cost': 70}, {'i': 1, 'j': 5, 'k': 5, 'cost': 59}, {'i': 1, 'j': 5, 'k': 6, 'cost': 70}, {'i': 1, 'j': 5, 'k': 7, 'cost': 12}, {'i': 1, 'j': 5, 'k': 8, 'cost': 23}, {'i': 1, 'j': 5, 'k': 9, 'cost': 29}, {'i': 1, 'j': 5, 'k': 10, 'cost': 51}, {'i': 1, 'j': 5, 'k': 11, 'cost': 8}, {'i': 1, 'j': 5, 'k': 12, 'cost': 42}, {'i': 1, 'j': 6, 'k': 1, 'cost': 0}, {'i': 1, 'j': 6, 'k': 2, 'cost': 49}, {'i': 1, 'j': 6, 'k': 3, 'cost': 25}, {'i': 1, 'j': 6, 'k': 4, 'cost': 12}, {'i': 1, 'j': 6, 'k': 5, 'cost': 75}, {'i': 1, 'j': 6, 'k': 6, 'cost': 18}, {'i': 1, 'j': 6, 'k': 7, 'cost': 3}, {'i': 1, 'j': 6, 'k': 8, 'cost': 76}, {'i': 1, 'j': 6, 'k': 9, 'cost': 60}, {'i': 1, 'j': 6, 'k': 10, 'cost': 92}, {'i': 1, 'j': 6, 'k': 11, 'cost': 80}, {'i': 1, 'j': 6, 'k': 12, 'cost': 96}, {'i': 1, 'j': 7, 'k': 1, 'cost': 47}, {'i': 1, 'j': 7, 'k': 2, 'cost': 8}, {'i': 1, 'j': 7, 'k': 3, 'cost': 18}, {'i': 1, 'j': 7, 'k': 4, 'cost': 15}, {'i': 1, 'j': 7, 'k': 5, 'cost': 91}, {'i': 1, 'j': 7, 'k': 6, 'cost': 37}, {'i': 1, 'j': 7, 'k': 7, 'cost': 15}, {'i': 1, 'j': 7, 'k': 8, 'cost': 4}, {'i': 1, 'j': 7, 'k': 9, 'cost': 52}, {'i': 1, 'j': 7, 'k': 10, 'cost': 14}, {'i': 1, 'j': 7, 'k': 11, 'cost': 39}, {'i': 1, 'j': 7, 'k': 12, 'cost': 46}, {'i': 1, 'j': 8, 'k': 1, 'cost': 90}, {'i': 1, 'j': 8, 'k': 2, 'cost': 19}, {'i': 1, 'j': 8, 'k': 3, 'cost': 84}, {'i': 1, 'j': 8, 'k': 4, 'cost': 46}, {'i': 1, 'j': 8, 'k': 5, 'cost': 91}, {'i': 1, 'j': 8, 'k': 6, 'cost': 94}, {'i': 1, 'j': 8, 'k': 7, 'cost': 44}, {'i': 1, 'j': 8, 'k': 8, 'cost': 64}, {'i': 1, 'j': 8, 'k': 9, 'cost': 91}, {'i': 1, 'j': 8, 'k': 10, 'cost': 70}, {'i': 1, 'j': 8, 'k': 11, 'cost': 42}, {'i': 1, 'j': 8, 'k': 12, 'cost': 9}, {'i': 1, 'j': 9, 'k': 1, 'cost': 18}, {'i': 1, 'j': 9, 'k': 2, 'cost': 62}, {'i': 1, 'j': 9, 'k': 3, 'cost': 82}, {'i': 1, 'j': 9, 'k': 4, 'cost': 88}, {'i': 1, 'j': 9, 'k': 5, 'cost': 13}, {'i': 1, 'j': 9, 'k': 6, 'cost': 75}, {'i': 1, 'j': 9, 'k': 7, 'cost': 36}, {'i': 1, 'j': 9, 'k': 8, 'cost': 84}, {'i': 1, 'j': 9, 'k': 9, 'cost': 22}, {'i': 1, 'j': 9, 'k': 10, 'cost': 16}, {'i': 1, 'j': 9, 'k': 11, 'cost': 10}, {'i': 1, 'j': 9, 'k': 12, 'cost': 5}, {'i': 1, 'j': 10, 'k': 1, 'cost': 63}, {'i': 1, 'j': 10, 'k': 2, 'cost': 31}, {'i': 1, 'j': 10, 'k': 3, 'cost': 5}, {'i': 1, 'j': 10, 'k': 4, 'cost': 46}, {'i': 1, 'j': 10, 'k': 5, 'cost': 77}, {'i': 1, 'j': 10, 'k': 6, 'cost': 63}, {'i': 1, 'j': 10, 'k': 7, 'cost': 1}, {'i': 1, 'j': 10, 'k': 8, 'cost': 13}, {'i': 1, 'j': 10, 'k': 9, 'cost': 12}, {'i': 1, 'j': 10, 'k': 10, 'cost': 78}, {'i': 1, 'j': 10, 'k': 11, 'cost': 6}, {'i': 1, 'j': 10, 'k': 12, 'cost': 7}, {'i': 1, 'j': 11, 'k': 1, 'cost': 50}, {'i': 1, 'j': 11, 'k': 2, 'cost': 15}, {'i': 1, 'j': 11, 'k': 3, 'cost': 33}, {'i': 1, 'j': 11, 'k': 4, 'cost': 15}, {'i': 1, 'j': 11, 'k': 5, 'cost': 80}, {'i': 1, 'j': 11, 'k': 6, 'cost': 89}, {'i': 1, 'j': 11, 'k': 7, 'cost': 79}, {'i': 1, 'j': 11, 'k': 8, 'cost': 74}, {'i': 1, 'j': 11, 'k': 9, 'cost': 45}, {'i': 1, 'j': 11, 'k': 10, 'cost': 41}, {'i': 1, 'j': 11, 'k': 11, 'cost': 43}, {'i': 1, 'j': 11, 'k': 12, 'cost': 55}, {'i': 1, 'j': 12, 'k': 1, 'cost': 74}, {'i': 1, 'j': 12, 'k': 2, 'cost': 44}, {'i': 1, 'j': 12, 'k': 3, 'cost': 19}, {'i': 1, 'j': 12, 'k': 4, 'cost': 49}, {'i': 1, 'j': 12, 'k': 5, 'cost': 53}, {'i': 1, 'j': 12, 'k': 6, 'cost': 80}, {'i': 1, 'j': 12, 'k': 7, 'cost': 55}, {'i': 1, 'j': 12, 'k': 8, 'cost': 37}, {'i': 1, 'j': 12, 'k': 9, 'cost': 60}, {'i': 1, 'j': 12, 'k': 10, 'cost': 67}, {'i': 1, 'j': 12, 'k': 11, 'cost': 2}, {'i': 1, 'j': 12, 'k': 12, 'cost': 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99}, {'i': 11, 'j': 5, 'k': 6, 'cost': 54}, {'i': 11, 'j': 5, 'k': 7, 'cost': 59}, {'i': 11, 'j': 5, 'k': 8, 'cost': 13}, {'i': 11, 'j': 5, 'k': 9, 'cost': 98}, {'i': 11, 'j': 5, 'k': 10, 'cost': 55}, {'i': 11, 'j': 5, 'k': 11, 'cost': 20}, {'i': 11, 'j': 5, 'k': 12, 'cost': 3}, {'i': 11, 'j': 6, 'k': 1, 'cost': 51}, {'i': 11, 'j': 6, 'k': 2, 'cost': 84}, {'i': 11, 'j': 6, 'k': 3, 'cost': 98}, {'i': 11, 'j': 6, 'k': 4, 'cost': 76}, {'i': 11, 'j': 6, 'k': 5, 'cost': 53}, {'i': 11, 'j': 6, 'k': 6, 'cost': 40}, {'i': 11, 'j': 6, 'k': 7, 'cost': 96}, {'i': 11, 'j': 6, 'k': 8, 'cost': 59}, {'i': 11, 'j': 6, 'k': 9, 'cost': 76}, {'i': 11, 'j': 6, 'k': 10, 'cost': 77}, {'i': 11, 'j': 6, 'k': 11, 'cost': 41}, {'i': 11, 'j': 6, 'k': 12, 'cost': 49}, {'i': 11, 'j': 7, 'k': 1, 'cost': 69}, {'i': 11, 'j': 7, 'k': 2, 'cost': 95}, {'i': 11, 'j': 7, 'k': 3, 'cost': 52}, {'i': 11, 'j': 7, 'k': 4, 'cost': 7}, {'i': 11, 'j': 7, 'k': 5, 'cost': 8}, {'i': 11, 'j': 7, 'k': 6, 'cost': 46}, {'i': 11, 'j': 7, 'k': 7, 'cost': 59}, {'i': 11, 'j': 7, 'k': 8, 'cost': 39}, {'i': 11, 'j': 7, 'k': 9, 'cost': 31}, {'i': 11, 'j': 7, 'k': 10, 'cost': 63}, {'i': 11, 'j': 7, 'k': 11, 'cost': 97}, {'i': 11, 'j': 7, 'k': 12, 'cost': 74}, {'i': 11, 'j': 8, 'k': 1, 'cost': 71}, {'i': 11, 'j': 8, 'k': 2, 'cost': 88}, {'i': 11, 'j': 8, 'k': 3, 'cost': 63}, {'i': 11, 'j': 8, 'k': 4, 'cost': 25}, {'i': 11, 'j': 8, 'k': 5, 'cost': 87}, {'i': 11, 'j': 8, 'k': 6, 'cost': 2}, {'i': 11, 'j': 8, 'k': 7, 'cost': 75}, {'i': 11, 'j': 8, 'k': 8, 'cost': 24}, {'i': 11, 'j': 8, 'k': 9, 'cost': 33}, {'i': 11, 'j': 8, 'k': 10, 'cost': 38}, {'i': 11, 'j': 8, 'k': 11, 'cost': 56}, {'i': 11, 'j': 8, 'k': 12, 'cost': 91}, {'i': 11, 'j': 9, 'k': 1, 'cost': 59}, {'i': 11, 'j': 9, 'k': 2, 'cost': 96}, {'i': 11, 'j': 9, 'k': 3, 'cost': 55}, {'i': 11, 'j': 9, 'k': 4, 'cost': 56}, {'i': 11, 'j': 9, 'k': 5, 'cost': 4}, {'i': 11, 'j': 9, 'k': 6, 'cost': 32}, {'i': 11, 'j': 9, 'k': 7, 'cost': 45}, {'i': 11, 'j': 9, 'k': 8, 'cost': 47}, {'i': 11, 'j': 9, 'k': 9, 'cost': 0}, {'i': 11, 'j': 9, 'k': 10, 'cost': 85}, {'i': 11, 'j': 9, 'k': 11, 'cost': 35}, {'i': 11, 'j': 9, 'k': 12, 'cost': 75}, {'i': 11, 'j': 10, 'k': 1, 'cost': 88}, {'i': 11, 'j': 10, 'k': 2, 'cost': 75}, {'i': 11, 'j': 10, 'k': 3, 'cost': 77}, {'i': 11, 'j': 10, 'k': 4, 'cost': 28}, {'i': 11, 'j': 10, 'k': 5, 'cost': 48}, {'i': 11, 'j': 10, 'k': 6, 'cost': 69}, {'i': 11, 'j': 10, 'k': 7, 'cost': 38}, {'i': 11, 'j': 10, 'k': 8, 'cost': 74}, {'i': 11, 'j': 10, 'k': 9, 'cost': 44}, {'i': 11, 'j': 10, 'k': 10, 'cost': 16}, {'i': 11, 'j': 10, 'k': 11, 'cost': 48}, {'i': 11, 'j': 10, 'k': 12, 'cost': 76}, {'i': 11, 'j': 11, 'k': 1, 'cost': 76}, {'i': 11, 'j': 11, 'k': 2, 'cost': 51}, {'i': 11, 'j': 11, 'k': 3, 'cost': 86}, {'i': 11, 'j': 11, 'k': 4, 'cost': 52}, {'i': 11, 'j': 11, 'k': 5, 'cost': 53}, {'i': 11, 'j': 11, 'k': 6, 'cost': 71}, {'i': 11, 'j': 11, 'k': 7, 'cost': 68}, {'i': 11, 'j': 11, 'k': 8, 'cost': 67}, {'i': 11, 'j': 11, 'k': 9, 'cost': 7}, {'i': 11, 'j': 11, 'k': 10, 'cost': 91}, {'i': 11, 'j': 11, 'k': 11, 'cost': 28}, {'i': 11, 'j': 11, 'k': 12, 'cost': 75}, {'i': 11, 'j': 12, 'k': 1, 'cost': 66}, {'i': 11, 'j': 12, 'k': 2, 'cost': 40}, {'i': 11, 'j': 12, 'k': 3, 'cost': 0}, {'i': 11, 'j': 12, 'k': 4, 'cost': 86}, {'i': 11, 'j': 12, 'k': 5, 'cost': 92}, {'i': 11, 'j': 12, 'k': 6, 'cost': 94}, {'i': 11, 'j': 12, 'k': 7, 'cost': 25}, {'i': 11, 'j': 12, 'k': 8, 'cost': 37}, {'i': 11, 'j': 12, 'k': 9, 'cost': 52}, {'i': 11, 'j': 12, 'k': 10, 'cost': 86}, {'i': 11, 'j': 12, 'k': 11, 'cost': 54}, {'i': 11, 'j': 12, 'k': 12, 'cost': 55}, {'i': 12, 'j': 1, 'k': 1, 'cost': 93}, {'i': 12, 'j': 1, 'k': 2, 'cost': 45}, {'i': 12, 'j': 1, 'k': 3, 'cost': 13}, {'i': 12, 'j': 1, 'k': 4, 'cost': 26}, {'i': 12, 'j': 1, 'k': 5, 'cost': 14}, {'i': 12, 'j': 1, 'k': 6, 'cost': 63}, {'i': 12, 'j': 1, 'k': 7, 'cost': 89}, {'i': 12, 'j': 1, 'k': 8, 'cost': 61}, {'i': 12, 'j': 1, 'k': 9, 'cost': 3}, {'i': 12, 'j': 1, 'k': 10, 'cost': 97}, {'i': 12, 'j': 1, 'k': 11, 'cost': 81}, {'i': 12, 'j': 1, 'k': 12, 'cost': 43}, {'i': 12, 'j': 2, 'k': 1, 'cost': 36}, {'i': 12, 'j': 2, 'k': 2, 'cost': 83}, {'i': 12, 'j': 2, 'k': 3, 'cost': 87}, {'i': 12, 'j': 2, 'k': 4, 'cost': 2}, {'i': 12, 'j': 2, 'k': 5, 'cost': 40}, {'i': 12, 'j': 2, 'k': 6, 'cost': 40}, {'i': 12, 'j': 2, 'k': 7, 'cost': 13}, {'i': 12, 'j': 2, 'k': 8, 'cost': 31}, {'i': 12, 'j': 2, 'k': 9, 'cost': 16}, {'i': 12, 'j': 2, 'k': 10, 'cost': 34}, {'i': 12, 'j': 2, 'k': 11, 'cost': 13}, {'i': 12, 'j': 2, 'k': 12, 'cost': 83}, {'i': 12, 'j': 3, 'k': 1, 'cost': 59}, {'i': 12, 'j': 3, 'k': 2, 'cost': 80}, {'i': 12, 'j': 3, 'k': 3, 'cost': 54}, {'i': 12, 'j': 3, 'k': 4, 'cost': 3}, {'i': 12, 'j': 3, 'k': 5, 'cost': 30}, {'i': 12, 'j': 3, 'k': 6, 'cost': 85}, {'i': 12, 'j': 3, 'k': 7, 'cost': 50}, {'i': 12, 'j': 3, 'k': 8, 'cost': 32}, {'i': 12, 'j': 3, 'k': 9, 'cost': 6}, {'i': 12, 'j': 3, 'k': 10, 'cost': 41}, {'i': 12, 'j': 3, 'k': 11, 'cost': 84}, {'i': 12, 'j': 3, 'k': 12, 'cost': 90}, {'i': 12, 'j': 4, 'k': 1, 'cost': 82}, {'i': 12, 'j': 4, 'k': 2, 'cost': 18}, {'i': 12, 'j': 4, 'k': 3, 'cost': 60}, {'i': 12, 'j': 4, 'k': 4, 'cost': 22}, {'i': 12, 'j': 4, 'k': 5, 'cost': 84}, {'i': 12, 'j': 4, 'k': 6, 'cost': 48}, {'i': 12, 'j': 4, 'k': 7, 'cost': 47}, {'i': 12, 'j': 4, 'k': 8, 'cost': 87}, {'i': 12, 'j': 4, 'k': 9, 'cost': 21}, {'i': 12, 'j': 4, 'k': 10, 'cost': 76}, {'i': 12, 'j': 4, 'k': 11, 'cost': 61}, {'i': 12, 'j': 4, 'k': 12, 'cost': 76}, {'i': 12, 'j': 5, 'k': 1, 'cost': 57}, {'i': 12, 'j': 5, 'k': 2, 'cost': 98}, {'i': 12, 'j': 5, 'k': 3, 'cost': 6}, {'i': 12, 'j': 5, 'k': 4, 'cost': 36}, {'i': 12, 'j': 5, 'k': 5, 'cost': 26}, {'i': 12, 'j': 5, 'k': 6, 'cost': 23}, {'i': 12, 'j': 5, 'k': 7, 'cost': 46}, {'i': 12, 'j': 5, 'k': 8, 'cost': 59}, {'i': 12, 'j': 5, 'k': 9, 'cost': 70}, {'i': 12, 'j': 5, 'k': 10, 'cost': 26}, {'i': 12, 'j': 5, 'k': 11, 'cost': 92}, {'i': 12, 'j': 5, 'k': 12, 'cost': 43}, {'i': 12, 'j': 6, 'k': 1, 'cost': 84}, {'i': 12, 'j': 6, 'k': 2, 'cost': 31}, {'i': 12, 'j': 6, 'k': 3, 'cost': 31}, {'i': 12, 'j': 6, 'k': 4, 'cost': 23}, {'i': 12, 'j': 6, 'k': 5, 'cost': 11}, {'i': 12, 'j': 6, 'k': 6, 'cost': 22}, {'i': 12, 'j': 6, 'k': 7, 'cost': 33}, {'i': 12, 'j': 6, 'k': 8, 'cost': 29}, {'i': 12, 'j': 6, 'k': 9, 'cost': 3}, {'i': 12, 'j': 6, 'k': 10, 'cost': 2}, {'i': 12, 'j': 6, 'k': 11, 'cost': 39}, {'i': 12, 'j': 6, 'k': 12, 'cost': 21}, {'i': 12, 'j': 7, 'k': 1, 'cost': 38}, {'i': 12, 'j': 7, 'k': 2, 'cost': 28}, {'i': 12, 'j': 7, 'k': 3, 'cost': 69}, {'i': 12, 'j': 7, 'k': 4, 'cost': 61}, {'i': 12, 'j': 7, 'k': 5, 'cost': 60}, {'i': 12, 'j': 7, 'k': 6, 'cost': 5}, {'i': 12, 'j': 7, 'k': 7, 'cost': 77}, {'i': 12, 'j': 7, 'k': 8, 'cost': 80}, {'i': 12, 'j': 7, 'k': 9, 'cost': 60}, {'i': 12, 'j': 7, 'k': 10, 'cost': 49}, {'i': 12, 'j': 7, 'k': 11, 'cost': 11}, {'i': 12, 'j': 7, 'k': 12, 'cost': 0}, {'i': 12, 'j': 8, 'k': 1, 'cost': 62}, {'i': 12, 'j': 8, 'k': 2, 'cost': 39}, {'i': 12, 'j': 8, 'k': 3, 'cost': 70}, {'i': 12, 'j': 8, 'k': 4, 'cost': 31}, {'i': 12, 'j': 8, 'k': 5, 'cost': 95}, {'i': 12, 'j': 8, 'k': 6, 'cost': 41}, {'i': 12, 'j': 8, 'k': 7, 'cost': 58}, {'i': 12, 'j': 8, 'k': 8, 'cost': 4}, {'i': 12, 'j': 8, 'k': 9, 'cost': 45}, {'i': 12, 'j': 8, 'k': 10, 'cost': 49}, {'i': 12, 'j': 8, 'k': 11, 'cost': 38}, {'i': 12, 'j': 8, 'k': 12, 'cost': 27}, {'i': 12, 'j': 9, 'k': 1, 'cost': 89}, {'i': 12, 'j': 9, 'k': 2, 'cost': 17}, {'i': 12, 'j': 9, 'k': 3, 'cost': 3}, {'i': 12, 'j': 9, 'k': 4, 'cost': 98}, {'i': 12, 'j': 9, 'k': 5, 'cost': 61}, {'i': 12, 'j': 9, 'k': 6, 'cost': 89}, {'i': 12, 'j': 9, 'k': 7, 'cost': 39}, {'i': 12, 'j': 9, 'k': 8, 'cost': 43}, {'i': 12, 'j': 9, 'k': 9, 'cost': 63}, {'i': 12, 'j': 9, 'k': 10, 'cost': 23}, {'i': 12, 'j': 9, 'k': 11, 'cost': 88}, {'i': 12, 'j': 9, 'k': 12, 'cost': 14}, {'i': 12, 'j': 10, 'k': 1, 'cost': 2}, {'i': 12, 'j': 10, 'k': 2, 'cost': 21}, {'i': 12, 'j': 10, 'k': 3, 'cost': 99}, {'i': 12, 'j': 10, 'k': 4, 'cost': 15}, {'i': 12, 'j': 10, 'k': 5, 'cost': 11}, {'i': 12, 'j': 10, 'k': 6, 'cost': 0}, {'i': 12, 'j': 10, 'k': 7, 'cost': 72}, {'i': 12, 'j': 10, 'k': 8, 'cost': 62}, {'i': 12, 'j': 10, 'k': 9, 'cost': 45}, {'i': 12, 'j': 10, 'k': 10, 'cost': 2}, {'i': 12, 'j': 10, 'k': 11, 'cost': 7}, {'i': 12, 'j': 10, 'k': 12, 'cost': 76}, {'i': 12, 'j': 11, 'k': 1, 'cost': 51}, {'i': 12, 'j': 11, 'k': 2, 'cost': 78}, {'i': 12, 'j': 11, 'k': 3, 'cost': 39}, {'i': 12, 'j': 11, 'k': 4, 'cost': 5}, {'i': 12, 'j': 11, 'k': 5, 'cost': 91}, {'i': 12, 'j': 11, 'k': 6, 'cost': 94}, {'i': 12, 'j': 11, 'k': 7, 'cost': 21}, {'i': 12, 'j': 11, 'k': 8, 'cost': 69}, {'i': 12, 'j': 11, 'k': 9, 'cost': 94}, {'i': 12, 'j': 11, 'k': 10, 'cost': 27}, {'i': 12, 'j': 11, 'k': 11, 'cost': 26}, {'i': 12, 'j': 11, 'k': 12, 'cost': 91}, {'i': 12, 'j': 12, 'k': 1, 'cost': 9}, {'i': 12, 'j': 12, 'k': 2, 'cost': 31}, {'i': 12, 'j': 12, 'k': 3, 'cost': 56}, {'i': 12, 'j': 12, 'k': 4, 'cost': 47}, {'i': 12, 'j': 12, 'k': 5, 'cost': 21}, {'i': 12, 'j': 12, 'k': 6, 'cost': 34}, {'i': 12, 'j': 12, 'k': 7, 'cost': 24}, {'i': 12, 'j': 12, 'k': 8, 'cost': 23}, {'i': 12, 'j': 12, 'k': 9, 'cost': 73}, {'i': 12, 'j': 12, 'k': 10, 'cost': 74}, {'i': 12, 'j': 12, 'k': 11, 'cost': 13}, {'i': 12, 'j': 12, 'k': 12, 'cost': 84}]}","[[1, 6, 1], [2, 1, 12], [3, 12, 10], [4, 11, 5], [5, 4, 6], [6, 5, 8], [7, 7, 2], [8, 2, 3], [9, 8, 11], [10, 10, 7], [11, 9, 9], [12, 3, 4]]",3,csv,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 12 students, 12 projects and 12 supervisors, identified as A, B, C, D, E, F, G, H, I, J, K, L.
+
+*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=A
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 24 | 10 | 1 | 69 | 26 | 45 | 91 | 39 | 8 | 1 | 32 | 66 |
+| B | 59 | 69 | 8 | 28 | 78 | 59 | 42 | 27 | 72 | 28 | 14 | 43 |
+| C | 42 | 11 | 62 | 18 | 61 | 64 | 80 | 85 | 32 | 13 | 47 | 9 |
+| D | 42 | 2 | 49 | 90 | 89 | 89 | 14 | 58 | 17 | 73 | 81 | 76 |
+| E | 12 | 27 | 62 | 55 | 18 | 33 | 58 | 43 | 93 | 62 | 58 | 50 |
+| F | 23 | 57 | 50 | 67 | 43 | 87 | 36 | 77 | 37 | 92 | 74 | 16 |
+| G | 24 | 42 | 92 | 64 | 34 | 40 | 71 | 69 | 70 | 35 | 99 | 62 |
+| H | 56 | 94 | 5 | 48 | 77 | 2 | 88 | 61 | 1 | 36 | 86 | 2 |
+| I | 15 | 51 | 4 | 27 | 43 | 34 | 65 | 96 | 41 | 78 | 3 | 84 |
+| J | 25 | 56 | 36 | 71 | 89 | 2 | 0 | 14 | 53 | 43 | 67 | 98 |
+| K | 75 | 14 | 23 | 1 | 73 | 93 | 53 | 24 | 75 | 60 | 5 | 89 |
+| L | 54 | 50 | 23 | 67 | 56 | 3 | 94 | 89 | 11 | 95 | 92 | 1 |
+
+## student_id=B
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 85 | 40 | 78 | 95 | 33 | 59 | 97 | 32 | 63 | 28 | 88 | 72 |
+| B | 80 | 41 | 60 | 19 | 15 | 92 | 11 | 58 | 32 | 99 | 70 | 99 |
+| C | 11 | 84 | 86 | 88 | 23 | 10 | 24 | 63 | 93 | 68 | 81 | 76 |
+| D | 9 | 54 | 90 | 14 | 16 | 45 | 23 | 9 | 93 | 31 | 16 | 72 |
+| E | 23 | 99 | 88 | 17 | 70 | 72 | 87 | 33 | 25 | 40 | 86 | 70 |
+| F | 12 | 38 | 71 | 39 | 24 | 83 | 98 | 42 | 28 | 36 | 38 | 58 |
+| G | 44 | 32 | 81 | 11 | 29 | 53 | 78 | 64 | 31 | 63 | 80 | 73 |
+| H | 45 | 49 | 64 | 21 | 44 | 27 | 96 | 37 | 9 | 13 | 5 | 88 |
+| I | 79 | 84 | 86 | 5 | 87 | 85 | 18 | 32 | 39 | 94 | 19 | 84 |
+| J | 19 | 18 | 52 | 14 | 87 | 83 | 81 | 20 | 22 | 25 | 37 | 29 |
+| K | 7 | 50 | 45 | 70 | 7 | 78 | 77 | 67 | 17 | 64 | 16 | 16 |
+| L | 3 | 40 | 6 | 29 | 22 | 70 | 42 | 16 | 38 | 31 | 0 | 74 |
+
+## student_id=C
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 54 | 3 | 74 | 16 | 66 | 60 | 26 | 13 | 70 | 18 | 58 | 69 |
+| B | 56 | 70 | 39 | 59 | 68 | 49 | 59 | 58 | 99 | 94 | 70 | 8 |
+| C | 82 | 52 | 65 | 13 | 63 | 7 | 96 | 26 | 65 | 44 | 91 | 14 |
+| D | 63 | 57 | 24 | 71 | 7 | 23 | 15 | 44 | 39 | 72 | 86 | 75 |
+| E | 0 | 12 | 6 | 62 | 38 | 12 | 92 | 8 | 29 | 93 | 27 | 31 |
+| F | 8 | 4 | 37 | 66 | 5 | 36 | 38 | 43 | 39 | 9 | 64 | 48 |
+| G | 13 | 63 | 84 | 36 | 80 | 68 | 54 | 79 | 12 | 12 | 72 | 93 |
+| H | 46 | 43 | 51 | 73 | 23 | 16 | 85 | 76 | 8 | 63 | 12 | 26 |
+| I | 18 | 16 | 82 | 1 | 87 | 1 | 52 | 0 | 81 | 46 | 97 | 26 |
+| J | 24 | 14 | 75 | 50 | 93 | 67 | 76 | 37 | 2 | 57 | 49 | 33 |
+| K | 33 | 91 | 92 | 82 | 72 | 50 | 80 | 26 | 60 | 61 | 95 | 39 |
+| L | 27 | 22 | 50 | 35 | 17 | 98 | 28 | 95 | 5 | 42 | 4 | 20 |
+
+## student_id=D
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 22 | 84 | 10 | 96 | 74 | 63 | 19 | 45 | 81 | 76 | 67 | 83 |
+| B | 44 | 53 | 89 | 71 | 83 | 5 | 61 | 4 | 36 | 41 | 3 | 43 |
+| C | 45 | 52 | 85 | 70 | 32 | 11 | 80 | 17 | 58 | 28 | 6 | 54 |
+| D | 28 | 83 | 73 | 86 | 76 | 78 | 33 | 27 | 46 | 62 | 18 | 62 |
+| E | 46 | 90 | 43 | 27 | 94 | 16 | 41 | 4 | 61 | 9 | 40 | 43 |
+| F | 71 | 59 | 47 | 66 | 5 | 81 | 2 | 86 | 3 | 26 | 81 | 93 |
+| G | 49 | 23 | 41 | 37 | 48 | 38 | 99 | 32 | 86 | 13 | 52 | 12 |
+| H | 82 | 40 | 53 | 21 | 22 | 32 | 47 | 22 | 86 | 96 | 65 | 59 |
+| I | 1 | 0 | 94 | 38 | 80 | 20 | 10 | 58 | 56 | 33 | 12 | 88 |
+| J | 70 | 50 | 73 | 2 | 60 | 72 | 69 | 71 | 40 | 6 | 99 | 23 |
+| K | 42 | 50 | 83 | 21 | 68 | 86 | 4 | 71 | 38 | 89 | 65 | 25 |
+| L | 30 | 80 | 60 | 28 | 1 | 10 | 64 | 91 | 1 | 13 | 82 | 50 |
+
+## student_id=E
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 9 | 30 | 83 | 47 | 46 | 89 | 58 | 51 | 47 | 91 | 61 | 17 |
+| B | 3 | 44 | 79 | 53 | 86 | 45 | 41 | 88 | 52 | 13 | 9 | 84 |
+| C | 27 | 34 | 11 | 66 | 83 | 68 | 11 | 11 | 96 | 38 | 1 | 84 |
+| D | 58 | 67 | 44 | 24 | 67 | 97 | 75 | 75 | 7 | 10 | 32 | 38 |
+| E | 40 | 5 | 73 | 39 | 23 | 71 | 22 | 48 | 40 | 89 | 25 | 35 |
+| F | 79 | 62 | 47 | 80 | 48 | 6 | 24 | 59 | 81 | 18 | 26 | 97 |
+| G | 20 | 75 | 47 | 88 | 96 | 26 | 65 | 99 | 85 | 33 | 36 | 67 |
+| H | 61 | 30 | 49 | 55 | 32 | 39 | 54 | 95 | 66 | 48 | 46 | 32 |
+| I | 11 | 43 | 4 | 47 | 6 | 69 | 38 | 87 | 19 | 41 | 37 | 38 |
+| J | 63 | 63 | 4 | 95 | 21 | 51 | 30 | 95 | 68 | 85 | 84 | 87 |
+| K | 62 | 50 | 94 | 71 | 93 | 80 | 14 | 66 | 40 | 75 | 30 | 4 |
+| L | 0 | 75 | 40 | 74 | 17 | 71 | 39 | 99 | 97 | 2 | 34 | 92 |
+
+## student_id=F
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 71 | 99 | 29 | 80 | 27 | 97 | 88 | 0 | 96 | 25 | 19 | 30 |
+| B | 80 | 23 | 45 | 48 | 85 | 44 | 60 | 7 | 24 | 50 | 76 | 19 |
+| C | 1 | 0 | 38 | 55 | 87 | 73 | 75 | 78 | 81 | 11 | 73 | 48 |
+| D | 41 | 82 | 16 | 21 | 42 | 2 | 75 | 27 | 5 | 6 | 98 | 43 |
+| E | 22 | 81 | 51 | 98 | 70 | 17 | 8 | 71 | 36 | 69 | 44 | 69 |
+| F | 44 | 65 | 16 | 95 | 62 | 34 | 19 | 39 | 4 | 73 | 40 | 76 |
+| G | 16 | 22 | 22 | 43 | 54 | 12 | 24 | 59 | 41 | 75 | 44 | 82 |
+| H | 18 | 97 | 76 | 18 | 86 | 99 | 79 | 55 | 24 | 35 | 87 | 32 |
+| I | 15 | 44 | 22 | 11 | 65 | 41 | 81 | 33 | 52 | 54 | 34 | 60 |
+| J | 83 | 74 | 97 | 18 | 45 | 60 | 68 | 49 | 7 | 63 | 79 | 94 |
+| K | 51 | 78 | 12 | 91 | 15 | 42 | 94 | 63 | 45 | 7 | 49 | 55 |
+| L | 30 | 19 | 83 | 76 | 27 | 82 | 89 | 55 | 74 | 95 | 52 | 81 |
+
+## student_id=G
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 52 | 95 | 43 | 77 | 96 | 33 | 40 | 68 | 7 | 8 | 60 | 57 |
+| B | 73 | 1 | 36 | 8 | 11 | 60 | 7 | 76 | 64 | 47 | 3 | 81 |
+| C | 88 | 54 | 67 | 64 | 31 | 72 | 66 | 59 | 87 | 90 | 88 | 5 |
+| D | 72 | 92 | 79 | 68 | 91 | 21 | 8 | 42 | 34 | 22 | 15 | 27 |
+| E | 82 | 90 | 69 | 7 | 95 | 6 | 69 | 9 | 15 | 10 | 45 | 68 |
+| F | 78 | 94 | 28 | 81 | 86 | 11 | 40 | 34 | 9 | 93 | 33 | 77 |
+| G | 72 | 3 | 59 | 42 | 29 | 44 | 51 | 69 | 27 | 24 | 30 | 29 |
+| H | 50 | 46 | 29 | 76 | 63 | 15 | 32 | 58 | 34 | 31 | 34 | 57 |
+| I | 6 | 36 | 2 | 61 | 43 | 21 | 3 | 40 | 39 | 90 | 60 | 48 |
+| J | 25 | 12 | 45 | 2 | 38 | 15 | 18 | 44 | 67 | 76 | 84 | 98 |
+| K | 94 | 53 | 54 | 72 | 79 | 83 | 3 | 56 | 11 | 69 | 54 | 75 |
+| L | 45 | 46 | 35 | 90 | 26 | 97 | 75 | 94 | 1 | 48 | 34 | 66 |
+
+## student_id=H
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 77 | 89 | 93 | 47 | 73 | 92 | 24 | 94 | 93 | 26 | 28 | 1 |
+| B | 90 | 9 | 54 | 0 | 64 | 42 | 24 | 41 | 65 | 70 | 94 | 3 |
+| C | 77 | 84 | 31 | 16 | 97 | 71 | 58 | 10 | 92 | 25 | 3 | 21 |
+| D | 84 | 51 | 56 | 55 | 42 | 29 | 41 | 94 | 14 | 48 | 10 | 50 |
+| E | 95 | 57 | 46 | 25 | 67 | 81 | 67 | 53 | 41 | 48 | 22 | 85 |
+| F | 38 | 30 | 32 | 53 | 71 | 36 | 79 | 43 | 41 | 96 | 57 | 82 |
+| G | 26 | 54 | 40 | 56 | 55 | 76 | 71 | 32 | 70 | 76 | 3 | 25 |
+| H | 76 | 69 | 21 | 58 | 78 | 98 | 71 | 13 | 5 | 15 | 52 | 53 |
+| I | 10 | 94 | 13 | 5 | 58 | 2 | 16 | 50 | 95 | 34 | 62 | 5 |
+| J | 41 | 76 | 42 | 80 | 45 | 34 | 17 | 46 | 87 | 35 | 69 | 28 |
+| K | 23 | 32 | 45 | 2 | 11 | 80 | 9 | 17 | 58 | 54 | 72 | 24 |
+| L | 60 | 68 | 53 | 61 | 23 | 48 | 98 | 94 | 79 | 37 | 63 | 38 |
+
+## student_id=I
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 4 | 48 | 77 | 70 | 73 | 62 | 75 | 47 | 42 | 42 | 94 | 78 |
+| B | 1 | 57 | 20 | 87 | 96 | 48 | 97 | 86 | 33 | 31 | 72 | 16 |
+| C | 62 | 84 | 38 | 38 | 52 | 29 | 57 | 76 | 57 | 14 | 38 | 85 |
+| D | 10 | 25 | 42 | 23 | 30 | 80 | 24 | 33 | 80 | 60 | 7 | 24 |
+| E | 41 | 95 | 59 | 81 | 97 | 49 | 98 | 51 | 6 | 40 | 8 | 92 |
+| F | 52 | 18 | 78 | 15 | 19 | 57 | 31 | 89 | 88 | 38 | 59 | 32 |
+| G | 29 | 47 | 44 | 49 | 69 | 82 | 36 | 80 | 59 | 46 | 69 | 59 |
+| H | 23 | 45 | 92 | 62 | 93 | 35 | 6 | 31 | 36 | 45 | 66 | 31 |
+| I | 40 | 59 | 43 | 37 | 1 | 58 | 84 | 88 | 78 | 90 | 1 | 25 |
+| J | 16 | 49 | 41 | 45 | 67 | 9 | 66 | 92 | 46 | 95 | 87 | 41 |
+| K | 9 | 5 | 93 | 31 | 22 | 65 | 88 | 75 | 12 | 27 | 5 | 67 |
+| L | 1 | 8 | 92 | 86 | 33 | 76 | 55 | 77 | 85 | 68 | 40 | 65 |
+
+## student_id=J
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 36 | 89 | 11 | 54 | 70 | 65 | 57 | 21 | 5 | 59 | 19 | 94 |
+| B | 27 | 71 | 86 | 39 | 72 | 63 | 2 | 79 | 18 | 82 | 61 | 10 |
+| C | 79 | 51 | 88 | 76 | 74 | 25 | 42 | 78 | 92 | 28 | 69 | 88 |
+| D | 92 | 84 | 85 | 66 | 36 | 30 | 50 | 97 | 91 | 96 | 11 | 32 |
+| E | 87 | 63 | 87 | 42 | 79 | 47 | 59 | 7 | 64 | 93 | 25 | 28 |
+| F | 26 | 47 | 88 | 34 | 34 | 37 | 61 | 29 | 47 | 77 | 99 | 2 |
+| G | 94 | 67 | 77 | 49 | 53 | 67 | 81 | 71 | 12 | 15 | 14 | 32 |
+| H | 19 | 75 | 69 | 59 | 19 | 48 | 57 | 81 | 78 | 19 | 16 | 63 |
+| I | 12 | 32 | 95 | 90 | 54 | 3 | 29 | 23 | 94 | 28 | 75 | 51 |
+| J | 4 | 4 | 17 | 61 | 26 | 60 | 55 | 90 | 26 | 57 | 14 | 12 |
+| K | 11 | 46 | 84 | 38 | 84 | 51 | 73 | 23 | 95 | 36 | 42 | 61 |
+| L | 79 | 97 | 75 | 12 | 80 | 0 | 71 | 11 | 62 | 41 | 73 | 62 |
+
+## student_id=K
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 62 | 51 | 89 | 7 | 29 | 46 | 50 | 1 | 8 | 42 | 89 | 68 |
+| B | 2 | 43 | 50 | 96 | 78 | 96 | 23 | 25 | 72 | 57 | 2 | 17 |
+| C | 75 | 89 | 96 | 99 | 6 | 2 | 62 | 73 | 76 | 67 | 5 | 97 |
+| D | 13 | 78 | 80 | 80 | 46 | 91 | 64 | 97 | 86 | 89 | 80 | 0 |
+| E | 38 | 27 | 70 | 54 | 84 | 37 | 57 | 25 | 70 | 65 | 41 | 35 |
+| F | 19 | 64 | 54 | 71 | 61 | 94 | 32 | 26 | 32 | 37 | 97 | 89 |
+| G | 68 | 33 | 56 | 21 | 70 | 46 | 96 | 73 | 73 | 16 | 20 | 54 |
+| H | 94 | 43 | 24 | 64 | 69 | 42 | 32 | 12 | 74 | 60 | 98 | 37 |
+| I | 92 | 17 | 92 | 40 | 52 | 91 | 33 | 28 | 93 | 76 | 51 | 58 |
+| J | 78 | 72 | 52 | 14 | 53 | 95 | 3 | 11 | 83 | 66 | 5 | 35 |
+| K | 99 | 95 | 23 | 93 | 51 | 62 | 16 | 48 | 58 | 1 | 82 | 50 |
+| L | 45 | 3 | 34 | 82 | 69 | 61 | 50 | 57 | 27 | 7 | 64 | 76 |
+
+## student_id=L
+| project_id\supervisor_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 23 | 27 | 56 | 25 | 16 | 69 | 12 | 93 | 40 | 4 | 93 | 92 |
+| B | 85 | 78 | 38 | 96 | 27 | 33 | 94 | 91 | 35 | 95 | 29 | 59 |
+| C | 50 | 55 | 79 | 93 | 69 | 37 | 6 | 26 | 99 | 92 | 85 | 85 |
+| D | 74 | 31 | 63 | 21 | 46 | 55 | 33 | 29 | 53 | 5 | 27 | 59 |
+| E | 84 | 13 | 16 | 18 | 7 | 84 | 78 | 53 | 26 | 28 | 88 | 43 |
+| F | 73 | 71 | 61 | 54 | 13 | 88 | 52 | 9 | 41 | 67 | 98 | 7 |
+| G | 67 | 71 | 71 | 88 | 95 | 34 | 76 | 70 | 81 | 2 | 4 | 94 |
+| H | 85 | 6 | 54 | 91 | 7 | 31 | 9 | 5 | 15 | 63 | 62 | 95 |
+| I | 75 | 82 | 74 | 78 | 9 | 99 | 64 | 90 | 12 | 76 | 8 | 66 |
+| J | 90 | 56 | 64 | 28 | 91 | 89 | 12 | 68 | 28 | 40 | 56 | 90 |
+| K | 33 | 55 | 84 | 84 | 77 | 40 | 10 | 37 | 23 | 99 | 33 | 18 |
+| L | 63 | 32 | 75 | 15 | 39 | 89 | 63 | 30 | 59 | 13 | 20 | 71 |
+
+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': [[[24, 10, 1, 69, 26, 45, 91, 39, 8, 1, 32, 66], [59, 69, 8, 28, 78, 59, 42, 27, 72, 28, 14, 43], [42, 11, 62, 18, 61, 64, 80, 85, 32, 13, 47, 9], [42, 2, 49, 90, 89, 89, 14, 58, 17, 73, 81, 76], [12, 27, 62, 55, 18, 33, 58, 43, 93, 62, 58, 50], [23, 57, 50, 67, 43, 87, 36, 77, 37, 92, 74, 16], [24, 42, 92, 64, 34, 40, 71, 69, 70, 35, 99, 62], [56, 94, 5, 48, 77, 2, 88, 61, 1, 36, 86, 2], [15, 51, 4, 27, 43, 34, 65, 96, 41, 78, 3, 84], [25, 56, 36, 71, 89, 2, 0, 14, 53, 43, 67, 98], [75, 14, 23, 1, 73, 93, 53, 24, 75, 60, 5, 89], [54, 50, 23, 67, 56, 3, 94, 89, 11, 95, 92, 1]], [[85, 40, 78, 95, 33, 59, 97, 32, 63, 28, 88, 72], [80, 41, 60, 19, 15, 92, 11, 58, 32, 99, 70, 99], [11, 84, 86, 88, 23, 10, 24, 63, 93, 68, 81, 76], [9, 54, 90, 14, 16, 45, 23, 9, 93, 31, 16, 72], [23, 99, 88, 17, 70, 72, 87, 33, 25, 40, 86, 70], [12, 38, 71, 39, 24, 83, 98, 42, 28, 36, 38, 58], [44, 32, 81, 11, 29, 53, 78, 64, 31, 63, 80, 73], [45, 49, 64, 21, 44, 27, 96, 37, 9, 13, 5, 88], [79, 84, 86, 5, 87, 85, 18, 32, 39, 94, 19, 84], [19, 18, 52, 14, 87, 83, 81, 20, 22, 25, 37, 29], [7, 50, 45, 70, 7, 78, 77, 67, 17, 64, 16, 16], [3, 40, 6, 29, 22, 70, 42, 16, 38, 31, 0, 74]], [[54, 3, 74, 16, 66, 60, 26, 13, 70, 18, 58, 69], [56, 70, 39, 59, 68, 49, 59, 58, 99, 94, 70, 8], [82, 52, 65, 13, 63, 7, 96, 26, 65, 44, 91, 14], [63, 57, 24, 71, 7, 23, 15, 44, 39, 72, 86, 75], [0, 12, 6, 62, 38, 12, 92, 8, 29, 93, 27, 31], [8, 4, 37, 66, 5, 36, 38, 43, 39, 9, 64, 48], [13, 63, 84, 36, 80, 68, 54, 79, 12, 12, 72, 93], [46, 43, 51, 73, 23, 16, 85, 76, 8, 63, 12, 26], [18, 16, 82, 1, 87, 1, 52, 0, 81, 46, 97, 26], [24, 14, 75, 50, 93, 67, 76, 37, 2, 57, 49, 33], [33, 91, 92, 82, 72, 50, 80, 26, 60, 61, 95, 39], [27, 22, 50, 35, 17, 98, 28, 95, 5, 42, 4, 20]], [[22, 84, 10, 96, 74, 63, 19, 45, 81, 76, 67, 83], [44, 53, 89, 71, 83, 5, 61, 4, 36, 41, 3, 43], [45, 52, 85, 70, 32, 11, 80, 17, 58, 28, 6, 54], [28, 83, 73, 86, 76, 78, 33, 27, 46, 62, 18, 62], [46, 90, 43, 27, 94, 16, 41, 4, 61, 9, 40, 43], [71, 59, 47, 66, 5, 81, 2, 86, 3, 26, 81, 93], [49, 23, 41, 37, 48, 38, 99, 32, 86, 13, 52, 12], [82, 40, 53, 21, 22, 32, 47, 22, 86, 96, 65, 59], [1, 0, 94, 38, 80, 20, 10, 58, 56, 33, 12, 88], [70, 50, 73, 2, 60, 72, 69, 71, 40, 6, 99, 23], [42, 50, 83, 21, 68, 86, 4, 71, 38, 89, 65, 25], [30, 80, 60, 28, 1, 10, 64, 91, 1, 13, 82, 50]], [[9, 30, 83, 47, 46, 89, 58, 51, 47, 91, 61, 17], [3, 44, 79, 53, 86, 45, 41, 88, 52, 13, 9, 84], [27, 34, 11, 66, 83, 68, 11, 11, 96, 38, 1, 84], [58, 67, 44, 24, 67, 97, 75, 75, 7, 10, 32, 38], [40, 5, 73, 39, 23, 71, 22, 48, 40, 89, 25, 35], [79, 62, 47, 80, 48, 6, 24, 59, 81, 18, 26, 97], [20, 75, 47, 88, 96, 26, 65, 99, 85, 33, 36, 67], [61, 30, 49, 55, 32, 39, 54, 95, 66, 48, 46, 32], [11, 43, 4, 47, 6, 69, 38, 87, 19, 41, 37, 38], [63, 63, 4, 95, 21, 51, 30, 95, 68, 85, 84, 87], [62, 50, 94, 71, 93, 80, 14, 66, 40, 75, 30, 4], [0, 75, 40, 74, 17, 71, 39, 99, 97, 2, 34, 92]], [[71, 99, 29, 80, 27, 97, 88, 0, 96, 25, 19, 30], [80, 23, 45, 48, 85, 44, 60, 7, 24, 50, 76, 19], [1, 0, 38, 55, 87, 73, 75, 78, 81, 11, 73, 48], [41, 82, 16, 21, 42, 2, 75, 27, 5, 6, 98, 43], [22, 81, 51, 98, 70, 17, 8, 71, 36, 69, 44, 69], [44, 65, 16, 95, 62, 34, 19, 39, 4, 73, 40, 76], [16, 22, 22, 43, 54, 12, 24, 59, 41, 75, 44, 82], [18, 97, 76, 18, 86, 99, 79, 55, 24, 35, 87, 32], [15, 44, 22, 11, 65, 41, 81, 33, 52, 54, 34, 60], [83, 74, 97, 18, 45, 60, 68, 49, 7, 63, 79, 94], [51, 78, 12, 91, 15, 42, 94, 63, 45, 7, 49, 55], [30, 19, 83, 76, 27, 82, 89, 55, 74, 95, 52, 81]], [[52, 95, 43, 77, 96, 33, 40, 68, 7, 8, 60, 57], [73, 1, 36, 8, 11, 60, 7, 76, 64, 47, 3, 81], [88, 54, 67, 64, 31, 72, 66, 59, 87, 90, 88, 5], [72, 92, 79, 68, 91, 21, 8, 42, 34, 22, 15, 27], [82, 90, 69, 7, 95, 6, 69, 9, 15, 10, 45, 68], [78, 94, 28, 81, 86, 11, 40, 34, 9, 93, 33, 77], [72, 3, 59, 42, 29, 44, 51, 69, 27, 24, 30, 29], [50, 46, 29, 76, 63, 15, 32, 58, 34, 31, 34, 57], [6, 36, 2, 61, 43, 21, 3, 40, 39, 90, 60, 48], [25, 12, 45, 2, 38, 15, 18, 44, 67, 76, 84, 98], [94, 53, 54, 72, 79, 83, 3, 56, 11, 69, 54, 75], [45, 46, 35, 90, 26, 97, 75, 94, 1, 48, 34, 66]], [[77, 89, 93, 47, 73, 92, 24, 94, 93, 26, 28, 1], [90, 9, 54, 0, 64, 42, 24, 41, 65, 70, 94, 3], [77, 84, 31, 16, 97, 71, 58, 10, 92, 25, 3, 21], [84, 51, 56, 55, 42, 29, 41, 94, 14, 48, 10, 50], [95, 57, 46, 25, 67, 81, 67, 53, 41, 48, 22, 85], [38, 30, 32, 53, 71, 36, 79, 43, 41, 96, 57, 82], [26, 54, 40, 56, 55, 76, 71, 32, 70, 76, 3, 25], [76, 69, 21, 58, 78, 98, 71, 13, 5, 15, 52, 53], [10, 94, 13, 5, 58, 2, 16, 50, 95, 34, 62, 5], [41, 76, 42, 80, 45, 34, 17, 46, 87, 35, 69, 28], [23, 32, 45, 2, 11, 80, 9, 17, 58, 54, 72, 24], [60, 68, 53, 61, 23, 48, 98, 94, 79, 37, 63, 38]], [[4, 48, 77, 70, 73, 62, 75, 47, 42, 42, 94, 78], [1, 57, 20, 87, 96, 48, 97, 86, 33, 31, 72, 16], [62, 84, 38, 38, 52, 29, 57, 76, 57, 14, 38, 85], [10, 25, 42, 23, 30, 80, 24, 33, 80, 60, 7, 24], [41, 95, 59, 81, 97, 49, 98, 51, 6, 40, 8, 92], [52, 18, 78, 15, 19, 57, 31, 89, 88, 38, 59, 32], [29, 47, 44, 49, 69, 82, 36, 80, 59, 46, 69, 59], [23, 45, 92, 62, 93, 35, 6, 31, 36, 45, 66, 31], [40, 59, 43, 37, 1, 58, 84, 88, 78, 90, 1, 25], [16, 49, 41, 45, 67, 9, 66, 92, 46, 95, 87, 41], [9, 5, 93, 31, 22, 65, 88, 75, 12, 27, 5, 67], [1, 8, 92, 86, 33, 76, 55, 77, 85, 68, 40, 65]], [[36, 89, 11, 54, 70, 65, 57, 21, 5, 59, 19, 94], [27, 71, 86, 39, 72, 63, 2, 79, 18, 82, 61, 10], [79, 51, 88, 76, 74, 25, 42, 78, 92, 28, 69, 88], [92, 84, 85, 66, 36, 30, 50, 97, 91, 96, 11, 32], [87, 63, 87, 42, 79, 47, 59, 7, 64, 93, 25, 28], [26, 47, 88, 34, 34, 37, 61, 29, 47, 77, 99, 2], [94, 67, 77, 49, 53, 67, 81, 71, 12, 15, 14, 32], [19, 75, 69, 59, 19, 48, 57, 81, 78, 19, 16, 63], [12, 32, 95, 90, 54, 3, 29, 23, 94, 28, 75, 51], [4, 4, 17, 61, 26, 60, 55, 90, 26, 57, 14, 12], [11, 46, 84, 38, 84, 51, 73, 23, 95, 36, 42, 61], [79, 97, 75, 12, 80, 0, 71, 11, 62, 41, 73, 62]], [[62, 51, 89, 7, 29, 46, 50, 1, 8, 42, 89, 68], [2, 43, 50, 96, 78, 96, 23, 25, 72, 57, 2, 17], [75, 89, 96, 99, 6, 2, 62, 73, 76, 67, 5, 97], [13, 78, 80, 80, 46, 91, 64, 97, 86, 89, 80, 0], [38, 27, 70, 54, 84, 37, 57, 25, 70, 65, 41, 35], [19, 64, 54, 71, 61, 94, 32, 26, 32, 37, 97, 89], [68, 33, 56, 21, 70, 46, 96, 73, 73, 16, 20, 54], [94, 43, 24, 64, 69, 42, 32, 12, 74, 60, 98, 37], [92, 17, 92, 40, 52, 91, 33, 28, 93, 76, 51, 58], [78, 72, 52, 14, 53, 95, 3, 11, 83, 66, 5, 35], [99, 95, 23, 93, 51, 62, 16, 48, 58, 1, 82, 50], [45, 3, 34, 82, 69, 61, 50, 57, 27, 7, 64, 76]], [[23, 27, 56, 25, 16, 69, 12, 93, 40, 4, 93, 92], [85, 78, 38, 96, 27, 33, 94, 91, 35, 95, 29, 59], [50, 55, 79, 93, 69, 37, 6, 26, 99, 92, 85, 85], [74, 31, 63, 21, 46, 55, 33, 29, 53, 5, 27, 59], [84, 13, 16, 18, 7, 84, 78, 53, 26, 28, 88, 43], [73, 71, 61, 54, 13, 88, 52, 9, 41, 67, 98, 7], [67, 71, 71, 88, 95, 34, 76, 70, 81, 2, 4, 94], [85, 6, 54, 91, 7, 31, 9, 5, 15, 63, 62, 95], [75, 82, 74, 78, 9, 99, 64, 90, 12, 76, 8, 66], [90, 56, 64, 28, 91, 89, 12, 68, 28, 40, 56, 90], [33, 55, 84, 84, 77, 40, 10, 37, 23, 99, 33, 18], [63, 32, 75, 15, 39, 89, 63, 30, 59, 13, 20, 71]]], 'objective': 22.0}","[[0, 7, 8], [1, 11, 10], [2, 4, 0], [3, 10, 6], [4, 9, 2], [5, 0, 7], [6, 6, 1], [7, 1, 3], [8, 8, 4], [9, 5, 11], [10, 2, 5], [11, 3, 9]]",22.0,"{'problem_type': 'AP3', 'n': 12, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 24}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 10}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 1}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 69}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 26}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 45}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 91}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 39}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 8}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 1}, {'i': 'A', 'j': 'A', 'k': 'K', 'cost': 32}, {'i': 'A', 'j': 'A', 'k': 'L', 'cost': 66}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 59}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 69}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 8}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 28}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 78}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 59}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 42}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 27}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 72}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 28}, {'i': 'A', 'j': 'B', 'k': 'K', 'cost': 14}, {'i': 'A', 'j': 'B', 'k': 'L', 'cost': 43}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 42}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 11}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 62}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 18}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 61}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 64}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 80}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 85}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 32}, {'i': 'A', 'j': 'C', 'k': 'J', 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'cost': 66}, {'i': 'K', 'j': 'J', 'k': 'K', 'cost': 5}, {'i': 'K', 'j': 'J', 'k': 'L', 'cost': 35}, {'i': 'K', 'j': 'K', 'k': 'A', 'cost': 99}, {'i': 'K', 'j': 'K', 'k': 'B', 'cost': 95}, {'i': 'K', 'j': 'K', 'k': 'C', 'cost': 23}, {'i': 'K', 'j': 'K', 'k': 'D', 'cost': 93}, {'i': 'K', 'j': 'K', 'k': 'E', 'cost': 51}, {'i': 'K', 'j': 'K', 'k': 'F', 'cost': 62}, {'i': 'K', 'j': 'K', 'k': 'G', 'cost': 16}, {'i': 'K', 'j': 'K', 'k': 'H', 'cost': 48}, {'i': 'K', 'j': 'K', 'k': 'I', 'cost': 58}, {'i': 'K', 'j': 'K', 'k': 'J', 'cost': 1}, {'i': 'K', 'j': 'K', 'k': 'K', 'cost': 82}, {'i': 'K', 'j': 'K', 'k': 'L', 'cost': 50}, {'i': 'K', 'j': 'L', 'k': 'A', 'cost': 45}, {'i': 'K', 'j': 'L', 'k': 'B', 'cost': 3}, {'i': 'K', 'j': 'L', 'k': 'C', 'cost': 34}, {'i': 'K', 'j': 'L', 'k': 'D', 'cost': 82}, {'i': 'K', 'j': 'L', 'k': 'E', 'cost': 69}, {'i': 'K', 'j': 'L', 'k': 'F', 'cost': 61}, {'i': 'K', 'j': 'L', 'k': 'G', 'cost': 50}, {'i': 'K', 'j': 'L', 'k': 'H', 'cost': 57}, {'i': 'K', 'j': 'L', 'k': 'I', 'cost': 27}, {'i': 'K', 'j': 'L', 'k': 'J', 'cost': 7}, {'i': 'K', 'j': 'L', 'k': 'K', 'cost': 64}, {'i': 'K', 'j': 'L', 'k': 'L', 'cost': 76}, {'i': 'L', 'j': 'A', 'k': 'A', 'cost': 23}, {'i': 'L', 'j': 'A', 'k': 'B', 'cost': 27}, {'i': 'L', 'j': 'A', 'k': 'C', 'cost': 56}, {'i': 'L', 'j': 'A', 'k': 'D', 'cost': 25}, {'i': 'L', 'j': 'A', 'k': 'E', 'cost': 16}, {'i': 'L', 'j': 'A', 'k': 'F', 'cost': 69}, {'i': 'L', 'j': 'A', 'k': 'G', 'cost': 12}, {'i': 'L', 'j': 'A', 'k': 'H', 'cost': 93}, {'i': 'L', 'j': 'A', 'k': 'I', 'cost': 40}, {'i': 'L', 'j': 'A', 'k': 'J', 'cost': 4}, {'i': 'L', 'j': 'A', 'k': 'K', 'cost': 93}, {'i': 'L', 'j': 'A', 'k': 'L', 'cost': 92}, {'i': 'L', 'j': 'B', 'k': 'A', 'cost': 85}, {'i': 'L', 'j': 'B', 'k': 'B', 'cost': 78}, {'i': 'L', 'j': 'B', 'k': 'C', 'cost': 38}, {'i': 'L', 'j': 'B', 'k': 'D', 'cost': 96}, {'i': 'L', 'j': 'B', 'k': 'E', 'cost': 27}, {'i': 'L', 'j': 'B', 'k': 'F', 'cost': 33}, {'i': 'L', 'j': 'B', 'k': 'G', 'cost': 94}, {'i': 'L', 'j': 'B', 'k': 'H', 'cost': 91}, {'i': 'L', 'j': 'B', 'k': 'I', 'cost': 35}, {'i': 'L', 'j': 'B', 'k': 'J', 'cost': 95}, {'i': 'L', 'j': 'B', 'k': 'K', 'cost': 29}, {'i': 'L', 'j': 'B', 'k': 'L', 'cost': 59}, {'i': 'L', 'j': 'C', 'k': 'A', 'cost': 50}, {'i': 'L', 'j': 'C', 'k': 'B', 'cost': 55}, {'i': 'L', 'j': 'C', 'k': 'C', 'cost': 79}, {'i': 'L', 'j': 'C', 'k': 'D', 'cost': 93}, {'i': 'L', 'j': 'C', 'k': 'E', 'cost': 69}, {'i': 'L', 'j': 'C', 'k': 'F', 'cost': 37}, {'i': 'L', 'j': 'C', 'k': 'G', 'cost': 6}, {'i': 'L', 'j': 'C', 'k': 'H', 'cost': 26}, {'i': 'L', 'j': 'C', 'k': 'I', 'cost': 99}, {'i': 'L', 'j': 'C', 'k': 'J', 'cost': 92}, {'i': 'L', 'j': 'C', 'k': 'K', 'cost': 85}, {'i': 'L', 'j': 'C', 'k': 'L', 'cost': 85}, {'i': 'L', 'j': 'D', 'k': 'A', 'cost': 74}, {'i': 'L', 'j': 'D', 'k': 'B', 'cost': 31}, {'i': 'L', 'j': 'D', 'k': 'C', 'cost': 63}, {'i': 'L', 'j': 'D', 'k': 'D', 'cost': 21}, {'i': 'L', 'j': 'D', 'k': 'E', 'cost': 46}, {'i': 'L', 'j': 'D', 'k': 'F', 'cost': 55}, {'i': 'L', 'j': 'D', 'k': 'G', 'cost': 33}, {'i': 'L', 'j': 'D', 'k': 'H', 'cost': 29}, {'i': 'L', 'j': 'D', 'k': 'I', 'cost': 53}, {'i': 'L', 'j': 'D', 'k': 'J', 'cost': 5}, {'i': 'L', 'j': 'D', 'k': 'K', 'cost': 27}, {'i': 'L', 'j': 'D', 'k': 'L', 'cost': 59}, {'i': 'L', 'j': 'E', 'k': 'A', 'cost': 84}, {'i': 'L', 'j': 'E', 'k': 'B', 'cost': 13}, {'i': 'L', 'j': 'E', 'k': 'C', 'cost': 16}, {'i': 'L', 'j': 'E', 'k': 'D', 'cost': 18}, {'i': 'L', 'j': 'E', 'k': 'E', 'cost': 7}, {'i': 'L', 'j': 'E', 'k': 'F', 'cost': 84}, {'i': 'L', 'j': 'E', 'k': 'G', 'cost': 78}, {'i': 'L', 'j': 'E', 'k': 'H', 'cost': 53}, {'i': 'L', 'j': 'E', 'k': 'I', 'cost': 26}, {'i': 'L', 'j': 'E', 'k': 'J', 'cost': 28}, {'i': 'L', 'j': 'E', 'k': 'K', 'cost': 88}, {'i': 'L', 'j': 'E', 'k': 'L', 'cost': 43}, {'i': 'L', 'j': 'F', 'k': 'A', 'cost': 73}, {'i': 'L', 'j': 'F', 'k': 'B', 'cost': 71}, {'i': 'L', 'j': 'F', 'k': 'C', 'cost': 61}, {'i': 'L', 'j': 'F', 'k': 'D', 'cost': 54}, {'i': 'L', 'j': 'F', 'k': 'E', 'cost': 13}, {'i': 'L', 'j': 'F', 'k': 'F', 'cost': 88}, {'i': 'L', 'j': 'F', 'k': 'G', 'cost': 52}, {'i': 'L', 'j': 'F', 'k': 'H', 'cost': 9}, {'i': 'L', 'j': 'F', 'k': 'I', 'cost': 41}, {'i': 'L', 'j': 'F', 'k': 'J', 'cost': 67}, {'i': 'L', 'j': 'F', 'k': 'K', 'cost': 98}, {'i': 'L', 'j': 'F', 'k': 'L', 'cost': 7}, {'i': 'L', 'j': 'G', 'k': 'A', 'cost': 67}, {'i': 'L', 'j': 'G', 'k': 'B', 'cost': 71}, {'i': 'L', 'j': 'G', 'k': 'C', 'cost': 71}, {'i': 'L', 'j': 'G', 'k': 'D', 'cost': 88}, {'i': 'L', 'j': 'G', 'k': 'E', 'cost': 95}, {'i': 'L', 'j': 'G', 'k': 'F', 'cost': 34}, {'i': 'L', 'j': 'G', 'k': 'G', 'cost': 76}, {'i': 'L', 'j': 'G', 'k': 'H', 'cost': 70}, {'i': 'L', 'j': 'G', 'k': 'I', 'cost': 81}, {'i': 'L', 'j': 'G', 'k': 'J', 'cost': 2}, {'i': 'L', 'j': 'G', 'k': 'K', 'cost': 4}, {'i': 'L', 'j': 'G', 'k': 'L', 'cost': 94}, {'i': 'L', 'j': 'H', 'k': 'A', 'cost': 85}, {'i': 'L', 'j': 'H', 'k': 'B', 'cost': 6}, {'i': 'L', 'j': 'H', 'k': 'C', 'cost': 54}, {'i': 'L', 'j': 'H', 'k': 'D', 'cost': 91}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 7}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 31}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 9}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 5}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 15}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 63}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 62}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 95}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 75}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 82}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 74}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 78}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 9}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 99}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 64}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 90}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 12}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 76}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 8}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 66}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 90}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 56}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 64}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 28}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 91}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 89}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 12}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 68}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 28}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 40}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 56}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 90}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 33}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 55}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 84}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 84}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 77}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 40}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 10}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 37}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 23}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 99}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 33}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 18}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 63}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 32}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 75}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 15}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 39}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 89}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 63}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 30}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 59}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 13}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 20}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 71}]}","[['A', 'H', 'I'], ['B', 'L', 'K'], ['C', 'E', 'A'], ['D', 'K', 'G'], ['E', 'J', 'C'], ['F', 'A', 'H'], ['G', 'G', 'B'], ['H', 'B', 'D'], ['I', 'I', 'E'], ['J', 'F', 'L'], ['K', 'C', 'F'], ['L', 'D', 'J']]",4,markdown_table,names
+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.
+
+There were 11 models to schedule, listed as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
+
+*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=1
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 21 | 55 | 20 | 85 | 90 | 92 | 71 | 80 | 46 | 88 | 71 |
+| 2 | 20 | 99 | 13 | 48 | 72 | 18 | 82 | 79 | 92 | 57 | 72 |
+| 3 | 96 | 13 | 48 | 95 | 59 | 46 | 31 | 33 | 12 | 28 | 59 |
+| 4 | 38 | 5 | 87 | 23 | 5 | 24 | 76 | 53 | 65 | 54 | 51 |
+| 5 | 66 | 84 | 55 | 88 | 87 | 97 | 93 | 47 | 60 | 14 | 1 |
+| 6 | 90 | 16 | 12 | 53 | 19 | 24 | 67 | 38 | 67 | 52 | 52 |
+| 7 | 80 | 9 | 84 | 48 | 22 | 73 | 53 | 13 | 55 | 7 | 29 |
+| 8 | 12 | 32 | 40 | 73 | 46 | 50 | 37 | 76 | 27 | 7 | 48 |
+| 9 | 89 | 2 | 42 | 88 | 3 | 35 | 89 | 28 | 45 | 83 | 62 |
+| 10 | 82 | 26 | 49 | 25 | 14 | 79 | 18 | 28 | 99 | 75 | 27 |
+| 11 | 5 | 46 | 90 | 73 | 15 | 50 | 14 | 52 | 28 | 92 | 14 |
+
+## model_id=2
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 80 | 69 | 70 | 26 | 86 | 60 | 53 | 40 | 52 | 0 | 30 |
+| 2 | 10 | 98 | 67 | 79 | 2 | 97 | 48 | 5 | 46 | 25 | 95 |
+| 3 | 38 | 13 | 74 | 24 | 18 | 20 | 71 | 78 | 49 | 14 | 68 |
+| 4 | 24 | 43 | 4 | 50 | 60 | 79 | 60 | 18 | 75 | 24 | 49 |
+| 5 | 35 | 91 | 45 | 80 | 53 | 45 | 30 | 86 | 12 | 7 | 15 |
+| 6 | 24 | 12 | 82 | 56 | 74 | 24 | 28 | 52 | 72 | 5 | 45 |
+| 7 | 59 | 25 | 18 | 19 | 84 | 26 | 88 | 33 | 12 | 19 | 37 |
+| 8 | 65 | 28 | 73 | 25 | 66 | 64 | 40 | 19 | 89 | 35 | 57 |
+| 9 | 69 | 81 | 1 | 30 | 97 | 44 | 31 | 14 | 42 | 49 | 77 |
+| 10 | 21 | 21 | 93 | 88 | 76 | 0 | 95 | 40 | 54 | 85 | 67 |
+| 11 | 72 | 84 | 90 | 13 | 52 | 69 | 48 | 37 | 9 | 39 | 74 |
+
+## model_id=3
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 30 | 23 | 19 | 15 | 4 | 49 | 42 | 82 | 58 | 36 | 38 |
+| 2 | 60 | 16 | 94 | 60 | 25 | 24 | 66 | 88 | 0 | 66 | 65 |
+| 3 | 19 | 45 | 57 | 48 | 57 | 77 | 71 | 53 | 37 | 51 | 48 |
+| 4 | 5 | 74 | 11 | 40 | 17 | 62 | 94 | 79 | 68 | 98 | 16 |
+| 5 | 10 | 34 | 32 | 1 | 61 | 59 | 41 | 19 | 93 | 0 | 95 |
+| 6 | 68 | 82 | 88 | 72 | 19 | 16 | 54 | 29 | 59 | 38 | 72 |
+| 7 | 95 | 77 | 98 | 28 | 44 | 60 | 20 | 42 | 14 | 37 | 60 |
+| 8 | 67 | 50 | 14 | 46 | 10 | 3 | 67 | 18 | 33 | 74 | 59 |
+| 9 | 56 | 25 | 41 | 41 | 76 | 40 | 7 | 89 | 3 | 67 | 29 |
+| 10 | 62 | 69 | 98 | 2 | 50 | 77 | 73 | 69 | 32 | 49 | 58 |
+| 11 | 56 | 26 | 17 | 72 | 82 | 79 | 18 | 35 | 89 | 54 | 51 |
+
+## model_id=4
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 87 | 64 | 29 | 38 | 81 | 88 | 33 | 53 | 81 | 11 | 23 |
+| 2 | 53 | 48 | 82 | 70 | 18 | 53 | 58 | 53 | 89 | 62 | 48 |
+| 3 | 35 | 74 | 51 | 81 | 73 | 5 | 58 | 89 | 54 | 86 | 21 |
+| 4 | 48 | 19 | 81 | 44 | 91 | 76 | 98 | 65 | 96 | 51 | 53 |
+| 5 | 2 | 42 | 71 | 7 | 52 | 88 | 41 | 29 | 74 | 21 | 67 |
+| 6 | 63 | 75 | 43 | 96 | 41 | 98 | 73 | 25 | 76 | 18 | 30 |
+| 7 | 51 | 6 | 90 | 0 | 68 | 82 | 16 | 50 | 60 | 16 | 34 |
+| 8 | 14 | 66 | 80 | 46 | 69 | 6 | 62 | 76 | 91 | 77 | 9 |
+| 9 | 96 | 30 | 47 | 37 | 18 | 83 | 91 | 59 | 89 | 63 | 81 |
+| 10 | 38 | 56 | 43 | 68 | 70 | 38 | 24 | 91 | 32 | 4 | 69 |
+| 11 | 26 | 73 | 84 | 79 | 78 | 89 | 66 | 20 | 27 | 83 | 37 |
+
+## model_id=5
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 69 | 45 | 54 | 56 | 73 | 31 | 96 | 69 | 10 | 40 | 16 |
+| 2 | 55 | 7 | 13 | 0 | 0 | 28 | 74 | 83 | 99 | 7 | 21 |
+| 3 | 93 | 49 | 56 | 38 | 84 | 4 | 88 | 15 | 54 | 46 | 69 |
+| 4 | 12 | 1 | 35 | 58 | 44 | 94 | 77 | 94 | 65 | 52 | 31 |
+| 5 | 42 | 11 | 20 | 91 | 92 | 71 | 34 | 31 | 8 | 57 | 76 |
+| 6 | 43 | 18 | 70 | 98 | 81 | 22 | 52 | 18 | 36 | 86 | 42 |
+| 7 | 12 | 99 | 17 | 26 | 56 | 66 | 85 | 28 | 39 | 48 | 74 |
+| 8 | 1 | 7 | 51 | 44 | 97 | 47 | 65 | 53 | 63 | 54 | 40 |
+| 9 | 66 | 24 | 17 | 30 | 38 | 82 | 59 | 25 | 58 | 85 | 25 |
+| 10 | 89 | 13 | 25 | 20 | 36 | 28 | 69 | 66 | 29 | 24 | 5 |
+| 11 | 81 | 37 | 77 | 88 | 57 | 38 | 90 | 94 | 83 | 76 | 14 |
+
+## model_id=6
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 38 | 9 | 71 | 88 | 82 | 48 | 14 | 4 | 43 | 19 | 99 |
+| 2 | 51 | 16 | 98 | 41 | 67 | 76 | 28 | 6 | 6 | 0 | 9 |
+| 3 | 48 | 95 | 56 | 23 | 65 | 66 | 87 | 49 | 9 | 25 | 82 |
+| 4 | 80 | 32 | 81 | 6 | 24 | 54 | 55 | 65 | 76 | 56 | 24 |
+| 5 | 12 | 91 | 76 | 67 | 8 | 23 | 47 | 57 | 75 | 43 | 25 |
+| 6 | 74 | 10 | 31 | 11 | 72 | 79 | 36 | 95 | 50 | 46 | 92 |
+| 7 | 24 | 77 | 0 | 50 | 75 | 48 | 14 | 97 | 69 | 60 | 11 |
+| 8 | 62 | 58 | 5 | 50 | 45 | 24 | 50 | 46 | 57 | 60 | 5 |
+| 9 | 9 | 48 | 5 | 16 | 29 | 85 | 19 | 66 | 4 | 94 | 25 |
+| 10 | 0 | 4 | 97 | 22 | 53 | 95 | 20 | 25 | 9 | 11 | 46 |
+| 11 | 96 | 28 | 89 | 68 | 21 | 88 | 81 | 68 | 62 | 77 | 92 |
+
+## model_id=7
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 80 | 26 | 0 | 1 | 9 | 17 | 75 | 28 | 21 | 35 |
+| 2 | 81 | 90 | 17 | 70 | 34 | 88 | 37 | 88 | 9 | 24 | 25 |
+| 3 | 39 | 95 | 55 | 20 | 82 | 69 | 84 | 82 | 43 | 71 | 84 |
+| 4 | 98 | 0 | 51 | 33 | 0 | 38 | 15 | 41 | 62 | 83 | 52 |
+| 5 | 85 | 72 | 12 | 57 | 31 | 22 | 69 | 48 | 11 | 51 | 14 |
+| 6 | 90 | 10 | 69 | 15 | 72 | 94 | 84 | 39 | 70 | 56 | 63 |
+| 7 | 29 | 87 | 90 | 55 | 0 | 4 | 11 | 15 | 35 | 91 | 24 |
+| 8 | 4 | 40 | 57 | 57 | 97 | 44 | 61 | 81 | 25 | 83 | 11 |
+| 9 | 69 | 50 | 51 | 62 | 95 | 68 | 56 | 33 | 92 | 48 | 56 |
+| 10 | 38 | 15 | 4 | 46 | 64 | 81 | 17 | 58 | 11 | 81 | 82 |
+| 11 | 54 | 41 | 60 | 92 | 86 | 8 | 60 | 55 | 45 | 8 | 44 |
+
+## model_id=8
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 11 | 49 | 65 | 90 | 47 | 72 | 22 | 28 | 97 | 79 | 8 |
+| 2 | 81 | 30 | 54 | 41 | 68 | 12 | 57 | 12 | 73 | 42 | 7 |
+| 3 | 28 | 82 | 17 | 78 | 38 | 56 | 52 | 69 | 73 | 74 | 80 |
+| 4 | 12 | 59 | 37 | 88 | 2 | 67 | 37 | 36 | 27 | 14 | 11 |
+| 5 | 66 | 76 | 17 | 81 | 29 | 99 | 88 | 35 | 52 | 74 | 74 |
+| 6 | 35 | 18 | 47 | 31 | 9 | 6 | 7 | 18 | 20 | 11 | 75 |
+| 7 | 4 | 87 | 13 | 55 | 51 | 46 | 38 | 66 | 25 | 88 | 86 |
+| 8 | 50 | 1 | 96 | 24 | 13 | 16 | 50 | 0 | 2 | 29 | 58 |
+| 9 | 36 | 69 | 25 | 94 | 92 | 20 | 66 | 32 | 99 | 91 | 36 |
+| 10 | 90 | 36 | 22 | 65 | 94 | 6 | 62 | 5 | 62 | 51 | 55 |
+| 11 | 85 | 45 | 11 | 23 | 30 | 61 | 16 | 55 | 29 | 56 | 47 |
+
+## model_id=9
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 78 | 60 | 74 | 82 | 0 | 72 | 70 | 29 | 2 | 74 | 60 |
+| 2 | 19 | 5 | 37 | 68 | 26 | 34 | 22 | 75 | 60 | 80 | 51 |
+| 3 | 37 | 24 | 99 | 98 | 2 | 34 | 44 | 14 | 43 | 54 | 89 |
+| 4 | 8 | 10 | 34 | 15 | 57 | 84 | 33 | 8 | 79 | 75 | 20 |
+| 5 | 21 | 42 | 33 | 42 | 45 | 22 | 27 | 33 | 67 | 20 | 11 |
+| 6 | 94 | 69 | 82 | 4 | 13 | 59 | 6 | 72 | 41 | 33 | 21 |
+| 7 | 1 | 30 | 0 | 77 | 29 | 6 | 49 | 45 | 69 | 89 | 95 |
+| 8 | 73 | 4 | 23 | 68 | 60 | 31 | 16 | 49 | 40 | 16 | 78 |
+| 9 | 73 | 24 | 58 | 87 | 63 | 30 | 94 | 11 | 47 | 40 | 67 |
+| 10 | 97 | 55 | 95 | 42 | 83 | 58 | 61 | 35 | 13 | 26 | 89 |
+| 11 | 7 | 70 | 87 | 3 | 22 | 94 | 43 | 44 | 66 | 66 | 16 |
+
+## model_id=10
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 38 | 1 | 17 | 4 | 41 | 9 | 64 | 50 | 60 | 21 | 30 |
+| 2 | 32 | 42 | 73 | 16 | 96 | 75 | 80 | 68 | 72 | 14 | 55 |
+| 3 | 86 | 13 | 94 | 22 | 49 | 49 | 32 | 57 | 65 | 46 | 81 |
+| 4 | 45 | 98 | 68 | 40 | 27 | 42 | 86 | 39 | 72 | 24 | 48 |
+| 5 | 25 | 12 | 89 | 17 | 35 | 88 | 86 | 24 | 99 | 90 | 36 |
+| 6 | 36 | 18 | 82 | 88 | 56 | 90 | 8 | 99 | 22 | 58 | 7 |
+| 7 | 79 | 59 | 30 | 51 | 54 | 22 | 31 | 48 | 74 | 11 | 14 |
+| 8 | 33 | 13 | 86 | 49 | 53 | 54 | 42 | 61 | 49 | 53 | 67 |
+| 9 | 64 | 2 | 88 | 48 | 76 | 79 | 70 | 51 | 45 | 73 | 73 |
+| 10 | 98 | 42 | 72 | 11 | 24 | 77 | 61 | 43 | 78 | 88 | 37 |
+| 11 | 58 | 92 | 89 | 37 | 63 | 22 | 77 | 57 | 99 | 24 | 43 |
+
+## model_id=11
+| photographer_id\backdrop_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 17 | 89 | 70 | 86 | 90 | 33 | 7 | 58 | 80 | 62 | 89 |
+| 2 | 63 | 14 | 89 | 88 | 31 | 68 | 31 | 66 | 89 | 60 | 53 |
+| 3 | 28 | 51 | 66 | 21 | 2 | 84 | 40 | 65 | 52 | 94 | 16 |
+| 4 | 98 | 90 | 44 | 56 | 48 | 93 | 88 | 31 | 42 | 38 | 60 |
+| 5 | 90 | 20 | 44 | 39 | 5 | 6 | 73 | 46 | 99 | 74 | 7 |
+| 6 | 49 | 26 | 87 | 42 | 88 | 14 | 8 | 44 | 40 | 24 | 86 |
+| 7 | 47 | 86 | 65 | 99 | 4 | 28 | 35 | 57 | 64 | 38 | 7 |
+| 8 | 16 | 81 | 22 | 59 | 94 | 13 | 30 | 50 | 35 | 33 | 29 |
+| 9 | 45 | 42 | 89 | 7 | 65 | 21 | 51 | 50 | 23 | 16 | 35 |
+| 10 | 61 | 37 | 43 | 69 | 3 | 49 | 82 | 31 | 75 | 84 | 10 |
+| 11 | 35 | 27 | 16 | 86 | 26 | 20 | 36 | 81 | 99 | 43 | 38 |
+
+The team aimed to pick one such triple for each of the 11 models (from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11) so as to minimize the total retouch time.
+
+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': [[[21, 55, 20, 85, 90, 92, 71, 80, 46, 88, 71], [20, 99, 13, 48, 72, 18, 82, 79, 92, 57, 72], [96, 13, 48, 95, 59, 46, 31, 33, 12, 28, 59], [38, 5, 87, 23, 5, 24, 76, 53, 65, 54, 51], [66, 84, 55, 88, 87, 97, 93, 47, 60, 14, 1], [90, 16, 12, 53, 19, 24, 67, 38, 67, 52, 52], [80, 9, 84, 48, 22, 73, 53, 13, 55, 7, 29], [12, 32, 40, 73, 46, 50, 37, 76, 27, 7, 48], [89, 2, 42, 88, 3, 35, 89, 28, 45, 83, 62], [82, 26, 49, 25, 14, 79, 18, 28, 99, 75, 27], [5, 46, 90, 73, 15, 50, 14, 52, 28, 92, 14]], [[80, 69, 70, 26, 86, 60, 53, 40, 52, 0, 30], [10, 98, 67, 79, 2, 97, 48, 5, 46, 25, 95], [38, 13, 74, 24, 18, 20, 71, 78, 49, 14, 68], [24, 43, 4, 50, 60, 79, 60, 18, 75, 24, 49], [35, 91, 45, 80, 53, 45, 30, 86, 12, 7, 15], [24, 12, 82, 56, 74, 24, 28, 52, 72, 5, 45], [59, 25, 18, 19, 84, 26, 88, 33, 12, 19, 37], [65, 28, 73, 25, 66, 64, 40, 19, 89, 35, 57], [69, 81, 1, 30, 97, 44, 31, 14, 42, 49, 77], [21, 21, 93, 88, 76, 0, 95, 40, 54, 85, 67], [72, 84, 90, 13, 52, 69, 48, 37, 9, 39, 74]], [[30, 23, 19, 15, 4, 49, 42, 82, 58, 36, 38], [60, 16, 94, 60, 25, 24, 66, 88, 0, 66, 65], [19, 45, 57, 48, 57, 77, 71, 53, 37, 51, 48], [5, 74, 11, 40, 17, 62, 94, 79, 68, 98, 16], [10, 34, 32, 1, 61, 59, 41, 19, 93, 0, 95], [68, 82, 88, 72, 19, 16, 54, 29, 59, 38, 72], [95, 77, 98, 28, 44, 60, 20, 42, 14, 37, 60], [67, 50, 14, 46, 10, 3, 67, 18, 33, 74, 59], [56, 25, 41, 41, 76, 40, 7, 89, 3, 67, 29], [62, 69, 98, 2, 50, 77, 73, 69, 32, 49, 58], [56, 26, 17, 72, 82, 79, 18, 35, 89, 54, 51]], [[87, 64, 29, 38, 81, 88, 33, 53, 81, 11, 23], [53, 48, 82, 70, 18, 53, 58, 53, 89, 62, 48], [35, 74, 51, 81, 73, 5, 58, 89, 54, 86, 21], [48, 19, 81, 44, 91, 76, 98, 65, 96, 51, 53], [2, 42, 71, 7, 52, 88, 41, 29, 74, 21, 67], [63, 75, 43, 96, 41, 98, 73, 25, 76, 18, 30], [51, 6, 90, 0, 68, 82, 16, 50, 60, 16, 34], [14, 66, 80, 46, 69, 6, 62, 76, 91, 77, 9], [96, 30, 47, 37, 18, 83, 91, 59, 89, 63, 81], [38, 56, 43, 68, 70, 38, 24, 91, 32, 4, 69], [26, 73, 84, 79, 78, 89, 66, 20, 27, 83, 37]], [[69, 45, 54, 56, 73, 31, 96, 69, 10, 40, 16], [55, 7, 13, 0, 0, 28, 74, 83, 99, 7, 21], [93, 49, 56, 38, 84, 4, 88, 15, 54, 46, 69], [12, 1, 35, 58, 44, 94, 77, 94, 65, 52, 31], [42, 11, 20, 91, 92, 71, 34, 31, 8, 57, 76], [43, 18, 70, 98, 81, 22, 52, 18, 36, 86, 42], [12, 99, 17, 26, 56, 66, 85, 28, 39, 48, 74], [1, 7, 51, 44, 97, 47, 65, 53, 63, 54, 40], [66, 24, 17, 30, 38, 82, 59, 25, 58, 85, 25], [89, 13, 25, 20, 36, 28, 69, 66, 29, 24, 5], [81, 37, 77, 88, 57, 38, 90, 94, 83, 76, 14]], [[38, 9, 71, 88, 82, 48, 14, 4, 43, 19, 99], [51, 16, 98, 41, 67, 76, 28, 6, 6, 0, 9], [48, 95, 56, 23, 65, 66, 87, 49, 9, 25, 82], [80, 32, 81, 6, 24, 54, 55, 65, 76, 56, 24], [12, 91, 76, 67, 8, 23, 47, 57, 75, 43, 25], [74, 10, 31, 11, 72, 79, 36, 95, 50, 46, 92], [24, 77, 0, 50, 75, 48, 14, 97, 69, 60, 11], [62, 58, 5, 50, 45, 24, 50, 46, 57, 60, 5], [9, 48, 5, 16, 29, 85, 19, 66, 4, 94, 25], [0, 4, 97, 22, 53, 95, 20, 25, 9, 11, 46], [96, 28, 89, 68, 21, 88, 81, 68, 62, 77, 92]], [[34, 80, 26, 0, 1, 9, 17, 75, 28, 21, 35], [81, 90, 17, 70, 34, 88, 37, 88, 9, 24, 25], [39, 95, 55, 20, 82, 69, 84, 82, 43, 71, 84], [98, 0, 51, 33, 0, 38, 15, 41, 62, 83, 52], [85, 72, 12, 57, 31, 22, 69, 48, 11, 51, 14], [90, 10, 69, 15, 72, 94, 84, 39, 70, 56, 63], [29, 87, 90, 55, 0, 4, 11, 15, 35, 91, 24], [4, 40, 57, 57, 97, 44, 61, 81, 25, 83, 11], [69, 50, 51, 62, 95, 68, 56, 33, 92, 48, 56], [38, 15, 4, 46, 64, 81, 17, 58, 11, 81, 82], [54, 41, 60, 92, 86, 8, 60, 55, 45, 8, 44]], [[11, 49, 65, 90, 47, 72, 22, 28, 97, 79, 8], [81, 30, 54, 41, 68, 12, 57, 12, 73, 42, 7], [28, 82, 17, 78, 38, 56, 52, 69, 73, 74, 80], [12, 59, 37, 88, 2, 67, 37, 36, 27, 14, 11], [66, 76, 17, 81, 29, 99, 88, 35, 52, 74, 74], [35, 18, 47, 31, 9, 6, 7, 18, 20, 11, 75], [4, 87, 13, 55, 51, 46, 38, 66, 25, 88, 86], [50, 1, 96, 24, 13, 16, 50, 0, 2, 29, 58], [36, 69, 25, 94, 92, 20, 66, 32, 99, 91, 36], [90, 36, 22, 65, 94, 6, 62, 5, 62, 51, 55], [85, 45, 11, 23, 30, 61, 16, 55, 29, 56, 47]], [[78, 60, 74, 82, 0, 72, 70, 29, 2, 74, 60], [19, 5, 37, 68, 26, 34, 22, 75, 60, 80, 51], [37, 24, 99, 98, 2, 34, 44, 14, 43, 54, 89], [8, 10, 34, 15, 57, 84, 33, 8, 79, 75, 20], [21, 42, 33, 42, 45, 22, 27, 33, 67, 20, 11], [94, 69, 82, 4, 13, 59, 6, 72, 41, 33, 21], [1, 30, 0, 77, 29, 6, 49, 45, 69, 89, 95], [73, 4, 23, 68, 60, 31, 16, 49, 40, 16, 78], [73, 24, 58, 87, 63, 30, 94, 11, 47, 40, 67], [97, 55, 95, 42, 83, 58, 61, 35, 13, 26, 89], [7, 70, 87, 3, 22, 94, 43, 44, 66, 66, 16]], [[38, 1, 17, 4, 41, 9, 64, 50, 60, 21, 30], [32, 42, 73, 16, 96, 75, 80, 68, 72, 14, 55], [86, 13, 94, 22, 49, 49, 32, 57, 65, 46, 81], [45, 98, 68, 40, 27, 42, 86, 39, 72, 24, 48], [25, 12, 89, 17, 35, 88, 86, 24, 99, 90, 36], [36, 18, 82, 88, 56, 90, 8, 99, 22, 58, 7], [79, 59, 30, 51, 54, 22, 31, 48, 74, 11, 14], [33, 13, 86, 49, 53, 54, 42, 61, 49, 53, 67], [64, 2, 88, 48, 76, 79, 70, 51, 45, 73, 73], [98, 42, 72, 11, 24, 77, 61, 43, 78, 88, 37], [58, 92, 89, 37, 63, 22, 77, 57, 99, 24, 43]], [[17, 89, 70, 86, 90, 33, 7, 58, 80, 62, 89], [63, 14, 89, 88, 31, 68, 31, 66, 89, 60, 53], [28, 51, 66, 21, 2, 84, 40, 65, 52, 94, 16], [98, 90, 44, 56, 48, 93, 88, 31, 42, 38, 60], [90, 20, 44, 39, 5, 6, 73, 46, 99, 74, 7], [49, 26, 87, 42, 88, 14, 8, 44, 40, 24, 86], [47, 86, 65, 99, 4, 28, 35, 57, 64, 38, 7], [16, 81, 22, 59, 94, 13, 30, 50, 35, 33, 29], [45, 42, 89, 7, 65, 21, 51, 50, 23, 16, 35], [61, 37, 43, 69, 3, 49, 82, 31, 75, 84, 10], [35, 27, 16, 86, 26, 20, 36, 81, 99, 43, 38]]], 'objective': 25.0}","[[0, 4, 10], [1, 0, 9], [2, 1, 8], [3, 2, 5], [4, 7, 0], [5, 6, 2], [6, 3, 4], [7, 9, 7], [8, 10, 3], [9, 8, 1], [10, 5, 6]]",25.0,"{'problem_type': 'AP3', 'n': 11, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], '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': 92}, {'i': 1, 'j': 1, 'k': 7, 'cost': 71}, {'i': 1, 'j': 1, 'k': 8, 'cost': 80}, {'i': 1, 'j': 1, 'k': 9, 'cost': 46}, {'i': 1, 'j': 1, 'k': 10, 'cost': 88}, {'i': 1, 'j': 1, 'k': 11, '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}, {'i': 1, 'j': 2, 'k': 5, 'cost': 72}, {'i': 1, 'j': 2, 'k': 6, 'cost': 18}, {'i': 1, 'j': 2, 'k': 7, 'cost': 82}, {'i': 1, 'j': 2, 'k': 8, 'cost': 79}, {'i': 1, 'j': 2, 'k': 9, 'cost': 92}, {'i': 1, 'j': 2, 'k': 10, 'cost': 57}, {'i': 1, 'j': 2, 'k': 11, 'cost': 72}, {'i': 1, 'j': 3, 'k': 1, 'cost': 96}, {'i': 1, 'j': 3, 'k': 2, 'cost': 13}, {'i': 1, 'j': 3, 'k': 3, 'cost': 48}, {'i': 1, 'j': 3, 'k': 4, 'cost': 95}, {'i': 1, 'j': 3, 'k': 5, 'cost': 59}, {'i': 1, 'j': 3, 'k': 6, 'cost': 46}, {'i': 1, 'j': 3, 'k': 7, 'cost': 31}, {'i': 1, 'j': 3, 'k': 8, 'cost': 33}, {'i': 1, 'j': 3, 'k': 9, 'cost': 12}, {'i': 1, 'j': 3, 'k': 10, 'cost': 28}, {'i': 1, 'j': 3, 'k': 11, 'cost': 59}, {'i': 1, 'j': 4, 'k': 1, 'cost': 38}, {'i': 1, 'j': 4, 'k': 2, 'cost': 5}, {'i': 1, 'j': 4, 'k': 3, 'cost': 87}, {'i': 1, 'j': 4, 'k': 4, 'cost': 23}, {'i': 1, 'j': 4, 'k': 5, 'cost': 5}, {'i': 1, 'j': 4, 'k': 6, 'cost': 24}, {'i': 1, 'j': 4, 'k': 7, 'cost': 76}, {'i': 1, 'j': 4, 'k': 8, 'cost': 53}, {'i': 1, 'j': 4, 'k': 9, 'cost': 65}, {'i': 1, 'j': 4, 'k': 10, 'cost': 54}, {'i': 1, 'j': 4, 'k': 11, 'cost': 51}, {'i': 1, 'j': 5, 'k': 1, 'cost': 66}, {'i': 1, 'j': 5, 'k': 2, 'cost': 84}, {'i': 1, 'j': 5, 'k': 3, 'cost': 55}, {'i': 1, 'j': 5, 'k': 4, 'cost': 88}, {'i': 1, 'j': 5, 'k': 5, 'cost': 87}, {'i': 1, 'j': 5, 'k': 6, 'cost': 97}, {'i': 1, 'j': 5, 'k': 7, 'cost': 93}, {'i': 1, 'j': 5, 'k': 8, 'cost': 47}, {'i': 1, 'j': 5, 'k': 9, 'cost': 60}, {'i': 1, 'j': 5, 'k': 10, 'cost': 14}, {'i': 1, 'j': 5, 'k': 11, 'cost': 1}, {'i': 1, 'j': 6, 'k': 1, 'cost': 90}, {'i': 1, 'j': 6, 'k': 2, 'cost': 16}, {'i': 1, 'j': 6, 'k': 3, 'cost': 12}, {'i': 1, 'j': 6, 'k': 4, 'cost': 53}, {'i': 1, 'j': 6, 'k': 5, 'cost': 19}, {'i': 1, 'j': 6, 'k': 6, 'cost': 24}, {'i': 1, 'j': 6, 'k': 7, 'cost': 67}, {'i': 1, 'j': 6, 'k': 8, 'cost': 38}, {'i': 1, 'j': 6, 'k': 9, 'cost': 67}, {'i': 1, 'j': 6, 'k': 10, 'cost': 52}, {'i': 1, 'j': 6, 'k': 11, 'cost': 52}, {'i': 1, 'j': 7, 'k': 1, 'cost': 80}, {'i': 1, 'j': 7, 'k': 2, 'cost': 9}, {'i': 1, 'j': 7, 'k': 3, 'cost': 84}, {'i': 1, 'j': 7, 'k': 4, 'cost': 48}, {'i': 1, 'j': 7, 'k': 5, 'cost': 22}, {'i': 1, 'j': 7, 'k': 6, 'cost': 73}, {'i': 1, 'j': 7, 'k': 7, 'cost': 53}, {'i': 1, 'j': 7, 'k': 8, 'cost': 13}, {'i': 1, 'j': 7, 'k': 9, 'cost': 55}, {'i': 1, 'j': 7, 'k': 10, 'cost': 7}, {'i': 1, 'j': 7, 'k': 11, 'cost': 29}, {'i': 1, 'j': 8, 'k': 1, 'cost': 12}, {'i': 1, 'j': 8, 'k': 2, 'cost': 32}, {'i': 1, 'j': 8, 'k': 3, 'cost': 40}, {'i': 1, 'j': 8, 'k': 4, 'cost': 73}, {'i': 1, 'j': 8, 'k': 5, 'cost': 46}, {'i': 1, 'j': 8, 'k': 6, 'cost': 50}, {'i': 1, 'j': 8, 'k': 7, 'cost': 37}, {'i': 1, 'j': 8, 'k': 8, 'cost': 76}, {'i': 1, 'j': 8, 'k': 9, 'cost': 27}, {'i': 1, 'j': 8, 'k': 10, 'cost': 7}, {'i': 1, 'j': 8, 'k': 11, 'cost': 48}, {'i': 1, 'j': 9, 'k': 1, 'cost': 89}, {'i': 1, 'j': 9, 'k': 2, 'cost': 2}, {'i': 1, 'j': 9, 'k': 3, 'cost': 42}, {'i': 1, 'j': 9, 'k': 4, 'cost': 88}, {'i': 1, 'j': 9, 'k': 5, 'cost': 3}, {'i': 1, 'j': 9, 'k': 6, 'cost': 35}, {'i': 1, 'j': 9, 'k': 7, 'cost': 89}, {'i': 1, 'j': 9, 'k': 8, 'cost': 28}, {'i': 1, 'j': 9, 'k': 9, 'cost': 45}, {'i': 1, 'j': 9, 'k': 10, 'cost': 83}, {'i': 1, 'j': 9, 'k': 11, 'cost': 62}, {'i': 1, 'j': 10, 'k': 1, 'cost': 82}, {'i': 1, 'j': 10, 'k': 2, 'cost': 26}, {'i': 1, 'j': 10, 'k': 3, 'cost': 49}, {'i': 1, 'j': 10, 'k': 4, 'cost': 25}, {'i': 1, 'j': 10, 'k': 5, 'cost': 14}, {'i': 1, 'j': 10, 'k': 6, 'cost': 79}, {'i': 1, 'j': 10, 'k': 7, 'cost': 18}, {'i': 1, 'j': 10, 'k': 8, 'cost': 28}, {'i': 1, 'j': 10, 'k': 9, 'cost': 99}, {'i': 1, 'j': 10, 'k': 10, 'cost': 75}, {'i': 1, 'j': 10, 'k': 11, 'cost': 27}, {'i': 1, 'j': 11, 'k': 1, 'cost': 5}, {'i': 1, 'j': 11, 'k': 2, 'cost': 46}, {'i': 1, 'j': 11, 'k': 3, 'cost': 90}, {'i': 1, 'j': 11, 'k': 4, 'cost': 73}, {'i': 1, 'j': 11, 'k': 5, 'cost': 15}, {'i': 1, 'j': 11, 'k': 6, 'cost': 50}, {'i': 1, 'j': 11, 'k': 7, 'cost': 14}, {'i': 1, 'j': 11, 'k': 8, 'cost': 52}, {'i': 1, 'j': 11, 'k': 9, 'cost': 28}, {'i': 1, 'j': 11, 'k': 10, 'cost': 92}, {'i': 1, 'j': 11, 'k': 11, 'cost': 14}, {'i': 2, 'j': 1, 'k': 1, 'cost': 80}, {'i': 2, 'j': 1, 'k': 2, 'cost': 69}, {'i': 2, 'j': 1, 'k': 3, 'cost': 70}, {'i': 2, 'j': 1, 'k': 4, 'cost': 26}, {'i': 2, 'j': 1, 'k': 5, 'cost': 86}, {'i': 2, 'j': 1, 'k': 6, 'cost': 60}, {'i': 2, 'j': 1, 'k': 7, 'cost': 53}, {'i': 2, 'j': 1, 'k': 8, 'cost': 40}, {'i': 2, 'j': 1, 'k': 9, 'cost': 52}, {'i': 2, 'j': 1, 'k': 10, 'cost': 0}, {'i': 2, 'j': 1, 'k': 11, 'cost': 30}, {'i': 2, 'j': 2, 'k': 1, 'cost': 10}, {'i': 2, 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90}, {'i': 10, 'j': 6, 'k': 7, 'cost': 8}, {'i': 10, 'j': 6, 'k': 8, 'cost': 99}, {'i': 10, 'j': 6, 'k': 9, 'cost': 22}, {'i': 10, 'j': 6, 'k': 10, 'cost': 58}, {'i': 10, 'j': 6, 'k': 11, 'cost': 7}, {'i': 10, 'j': 7, 'k': 1, 'cost': 79}, {'i': 10, 'j': 7, 'k': 2, 'cost': 59}, {'i': 10, 'j': 7, 'k': 3, 'cost': 30}, {'i': 10, 'j': 7, 'k': 4, 'cost': 51}, {'i': 10, 'j': 7, 'k': 5, 'cost': 54}, {'i': 10, 'j': 7, 'k': 6, 'cost': 22}, {'i': 10, 'j': 7, 'k': 7, 'cost': 31}, {'i': 10, 'j': 7, 'k': 8, 'cost': 48}, {'i': 10, 'j': 7, 'k': 9, 'cost': 74}, {'i': 10, 'j': 7, 'k': 10, 'cost': 11}, {'i': 10, 'j': 7, 'k': 11, 'cost': 14}, {'i': 10, 'j': 8, 'k': 1, 'cost': 33}, {'i': 10, 'j': 8, 'k': 2, 'cost': 13}, {'i': 10, 'j': 8, 'k': 3, 'cost': 86}, {'i': 10, 'j': 8, 'k': 4, 'cost': 49}, {'i': 10, 'j': 8, 'k': 5, 'cost': 53}, {'i': 10, 'j': 8, 'k': 6, 'cost': 54}, {'i': 10, 'j': 8, 'k': 7, 'cost': 42}, {'i': 10, 'j': 8, 'k': 8, 'cost': 61}, {'i': 10, 'j': 8, 'k': 9, 'cost': 49}, {'i': 10, 'j': 8, 'k': 10, 'cost': 53}, {'i': 10, 'j': 8, 'k': 11, 'cost': 67}, {'i': 10, 'j': 9, 'k': 1, 'cost': 64}, {'i': 10, 'j': 9, 'k': 2, 'cost': 2}, {'i': 10, 'j': 9, 'k': 3, 'cost': 88}, {'i': 10, 'j': 9, 'k': 4, 'cost': 48}, {'i': 10, 'j': 9, 'k': 5, 'cost': 76}, {'i': 10, 'j': 9, 'k': 6, 'cost': 79}, {'i': 10, 'j': 9, 'k': 7, 'cost': 70}, {'i': 10, 'j': 9, 'k': 8, 'cost': 51}, {'i': 10, 'j': 9, 'k': 9, 'cost': 45}, {'i': 10, 'j': 9, 'k': 10, 'cost': 73}, {'i': 10, 'j': 9, 'k': 11, 'cost': 73}, {'i': 10, 'j': 10, 'k': 1, 'cost': 98}, {'i': 10, 'j': 10, 'k': 2, 'cost': 42}, {'i': 10, 'j': 10, 'k': 3, 'cost': 72}, {'i': 10, 'j': 10, 'k': 4, 'cost': 11}, {'i': 10, 'j': 10, 'k': 5, 'cost': 24}, {'i': 10, 'j': 10, 'k': 6, 'cost': 77}, {'i': 10, 'j': 10, 'k': 7, 'cost': 61}, {'i': 10, 'j': 10, 'k': 8, 'cost': 43}, {'i': 10, 'j': 10, 'k': 9, 'cost': 78}, {'i': 10, 'j': 10, 'k': 10, 'cost': 88}, {'i': 10, 'j': 10, 'k': 11, 'cost': 37}, {'i': 10, 'j': 11, 'k': 1, 'cost': 58}, {'i': 10, 'j': 11, 'k': 2, 'cost': 92}, {'i': 10, 'j': 11, 'k': 3, 'cost': 89}, {'i': 10, 'j': 11, 'k': 4, 'cost': 37}, {'i': 10, 'j': 11, 'k': 5, 'cost': 63}, {'i': 10, 'j': 11, 'k': 6, 'cost': 22}, {'i': 10, 'j': 11, 'k': 7, 'cost': 77}, {'i': 10, 'j': 11, 'k': 8, 'cost': 57}, {'i': 10, 'j': 11, 'k': 9, 'cost': 99}, {'i': 10, 'j': 11, 'k': 10, 'cost': 24}, {'i': 10, 'j': 11, 'k': 11, 'cost': 43}, {'i': 11, 'j': 1, 'k': 1, 'cost': 17}, {'i': 11, 'j': 1, 'k': 2, 'cost': 89}, {'i': 11, 'j': 1, 'k': 3, 'cost': 70}, {'i': 11, 'j': 1, 'k': 4, 'cost': 86}, {'i': 11, 'j': 1, 'k': 5, 'cost': 90}, {'i': 11, 'j': 1, 'k': 6, 'cost': 33}, {'i': 11, 'j': 1, 'k': 7, 'cost': 7}, {'i': 11, 'j': 1, 'k': 8, 'cost': 58}, {'i': 11, 'j': 1, 'k': 9, 'cost': 80}, {'i': 11, 'j': 1, 'k': 10, 'cost': 62}, {'i': 11, 'j': 1, 'k': 11, 'cost': 89}, {'i': 11, 'j': 2, 'k': 1, 'cost': 63}, {'i': 11, 'j': 2, 'k': 2, 'cost': 14}, {'i': 11, 'j': 2, 'k': 3, 'cost': 89}, {'i': 11, 'j': 2, 'k': 4, 'cost': 88}, {'i': 11, 'j': 2, 'k': 5, 'cost': 31}, {'i': 11, 'j': 2, 'k': 6, 'cost': 68}, {'i': 11, 'j': 2, 'k': 7, 'cost': 31}, {'i': 11, 'j': 2, 'k': 8, 'cost': 66}, {'i': 11, 'j': 2, 'k': 9, 'cost': 89}, {'i': 11, 'j': 2, 'k': 10, 'cost': 60}, {'i': 11, 'j': 2, 'k': 11, 'cost': 53}, {'i': 11, 'j': 3, 'k': 1, 'cost': 28}, {'i': 11, 'j': 3, 'k': 2, 'cost': 51}, {'i': 11, 'j': 3, 'k': 3, 'cost': 66}, {'i': 11, 'j': 3, 'k': 4, 'cost': 21}, {'i': 11, 'j': 3, 'k': 5, 'cost': 2}, {'i': 11, 'j': 3, 'k': 6, 'cost': 84}, {'i': 11, 'j': 3, 'k': 7, 'cost': 40}, {'i': 11, 'j': 3, 'k': 8, 'cost': 65}, {'i': 11, 'j': 3, 'k': 9, 'cost': 52}, {'i': 11, 'j': 3, 'k': 10, 'cost': 94}, {'i': 11, 'j': 3, 'k': 11, 'cost': 16}, {'i': 11, 'j': 4, 'k': 1, 'cost': 98}, {'i': 11, 'j': 4, 'k': 2, 'cost': 90}, {'i': 11, 'j': 4, 'k': 3, 'cost': 44}, {'i': 11, 'j': 4, 'k': 4, 'cost': 56}, {'i': 11, 'j': 4, 'k': 5, 'cost': 48}, {'i': 11, 'j': 4, 'k': 6, 'cost': 93}, {'i': 11, 'j': 4, 'k': 7, 'cost': 88}, {'i': 11, 'j': 4, 'k': 8, 'cost': 31}, {'i': 11, 'j': 4, 'k': 9, 'cost': 42}, {'i': 11, 'j': 4, 'k': 10, 'cost': 38}, {'i': 11, 'j': 4, 'k': 11, 'cost': 60}, {'i': 11, 'j': 5, 'k': 1, 'cost': 90}, {'i': 11, 'j': 5, 'k': 2, 'cost': 20}, {'i': 11, 'j': 5, 'k': 3, 'cost': 44}, {'i': 11, 'j': 5, 'k': 4, 'cost': 39}, {'i': 11, 'j': 5, 'k': 5, 'cost': 5}, {'i': 11, 'j': 5, 'k': 6, 'cost': 6}, {'i': 11, 'j': 5, 'k': 7, 'cost': 73}, {'i': 11, 'j': 5, 'k': 8, 'cost': 46}, {'i': 11, 'j': 5, 'k': 9, 'cost': 99}, {'i': 11, 'j': 5, 'k': 10, 'cost': 74}, {'i': 11, 'j': 5, 'k': 11, 'cost': 7}, {'i': 11, 'j': 6, 'k': 1, 'cost': 49}, {'i': 11, 'j': 6, 'k': 2, 'cost': 26}, {'i': 11, 'j': 6, 'k': 3, 'cost': 87}, {'i': 11, 'j': 6, 'k': 4, 'cost': 42}, {'i': 11, 'j': 6, 'k': 5, 'cost': 88}, {'i': 11, 'j': 6, 'k': 6, 'cost': 14}, {'i': 11, 'j': 6, 'k': 7, 'cost': 8}, {'i': 11, 'j': 6, 'k': 8, 'cost': 44}, {'i': 11, 'j': 6, 'k': 9, 'cost': 40}, {'i': 11, 'j': 6, 'k': 10, 'cost': 24}, {'i': 11, 'j': 6, 'k': 11, 'cost': 86}, {'i': 11, 'j': 7, 'k': 1, 'cost': 47}, {'i': 11, 'j': 7, 'k': 2, 'cost': 86}, {'i': 11, 'j': 7, 'k': 3, 'cost': 65}, {'i': 11, 'j': 7, 'k': 4, 'cost': 99}, {'i': 11, 'j': 7, 'k': 5, 'cost': 4}, {'i': 11, 'j': 7, 'k': 6, 'cost': 28}, {'i': 11, 'j': 7, 'k': 7, 'cost': 35}, {'i': 11, 'j': 7, 'k': 8, 'cost': 57}, {'i': 11, 'j': 7, 'k': 9, 'cost': 64}, {'i': 11, 'j': 7, 'k': 10, 'cost': 38}, {'i': 11, 'j': 7, 'k': 11, 'cost': 7}, {'i': 11, 'j': 8, 'k': 1, 'cost': 16}, {'i': 11, 'j': 8, 'k': 2, 'cost': 81}, {'i': 11, 'j': 8, 'k': 3, 'cost': 22}, {'i': 11, 'j': 8, 'k': 4, 'cost': 59}, {'i': 11, 'j': 8, 'k': 5, 'cost': 94}, {'i': 11, 'j': 8, 'k': 6, 'cost': 13}, {'i': 11, 'j': 8, 'k': 7, 'cost': 30}, {'i': 11, 'j': 8, 'k': 8, 'cost': 50}, {'i': 11, 'j': 8, 'k': 9, 'cost': 35}, {'i': 11, 'j': 8, 'k': 10, 'cost': 33}, {'i': 11, 'j': 8, 'k': 11, 'cost': 29}, {'i': 11, 'j': 9, 'k': 1, 'cost': 45}, {'i': 11, 'j': 9, 'k': 2, 'cost': 42}, {'i': 11, 'j': 9, 'k': 3, 'cost': 89}, {'i': 11, 'j': 9, 'k': 4, 'cost': 7}, {'i': 11, 'j': 9, 'k': 5, 'cost': 65}, {'i': 11, 'j': 9, 'k': 6, 'cost': 21}, {'i': 11, 'j': 9, 'k': 7, 'cost': 51}, {'i': 11, 'j': 9, 'k': 8, 'cost': 50}, {'i': 11, 'j': 9, 'k': 9, 'cost': 23}, {'i': 11, 'j': 9, 'k': 10, 'cost': 16}, {'i': 11, 'j': 9, 'k': 11, 'cost': 35}, {'i': 11, 'j': 10, 'k': 1, 'cost': 61}, {'i': 11, 'j': 10, 'k': 2, 'cost': 37}, {'i': 11, 'j': 10, 'k': 3, 'cost': 43}, {'i': 11, 'j': 10, 'k': 4, 'cost': 69}, {'i': 11, 'j': 10, 'k': 5, 'cost': 3}, {'i': 11, 'j': 10, 'k': 6, 'cost': 49}, {'i': 11, 'j': 10, 'k': 7, 'cost': 82}, {'i': 11, 'j': 10, 'k': 8, 'cost': 31}, {'i': 11, 'j': 10, 'k': 9, 'cost': 75}, {'i': 11, 'j': 10, 'k': 10, 'cost': 84}, {'i': 11, 'j': 10, 'k': 11, 'cost': 10}, {'i': 11, 'j': 11, 'k': 1, 'cost': 35}, {'i': 11, 'j': 11, 'k': 2, 'cost': 27}, {'i': 11, 'j': 11, 'k': 3, 'cost': 16}, {'i': 11, 'j': 11, 'k': 4, 'cost': 86}, {'i': 11, 'j': 11, 'k': 5, 'cost': 26}, {'i': 11, 'j': 11, 'k': 6, 'cost': 20}, {'i': 11, 'j': 11, 'k': 7, 'cost': 36}, {'i': 11, 'j': 11, 'k': 8, 'cost': 81}, {'i': 11, 'j': 11, 'k': 9, 'cost': 99}, {'i': 11, 'j': 11, 'k': 10, 'cost': 43}, {'i': 11, 'j': 11, 'k': 11, 'cost': 38}]}","[[1, 5, 11], [2, 1, 10], [3, 2, 9], [4, 3, 6], [5, 8, 1], [6, 7, 3], [7, 4, 5], [8, 10, 8], [9, 11, 4], [10, 9, 2], [11, 6, 7]]",5,markdown_table,1
+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=9
+# index_ids=0, 1, 2, 3, 4, 5, 6, 7, 8
+
+# 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 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 9 | 56 | 8 | 27 | 54 | 10 | 8 | 98 | 67 |
+| 1 | 66 | 64 | 14 | 31 | 56 | 45 | 18 | 61 | 26 |
+| 2 | 12 | 23 | 94 | 80 | 87 | 23 | 34 | 82 | 53 |
+| 3 | 69 | 59 | 77 | 17 | 7 | 1 | 74 | 32 | 50 |
+| 4 | 51 | 33 | 20 | 58 | 16 | 99 | 2 | 38 | 8 |
+| 5 | 63 | 70 | 29 | 74 | 24 | 10 | 44 | 55 | 64 |
+| 6 | 68 | 77 | 64 | 35 | 38 | 21 | 98 | 83 | 40 |
+| 7 | 38 | 26 | 48 | 28 | 14 | 35 | 73 | 49 | 75 |
+| 8 | 78 | 61 | 25 | 3 | 65 | 84 | 4 | 37 | 34 |
+
+## table_id=1
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 62 | 45 | 3 | 82 | 56 | 10 | 85 | 46 | 14 |
+| 1 | 85 | 40 | 87 | 55 | 66 | 20 | 20 | 86 | 46 |
+| 2 | 38 | 71 | 31 | 33 | 35 | 37 | 19 | 97 | 88 |
+| 3 | 15 | 88 | 75 | 64 | 17 | 92 | 89 | 44 | 51 |
+| 4 | 29 | 60 | 69 | 32 | 94 | 78 | 89 | 81 | 60 |
+| 5 | 22 | 3 | 43 | 84 | 20 | 74 | 75 | 30 | 9 |
+| 6 | 20 | 76 | 11 | 73 | 93 | 65 | 1 | 66 | 64 |
+| 7 | 35 | 75 | 90 | 80 | 24 | 76 | 46 | 34 | 97 |
+| 8 | 46 | 13 | 16 | 63 | 10 | 32 | 79 | 12 | 40 |
+
+## table_id=2
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 26 | 31 | 46 | 33 | 31 | 80 | 77 | 43 | 64 |
+| 1 | 24 | 33 | 48 | 28 | 86 | 96 | 84 | 28 | 4 |
+| 2 | 83 | 56 | 68 | 3 | 95 | 91 | 10 | 6 | 78 |
+| 3 | 9 | 92 | 84 | 86 | 22 | 26 | 43 | 45 | 76 |
+| 4 | 39 | 28 | 38 | 97 | 36 | 96 | 55 | 91 | 86 |
+| 5 | 92 | 77 | 72 | 60 | 3 | 14 | 18 | 91 | 37 |
+| 6 | 38 | 20 | 94 | 20 | 68 | 54 | 13 | 10 | 99 |
+| 7 | 56 | 41 | 12 | 70 | 87 | 34 | 25 | 78 | 38 |
+| 8 | 20 | 20 | 81 | 58 | 87 | 71 | 52 | 88 | 57 |
+
+## table_id=3
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 91 | 85 | 94 | 64 | 56 | 20 | 6 | 60 | 3 |
+| 1 | 22 | 17 | 26 | 86 | 96 | 72 | 77 | 93 | 90 |
+| 2 | 23 | 40 | 20 | 68 | 74 | 19 | 32 | 58 | 78 |
+| 3 | 86 | 45 | 10 | 17 | 61 | 77 | 50 | 80 | 17 |
+| 4 | 1 | 57 | 66 | 94 | 7 | 35 | 46 | 6 | 59 |
+| 5 | 8 | 93 | 63 | 81 | 84 | 43 | 86 | 82 | 44 |
+| 6 | 18 | 30 | 20 | 85 | 78 | 53 | 51 | 64 | 2 |
+| 7 | 47 | 30 | 29 | 75 | 0 | 36 | 38 | 54 | 64 |
+| 8 | 96 | 85 | 3 | 95 | 23 | 72 | 98 | 11 | 48 |
+
+## table_id=4
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 1 | 87 | 65 | 55 | 99 | 34 | 90 | 23 | 83 |
+| 1 | 62 | 32 | 81 | 89 | 98 | 77 | 27 | 57 | 36 |
+| 2 | 22 | 54 | 61 | 77 | 66 | 55 | 15 | 74 | 1 |
+| 3 | 58 | 16 | 51 | 31 | 41 | 44 | 67 | 64 | 19 |
+| 4 | 15 | 73 | 49 | 12 | 17 | 3 | 9 | 54 | 29 |
+| 5 | 49 | 85 | 13 | 4 | 0 | 56 | 82 | 81 | 80 |
+| 6 | 76 | 97 | 62 | 87 | 35 | 59 | 41 | 37 | 29 |
+| 7 | 84 | 20 | 84 | 92 | 98 | 75 | 96 | 86 | 30 |
+| 8 | 19 | 2 | 58 | 2 | 97 | 96 | 63 | 37 | 57 |
+
+## table_id=5
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 65 | 1 | 65 | 96 | 57 | 67 | 71 | 38 | 63 |
+| 1 | 22 | 70 | 74 | 52 | 21 | 30 | 17 | 73 | 23 |
+| 2 | 59 | 17 | 11 | 67 | 6 | 63 | 94 | 7 | 21 |
+| 3 | 84 | 52 | 94 | 94 | 76 | 99 | 23 | 9 | 7 |
+| 4 | 97 | 43 | 99 | 50 | 81 | 49 | 85 | 79 | 38 |
+| 5 | 33 | 70 | 80 | 37 | 33 | 92 | 59 | 63 | 57 |
+| 6 | 60 | 75 | 83 | 55 | 99 | 91 | 53 | 78 | 70 |
+| 7 | 87 | 5 | 47 | 35 | 40 | 54 | 91 | 82 | 5 |
+| 8 | 55 | 33 | 73 | 91 | 27 | 58 | 40 | 89 | 68 |
+
+## table_id=6
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 67 | 78 | 22 | 90 | 58 | 86 | 78 | 37 | 46 |
+| 1 | 79 | 56 | 66 | 55 | 0 | 90 | 44 | 76 | 64 |
+| 2 | 68 | 68 | 2 | 67 | 53 | 78 | 7 | 85 | 43 |
+| 3 | 39 | 84 | 46 | 26 | 29 | 42 | 26 | 89 | 35 |
+| 4 | 20 | 9 | 32 | 0 | 47 | 32 | 28 | 61 | 53 |
+| 5 | 41 | 81 | 41 | 77 | 49 | 20 | 76 | 6 | 94 |
+| 6 | 50 | 28 | 65 | 22 | 19 | 34 | 47 | 48 | 92 |
+| 7 | 94 | 51 | 84 | 57 | 58 | 80 | 26 | 66 | 14 |
+| 8 | 54 | 79 | 51 | 40 | 50 | 87 | 88 | 78 | 24 |
+
+## table_id=7
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 87 | 48 | 72 | 54 | 78 | 10 | 52 | 40 | 86 |
+| 1 | 3 | 68 | 50 | 94 | 23 | 65 | 71 | 49 | 49 |
+| 2 | 19 | 75 | 4 | 50 | 44 | 95 | 18 | 2 | 26 |
+| 3 | 8 | 4 | 50 | 41 | 97 | 10 | 48 | 13 | 55 |
+| 4 | 29 | 28 | 54 | 7 | 14 | 86 | 9 | 43 | 44 |
+| 5 | 80 | 64 | 24 | 2 | 58 | 53 | 41 | 13 | 13 |
+| 6 | 95 | 61 | 73 | 77 | 42 | 82 | 95 | 39 | 52 |
+| 7 | 16 | 60 | 80 | 16 | 92 | 46 | 55 | 10 | 16 |
+| 8 | 42 | 24 | 41 | 90 | 1 | 61 | 38 | 70 | 4 |
+
+## table_id=8
+| appetizer_vendor_id\dessert_vendor_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 34 | 9 | 21 | 25 | 10 | 42 | 54 | 36 | 86 |
+| 1 | 48 | 69 | 77 | 21 | 80 | 96 | 90 | 17 | 0 |
+| 2 | 59 | 32 | 24 | 71 | 70 | 33 | 6 | 78 | 53 |
+| 3 | 8 | 11 | 75 | 96 | 39 | 79 | 0 | 50 | 65 |
+| 4 | 55 | 56 | 53 | 69 | 90 | 43 | 99 | 83 | 21 |
+| 5 | 24 | 35 | 4 | 37 | 83 | 16 | 0 | 48 | 69 |
+| 6 | 79 | 4 | 25 | 8 | 85 | 44 | 0 | 42 | 5 |
+| 7 | 26 | 93 | 48 | 16 | 80 | 94 | 14 | 71 | 53 |
+| 8 | 29 | 20 | 16 | 76 | 11 | 19 | 90 | 56 | 68 |
+
+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': [[[9, 56, 8, 27, 54, 10, 8, 98, 67], [66, 64, 14, 31, 56, 45, 18, 61, 26], [12, 23, 94, 80, 87, 23, 34, 82, 53], [69, 59, 77, 17, 7, 1, 74, 32, 50], [51, 33, 20, 58, 16, 99, 2, 38, 8], [63, 70, 29, 74, 24, 10, 44, 55, 64], [68, 77, 64, 35, 38, 21, 98, 83, 40], [38, 26, 48, 28, 14, 35, 73, 49, 75], [78, 61, 25, 3, 65, 84, 4, 37, 34]], [[62, 45, 3, 82, 56, 10, 85, 46, 14], [85, 40, 87, 55, 66, 20, 20, 86, 46], [38, 71, 31, 33, 35, 37, 19, 97, 88], [15, 88, 75, 64, 17, 92, 89, 44, 51], [29, 60, 69, 32, 94, 78, 89, 81, 60], [22, 3, 43, 84, 20, 74, 75, 30, 9], [20, 76, 11, 73, 93, 65, 1, 66, 64], [35, 75, 90, 80, 24, 76, 46, 34, 97], [46, 13, 16, 63, 10, 32, 79, 12, 40]], [[26, 31, 46, 33, 31, 80, 77, 43, 64], [24, 33, 48, 28, 86, 96, 84, 28, 4], [83, 56, 68, 3, 95, 91, 10, 6, 78], [9, 92, 84, 86, 22, 26, 43, 45, 76], [39, 28, 38, 97, 36, 96, 55, 91, 86], [92, 77, 72, 60, 3, 14, 18, 91, 37], [38, 20, 94, 20, 68, 54, 13, 10, 99], [56, 41, 12, 70, 87, 34, 25, 78, 38], [20, 20, 81, 58, 87, 71, 52, 88, 57]], [[91, 85, 94, 64, 56, 20, 6, 60, 3], [22, 17, 26, 86, 96, 72, 77, 93, 90], [23, 40, 20, 68, 74, 19, 32, 58, 78], [86, 45, 10, 17, 61, 77, 50, 80, 17], [1, 57, 66, 94, 7, 35, 46, 6, 59], [8, 93, 63, 81, 84, 43, 86, 82, 44], [18, 30, 20, 85, 78, 53, 51, 64, 2], [47, 30, 29, 75, 0, 36, 38, 54, 64], [96, 85, 3, 95, 23, 72, 98, 11, 48]], [[1, 87, 65, 55, 99, 34, 90, 23, 83], [62, 32, 81, 89, 98, 77, 27, 57, 36], [22, 54, 61, 77, 66, 55, 15, 74, 1], [58, 16, 51, 31, 41, 44, 67, 64, 19], [15, 73, 49, 12, 17, 3, 9, 54, 29], [49, 85, 13, 4, 0, 56, 82, 81, 80], [76, 97, 62, 87, 35, 59, 41, 37, 29], [84, 20, 84, 92, 98, 75, 96, 86, 30], [19, 2, 58, 2, 97, 96, 63, 37, 57]], [[65, 1, 65, 96, 57, 67, 71, 38, 63], [22, 70, 74, 52, 21, 30, 17, 73, 23], [59, 17, 11, 67, 6, 63, 94, 7, 21], [84, 52, 94, 94, 76, 99, 23, 9, 7], [97, 43, 99, 50, 81, 49, 85, 79, 38], [33, 70, 80, 37, 33, 92, 59, 63, 57], [60, 75, 83, 55, 99, 91, 53, 78, 70], [87, 5, 47, 35, 40, 54, 91, 82, 5], [55, 33, 73, 91, 27, 58, 40, 89, 68]], [[67, 78, 22, 90, 58, 86, 78, 37, 46], [79, 56, 66, 55, 0, 90, 44, 76, 64], [68, 68, 2, 67, 53, 78, 7, 85, 43], [39, 84, 46, 26, 29, 42, 26, 89, 35], [20, 9, 32, 0, 47, 32, 28, 61, 53], [41, 81, 41, 77, 49, 20, 76, 6, 94], [50, 28, 65, 22, 19, 34, 47, 48, 92], [94, 51, 84, 57, 58, 80, 26, 66, 14], [54, 79, 51, 40, 50, 87, 88, 78, 24]], [[87, 48, 72, 54, 78, 10, 52, 40, 86], [3, 68, 50, 94, 23, 65, 71, 49, 49], [19, 75, 4, 50, 44, 95, 18, 2, 26], [8, 4, 50, 41, 97, 10, 48, 13, 55], [29, 28, 54, 7, 14, 86, 9, 43, 44], [80, 64, 24, 2, 58, 53, 41, 13, 13], [95, 61, 73, 77, 42, 82, 95, 39, 52], [16, 60, 80, 16, 92, 46, 55, 10, 16], [42, 24, 41, 90, 1, 61, 38, 70, 4]], [[34, 9, 21, 25, 10, 42, 54, 36, 86], [48, 69, 77, 21, 80, 96, 90, 17, 0], [59, 32, 24, 71, 70, 33, 6, 78, 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{'i': 7, 'j': 8, 'k': 8, 'cost': 4}, {'i': 8, 'j': 0, 'k': 0, 'cost': 34}, {'i': 8, 'j': 0, 'k': 1, 'cost': 9}, {'i': 8, 'j': 0, 'k': 2, 'cost': 21}, {'i': 8, 'j': 0, 'k': 3, 'cost': 25}, {'i': 8, 'j': 0, 'k': 4, 'cost': 10}, {'i': 8, 'j': 0, 'k': 5, 'cost': 42}, {'i': 8, 'j': 0, 'k': 6, 'cost': 54}, {'i': 8, 'j': 0, 'k': 7, 'cost': 36}, {'i': 8, 'j': 0, 'k': 8, 'cost': 86}, {'i': 8, 'j': 1, 'k': 0, 'cost': 48}, {'i': 8, 'j': 1, 'k': 1, 'cost': 69}, {'i': 8, 'j': 1, 'k': 2, 'cost': 77}, {'i': 8, 'j': 1, 'k': 3, 'cost': 21}, {'i': 8, 'j': 1, 'k': 4, 'cost': 80}, {'i': 8, 'j': 1, 'k': 5, 'cost': 96}, {'i': 8, 'j': 1, 'k': 6, 'cost': 90}, {'i': 8, 'j': 1, 'k': 7, 'cost': 17}, {'i': 8, 'j': 1, 'k': 8, 'cost': 0}, {'i': 8, 'j': 2, 'k': 0, 'cost': 59}, {'i': 8, 'j': 2, 'k': 1, 'cost': 32}, {'i': 8, 'j': 2, 'k': 2, 'cost': 24}, {'i': 8, 'j': 2, 'k': 3, 'cost': 71}, {'i': 8, 'j': 2, 'k': 4, 'cost': 70}, {'i': 8, 'j': 2, 'k': 5, 'cost': 33}, {'i': 8, 'j': 2, 'k': 6, 'cost': 6}, {'i': 8, 'j': 2, 'k': 7, 'cost': 78}, {'i': 8, 'j': 2, 'k': 8, 'cost': 53}, {'i': 8, 'j': 3, 'k': 0, 'cost': 8}, {'i': 8, 'j': 3, 'k': 1, 'cost': 11}, {'i': 8, 'j': 3, 'k': 2, 'cost': 75}, {'i': 8, 'j': 3, 'k': 3, 'cost': 96}, {'i': 8, 'j': 3, 'k': 4, 'cost': 39}, {'i': 8, 'j': 3, 'k': 5, 'cost': 79}, {'i': 8, 'j': 3, 'k': 6, 'cost': 0}, {'i': 8, 'j': 3, 'k': 7, 'cost': 50}, {'i': 8, 'j': 3, 'k': 8, 'cost': 65}, {'i': 8, 'j': 4, 'k': 0, 'cost': 55}, {'i': 8, 'j': 4, 'k': 1, 'cost': 56}, {'i': 8, 'j': 4, 'k': 2, 'cost': 53}, {'i': 8, 'j': 4, 'k': 3, 'cost': 69}, {'i': 8, 'j': 4, 'k': 4, 'cost': 90}, {'i': 8, 'j': 4, 'k': 5, 'cost': 43}, {'i': 8, 'j': 4, 'k': 6, 'cost': 99}, {'i': 8, 'j': 4, 'k': 7, 'cost': 83}, {'i': 8, 'j': 4, 'k': 8, 'cost': 21}, {'i': 8, 'j': 5, 'k': 0, 'cost': 24}, {'i': 8, 'j': 5, 'k': 1, 'cost': 35}, {'i': 8, 'j': 5, 'k': 2, 'cost': 4}, {'i': 8, 'j': 5, 'k': 3, 'cost': 37}, {'i': 8, 'j': 5, 'k': 4, 'cost': 83}, {'i': 8, 'j': 5, 'k': 5, 'cost': 16}, {'i': 8, 'j': 5, 'k': 6, 'cost': 0}, {'i': 8, 'j': 5, 'k': 7, 'cost': 48}, {'i': 8, 'j': 5, 'k': 8, 'cost': 69}, {'i': 8, 'j': 6, 'k': 0, 'cost': 79}, {'i': 8, 'j': 6, 'k': 1, 'cost': 4}, {'i': 8, 'j': 6, 'k': 2, 'cost': 25}, {'i': 8, 'j': 6, 'k': 3, 'cost': 8}, {'i': 8, 'j': 6, 'k': 4, 'cost': 85}, {'i': 8, 'j': 6, 'k': 5, 'cost': 44}, {'i': 8, 'j': 6, 'k': 6, 'cost': 0}, {'i': 8, 'j': 6, 'k': 7, 'cost': 42}, {'i': 8, 'j': 6, 'k': 8, 'cost': 5}, {'i': 8, 'j': 7, 'k': 0, 'cost': 26}, {'i': 8, 'j': 7, 'k': 1, 'cost': 93}, {'i': 8, 'j': 7, 'k': 2, 'cost': 48}, {'i': 8, 'j': 7, 'k': 3, 'cost': 16}, {'i': 8, 'j': 7, 'k': 4, 'cost': 80}, {'i': 8, 'j': 7, 'k': 5, 'cost': 94}, {'i': 8, 'j': 7, 'k': 6, 'cost': 14}, {'i': 8, 'j': 7, 'k': 7, 'cost': 71}, {'i': 8, 'j': 7, 'k': 8, 'cost': 53}, {'i': 8, 'j': 8, 'k': 0, 'cost': 29}, {'i': 8, 'j': 8, 'k': 1, 'cost': 20}, {'i': 8, 'j': 8, 'k': 2, 'cost': 16}, {'i': 8, 'j': 8, 'k': 3, 'cost': 76}, {'i': 8, 'j': 8, 'k': 4, 'cost': 11}, {'i': 8, 'j': 8, 'k': 5, 'cost': 19}, {'i': 8, 'j': 8, 'k': 6, 'cost': 90}, {'i': 8, 'j': 8, 'k': 7, 'cost': 56}, {'i': 8, 'j': 8, 'k': 8, 'cost': 68}]}","[[0, 3, 5], [1, 6, 6], [2, 5, 4], [3, 8, 2], [4, 0, 0], [5, 7, 1], [6, 4, 3], [7, 2, 7], [8, 1, 8]]",6,csv,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.
+
+I saw 9 pallets, and their identifiers are 1, 2, 3, 4, 5, 6, 7, 8, 9.
+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=1
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 85 | 94 | 75 | 7 | 95 | 98 | 46 | 50 | 52 |
+| 2 | 54 | 80 | 52 | 15 | 30 | 88 | 53 | 20 | 18 |
+| 3 | 67 | 0 | 94 | 45 | 93 | 10 | 4 | 96 | 68 |
+| 4 | 70 | 53 | 24 | 36 | 64 | 52 | 93 | 91 | 87 |
+| 5 | 9 | 79 | 84 | 44 | 78 | 28 | 65 | 13 | 23 |
+| 6 | 13 | 97 | 18 | 56 | 23 | 95 | 93 | 53 | 26 |
+| 7 | 91 | 4 | 85 | 78 | 96 | 98 | 89 | 73 | 4 |
+| 8 | 62 | 56 | 72 | 62 | 12 | 19 | 77 | 77 | 13 |
+| 9 | 57 | 98 | 4 | 0 | 49 | 30 | 59 | 58 | 57 |
+
+## pallet_id=2
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 59 | 97 | 56 | 92 | 28 | 38 | 43 | 35 | 61 |
+| 2 | 54 | 55 | 54 | 70 | 72 | 46 | 41 | 64 | 77 |
+| 3 | 34 | 50 | 96 | 22 | 72 | 14 | 15 | 17 | 52 |
+| 4 | 97 | 61 | 78 | 54 | 92 | 17 | 38 | 77 | 88 |
+| 5 | 32 | 22 | 59 | 63 | 37 | 12 | 73 | 97 | 25 |
+| 6 | 90 | 47 | 62 | 80 | 51 | 32 | 53 | 64 | 80 |
+| 7 | 33 | 30 | 3 | 30 | 2 | 97 | 39 | 80 | 51 |
+| 8 | 89 | 83 | 24 | 66 | 45 | 77 | 19 | 36 | 82 |
+| 9 | 58 | 2 | 5 | 83 | 97 | 80 | 42 | 13 | 68 |
+
+## pallet_id=3
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 93 | 48 | 28 | 61 | 60 | 96 | 21 | 84 | 89 |
+| 2 | 49 | 97 | 13 | 33 | 16 | 36 | 15 | 29 | 23 |
+| 3 | 73 | 18 | 6 | 40 | 75 | 50 | 14 | 74 | 43 |
+| 4 | 53 | 73 | 88 | 59 | 35 | 82 | 92 | 47 | 46 |
+| 5 | 49 | 41 | 31 | 11 | 87 | 61 | 21 | 21 | 67 |
+| 6 | 67 | 37 | 70 | 8 | 59 | 79 | 15 | 17 | 47 |
+| 7 | 52 | 52 | 23 | 25 | 96 | 21 | 9 | 22 | 89 |
+| 8 | 86 | 69 | 87 | 5 | 68 | 80 | 24 | 34 | 39 |
+| 9 | 40 | 82 | 68 | 23 | 86 | 1 | 68 | 93 | 38 |
+
+## pallet_id=4
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 10 | 49 | 5 | 97 | 52 | 29 | 2 | 88 | 17 |
+| 2 | 25 | 25 | 94 | 38 | 25 | 49 | 59 | 71 | 28 |
+| 3 | 68 | 66 | 72 | 60 | 70 | 59 | 92 | 46 | 50 |
+| 4 | 87 | 7 | 38 | 79 | 48 | 19 | 83 | 19 | 24 |
+| 5 | 18 | 75 | 75 | 35 | 34 | 31 | 14 | 83 | 85 |
+| 6 | 20 | 21 | 51 | 99 | 45 | 95 | 49 | 19 | 58 |
+| 7 | 19 | 96 | 68 | 17 | 2 | 11 | 28 | 72 | 87 |
+| 8 | 55 | 22 | 59 | 53 | 80 | 49 | 35 | 27 | 62 |
+| 9 | 92 | 62 | 56 | 43 | 68 | 36 | 68 | 92 | 34 |
+
+## pallet_id=5
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 95 | 88 | 25 | 88 | 42 | 24 | 24 | 33 | 31 |
+| 2 | 68 | 26 | 35 | 71 | 36 | 74 | 11 | 79 | 82 |
+| 3 | 4 | 79 | 30 | 71 | 95 | 28 | 85 | 21 | 60 |
+| 4 | 88 | 50 | 65 | 0 | 69 | 16 | 48 | 80 | 12 |
+| 5 | 27 | 11 | 30 | 24 | 15 | 10 | 92 | 71 | 67 |
+| 6 | 35 | 86 | 44 | 37 | 48 | 67 | 93 | 56 | 99 |
+| 7 | 21 | 51 | 75 | 93 | 56 | 56 | 31 | 18 | 32 |
+| 8 | 85 | 27 | 76 | 95 | 18 | 70 | 90 | 2 | 36 |
+| 9 | 3 | 32 | 7 | 33 | 81 | 73 | 78 | 97 | 44 |
+
+## pallet_id=6
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 42 | 4 | 14 | 65 | 74 | 61 | 6 | 98 | 72 |
+| 2 | 79 | 45 | 91 | 15 | 59 | 88 | 88 | 71 | 4 |
+| 3 | 39 | 94 | 40 | 18 | 25 | 71 | 39 | 33 | 86 |
+| 4 | 63 | 10 | 82 | 51 | 48 | 38 | 69 | 70 | 2 |
+| 5 | 71 | 8 | 32 | 44 | 42 | 74 | 99 | 64 | 75 |
+| 6 | 34 | 45 | 64 | 21 | 31 | 96 | 53 | 57 | 80 |
+| 7 | 17 | 51 | 42 | 99 | 84 | 88 | 26 | 6 | 23 |
+| 8 | 6 | 38 | 74 | 72 | 63 | 30 | 90 | 99 | 51 |
+| 9 | 60 | 51 | 11 | 92 | 78 | 68 | 49 | 24 | 27 |
+
+## pallet_id=7
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 62 | 8 | 35 | 88 | 36 | 12 | 3 | 91 | 44 |
+| 2 | 49 | 75 | 33 | 65 | 55 | 51 | 83 | 3 | 8 |
+| 3 | 0 | 56 | 39 | 26 | 72 | 7 | 88 | 15 | 91 |
+| 4 | 82 | 5 | 39 | 68 | 41 | 45 | 14 | 11 | 21 |
+| 5 | 29 | 75 | 78 | 87 | 29 | 66 | 7 | 38 | 11 |
+| 6 | 50 | 84 | 34 | 93 | 14 | 82 | 46 | 31 | 88 |
+| 7 | 84 | 92 | 17 | 10 | 0 | 57 | 36 | 9 | 88 |
+| 8 | 17 | 76 | 33 | 59 | 91 | 18 | 33 | 91 | 88 |
+| 9 | 92 | 22 | 30 | 22 | 0 | 29 | 67 | 57 | 82 |
+
+## pallet_id=8
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 59 | 1 | 14 | 61 | 95 | 58 | 82 | 17 |
+| 2 | 16 | 40 | 41 | 47 | 34 | 2 | 39 | 19 | 46 |
+| 3 | 80 | 84 | 0 | 17 | 56 | 48 | 46 | 55 | 74 |
+| 4 | 95 | 63 | 54 | 53 | 62 | 8 | 53 | 44 | 20 |
+| 5 | 71 | 78 | 56 | 70 | 2 | 55 | 19 | 56 | 93 |
+| 6 | 56 | 68 | 54 | 23 | 82 | 99 | 4 | 68 | 93 |
+| 7 | 86 | 68 | 7 | 23 | 44 | 29 | 85 | 77 | 12 |
+| 8 | 15 | 3 | 18 | 21 | 60 | 62 | 43 | 95 | 80 |
+| 9 | 61 | 65 | 70 | 44 | 76 | 27 | 3 | 55 | 36 |
+
+## pallet_id=9
+| truck_id\route_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 17 | 61 | 99 | 18 | 41 | 38 | 26 | 76 | 11 |
+| 2 | 40 | 78 | 74 | 83 | 36 | 26 | 10 | 36 | 54 |
+| 3 | 51 | 28 | 40 | 58 | 50 | 98 | 47 | 29 | 39 |
+| 4 | 8 | 96 | 50 | 15 | 62 | 99 | 95 | 65 | 32 |
+| 5 | 62 | 77 | 80 | 14 | 89 | 48 | 29 | 56 | 37 |
+| 6 | 45 | 67 | 67 | 16 | 7 | 88 | 85 | 39 | 83 |
+| 7 | 84 | 38 | 12 | 88 | 15 | 24 | 74 | 88 | 89 |
+| 8 | 78 | 5 | 64 | 20 | 14 | 98 | 31 | 39 | 10 |
+| 9 | 61 | 6 | 76 | 85 | 59 | 16 | 44 | 57 | 71 |
+I'll pick the set of one-to-one assignments that gives the smallest total fuel.
+
+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': [[[85, 94, 75, 7, 95, 98, 46, 50, 52], [54, 80, 52, 15, 30, 88, 53, 20, 18], [67, 0, 94, 45, 93, 10, 4, 96, 68], [70, 53, 24, 36, 64, 52, 93, 91, 87], [9, 79, 84, 44, 78, 28, 65, 13, 23], [13, 97, 18, 56, 23, 95, 93, 53, 26], [91, 4, 85, 78, 96, 98, 89, 73, 4], [62, 56, 72, 62, 12, 19, 77, 77, 13], [57, 98, 4, 0, 49, 30, 59, 58, 57]], [[59, 97, 56, 92, 28, 38, 43, 35, 61], [54, 55, 54, 70, 72, 46, 41, 64, 77], [34, 50, 96, 22, 72, 14, 15, 17, 52], [97, 61, 78, 54, 92, 17, 38, 77, 88], [32, 22, 59, 63, 37, 12, 73, 97, 25], [90, 47, 62, 80, 51, 32, 53, 64, 80], [33, 30, 3, 30, 2, 97, 39, 80, 51], [89, 83, 24, 66, 45, 77, 19, 36, 82], [58, 2, 5, 83, 97, 80, 42, 13, 68]], [[93, 48, 28, 61, 60, 96, 21, 84, 89], [49, 97, 13, 33, 16, 36, 15, 29, 23], [73, 18, 6, 40, 75, 50, 14, 74, 43], [53, 73, 88, 59, 35, 82, 92, 47, 46], [49, 41, 31, 11, 87, 61, 21, 21, 67], [67, 37, 70, 8, 59, 79, 15, 17, 47], [52, 52, 23, 25, 96, 21, 9, 22, 89], [86, 69, 87, 5, 68, 80, 24, 34, 39], [40, 82, 68, 23, 86, 1, 68, 93, 38]], [[10, 49, 5, 97, 52, 29, 2, 88, 17], [25, 25, 94, 38, 25, 49, 59, 71, 28], [68, 66, 72, 60, 70, 59, 92, 46, 50], [87, 7, 38, 79, 48, 19, 83, 19, 24], [18, 75, 75, 35, 34, 31, 14, 83, 85], [20, 21, 51, 99, 45, 95, 49, 19, 58], [19, 96, 68, 17, 2, 11, 28, 72, 87], [55, 22, 59, 53, 80, 49, 35, 27, 62], [92, 62, 56, 43, 68, 36, 68, 92, 34]], [[95, 88, 25, 88, 42, 24, 24, 33, 31], [68, 26, 35, 71, 36, 74, 11, 79, 82], [4, 79, 30, 71, 95, 28, 85, 21, 60], [88, 50, 65, 0, 69, 16, 48, 80, 12], [27, 11, 30, 24, 15, 10, 92, 71, 67], [35, 86, 44, 37, 48, 67, 93, 56, 99], [21, 51, 75, 93, 56, 56, 31, 18, 32], [85, 27, 76, 95, 18, 70, 90, 2, 36], [3, 32, 7, 33, 81, 73, 78, 97, 44]], [[42, 4, 14, 65, 74, 61, 6, 98, 72], [79, 45, 91, 15, 59, 88, 88, 71, 4], [39, 94, 40, 18, 25, 71, 39, 33, 86], [63, 10, 82, 51, 48, 38, 69, 70, 2], [71, 8, 32, 44, 42, 74, 99, 64, 75], [34, 45, 64, 21, 31, 96, 53, 57, 80], [17, 51, 42, 99, 84, 88, 26, 6, 23], [6, 38, 74, 72, 63, 30, 90, 99, 51], [60, 51, 11, 92, 78, 68, 49, 24, 27]], [[62, 8, 35, 88, 36, 12, 3, 91, 44], [49, 75, 33, 65, 55, 51, 83, 3, 8], [0, 56, 39, 26, 72, 7, 88, 15, 91], [82, 5, 39, 68, 41, 45, 14, 11, 21], [29, 75, 78, 87, 29, 66, 7, 38, 11], [50, 84, 34, 93, 14, 82, 46, 31, 88], [84, 92, 17, 10, 0, 57, 36, 9, 88], [17, 76, 33, 59, 91, 18, 33, 91, 88], [92, 22, 30, 22, 0, 29, 67, 57, 82]], [[82, 59, 1, 14, 61, 95, 58, 82, 17], [16, 40, 41, 47, 34, 2, 39, 19, 46], [80, 84, 0, 17, 56, 48, 46, 55, 74], [95, 63, 54, 53, 62, 8, 53, 44, 20], [71, 78, 56, 70, 2, 55, 19, 56, 93], [56, 68, 54, 23, 82, 99, 4, 68, 93], [86, 68, 7, 23, 44, 29, 85, 77, 12], [15, 3, 18, 21, 60, 62, 43, 95, 80], [61, 65, 70, 44, 76, 27, 3, 55, 36]], [[17, 61, 99, 18, 41, 38, 26, 76, 11], [40, 78, 74, 83, 36, 26, 10, 36, 54], [51, 28, 40, 58, 50, 98, 47, 29, 39], [8, 96, 50, 15, 62, 99, 95, 65, 32], [62, 77, 80, 14, 89, 48, 29, 56, 37], [45, 67, 67, 16, 7, 88, 85, 39, 83], [84, 38, 12, 88, 15, 24, 74, 88, 89], [78, 5, 64, 20, 14, 98, 31, 39, 10], [61, 6, 76, 85, 59, 16, 44, 57, 71]]], 'objective': 33.0}","[[0, 4, 7], [1, 6, 2], [2, 8, 5], [3, 0, 6], [4, 3, 3], [5, 1, 8], [6, 2, 0], [7, 7, 1], [8, 5, 4]]",33.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 85}, {'i': 1, 'j': 1, 'k': 2, 'cost': 94}, {'i': 1, 'j': 1, 'k': 3, 'cost': 75}, {'i': 1, 'j': 1, 'k': 4, 'cost': 7}, {'i': 1, 'j': 1, 'k': 5, 'cost': 95}, {'i': 1, 'j': 1, 'k': 6, 'cost': 98}, {'i': 1, 'j': 1, 'k': 7, 'cost': 46}, {'i': 1, 'j': 1, 'k': 8, 'cost': 50}, {'i': 1, 'j': 1, 'k': 9, 'cost': 52}, {'i': 1, 'j': 2, 'k': 1, 'cost': 54}, {'i': 1, 'j': 2, 'k': 2, 'cost': 80}, {'i': 1, 'j': 2, 'k': 3, 'cost': 52}, {'i': 1, 'j': 2, 'k': 4, 'cost': 15}, {'i': 1, 'j': 2, 'k': 5, 'cost': 30}, {'i': 1, 'j': 2, 'k': 6, 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{'i': 5, 'j': 4, 'k': 7, 'cost': 48}, {'i': 5, 'j': 4, 'k': 8, 'cost': 80}, {'i': 5, 'j': 4, 'k': 9, 'cost': 12}, {'i': 5, 'j': 5, 'k': 1, 'cost': 27}, {'i': 5, 'j': 5, 'k': 2, 'cost': 11}, {'i': 5, 'j': 5, 'k': 3, 'cost': 30}, {'i': 5, 'j': 5, 'k': 4, 'cost': 24}, {'i': 5, 'j': 5, 'k': 5, 'cost': 15}, {'i': 5, 'j': 5, 'k': 6, 'cost': 10}, {'i': 5, 'j': 5, 'k': 7, 'cost': 92}, {'i': 5, 'j': 5, 'k': 8, 'cost': 71}, {'i': 5, 'j': 5, 'k': 9, 'cost': 67}, {'i': 5, 'j': 6, 'k': 1, 'cost': 35}, {'i': 5, 'j': 6, 'k': 2, 'cost': 86}, {'i': 5, 'j': 6, 'k': 3, 'cost': 44}, {'i': 5, 'j': 6, 'k': 4, 'cost': 37}, {'i': 5, 'j': 6, 'k': 5, 'cost': 48}, {'i': 5, 'j': 6, 'k': 6, 'cost': 67}, {'i': 5, 'j': 6, 'k': 7, 'cost': 93}, {'i': 5, 'j': 6, 'k': 8, 'cost': 56}, {'i': 5, 'j': 6, 'k': 9, 'cost': 99}, {'i': 5, 'j': 7, 'k': 1, 'cost': 21}, {'i': 5, 'j': 7, 'k': 2, 'cost': 51}, {'i': 5, 'j': 7, 'k': 3, 'cost': 75}, {'i': 5, 'j': 7, 'k': 4, 'cost': 93}, {'i': 5, 'j': 7, 'k': 5, 'cost': 56}, {'i': 5, 'j': 7, 'k': 6, 'cost': 56}, {'i': 5, 'j': 7, 'k': 7, 'cost': 31}, {'i': 5, 'j': 7, 'k': 8, 'cost': 18}, {'i': 5, 'j': 7, 'k': 9, 'cost': 32}, {'i': 5, 'j': 8, 'k': 1, 'cost': 85}, {'i': 5, 'j': 8, 'k': 2, 'cost': 27}, {'i': 5, 'j': 8, 'k': 3, 'cost': 76}, {'i': 5, 'j': 8, 'k': 4, 'cost': 95}, {'i': 5, 'j': 8, 'k': 5, 'cost': 18}, {'i': 5, 'j': 8, 'k': 6, 'cost': 70}, {'i': 5, 'j': 8, 'k': 7, 'cost': 90}, {'i': 5, 'j': 8, 'k': 8, 'cost': 2}, {'i': 5, 'j': 8, 'k': 9, 'cost': 36}, {'i': 5, 'j': 9, 'k': 1, 'cost': 3}, {'i': 5, 'j': 9, 'k': 2, 'cost': 32}, {'i': 5, 'j': 9, 'k': 3, 'cost': 7}, {'i': 5, 'j': 9, 'k': 4, 'cost': 33}, {'i': 5, 'j': 9, 'k': 5, 'cost': 81}, {'i': 5, 'j': 9, 'k': 6, 'cost': 73}, {'i': 5, 'j': 9, 'k': 7, 'cost': 78}, {'i': 5, 'j': 9, 'k': 8, 'cost': 97}, {'i': 5, 'j': 9, 'k': 9, 'cost': 44}, {'i': 6, 'j': 1, 'k': 1, 'cost': 42}, {'i': 6, 'j': 1, 'k': 2, 'cost': 4}, {'i': 6, 'j': 1, 'k': 3, 'cost': 14}, {'i': 6, 'j': 1, 'k': 4, 'cost': 65}, {'i': 6, 'j': 1, 'k': 5, 'cost': 74}, {'i': 6, 'j': 1, 'k': 6, 'cost': 61}, {'i': 6, 'j': 1, 'k': 7, 'cost': 6}, {'i': 6, 'j': 1, 'k': 8, 'cost': 98}, {'i': 6, 'j': 1, 'k': 9, 'cost': 72}, {'i': 6, 'j': 2, 'k': 1, 'cost': 79}, {'i': 6, 'j': 2, 'k': 2, 'cost': 45}, {'i': 6, 'j': 2, 'k': 3, 'cost': 91}, {'i': 6, 'j': 2, 'k': 4, 'cost': 15}, {'i': 6, 'j': 2, 'k': 5, 'cost': 59}, {'i': 6, 'j': 2, 'k': 6, 'cost': 88}, {'i': 6, 'j': 2, 'k': 7, 'cost': 88}, {'i': 6, 'j': 2, 'k': 8, 'cost': 71}, {'i': 6, 'j': 2, 'k': 9, 'cost': 4}, {'i': 6, 'j': 3, 'k': 1, 'cost': 39}, {'i': 6, 'j': 3, 'k': 2, 'cost': 94}, {'i': 6, 'j': 3, 'k': 3, 'cost': 40}, {'i': 6, 'j': 3, 'k': 4, 'cost': 18}, {'i': 6, 'j': 3, 'k': 5, 'cost': 25}, {'i': 6, 'j': 3, 'k': 6, 'cost': 71}, {'i': 6, 'j': 3, 'k': 7, 'cost': 39}, {'i': 6, 'j': 3, 'k': 8, 'cost': 33}, {'i': 6, 'j': 3, 'k': 9, 'cost': 86}, {'i': 6, 'j': 4, 'k': 1, 'cost': 63}, {'i': 6, 'j': 4, 'k': 2, 'cost': 10}, {'i': 6, 'j': 4, 'k': 3, 'cost': 82}, {'i': 6, 'j': 4, 'k': 4, 'cost': 51}, {'i': 6, 'j': 4, 'k': 5, 'cost': 48}, {'i': 6, 'j': 4, 'k': 6, 'cost': 38}, {'i': 6, 'j': 4, 'k': 7, 'cost': 69}, {'i': 6, 'j': 4, 'k': 8, 'cost': 70}, {'i': 6, 'j': 4, 'k': 9, 'cost': 2}, {'i': 6, 'j': 5, 'k': 1, 'cost': 71}, {'i': 6, 'j': 5, 'k': 2, 'cost': 8}, {'i': 6, 'j': 5, 'k': 3, 'cost': 32}, {'i': 6, 'j': 5, 'k': 4, 'cost': 44}, {'i': 6, 'j': 5, 'k': 5, 'cost': 42}, {'i': 6, 'j': 5, 'k': 6, 'cost': 74}, {'i': 6, 'j': 5, 'k': 7, 'cost': 99}, {'i': 6, 'j': 5, 'k': 8, 'cost': 64}, {'i': 6, 'j': 5, 'k': 9, 'cost': 75}, {'i': 6, 'j': 6, 'k': 1, 'cost': 34}, {'i': 6, 'j': 6, 'k': 2, 'cost': 45}, {'i': 6, 'j': 6, 'k': 3, 'cost': 64}, {'i': 6, 'j': 6, 'k': 4, 'cost': 21}, {'i': 6, 'j': 6, 'k': 5, 'cost': 31}, {'i': 6, 'j': 6, 'k': 6, 'cost': 96}, {'i': 6, 'j': 6, 'k': 7, 'cost': 53}, {'i': 6, 'j': 6, 'k': 8, 'cost': 57}, {'i': 6, 'j': 6, 'k': 9, 'cost': 80}, {'i': 6, 'j': 7, 'k': 1, 'cost': 17}, {'i': 6, 'j': 7, 'k': 2, 'cost': 51}, {'i': 6, 'j': 7, 'k': 3, 'cost': 42}, {'i': 6, 'j': 7, 'k': 4, 'cost': 99}, {'i': 6, 'j': 7, 'k': 5, 'cost': 84}, {'i': 6, 'j': 7, 'k': 6, 'cost': 88}, {'i': 6, 'j': 7, 'k': 7, 'cost': 26}, {'i': 6, 'j': 7, 'k': 8, 'cost': 6}, {'i': 6, 'j': 7, 'k': 9, 'cost': 23}, {'i': 6, 'j': 8, 'k': 1, 'cost': 6}, {'i': 6, 'j': 8, 'k': 2, 'cost': 38}, {'i': 6, 'j': 8, 'k': 3, 'cost': 74}, {'i': 6, 'j': 8, 'k': 4, 'cost': 72}, {'i': 6, 'j': 8, 'k': 5, 'cost': 63}, {'i': 6, 'j': 8, 'k': 6, 'cost': 30}, {'i': 6, 'j': 8, 'k': 7, 'cost': 90}, {'i': 6, 'j': 8, 'k': 8, 'cost': 99}, {'i': 6, 'j': 8, 'k': 9, 'cost': 51}, {'i': 6, 'j': 9, 'k': 1, 'cost': 60}, {'i': 6, 'j': 9, 'k': 2, 'cost': 51}, {'i': 6, 'j': 9, 'k': 3, 'cost': 11}, {'i': 6, 'j': 9, 'k': 4, 'cost': 92}, {'i': 6, 'j': 9, 'k': 5, 'cost': 78}, {'i': 6, 'j': 9, 'k': 6, 'cost': 68}, {'i': 6, 'j': 9, 'k': 7, 'cost': 49}, {'i': 6, 'j': 9, 'k': 8, 'cost': 24}, {'i': 6, 'j': 9, 'k': 9, 'cost': 27}, {'i': 7, 'j': 1, 'k': 1, 'cost': 62}, {'i': 7, 'j': 1, 'k': 2, 'cost': 8}, {'i': 7, 'j': 1, 'k': 3, 'cost': 35}, {'i': 7, 'j': 1, 'k': 4, 'cost': 88}, {'i': 7, 'j': 1, 'k': 5, 'cost': 36}, {'i': 7, 'j': 1, 'k': 6, 'cost': 12}, {'i': 7, 'j': 1, 'k': 7, 'cost': 3}, {'i': 7, 'j': 1, 'k': 8, 'cost': 91}, {'i': 7, 'j': 1, 'k': 9, 'cost': 44}, {'i': 7, 'j': 2, 'k': 1, 'cost': 49}, {'i': 7, 'j': 2, 'k': 2, 'cost': 75}, {'i': 7, 'j': 2, 'k': 3, 'cost': 33}, {'i': 7, 'j': 2, 'k': 4, 'cost': 65}, {'i': 7, 'j': 2, 'k': 5, 'cost': 55}, {'i': 7, 'j': 2, 'k': 6, 'cost': 51}, {'i': 7, 'j': 2, 'k': 7, 'cost': 83}, {'i': 7, 'j': 2, 'k': 8, 'cost': 3}, {'i': 7, 'j': 2, 'k': 9, 'cost': 8}, {'i': 7, 'j': 3, 'k': 1, 'cost': 0}, {'i': 7, 'j': 3, 'k': 2, 'cost': 56}, {'i': 7, 'j': 3, 'k': 3, 'cost': 39}, {'i': 7, 'j': 3, 'k': 4, 'cost': 26}, {'i': 7, 'j': 3, 'k': 5, 'cost': 72}, {'i': 7, 'j': 3, 'k': 6, 'cost': 7}, {'i': 7, 'j': 3, 'k': 7, 'cost': 88}, {'i': 7, 'j': 3, 'k': 8, 'cost': 15}, {'i': 7, 'j': 3, 'k': 9, 'cost': 91}, {'i': 7, 'j': 4, 'k': 1, 'cost': 82}, {'i': 7, 'j': 4, 'k': 2, 'cost': 5}, {'i': 7, 'j': 4, 'k': 3, 'cost': 39}, {'i': 7, 'j': 4, 'k': 4, 'cost': 68}, {'i': 7, 'j': 4, 'k': 5, 'cost': 41}, {'i': 7, 'j': 4, 'k': 6, 'cost': 45}, {'i': 7, 'j': 4, 'k': 7, 'cost': 14}, {'i': 7, 'j': 4, 'k': 8, 'cost': 11}, {'i': 7, 'j': 4, 'k': 9, 'cost': 21}, {'i': 7, 'j': 5, 'k': 1, 'cost': 29}, {'i': 7, 'j': 5, 'k': 2, 'cost': 75}, {'i': 7, 'j': 5, 'k': 3, 'cost': 78}, {'i': 7, 'j': 5, 'k': 4, 'cost': 87}, {'i': 7, 'j': 5, 'k': 5, 'cost': 29}, {'i': 7, 'j': 5, 'k': 6, 'cost': 66}, {'i': 7, 'j': 5, 'k': 7, 'cost': 7}, {'i': 7, 'j': 5, 'k': 8, 'cost': 38}, {'i': 7, 'j': 5, 'k': 9, 'cost': 11}, {'i': 7, 'j': 6, 'k': 1, 'cost': 50}, {'i': 7, 'j': 6, 'k': 2, 'cost': 84}, {'i': 7, 'j': 6, 'k': 3, 'cost': 34}, {'i': 7, 'j': 6, 'k': 4, 'cost': 93}, {'i': 7, 'j': 6, 'k': 5, 'cost': 14}, {'i': 7, 'j': 6, 'k': 6, 'cost': 82}, {'i': 7, 'j': 6, 'k': 7, 'cost': 46}, {'i': 7, 'j': 6, 'k': 8, 'cost': 31}, {'i': 7, 'j': 6, 'k': 9, 'cost': 88}, {'i': 7, 'j': 7, 'k': 1, 'cost': 84}, {'i': 7, 'j': 7, 'k': 2, 'cost': 92}, {'i': 7, 'j': 7, 'k': 3, 'cost': 17}, {'i': 7, 'j': 7, 'k': 4, 'cost': 10}, {'i': 7, 'j': 7, 'k': 5, 'cost': 0}, {'i': 7, 'j': 7, 'k': 6, 'cost': 57}, {'i': 7, 'j': 7, 'k': 7, 'cost': 36}, {'i': 7, 'j': 7, 'k': 8, 'cost': 9}, {'i': 7, 'j': 7, 'k': 9, 'cost': 88}, {'i': 7, 'j': 8, 'k': 1, 'cost': 17}, {'i': 7, 'j': 8, 'k': 2, 'cost': 76}, {'i': 7, 'j': 8, 'k': 3, 'cost': 33}, {'i': 7, 'j': 8, 'k': 4, 'cost': 59}, {'i': 7, 'j': 8, 'k': 5, 'cost': 91}, {'i': 7, 'j': 8, 'k': 6, 'cost': 18}, {'i': 7, 'j': 8, 'k': 7, 'cost': 33}, {'i': 7, 'j': 8, 'k': 8, 'cost': 91}, {'i': 7, 'j': 8, 'k': 9, 'cost': 88}, {'i': 7, 'j': 9, 'k': 1, 'cost': 92}, {'i': 7, 'j': 9, 'k': 2, 'cost': 22}, {'i': 7, 'j': 9, 'k': 3, 'cost': 30}, {'i': 7, 'j': 9, 'k': 4, 'cost': 22}, {'i': 7, 'j': 9, 'k': 5, 'cost': 0}, {'i': 7, 'j': 9, 'k': 6, 'cost': 29}, {'i': 7, 'j': 9, 'k': 7, 'cost': 67}, {'i': 7, 'j': 9, 'k': 8, 'cost': 57}, {'i': 7, 'j': 9, 'k': 9, 'cost': 82}, {'i': 8, 'j': 1, 'k': 1, 'cost': 82}, {'i': 8, 'j': 1, 'k': 2, 'cost': 59}, {'i': 8, 'j': 1, 'k': 3, 'cost': 1}, {'i': 8, 'j': 1, 'k': 4, 'cost': 14}, {'i': 8, 'j': 1, 'k': 5, 'cost': 61}, {'i': 8, 'j': 1, 'k': 6, 'cost': 95}, {'i': 8, 'j': 1, 'k': 7, 'cost': 58}, {'i': 8, 'j': 1, 'k': 8, 'cost': 82}, {'i': 8, 'j': 1, 'k': 9, 'cost': 17}, {'i': 8, 'j': 2, 'k': 1, 'cost': 16}, {'i': 8, 'j': 2, 'k': 2, 'cost': 40}, {'i': 8, 'j': 2, 'k': 3, 'cost': 41}, {'i': 8, 'j': 2, 'k': 4, 'cost': 47}, {'i': 8, 'j': 2, 'k': 5, 'cost': 34}, {'i': 8, 'j': 2, 'k': 6, 'cost': 2}, {'i': 8, 'j': 2, 'k': 7, 'cost': 39}, {'i': 8, 'j': 2, 'k': 8, 'cost': 19}, {'i': 8, 'j': 2, 'k': 9, 'cost': 46}, {'i': 8, 'j': 3, 'k': 1, 'cost': 80}, {'i': 8, 'j': 3, 'k': 2, 'cost': 84}, {'i': 8, 'j': 3, 'k': 3, 'cost': 0}, {'i': 8, 'j': 3, 'k': 4, 'cost': 17}, {'i': 8, 'j': 3, 'k': 5, 'cost': 56}, {'i': 8, 'j': 3, 'k': 6, 'cost': 48}, {'i': 8, 'j': 3, 'k': 7, 'cost': 46}, {'i': 8, 'j': 3, 'k': 8, 'cost': 55}, {'i': 8, 'j': 3, 'k': 9, 'cost': 74}, {'i': 8, 'j': 4, 'k': 1, 'cost': 95}, {'i': 8, 'j': 4, 'k': 2, 'cost': 63}, {'i': 8, 'j': 4, 'k': 3, 'cost': 54}, {'i': 8, 'j': 4, 'k': 4, 'cost': 53}, {'i': 8, 'j': 4, 'k': 5, 'cost': 62}, {'i': 8, 'j': 4, 'k': 6, 'cost': 8}, {'i': 8, 'j': 4, 'k': 7, 'cost': 53}, {'i': 8, 'j': 4, 'k': 8, 'cost': 44}, {'i': 8, 'j': 4, 'k': 9, 'cost': 20}, {'i': 8, 'j': 5, 'k': 1, 'cost': 71}, {'i': 8, 'j': 5, 'k': 2, 'cost': 78}, {'i': 8, 'j': 5, 'k': 3, 'cost': 56}, {'i': 8, 'j': 5, 'k': 4, 'cost': 70}, {'i': 8, 'j': 5, 'k': 5, 'cost': 2}, {'i': 8, 'j': 5, 'k': 6, 'cost': 55}, {'i': 8, 'j': 5, 'k': 7, 'cost': 19}, {'i': 8, 'j': 5, 'k': 8, 'cost': 56}, {'i': 8, 'j': 5, 'k': 9, 'cost': 93}, {'i': 8, 'j': 6, 'k': 1, 'cost': 56}, {'i': 8, 'j': 6, 'k': 2, 'cost': 68}, {'i': 8, 'j': 6, 'k': 3, 'cost': 54}, {'i': 8, 'j': 6, 'k': 4, 'cost': 23}, {'i': 8, 'j': 6, 'k': 5, 'cost': 82}, {'i': 8, 'j': 6, 'k': 6, 'cost': 99}, {'i': 8, 'j': 6, 'k': 7, 'cost': 4}, {'i': 8, 'j': 6, 'k': 8, 'cost': 68}, {'i': 8, 'j': 6, 'k': 9, 'cost': 93}, {'i': 8, 'j': 7, 'k': 1, 'cost': 86}, {'i': 8, 'j': 7, 'k': 2, 'cost': 68}, {'i': 8, 'j': 7, 'k': 3, 'cost': 7}, {'i': 8, 'j': 7, 'k': 4, 'cost': 23}, {'i': 8, 'j': 7, 'k': 5, 'cost': 44}, {'i': 8, 'j': 7, 'k': 6, 'cost': 29}, {'i': 8, 'j': 7, 'k': 7, 'cost': 85}, {'i': 8, 'j': 7, 'k': 8, 'cost': 77}, {'i': 8, 'j': 7, 'k': 9, 'cost': 12}, {'i': 8, 'j': 8, 'k': 1, 'cost': 15}, {'i': 8, 'j': 8, 'k': 2, 'cost': 3}, {'i': 8, 'j': 8, 'k': 3, 'cost': 18}, {'i': 8, 'j': 8, 'k': 4, 'cost': 21}, {'i': 8, 'j': 8, 'k': 5, 'cost': 60}, {'i': 8, 'j': 8, 'k': 6, 'cost': 62}, {'i': 8, 'j': 8, 'k': 7, 'cost': 43}, {'i': 8, 'j': 8, 'k': 8, 'cost': 95}, {'i': 8, 'j': 8, 'k': 9, 'cost': 80}, {'i': 8, 'j': 9, 'k': 1, 'cost': 61}, {'i': 8, 'j': 9, 'k': 2, 'cost': 65}, {'i': 8, 'j': 9, 'k': 3, 'cost': 70}, {'i': 8, 'j': 9, 'k': 4, 'cost': 44}, {'i': 8, 'j': 9, 'k': 5, 'cost': 76}, {'i': 8, 'j': 9, 'k': 6, 'cost': 27}, {'i': 8, 'j': 9, 'k': 7, 'cost': 3}, {'i': 8, 'j': 9, 'k': 8, 'cost': 55}, {'i': 8, 'j': 9, 'k': 9, 'cost': 36}, {'i': 9, 'j': 1, 'k': 1, 'cost': 17}, {'i': 9, 'j': 1, 'k': 2, 'cost': 61}, {'i': 9, 'j': 1, 'k': 3, 'cost': 99}, {'i': 9, 'j': 1, 'k': 4, 'cost': 18}, {'i': 9, 'j': 1, 'k': 5, 'cost': 41}, {'i': 9, 'j': 1, 'k': 6, 'cost': 38}, {'i': 9, 'j': 1, 'k': 7, 'cost': 26}, {'i': 9, 'j': 1, 'k': 8, 'cost': 76}, {'i': 9, 'j': 1, 'k': 9, 'cost': 11}, {'i': 9, 'j': 2, 'k': 1, 'cost': 40}, {'i': 9, 'j': 2, 'k': 2, 'cost': 78}, {'i': 9, 'j': 2, 'k': 3, 'cost': 74}, {'i': 9, 'j': 2, 'k': 4, 'cost': 83}, {'i': 9, 'j': 2, 'k': 5, 'cost': 36}, {'i': 9, 'j': 2, 'k': 6, 'cost': 26}, {'i': 9, 'j': 2, 'k': 7, 'cost': 10}, {'i': 9, 'j': 2, 'k': 8, 'cost': 36}, {'i': 9, 'j': 2, 'k': 9, 'cost': 54}, {'i': 9, 'j': 3, 'k': 1, 'cost': 51}, {'i': 9, 'j': 3, 'k': 2, 'cost': 28}, {'i': 9, 'j': 3, 'k': 3, 'cost': 40}, {'i': 9, 'j': 3, 'k': 4, 'cost': 58}, {'i': 9, 'j': 3, 'k': 5, 'cost': 50}, {'i': 9, 'j': 3, 'k': 6, 'cost': 98}, {'i': 9, 'j': 3, 'k': 7, 'cost': 47}, {'i': 9, 'j': 3, 'k': 8, 'cost': 29}, {'i': 9, 'j': 3, 'k': 9, 'cost': 39}, {'i': 9, 'j': 4, 'k': 1, 'cost': 8}, {'i': 9, 'j': 4, 'k': 2, 'cost': 96}, {'i': 9, 'j': 4, 'k': 3, 'cost': 50}, {'i': 9, 'j': 4, 'k': 4, 'cost': 15}, {'i': 9, 'j': 4, 'k': 5, 'cost': 62}, {'i': 9, 'j': 4, 'k': 6, 'cost': 99}, {'i': 9, 'j': 4, 'k': 7, 'cost': 95}, {'i': 9, 'j': 4, 'k': 8, 'cost': 65}, {'i': 9, 'j': 4, 'k': 9, 'cost': 32}, {'i': 9, 'j': 5, 'k': 1, 'cost': 62}, {'i': 9, 'j': 5, 'k': 2, 'cost': 77}, {'i': 9, 'j': 5, 'k': 3, 'cost': 80}, {'i': 9, 'j': 5, 'k': 4, 'cost': 14}, {'i': 9, 'j': 5, 'k': 5, 'cost': 89}, {'i': 9, 'j': 5, 'k': 6, 'cost': 48}, {'i': 9, 'j': 5, 'k': 7, 'cost': 29}, {'i': 9, 'j': 5, 'k': 8, 'cost': 56}, {'i': 9, 'j': 5, 'k': 9, 'cost': 37}, {'i': 9, 'j': 6, 'k': 1, 'cost': 45}, {'i': 9, 'j': 6, 'k': 2, 'cost': 67}, {'i': 9, 'j': 6, 'k': 3, 'cost': 67}, {'i': 9, 'j': 6, 'k': 4, 'cost': 16}, {'i': 9, 'j': 6, 'k': 5, 'cost': 7}, {'i': 9, 'j': 6, 'k': 6, 'cost': 88}, {'i': 9, 'j': 6, 'k': 7, 'cost': 85}, {'i': 9, 'j': 6, 'k': 8, 'cost': 39}, {'i': 9, 'j': 6, 'k': 9, 'cost': 83}, {'i': 9, 'j': 7, 'k': 1, 'cost': 84}, {'i': 9, 'j': 7, 'k': 2, 'cost': 38}, {'i': 9, 'j': 7, 'k': 3, 'cost': 12}, {'i': 9, 'j': 7, 'k': 4, 'cost': 88}, {'i': 9, 'j': 7, 'k': 5, 'cost': 15}, {'i': 9, 'j': 7, 'k': 6, 'cost': 24}, {'i': 9, 'j': 7, 'k': 7, 'cost': 74}, {'i': 9, 'j': 7, 'k': 8, 'cost': 88}, {'i': 9, 'j': 7, 'k': 9, 'cost': 89}, {'i': 9, 'j': 8, 'k': 1, 'cost': 78}, {'i': 9, 'j': 8, 'k': 2, 'cost': 5}, {'i': 9, 'j': 8, 'k': 3, 'cost': 64}, {'i': 9, 'j': 8, 'k': 4, 'cost': 20}, {'i': 9, 'j': 8, 'k': 5, 'cost': 14}, {'i': 9, 'j': 8, 'k': 6, 'cost': 98}, {'i': 9, 'j': 8, 'k': 7, 'cost': 31}, {'i': 9, 'j': 8, 'k': 8, 'cost': 39}, {'i': 9, 'j': 8, 'k': 9, 'cost': 10}, {'i': 9, 'j': 9, 'k': 1, 'cost': 61}, {'i': 9, 'j': 9, 'k': 2, 'cost': 6}, {'i': 9, 'j': 9, 'k': 3, 'cost': 76}, {'i': 9, 'j': 9, 'k': 4, 'cost': 85}, {'i': 9, 'j': 9, 'k': 5, 'cost': 59}, {'i': 9, 'j': 9, 'k': 6, 'cost': 16}, {'i': 9, 'j': 9, 'k': 7, 'cost': 44}, {'i': 9, 'j': 9, 'k': 8, 'cost': 57}, {'i': 9, 'j': 9, 'k': 9, 'cost': 71}]}","[[1, 5, 8], [2, 7, 3], [3, 9, 6], [4, 1, 7], [5, 4, 4], [6, 2, 9], [7, 3, 1], [8, 8, 2], [9, 6, 5]]",7,nl,1
+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 12 clients (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) 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 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 78 | 78 | 44 | 97 | 2 | 32 | 66 | 54 | 91 | 29 | 2 | 30 |
+| 2 | 57 | 17 | 90 | 98 | 17 | 93 | 31 | 48 | 39 | 58 | 13 | 99 |
+| 3 | 51 | 98 | 41 | 2 | 49 | 67 | 59 | 59 | 24 | 48 | 64 | 14 |
+| 4 | 50 | 23 | 75 | 44 | 87 | 42 | 95 | 95 | 71 | 18 | 31 | 23 |
+| 5 | 10 | 91 | 77 | 80 | 97 | 22 | 6 | 33 | 30 | 47 | 10 | 87 |
+| 6 | 27 | 75 | 24 | 36 | 63 | 19 | 79 | 51 | 66 | 33 | 48 | 43 |
+| 7 | 45 | 37 | 26 | 70 | 10 | 90 | 70 | 91 | 46 | 39 | 0 | 25 |
+| 8 | 92 | 52 | 40 | 20 | 76 | 74 | 40 | 92 | 61 | 37 | 42 | 55 |
+| 9 | 6 | 10 | 7 | 81 | 10 | 72 | 9 | 8 | 80 | 40 | 71 | 14 |
+| 10 | 65 | 9 | 29 | 6 | 11 | 41 | 18 | 79 | 7 | 0 | 56 | 45 |
+| 11 | 16 | 75 | 75 | 63 | 48 | 35 | 54 | 11 | 91 | 11 | 31 | 62 |
+| 12 | 87 | 18 | 95 | 75 | 28 | 48 | 10 | 85 | 25 | 82 | 20 | 30 |
+
+## client_id=2
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 92 | 39 | 90 | 78 | 71 | 11 | 14 | 87 | 88 | 35 | 19 | 99 |
+| 2 | 40 | 4 | 28 | 77 | 95 | 86 | 79 | 83 | 27 | 66 | 6 | 79 |
+| 3 | 57 | 98 | 14 | 52 | 85 | 87 | 4 | 81 | 6 | 29 | 25 | 60 |
+| 4 | 60 | 35 | 59 | 43 | 61 | 73 | 7 | 40 | 66 | 67 | 88 | 13 |
+| 5 | 90 | 87 | 72 | 15 | 58 | 6 | 47 | 79 | 43 | 27 | 74 | 42 |
+| 6 | 10 | 50 | 30 | 90 | 6 | 93 | 24 | 77 | 98 | 90 | 32 | 74 |
+| 7 | 84 | 66 | 13 | 55 | 34 | 16 | 4 | 2 | 62 | 23 | 76 | 22 |
+| 8 | 15 | 21 | 1 | 96 | 80 | 47 | 21 | 29 | 21 | 43 | 33 | 30 |
+| 9 | 76 | 70 | 26 | 26 | 83 | 39 | 81 | 73 | 67 | 71 | 97 | 56 |
+| 10 | 22 | 5 | 96 | 83 | 16 | 34 | 83 | 2 | 21 | 68 | 1 | 78 |
+| 11 | 11 | 44 | 74 | 95 | 64 | 9 | 95 | 17 | 2 | 60 | 81 | 33 |
+| 12 | 28 | 19 | 0 | 18 | 74 | 23 | 37 | 32 | 20 | 93 | 53 | 30 |
+
+## client_id=3
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 9 | 37 | 0 | 43 | 16 | 48 | 52 | 60 | 29 | 94 | 11 | 77 |
+| 2 | 45 | 41 | 57 | 51 | 96 | 51 | 9 | 48 | 50 | 78 | 23 | 26 |
+| 3 | 74 | 29 | 71 | 22 | 45 | 14 | 92 | 82 | 95 | 40 | 50 | 65 |
+| 4 | 28 | 89 | 20 | 85 | 48 | 46 | 16 | 62 | 95 | 70 | 87 | 50 |
+| 5 | 3 | 80 | 42 | 32 | 69 | 7 | 65 | 99 | 0 | 59 | 27 | 86 |
+| 6 | 46 | 9 | 56 | 64 | 42 | 0 | 27 | 7 | 83 | 56 | 28 | 64 |
+| 7 | 46 | 88 | 10 | 5 | 87 | 15 | 67 | 77 | 99 | 91 | 99 | 96 |
+| 8 | 70 | 55 | 42 | 38 | 39 | 73 | 87 | 1 | 87 | 76 | 26 | 38 |
+| 9 | 82 | 68 | 41 | 54 | 6 | 78 | 25 | 6 | 87 | 78 | 84 | 3 |
+| 10 | 12 | 1 | 65 | 53 | 26 | 90 | 50 | 18 | 88 | 9 | 48 | 22 |
+| 11 | 66 | 36 | 6 | 91 | 31 | 9 | 61 | 73 | 36 | 49 | 22 | 88 |
+| 12 | 23 | 82 | 66 | 82 | 82 | 14 | 44 | 9 | 57 | 0 | 56 | 75 |
+
+## client_id=4
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 55 | 49 | 37 | 20 | 46 | 80 | 45 | 66 | 3 | 46 | 48 | 90 |
+| 2 | 88 | 48 | 36 | 34 | 79 | 27 | 67 | 96 | 64 | 38 | 20 | 82 |
+| 3 | 9 | 2 | 22 | 20 | 63 | 24 | 0 | 87 | 99 | 66 | 83 | 35 |
+| 4 | 55 | 65 | 37 | 79 | 67 | 72 | 94 | 17 | 64 | 0 | 39 | 62 |
+| 5 | 36 | 30 | 77 | 56 | 2 | 25 | 99 | 90 | 10 | 94 | 26 | 18 |
+| 6 | 97 | 2 | 74 | 74 | 43 | 63 | 22 | 25 | 54 | 99 | 68 | 74 |
+| 7 | 80 | 28 | 19 | 89 | 7 | 99 | 14 | 32 | 89 | 1 | 96 | 6 |
+| 8 | 52 | 98 | 92 | 14 | 43 | 47 | 18 | 29 | 5 | 17 | 12 | 72 |
+| 9 | 60 | 92 | 20 | 58 | 75 | 52 | 75 | 27 | 89 | 25 | 18 | 87 |
+| 10 | 73 | 77 | 68 | 4 | 37 | 83 | 99 | 26 | 52 | 48 | 64 | 0 |
+| 11 | 1 | 11 | 0 | 77 | 64 | 69 | 23 | 18 | 9 | 2 | 45 | 54 |
+| 12 | 15 | 81 | 36 | 67 | 49 | 48 | 61 | 7 | 53 | 31 | 87 | 70 |
+
+## client_id=5
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 29 | 39 | 31 | 90 | 58 | 11 | 64 | 23 | 50 | 29 | 59 | 46 |
+| 2 | 31 | 7 | 47 | 81 | 3 | 86 | 59 | 70 | 0 | 2 | 92 | 46 |
+| 3 | 31 | 28 | 25 | 18 | 74 | 46 | 26 | 30 | 24 | 69 | 67 | 46 |
+| 4 | 50 | 26 | 19 | 85 | 83 | 0 | 0 | 71 | 53 | 65 | 55 | 47 |
+| 5 | 57 | 70 | 55 | 96 | 38 | 83 | 74 | 23 | 23 | 25 | 13 | 80 |
+| 6 | 3 | 30 | 91 | 21 | 26 | 17 | 46 | 18 | 6 | 17 | 24 | 12 |
+| 7 | 92 | 49 | 67 | 38 | 11 | 45 | 71 | 16 | 34 | 65 | 5 | 24 |
+| 8 | 33 | 55 | 45 | 58 | 43 | 62 | 15 | 92 | 38 | 80 | 26 | 88 |
+| 9 | 63 | 1 | 79 | 28 | 51 | 3 | 89 | 53 | 65 | 90 | 37 | 65 |
+| 10 | 41 | 8 | 36 | 67 | 7 | 69 | 29 | 53 | 96 | 55 | 90 | 3 |
+| 11 | 30 | 79 | 51 | 52 | 75 | 86 | 42 | 26 | 38 | 89 | 66 | 41 |
+| 12 | 9 | 68 | 23 | 83 | 71 | 5 | 51 | 58 | 39 | 81 | 37 | 54 |
+
+## client_id=6
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 44 | 43 | 82 | 6 | 51 | 52 | 97 | 68 | 0 | 19 | 62 | 80 |
+| 2 | 94 | 70 | 62 | 61 | 93 | 3 | 25 | 0 | 74 | 11 | 97 | 37 |
+| 3 | 62 | 55 | 56 | 52 | 92 | 32 | 87 | 97 | 34 | 38 | 12 | 20 |
+| 4 | 22 | 97 | 83 | 23 | 95 | 76 | 49 | 46 | 26 | 5 | 75 | 20 |
+| 5 | 34 | 62 | 97 | 67 | 97 | 21 | 55 | 83 | 38 | 22 | 70 | 57 |
+| 6 | 45 | 51 | 36 | 12 | 12 | 89 | 8 | 98 | 5 | 81 | 67 | 93 |
+| 7 | 26 | 40 | 38 | 31 | 30 | 43 | 21 | 66 | 82 | 13 | 73 | 54 |
+| 8 | 74 | 49 | 71 | 0 | 74 | 14 | 52 | 22 | 92 | 41 | 77 | 70 |
+| 9 | 76 | 95 | 98 | 41 | 39 | 46 | 31 | 63 | 68 | 10 | 13 | 84 |
+| 10 | 27 | 6 | 79 | 10 | 0 | 73 | 67 | 56 | 56 | 3 | 71 | 11 |
+| 11 | 43 | 62 | 69 | 96 | 98 | 51 | 89 | 63 | 66 | 31 | 13 | 66 |
+| 12 | 27 | 23 | 41 | 19 | 24 | 30 | 25 | 98 | 94 | 91 | 67 | 48 |
+
+## client_id=7
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 66 | 10 | 45 | 33 | 7 | 60 | 35 | 44 | 15 | 74 | 56 | 91 |
+| 2 | 90 | 93 | 28 | 98 | 27 | 89 | 24 | 95 | 29 | 29 | 39 | 32 |
+| 3 | 15 | 9 | 3 | 55 | 93 | 95 | 7 | 5 | 87 | 37 | 86 | 58 |
+| 4 | 18 | 0 | 37 | 12 | 26 | 78 | 93 | 11 | 61 | 26 | 55 | 44 |
+| 5 | 67 | 44 | 53 | 28 | 37 | 35 | 31 | 61 | 47 | 66 | 2 | 3 |
+| 6 | 88 | 15 | 55 | 94 | 14 | 34 | 75 | 89 | 30 | 73 | 53 | 80 |
+| 7 | 7 | 56 | 66 | 35 | 95 | 30 | 91 | 92 | 63 | 33 | 45 | 63 |
+| 8 | 54 | 62 | 9 | 99 | 40 | 43 | 66 | 95 | 47 | 79 | 42 | 59 |
+| 9 | 51 | 55 | 5 | 6 | 73 | 14 | 63 | 89 | 52 | 21 | 44 | 29 |
+| 10 | 56 | 55 | 76 | 72 | 82 | 31 | 55 | 16 | 63 | 6 | 41 | 34 |
+| 11 | 37 | 26 | 64 | 8 | 75 | 85 | 36 | 75 | 4 | 41 | 16 | 98 |
+| 12 | 49 | 97 | 91 | 82 | 50 | 70 | 25 | 50 | 83 | 89 | 2 | 94 |
+
+## client_id=8
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 62 | 13 | 32 | 46 | 97 | 60 | 26 | 33 | 61 | 25 | 34 | 92 |
+| 2 | 31 | 97 | 94 | 29 | 45 | 48 | 3 | 19 | 87 | 83 | 14 | 62 |
+| 3 | 22 | 15 | 67 | 40 | 93 | 39 | 71 | 34 | 69 | 40 | 10 | 59 |
+| 4 | 82 | 20 | 43 | 26 | 77 | 69 | 8 | 36 | 56 | 84 | 36 | 92 |
+| 5 | 10 | 97 | 62 | 6 | 69 | 82 | 75 | 87 | 81 | 16 | 81 | 23 |
+| 6 | 71 | 58 | 73 | 46 | 1 | 13 | 19 | 6 | 51 | 34 | 37 | 71 |
+| 7 | 21 | 25 | 71 | 16 | 24 | 98 | 44 | 98 | 95 | 50 | 66 | 68 |
+| 8 | 95 | 92 | 14 | 99 | 76 | 32 | 5 | 0 | 94 | 21 | 56 | 69 |
+| 9 | 74 | 25 | 69 | 87 | 87 | 48 | 57 | 93 | 97 | 68 | 90 | 22 |
+| 10 | 31 | 48 | 15 | 98 | 86 | 12 | 53 | 45 | 22 | 62 | 83 | 16 |
+| 11 | 35 | 19 | 78 | 57 | 18 | 18 | 40 | 26 | 89 | 63 | 45 | 24 |
+| 12 | 34 | 62 | 52 | 18 | 48 | 18 | 80 | 55 | 83 | 8 | 6 | 47 |
+
+## client_id=9
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 56 | 40 | 35 | 47 | 12 | 33 | 61 | 60 | 4 | 65 | 0 | 42 |
+| 2 | 11 | 54 | 49 | 76 | 47 | 83 | 1 | 33 | 31 | 98 | 86 | 82 |
+| 3 | 96 | 43 | 91 | 34 | 52 | 92 | 79 | 59 | 32 | 50 | 73 | 63 |
+| 4 | 72 | 16 | 69 | 12 | 46 | 20 | 76 | 45 | 2 | 0 | 23 | 45 |
+| 5 | 34 | 32 | 40 | 0 | 22 | 20 | 33 | 27 | 73 | 91 | 61 | 16 |
+| 6 | 88 | 40 | 9 | 54 | 59 | 30 | 13 | 39 | 0 | 52 | 63 | 65 |
+| 7 | 34 | 48 | 33 | 6 | 44 | 38 | 86 | 52 | 61 | 44 | 64 | 79 |
+| 8 | 67 | 3 | 69 | 18 | 92 | 22 | 4 | 79 | 71 | 20 | 61 | 20 |
+| 9 | 14 | 35 | 22 | 0 | 68 | 88 | 14 | 77 | 97 | 99 | 3 | 42 |
+| 10 | 30 | 70 | 46 | 41 | 15 | 83 | 11 | 61 | 36 | 88 | 75 | 65 |
+| 11 | 21 | 47 | 24 | 28 | 93 | 49 | 27 | 42 | 16 | 75 | 25 | 37 |
+| 12 | 78 | 29 | 90 | 21 | 26 | 69 | 80 | 88 | 95 | 45 | 13 | 79 |
+
+## client_id=10
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 78 | 34 | 19 | 66 | 77 | 40 | 86 | 14 | 56 | 45 | 32 | 44 |
+| 2 | 57 | 80 | 91 | 41 | 90 | 35 | 12 | 94 | 45 | 80 | 46 | 99 |
+| 3 | 87 | 36 | 9 | 22 | 11 | 73 | 48 | 9 | 33 | 95 | 57 | 3 |
+| 4 | 76 | 91 | 45 | 94 | 13 | 5 | 70 | 65 | 59 | 67 | 77 | 88 |
+| 5 | 6 | 24 | 6 | 95 | 98 | 25 | 23 | 68 | 64 | 23 | 28 | 42 |
+| 6 | 41 | 39 | 60 | 6 | 73 | 38 | 35 | 24 | 10 | 80 | 45 | 92 |
+| 7 | 78 | 48 | 33 | 99 | 48 | 14 | 68 | 34 | 31 | 91 | 14 | 37 |
+| 8 | 80 | 8 | 42 | 45 | 9 | 61 | 49 | 64 | 94 | 88 | 84 | 75 |
+| 9 | 16 | 30 | 67 | 95 | 3 | 76 | 53 | 55 | 9 | 15 | 16 | 24 |
+| 10 | 44 | 87 | 55 | 47 | 80 | 42 | 28 | 52 | 46 | 40 | 83 | 78 |
+| 11 | 72 | 29 | 74 | 59 | 67 | 60 | 86 | 33 | 86 | 23 | 58 | 96 |
+| 12 | 20 | 49 | 94 | 61 | 57 | 15 | 93 | 72 | 13 | 24 | 32 | 1 |
+
+## client_id=11
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 42 | 75 | 77 | 71 | 86 | 44 | 37 | 65 | 71 | 14 | 19 | 56 |
+| 2 | 37 | 69 | 43 | 46 | 38 | 65 | 36 | 46 | 13 | 72 | 25 | 44 |
+| 3 | 85 | 52 | 27 | 44 | 17 | 55 | 72 | 16 | 93 | 64 | 99 | 75 |
+| 4 | 53 | 57 | 93 | 47 | 61 | 15 | 98 | 58 | 75 | 7 | 96 | 32 |
+| 5 | 92 | 83 | 49 | 52 | 40 | 42 | 57 | 51 | 81 | 40 | 70 | 50 |
+| 6 | 58 | 28 | 48 | 45 | 16 | 86 | 98 | 30 | 4 | 10 | 6 | 3 |
+| 7 | 73 | 94 | 97 | 57 | 60 | 16 | 92 | 36 | 64 | 94 | 47 | 19 |
+| 8 | 81 | 59 | 1 | 76 | 41 | 10 | 5 | 32 | 0 | 67 | 4 | 92 |
+| 9 | 98 | 9 | 15 | 58 | 97 | 0 | 73 | 26 | 67 | 93 | 15 | 70 |
+| 10 | 3 | 17 | 96 | 36 | 75 | 41 | 91 | 57 | 73 | 98 | 34 | 6 |
+| 11 | 91 | 71 | 86 | 81 | 83 | 65 | 49 | 23 | 9 | 99 | 35 | 67 |
+| 12 | 52 | 96 | 73 | 39 | 80 | 78 | 19 | 98 | 53 | 4 | 8 | 56 |
+
+## client_id=12
+| outfit_id\accessory_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 27 | 92 | 53 | 60 | 91 | 49 | 58 | 21 | 79 | 0 | 63 | 2 |
+| 2 | 35 | 11 | 13 | 27 | 63 | 18 | 78 | 8 | 70 | 99 | 71 | 22 |
+| 3 | 1 | 90 | 81 | 50 | 79 | 81 | 36 | 55 | 48 | 84 | 15 | 18 |
+| 4 | 97 | 42 | 62 | 57 | 89 | 87 | 78 | 34 | 62 | 66 | 0 | 92 |
+| 5 | 74 | 15 | 77 | 7 | 16 | 8 | 55 | 67 | 86 | 97 | 26 | 43 |
+| 6 | 70 | 58 | 9 | 7 | 90 | 91 | 49 | 66 | 45 | 62 | 58 | 87 |
+| 7 | 36 | 4 | 95 | 18 | 28 | 99 | 94 | 82 | 33 | 25 | 94 | 18 |
+| 8 | 66 | 91 | 10 | 31 | 55 | 63 | 88 | 90 | 85 | 31 | 99 | 93 |
+| 9 | 9 | 20 | 96 | 80 | 50 | 28 | 77 | 17 | 2 | 86 | 40 | 12 |
+| 10 | 92 | 22 | 14 | 99 | 10 | 21 | 81 | 84 | 2 | 12 | 55 | 17 |
+| 11 | 5 | 95 | 93 | 60 | 5 | 83 | 57 | 82 | 64 | 28 | 69 | 44 |
+| 12 | 89 | 56 | 86 | 89 | 97 | 94 | 88 | 41 | 57 | 91 | 2 | 96 |
+
+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': [[[78, 78, 44, 97, 2, 32, 66, 54, 91, 29, 2, 30], [57, 17, 90, 98, 17, 93, 31, 48, 39, 58, 13, 99], [51, 98, 41, 2, 49, 67, 59, 59, 24, 48, 64, 14], [50, 23, 75, 44, 87, 42, 95, 95, 71, 18, 31, 23], [10, 91, 77, 80, 97, 22, 6, 33, 30, 47, 10, 87], [27, 75, 24, 36, 63, 19, 79, 51, 66, 33, 48, 43], [45, 37, 26, 70, 10, 90, 70, 91, 46, 39, 0, 25], [92, 52, 40, 20, 76, 74, 40, 92, 61, 37, 42, 55], [6, 10, 7, 81, 10, 72, 9, 8, 80, 40, 71, 14], [65, 9, 29, 6, 11, 41, 18, 79, 7, 0, 56, 45], [16, 75, 75, 63, 48, 35, 54, 11, 91, 11, 31, 62], [87, 18, 95, 75, 28, 48, 10, 85, 25, 82, 20, 30]], [[92, 39, 90, 78, 71, 11, 14, 87, 88, 35, 19, 99], [40, 4, 28, 77, 95, 86, 79, 83, 27, 66, 6, 79], [57, 98, 14, 52, 85, 87, 4, 81, 6, 29, 25, 60], [60, 35, 59, 43, 61, 73, 7, 40, 66, 67, 88, 13], [90, 87, 72, 15, 58, 6, 47, 79, 43, 27, 74, 42], [10, 50, 30, 90, 6, 93, 24, 77, 98, 90, 32, 74], [84, 66, 13, 55, 34, 16, 4, 2, 62, 23, 76, 22], [15, 21, 1, 96, 80, 47, 21, 29, 21, 43, 33, 30], [76, 70, 26, 26, 83, 39, 81, 73, 67, 71, 97, 56], [22, 5, 96, 83, 16, 34, 83, 2, 21, 68, 1, 78], [11, 44, 74, 95, 64, 9, 95, 17, 2, 60, 81, 33], [28, 19, 0, 18, 74, 23, 37, 32, 20, 93, 53, 30]], [[9, 37, 0, 43, 16, 48, 52, 60, 29, 94, 11, 77], [45, 41, 57, 51, 96, 51, 9, 48, 50, 78, 23, 26], [74, 29, 71, 22, 45, 14, 92, 82, 95, 40, 50, 65], [28, 89, 20, 85, 48, 46, 16, 62, 95, 70, 87, 50], [3, 80, 42, 32, 69, 7, 65, 99, 0, 59, 27, 86], [46, 9, 56, 64, 42, 0, 27, 7, 83, 56, 28, 64], [46, 88, 10, 5, 87, 15, 67, 77, 99, 91, 99, 96], [70, 55, 42, 38, 39, 73, 87, 1, 87, 76, 26, 38], [82, 68, 41, 54, 6, 78, 25, 6, 87, 78, 84, 3], [12, 1, 65, 53, 26, 90, 50, 18, 88, 9, 48, 22], [66, 36, 6, 91, 31, 9, 61, 73, 36, 49, 22, 88], [23, 82, 66, 82, 82, 14, 44, 9, 57, 0, 56, 75]], [[55, 49, 37, 20, 46, 80, 45, 66, 3, 46, 48, 90], [88, 48, 36, 34, 79, 27, 67, 96, 64, 38, 20, 82], [9, 2, 22, 20, 63, 24, 0, 87, 99, 66, 83, 35], [55, 65, 37, 79, 67, 72, 94, 17, 64, 0, 39, 62], [36, 30, 77, 56, 2, 25, 99, 90, 10, 94, 26, 18], [97, 2, 74, 74, 43, 63, 22, 25, 54, 99, 68, 74], [80, 28, 19, 89, 7, 99, 14, 32, 89, 1, 96, 6], [52, 98, 92, 14, 43, 47, 18, 29, 5, 17, 12, 72], [60, 92, 20, 58, 75, 52, 75, 27, 89, 25, 18, 87], [73, 77, 68, 4, 37, 83, 99, 26, 52, 48, 64, 0], [1, 11, 0, 77, 64, 69, 23, 18, 9, 2, 45, 54], [15, 81, 36, 67, 49, 48, 61, 7, 53, 31, 87, 70]], [[29, 39, 31, 90, 58, 11, 64, 23, 50, 29, 59, 46], [31, 7, 47, 81, 3, 86, 59, 70, 0, 2, 92, 46], [31, 28, 25, 18, 74, 46, 26, 30, 24, 69, 67, 46], [50, 26, 19, 85, 83, 0, 0, 71, 53, 65, 55, 47], [57, 70, 55, 96, 38, 83, 74, 23, 23, 25, 13, 80], [3, 30, 91, 21, 26, 17, 46, 18, 6, 17, 24, 12], [92, 49, 67, 38, 11, 45, 71, 16, 34, 65, 5, 24], [33, 55, 45, 58, 43, 62, 15, 92, 38, 80, 26, 88], [63, 1, 79, 28, 51, 3, 89, 53, 65, 90, 37, 65], [41, 8, 36, 67, 7, 69, 29, 53, 96, 55, 90, 3], [30, 79, 51, 52, 75, 86, 42, 26, 38, 89, 66, 41], [9, 68, 23, 83, 71, 5, 51, 58, 39, 81, 37, 54]], [[44, 43, 82, 6, 51, 52, 97, 68, 0, 19, 62, 80], [94, 70, 62, 61, 93, 3, 25, 0, 74, 11, 97, 37], [62, 55, 56, 52, 92, 32, 87, 97, 34, 38, 12, 20], [22, 97, 83, 23, 95, 76, 49, 46, 26, 5, 75, 20], [34, 62, 97, 67, 97, 21, 55, 83, 38, 22, 70, 57], [45, 51, 36, 12, 12, 89, 8, 98, 5, 81, 67, 93], [26, 40, 38, 31, 30, 43, 21, 66, 82, 13, 73, 54], [74, 49, 71, 0, 74, 14, 52, 22, 92, 41, 77, 70], [76, 95, 98, 41, 39, 46, 31, 63, 68, 10, 13, 84], [27, 6, 79, 10, 0, 73, 67, 56, 56, 3, 71, 11], [43, 62, 69, 96, 98, 51, 89, 63, 66, 31, 13, 66], [27, 23, 41, 19, 24, 30, 25, 98, 94, 91, 67, 48]], [[66, 10, 45, 33, 7, 60, 35, 44, 15, 74, 56, 91], [90, 93, 28, 98, 27, 89, 24, 95, 29, 29, 39, 32], [15, 9, 3, 55, 93, 95, 7, 5, 87, 37, 86, 58], [18, 0, 37, 12, 26, 78, 93, 11, 61, 26, 55, 44], [67, 44, 53, 28, 37, 35, 31, 61, 47, 66, 2, 3], [88, 15, 55, 94, 14, 34, 75, 89, 30, 73, 53, 80], [7, 56, 66, 35, 95, 30, 91, 92, 63, 33, 45, 63], [54, 62, 9, 99, 40, 43, 66, 95, 47, 79, 42, 59], [51, 55, 5, 6, 73, 14, 63, 89, 52, 21, 44, 29], [56, 55, 76, 72, 82, 31, 55, 16, 63, 6, 41, 34], [37, 26, 64, 8, 75, 85, 36, 75, 4, 41, 16, 98], [49, 97, 91, 82, 50, 70, 25, 50, 83, 89, 2, 94]], [[62, 13, 32, 46, 97, 60, 26, 33, 61, 25, 34, 92], [31, 97, 94, 29, 45, 48, 3, 19, 87, 83, 14, 62], [22, 15, 67, 40, 93, 39, 71, 34, 69, 40, 10, 59], [82, 20, 43, 26, 77, 69, 8, 36, 56, 84, 36, 92], [10, 97, 62, 6, 69, 82, 75, 87, 81, 16, 81, 23], [71, 58, 73, 46, 1, 13, 19, 6, 51, 34, 37, 71], [21, 25, 71, 16, 24, 98, 44, 98, 95, 50, 66, 68], [95, 92, 14, 99, 76, 32, 5, 0, 94, 21, 56, 69], [74, 25, 69, 87, 87, 48, 57, 93, 97, 68, 90, 22], [31, 48, 15, 98, 86, 12, 53, 45, 22, 62, 83, 16], [35, 19, 78, 57, 18, 18, 40, 26, 89, 63, 45, 24], [34, 62, 52, 18, 48, 18, 80, 55, 83, 8, 6, 47]], [[56, 40, 35, 47, 12, 33, 61, 60, 4, 65, 0, 42], [11, 54, 49, 76, 47, 83, 1, 33, 31, 98, 86, 82], [96, 43, 91, 34, 52, 92, 79, 59, 32, 50, 73, 63], [72, 16, 69, 12, 46, 20, 76, 45, 2, 0, 23, 45], [34, 32, 40, 0, 22, 20, 33, 27, 73, 91, 61, 16], [88, 40, 9, 54, 59, 30, 13, 39, 0, 52, 63, 65], [34, 48, 33, 6, 44, 38, 86, 52, 61, 44, 64, 79], [67, 3, 69, 18, 92, 22, 4, 79, 71, 20, 61, 20], [14, 35, 22, 0, 68, 88, 14, 77, 97, 99, 3, 42], [30, 70, 46, 41, 15, 83, 11, 61, 36, 88, 75, 65], [21, 47, 24, 28, 93, 49, 27, 42, 16, 75, 25, 37], [78, 29, 90, 21, 26, 69, 80, 88, 95, 45, 13, 79]], [[78, 34, 19, 66, 77, 40, 86, 14, 56, 45, 32, 44], [57, 80, 91, 41, 90, 35, 12, 94, 45, 80, 46, 99], [87, 36, 9, 22, 11, 73, 48, 9, 33, 95, 57, 3], [76, 91, 45, 94, 13, 5, 70, 65, 59, 67, 77, 88], [6, 24, 6, 95, 98, 25, 23, 68, 64, 23, 28, 42], [41, 39, 60, 6, 73, 38, 35, 24, 10, 80, 45, 92], [78, 48, 33, 99, 48, 14, 68, 34, 31, 91, 14, 37], [80, 8, 42, 45, 9, 61, 49, 64, 94, 88, 84, 75], [16, 30, 67, 95, 3, 76, 53, 55, 9, 15, 16, 24], [44, 87, 55, 47, 80, 42, 28, 52, 46, 40, 83, 78], [72, 29, 74, 59, 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{'i': 12, 'j': 3, 'k': 10, 'cost': 84}, {'i': 12, 'j': 3, 'k': 11, 'cost': 15}, {'i': 12, 'j': 3, 'k': 12, 'cost': 18}, {'i': 12, 'j': 4, 'k': 1, 'cost': 97}, {'i': 12, 'j': 4, 'k': 2, 'cost': 42}, {'i': 12, 'j': 4, 'k': 3, 'cost': 62}, {'i': 12, 'j': 4, 'k': 4, 'cost': 57}, {'i': 12, 'j': 4, 'k': 5, 'cost': 89}, {'i': 12, 'j': 4, 'k': 6, 'cost': 87}, {'i': 12, 'j': 4, 'k': 7, 'cost': 78}, {'i': 12, 'j': 4, 'k': 8, 'cost': 34}, {'i': 12, 'j': 4, 'k': 9, 'cost': 62}, {'i': 12, 'j': 4, 'k': 10, 'cost': 66}, {'i': 12, 'j': 4, 'k': 11, 'cost': 0}, {'i': 12, 'j': 4, 'k': 12, 'cost': 92}, {'i': 12, 'j': 5, 'k': 1, 'cost': 74}, {'i': 12, 'j': 5, 'k': 2, 'cost': 15}, {'i': 12, 'j': 5, 'k': 3, 'cost': 77}, {'i': 12, 'j': 5, 'k': 4, 'cost': 7}, {'i': 12, 'j': 5, 'k': 5, 'cost': 16}, {'i': 12, 'j': 5, 'k': 6, 'cost': 8}, {'i': 12, 'j': 5, 'k': 7, 'cost': 55}, {'i': 12, 'j': 5, 'k': 8, 'cost': 67}, {'i': 12, 'j': 5, 'k': 9, 'cost': 86}, {'i': 12, 'j': 5, 'k': 10, 'cost': 97}, {'i': 12, 'j': 5, 'k': 11, 'cost': 26}, {'i': 12, 'j': 5, 'k': 12, 'cost': 43}, {'i': 12, 'j': 6, 'k': 1, 'cost': 70}, {'i': 12, 'j': 6, 'k': 2, 'cost': 58}, {'i': 12, 'j': 6, 'k': 3, 'cost': 9}, {'i': 12, 'j': 6, 'k': 4, 'cost': 7}, {'i': 12, 'j': 6, 'k': 5, 'cost': 90}, {'i': 12, 'j': 6, 'k': 6, 'cost': 91}, {'i': 12, 'j': 6, 'k': 7, 'cost': 49}, {'i': 12, 'j': 6, 'k': 8, 'cost': 66}, {'i': 12, 'j': 6, 'k': 9, 'cost': 45}, {'i': 12, 'j': 6, 'k': 10, 'cost': 62}, {'i': 12, 'j': 6, 'k': 11, 'cost': 58}, {'i': 12, 'j': 6, 'k': 12, 'cost': 87}, {'i': 12, 'j': 7, 'k': 1, 'cost': 36}, {'i': 12, 'j': 7, 'k': 2, 'cost': 4}, {'i': 12, 'j': 7, 'k': 3, 'cost': 95}, {'i': 12, 'j': 7, 'k': 4, 'cost': 18}, {'i': 12, 'j': 7, 'k': 5, 'cost': 28}, {'i': 12, 'j': 7, 'k': 6, 'cost': 99}, {'i': 12, 'j': 7, 'k': 7, 'cost': 94}, {'i': 12, 'j': 7, 'k': 8, 'cost': 82}, {'i': 12, 'j': 7, 'k': 9, 'cost': 33}, {'i': 12, 'j': 7, 'k': 10, 'cost': 25}, {'i': 12, 'j': 7, 'k': 11, 'cost': 94}, {'i': 12, 'j': 7, 'k': 12, 'cost': 18}, {'i': 12, 'j': 8, 'k': 1, 'cost': 66}, {'i': 12, 'j': 8, 'k': 2, 'cost': 91}, {'i': 12, 'j': 8, 'k': 3, 'cost': 10}, {'i': 12, 'j': 8, 'k': 4, 'cost': 31}, {'i': 12, 'j': 8, 'k': 5, 'cost': 55}, {'i': 12, 'j': 8, 'k': 6, 'cost': 63}, {'i': 12, 'j': 8, 'k': 7, 'cost': 88}, {'i': 12, 'j': 8, 'k': 8, 'cost': 90}, {'i': 12, 'j': 8, 'k': 9, 'cost': 85}, {'i': 12, 'j': 8, 'k': 10, 'cost': 31}, {'i': 12, 'j': 8, 'k': 11, 'cost': 99}, {'i': 12, 'j': 8, 'k': 12, 'cost': 93}, {'i': 12, 'j': 9, 'k': 1, 'cost': 9}, {'i': 12, 'j': 9, 'k': 2, 'cost': 20}, {'i': 12, 'j': 9, 'k': 3, 'cost': 96}, {'i': 12, 'j': 9, 'k': 4, 'cost': 80}, {'i': 12, 'j': 9, 'k': 5, 'cost': 50}, {'i': 12, 'j': 9, 'k': 6, 'cost': 28}, {'i': 12, 'j': 9, 'k': 7, 'cost': 77}, {'i': 12, 'j': 9, 'k': 8, 'cost': 17}, {'i': 12, 'j': 9, 'k': 9, 'cost': 2}, {'i': 12, 'j': 9, 'k': 10, 'cost': 86}, {'i': 12, 'j': 9, 'k': 11, 'cost': 40}, {'i': 12, 'j': 9, 'k': 12, 'cost': 12}, {'i': 12, 'j': 10, 'k': 1, 'cost': 92}, {'i': 12, 'j': 10, 'k': 2, 'cost': 22}, {'i': 12, 'j': 10, 'k': 3, 'cost': 14}, {'i': 12, 'j': 10, 'k': 4, 'cost': 99}, {'i': 12, 'j': 10, 'k': 5, 'cost': 10}, {'i': 12, 'j': 10, 'k': 6, 'cost': 21}, {'i': 12, 'j': 10, 'k': 7, 'cost': 81}, {'i': 12, 'j': 10, 'k': 8, 'cost': 84}, {'i': 12, 'j': 10, 'k': 9, 'cost': 2}, {'i': 12, 'j': 10, 'k': 10, 'cost': 12}, {'i': 12, 'j': 10, 'k': 11, 'cost': 55}, {'i': 12, 'j': 10, 'k': 12, 'cost': 17}, {'i': 12, 'j': 11, 'k': 1, 'cost': 5}, {'i': 12, 'j': 11, 'k': 2, 'cost': 95}, {'i': 12, 'j': 11, 'k': 3, 'cost': 93}, {'i': 12, 'j': 11, 'k': 4, 'cost': 60}, {'i': 12, 'j': 11, 'k': 5, 'cost': 5}, {'i': 12, 'j': 11, 'k': 6, 'cost': 83}, {'i': 12, 'j': 11, 'k': 7, 'cost': 57}, {'i': 12, 'j': 11, 'k': 8, 'cost': 82}, {'i': 12, 'j': 11, 'k': 9, 'cost': 64}, {'i': 12, 'j': 11, 'k': 10, 'cost': 28}, {'i': 12, 'j': 11, 'k': 11, 'cost': 69}, {'i': 12, 'j': 11, 'k': 12, 'cost': 44}, {'i': 12, 'j': 12, 'k': 1, 'cost': 89}, {'i': 12, 'j': 12, 'k': 2, 'cost': 56}, {'i': 12, 'j': 12, 'k': 3, 'cost': 86}, {'i': 12, 'j': 12, 'k': 4, 'cost': 89}, {'i': 12, 'j': 12, 'k': 5, 'cost': 97}, {'i': 12, 'j': 12, 'k': 6, 'cost': 94}, {'i': 12, 'j': 12, 'k': 7, 'cost': 88}, {'i': 12, 'j': 12, 'k': 8, 'cost': 41}, {'i': 12, 'j': 12, 'k': 9, 'cost': 57}, {'i': 12, 'j': 12, 'k': 10, 'cost': 91}, {'i': 12, 'j': 12, 'k': 11, 'cost': 2}, {'i': 12, 'j': 12, 'k': 12, 'cost': 96}]}","[[1, 1, 11], [2, 8, 3], [3, 10, 2], [4, 7, 10], [5, 4, 7], [6, 2, 8], [7, 11, 9], [8, 6, 5], [9, 5, 4], [10, 12, 12], [11, 9, 6], [12, 3, 1]]",8,markdown_table,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.
+
+I remember helping put together that tiny festival for 11 bands (and the same number of stages and time slots); the ordered identifiers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
+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 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 98 | 21 | 40 | 81 | 69 | 24 | 30 | 59 | 57 | 67 | 86 |
+| 1 | 82 | 71 | 95 | 93 | 19 | 99 | 33 | 40 | 9 | 51 | 97 |
+| 2 | 5 | 68 | 64 | 46 | 4 | 41 | 56 | 53 | 10 | 54 | 7 |
+| 3 | 26 | 65 | 13 | 26 | 42 | 46 | 47 | 67 | 18 | 17 | 99 |
+| 4 | 52 | 26 | 60 | 6 | 94 | 99 | 47 | 17 | 3 | 30 | 86 |
+| 5 | 62 | 22 | 78 | 48 | 15 | 38 | 69 | 98 | 85 | 17 | 90 |
+| 6 | 34 | 34 | 10 | 78 | 56 | 61 | 60 | 95 | 32 | 74 | 91 |
+| 7 | 75 | 37 | 9 | 6 | 28 | 73 | 54 | 29 | 81 | 21 | 63 |
+| 8 | 81 | 11 | 45 | 38 | 64 | 12 | 30 | 70 | 88 | 35 | 54 |
+| 9 | 65 | 91 | 22 | 13 | 10 | 33 | 30 | 49 | 36 | 36 | 20 |
+| 10 | 29 | 63 | 31 | 92 | 14 | 7 | 18 | 27 | 23 | 28 | 40 |
+
+## band_id=1
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 12 | 48 | 91 | 60 | 56 | 76 | 70 | 85 | 14 | 47 | 93 |
+| 1 | 47 | 85 | 70 | 75 | 95 | 58 | 11 | 98 | 65 | 46 | 52 |
+| 2 | 11 | 76 | 66 | 5 | 48 | 65 | 67 | 60 | 39 | 15 | 91 |
+| 3 | 17 | 67 | 7 | 94 | 93 | 55 | 40 | 10 | 4 | 4 | 68 |
+| 4 | 96 | 9 | 62 | 84 | 78 | 82 | 10 | 28 | 6 | 65 | 23 |
+| 5 | 81 | 8 | 27 | 5 | 24 | 22 | 22 | 21 | 38 | 19 | 8 |
+| 6 | 73 | 60 | 12 | 43 | 73 | 82 | 53 | 79 | 89 | 53 | 52 |
+| 7 | 39 | 13 | 6 | 18 | 23 | 67 | 96 | 95 | 46 | 93 | 26 |
+| 8 | 46 | 1 | 94 | 93 | 59 | 43 | 36 | 46 | 63 | 85 | 81 |
+| 9 | 24 | 91 | 97 | 85 | 96 | 22 | 69 | 98 | 7 | 89 | 4 |
+| 10 | 60 | 57 | 95 | 4 | 49 | 91 | 73 | 30 | 14 | 59 | 57 |
+
+## band_id=2
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 61 | 70 | 4 | 47 | 13 | 88 | 0 | 24 | 43 | 59 | 30 |
+| 1 | 94 | 18 | 48 | 51 | 19 | 8 | 2 | 68 | 10 | 30 | 44 |
+| 2 | 95 | 77 | 59 | 91 | 66 | 60 | 60 | 28 | 25 | 74 | 67 |
+| 3 | 28 | 61 | 22 | 5 | 24 | 45 | 8 | 63 | 33 | 58 | 90 |
+| 4 | 2 | 82 | 15 | 23 | 47 | 58 | 39 | 97 | 40 | 33 | 73 |
+| 5 | 9 | 8 | 66 | 7 | 94 | 28 | 63 | 2 | 38 | 14 | 46 |
+| 6 | 18 | 75 | 95 | 87 | 80 | 7 | 5 | 70 | 62 | 32 | 89 |
+| 7 | 54 | 1 | 24 | 91 | 85 | 95 | 19 | 66 | 44 | 24 | 69 |
+| 8 | 4 | 3 | 93 | 27 | 26 | 19 | 14 | 77 | 58 | 62 | 50 |
+| 9 | 72 | 75 | 12 | 69 | 81 | 36 | 51 | 52 | 67 | 78 | 85 |
+| 10 | 69 | 60 | 69 | 29 | 64 | 42 | 84 | 85 | 96 | 51 | 37 |
+
+## band_id=3
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 20 | 49 | 65 | 98 | 89 | 43 | 83 | 93 | 69 | 28 | 51 |
+| 1 | 87 | 93 | 58 | 28 | 60 | 30 | 67 | 96 | 22 | 21 | 89 |
+| 2 | 49 | 11 | 71 | 89 | 79 | 12 | 46 | 0 | 23 | 41 | 46 |
+| 3 | 64 | 73 | 67 | 6 | 75 | 23 | 20 | 50 | 75 | 14 | 43 |
+| 4 | 54 | 49 | 25 | 31 | 87 | 38 | 50 | 61 | 47 | 21 | 67 |
+| 5 | 42 | 2 | 68 | 92 | 70 | 61 | 60 | 88 | 33 | 30 | 31 |
+| 6 | 72 | 21 | 53 | 56 | 11 | 18 | 38 | 24 | 7 | 43 | 37 |
+| 7 | 89 | 67 | 71 | 70 | 59 | 3 | 56 | 79 | 93 | 15 | 47 |
+| 8 | 50 | 90 | 93 | 80 | 23 | 56 | 38 | 53 | 57 | 45 | 62 |
+| 9 | 88 | 52 | 13 | 23 | 96 | 92 | 97 | 21 | 0 | 9 | 89 |
+| 10 | 71 | 40 | 96 | 68 | 86 | 95 | 29 | 1 | 86 | 68 | 38 |
+
+## band_id=4
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 74 | 57 | 25 | 34 | 97 | 87 | 78 | 65 | 33 | 75 | 47 |
+| 1 | 59 | 95 | 27 | 25 | 42 | 63 | 30 | 24 | 45 | 24 | 31 |
+| 2 | 68 | 68 | 0 | 42 | 43 | 97 | 13 | 68 | 3 | 54 | 45 |
+| 3 | 32 | 4 | 48 | 30 | 95 | 77 | 82 | 28 | 43 | 85 | 60 |
+| 4 | 8 | 27 | 90 | 30 | 15 | 39 | 79 | 10 | 24 | 92 | 67 |
+| 5 | 61 | 4 | 83 | 2 | 44 | 37 | 60 | 55 | 70 | 63 | 44 |
+| 6 | 97 | 71 | 84 | 85 | 48 | 94 | 58 | 56 | 65 | 5 | 36 |
+| 7 | 78 | 35 | 50 | 44 | 48 | 99 | 64 | 67 | 28 | 93 | 99 |
+| 8 | 20 | 74 | 43 | 96 | 54 | 24 | 4 | 99 | 86 | 83 | 91 |
+| 9 | 11 | 21 | 24 | 75 | 56 | 0 | 68 | 56 | 34 | 31 | 32 |
+| 10 | 33 | 3 | 12 | 7 | 81 | 66 | 52 | 73 | 93 | 78 | 44 |
+
+## band_id=5
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 68 | 67 | 10 | 27 | 69 | 11 | 24 | 83 | 36 | 8 | 54 |
+| 1 | 81 | 37 | 76 | 25 | 68 | 78 | 41 | 70 | 54 | 23 | 20 |
+| 2 | 7 | 50 | 14 | 20 | 0 | 58 | 83 | 58 | 93 | 71 | 96 |
+| 3 | 10 | 69 | 33 | 20 | 88 | 89 | 88 | 44 | 6 | 33 | 61 |
+| 4 | 92 | 64 | 61 | 33 | 69 | 92 | 7 | 85 | 21 | 90 | 1 |
+| 5 | 97 | 89 | 40 | 86 | 86 | 72 | 5 | 38 | 23 | 81 | 93 |
+| 6 | 29 | 42 | 33 | 78 | 63 | 50 | 70 | 95 | 31 | 50 | 61 |
+| 7 | 12 | 1 | 34 | 85 | 5 | 10 | 52 | 83 | 9 | 83 | 58 |
+| 8 | 7 | 45 | 57 | 85 | 39 | 38 | 8 | 16 | 93 | 54 | 81 |
+| 9 | 70 | 47 | 3 | 81 | 96 | 55 | 32 | 42 | 45 | 57 | 11 |
+| 10 | 94 | 60 | 97 | 58 | 62 | 65 | 11 | 99 | 47 | 37 | 54 |
+
+## band_id=6
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 23 | 96 | 82 | 55 | 36 | 20 | 86 | 40 | 36 | 99 | 18 |
+| 1 | 11 | 24 | 53 | 42 | 66 | 8 | 89 | 53 | 78 | 38 | 71 |
+| 2 | 50 | 49 | 46 | 49 | 57 | 16 | 61 | 35 | 66 | 13 | 63 |
+| 3 | 33 | 52 | 64 | 77 | 85 | 9 | 94 | 97 | 38 | 71 | 41 |
+| 4 | 64 | 16 | 9 | 21 | 32 | 62 | 27 | 44 | 72 | 46 | 75 |
+| 5 | 66 | 14 | 13 | 39 | 14 | 55 | 63 | 4 | 49 | 15 | 87 |
+| 6 | 92 | 27 | 88 | 75 | 93 | 34 | 66 | 67 | 37 | 21 | 86 |
+| 7 | 22 | 5 | 63 | 12 | 54 | 81 | 45 | 30 | 49 | 57 | 22 |
+| 8 | 13 | 53 | 46 | 76 | 21 | 22 | 10 | 13 | 45 | 77 | 37 |
+| 9 | 43 | 83 | 46 | 24 | 60 | 61 | 64 | 57 | 70 | 43 | 12 |
+| 10 | 57 | 50 | 17 | 47 | 48 | 55 | 53 | 2 | 17 | 81 | 53 |
+
+## band_id=7
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 78 | 33 | 79 | 54 | 37 | 2 | 1 | 23 | 21 | 84 | 26 |
+| 1 | 86 | 42 | 93 | 14 | 74 | 41 | 12 | 61 | 5 | 6 | 72 |
+| 2 | 34 | 55 | 31 | 67 | 52 | 57 | 84 | 85 | 10 | 16 | 36 |
+| 3 | 40 | 39 | 79 | 40 | 25 | 22 | 37 | 71 | 26 | 39 | 86 |
+| 4 | 61 | 71 | 70 | 32 | 42 | 37 | 77 | 74 | 66 | 99 | 75 |
+| 5 | 7 | 66 | 39 | 98 | 68 | 74 | 72 | 40 | 36 | 4 | 12 |
+| 6 | 22 | 13 | 86 | 11 | 74 | 35 | 84 | 58 | 72 | 54 | 99 |
+| 7 | 46 | 34 | 75 | 64 | 31 | 98 | 81 | 96 | 35 | 53 | 80 |
+| 8 | 75 | 85 | 47 | 9 | 36 | 64 | 47 | 78 | 29 | 88 | 47 |
+| 9 | 67 | 17 | 92 | 42 | 84 | 4 | 3 | 88 | 94 | 26 | 23 |
+| 10 | 60 | 60 | 9 | 11 | 78 | 25 | 14 | 68 | 92 | 49 | 27 |
+
+## band_id=8
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 33 | 79 | 97 | 16 | 86 | 33 | 40 | 16 | 95 | 86 | 24 |
+| 1 | 20 | 24 | 18 | 73 | 72 | 65 | 29 | 3 | 18 | 51 | 70 |
+| 2 | 76 | 34 | 15 | 17 | 4 | 38 | 17 | 60 | 60 | 57 | 46 |
+| 3 | 53 | 75 | 11 | 34 | 81 | 83 | 87 | 39 | 23 | 10 | 24 |
+| 4 | 81 | 40 | 83 | 73 | 53 | 53 | 17 | 97 | 32 | 42 | 5 |
+| 5 | 54 | 1 | 2 | 87 | 97 | 70 | 93 | 74 | 41 | 95 | 11 |
+| 6 | 36 | 38 | 63 | 53 | 41 | 35 | 36 | 49 | 78 | 61 | 37 |
+| 7 | 84 | 19 | 98 | 87 | 24 | 23 | 33 | 35 | 97 | 60 | 25 |
+| 8 | 16 | 70 | 39 | 46 | 18 | 70 | 77 | 58 | 45 | 28 | 79 |
+| 9 | 23 | 30 | 43 | 51 | 67 | 56 | 50 | 51 | 95 | 35 | 23 |
+| 10 | 38 | 94 | 59 | 15 | 16 | 53 | 45 | 44 | 4 | 4 | 55 |
+
+## band_id=9
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 9 | 64 | 93 | 54 | 11 | 57 | 40 | 2 | 59 | 79 | 89 |
+| 1 | 55 | 62 | 77 | 35 | 36 | 32 | 0 | 12 | 78 | 3 | 44 |
+| 2 | 8 | 83 | 88 | 26 | 36 | 54 | 2 | 59 | 41 | 70 | 59 |
+| 3 | 34 | 0 | 3 | 39 | 72 | 4 | 68 | 7 | 7 | 88 | 91 |
+| 4 | 80 | 29 | 10 | 78 | 29 | 70 | 81 | 66 | 78 | 7 | 11 |
+| 5 | 35 | 59 | 13 | 90 | 48 | 21 | 80 | 46 | 34 | 73 | 58 |
+| 6 | 94 | 53 | 16 | 35 | 2 | 10 | 45 | 24 | 24 | 9 | 38 |
+| 7 | 74 | 50 | 85 | 34 | 14 | 5 | 23 | 82 | 48 | 46 | 88 |
+| 8 | 70 | 98 | 4 | 26 | 59 | 10 | 45 | 50 | 51 | 31 | 76 |
+| 9 | 29 | 84 | 22 | 17 | 0 | 39 | 32 | 57 | 46 | 36 | 88 |
+| 10 | 87 | 92 | 93 | 30 | 0 | 86 | 90 | 29 | 17 | 67 | 82 |
+
+## band_id=10
+| stage_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 79 | 12 | 77 | 45 | 31 | 15 | 7 | 63 | 10 | 74 | 97 |
+| 1 | 79 | 17 | 90 | 99 | 41 | 0 | 6 | 38 | 25 | 26 | 11 |
+| 2 | 1 | 14 | 83 | 31 | 10 | 52 | 77 | 51 | 58 | 28 | 75 |
+| 3 | 28 | 51 | 33 | 40 | 50 | 85 | 86 | 98 | 47 | 47 | 39 |
+| 4 | 77 | 62 | 23 | 80 | 89 | 99 | 2 | 48 | 24 | 29 | 37 |
+| 5 | 56 | 45 | 18 | 90 | 98 | 40 | 94 | 36 | 27 | 82 | 44 |
+| 6 | 24 | 55 | 85 | 69 | 45 | 81 | 53 | 16 | 82 | 81 | 17 |
+| 7 | 77 | 45 | 93 | 67 | 7 | 82 | 1 | 88 | 29 | 85 | 83 |
+| 8 | 19 | 77 | 26 | 61 | 35 | 24 | 9 | 77 | 15 | 24 | 43 |
+| 9 | 9 | 84 | 26 | 12 | 15 | 65 | 68 | 24 | 50 | 74 | 89 |
+| 10 | 27 | 61 | 77 | 76 | 59 | 13 | 92 | 16 | 30 | 44 | 71 |
+I then used these numbers to assign exactly one stage-and-time pair to each band so the sum of expected conflict costs is as small as possible.
+
+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': [[[98, 21, 40, 81, 69, 24, 30, 59, 57, 67, 86], [82, 71, 95, 93, 19, 99, 33, 40, 9, 51, 97], [5, 68, 64, 46, 4, 41, 56, 53, 10, 54, 7], [26, 65, 13, 26, 42, 46, 47, 67, 18, 17, 99], [52, 26, 60, 6, 94, 99, 47, 17, 3, 30, 86], [62, 22, 78, 48, 15, 38, 69, 98, 85, 17, 90], [34, 34, 10, 78, 56, 61, 60, 95, 32, 74, 91], [75, 37, 9, 6, 28, 73, 54, 29, 81, 21, 63], [81, 11, 45, 38, 64, 12, 30, 70, 88, 35, 54], [65, 91, 22, 13, 10, 33, 30, 49, 36, 36, 20], [29, 63, 31, 92, 14, 7, 18, 27, 23, 28, 40]], [[12, 48, 91, 60, 56, 76, 70, 85, 14, 47, 93], [47, 85, 70, 75, 95, 58, 11, 98, 65, 46, 52], [11, 76, 66, 5, 48, 65, 67, 60, 39, 15, 91], [17, 67, 7, 94, 93, 55, 40, 10, 4, 4, 68], [96, 9, 62, 84, 78, 82, 10, 28, 6, 65, 23], [81, 8, 27, 5, 24, 22, 22, 21, 38, 19, 8], [73, 60, 12, 43, 73, 82, 53, 79, 89, 53, 52], [39, 13, 6, 18, 23, 67, 96, 95, 46, 93, 26], [46, 1, 94, 93, 59, 43, 36, 46, 63, 85, 81], [24, 91, 97, 85, 96, 22, 69, 98, 7, 89, 4], [60, 57, 95, 4, 49, 91, 73, 30, 14, 59, 57]], [[61, 70, 4, 47, 13, 88, 0, 24, 43, 59, 30], [94, 18, 48, 51, 19, 8, 2, 68, 10, 30, 44], [95, 77, 59, 91, 66, 60, 60, 28, 25, 74, 67], [28, 61, 22, 5, 24, 45, 8, 63, 33, 58, 90], [2, 82, 15, 23, 47, 58, 39, 97, 40, 33, 73], [9, 8, 66, 7, 94, 28, 63, 2, 38, 14, 46], [18, 75, 95, 87, 80, 7, 5, 70, 62, 32, 89], [54, 1, 24, 91, 85, 95, 19, 66, 44, 24, 69], [4, 3, 93, 27, 26, 19, 14, 77, 58, 62, 50], [72, 75, 12, 69, 81, 36, 51, 52, 67, 78, 85], [69, 60, 69, 29, 64, 42, 84, 85, 96, 51, 37]], [[20, 49, 65, 98, 89, 43, 83, 93, 69, 28, 51], [87, 93, 58, 28, 60, 30, 67, 96, 22, 21, 89], [49, 11, 71, 89, 79, 12, 46, 0, 23, 41, 46], [64, 73, 67, 6, 75, 23, 20, 50, 75, 14, 43], [54, 49, 25, 31, 87, 38, 50, 61, 47, 21, 67], [42, 2, 68, 92, 70, 61, 60, 88, 33, 30, 31], [72, 21, 53, 56, 11, 18, 38, 24, 7, 43, 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'cost': 67}, {'i': 9, 'j': 10, 'k': 10, 'cost': 82}, {'i': 10, 'j': 0, 'k': 0, 'cost': 79}, {'i': 10, 'j': 0, 'k': 1, 'cost': 12}, {'i': 10, 'j': 0, 'k': 2, 'cost': 77}, {'i': 10, 'j': 0, 'k': 3, 'cost': 45}, {'i': 10, 'j': 0, 'k': 4, 'cost': 31}, {'i': 10, 'j': 0, 'k': 5, 'cost': 15}, {'i': 10, 'j': 0, 'k': 6, 'cost': 7}, {'i': 10, 'j': 0, 'k': 7, 'cost': 63}, {'i': 10, 'j': 0, 'k': 8, 'cost': 10}, {'i': 10, 'j': 0, 'k': 9, 'cost': 74}, {'i': 10, 'j': 0, 'k': 10, 'cost': 97}, {'i': 10, 'j': 1, 'k': 0, 'cost': 79}, {'i': 10, 'j': 1, 'k': 1, 'cost': 17}, {'i': 10, 'j': 1, 'k': 2, 'cost': 90}, {'i': 10, 'j': 1, 'k': 3, 'cost': 99}, {'i': 10, 'j': 1, 'k': 4, 'cost': 41}, {'i': 10, 'j': 1, 'k': 5, 'cost': 0}, {'i': 10, 'j': 1, 'k': 6, 'cost': 6}, {'i': 10, 'j': 1, 'k': 7, 'cost': 38}, {'i': 10, 'j': 1, 'k': 8, 'cost': 25}, {'i': 10, 'j': 1, 'k': 9, 'cost': 26}, {'i': 10, 'j': 1, 'k': 10, 'cost': 11}, {'i': 10, 'j': 2, 'k': 0, 'cost': 1}, {'i': 10, 'j': 2, 'k': 1, 'cost': 14}, {'i': 10, 'j': 2, 'k': 2, 'cost': 83}, {'i': 10, 'j': 2, 'k': 3, 'cost': 31}, {'i': 10, 'j': 2, 'k': 4, 'cost': 10}, {'i': 10, 'j': 2, 'k': 5, 'cost': 52}, {'i': 10, 'j': 2, 'k': 6, 'cost': 77}, {'i': 10, 'j': 2, 'k': 7, 'cost': 51}, {'i': 10, 'j': 2, 'k': 8, 'cost': 58}, {'i': 10, 'j': 2, 'k': 9, 'cost': 28}, {'i': 10, 'j': 2, 'k': 10, 'cost': 75}, {'i': 10, 'j': 3, 'k': 0, 'cost': 28}, {'i': 10, 'j': 3, 'k': 1, 'cost': 51}, {'i': 10, 'j': 3, 'k': 2, 'cost': 33}, {'i': 10, 'j': 3, 'k': 3, 'cost': 40}, {'i': 10, 'j': 3, 'k': 4, 'cost': 50}, {'i': 10, 'j': 3, 'k': 5, 'cost': 85}, {'i': 10, 'j': 3, 'k': 6, 'cost': 86}, {'i': 10, 'j': 3, 'k': 7, 'cost': 98}, {'i': 10, 'j': 3, 'k': 8, 'cost': 47}, {'i': 10, 'j': 3, 'k': 9, 'cost': 47}, {'i': 10, 'j': 3, 'k': 10, 'cost': 39}, {'i': 10, 'j': 4, 'k': 0, 'cost': 77}, {'i': 10, 'j': 4, 'k': 1, 'cost': 62}, {'i': 10, 'j': 4, 'k': 2, 'cost': 23}, {'i': 10, 'j': 4, 'k': 3, 'cost': 80}, {'i': 10, 'j': 4, 'k': 4, 'cost': 89}, {'i': 10, 'j': 4, 'k': 5, 'cost': 99}, {'i': 10, 'j': 4, 'k': 6, 'cost': 2}, {'i': 10, 'j': 4, 'k': 7, 'cost': 48}, {'i': 10, 'j': 4, 'k': 8, 'cost': 24}, {'i': 10, 'j': 4, 'k': 9, 'cost': 29}, {'i': 10, 'j': 4, 'k': 10, 'cost': 37}, {'i': 10, 'j': 5, 'k': 0, 'cost': 56}, {'i': 10, 'j': 5, 'k': 1, 'cost': 45}, {'i': 10, 'j': 5, 'k': 2, 'cost': 18}, {'i': 10, 'j': 5, 'k': 3, 'cost': 90}, {'i': 10, 'j': 5, 'k': 4, 'cost': 98}, {'i': 10, 'j': 5, 'k': 5, 'cost': 40}, {'i': 10, 'j': 5, 'k': 6, 'cost': 94}, {'i': 10, 'j': 5, 'k': 7, 'cost': 36}, {'i': 10, 'j': 5, 'k': 8, 'cost': 27}, {'i': 10, 'j': 5, 'k': 9, 'cost': 82}, {'i': 10, 'j': 5, 'k': 10, 'cost': 44}, {'i': 10, 'j': 6, 'k': 0, 'cost': 24}, {'i': 10, 'j': 6, 'k': 1, 'cost': 55}, {'i': 10, 'j': 6, 'k': 2, 'cost': 85}, {'i': 10, 'j': 6, 'k': 3, 'cost': 69}, {'i': 10, 'j': 6, 'k': 4, 'cost': 45}, {'i': 10, 'j': 6, 'k': 5, 'cost': 81}, {'i': 10, 'j': 6, 'k': 6, 'cost': 53}, {'i': 10, 'j': 6, 'k': 7, 'cost': 16}, {'i': 10, 'j': 6, 'k': 8, 'cost': 82}, {'i': 10, 'j': 6, 'k': 9, 'cost': 81}, {'i': 10, 'j': 6, 'k': 10, 'cost': 17}, {'i': 10, 'j': 7, 'k': 0, 'cost': 77}, {'i': 10, 'j': 7, 'k': 1, 'cost': 45}, {'i': 10, 'j': 7, 'k': 2, 'cost': 93}, {'i': 10, 'j': 7, 'k': 3, 'cost': 67}, {'i': 10, 'j': 7, 'k': 4, 'cost': 7}, {'i': 10, 'j': 7, 'k': 5, 'cost': 82}, {'i': 10, 'j': 7, 'k': 6, 'cost': 1}, {'i': 10, 'j': 7, 'k': 7, 'cost': 88}, {'i': 10, 'j': 7, 'k': 8, 'cost': 29}, {'i': 10, 'j': 7, 'k': 9, 'cost': 85}, {'i': 10, 'j': 7, 'k': 10, 'cost': 83}, {'i': 10, 'j': 8, 'k': 0, 'cost': 19}, {'i': 10, 'j': 8, 'k': 1, 'cost': 77}, {'i': 10, 'j': 8, 'k': 2, 'cost': 26}, {'i': 10, 'j': 8, 'k': 3, 'cost': 61}, {'i': 10, 'j': 8, 'k': 4, 'cost': 35}, {'i': 10, 'j': 8, 'k': 5, 'cost': 24}, {'i': 10, 'j': 8, 'k': 6, 'cost': 9}, {'i': 10, 'j': 8, 'k': 7, 'cost': 77}, {'i': 10, 'j': 8, 'k': 8, 'cost': 15}, {'i': 10, 'j': 8, 'k': 9, 'cost': 24}, {'i': 10, 'j': 8, 'k': 10, 'cost': 43}, {'i': 10, 'j': 9, 'k': 0, 'cost': 9}, {'i': 10, 'j': 9, 'k': 1, 'cost': 84}, {'i': 10, 'j': 9, 'k': 2, 'cost': 26}, {'i': 10, 'j': 9, 'k': 3, 'cost': 12}, {'i': 10, 'j': 9, 'k': 4, 'cost': 15}, {'i': 10, 'j': 9, 'k': 5, 'cost': 65}, {'i': 10, 'j': 9, 'k': 6, 'cost': 68}, {'i': 10, 'j': 9, 'k': 7, 'cost': 24}, {'i': 10, 'j': 9, 'k': 8, 'cost': 50}, {'i': 10, 'j': 9, 'k': 9, 'cost': 74}, {'i': 10, 'j': 9, 'k': 10, 'cost': 89}, {'i': 10, 'j': 10, 'k': 0, 'cost': 27}, {'i': 10, 'j': 10, 'k': 1, 'cost': 61}, {'i': 10, 'j': 10, 'k': 2, 'cost': 77}, {'i': 10, 'j': 10, 'k': 3, 'cost': 76}, {'i': 10, 'j': 10, 'k': 4, 'cost': 59}, {'i': 10, 'j': 10, 'k': 5, 'cost': 13}, {'i': 10, 'j': 10, 'k': 6, 'cost': 92}, {'i': 10, 'j': 10, 'k': 7, 'cost': 16}, {'i': 10, 'j': 10, 'k': 8, 'cost': 30}, {'i': 10, 'j': 10, 'k': 9, 'cost': 44}, {'i': 10, 'j': 10, 'k': 10, 'cost': 71}]}","[[0, 7, 3], [1, 3, 9], [2, 8, 0], [3, 9, 8], [4, 2, 2], [5, 4, 10], [6, 10, 7], [7, 0, 6], [8, 5, 1], [9, 6, 4], [10, 1, 5]]",9,nl,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"": 12,
+  ""index_identifiers"": [
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8,
+    9,
+    10,
+    11,
+    12
+  ]
+}
+
+# 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=1
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 23 | 9 | 26 | 84 | 11 | 48 | 53 | 10 | 9 | 58 | 34 | 67 |
+| 2 | 14 | 10 | 72 | 56 | 4 | 55 | 58 | 26 | 45 | 39 | 87 | 6 |
+| 3 | 58 | 24 | 97 | 63 | 10 | 84 | 66 | 72 | 83 | 22 | 4 | 39 |
+| 4 | 99 | 65 | 34 | 51 | 95 | 51 | 51 | 93 | 72 | 47 | 89 | 46 |
+| 5 | 7 | 46 | 78 | 19 | 94 | 47 | 85 | 25 | 60 | 23 | 31 | 93 |
+| 6 | 79 | 13 | 39 | 18 | 93 | 40 | 53 | 29 | 45 | 68 | 30 | 10 |
+| 7 | 23 | 15 | 30 | 94 | 78 | 99 | 12 | 5 | 30 | 97 | 30 | 19 |
+| 8 | 78 | 2 | 32 | 13 | 64 | 88 | 18 | 72 | 17 | 22 | 70 | 18 |
+| 9 | 61 | 6 | 47 | 13 | 52 | 55 | 7 | 3 | 56 | 94 | 43 | 9 |
+| 10 | 8 | 15 | 61 | 47 | 97 | 46 | 88 | 66 | 76 | 24 | 86 | 97 |
+| 11 | 91 | 7 | 48 | 80 | 54 | 60 | 42 | 97 | 77 | 32 | 2 | 88 |
+| 12 | 3 | 31 | 62 | 65 | 29 | 50 | 80 | 81 | 10 | 0 | 38 | 69 |
+
+## document_id=2
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 2 | 31 | 98 | 42 | 89 | 24 | 94 | 44 | 63 | 98 | 94 | 61 |
+| 2 | 15 | 17 | 30 | 99 | 44 | 66 | 57 | 66 | 27 | 64 | 11 | 93 |
+| 3 | 0 | 6 | 59 | 2 | 14 | 45 | 27 | 79 | 21 | 79 | 8 | 49 |
+| 4 | 61 | 81 | 52 | 16 | 98 | 36 | 32 | 55 | 78 | 35 | 91 | 52 |
+| 5 | 94 | 77 | 80 | 23 | 3 | 1 | 16 | 20 | 40 | 27 | 35 | 46 |
+| 6 | 9 | 28 | 1 | 68 | 9 | 26 | 26 | 97 | 90 | 55 | 59 | 16 |
+| 7 | 3 | 39 | 74 | 92 | 18 | 33 | 98 | 84 | 69 | 83 | 59 | 26 |
+| 8 | 92 | 67 | 96 | 2 | 11 | 74 | 87 | 22 | 22 | 47 | 27 | 43 |
+| 9 | 32 | 76 | 16 | 98 | 24 | 57 | 14 | 59 | 90 | 96 | 30 | 87 |
+| 10 | 49 | 73 | 61 | 34 | 75 | 78 | 8 | 33 | 35 | 57 | 72 | 34 |
+| 11 | 74 | 51 | 33 | 51 | 21 | 62 | 32 | 64 | 18 | 6 | 39 | 29 |
+| 12 | 54 | 55 | 37 | 78 | 32 | 98 | 25 | 87 | 77 | 44 | 2 | 60 |
+
+## document_id=3
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 83 | 28 | 87 | 90 | 63 | 38 | 39 | 25 | 81 | 35 | 55 | 53 |
+| 2 | 2 | 87 | 7 | 72 | 50 | 88 | 42 | 93 | 29 | 79 | 34 | 61 |
+| 3 | 21 | 88 | 22 | 67 | 86 | 82 | 71 | 52 | 10 | 41 | 9 | 22 |
+| 4 | 83 | 71 | 54 | 70 | 17 | 48 | 94 | 71 | 79 | 81 | 80 | 61 |
+| 5 | 85 | 98 | 60 | 14 | 3 | 24 | 80 | 35 | 81 | 7 | 94 | 14 |
+| 6 | 32 | 81 | 12 | 18 | 89 | 56 | 29 | 52 | 63 | 9 | 30 | 96 |
+| 7 | 73 | 26 | 48 | 81 | 6 | 68 | 48 | 78 | 91 | 51 | 56 | 34 |
+| 8 | 95 | 0 | 8 | 65 | 61 | 3 | 41 | 81 | 26 | 22 | 58 | 41 |
+| 9 | 9 | 25 | 73 | 80 | 49 | 66 | 33 | 97 | 87 | 41 | 15 | 59 |
+| 10 | 80 | 87 | 98 | 9 | 77 | 59 | 31 | 16 | 37 | 27 | 19 | 38 |
+| 11 | 10 | 91 | 12 | 84 | 22 | 99 | 42 | 35 | 15 | 2 | 47 | 35 |
+| 12 | 86 | 55 | 76 | 52 | 75 | 23 | 26 | 65 | 32 | 43 | 59 | 88 |
+
+## document_id=4
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 26 | 82 | 7 | 19 | 14 | 3 | 52 | 76 | 31 | 96 | 77 | 45 |
+| 2 | 63 | 2 | 65 | 11 | 84 | 52 | 36 | 38 | 49 | 17 | 38 | 71 |
+| 3 | 61 | 43 | 42 | 42 | 23 | 84 | 73 | 88 | 15 | 62 | 98 | 92 |
+| 4 | 41 | 99 | 43 | 33 | 42 | 17 | 90 | 64 | 32 | 77 | 82 | 43 |
+| 5 | 88 | 56 | 53 | 18 | 62 | 21 | 27 | 63 | 33 | 80 | 32 | 68 |
+| 6 | 16 | 26 | 85 | 22 | 19 | 4 | 54 | 58 | 17 | 25 | 37 | 13 |
+| 7 | 69 | 47 | 95 | 56 | 69 | 52 | 28 | 72 | 89 | 21 | 4 | 54 |
+| 8 | 63 | 46 | 3 | 53 | 35 | 37 | 76 | 14 | 50 | 5 | 39 | 20 |
+| 9 | 82 | 62 | 58 | 92 | 82 | 75 | 20 | 60 | 2 | 7 | 16 | 62 |
+| 10 | 48 | 67 | 32 | 18 | 38 | 5 | 79 | 61 | 97 | 47 | 58 | 22 |
+| 11 | 4 | 54 | 44 | 73 | 61 | 65 | 92 | 93 | 95 | 99 | 56 | 29 |
+| 12 | 37 | 18 | 34 | 2 | 21 | 10 | 98 | 92 | 91 | 93 | 61 | 46 |
+
+## document_id=5
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 52 | 37 | 84 | 60 | 0 | 28 | 3 | 19 | 92 | 23 | 11 | 76 |
+| 2 | 3 | 71 | 86 | 28 | 44 | 81 | 92 | 27 | 61 | 41 | 57 | 55 |
+| 3 | 37 | 58 | 58 | 71 | 41 | 54 | 93 | 57 | 67 | 95 | 58 | 0 |
+| 4 | 53 | 80 | 59 | 35 | 82 | 23 | 66 | 47 | 2 | 94 | 75 | 71 |
+| 5 | 97 | 19 | 14 | 44 | 19 | 55 | 54 | 77 | 60 | 99 | 19 | 8 |
+| 6 | 8 | 43 | 42 | 93 | 17 | 72 | 48 | 69 | 76 | 61 | 67 | 41 |
+| 7 | 75 | 29 | 52 | 20 | 41 | 66 | 5 | 50 | 55 | 88 | 17 | 37 |
+| 8 | 92 | 0 | 3 | 98 | 46 | 88 | 75 | 5 | 33 | 51 | 39 | 59 |
+| 9 | 51 | 80 | 42 | 40 | 10 | 24 | 25 | 13 | 30 | 80 | 12 | 5 |
+| 10 | 60 | 32 | 47 | 14 | 94 | 62 | 25 | 11 | 28 | 57 | 2 | 72 |
+| 11 | 97 | 32 | 41 | 69 | 65 | 89 | 45 | 68 | 88 | 65 | 50 | 34 |
+| 12 | 22 | 95 | 13 | 35 | 76 | 69 | 2 | 15 | 52 | 10 | 81 | 88 |
+
+## document_id=6
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 24 | 64 | 34 | 89 | 50 | 37 | 78 | 74 | 15 | 5 | 65 | 87 |
+| 2 | 50 | 57 | 73 | 54 | 11 | 14 | 45 | 83 | 6 | 7 | 80 | 22 |
+| 3 | 64 | 78 | 8 | 63 | 37 | 76 | 74 | 94 | 87 | 64 | 58 | 96 |
+| 4 | 89 | 72 | 1 | 48 | 98 | 38 | 41 | 68 | 96 | 99 | 29 | 53 |
+| 5 | 16 | 81 | 72 | 79 | 8 | 47 | 34 | 80 | 2 | 69 | 85 | 27 |
+| 6 | 70 | 86 | 66 | 87 | 24 | 59 | 61 | 75 | 64 | 53 | 65 | 55 |
+| 7 | 12 | 15 | 47 | 32 | 26 | 50 | 99 | 64 | 99 | 69 | 41 | 18 |
+| 8 | 12 | 84 | 22 | 28 | 66 | 7 | 34 | 5 | 21 | 56 | 14 | 85 |
+| 9 | 14 | 56 | 64 | 61 | 25 | 56 | 96 | 17 | 42 | 79 | 55 | 57 |
+| 10 | 80 | 35 | 91 | 51 | 65 | 46 | 4 | 47 | 80 | 80 | 41 | 76 |
+| 11 | 87 | 75 | 71 | 32 | 38 | 37 | 33 | 98 | 13 | 55 | 33 | 96 |
+| 12 | 81 | 7 | 42 | 45 | 90 | 23 | 45 | 10 | 27 | 10 | 14 | 76 |
+
+## document_id=7
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 52 | 1 | 51 | 92 | 67 | 48 | 61 | 46 | 63 | 54 | 67 | 0 |
+| 2 | 73 | 33 | 16 | 69 | 1 | 12 | 59 | 63 | 24 | 70 | 87 | 93 |
+| 3 | 64 | 53 | 20 | 68 | 64 | 50 | 92 | 76 | 94 | 90 | 22 | 32 |
+| 4 | 13 | 52 | 90 | 2 | 38 | 20 | 82 | 76 | 89 | 71 | 11 | 89 |
+| 5 | 53 | 41 | 57 | 93 | 93 | 96 | 75 | 91 | 85 | 32 | 60 | 89 |
+| 6 | 14 | 72 | 62 | 83 | 5 | 95 | 77 | 37 | 87 | 97 | 41 | 70 |
+| 7 | 95 | 36 | 15 | 37 | 63 | 31 | 66 | 88 | 34 | 87 | 47 | 62 |
+| 8 | 23 | 38 | 59 | 94 | 4 | 74 | 86 | 78 | 90 | 25 | 11 | 94 |
+| 9 | 70 | 85 | 65 | 14 | 94 | 37 | 35 | 63 | 23 | 7 | 15 | 38 |
+| 10 | 22 | 32 | 99 | 78 | 81 | 48 | 15 | 91 | 47 | 71 | 70 | 4 |
+| 11 | 21 | 18 | 85 | 74 | 82 | 46 | 22 | 4 | 54 | 26 | 82 | 11 |
+| 12 | 51 | 52 | 10 | 43 | 23 | 52 | 50 | 53 | 77 | 59 | 90 | 10 |
+
+## document_id=8
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 33 | 98 | 41 | 72 | 32 | 86 | 32 | 17 | 19 | 98 | 5 | 10 |
+| 2 | 58 | 46 | 46 | 24 | 69 | 71 | 11 | 22 | 82 | 24 | 76 | 76 |
+| 3 | 26 | 4 | 31 | 19 | 17 | 18 | 66 | 44 | 13 | 19 | 56 | 28 |
+| 4 | 38 | 14 | 99 | 93 | 85 | 33 | 20 | 95 | 31 | 83 | 19 | 51 |
+| 5 | 31 | 11 | 66 | 44 | 29 | 22 | 39 | 54 | 78 | 79 | 37 | 63 |
+| 6 | 92 | 60 | 86 | 88 | 80 | 49 | 54 | 43 | 39 | 96 | 29 | 91 |
+| 7 | 76 | 96 | 14 | 14 | 88 | 98 | 58 | 78 | 89 | 44 | 70 | 30 |
+| 8 | 77 | 16 | 62 | 25 | 98 | 25 | 16 | 87 | 32 | 9 | 60 | 69 |
+| 9 | 30 | 86 | 11 | 61 | 57 | 0 | 91 | 3 | 94 | 30 | 78 | 19 |
+| 10 | 16 | 68 | 40 | 54 | 35 | 67 | 23 | 20 | 45 | 4 | 16 | 32 |
+| 11 | 67 | 38 | 28 | 18 | 2 | 32 | 91 | 35 | 36 | 47 | 3 | 19 |
+| 12 | 8 | 78 | 74 | 48 | 17 | 87 | 75 | 6 | 92 | 47 | 5 | 14 |
+
+## document_id=9
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 93 | 89 | 44 | 70 | 91 | 77 | 66 | 47 | 44 | 85 | 25 |
+| 2 | 93 | 64 | 72 | 52 | 2 | 15 | 38 | 9 | 72 | 89 | 74 | 86 |
+| 3 | 46 | 34 | 17 | 87 | 77 | 47 | 52 | 16 | 39 | 76 | 94 | 76 |
+| 4 | 47 | 65 | 66 | 43 | 21 | 29 | 97 | 52 | 53 | 60 | 77 | 50 |
+| 5 | 84 | 37 | 37 | 62 | 9 | 64 | 50 | 79 | 2 | 23 | 11 | 1 |
+| 6 | 70 | 89 | 53 | 0 | 88 | 60 | 99 | 84 | 79 | 93 | 82 | 64 |
+| 7 | 58 | 93 | 81 | 28 | 37 | 99 | 8 | 75 | 74 | 35 | 68 | 7 |
+| 8 | 11 | 98 | 76 | 82 | 41 | 77 | 15 | 43 | 80 | 39 | 65 | 87 |
+| 9 | 84 | 64 | 13 | 97 | 69 | 64 | 21 | 34 | 68 | 55 | 40 | 68 |
+| 10 | 94 | 53 | 72 | 44 | 64 | 11 | 14 | 46 | 5 | 55 | 63 | 45 |
+| 11 | 19 | 27 | 69 | 14 | 96 | 80 | 44 | 13 | 30 | 66 | 70 | 49 |
+| 12 | 75 | 8 | 15 | 54 | 45 | 29 | 68 | 97 | 65 | 51 | 50 | 30 |
+
+## document_id=10
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 75 | 93 | 26 | 65 | 54 | 16 | 46 | 85 | 50 | 92 | 62 | 69 |
+| 2 | 14 | 64 | 50 | 1 | 1 | 9 | 85 | 91 | 90 | 8 | 18 | 95 |
+| 3 | 71 | 64 | 18 | 57 | 54 | 41 | 72 | 40 | 42 | 22 | 85 | 35 |
+| 4 | 0 | 0 | 18 | 24 | 26 | 2 | 57 | 47 | 63 | 29 | 64 | 50 |
+| 5 | 57 | 35 | 35 | 60 | 92 | 43 | 94 | 84 | 97 | 43 | 80 | 23 |
+| 6 | 1 | 35 | 11 | 61 | 4 | 34 | 7 | 29 | 52 | 89 | 44 | 58 |
+| 7 | 57 | 82 | 82 | 21 | 29 | 13 | 78 | 92 | 13 | 12 | 79 | 40 |
+| 8 | 55 | 6 | 45 | 67 | 66 | 82 | 31 | 28 | 88 | 95 | 23 | 29 |
+| 9 | 49 | 76 | 47 | 94 | 20 | 5 | 13 | 62 | 18 | 67 | 78 | 21 |
+| 10 | 45 | 89 | 53 | 59 | 83 | 0 | 36 | 77 | 77 | 6 | 87 | 26 |
+| 11 | 95 | 74 | 53 | 63 | 53 | 42 | 13 | 29 | 84 | 41 | 85 | 57 |
+| 12 | 42 | 81 | 30 | 12 | 44 | 73 | 39 | 29 | 25 | 88 | 33 | 73 |
+
+## document_id=11
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 3 | 52 | 10 | 52 | 75 | 50 | 22 | 14 | 58 | 99 | 92 | 89 |
+| 2 | 48 | 45 | 83 | 17 | 16 | 57 | 62 | 34 | 20 | 36 | 63 | 96 |
+| 3 | 14 | 11 | 11 | 54 | 68 | 15 | 26 | 65 | 85 | 53 | 77 | 65 |
+| 4 | 60 | 7 | 19 | 10 | 76 | 44 | 41 | 95 | 16 | 62 | 99 | 66 |
+| 5 | 70 | 28 | 95 | 66 | 68 | 4 | 68 | 72 | 45 | 82 | 99 | 76 |
+| 6 | 37 | 66 | 88 | 58 | 90 | 75 | 31 | 54 | 54 | 58 | 63 | 86 |
+| 7 | 58 | 33 | 32 | 41 | 96 | 17 | 91 | 19 | 93 | 31 | 24 | 92 |
+| 8 | 39 | 33 | 63 | 40 | 58 | 18 | 46 | 0 | 5 | 43 | 2 | 42 |
+| 9 | 69 | 56 | 2 | 64 | 4 | 80 | 86 | 62 | 29 | 48 | 13 | 67 |
+| 10 | 4 | 55 | 94 | 58 | 59 | 22 | 87 | 18 | 30 | 3 | 31 | 83 |
+| 11 | 53 | 85 | 10 | 66 | 0 | 52 | 79 | 52 | 75 | 29 | 4 | 82 |
+| 12 | 92 | 17 | 31 | 26 | 75 | 4 | 76 | 33 | 4 | 27 | 24 | 82 |
+
+## document_id=12
+| translator_id\language_pair_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 52 | 47 | 80 | 73 | 86 | 41 | 10 | 96 | 97 | 63 | 95 | 76 |
+| 2 | 54 | 95 | 79 | 92 | 62 | 93 | 5 | 57 | 82 | 65 | 90 | 16 |
+| 3 | 34 | 34 | 28 | 15 | 37 | 50 | 43 | 65 | 57 | 87 | 69 | 53 |
+| 4 | 69 | 78 | 34 | 31 | 59 | 6 | 5 | 82 | 3 | 96 | 24 | 15 |
+| 5 | 94 | 48 | 80 | 71 | 61 | 2 | 13 | 87 | 33 | 70 | 82 | 28 |
+| 6 | 8 | 70 | 41 | 55 | 75 | 87 | 2 | 75 | 21 | 0 | 27 | 90 |
+| 7 | 13 | 21 | 85 | 33 | 24 | 36 | 25 | 61 | 94 | 70 | 33 | 6 |
+| 8 | 8 | 15 | 28 | 3 | 54 | 16 | 36 | 1 | 72 | 75 | 60 | 81 |
+| 9 | 48 | 39 | 19 | 72 | 66 | 98 | 72 | 26 | 97 | 5 | 5 | 97 |
+| 10 | 88 | 82 | 49 | 19 | 33 | 11 | 16 | 78 | 92 | 34 | 52 | 33 |
+| 11 | 93 | 40 | 14 | 47 | 24 | 4 | 51 | 83 | 85 | 1 | 93 | 80 |
+| 12 | 64 | 27 | 7 | 41 | 2 | 11 | 25 | 69 | 47 | 54 | 3 | 6 |
+
+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': [[[23, 9, 26, 84, 11, 48, 53, 10, 9, 58, 34, 67], [14, 10, 72, 56, 4, 55, 58, 26, 45, 39, 87, 6], [58, 24, 97, 63, 10, 84, 66, 72, 83, 22, 4, 39], [99, 65, 34, 51, 95, 51, 51, 93, 72, 47, 89, 46], [7, 46, 78, 19, 94, 47, 85, 25, 60, 23, 31, 93], [79, 13, 39, 18, 93, 40, 53, 29, 45, 68, 30, 10], [23, 15, 30, 94, 78, 99, 12, 5, 30, 97, 30, 19], [78, 2, 32, 13, 64, 88, 18, 72, 17, 22, 70, 18], [61, 6, 47, 13, 52, 55, 7, 3, 56, 94, 43, 9], [8, 15, 61, 47, 97, 46, 88, 66, 76, 24, 86, 97], [91, 7, 48, 80, 54, 60, 42, 97, 77, 32, 2, 88], [3, 31, 62, 65, 29, 50, 80, 81, 10, 0, 38, 69]], [[2, 31, 98, 42, 89, 24, 94, 44, 63, 98, 94, 61], [15, 17, 30, 99, 44, 66, 57, 66, 27, 64, 11, 93], [0, 6, 59, 2, 14, 45, 27, 79, 21, 79, 8, 49], [61, 81, 52, 16, 98, 36, 32, 55, 78, 35, 91, 52], [94, 77, 80, 23, 3, 1, 16, 20, 40, 27, 35, 46], [9, 28, 1, 68, 9, 26, 26, 97, 90, 55, 59, 16], [3, 39, 74, 92, 18, 33, 98, 84, 69, 83, 59, 26], [92, 67, 96, 2, 11, 74, 87, 22, 22, 47, 27, 43], [32, 76, 16, 98, 24, 57, 14, 59, 90, 96, 30, 87], [49, 73, 61, 34, 75, 78, 8, 33, 35, 57, 72, 34], [74, 51, 33, 51, 21, 62, 32, 64, 18, 6, 39, 29], [54, 55, 37, 78, 32, 98, 25, 87, 77, 44, 2, 60]], [[83, 28, 87, 90, 63, 38, 39, 25, 81, 35, 55, 53], [2, 87, 7, 72, 50, 88, 42, 93, 29, 79, 34, 61], [21, 88, 22, 67, 86, 82, 71, 52, 10, 41, 9, 22], [83, 71, 54, 70, 17, 48, 94, 71, 79, 81, 80, 61], [85, 98, 60, 14, 3, 24, 80, 35, 81, 7, 94, 14], [32, 81, 12, 18, 89, 56, 29, 52, 63, 9, 30, 96], [73, 26, 48, 81, 6, 68, 48, 78, 91, 51, 56, 34], [95, 0, 8, 65, 61, 3, 41, 81, 26, 22, 58, 41], [9, 25, 73, 80, 49, 66, 33, 97, 87, 41, 15, 59], [80, 87, 98, 9, 77, 59, 31, 16, 37, 27, 19, 38], [10, 91, 12, 84, 22, 99, 42, 35, 15, 2, 47, 35], [86, 55, 76, 52, 75, 23, 26, 65, 32, 43, 59, 88]], [[26, 82, 7, 19, 14, 3, 52, 76, 31, 96, 77, 45], [63, 2, 65, 11, 84, 52, 36, 38, 49, 17, 38, 71], [61, 43, 42, 42, 23, 84, 73, 88, 15, 62, 98, 92], [41, 99, 43, 33, 42, 17, 90, 64, 32, 77, 82, 43], [88, 56, 53, 18, 62, 21, 27, 63, 33, 80, 32, 68], [16, 26, 85, 22, 19, 4, 54, 58, 17, 25, 37, 13], [69, 47, 95, 56, 69, 52, 28, 72, 89, 21, 4, 54], [63, 46, 3, 53, 35, 37, 76, 14, 50, 5, 39, 20], [82, 62, 58, 92, 82, 75, 20, 60, 2, 7, 16, 62], [48, 67, 32, 18, 38, 5, 79, 61, 97, 47, 58, 22], [4, 54, 44, 73, 61, 65, 92, 93, 95, 99, 56, 29], [37, 18, 34, 2, 21, 10, 98, 92, 91, 93, 61, 46]], [[52, 37, 84, 60, 0, 28, 3, 19, 92, 23, 11, 76], [3, 71, 86, 28, 44, 81, 92, 27, 61, 41, 57, 55], [37, 58, 58, 71, 41, 54, 93, 57, 67, 95, 58, 0], [53, 80, 59, 35, 82, 23, 66, 47, 2, 94, 75, 71], [97, 19, 14, 44, 19, 55, 54, 77, 60, 99, 19, 8], [8, 43, 42, 93, 17, 72, 48, 69, 76, 61, 67, 41], [75, 29, 52, 20, 41, 66, 5, 50, 55, 88, 17, 37], [92, 0, 3, 98, 46, 88, 75, 5, 33, 51, 39, 59], [51, 80, 42, 40, 10, 24, 25, 13, 30, 80, 12, 5], [60, 32, 47, 14, 94, 62, 25, 11, 28, 57, 2, 72], [97, 32, 41, 69, 65, 89, 45, 68, 88, 65, 50, 34], [22, 95, 13, 35, 76, 69, 2, 15, 52, 10, 81, 88]], [[24, 64, 34, 89, 50, 37, 78, 74, 15, 5, 65, 87], [50, 57, 73, 54, 11, 14, 45, 83, 6, 7, 80, 22], [64, 78, 8, 63, 37, 76, 74, 94, 87, 64, 58, 96], [89, 72, 1, 48, 98, 38, 41, 68, 96, 99, 29, 53], [16, 81, 72, 79, 8, 47, 34, 80, 2, 69, 85, 27], [70, 86, 66, 87, 24, 59, 61, 75, 64, 53, 65, 55], [12, 15, 47, 32, 26, 50, 99, 64, 99, 69, 41, 18], [12, 84, 22, 28, 66, 7, 34, 5, 21, 56, 14, 85], [14, 56, 64, 61, 25, 56, 96, 17, 42, 79, 55, 57], [80, 35, 91, 51, 65, 46, 4, 47, 80, 80, 41, 76], [87, 75, 71, 32, 38, 37, 33, 98, 13, 55, 33, 96], [81, 7, 42, 45, 90, 23, 45, 10, 27, 10, 14, 76]], [[52, 1, 51, 92, 67, 48, 61, 46, 63, 54, 67, 0], [73, 33, 16, 69, 1, 12, 59, 63, 24, 70, 87, 93], [64, 53, 20, 68, 64, 50, 92, 76, 94, 90, 22, 32], [13, 52, 90, 2, 38, 20, 82, 76, 89, 71, 11, 89], [53, 41, 57, 93, 93, 96, 75, 91, 85, 32, 60, 89], [14, 72, 62, 83, 5, 95, 77, 37, 87, 97, 41, 70], [95, 36, 15, 37, 63, 31, 66, 88, 34, 87, 47, 62], [23, 38, 59, 94, 4, 74, 86, 78, 90, 25, 11, 94], [70, 85, 65, 14, 94, 37, 35, 63, 23, 7, 15, 38], [22, 32, 99, 78, 81, 48, 15, 91, 47, 71, 70, 4], [21, 18, 85, 74, 82, 46, 22, 4, 54, 26, 82, 11], [51, 52, 10, 43, 23, 52, 50, 53, 77, 59, 90, 10]], [[33, 98, 41, 72, 32, 86, 32, 17, 19, 98, 5, 10], [58, 46, 46, 24, 69, 71, 11, 22, 82, 24, 76, 76], [26, 4, 31, 19, 17, 18, 66, 44, 13, 19, 56, 28], [38, 14, 99, 93, 85, 33, 20, 95, 31, 83, 19, 51], [31, 11, 66, 44, 29, 22, 39, 54, 78, 79, 37, 63], [92, 60, 86, 88, 80, 49, 54, 43, 39, 96, 29, 91], [76, 96, 14, 14, 88, 98, 58, 78, 89, 44, 70, 30], [77, 16, 62, 25, 98, 25, 16, 87, 32, 9, 60, 69], [30, 86, 11, 61, 57, 0, 91, 3, 94, 30, 78, 19], [16, 68, 40, 54, 35, 67, 23, 20, 45, 4, 16, 32], [67, 38, 28, 18, 2, 32, 91, 35, 36, 47, 3, 19], [8, 78, 74, 48, 17, 87, 75, 6, 92, 47, 5, 14]], [[82, 93, 89, 44, 70, 91, 77, 66, 47, 44, 85, 25], [93, 64, 72, 52, 2, 15, 38, 9, 72, 89, 74, 86], [46, 34, 17, 87, 77, 47, 52, 16, 39, 76, 94, 76], [47, 65, 66, 43, 21, 29, 97, 52, 53, 60, 77, 50], [84, 37, 37, 62, 9, 64, 50, 79, 2, 23, 11, 1], [70, 89, 53, 0, 88, 60, 99, 84, 79, 93, 82, 64], [58, 93, 81, 28, 37, 99, 8, 75, 74, 35, 68, 7], [11, 98, 76, 82, 41, 77, 15, 43, 80, 39, 65, 87], [84, 64, 13, 97, 69, 64, 21, 34, 68, 55, 40, 68], [94, 53, 72, 44, 64, 11, 14, 46, 5, 55, 63, 45], [19, 27, 69, 14, 96, 80, 44, 13, 30, 66, 70, 49], [75, 8, 15, 54, 45, 29, 68, 97, 65, 51, 50, 30]], [[75, 93, 26, 65, 54, 16, 46, 85, 50, 92, 62, 69], [14, 64, 50, 1, 1, 9, 85, 91, 90, 8, 18, 95], [71, 64, 18, 57, 54, 41, 72, 40, 42, 22, 85, 35], [0, 0, 18, 24, 26, 2, 57, 47, 63, 29, 64, 50], [57, 35, 35, 60, 92, 43, 94, 84, 97, 43, 80, 23], [1, 35, 11, 61, 4, 34, 7, 29, 52, 89, 44, 58], [57, 82, 82, 21, 29, 13, 78, 92, 13, 12, 79, 40], [55, 6, 45, 67, 66, 82, 31, 28, 88, 95, 23, 29], [49, 76, 47, 94, 20, 5, 13, 62, 18, 67, 78, 21], [45, 89, 53, 59, 83, 0, 36, 77, 77, 6, 87, 26], [95, 74, 53, 63, 53, 42, 13, 29, 84, 41, 85, 57], [42, 81, 30, 12, 44, 73, 39, 29, 25, 88, 33, 73]], [[3, 52, 10, 52, 75, 50, 22, 14, 58, 99, 92, 89], [48, 45, 83, 17, 16, 57, 62, 34, 20, 36, 63, 96], [14, 11, 11, 54, 68, 15, 26, 65, 85, 53, 77, 65], [60, 7, 19, 10, 76, 44, 41, 95, 16, 62, 99, 66], [70, 28, 95, 66, 68, 4, 68, 72, 45, 82, 99, 76], [37, 66, 88, 58, 90, 75, 31, 54, 54, 58, 63, 86], [58, 33, 32, 41, 96, 17, 91, 19, 93, 31, 24, 92], [39, 33, 63, 40, 58, 18, 46, 0, 5, 43, 2, 42], [69, 56, 2, 64, 4, 80, 86, 62, 29, 48, 13, 67], [4, 55, 94, 58, 59, 22, 87, 18, 30, 3, 31, 83], [53, 85, 10, 66, 0, 52, 79, 52, 75, 29, 4, 82], [92, 17, 31, 26, 75, 4, 76, 33, 4, 27, 24, 82]], [[52, 47, 80, 73, 86, 41, 10, 96, 97, 63, 95, 76], [54, 95, 79, 92, 62, 93, 5, 57, 82, 65, 90, 16], [34, 34, 28, 15, 37, 50, 43, 65, 57, 87, 69, 53], [69, 78, 34, 31, 59, 6, 5, 82, 3, 96, 24, 15], [94, 48, 80, 71, 61, 2, 13, 87, 33, 70, 82, 28], [8, 70, 41, 55, 75, 87, 2, 75, 21, 0, 27, 90], [13, 21, 85, 33, 24, 36, 25, 61, 94, 70, 33, 6], [8, 15, 28, 3, 54, 16, 36, 1, 72, 75, 60, 81], [48, 39, 19, 72, 66, 98, 72, 26, 97, 5, 5, 97], [88, 82, 49, 19, 33, 11, 16, 78, 92, 34, 52, 33], [93, 40, 14, 47, 24, 4, 51, 83, 85, 1, 93, 80], [64, 27, 7, 41, 2, 11, 25, 69, 47, 54, 3, 6]]], 'objective': 16.0}","[[0, 11, 9], [1, 2, 3], [2, 1, 0], [3, 6, 10], [4, 7, 1], [5, 3, 2], [6, 0, 11], [7, 8, 7], [8, 4, 8], [9, 9, 5], [10, 10, 4], [11, 5, 6]]",16.0,"{'problem_type': 'AP3', 'n': 12, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 23}, {'i': 1, 'j': 1, 'k': 2, 'cost': 9}, {'i': 1, 'j': 1, 'k': 3, 'cost': 26}, {'i': 1, 'j': 1, 'k': 4, 'cost': 84}, {'i': 1, 'j': 1, 'k': 5, 'cost': 11}, {'i': 1, 'j': 1, 'k': 6, 'cost': 48}, {'i': 1, 'j': 1, 'k': 7, 'cost': 53}, {'i': 1, 'j': 1, 'k': 8, 'cost': 10}, {'i': 1, 'j': 1, 'k': 9, 'cost': 9}, {'i': 1, 'j': 1, 'k': 10, 'cost': 58}, {'i': 1, 'j': 1, 'k': 11, 'cost': 34}, {'i': 1, 'j': 1, 'k': 12, 'cost': 67}, {'i': 1, 'j': 2, 'k': 1, 'cost': 14}, {'i': 1, 'j': 2, 'k': 2, 'cost': 10}, {'i': 1, 'j': 2, 'k': 3, 'cost': 72}, {'i': 1, 'j': 2, 'k': 4, 'cost': 56}, {'i': 1, 'j': 2, 'k': 5, 'cost': 4}, {'i': 1, 'j': 2, 'k': 6, 'cost': 55}, {'i': 1, 'j': 2, 'k': 7, 'cost': 58}, {'i': 1, 'j': 2, 'k': 8, 'cost': 26}, {'i': 1, 'j': 2, 'k': 9, 'cost': 45}, {'i': 1, 'j': 2, 'k': 10, 'cost': 39}, {'i': 1, 'j': 2, 'k': 11, 'cost': 87}, {'i': 1, 'j': 2, 'k': 12, 'cost': 6}, {'i': 1, 'j': 3, 'k': 1, 'cost': 58}, {'i': 1, 'j': 3, 'k': 2, 'cost': 24}, {'i': 1, 'j': 3, 'k': 3, 'cost': 97}, {'i': 1, 'j': 3, 'k': 4, 'cost': 63}, {'i': 1, 'j': 3, 'k': 5, 'cost': 10}, {'i': 1, 'j': 3, 'k': 6, 'cost': 84}, {'i': 1, 'j': 3, 'k': 7, 'cost': 66}, {'i': 1, 'j': 3, 'k': 8, 'cost': 72}, {'i': 1, 'j': 3, 'k': 9, 'cost': 83}, {'i': 1, 'j': 3, 'k': 10, 'cost': 22}, {'i': 1, 'j': 3, 'k': 11, 'cost': 4}, {'i': 1, 'j': 3, 'k': 12, 'cost': 39}, {'i': 1, 'j': 4, 'k': 1, 'cost': 99}, {'i': 1, 'j': 4, 'k': 2, 'cost': 65}, {'i': 1, 'j': 4, 'k': 3, 'cost': 34}, {'i': 1, 'j': 4, 'k': 4, 'cost': 51}, {'i': 1, 'j': 4, 'k': 5, 'cost': 95}, {'i': 1, 'j': 4, 'k': 6, 'cost': 51}, {'i': 1, 'j': 4, 'k': 7, 'cost': 51}, {'i': 1, 'j': 4, 'k': 8, 'cost': 93}, {'i': 1, 'j': 4, 'k': 9, 'cost': 72}, {'i': 1, 'j': 4, 'k': 10, 'cost': 47}, {'i': 1, 'j': 4, 'k': 11, 'cost': 89}, {'i': 1, 'j': 4, 'k': 12, 'cost': 46}, {'i': 1, 'j': 5, 'k': 1, 'cost': 7}, {'i': 1, 'j': 5, 'k': 2, 'cost': 46}, {'i': 1, 'j': 5, 'k': 3, 'cost': 78}, {'i': 1, 'j': 5, 'k': 4, 'cost': 19}, {'i': 1, 'j': 5, 'k': 5, 'cost': 94}, {'i': 1, 'j': 5, 'k': 6, 'cost': 47}, {'i': 1, 'j': 5, 'k': 7, 'cost': 85}, {'i': 1, 'j': 5, 'k': 8, 'cost': 25}, {'i': 1, 'j': 5, 'k': 9, 'cost': 60}, {'i': 1, 'j': 5, 'k': 10, 'cost': 23}, {'i': 1, 'j': 5, 'k': 11, 'cost': 31}, {'i': 1, 'j': 5, 'k': 12, 'cost': 93}, {'i': 1, 'j': 6, 'k': 1, 'cost': 79}, {'i': 1, 'j': 6, 'k': 2, 'cost': 13}, {'i': 1, 'j': 6, 'k': 3, 'cost': 39}, {'i': 1, 'j': 6, 'k': 4, 'cost': 18}, {'i': 1, 'j': 6, 'k': 5, 'cost': 93}, {'i': 1, 'j': 6, 'k': 6, 'cost': 40}, {'i': 1, 'j': 6, 'k': 7, 'cost': 53}, {'i': 1, 'j': 6, 'k': 8, 'cost': 29}, {'i': 1, 'j': 6, 'k': 9, 'cost': 45}, {'i': 1, 'j': 6, 'k': 10, 'cost': 68}, {'i': 1, 'j': 6, 'k': 11, 'cost': 30}, {'i': 1, 'j': 6, 'k': 12, 'cost': 10}, {'i': 1, 'j': 7, 'k': 1, 'cost': 23}, {'i': 1, 'j': 7, 'k': 2, 'cost': 15}, {'i': 1, 'j': 7, 'k': 3, 'cost': 30}, {'i': 1, 'j': 7, 'k': 4, 'cost': 94}, {'i': 1, 'j': 7, 'k': 5, 'cost': 78}, {'i': 1, 'j': 7, 'k': 6, 'cost': 99}, {'i': 1, 'j': 7, 'k': 7, 'cost': 12}, {'i': 1, 'j': 7, 'k': 8, 'cost': 5}, {'i': 1, 'j': 7, 'k': 9, 'cost': 30}, {'i': 1, 'j': 7, 'k': 10, 'cost': 97}, {'i': 1, 'j': 7, 'k': 11, 'cost': 30}, {'i': 1, 'j': 7, 'k': 12, 'cost': 19}, {'i': 1, 'j': 8, 'k': 1, 'cost': 78}, {'i': 1, 'j': 8, 'k': 2, 'cost': 2}, {'i': 1, 'j': 8, 'k': 3, 'cost': 32}, {'i': 1, 'j': 8, 'k': 4, 'cost': 13}, {'i': 1, 'j': 8, 'k': 5, 'cost': 64}, {'i': 1, 'j': 8, 'k': 6, 'cost': 88}, {'i': 1, 'j': 8, 'k': 7, 'cost': 18}, {'i': 1, 'j': 8, 'k': 8, 'cost': 72}, {'i': 1, 'j': 8, 'k': 9, 'cost': 17}, {'i': 1, 'j': 8, 'k': 10, 'cost': 22}, {'i': 1, 'j': 8, 'k': 11, 'cost': 70}, {'i': 1, 'j': 8, 'k': 12, 'cost': 18}, {'i': 1, 'j': 9, 'k': 1, 'cost': 61}, {'i': 1, 'j': 9, 'k': 2, 'cost': 6}, {'i': 1, 'j': 9, 'k': 3, 'cost': 47}, {'i': 1, 'j': 9, 'k': 4, 'cost': 13}, {'i': 1, 'j': 9, 'k': 5, 'cost': 52}, {'i': 1, 'j': 9, 'k': 6, 'cost': 55}, {'i': 1, 'j': 9, 'k': 7, 'cost': 7}, {'i': 1, 'j': 9, 'k': 8, 'cost': 3}, {'i': 1, 'j': 9, 'k': 9, 'cost': 56}, {'i': 1, 'j': 9, 'k': 10, 'cost': 94}, {'i': 1, 'j': 9, 'k': 11, 'cost': 43}, {'i': 1, 'j': 9, 'k': 12, 'cost': 9}, {'i': 1, 'j': 10, 'k': 1, 'cost': 8}, {'i': 1, 'j': 10, 'k': 2, 'cost': 15}, {'i': 1, 'j': 10, 'k': 3, 'cost': 61}, {'i': 1, 'j': 10, 'k': 4, 'cost': 47}, {'i': 1, 'j': 10, 'k': 5, 'cost': 97}, {'i': 1, 'j': 10, 'k': 6, 'cost': 46}, {'i': 1, 'j': 10, 'k': 7, 'cost': 88}, {'i': 1, 'j': 10, 'k': 8, 'cost': 66}, {'i': 1, 'j': 10, 'k': 9, 'cost': 76}, {'i': 1, 'j': 10, 'k': 10, 'cost': 24}, {'i': 1, 'j': 10, 'k': 11, 'cost': 86}, {'i': 1, 'j': 10, 'k': 12, 'cost': 97}, {'i': 1, 'j': 11, 'k': 1, 'cost': 91}, {'i': 1, 'j': 11, 'k': 2, 'cost': 7}, {'i': 1, 'j': 11, 'k': 3, 'cost': 48}, {'i': 1, 'j': 11, 'k': 4, 'cost': 80}, {'i': 1, 'j': 11, 'k': 5, 'cost': 54}, {'i': 1, 'j': 11, 'k': 6, 'cost': 60}, {'i': 1, 'j': 11, 'k': 7, 'cost': 42}, {'i': 1, 'j': 11, 'k': 8, 'cost': 97}, {'i': 1, 'j': 11, 'k': 9, 'cost': 77}, {'i': 1, 'j': 11, 'k': 10, 'cost': 32}, {'i': 1, 'j': 11, 'k': 11, 'cost': 2}, {'i': 1, 'j': 11, 'k': 12, 'cost': 88}, {'i': 1, 'j': 12, 'k': 1, 'cost': 3}, {'i': 1, 'j': 12, 'k': 2, 'cost': 31}, {'i': 1, 'j': 12, 'k': 3, 'cost': 62}, {'i': 1, 'j': 12, 'k': 4, 'cost': 65}, {'i': 1, 'j': 12, 'k': 5, 'cost': 29}, {'i': 1, 'j': 12, 'k': 6, 'cost': 50}, {'i': 1, 'j': 12, 'k': 7, 'cost': 80}, {'i': 1, 'j': 12, 'k': 8, 'cost': 81}, {'i': 1, 'j': 12, 'k': 9, 'cost': 10}, {'i': 1, 'j': 12, 'k': 10, 'cost': 0}, {'i': 1, 'j': 12, 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11, 'j': 5, 'k': 2, 'cost': 28}, {'i': 11, 'j': 5, 'k': 3, 'cost': 95}, {'i': 11, 'j': 5, 'k': 4, 'cost': 66}, {'i': 11, 'j': 5, 'k': 5, 'cost': 68}, {'i': 11, 'j': 5, 'k': 6, 'cost': 4}, {'i': 11, 'j': 5, 'k': 7, 'cost': 68}, {'i': 11, 'j': 5, 'k': 8, 'cost': 72}, {'i': 11, 'j': 5, 'k': 9, 'cost': 45}, {'i': 11, 'j': 5, 'k': 10, 'cost': 82}, {'i': 11, 'j': 5, 'k': 11, 'cost': 99}, {'i': 11, 'j': 5, 'k': 12, 'cost': 76}, {'i': 11, 'j': 6, 'k': 1, 'cost': 37}, {'i': 11, 'j': 6, 'k': 2, 'cost': 66}, {'i': 11, 'j': 6, 'k': 3, 'cost': 88}, {'i': 11, 'j': 6, 'k': 4, 'cost': 58}, {'i': 11, 'j': 6, 'k': 5, 'cost': 90}, {'i': 11, 'j': 6, 'k': 6, 'cost': 75}, {'i': 11, 'j': 6, 'k': 7, 'cost': 31}, {'i': 11, 'j': 6, 'k': 8, 'cost': 54}, {'i': 11, 'j': 6, 'k': 9, 'cost': 54}, {'i': 11, 'j': 6, 'k': 10, 'cost': 58}, {'i': 11, 'j': 6, 'k': 11, 'cost': 63}, {'i': 11, 'j': 6, 'k': 12, 'cost': 86}, {'i': 11, 'j': 7, 'k': 1, 'cost': 58}, {'i': 11, 'j': 7, 'k': 2, 'cost': 33}, {'i': 11, 'j': 7, 'k': 3, 'cost': 32}, {'i': 11, 'j': 7, 'k': 4, 'cost': 41}, {'i': 11, 'j': 7, 'k': 5, 'cost': 96}, {'i': 11, 'j': 7, 'k': 6, 'cost': 17}, {'i': 11, 'j': 7, 'k': 7, 'cost': 91}, {'i': 11, 'j': 7, 'k': 8, 'cost': 19}, {'i': 11, 'j': 7, 'k': 9, 'cost': 93}, {'i': 11, 'j': 7, 'k': 10, 'cost': 31}, {'i': 11, 'j': 7, 'k': 11, 'cost': 24}, {'i': 11, 'j': 7, 'k': 12, 'cost': 92}, {'i': 11, 'j': 8, 'k': 1, 'cost': 39}, {'i': 11, 'j': 8, 'k': 2, 'cost': 33}, {'i': 11, 'j': 8, 'k': 3, 'cost': 63}, {'i': 11, 'j': 8, 'k': 4, 'cost': 40}, {'i': 11, 'j': 8, 'k': 5, 'cost': 58}, {'i': 11, 'j': 8, 'k': 6, 'cost': 18}, {'i': 11, 'j': 8, 'k': 7, 'cost': 46}, {'i': 11, 'j': 8, 'k': 8, 'cost': 0}, {'i': 11, 'j': 8, 'k': 9, 'cost': 5}, {'i': 11, 'j': 8, 'k': 10, 'cost': 43}, {'i': 11, 'j': 8, 'k': 11, 'cost': 2}, {'i': 11, 'j': 8, 'k': 12, 'cost': 42}, {'i': 11, 'j': 9, 'k': 1, 'cost': 69}, {'i': 11, 'j': 9, 'k': 2, 'cost': 56}, {'i': 11, 'j': 9, 'k': 3, 'cost': 2}, {'i': 11, 'j': 9, 'k': 4, 'cost': 64}, {'i': 11, 'j': 9, 'k': 5, 'cost': 4}, {'i': 11, 'j': 9, 'k': 6, 'cost': 80}, {'i': 11, 'j': 9, 'k': 7, 'cost': 86}, {'i': 11, 'j': 9, 'k': 8, 'cost': 62}, {'i': 11, 'j': 9, 'k': 9, 'cost': 29}, {'i': 11, 'j': 9, 'k': 10, 'cost': 48}, {'i': 11, 'j': 9, 'k': 11, 'cost': 13}, {'i': 11, 'j': 9, 'k': 12, 'cost': 67}, {'i': 11, 'j': 10, 'k': 1, 'cost': 4}, {'i': 11, 'j': 10, 'k': 2, 'cost': 55}, {'i': 11, 'j': 10, 'k': 3, 'cost': 94}, {'i': 11, 'j': 10, 'k': 4, 'cost': 58}, {'i': 11, 'j': 10, 'k': 5, 'cost': 59}, {'i': 11, 'j': 10, 'k': 6, 'cost': 22}, {'i': 11, 'j': 10, 'k': 7, 'cost': 87}, {'i': 11, 'j': 10, 'k': 8, 'cost': 18}, {'i': 11, 'j': 10, 'k': 9, 'cost': 30}, {'i': 11, 'j': 10, 'k': 10, 'cost': 3}, {'i': 11, 'j': 10, 'k': 11, 'cost': 31}, {'i': 11, 'j': 10, 'k': 12, 'cost': 83}, {'i': 11, 'j': 11, 'k': 1, 'cost': 53}, {'i': 11, 'j': 11, 'k': 2, 'cost': 85}, {'i': 11, 'j': 11, 'k': 3, 'cost': 10}, {'i': 11, 'j': 11, 'k': 4, 'cost': 66}, {'i': 11, 'j': 11, 'k': 5, 'cost': 0}, {'i': 11, 'j': 11, 'k': 6, 'cost': 52}, {'i': 11, 'j': 11, 'k': 7, 'cost': 79}, {'i': 11, 'j': 11, 'k': 8, 'cost': 52}, {'i': 11, 'j': 11, 'k': 9, 'cost': 75}, {'i': 11, 'j': 11, 'k': 10, 'cost': 29}, {'i': 11, 'j': 11, 'k': 11, 'cost': 4}, {'i': 11, 'j': 11, 'k': 12, 'cost': 82}, {'i': 11, 'j': 12, 'k': 1, 'cost': 92}, {'i': 11, 'j': 12, 'k': 2, 'cost': 17}, {'i': 11, 'j': 12, 'k': 3, 'cost': 31}, {'i': 11, 'j': 12, 'k': 4, 'cost': 26}, {'i': 11, 'j': 12, 'k': 5, 'cost': 75}, {'i': 11, 'j': 12, 'k': 6, 'cost': 4}, {'i': 11, 'j': 12, 'k': 7, 'cost': 76}, {'i': 11, 'j': 12, 'k': 8, 'cost': 33}, {'i': 11, 'j': 12, 'k': 9, 'cost': 4}, {'i': 11, 'j': 12, 'k': 10, 'cost': 27}, {'i': 11, 'j': 12, 'k': 11, 'cost': 24}, {'i': 11, 'j': 12, 'k': 12, 'cost': 82}, {'i': 12, 'j': 1, 'k': 1, 'cost': 52}, {'i': 12, 'j': 1, 'k': 2, 'cost': 47}, {'i': 12, 'j': 1, 'k': 3, 'cost': 80}, {'i': 12, 'j': 1, 'k': 4, 'cost': 73}, {'i': 12, 'j': 1, 'k': 5, 'cost': 86}, {'i': 12, 'j': 1, 'k': 6, 'cost': 41}, {'i': 12, 'j': 1, 'k': 7, 'cost': 10}, {'i': 12, 'j': 1, 'k': 8, 'cost': 96}, {'i': 12, 'j': 1, 'k': 9, 'cost': 97}, {'i': 12, 'j': 1, 'k': 10, 'cost': 63}, {'i': 12, 'j': 1, 'k': 11, 'cost': 95}, {'i': 12, 'j': 1, 'k': 12, 'cost': 76}, {'i': 12, 'j': 2, 'k': 1, 'cost': 54}, {'i': 12, 'j': 2, 'k': 2, 'cost': 95}, {'i': 12, 'j': 2, 'k': 3, 'cost': 79}, {'i': 12, 'j': 2, 'k': 4, 'cost': 92}, {'i': 12, 'j': 2, 'k': 5, 'cost': 62}, {'i': 12, 'j': 2, 'k': 6, 'cost': 93}, {'i': 12, 'j': 2, 'k': 7, 'cost': 5}, {'i': 12, 'j': 2, 'k': 8, 'cost': 57}, {'i': 12, 'j': 2, 'k': 9, 'cost': 82}, {'i': 12, 'j': 2, 'k': 10, 'cost': 65}, {'i': 12, 'j': 2, 'k': 11, 'cost': 90}, {'i': 12, 'j': 2, 'k': 12, 'cost': 16}, {'i': 12, 'j': 3, 'k': 1, 'cost': 34}, {'i': 12, 'j': 3, 'k': 2, 'cost': 34}, {'i': 12, 'j': 3, 'k': 3, 'cost': 28}, {'i': 12, 'j': 3, 'k': 4, 'cost': 15}, {'i': 12, 'j': 3, 'k': 5, 'cost': 37}, {'i': 12, 'j': 3, 'k': 6, 'cost': 50}, {'i': 12, 'j': 3, 'k': 7, 'cost': 43}, {'i': 12, 'j': 3, 'k': 8, 'cost': 65}, {'i': 12, 'j': 3, 'k': 9, 'cost': 57}, {'i': 12, 'j': 3, 'k': 10, 'cost': 87}, {'i': 12, 'j': 3, 'k': 11, 'cost': 69}, {'i': 12, 'j': 3, 'k': 12, 'cost': 53}, {'i': 12, 'j': 4, 'k': 1, 'cost': 69}, {'i': 12, 'j': 4, 'k': 2, 'cost': 78}, {'i': 12, 'j': 4, 'k': 3, 'cost': 34}, {'i': 12, 'j': 4, 'k': 4, 'cost': 31}, {'i': 12, 'j': 4, 'k': 5, 'cost': 59}, {'i': 12, 'j': 4, 'k': 6, 'cost': 6}, {'i': 12, 'j': 4, 'k': 7, 'cost': 5}, {'i': 12, 'j': 4, 'k': 8, 'cost': 82}, {'i': 12, 'j': 4, 'k': 9, 'cost': 3}, {'i': 12, 'j': 4, 'k': 10, 'cost': 96}, {'i': 12, 'j': 4, 'k': 11, 'cost': 24}, {'i': 12, 'j': 4, 'k': 12, 'cost': 15}, {'i': 12, 'j': 5, 'k': 1, 'cost': 94}, {'i': 12, 'j': 5, 'k': 2, 'cost': 48}, {'i': 12, 'j': 5, 'k': 3, 'cost': 80}, {'i': 12, 'j': 5, 'k': 4, 'cost': 71}, {'i': 12, 'j': 5, 'k': 5, 'cost': 61}, {'i': 12, 'j': 5, 'k': 6, 'cost': 2}, {'i': 12, 'j': 5, 'k': 7, 'cost': 13}, {'i': 12, 'j': 5, 'k': 8, 'cost': 87}, {'i': 12, 'j': 5, 'k': 9, 'cost': 33}, {'i': 12, 'j': 5, 'k': 10, 'cost': 70}, {'i': 12, 'j': 5, 'k': 11, 'cost': 82}, {'i': 12, 'j': 5, 'k': 12, 'cost': 28}, {'i': 12, 'j': 6, 'k': 1, 'cost': 8}, {'i': 12, 'j': 6, 'k': 2, 'cost': 70}, {'i': 12, 'j': 6, 'k': 3, 'cost': 41}, {'i': 12, 'j': 6, 'k': 4, 'cost': 55}, {'i': 12, 'j': 6, 'k': 5, 'cost': 75}, {'i': 12, 'j': 6, 'k': 6, 'cost': 87}, {'i': 12, 'j': 6, 'k': 7, 'cost': 2}, {'i': 12, 'j': 6, 'k': 8, 'cost': 75}, {'i': 12, 'j': 6, 'k': 9, 'cost': 21}, {'i': 12, 'j': 6, 'k': 10, 'cost': 0}, {'i': 12, 'j': 6, 'k': 11, 'cost': 27}, {'i': 12, 'j': 6, 'k': 12, 'cost': 90}, {'i': 12, 'j': 7, 'k': 1, 'cost': 13}, {'i': 12, 'j': 7, 'k': 2, 'cost': 21}, {'i': 12, 'j': 7, 'k': 3, 'cost': 85}, {'i': 12, 'j': 7, 'k': 4, 'cost': 33}, {'i': 12, 'j': 7, 'k': 5, 'cost': 24}, {'i': 12, 'j': 7, 'k': 6, 'cost': 36}, {'i': 12, 'j': 7, 'k': 7, 'cost': 25}, {'i': 12, 'j': 7, 'k': 8, 'cost': 61}, {'i': 12, 'j': 7, 'k': 9, 'cost': 94}, {'i': 12, 'j': 7, 'k': 10, 'cost': 70}, {'i': 12, 'j': 7, 'k': 11, 'cost': 33}, {'i': 12, 'j': 7, 'k': 12, 'cost': 6}, {'i': 12, 'j': 8, 'k': 1, 'cost': 8}, {'i': 12, 'j': 8, 'k': 2, 'cost': 15}, {'i': 12, 'j': 8, 'k': 3, 'cost': 28}, {'i': 12, 'j': 8, 'k': 4, 'cost': 3}, {'i': 12, 'j': 8, 'k': 5, 'cost': 54}, {'i': 12, 'j': 8, 'k': 6, 'cost': 16}, {'i': 12, 'j': 8, 'k': 7, 'cost': 36}, {'i': 12, 'j': 8, 'k': 8, 'cost': 1}, {'i': 12, 'j': 8, 'k': 9, 'cost': 72}, {'i': 12, 'j': 8, 'k': 10, 'cost': 75}, {'i': 12, 'j': 8, 'k': 11, 'cost': 60}, {'i': 12, 'j': 8, 'k': 12, 'cost': 81}, {'i': 12, 'j': 9, 'k': 1, 'cost': 48}, {'i': 12, 'j': 9, 'k': 2, 'cost': 39}, {'i': 12, 'j': 9, 'k': 3, 'cost': 19}, {'i': 12, 'j': 9, 'k': 4, 'cost': 72}, {'i': 12, 'j': 9, 'k': 5, 'cost': 66}, {'i': 12, 'j': 9, 'k': 6, 'cost': 98}, {'i': 12, 'j': 9, 'k': 7, 'cost': 72}, {'i': 12, 'j': 9, 'k': 8, 'cost': 26}, {'i': 12, 'j': 9, 'k': 9, 'cost': 97}, {'i': 12, 'j': 9, 'k': 10, 'cost': 5}, {'i': 12, 'j': 9, 'k': 11, 'cost': 5}, {'i': 12, 'j': 9, 'k': 12, 'cost': 97}, {'i': 12, 'j': 10, 'k': 1, 'cost': 88}, {'i': 12, 'j': 10, 'k': 2, 'cost': 82}, {'i': 12, 'j': 10, 'k': 3, 'cost': 49}, {'i': 12, 'j': 10, 'k': 4, 'cost': 19}, {'i': 12, 'j': 10, 'k': 5, 'cost': 33}, {'i': 12, 'j': 10, 'k': 6, 'cost': 11}, {'i': 12, 'j': 10, 'k': 7, 'cost': 16}, {'i': 12, 'j': 10, 'k': 8, 'cost': 78}, {'i': 12, 'j': 10, 'k': 9, 'cost': 92}, {'i': 12, 'j': 10, 'k': 10, 'cost': 34}, {'i': 12, 'j': 10, 'k': 11, 'cost': 52}, {'i': 12, 'j': 10, 'k': 12, 'cost': 33}, {'i': 12, 'j': 11, 'k': 1, 'cost': 93}, {'i': 12, 'j': 11, 'k': 2, 'cost': 40}, {'i': 12, 'j': 11, 'k': 3, 'cost': 14}, {'i': 12, 'j': 11, 'k': 4, 'cost': 47}, {'i': 12, 'j': 11, 'k': 5, 'cost': 24}, {'i': 12, 'j': 11, 'k': 6, 'cost': 4}, {'i': 12, 'j': 11, 'k': 7, 'cost': 51}, {'i': 12, 'j': 11, 'k': 8, 'cost': 83}, {'i': 12, 'j': 11, 'k': 9, 'cost': 85}, {'i': 12, 'j': 11, 'k': 10, 'cost': 1}, {'i': 12, 'j': 11, 'k': 11, 'cost': 93}, {'i': 12, 'j': 11, 'k': 12, 'cost': 80}, {'i': 12, 'j': 12, 'k': 1, 'cost': 64}, {'i': 12, 'j': 12, 'k': 2, 'cost': 27}, {'i': 12, 'j': 12, 'k': 3, 'cost': 7}, {'i': 12, 'j': 12, 'k': 4, 'cost': 41}, {'i': 12, 'j': 12, 'k': 5, 'cost': 2}, {'i': 12, 'j': 12, 'k': 6, 'cost': 11}, {'i': 12, 'j': 12, 'k': 7, 'cost': 25}, {'i': 12, 'j': 12, 'k': 8, 'cost': 69}, {'i': 12, 'j': 12, 'k': 9, 'cost': 47}, {'i': 12, 'j': 12, 'k': 10, 'cost': 54}, {'i': 12, 'j': 12, 'k': 11, 'cost': 3}, {'i': 12, 'j': 12, 'k': 12, 'cost': 6}]}","[[1, 12, 10], [2, 3, 4], [3, 2, 1], [4, 7, 11], [5, 8, 2], [6, 4, 3], [7, 1, 12], [8, 9, 8], [9, 5, 9], [10, 10, 6], [11, 11, 5], [12, 6, 7]]",10,json,1
+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.
+
+They are listed here for the 9 orders 1, 2, 3, 4, 5, 6, 7, 8, 9.
+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=1
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 64 | 72 | 68 | 87 | 24 | 42 | 63 | 24 | 94 |
+| 2 | 85 | 50 | 50 | 1 | 99 | 49 | 40 | 31 | 1 |
+| 3 | 30 | 73 | 7 | 91 | 65 | 61 | 38 | 77 | 73 |
+| 4 | 48 | 11 | 8 | 49 | 80 | 84 | 55 | 14 | 43 |
+| 5 | 63 | 7 | 47 | 93 | 3 | 86 | 75 | 16 | 6 |
+| 6 | 63 | 26 | 23 | 66 | 79 | 72 | 50 | 9 | 22 |
+| 7 | 1 | 3 | 44 | 62 | 23 | 35 | 21 | 32 | 12 |
+| 8 | 66 | 35 | 47 | 28 | 23 | 3 | 77 | 26 | 93 |
+| 9 | 83 | 33 | 90 | 78 | 47 | 48 | 77 | 26 | 84 |
+
+## order_id=2
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 5 | 80 | 89 | 31 | 13 | 84 | 44 | 71 | 93 |
+| 2 | 27 | 95 | 46 | 99 | 46 | 80 | 70 | 35 | 81 |
+| 3 | 63 | 61 | 79 | 15 | 25 | 74 | 90 | 40 | 78 |
+| 4 | 67 | 94 | 73 | 81 | 25 | 80 | 65 | 96 | 74 |
+| 5 | 59 | 23 | 17 | 66 | 73 | 91 | 2 | 1 | 75 |
+| 6 | 30 | 32 | 96 | 97 | 37 | 68 | 32 | 36 | 62 |
+| 7 | 43 | 24 | 14 | 32 | 40 | 93 | 70 | 15 | 17 |
+| 8 | 38 | 70 | 48 | 6 | 79 | 73 | 10 | 56 | 14 |
+| 9 | 43 | 93 | 59 | 84 | 53 | 54 | 84 | 68 | 57 |
+
+## order_id=3
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 82 | 73 | 83 | 62 | 16 | 98 | 24 | 83 |
+| 2 | 52 | 59 | 45 | 89 | 82 | 22 | 89 | 30 | 3 |
+| 3 | 75 | 43 | 44 | 66 | 56 | 70 | 1 | 32 | 29 |
+| 4 | 5 | 68 | 60 | 57 | 53 | 50 | 19 | 29 | 5 |
+| 5 | 64 | 54 | 77 | 82 | 66 | 84 | 76 | 48 | 52 |
+| 6 | 2 | 27 | 50 | 5 | 98 | 22 | 29 | 61 | 11 |
+| 7 | 79 | 56 | 35 | 81 | 3 | 24 | 39 | 7 | 39 |
+| 8 | 47 | 15 | 29 | 81 | 91 | 9 | 49 | 18 | 5 |
+| 9 | 35 | 37 | 98 | 19 | 95 | 96 | 64 | 79 | 4 |
+
+## order_id=4
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 95 | 22 | 77 | 63 | 89 | 4 | 71 | 96 | 84 |
+| 2 | 99 | 95 | 98 | 96 | 77 | 93 | 50 | 47 | 27 |
+| 3 | 84 | 38 | 98 | 94 | 82 | 60 | 47 | 52 | 16 |
+| 4 | 95 | 42 | 46 | 88 | 3 | 66 | 9 | 3 | 17 |
+| 5 | 52 | 9 | 21 | 96 | 72 | 86 | 20 | 79 | 75 |
+| 6 | 11 | 34 | 50 | 4 | 83 | 59 | 22 | 61 | 87 |
+| 7 | 80 | 5 | 76 | 63 | 14 | 53 | 87 | 68 | 80 |
+| 8 | 20 | 85 | 81 | 67 | 33 | 24 | 94 | 92 | 52 |
+| 9 | 64 | 27 | 36 | 26 | 38 | 38 | 97 | 60 | 67 |
+
+## order_id=5
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 25 | 81 | 35 | 87 | 68 | 52 | 11 | 32 | 1 |
+| 2 | 26 | 30 | 79 | 37 | 85 | 24 | 4 | 51 | 70 |
+| 3 | 24 | 18 | 54 | 20 | 39 | 5 | 90 | 85 | 72 |
+| 4 | 23 | 79 | 25 | 96 | 81 | 41 | 12 | 43 | 69 |
+| 5 | 39 | 87 | 57 | 36 | 43 | 88 | 33 | 81 | 48 |
+| 6 | 50 | 97 | 43 | 21 | 25 | 99 | 18 | 40 | 7 |
+| 7 | 69 | 51 | 4 | 13 | 56 | 80 | 46 | 68 | 1 |
+| 8 | 34 | 52 | 46 | 99 | 54 | 71 | 92 | 84 | 40 |
+| 9 | 83 | 80 | 54 | 43 | 14 | 58 | 37 | 40 | 48 |
+
+## order_id=6
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 8 | 91 | 78 | 80 | 14 | 16 | 35 | 54 | 21 |
+| 2 | 33 | 47 | 76 | 69 | 2 | 24 | 3 | 36 | 36 |
+| 3 | 94 | 98 | 57 | 14 | 33 | 85 | 88 | 87 | 80 |
+| 4 | 74 | 42 | 28 | 18 | 37 | 49 | 69 | 27 | 86 |
+| 5 | 86 | 42 | 51 | 3 | 13 | 99 | 33 | 40 | 53 |
+| 6 | 40 | 62 | 69 | 82 | 46 | 97 | 49 | 98 | 98 |
+| 7 | 52 | 89 | 14 | 19 | 27 | 34 | 72 | 53 | 7 |
+| 8 | 43 | 94 | 94 | 34 | 40 | 83 | 4 | 80 | 44 |
+| 9 | 52 | 66 | 0 | 41 | 13 | 4 | 98 | 5 | 21 |
+
+## order_id=7
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 99 | 15 | 6 | 35 | 37 | 77 | 67 | 79 | 47 |
+| 2 | 74 | 38 | 5 | 45 | 20 | 21 | 65 | 70 | 17 |
+| 3 | 2 | 24 | 39 | 76 | 66 | 48 | 54 | 91 | 1 |
+| 4 | 76 | 7 | 88 | 70 | 21 | 49 | 27 | 19 | 60 |
+| 5 | 6 | 21 | 3 | 95 | 88 | 86 | 47 | 16 | 32 |
+| 6 | 66 | 15 | 58 | 55 | 58 | 74 | 62 | 92 | 52 |
+| 7 | 87 | 97 | 71 | 33 | 35 | 58 | 94 | 88 | 47 |
+| 8 | 10 | 4 | 45 | 38 | 59 | 34 | 97 | 90 | 7 |
+| 9 | 76 | 53 | 81 | 33 | 52 | 80 | 49 | 43 | 5 |
+
+## order_id=8
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 54 | 3 | 14 | 62 | 81 | 84 | 79 | 85 | 62 |
+| 2 | 93 | 58 | 80 | 3 | 80 | 91 | 87 | 81 | 97 |
+| 3 | 12 | 38 | 32 | 61 | 4 | 17 | 85 | 67 | 87 |
+| 4 | 27 | 72 | 48 | 66 | 81 | 4 | 49 | 71 | 54 |
+| 5 | 44 | 74 | 72 | 89 | 50 | 65 | 93 | 8 | 65 |
+| 6 | 54 | 57 | 99 | 38 | 46 | 68 | 81 | 12 | 80 |
+| 7 | 56 | 89 | 6 | 14 | 95 | 83 | 38 | 54 | 67 |
+| 8 | 11 | 89 | 25 | 31 | 47 | 4 | 85 | 89 | 16 |
+| 9 | 63 | 94 | 64 | 52 | 90 | 57 | 47 | 11 | 73 |
+
+## order_id=9
+| printer_id\finisher_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 93 | 70 | 67 | 45 | 75 | 30 | 24 | 27 | 62 |
+| 2 | 33 | 77 | 26 | 27 | 27 | 99 | 14 | 7 | 57 |
+| 3 | 91 | 67 | 22 | 48 | 11 | 32 | 19 | 29 | 3 |
+| 4 | 40 | 74 | 17 | 85 | 16 | 0 | 57 | 56 | 7 |
+| 5 | 82 | 4 | 49 | 58 | 47 | 43 | 69 | 28 | 48 |
+| 6 | 12 | 42 | 48 | 2 | 77 | 61 | 95 | 53 | 63 |
+| 7 | 38 | 83 | 55 | 28 | 24 | 11 | 71 | 82 | 7 |
+| 8 | 71 | 77 | 91 | 77 | 57 | 43 | 19 | 69 | 83 |
+| 9 | 60 | 71 | 67 | 62 | 95 | 56 | 39 | 81 | 22 |
+Compare these entries to identify the assignment with the lowest total processing time across all 9 orders.
+
+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': [[[64, 72, 68, 87, 24, 42, 63, 24, 94], [85, 50, 50, 1, 99, 49, 40, 31, 1], [30, 73, 7, 91, 65, 61, 38, 77, 73], [48, 11, 8, 49, 80, 84, 55, 14, 43], [63, 7, 47, 93, 3, 86, 75, 16, 6], [63, 26, 23, 66, 79, 72, 50, 9, 22], [1, 3, 44, 62, 23, 35, 21, 32, 12], [66, 35, 47, 28, 23, 3, 77, 26, 93], [83, 33, 90, 78, 47, 48, 77, 26, 84]], [[5, 80, 89, 31, 13, 84, 44, 71, 93], [27, 95, 46, 99, 46, 80, 70, 35, 81], [63, 61, 79, 15, 25, 74, 90, 40, 78], [67, 94, 73, 81, 25, 80, 65, 96, 74], [59, 23, 17, 66, 73, 91, 2, 1, 75], [30, 32, 96, 97, 37, 68, 32, 36, 62], [43, 24, 14, 32, 40, 93, 70, 15, 17], [38, 70, 48, 6, 79, 73, 10, 56, 14], [43, 93, 59, 84, 53, 54, 84, 68, 57]], [[82, 82, 73, 83, 62, 16, 98, 24, 83], [52, 59, 45, 89, 82, 22, 89, 30, 3], [75, 43, 44, 66, 56, 70, 1, 32, 29], [5, 68, 60, 57, 53, 50, 19, 29, 5], [64, 54, 77, 82, 66, 84, 76, 48, 52], [2, 27, 50, 5, 98, 22, 29, 61, 11], [79, 56, 35, 81, 3, 24, 39, 7, 39], [47, 15, 29, 81, 91, 9, 49, 18, 5], [35, 37, 98, 19, 95, 96, 64, 79, 4]], [[95, 22, 77, 63, 89, 4, 71, 96, 84], [99, 95, 98, 96, 77, 93, 50, 47, 27], [84, 38, 98, 94, 82, 60, 47, 52, 16], [95, 42, 46, 88, 3, 66, 9, 3, 17], [52, 9, 21, 96, 72, 86, 20, 79, 75], [11, 34, 50, 4, 83, 59, 22, 61, 87], [80, 5, 76, 63, 14, 53, 87, 68, 80], [20, 85, 81, 67, 33, 24, 94, 92, 52], [64, 27, 36, 26, 38, 38, 97, 60, 67]], [[25, 81, 35, 87, 68, 52, 11, 32, 1], [26, 30, 79, 37, 85, 24, 4, 51, 70], [24, 18, 54, 20, 39, 5, 90, 85, 72], [23, 79, 25, 96, 81, 41, 12, 43, 69], [39, 87, 57, 36, 43, 88, 33, 81, 48], [50, 97, 43, 21, 25, 99, 18, 40, 7], [69, 51, 4, 13, 56, 80, 46, 68, 1], [34, 52, 46, 99, 54, 71, 92, 84, 40], [83, 80, 54, 43, 14, 58, 37, 40, 48]], [[8, 91, 78, 80, 14, 16, 35, 54, 21], [33, 47, 76, 69, 2, 24, 3, 36, 36], [94, 98, 57, 14, 33, 85, 88, 87, 80], [74, 42, 28, 18, 37, 49, 69, 27, 86], [86, 42, 51, 3, 13, 99, 33, 40, 53], [40, 62, 69, 82, 46, 97, 49, 98, 98], [52, 89, 14, 19, 27, 34, 72, 53, 7], [43, 94, 94, 34, 40, 83, 4, 80, 44], [52, 66, 0, 41, 13, 4, 98, 5, 21]], [[99, 15, 6, 35, 37, 77, 67, 79, 47], [74, 38, 5, 45, 20, 21, 65, 70, 17], [2, 24, 39, 76, 66, 48, 54, 91, 1], [76, 7, 88, 70, 21, 49, 27, 19, 60], [6, 21, 3, 95, 88, 86, 47, 16, 32], [66, 15, 58, 55, 58, 74, 62, 92, 52], [87, 97, 71, 33, 35, 58, 94, 88, 47], [10, 4, 45, 38, 59, 34, 97, 90, 7], [76, 53, 81, 33, 52, 80, 49, 43, 5]], [[54, 3, 14, 62, 81, 84, 79, 85, 62], [93, 58, 80, 3, 80, 91, 87, 81, 97], [12, 38, 32, 61, 4, 17, 85, 67, 87], [27, 72, 48, 66, 81, 4, 49, 71, 54], [44, 74, 72, 89, 50, 65, 93, 8, 65], [54, 57, 99, 38, 46, 68, 81, 12, 80], [56, 89, 6, 14, 95, 83, 38, 54, 67], [11, 89, 25, 31, 47, 4, 85, 89, 16], [63, 94, 64, 52, 90, 57, 47, 11, 73]], [[93, 70, 67, 45, 75, 30, 24, 27, 62], [33, 77, 26, 27, 27, 99, 14, 7, 57], [91, 67, 22, 48, 11, 32, 19, 29, 3], [40, 74, 17, 85, 16, 0, 57, 56, 7], [82, 4, 49, 58, 47, 43, 69, 28, 48], [12, 42, 48, 2, 77, 61, 95, 53, 63], [38, 83, 55, 28, 24, 11, 71, 82, 7], [71, 77, 91, 77, 57, 43, 19, 69, 83], [60, 71, 67, 62, 95, 56, 39, 81, 22]]], 'objective': 24.0}","[[0, 6, 0], [1, 4, 7], [2, 7, 5], [3, 3, 4], [4, 1, 6], [5, 8, 2], [6, 2, 8], [7, 0, 1], [8, 5, 3]]",24.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 64}, {'i': 1, 'j': 1, 'k': 2, 'cost': 72}, {'i': 1, 'j': 1, 'k': 3, 'cost': 68}, {'i': 1, 'j': 1, 'k': 4, 'cost': 87}, {'i': 1, 'j': 1, 'k': 5, 'cost': 24}, {'i': 1, 'j': 1, 'k': 6, 'cost': 42}, {'i': 1, 'j': 1, 'k': 7, 'cost': 63}, {'i': 1, 'j': 1, 'k': 8, 'cost': 24}, {'i': 1, 'j': 1, 'k': 9, 'cost': 94}, {'i': 1, 'j': 2, 'k': 1, 'cost': 85}, {'i': 1, 'j': 2, 'k': 2, 'cost': 50}, {'i': 1, 'j': 2, 'k': 3, 'cost': 50}, {'i': 1, 'j': 2, 'k': 4, 'cost': 1}, {'i': 1, 'j': 2, 'k': 5, 'cost': 99}, {'i': 1, 'j': 2, 'k': 6, 'cost': 49}, {'i': 1, 'j': 2, 'k': 7, 'cost': 40}, {'i': 1, 'j': 2, 'k': 8, 'cost': 31}, {'i': 1, 'j': 2, 'k': 9, 'cost': 1}, {'i': 1, 'j': 3, 'k': 1, 'cost': 30}, {'i': 1, 'j': 3, 'k': 2, 'cost': 73}, {'i': 1, 'j': 3, 'k': 3, 'cost': 7}, {'i': 1, 'j': 3, 'k': 4, 'cost': 91}, {'i': 1, 'j': 3, 'k': 5, 'cost': 65}, {'i': 1, 'j': 3, 'k': 6, 'cost': 61}, {'i': 1, 'j': 3, 'k': 7, 'cost': 38}, {'i': 1, 'j': 3, 'k': 8, 'cost': 77}, {'i': 1, 'j': 3, 'k': 9, 'cost': 73}, {'i': 1, 'j': 4, 'k': 1, 'cost': 48}, {'i': 1, 'j': 4, 'k': 2, 'cost': 11}, {'i': 1, 'j': 4, 'k': 3, 'cost': 8}, {'i': 1, 'j': 4, 'k': 4, 'cost': 49}, {'i': 1, 'j': 4, 'k': 5, 'cost': 80}, {'i': 1, 'j': 4, 'k': 6, 'cost': 84}, {'i': 1, 'j': 4, 'k': 7, 'cost': 55}, {'i': 1, 'j': 4, 'k': 8, 'cost': 14}, {'i': 1, 'j': 4, 'k': 9, 'cost': 43}, {'i': 1, 'j': 5, 'k': 1, 'cost': 63}, {'i': 1, 'j': 5, 'k': 2, 'cost': 7}, {'i': 1, 'j': 5, 'k': 3, 'cost': 47}, {'i': 1, 'j': 5, 'k': 4, 'cost': 93}, {'i': 1, 'j': 5, 'k': 5, 'cost': 3}, {'i': 1, 'j': 5, 'k': 6, 'cost': 86}, {'i': 1, 'j': 5, 'k': 7, 'cost': 75}, {'i': 1, 'j': 5, 'k': 8, 'cost': 16}, {'i': 1, 'j': 5, 'k': 9, 'cost': 6}, {'i': 1, 'j': 6, 'k': 1, 'cost': 63}, {'i': 1, 'j': 6, 'k': 2, 'cost': 26}, {'i': 1, 'j': 6, 'k': 3, 'cost': 23}, {'i': 1, 'j': 6, 'k': 4, 'cost': 66}, {'i': 1, 'j': 6, 'k': 5, 'cost': 79}, {'i': 1, 'j': 6, 'k': 6, 'cost': 72}, {'i': 1, 'j': 6, 'k': 7, 'cost': 50}, {'i': 1, 'j': 6, 'k': 8, 'cost': 9}, {'i': 1, 'j': 6, 'k': 9, 'cost': 22}, {'i': 1, 'j': 7, 'k': 1, 'cost': 1}, {'i': 1, 'j': 7, 'k': 2, 'cost': 3}, {'i': 1, 'j': 7, 'k': 3, 'cost': 44}, {'i': 1, 'j': 7, 'k': 4, 'cost': 62}, {'i': 1, 'j': 7, 'k': 5, 'cost': 23}, {'i': 1, 'j': 7, 'k': 6, 'cost': 35}, {'i': 1, 'j': 7, 'k': 7, 'cost': 21}, {'i': 1, 'j': 7, 'k': 8, 'cost': 32}, {'i': 1, 'j': 7, 'k': 9, 'cost': 12}, {'i': 1, 'j': 8, 'k': 1, 'cost': 66}, {'i': 1, 'j': 8, 'k': 2, 'cost': 35}, {'i': 1, 'j': 8, 'k': 3, 'cost': 47}, {'i': 1, 'j': 8, 'k': 4, 'cost': 28}, {'i': 1, 'j': 8, 'k': 5, 'cost': 23}, {'i': 1, 'j': 8, 'k': 6, 'cost': 3}, {'i': 1, 'j': 8, 'k': 7, 'cost': 77}, {'i': 1, 'j': 8, 'k': 8, 'cost': 26}, {'i': 1, 'j': 8, 'k': 9, 'cost': 93}, {'i': 1, 'j': 9, 'k': 1, 'cost': 83}, {'i': 1, 'j': 9, 'k': 2, 'cost': 33}, {'i': 1, 'j': 9, 'k': 3, 'cost': 90}, {'i': 1, 'j': 9, 'k': 4, 'cost': 78}, {'i': 1, 'j': 9, 'k': 5, 'cost': 47}, {'i': 1, 'j': 9, 'k': 6, 'cost': 48}, {'i': 1, 'j': 9, 'k': 7, 'cost': 77}, {'i': 1, 'j': 9, 'k': 8, 'cost': 26}, {'i': 1, 'j': 9, 'k': 9, 'cost': 84}, {'i': 2, 'j': 1, 'k': 1, 'cost': 5}, {'i': 2, 'j': 1, 'k': 2, 'cost': 80}, {'i': 2, 'j': 1, 'k': 3, 'cost': 89}, {'i': 2, 'j': 1, 'k': 4, 'cost': 31}, {'i': 2, 'j': 1, 'k': 5, 'cost': 13}, {'i': 2, 'j': 1, 'k': 6, 'cost': 84}, {'i': 2, 'j': 1, 'k': 7, 'cost': 44}, {'i': 2, 'j': 1, 'k': 8, 'cost': 71}, {'i': 2, 'j': 1, 'k': 9, 'cost': 93}, {'i': 2, 'j': 2, 'k': 1, 'cost': 27}, {'i': 2, 'j': 2, 'k': 2, 'cost': 95}, {'i': 2, 'j': 2, 'k': 3, 'cost': 46}, {'i': 2, 'j': 2, 'k': 4, 'cost': 99}, {'i': 2, 'j': 2, 'k': 5, 'cost': 46}, {'i': 2, 'j': 2, 'k': 6, 'cost': 80}, {'i': 2, 'j': 2, 'k': 7, 'cost': 70}, {'i': 2, 'j': 2, 'k': 8, 'cost': 35}, {'i': 2, 'j': 2, 'k': 9, 'cost': 81}, {'i': 2, 'j': 3, 'k': 1, 'cost': 63}, {'i': 2, 'j': 3, 'k': 2, 'cost': 61}, {'i': 2, 'j': 3, 'k': 3, 'cost': 79}, {'i': 2, 'j': 3, 'k': 4, 'cost': 15}, {'i': 2, 'j': 3, 'k': 5, 'cost': 25}, {'i': 2, 'j': 3, 'k': 6, 'cost': 74}, {'i': 2, 'j': 3, 'k': 7, 'cost': 90}, {'i': 2, 'j': 3, 'k': 8, 'cost': 40}, {'i': 2, 'j': 3, 'k': 9, 'cost': 78}, {'i': 2, 'j': 4, 'k': 1, 'cost': 67}, {'i': 2, 'j': 4, 'k': 2, 'cost': 94}, {'i': 2, 'j': 4, 'k': 3, 'cost': 73}, {'i': 2, 'j': 4, 'k': 4, 'cost': 81}, {'i': 2, 'j': 4, 'k': 5, 'cost': 25}, {'i': 2, 'j': 4, 'k': 6, 'cost': 80}, {'i': 2, 'j': 4, 'k': 7, 'cost': 65}, {'i': 2, 'j': 4, 'k': 8, 'cost': 96}, {'i': 2, 'j': 4, 'k': 9, 'cost': 74}, {'i': 2, 'j': 5, 'k': 1, 'cost': 59}, {'i': 2, 'j': 5, 'k': 2, 'cost': 23}, {'i': 2, 'j': 5, 'k': 3, 'cost': 17}, {'i': 2, 'j': 5, 'k': 4, 'cost': 66}, {'i': 2, 'j': 5, 'k': 5, 'cost': 73}, {'i': 2, 'j': 5, 'k': 6, 'cost': 91}, {'i': 2, 'j': 5, 'k': 7, 'cost': 2}, {'i': 2, 'j': 5, 'k': 8, 'cost': 1}, {'i': 2, 'j': 5, 'k': 9, 'cost': 75}, {'i': 2, 'j': 6, 'k': 1, 'cost': 30}, {'i': 2, 'j': 6, 'k': 2, 'cost': 32}, {'i': 2, 'j': 6, 'k': 3, 'cost': 96}, {'i': 2, 'j': 6, 'k': 4, 'cost': 97}, {'i': 2, 'j': 6, 'k': 5, 'cost': 37}, {'i': 2, 'j': 6, 'k': 6, 'cost': 68}, {'i': 2, 'j': 6, 'k': 7, 'cost': 32}, {'i': 2, 'j': 6, 'k': 8, 'cost': 36}, {'i': 2, 'j': 6, 'k': 9, 'cost': 62}, {'i': 2, 'j': 7, 'k': 1, 'cost': 43}, {'i': 2, 'j': 7, 'k': 2, 'cost': 24}, {'i': 2, 'j': 7, 'k': 3, 'cost': 14}, {'i': 2, 'j': 7, 'k': 4, 'cost': 32}, {'i': 2, 'j': 7, 'k': 5, 'cost': 40}, {'i': 2, 'j': 7, 'k': 6, 'cost': 93}, {'i': 2, 'j': 7, 'k': 7, 'cost': 70}, {'i': 2, 'j': 7, 'k': 8, 'cost': 15}, {'i': 2, 'j': 7, 'k': 9, 'cost': 17}, {'i': 2, 'j': 8, 'k': 1, 'cost': 38}, {'i': 2, 'j': 8, 'k': 2, 'cost': 70}, {'i': 2, 'j': 8, 'k': 3, 'cost': 48}, {'i': 2, 'j': 8, 'k': 4, 'cost': 6}, {'i': 2, 'j': 8, 'k': 5, 'cost': 79}, {'i': 2, 'j': 8, 'k': 6, 'cost': 73}, {'i': 2, 'j': 8, 'k': 7, 'cost': 10}, {'i': 2, 'j': 8, 'k': 8, 'cost': 56}, {'i': 2, 'j': 8, 'k': 9, 'cost': 14}, {'i': 2, 'j': 9, 'k': 1, 'cost': 43}, {'i': 2, 'j': 9, 'k': 2, 'cost': 93}, {'i': 2, 'j': 9, 'k': 3, 'cost': 59}, {'i': 2, 'j': 9, 'k': 4, 'cost': 84}, {'i': 2, 'j': 9, 'k': 5, 'cost': 53}, {'i': 2, 'j': 9, 'k': 6, 'cost': 54}, {'i': 2, 'j': 9, 'k': 7, 'cost': 84}, {'i': 2, 'j': 9, 'k': 8, 'cost': 68}, {'i': 2, 'j': 9, 'k': 9, 'cost': 57}, {'i': 3, 'j': 1, 'k': 1, 'cost': 82}, {'i': 3, 'j': 1, 'k': 2, 'cost': 82}, {'i': 3, 'j': 1, 'k': 3, 'cost': 73}, {'i': 3, 'j': 1, 'k': 4, 'cost': 83}, {'i': 3, 'j': 1, 'k': 5, 'cost': 62}, {'i': 3, 'j': 1, 'k': 6, 'cost': 16}, {'i': 3, 'j': 1, 'k': 7, 'cost': 98}, {'i': 3, 'j': 1, 'k': 8, 'cost': 24}, {'i': 3, 'j': 1, 'k': 9, 'cost': 83}, {'i': 3, 'j': 2, 'k': 1, 'cost': 52}, {'i': 3, 'j': 2, 'k': 2, 'cost': 59}, {'i': 3, 'j': 2, 'k': 3, 'cost': 45}, {'i': 3, 'j': 2, 'k': 4, 'cost': 89}, {'i': 3, 'j': 2, 'k': 5, 'cost': 82}, {'i': 3, 'j': 2, 'k': 6, 'cost': 22}, {'i': 3, 'j': 2, 'k': 7, 'cost': 89}, {'i': 3, 'j': 2, 'k': 8, 'cost': 30}, {'i': 3, 'j': 2, 'k': 9, 'cost': 3}, {'i': 3, 'j': 3, 'k': 1, 'cost': 75}, {'i': 3, 'j': 3, 'k': 2, 'cost': 43}, {'i': 3, 'j': 3, 'k': 3, 'cost': 44}, {'i': 3, 'j': 3, 'k': 4, 'cost': 66}, {'i': 3, 'j': 3, 'k': 5, 'cost': 56}, {'i': 3, 'j': 3, 'k': 6, 'cost': 70}, {'i': 3, 'j': 3, 'k': 7, 'cost': 1}, {'i': 3, 'j': 3, 'k': 8, 'cost': 32}, {'i': 3, 'j': 3, 'k': 9, 'cost': 29}, {'i': 3, 'j': 4, 'k': 1, 'cost': 5}, {'i': 3, 'j': 4, 'k': 2, 'cost': 68}, {'i': 3, 'j': 4, 'k': 3, 'cost': 60}, {'i': 3, 'j': 4, 'k': 4, 'cost': 57}, {'i': 3, 'j': 4, 'k': 5, 'cost': 53}, {'i': 3, 'j': 4, 'k': 6, 'cost': 50}, {'i': 3, 'j': 4, 'k': 7, 'cost': 19}, {'i': 3, 'j': 4, 'k': 8, 'cost': 29}, {'i': 3, 'j': 4, 'k': 9, 'cost': 5}, {'i': 3, 'j': 5, 'k': 1, 'cost': 64}, {'i': 3, 'j': 5, 'k': 2, 'cost': 54}, {'i': 3, 'j': 5, 'k': 3, 'cost': 77}, {'i': 3, 'j': 5, 'k': 4, 'cost': 82}, {'i': 3, 'j': 5, 'k': 5, 'cost': 66}, {'i': 3, 'j': 5, 'k': 6, 'cost': 84}, {'i': 3, 'j': 5, 'k': 7, 'cost': 76}, {'i': 3, 'j': 5, 'k': 8, 'cost': 48}, {'i': 3, 'j': 5, 'k': 9, 'cost': 52}, {'i': 3, 'j': 6, 'k': 1, 'cost': 2}, {'i': 3, 'j': 6, 'k': 2, 'cost': 27}, {'i': 3, 'j': 6, 'k': 3, 'cost': 50}, {'i': 3, 'j': 6, 'k': 4, 'cost': 5}, {'i': 3, 'j': 6, 'k': 5, 'cost': 98}, {'i': 3, 'j': 6, 'k': 6, 'cost': 22}, {'i': 3, 'j': 6, 'k': 7, 'cost': 29}, {'i': 3, 'j': 6, 'k': 8, 'cost': 61}, {'i': 3, 'j': 6, 'k': 9, 'cost': 11}, {'i': 3, 'j': 7, 'k': 1, 'cost': 79}, {'i': 3, 'j': 7, 'k': 2, 'cost': 56}, {'i': 3, 'j': 7, 'k': 3, 'cost': 35}, {'i': 3, 'j': 7, 'k': 4, 'cost': 81}, {'i': 3, 'j': 7, 'k': 5, 'cost': 3}, {'i': 3, 'j': 7, 'k': 6, 'cost': 24}, {'i': 3, 'j': 7, 'k': 7, 'cost': 39}, {'i': 3, 'j': 7, 'k': 8, 'cost': 7}, {'i': 3, 'j': 7, 'k': 9, 'cost': 39}, {'i': 3, 'j': 8, 'k': 1, 'cost': 47}, {'i': 3, 'j': 8, 'k': 2, 'cost': 15}, {'i': 3, 'j': 8, 'k': 3, 'cost': 29}, {'i': 3, 'j': 8, 'k': 4, 'cost': 81}, {'i': 3, 'j': 8, 'k': 5, 'cost': 91}, {'i': 3, 'j': 8, 'k': 6, 'cost': 9}, {'i': 3, 'j': 8, 'k': 7, 'cost': 49}, {'i': 3, 'j': 8, 'k': 8, 'cost': 18}, {'i': 3, 'j': 8, 'k': 9, 'cost': 5}, {'i': 3, 'j': 9, 'k': 1, 'cost': 35}, {'i': 3, 'j': 9, 'k': 2, 'cost': 37}, {'i': 3, 'j': 9, 'k': 3, 'cost': 98}, {'i': 3, 'j': 9, 'k': 4, 'cost': 19}, {'i': 3, 'j': 9, 'k': 5, 'cost': 95}, {'i': 3, 'j': 9, 'k': 6, 'cost': 96}, {'i': 3, 'j': 9, 'k': 7, 'cost': 64}, {'i': 3, 'j': 9, 'k': 8, 'cost': 79}, {'i': 3, 'j': 9, 'k': 9, 'cost': 4}, {'i': 4, 'j': 1, 'k': 1, 'cost': 95}, {'i': 4, 'j': 1, 'k': 2, 'cost': 22}, {'i': 4, 'j': 1, 'k': 3, 'cost': 77}, {'i': 4, 'j': 1, 'k': 4, 'cost': 63}, {'i': 4, 'j': 1, 'k': 5, 'cost': 89}, {'i': 4, 'j': 1, 'k': 6, 'cost': 4}, {'i': 4, 'j': 1, 'k': 7, 'cost': 71}, {'i': 4, 'j': 1, 'k': 8, 'cost': 96}, {'i': 4, 'j': 1, 'k': 9, 'cost': 84}, 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'cost': 27}, {'i': 8, 'j': 4, 'k': 2, 'cost': 72}, {'i': 8, 'j': 4, 'k': 3, 'cost': 48}, {'i': 8, 'j': 4, 'k': 4, 'cost': 66}, {'i': 8, 'j': 4, 'k': 5, 'cost': 81}, {'i': 8, 'j': 4, 'k': 6, 'cost': 4}, {'i': 8, 'j': 4, 'k': 7, 'cost': 49}, {'i': 8, 'j': 4, 'k': 8, 'cost': 71}, {'i': 8, 'j': 4, 'k': 9, 'cost': 54}, {'i': 8, 'j': 5, 'k': 1, 'cost': 44}, {'i': 8, 'j': 5, 'k': 2, 'cost': 74}, {'i': 8, 'j': 5, 'k': 3, 'cost': 72}, {'i': 8, 'j': 5, 'k': 4, 'cost': 89}, {'i': 8, 'j': 5, 'k': 5, 'cost': 50}, {'i': 8, 'j': 5, 'k': 6, 'cost': 65}, {'i': 8, 'j': 5, 'k': 7, 'cost': 93}, {'i': 8, 'j': 5, 'k': 8, 'cost': 8}, {'i': 8, 'j': 5, 'k': 9, 'cost': 65}, {'i': 8, 'j': 6, 'k': 1, 'cost': 54}, {'i': 8, 'j': 6, 'k': 2, 'cost': 57}, {'i': 8, 'j': 6, 'k': 3, 'cost': 99}, {'i': 8, 'j': 6, 'k': 4, 'cost': 38}, {'i': 8, 'j': 6, 'k': 5, 'cost': 46}, {'i': 8, 'j': 6, 'k': 6, 'cost': 68}, {'i': 8, 'j': 6, 'k': 7, 'cost': 81}, {'i': 8, 'j': 6, 'k': 8, 'cost': 12}, {'i': 8, 'j': 6, 'k': 9, 'cost': 80}, {'i': 8, 'j': 7, 'k': 1, 'cost': 56}, {'i': 8, 'j': 7, 'k': 2, 'cost': 89}, {'i': 8, 'j': 7, 'k': 3, 'cost': 6}, {'i': 8, 'j': 7, 'k': 4, 'cost': 14}, {'i': 8, 'j': 7, 'k': 5, 'cost': 95}, {'i': 8, 'j': 7, 'k': 6, 'cost': 83}, {'i': 8, 'j': 7, 'k': 7, 'cost': 38}, {'i': 8, 'j': 7, 'k': 8, 'cost': 54}, {'i': 8, 'j': 7, 'k': 9, 'cost': 67}, {'i': 8, 'j': 8, 'k': 1, 'cost': 11}, {'i': 8, 'j': 8, 'k': 2, 'cost': 89}, {'i': 8, 'j': 8, 'k': 3, 'cost': 25}, {'i': 8, 'j': 8, 'k': 4, 'cost': 31}, {'i': 8, 'j': 8, 'k': 5, 'cost': 47}, {'i': 8, 'j': 8, 'k': 6, 'cost': 4}, {'i': 8, 'j': 8, 'k': 7, 'cost': 85}, {'i': 8, 'j': 8, 'k': 8, 'cost': 89}, {'i': 8, 'j': 8, 'k': 9, 'cost': 16}, {'i': 8, 'j': 9, 'k': 1, 'cost': 63}, {'i': 8, 'j': 9, 'k': 2, 'cost': 94}, {'i': 8, 'j': 9, 'k': 3, 'cost': 64}, {'i': 8, 'j': 9, 'k': 4, 'cost': 52}, {'i': 8, 'j': 9, 'k': 5, 'cost': 90}, {'i': 8, 'j': 9, 'k': 6, 'cost': 57}, {'i': 8, 'j': 9, 'k': 7, 'cost': 47}, {'i': 8, 'j': 9, 'k': 8, 'cost': 11}, {'i': 8, 'j': 9, 'k': 9, 'cost': 73}, {'i': 9, 'j': 1, 'k': 1, 'cost': 93}, {'i': 9, 'j': 1, 'k': 2, 'cost': 70}, {'i': 9, 'j': 1, 'k': 3, 'cost': 67}, {'i': 9, 'j': 1, 'k': 4, 'cost': 45}, {'i': 9, 'j': 1, 'k': 5, 'cost': 75}, {'i': 9, 'j': 1, 'k': 6, 'cost': 30}, {'i': 9, 'j': 1, 'k': 7, 'cost': 24}, {'i': 9, 'j': 1, 'k': 8, 'cost': 27}, {'i': 9, 'j': 1, 'k': 9, 'cost': 62}, {'i': 9, 'j': 2, 'k': 1, 'cost': 33}, {'i': 9, 'j': 2, 'k': 2, 'cost': 77}, {'i': 9, 'j': 2, 'k': 3, 'cost': 26}, {'i': 9, 'j': 2, 'k': 4, 'cost': 27}, {'i': 9, 'j': 2, 'k': 5, 'cost': 27}, {'i': 9, 'j': 2, 'k': 6, 'cost': 99}, {'i': 9, 'j': 2, 'k': 7, 'cost': 14}, {'i': 9, 'j': 2, 'k': 8, 'cost': 7}, {'i': 9, 'j': 2, 'k': 9, 'cost': 57}, {'i': 9, 'j': 3, 'k': 1, 'cost': 91}, {'i': 9, 'j': 3, 'k': 2, 'cost': 67}, {'i': 9, 'j': 3, 'k': 3, 'cost': 22}, {'i': 9, 'j': 3, 'k': 4, 'cost': 48}, {'i': 9, 'j': 3, 'k': 5, 'cost': 11}, {'i': 9, 'j': 3, 'k': 6, 'cost': 32}, {'i': 9, 'j': 3, 'k': 7, 'cost': 19}, {'i': 9, 'j': 3, 'k': 8, 'cost': 29}, {'i': 9, 'j': 3, 'k': 9, 'cost': 3}, {'i': 9, 'j': 4, 'k': 1, 'cost': 40}, {'i': 9, 'j': 4, 'k': 2, 'cost': 74}, {'i': 9, 'j': 4, 'k': 3, 'cost': 17}, {'i': 9, 'j': 4, 'k': 4, 'cost': 85}, {'i': 9, 'j': 4, 'k': 5, 'cost': 16}, {'i': 9, 'j': 4, 'k': 6, 'cost': 0}, {'i': 9, 'j': 4, 'k': 7, 'cost': 57}, {'i': 9, 'j': 4, 'k': 8, 'cost': 56}, {'i': 9, 'j': 4, 'k': 9, 'cost': 7}, {'i': 9, 'j': 5, 'k': 1, 'cost': 82}, {'i': 9, 'j': 5, 'k': 2, 'cost': 4}, {'i': 9, 'j': 5, 'k': 3, 'cost': 49}, {'i': 9, 'j': 5, 'k': 4, 'cost': 58}, {'i': 9, 'j': 5, 'k': 5, 'cost': 47}, {'i': 9, 'j': 5, 'k': 6, 'cost': 43}, {'i': 9, 'j': 5, 'k': 7, 'cost': 69}, {'i': 9, 'j': 5, 'k': 8, 'cost': 28}, {'i': 9, 'j': 5, 'k': 9, 'cost': 48}, {'i': 9, 'j': 6, 'k': 1, 'cost': 12}, {'i': 9, 'j': 6, 'k': 2, 'cost': 42}, {'i': 9, 'j': 6, 'k': 3, 'cost': 48}, {'i': 9, 'j': 6, 'k': 4, 'cost': 2}, {'i': 9, 'j': 6, 'k': 5, 'cost': 77}, {'i': 9, 'j': 6, 'k': 6, 'cost': 61}, {'i': 9, 'j': 6, 'k': 7, 'cost': 95}, {'i': 9, 'j': 6, 'k': 8, 'cost': 53}, {'i': 9, 'j': 6, 'k': 9, 'cost': 63}, {'i': 9, 'j': 7, 'k': 1, 'cost': 38}, {'i': 9, 'j': 7, 'k': 2, 'cost': 83}, {'i': 9, 'j': 7, 'k': 3, 'cost': 55}, {'i': 9, 'j': 7, 'k': 4, 'cost': 28}, {'i': 9, 'j': 7, 'k': 5, 'cost': 24}, {'i': 9, 'j': 7, 'k': 6, 'cost': 11}, {'i': 9, 'j': 7, 'k': 7, 'cost': 71}, {'i': 9, 'j': 7, 'k': 8, 'cost': 82}, {'i': 9, 'j': 7, 'k': 9, 'cost': 7}, {'i': 9, 'j': 8, 'k': 1, 'cost': 71}, {'i': 9, 'j': 8, 'k': 2, 'cost': 77}, {'i': 9, 'j': 8, 'k': 3, 'cost': 91}, {'i': 9, 'j': 8, 'k': 4, 'cost': 77}, {'i': 9, 'j': 8, 'k': 5, 'cost': 57}, {'i': 9, 'j': 8, 'k': 6, 'cost': 43}, {'i': 9, 'j': 8, 'k': 7, 'cost': 19}, {'i': 9, 'j': 8, 'k': 8, 'cost': 69}, {'i': 9, 'j': 8, 'k': 9, 'cost': 83}, {'i': 9, 'j': 9, 'k': 1, 'cost': 60}, {'i': 9, 'j': 9, 'k': 2, 'cost': 71}, {'i': 9, 'j': 9, 'k': 3, 'cost': 67}, {'i': 9, 'j': 9, 'k': 4, 'cost': 62}, {'i': 9, 'j': 9, 'k': 5, 'cost': 95}, {'i': 9, 'j': 9, 'k': 6, 'cost': 56}, {'i': 9, 'j': 9, 'k': 7, 'cost': 39}, {'i': 9, 'j': 9, 'k': 8, 'cost': 81}, {'i': 9, 'j': 9, 'k': 9, 'cost': 22}]}","[[1, 7, 1], [2, 5, 8], [3, 8, 6], [4, 4, 5], [5, 2, 7], [6, 9, 3], [7, 3, 9], [8, 1, 2], [9, 6, 4]]",11,nl,1
+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.
+
+There are 10 campaigns to assign, identified as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
+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=0
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 15 | 59 | 64 | 82 | 89 | 33 | 93 | 26 | 58 | 93 |
+| 1 | 37 | 73 | 4 | 20 | 13 | 55 | 92 | 9 | 55 | 27 |
+| 2 | 31 | 11 | 91 | 38 | 6 | 74 | 45 | 55 | 38 | 49 |
+| 3 | 71 | 86 | 81 | 91 | 88 | 89 | 22 | 78 | 84 | 7 |
+| 4 | 94 | 26 | 3 | 95 | 18 | 43 | 55 | 30 | 58 | 89 |
+| 5 | 19 | 90 | 61 | 15 | 75 | 73 | 25 | 13 | 63 | 84 |
+| 6 | 97 | 16 | 87 | 40 | 80 | 12 | 48 | 28 | 70 | 8 |
+| 7 | 37 | 40 | 37 | 28 | 39 | 84 | 8 | 67 | 16 | 93 |
+| 8 | 16 | 81 | 6 | 32 | 61 | 87 | 38 | 18 | 2 | 92 |
+| 9 | 76 | 0 | 94 | 1 | 8 | 97 | 61 | 36 | 54 | 16 |
+
+## campaign_id=1
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 48 | 98 | 36 | 10 | 41 | 76 | 81 | 87 | 21 | 63 |
+| 1 | 86 | 28 | 13 | 67 | 8 | 98 | 72 | 66 | 5 | 41 |
+| 2 | 50 | 64 | 35 | 32 | 62 | 43 | 31 | 52 | 21 | 41 |
+| 3 | 84 | 64 | 86 | 31 | 15 | 15 | 56 | 34 | 5 | 33 |
+| 4 | 18 | 49 | 98 | 91 | 97 | 0 | 32 | 53 | 43 | 44 |
+| 5 | 44 | 22 | 77 | 85 | 46 | 97 | 82 | 9 | 30 | 4 |
+| 6 | 54 | 56 | 58 | 75 | 98 | 63 | 66 | 85 | 24 | 4 |
+| 7 | 44 | 44 | 66 | 46 | 59 | 18 | 22 | 14 | 54 | 77 |
+| 8 | 52 | 97 | 89 | 27 | 94 | 70 | 18 | 80 | 4 | 12 |
+| 9 | 51 | 87 | 46 | 28 | 49 | 74 | 66 | 72 | 2 | 23 |
+
+## campaign_id=2
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 74 | 9 | 8 | 32 | 77 | 55 | 68 | 30 | 65 | 82 |
+| 1 | 57 | 91 | 2 | 30 | 81 | 63 | 68 | 39 | 77 | 39 |
+| 2 | 11 | 0 | 38 | 72 | 9 | 41 | 39 | 24 | 44 | 57 |
+| 3 | 19 | 94 | 50 | 60 | 58 | 61 | 82 | 14 | 76 | 77 |
+| 4 | 32 | 47 | 19 | 46 | 32 | 22 | 43 | 1 | 49 | 3 |
+| 5 | 34 | 32 | 53 | 7 | 50 | 37 | 34 | 61 | 4 | 43 |
+| 6 | 20 | 82 | 79 | 82 | 32 | 88 | 68 | 18 | 53 | 33 |
+| 7 | 21 | 60 | 12 | 63 | 9 | 19 | 85 | 18 | 27 | 89 |
+| 8 | 3 | 75 | 81 | 99 | 30 | 26 | 0 | 0 | 38 | 16 |
+| 9 | 87 | 1 | 79 | 57 | 63 | 35 | 83 | 62 | 30 | 17 |
+
+## campaign_id=3
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 91 | 38 | 58 | 78 | 58 | 75 | 76 | 17 | 10 | 30 |
+| 1 | 89 | 76 | 62 | 75 | 27 | 50 | 1 | 62 | 49 | 79 |
+| 2 | 99 | 97 | 59 | 14 | 79 | 82 | 92 | 65 | 70 | 35 |
+| 3 | 82 | 59 | 91 | 63 | 12 | 69 | 31 | 88 | 70 | 35 |
+| 4 | 33 | 3 | 50 | 96 | 24 | 34 | 89 | 92 | 74 | 72 |
+| 5 | 99 | 82 | 83 | 95 | 74 | 14 | 12 | 63 | 85 | 42 |
+| 6 | 17 | 36 | 93 | 65 | 60 | 50 | 8 | 97 | 30 | 39 |
+| 7 | 83 | 54 | 48 | 60 | 0 | 83 | 19 | 8 | 72 | 14 |
+| 8 | 58 | 48 | 16 | 93 | 19 | 70 | 48 | 54 | 72 | 62 |
+| 9 | 39 | 62 | 13 | 57 | 47 | 67 | 76 | 96 | 96 | 57 |
+
+## campaign_id=4
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 84 | 0 | 12 | 22 | 88 | 56 | 65 | 96 | 12 | 94 |
+| 1 | 64 | 2 | 52 | 39 | 21 | 43 | 25 | 19 | 8 | 38 |
+| 2 | 97 | 27 | 4 | 66 | 43 | 19 | 54 | 13 | 57 | 40 |
+| 3 | 96 | 17 | 10 | 40 | 90 | 89 | 91 | 10 | 67 | 65 |
+| 4 | 68 | 75 | 30 | 82 | 49 | 44 | 14 | 66 | 46 | 85 |
+| 5 | 70 | 29 | 77 | 86 | 88 | 11 | 53 | 1 | 58 | 35 |
+| 6 | 3 | 83 | 24 | 37 | 52 | 29 | 8 | 27 | 26 | 94 |
+| 7 | 53 | 8 | 74 | 25 | 54 | 46 | 34 | 53 | 51 | 51 |
+| 8 | 66 | 78 | 4 | 14 | 26 | 12 | 63 | 52 | 5 | 77 |
+| 9 | 85 | 15 | 42 | 6 | 71 | 37 | 14 | 60 | 16 | 89 |
+
+## campaign_id=5
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 74 | 29 | 11 | 70 | 65 | 17 | 71 | 34 | 80 | 8 |
+| 1 | 33 | 42 | 86 | 29 | 72 | 22 | 89 | 95 | 14 | 96 |
+| 2 | 81 | 18 | 82 | 71 | 22 | 17 | 5 | 73 | 5 | 52 |
+| 3 | 70 | 1 | 4 | 83 | 29 | 1 | 88 | 80 | 60 | 6 |
+| 4 | 19 | 73 | 23 | 21 | 80 | 57 | 39 | 76 | 41 | 44 |
+| 5 | 9 | 8 | 20 | 57 | 58 | 90 | 29 | 53 | 55 | 28 |
+| 6 | 50 | 33 | 21 | 84 | 58 | 66 | 37 | 35 | 74 | 18 |
+| 7 | 56 | 49 | 85 | 32 | 78 | 69 | 17 | 25 | 45 | 92 |
+| 8 | 77 | 94 | 70 | 94 | 53 | 7 | 1 | 80 | 32 | 63 |
+| 9 | 53 | 53 | 27 | 68 | 33 | 86 | 19 | 9 | 86 | 75 |
+
+## campaign_id=6
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 35 | 86 | 4 | 55 | 96 | 90 | 24 | 88 | 94 | 54 |
+| 1 | 52 | 98 | 55 | 9 | 56 | 46 | 1 | 95 | 59 | 80 |
+| 2 | 92 | 18 | 21 | 7 | 39 | 80 | 78 | 54 | 60 | 61 |
+| 3 | 40 | 56 | 40 | 98 | 2 | 24 | 69 | 20 | 87 | 95 |
+| 4 | 22 | 96 | 38 | 3 | 0 | 28 | 36 | 66 | 7 | 24 |
+| 5 | 56 | 1 | 83 | 20 | 54 | 7 | 78 | 48 | 12 | 21 |
+| 6 | 95 | 5 | 74 | 36 | 36 | 35 | 48 | 69 | 40 | 67 |
+| 7 | 83 | 19 | 84 | 98 | 83 | 95 | 68 | 60 | 48 | 74 |
+| 8 | 77 | 7 | 13 | 15 | 5 | 6 | 12 | 99 | 95 | 91 |
+| 9 | 87 | 18 | 87 | 26 | 18 | 11 | 45 | 49 | 35 | 66 |
+
+## campaign_id=7
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 24 | 61 | 32 | 93 | 95 | 34 | 98 | 55 | 11 | 0 |
+| 1 | 46 | 8 | 6 | 90 | 78 | 93 | 74 | 91 | 18 | 77 |
+| 2 | 78 | 11 | 90 | 84 | 10 | 55 | 54 | 14 | 85 | 82 |
+| 3 | 61 | 38 | 84 | 19 | 32 | 19 | 49 | 67 | 6 | 81 |
+| 4 | 68 | 49 | 23 | 17 | 23 | 43 | 2 | 78 | 98 | 70 |
+| 5 | 53 | 65 | 96 | 22 | 80 | 15 | 18 | 66 | 32 | 22 |
+| 6 | 77 | 80 | 89 | 62 | 70 | 74 | 86 | 45 | 89 | 37 |
+| 7 | 9 | 11 | 67 | 10 | 92 | 41 | 24 | 76 | 71 | 29 |
+| 8 | 55 | 73 | 63 | 5 | 56 | 90 | 95 | 6 | 17 | 17 |
+| 9 | 2 | 93 | 83 | 36 | 54 | 99 | 58 | 11 | 54 | 17 |
+
+## campaign_id=8
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 21 | 89 | 26 | 57 | 7 | 2 | 92 | 46 | 25 | 0 |
+| 1 | 74 | 32 | 91 | 16 | 10 | 38 | 56 | 81 | 70 | 42 |
+| 2 | 71 | 77 | 78 | 84 | 37 | 34 | 53 | 95 | 29 | 66 |
+| 3 | 13 | 52 | 95 | 30 | 39 | 11 | 34 | 98 | 71 | 53 |
+| 4 | 1 | 54 | 77 | 48 | 48 | 92 | 31 | 22 | 39 | 25 |
+| 5 | 91 | 29 | 34 | 82 | 69 | 1 | 22 | 90 | 0 | 74 |
+| 6 | 33 | 71 | 18 | 43 | 91 | 20 | 55 | 72 | 62 | 63 |
+| 7 | 34 | 18 | 26 | 10 | 22 | 3 | 23 | 2 | 9 | 92 |
+| 8 | 13 | 44 | 26 | 50 | 4 | 84 | 69 | 42 | 5 | 32 |
+| 9 | 14 | 88 | 19 | 67 | 81 | 28 | 14 | 65 | 5 | 46 |
+
+## campaign_id=9
+| channel_id\week_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 46 | 61 | 87 | 56 | 67 | 7 | 85 | 17 | 12 | 99 |
+| 1 | 38 | 19 | 85 | 55 | 62 | 17 | 15 | 66 | 43 | 85 |
+| 2 | 45 | 45 | 89 | 13 | 21 | 10 | 76 | 99 | 32 | 37 |
+| 3 | 54 | 78 | 11 | 6 | 1 | 28 | 48 | 31 | 37 | 3 |
+| 4 | 38 | 15 | 51 | 41 | 48 | 54 | 85 | 35 | 9 | 32 |
+| 5 | 85 | 52 | 45 | 41 | 14 | 27 | 58 | 64 | 34 | 68 |
+| 6 | 81 | 57 | 45 | 45 | 54 | 63 | 8 | 0 | 48 | 22 |
+| 7 | 95 | 30 | 77 | 56 | 13 | 95 | 66 | 59 | 7 | 7 |
+| 8 | 37 | 51 | 64 | 66 | 37 | 60 | 76 | 58 | 63 | 15 |
+| 9 | 7 | 42 | 71 | 43 | 47 | 11 | 54 | 56 | 12 | 11 |
+The person in charge will select one campaign+outlet+week triple for each of the 10 campaigns so every outlet and week is used exactly once and the total spend is minimized.
+
+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': [[[15, 59, 64, 82, 89, 33, 93, 26, 58, 93], [37, 73, 4, 20, 13, 55, 92, 9, 55, 27], [31, 11, 91, 38, 6, 74, 45, 55, 38, 49], [71, 86, 81, 91, 88, 89, 22, 78, 84, 7], [94, 26, 3, 95, 18, 43, 55, 30, 58, 89], [19, 90, 61, 15, 75, 73, 25, 13, 63, 84], [97, 16, 87, 40, 80, 12, 48, 28, 70, 8], [37, 40, 37, 28, 39, 84, 8, 67, 16, 93], [16, 81, 6, 32, 61, 87, 38, 18, 2, 92], [76, 0, 94, 1, 8, 97, 61, 36, 54, 16]], [[48, 98, 36, 10, 41, 76, 81, 87, 21, 63], [86, 28, 13, 67, 8, 98, 72, 66, 5, 41], [50, 64, 35, 32, 62, 43, 31, 52, 21, 41], [84, 64, 86, 31, 15, 15, 56, 34, 5, 33], [18, 49, 98, 91, 97, 0, 32, 53, 43, 44], [44, 22, 77, 85, 46, 97, 82, 9, 30, 4], [54, 56, 58, 75, 98, 63, 66, 85, 24, 4], [44, 44, 66, 46, 59, 18, 22, 14, 54, 77], [52, 97, 89, 27, 94, 70, 18, 80, 4, 12], [51, 87, 46, 28, 49, 74, 66, 72, 2, 23]], [[74, 9, 8, 32, 77, 55, 68, 30, 65, 82], [57, 91, 2, 30, 81, 63, 68, 39, 77, 39], [11, 0, 38, 72, 9, 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'cost': 31}, {'i': 9, 'j': 3, 'k': 8, 'cost': 37}, {'i': 9, 'j': 3, 'k': 9, 'cost': 3}, {'i': 9, 'j': 4, 'k': 0, 'cost': 38}, {'i': 9, 'j': 4, 'k': 1, 'cost': 15}, {'i': 9, 'j': 4, 'k': 2, 'cost': 51}, {'i': 9, 'j': 4, 'k': 3, 'cost': 41}, {'i': 9, 'j': 4, 'k': 4, 'cost': 48}, {'i': 9, 'j': 4, 'k': 5, 'cost': 54}, {'i': 9, 'j': 4, 'k': 6, 'cost': 85}, {'i': 9, 'j': 4, 'k': 7, 'cost': 35}, {'i': 9, 'j': 4, 'k': 8, 'cost': 9}, {'i': 9, 'j': 4, 'k': 9, 'cost': 32}, {'i': 9, 'j': 5, 'k': 0, 'cost': 85}, {'i': 9, 'j': 5, 'k': 1, 'cost': 52}, {'i': 9, 'j': 5, 'k': 2, 'cost': 45}, {'i': 9, 'j': 5, 'k': 3, 'cost': 41}, {'i': 9, 'j': 5, 'k': 4, 'cost': 14}, {'i': 9, 'j': 5, 'k': 5, 'cost': 27}, {'i': 9, 'j': 5, 'k': 6, 'cost': 58}, {'i': 9, 'j': 5, 'k': 7, 'cost': 64}, {'i': 9, 'j': 5, 'k': 8, 'cost': 34}, {'i': 9, 'j': 5, 'k': 9, 'cost': 68}, {'i': 9, 'j': 6, 'k': 0, 'cost': 81}, {'i': 9, 'j': 6, 'k': 1, 'cost': 57}, {'i': 9, 'j': 6, 'k': 2, 'cost': 45}, {'i': 9, 'j': 6, 'k': 3, 'cost': 45}, {'i': 9, 'j': 6, 'k': 4, 'cost': 54}, {'i': 9, 'j': 6, 'k': 5, 'cost': 63}, {'i': 9, 'j': 6, 'k': 6, 'cost': 8}, {'i': 9, 'j': 6, 'k': 7, 'cost': 0}, {'i': 9, 'j': 6, 'k': 8, 'cost': 48}, {'i': 9, 'j': 6, 'k': 9, 'cost': 22}, {'i': 9, 'j': 7, 'k': 0, 'cost': 95}, {'i': 9, 'j': 7, 'k': 1, 'cost': 30}, {'i': 9, 'j': 7, 'k': 2, 'cost': 77}, {'i': 9, 'j': 7, 'k': 3, 'cost': 56}, {'i': 9, 'j': 7, 'k': 4, 'cost': 13}, {'i': 9, 'j': 7, 'k': 5, 'cost': 95}, {'i': 9, 'j': 7, 'k': 6, 'cost': 66}, {'i': 9, 'j': 7, 'k': 7, 'cost': 59}, {'i': 9, 'j': 7, 'k': 8, 'cost': 7}, {'i': 9, 'j': 7, 'k': 9, 'cost': 7}, {'i': 9, 'j': 8, 'k': 0, 'cost': 37}, {'i': 9, 'j': 8, 'k': 1, 'cost': 51}, {'i': 9, 'j': 8, 'k': 2, 'cost': 64}, {'i': 9, 'j': 8, 'k': 3, 'cost': 66}, {'i': 9, 'j': 8, 'k': 4, 'cost': 37}, {'i': 9, 'j': 8, 'k': 5, 'cost': 60}, {'i': 9, 'j': 8, 'k': 6, 'cost': 76}, {'i': 9, 'j': 8, 'k': 7, 'cost': 58}, {'i': 9, 'j': 8, 'k': 8, 'cost': 63}, {'i': 9, 'j': 8, 'k': 9, 'cost': 15}, {'i': 9, 'j': 9, 'k': 0, 'cost': 7}, {'i': 9, 'j': 9, 'k': 1, 'cost': 42}, {'i': 9, 'j': 9, 'k': 2, 'cost': 71}, {'i': 9, 'j': 9, 'k': 3, 'cost': 43}, {'i': 9, 'j': 9, 'k': 4, 'cost': 47}, {'i': 9, 'j': 9, 'k': 5, 'cost': 11}, {'i': 9, 'j': 9, 'k': 6, 'cost': 54}, {'i': 9, 'j': 9, 'k': 7, 'cost': 56}, {'i': 9, 'j': 9, 'k': 8, 'cost': 12}, {'i': 9, 'j': 9, 'k': 9, 'cost': 11}]}","[[0, 9, 3], [1, 4, 5], [2, 8, 0], [3, 7, 4], [4, 2, 2], [5, 3, 1], [6, 1, 6], [7, 0, 9], [8, 5, 8], [9, 6, 7]]",12,nl,0
+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 11 family members — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 — 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=1
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 30 | 38 | 14 | 42 | 10 | 64 | 30 | 21 | 57 | 39 | 53 |
+| 2 | 14 | 68 | 54 | 15 | 85 | 4 | 67 | 6 | 58 | 0 | 93 |
+| 3 | 35 | 91 | 10 | 33 | 45 | 26 | 93 | 63 | 12 | 15 | 53 |
+| 4 | 85 | 65 | 66 | 84 | 35 | 13 | 29 | 36 | 35 | 42 | 79 |
+| 5 | 54 | 73 | 29 | 49 | 14 | 75 | 65 | 8 | 78 | 15 | 78 |
+| 6 | 46 | 32 | 68 | 90 | 25 | 17 | 92 | 80 | 95 | 45 | 57 |
+| 7 | 86 | 64 | 92 | 4 | 16 | 19 | 3 | 98 | 3 | 53 | 96 |
+| 8 | 99 | 22 | 92 | 48 | 72 | 11 | 15 | 69 | 81 | 99 | 74 |
+| 9 | 25 | 59 | 48 | 88 | 24 | 40 | 34 | 5 | 3 | 83 | 54 |
+| 10 | 81 | 65 | 19 | 0 | 7 | 79 | 46 | 32 | 93 | 14 | 50 |
+| 11 | 94 | 44 | 4 | 2 | 45 | 7 | 12 | 44 | 29 | 84 | 60 |
+
+## member_id=2
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 71 | 45 | 27 | 17 | 7 | 43 | 2 | 10 | 89 | 14 | 35 |
+| 2 | 11 | 29 | 3 | 7 | 14 | 24 | 24 | 24 | 2 | 10 | 47 |
+| 3 | 15 | 91 | 17 | 32 | 9 | 89 | 75 | 81 | 81 | 35 | 6 |
+| 4 | 5 | 35 | 47 | 53 | 68 | 10 | 64 | 55 | 24 | 95 | 97 |
+| 5 | 87 | 67 | 37 | 9 | 92 | 29 | 72 | 77 | 45 | 67 | 32 |
+| 6 | 80 | 7 | 52 | 33 | 9 | 20 | 98 | 9 | 85 | 13 | 97 |
+| 7 | 82 | 12 | 57 | 53 | 91 | 29 | 76 | 40 | 82 | 45 | 30 |
+| 8 | 83 | 27 | 19 | 56 | 69 | 52 | 22 | 83 | 80 | 46 | 8 |
+| 9 | 79 | 16 | 49 | 96 | 47 | 23 | 52 | 71 | 51 | 6 | 88 |
+| 10 | 54 | 5 | 87 | 15 | 29 | 0 | 31 | 90 | 95 | 7 | 80 |
+| 11 | 30 | 73 | 67 | 45 | 67 | 32 | 94 | 95 | 94 | 87 | 56 |
+
+## member_id=3
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 19 | 93 | 16 | 85 | 81 | 70 | 73 | 77 | 49 | 70 | 42 |
+| 2 | 89 | 19 | 20 | 54 | 1 | 63 | 30 | 87 | 84 | 36 | 81 |
+| 3 | 1 | 60 | 35 | 96 | 63 | 93 | 5 | 62 | 45 | 57 | 43 |
+| 4 | 27 | 4 | 74 | 61 | 0 | 40 | 96 | 23 | 75 | 74 | 61 |
+| 5 | 21 | 90 | 28 | 82 | 81 | 9 | 25 | 82 | 42 | 69 | 92 |
+| 6 | 91 | 1 | 12 | 52 | 85 | 20 | 97 | 41 | 12 | 69 | 99 |
+| 7 | 79 | 18 | 41 | 88 | 88 | 58 | 43 | 4 | 57 | 11 | 32 |
+| 8 | 66 | 19 | 1 | 24 | 0 | 4 | 72 | 3 | 43 | 90 | 72 |
+| 9 | 8 | 52 | 98 | 24 | 84 | 87 | 61 | 12 | 72 | 62 | 7 |
+| 10 | 23 | 62 | 45 | 63 | 94 | 23 | 7 | 41 | 29 | 20 | 0 |
+| 11 | 61 | 49 | 57 | 95 | 45 | 52 | 15 | 25 | 57 | 35 | 2 |
+
+## member_id=4
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 85 | 55 | 68 | 49 | 14 | 23 | 67 | 93 | 3 | 69 | 79 |
+| 2 | 37 | 38 | 8 | 59 | 0 | 53 | 41 | 1 | 6 | 86 | 39 |
+| 3 | 37 | 54 | 54 | 73 | 85 | 76 | 61 | 65 | 8 | 60 | 25 |
+| 4 | 33 | 89 | 19 | 45 | 16 | 51 | 1 | 60 | 14 | 62 | 78 |
+| 5 | 47 | 72 | 8 | 17 | 41 | 96 | 17 | 47 | 74 | 73 | 85 |
+| 6 | 92 | 93 | 10 | 62 | 59 | 60 | 31 | 67 | 31 | 89 | 41 |
+| 7 | 23 | 54 | 15 | 65 | 96 | 19 | 8 | 45 | 49 | 11 | 90 |
+| 8 | 80 | 17 | 78 | 89 | 8 | 87 | 48 | 17 | 11 | 18 | 36 |
+| 9 | 33 | 6 | 89 | 96 | 47 | 9 | 3 | 70 | 81 | 25 | 48 |
+| 10 | 5 | 80 | 84 | 8 | 6 | 27 | 81 | 74 | 40 | 56 | 60 |
+| 11 | 60 | 94 | 67 | 64 | 12 | 24 | 24 | 73 | 27 | 11 | 99 |
+
+## member_id=5
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 28 | 25 | 70 | 32 | 9 | 23 | 11 | 71 | 19 | 36 | 63 |
+| 2 | 59 | 23 | 17 | 32 | 83 | 74 | 98 | 47 | 24 | 52 | 66 |
+| 3 | 44 | 76 | 67 | 64 | 13 | 75 | 61 | 73 | 2 | 25 | 99 |
+| 4 | 4 | 18 | 2 | 36 | 80 | 46 | 44 | 44 | 53 | 6 | 30 |
+| 5 | 31 | 18 | 70 | 52 | 94 | 37 | 40 | 5 | 74 | 27 | 56 |
+| 6 | 48 | 9 | 61 | 20 | 48 | 38 | 92 | 57 | 52 | 6 | 84 |
+| 7 | 20 | 73 | 14 | 38 | 40 | 3 | 99 | 23 | 77 | 55 | 71 |
+| 8 | 39 | 17 | 23 | 43 | 97 | 62 | 43 | 11 | 84 | 83 | 66 |
+| 9 | 1 | 21 | 21 | 3 | 12 | 7 | 61 | 80 | 30 | 71 | 78 |
+| 10 | 26 | 18 | 35 | 36 | 42 | 91 | 68 | 30 | 26 | 24 | 31 |
+| 11 | 93 | 77 | 33 | 9 | 48 | 25 | 39 | 88 | 41 | 11 | 49 |
+
+## member_id=6
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 22 | 32 | 46 | 75 | 86 | 59 | 95 | 39 | 81 | 2 | 5 |
+| 2 | 54 | 22 | 86 | 62 | 75 | 78 | 64 | 51 | 51 | 72 | 12 |
+| 3 | 68 | 52 | 52 | 71 | 23 | 49 | 46 | 85 | 4 | 75 | 76 |
+| 4 | 57 | 44 | 76 | 53 | 24 | 7 | 74 | 73 | 78 | 31 | 38 |
+| 5 | 88 | 46 | 87 | 1 | 49 | 8 | 32 | 0 | 81 | 91 | 65 |
+| 6 | 53 | 57 | 13 | 23 | 92 | 85 | 78 | 20 | 33 | 7 | 12 |
+| 7 | 32 | 32 | 4 | 17 | 57 | 84 | 47 | 6 | 99 | 0 | 26 |
+| 8 | 29 | 11 | 91 | 22 | 3 | 27 | 17 | 81 | 29 | 24 | 88 |
+| 9 | 8 | 7 | 21 | 51 | 27 | 40 | 40 | 10 | 76 | 8 | 32 |
+| 10 | 95 | 26 | 59 | 62 | 38 | 88 | 10 | 61 | 77 | 50 | 13 |
+| 11 | 15 | 52 | 68 | 4 | 10 | 79 | 68 | 27 | 58 | 89 | 64 |
+
+## member_id=7
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 48 | 3 | 22 | 36 | 66 | 70 | 5 | 10 | 97 | 72 | 96 |
+| 2 | 54 | 75 | 49 | 71 | 50 | 27 | 3 | 26 | 39 | 33 | 62 |
+| 3 | 22 | 23 | 74 | 69 | 47 | 89 | 5 | 86 | 26 | 53 | 63 |
+| 4 | 39 | 93 | 22 | 35 | 93 | 26 | 25 | 77 | 91 | 6 | 17 |
+| 5 | 73 | 27 | 12 | 89 | 40 | 30 | 95 | 55 | 42 | 30 | 6 |
+| 6 | 59 | 48 | 65 | 26 | 52 | 53 | 83 | 11 | 76 | 19 | 28 |
+| 7 | 69 | 74 | 37 | 6 | 21 | 8 | 15 | 36 | 42 | 43 | 74 |
+| 8 | 43 | 18 | 38 | 85 | 66 | 27 | 58 | 84 | 63 | 86 | 63 |
+| 9 | 12 | 96 | 93 | 45 | 80 | 79 | 35 | 41 | 19 | 2 | 96 |
+| 10 | 87 | 76 | 99 | 46 | 2 | 14 | 68 | 9 | 85 | 22 | 11 |
+| 11 | 59 | 0 | 55 | 30 | 51 | 53 | 61 | 70 | 99 | 36 | 54 |
+
+## member_id=8
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 44 | 88 | 24 | 59 | 84 | 63 | 49 | 9 | 36 | 76 | 75 |
+| 2 | 24 | 94 | 2 | 77 | 0 | 11 | 56 | 38 | 50 | 29 | 28 |
+| 3 | 70 | 97 | 74 | 87 | 86 | 19 | 93 | 3 | 82 | 42 | 19 |
+| 4 | 38 | 13 | 79 | 41 | 56 | 91 | 44 | 59 | 28 | 62 | 40 |
+| 5 | 73 | 0 | 36 | 26 | 79 | 77 | 81 | 97 | 78 | 83 | 35 |
+| 6 | 25 | 10 | 22 | 80 | 71 | 6 | 1 | 29 | 3 | 29 | 72 |
+| 7 | 69 | 58 | 86 | 68 | 39 | 36 | 56 | 85 | 44 | 73 | 0 |
+| 8 | 94 | 20 | 21 | 16 | 16 | 83 | 91 | 37 | 48 | 25 | 26 |
+| 9 | 65 | 32 | 6 | 23 | 50 | 27 | 26 | 53 | 48 | 17 | 2 |
+| 10 | 86 | 54 | 75 | 38 | 86 | 96 | 80 | 12 | 19 | 51 | 2 |
+| 11 | 58 | 61 | 33 | 27 | 23 | 11 | 90 | 20 | 99 | 85 | 12 |
+
+## member_id=9
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 90 | 78 | 25 | 97 | 97 | 22 | 59 | 13 | 36 | 85 | 39 |
+| 2 | 68 | 35 | 68 | 48 | 50 | 21 | 43 | 50 | 48 | 39 | 18 |
+| 3 | 39 | 75 | 28 | 82 | 76 | 84 | 97 | 94 | 89 | 29 | 63 |
+| 4 | 31 | 58 | 66 | 41 | 24 | 11 | 86 | 11 | 28 | 17 | 58 |
+| 5 | 63 | 67 | 9 | 52 | 2 | 77 | 80 | 59 | 28 | 71 | 98 |
+| 6 | 60 | 56 | 2 | 6 | 4 | 66 | 90 | 31 | 61 | 1 | 76 |
+| 7 | 7 | 75 | 76 | 17 | 68 | 14 | 5 | 79 | 78 | 36 | 53 |
+| 8 | 5 | 91 | 32 | 58 | 77 | 14 | 59 | 62 | 73 | 77 | 89 |
+| 9 | 89 | 54 | 22 | 82 | 42 | 10 | 95 | 10 | 9 | 12 | 20 |
+| 10 | 70 | 57 | 87 | 21 | 81 | 28 | 10 | 41 | 20 | 83 | 70 |
+| 11 | 88 | 50 | 0 | 73 | 28 | 68 | 1 | 1 | 34 | 63 | 55 |
+
+## member_id=10
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 18 | 81 | 76 | 2 | 64 | 4 | 44 | 70 | 38 | 49 | 3 |
+| 2 | 67 | 81 | 77 | 49 | 34 | 27 | 55 | 83 | 57 | 40 | 64 |
+| 3 | 89 | 97 | 68 | 18 | 30 | 65 | 25 | 25 | 67 | 94 | 66 |
+| 4 | 2 | 78 | 74 | 54 | 67 | 40 | 0 | 88 | 65 | 73 | 97 |
+| 5 | 31 | 37 | 41 | 65 | 11 | 77 | 0 | 31 | 83 | 85 | 43 |
+| 6 | 46 | 95 | 32 | 82 | 4 | 97 | 48 | 11 | 32 | 35 | 17 |
+| 7 | 21 | 25 | 60 | 26 | 94 | 85 | 23 | 70 | 83 | 47 | 49 |
+| 8 | 90 | 24 | 72 | 35 | 46 | 30 | 44 | 69 | 38 | 2 | 56 |
+| 9 | 61 | 29 | 60 | 37 | 22 | 49 | 32 | 17 | 18 | 16 | 97 |
+| 10 | 26 | 52 | 64 | 13 | 94 | 38 | 6 | 39 | 28 | 11 | 2 |
+| 11 | 90 | 61 | 68 | 1 | 62 | 96 | 25 | 36 | 42 | 60 | 24 |
+
+## member_id=11
+| chore_id\cleaning_day_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 69 | 82 | 78 | 65 | 5 | 92 | 89 | 91 | 2 | 90 | 78 |
+| 2 | 84 | 34 | 73 | 88 | 51 | 73 | 2 | 60 | 61 | 67 | 69 |
+| 3 | 78 | 24 | 56 | 63 | 80 | 27 | 1 | 51 | 84 | 7 | 5 |
+| 4 | 30 | 88 | 6 | 75 | 28 | 74 | 95 | 67 | 1 | 41 | 90 |
+| 5 | 47 | 38 | 27 | 5 | 36 | 31 | 49 | 58 | 55 | 37 | 30 |
+| 6 | 22 | 4 | 95 | 32 | 52 | 25 | 24 | 57 | 63 | 37 | 63 |
+| 7 | 25 | 74 | 59 | 78 | 85 | 57 | 15 | 91 | 59 | 64 | 20 |
+| 8 | 31 | 29 | 93 | 43 | 57 | 67 | 15 | 81 | 34 | 15 | 52 |
+| 9 | 99 | 86 | 54 | 86 | 96 | 47 | 54 | 33 | 27 | 98 | 80 |
+| 10 | 4 | 70 | 65 | 70 | 27 | 40 | 44 | 88 | 10 | 1 | 13 |
+| 11 | 55 | 99 | 59 | 50 | 70 | 10 | 67 | 20 | 28 | 58 | 90 |
+We will choose the 11 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': [[[30, 38, 14, 42, 10, 64, 30, 21, 57, 39, 53], [14, 68, 54, 15, 85, 4, 67, 6, 58, 0, 93], [35, 91, 10, 33, 45, 26, 93, 63, 12, 15, 53], [85, 65, 66, 84, 35, 13, 29, 36, 35, 42, 79], [54, 73, 29, 49, 14, 75, 65, 8, 78, 15, 78], [46, 32, 68, 90, 25, 17, 92, 80, 95, 45, 57], [86, 64, 92, 4, 16, 19, 3, 98, 3, 53, 96], [99, 22, 92, 48, 72, 11, 15, 69, 81, 99, 74], [25, 59, 48, 88, 24, 40, 34, 5, 3, 83, 54], [81, 65, 19, 0, 7, 79, 46, 32, 93, 14, 50], [94, 44, 4, 2, 45, 7, 12, 44, 29, 84, 60]], [[71, 45, 27, 17, 7, 43, 2, 10, 89, 14, 35], [11, 29, 3, 7, 14, 24, 24, 24, 2, 10, 47], [15, 91, 17, 32, 9, 89, 75, 81, 81, 35, 6], [5, 35, 47, 53, 68, 10, 64, 55, 24, 95, 97], [87, 67, 37, 9, 92, 29, 72, 77, 45, 67, 32], [80, 7, 52, 33, 9, 20, 98, 9, 85, 13, 97], [82, 12, 57, 53, 91, 29, 76, 40, 82, 45, 30], [83, 27, 19, 56, 69, 52, 22, 83, 80, 46, 8], [79, 16, 49, 96, 47, 23, 52, 71, 51, 6, 88], [54, 5, 87, 15, 29, 0, 31, 90, 95, 7, 80], [30, 73, 67, 45, 67, 32, 94, 95, 94, 87, 56]], [[19, 93, 16, 85, 81, 70, 73, 77, 49, 70, 42], [89, 19, 20, 54, 1, 63, 30, 87, 84, 36, 81], [1, 60, 35, 96, 63, 93, 5, 62, 45, 57, 43], [27, 4, 74, 61, 0, 40, 96, 23, 75, 74, 61], [21, 90, 28, 82, 81, 9, 25, 82, 42, 69, 92], [91, 1, 12, 52, 85, 20, 97, 41, 12, 69, 99], [79, 18, 41, 88, 88, 58, 43, 4, 57, 11, 32], [66, 19, 1, 24, 0, 4, 72, 3, 43, 90, 72], [8, 52, 98, 24, 84, 87, 61, 12, 72, 62, 7], [23, 62, 45, 63, 94, 23, 7, 41, 29, 20, 0], [61, 49, 57, 95, 45, 52, 15, 25, 57, 35, 2]], [[85, 55, 68, 49, 14, 23, 67, 93, 3, 69, 79], [37, 38, 8, 59, 0, 53, 41, 1, 6, 86, 39], [37, 54, 54, 73, 85, 76, 61, 65, 8, 60, 25], [33, 89, 19, 45, 16, 51, 1, 60, 14, 62, 78], [47, 72, 8, 17, 41, 96, 17, 47, 74, 73, 85], [92, 93, 10, 62, 59, 60, 31, 67, 31, 89, 41], [23, 54, 15, 65, 96, 19, 8, 45, 49, 11, 90], [80, 17, 78, 89, 8, 87, 48, 17, 11, 18, 36], [33, 6, 89, 96, 47, 9, 3, 70, 81, 25, 48], [5, 80, 84, 8, 6, 27, 81, 74, 40, 56, 60], [60, 94, 67, 64, 12, 24, 24, 73, 27, 11, 99]], [[28, 25, 70, 32, 9, 23, 11, 71, 19, 36, 63], [59, 23, 17, 32, 83, 74, 98, 47, 24, 52, 66], [44, 76, 67, 64, 13, 75, 61, 73, 2, 25, 99], [4, 18, 2, 36, 80, 46, 44, 44, 53, 6, 30], [31, 18, 70, 52, 94, 37, 40, 5, 74, 27, 56], [48, 9, 61, 20, 48, 38, 92, 57, 52, 6, 84], [20, 73, 14, 38, 40, 3, 99, 23, 77, 55, 71], [39, 17, 23, 43, 97, 62, 43, 11, 84, 83, 66], [1, 21, 21, 3, 12, 7, 61, 80, 30, 71, 78], [26, 18, 35, 36, 42, 91, 68, 30, 26, 24, 31], [93, 77, 33, 9, 48, 25, 39, 88, 41, 11, 49]], [[22, 32, 46, 75, 86, 59, 95, 39, 81, 2, 5], [54, 22, 86, 62, 75, 78, 64, 51, 51, 72, 12], [68, 52, 52, 71, 23, 49, 46, 85, 4, 75, 76], [57, 44, 76, 53, 24, 7, 74, 73, 78, 31, 38], [88, 46, 87, 1, 49, 8, 32, 0, 81, 91, 65], [53, 57, 13, 23, 92, 85, 78, 20, 33, 7, 12], [32, 32, 4, 17, 57, 84, 47, 6, 99, 0, 26], [29, 11, 91, 22, 3, 27, 17, 81, 29, 24, 88], [8, 7, 21, 51, 27, 40, 40, 10, 76, 8, 32], [95, 26, 59, 62, 38, 88, 10, 61, 77, 50, 13], [15, 52, 68, 4, 10, 79, 68, 27, 58, 89, 64]], [[48, 3, 22, 36, 66, 70, 5, 10, 97, 72, 96], [54, 75, 49, 71, 50, 27, 3, 26, 39, 33, 62], [22, 23, 74, 69, 47, 89, 5, 86, 26, 53, 63], [39, 93, 22, 35, 93, 26, 25, 77, 91, 6, 17], [73, 27, 12, 89, 40, 30, 95, 55, 42, 30, 6], [59, 48, 65, 26, 52, 53, 83, 11, 76, 19, 28], [69, 74, 37, 6, 21, 8, 15, 36, 42, 43, 74], [43, 18, 38, 85, 66, 27, 58, 84, 63, 86, 63], [12, 96, 93, 45, 80, 79, 35, 41, 19, 2, 96], [87, 76, 99, 46, 2, 14, 68, 9, 85, 22, 11], [59, 0, 55, 30, 51, 53, 61, 70, 99, 36, 54]], [[44, 88, 24, 59, 84, 63, 49, 9, 36, 76, 75], [24, 94, 2, 77, 0, 11, 56, 38, 50, 29, 28], [70, 97, 74, 87, 86, 19, 93, 3, 82, 42, 19], [38, 13, 79, 41, 56, 91, 44, 59, 28, 62, 40], [73, 0, 36, 26, 79, 77, 81, 97, 78, 83, 35], [25, 10, 22, 80, 71, 6, 1, 29, 3, 29, 72], [69, 58, 86, 68, 39, 36, 56, 85, 44, 73, 0], [94, 20, 21, 16, 16, 83, 91, 37, 48, 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41}, {'i': 11, 'j': 4, 'k': 11, 'cost': 90}, {'i': 11, 'j': 5, 'k': 1, 'cost': 47}, {'i': 11, 'j': 5, 'k': 2, 'cost': 38}, {'i': 11, 'j': 5, 'k': 3, 'cost': 27}, {'i': 11, 'j': 5, 'k': 4, 'cost': 5}, {'i': 11, 'j': 5, 'k': 5, 'cost': 36}, {'i': 11, 'j': 5, 'k': 6, 'cost': 31}, {'i': 11, 'j': 5, 'k': 7, 'cost': 49}, {'i': 11, 'j': 5, 'k': 8, 'cost': 58}, {'i': 11, 'j': 5, 'k': 9, 'cost': 55}, {'i': 11, 'j': 5, 'k': 10, 'cost': 37}, {'i': 11, 'j': 5, 'k': 11, 'cost': 30}, {'i': 11, 'j': 6, 'k': 1, 'cost': 22}, {'i': 11, 'j': 6, 'k': 2, 'cost': 4}, {'i': 11, 'j': 6, 'k': 3, 'cost': 95}, {'i': 11, 'j': 6, 'k': 4, 'cost': 32}, {'i': 11, 'j': 6, 'k': 5, 'cost': 52}, {'i': 11, 'j': 6, 'k': 6, 'cost': 25}, {'i': 11, 'j': 6, 'k': 7, 'cost': 24}, {'i': 11, 'j': 6, 'k': 8, 'cost': 57}, {'i': 11, 'j': 6, 'k': 9, 'cost': 63}, {'i': 11, 'j': 6, 'k': 10, 'cost': 37}, {'i': 11, 'j': 6, 'k': 11, 'cost': 63}, {'i': 11, 'j': 7, 'k': 1, 'cost': 25}, {'i': 11, 'j': 7, 'k': 2, 'cost': 74}, {'i': 11, 'j': 7, 'k': 3, 'cost': 59}, {'i': 11, 'j': 7, 'k': 4, 'cost': 78}, {'i': 11, 'j': 7, 'k': 5, 'cost': 85}, {'i': 11, 'j': 7, 'k': 6, 'cost': 57}, {'i': 11, 'j': 7, 'k': 7, 'cost': 15}, {'i': 11, 'j': 7, 'k': 8, 'cost': 91}, {'i': 11, 'j': 7, 'k': 9, 'cost': 59}, {'i': 11, 'j': 7, 'k': 10, 'cost': 64}, {'i': 11, 'j': 7, 'k': 11, 'cost': 20}, {'i': 11, 'j': 8, 'k': 1, 'cost': 31}, {'i': 11, 'j': 8, 'k': 2, 'cost': 29}, {'i': 11, 'j': 8, 'k': 3, 'cost': 93}, {'i': 11, 'j': 8, 'k': 4, 'cost': 43}, {'i': 11, 'j': 8, 'k': 5, 'cost': 57}, {'i': 11, 'j': 8, 'k': 6, 'cost': 67}, {'i': 11, 'j': 8, 'k': 7, 'cost': 15}, {'i': 11, 'j': 8, 'k': 8, 'cost': 81}, {'i': 11, 'j': 8, 'k': 9, 'cost': 34}, {'i': 11, 'j': 8, 'k': 10, 'cost': 15}, {'i': 11, 'j': 8, 'k': 11, 'cost': 52}, {'i': 11, 'j': 9, 'k': 1, 'cost': 99}, {'i': 11, 'j': 9, 'k': 2, 'cost': 86}, {'i': 11, 'j': 9, 'k': 3, 'cost': 54}, {'i': 11, 'j': 9, 'k': 4, 'cost': 86}, {'i': 11, 'j': 9, 'k': 5, 'cost': 96}, {'i': 11, 'j': 9, 'k': 6, 'cost': 47}, {'i': 11, 'j': 9, 'k': 7, 'cost': 54}, {'i': 11, 'j': 9, 'k': 8, 'cost': 33}, {'i': 11, 'j': 9, 'k': 9, 'cost': 27}, {'i': 11, 'j': 9, 'k': 10, 'cost': 98}, {'i': 11, 'j': 9, 'k': 11, 'cost': 80}, {'i': 11, 'j': 10, 'k': 1, 'cost': 4}, {'i': 11, 'j': 10, 'k': 2, 'cost': 70}, {'i': 11, 'j': 10, 'k': 3, 'cost': 65}, {'i': 11, 'j': 10, 'k': 4, 'cost': 70}, {'i': 11, 'j': 10, 'k': 5, 'cost': 27}, {'i': 11, 'j': 10, 'k': 6, 'cost': 40}, {'i': 11, 'j': 10, 'k': 7, 'cost': 44}, {'i': 11, 'j': 10, 'k': 8, 'cost': 88}, {'i': 11, 'j': 10, 'k': 9, 'cost': 10}, {'i': 11, 'j': 10, 'k': 10, 'cost': 1}, {'i': 11, 'j': 10, 'k': 11, 'cost': 13}, {'i': 11, 'j': 11, 'k': 1, 'cost': 55}, {'i': 11, 'j': 11, 'k': 2, 'cost': 99}, {'i': 11, 'j': 11, 'k': 3, 'cost': 59}, {'i': 11, 'j': 11, 'k': 4, 'cost': 50}, {'i': 11, 'j': 11, 'k': 5, 'cost': 70}, {'i': 11, 'j': 11, 'k': 6, 'cost': 10}, {'i': 11, 'j': 11, 'k': 7, 'cost': 67}, {'i': 11, 'j': 11, 'k': 8, 'cost': 20}, {'i': 11, 'j': 11, 'k': 9, 'cost': 28}, {'i': 11, 'j': 11, 'k': 10, 'cost': 58}, {'i': 11, 'j': 11, 'k': 11, 'cost': 90}]}","[[1, 2, 10], [2, 10, 6], [3, 8, 5], [4, 1, 9], [5, 9, 4], [6, 5, 8], [7, 11, 2], [8, 7, 11], [9, 6, 3], [10, 4, 1], [11, 3, 7]]",13,nl,1
+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.
+
+# num_tables=12
+# table_waiter_wine_identifiers=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
+
+# 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=1
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 56 | 70 | 17 | 22 | 6 | 19 | 21 | 78 | 74 | 41 | 32 |
+| 2 | 88 | 26 | 68 | 37 | 36 | 28 | 61 | 99 | 16 | 22 | 64 | 28 |
+| 3 | 91 | 24 | 82 | 71 | 35 | 44 | 48 | 43 | 80 | 17 | 95 | 71 |
+| 4 | 78 | 32 | 93 | 71 | 50 | 93 | 6 | 70 | 10 | 95 | 8 | 92 |
+| 5 | 25 | 64 | 29 | 65 | 95 | 14 | 57 | 13 | 0 | 57 | 12 | 50 |
+| 6 | 17 | 22 | 35 | 30 | 1 | 18 | 47 | 87 | 42 | 14 | 44 | 9 |
+| 7 | 77 | 30 | 72 | 63 | 12 | 68 | 76 | 55 | 94 | 14 | 31 | 52 |
+| 8 | 40 | 97 | 66 | 11 | 85 | 57 | 27 | 37 | 79 | 49 | 24 | 69 |
+| 9 | 3 | 39 | 28 | 69 | 15 | 50 | 47 | 88 | 58 | 89 | 54 | 62 |
+| 10 | 33 | 21 | 21 | 45 | 49 | 62 | 86 | 29 | 82 | 95 | 54 | 15 |
+| 11 | 65 | 40 | 22 | 3 | 51 | 25 | 85 | 78 | 51 | 46 | 0 | 63 |
+| 12 | 11 | 64 | 67 | 55 | 96 | 58 | 39 | 9 | 8 | 12 | 82 | 30 |
+
+## table_id=2
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 9 | 66 | 48 | 0 | 94 | 0 | 82 | 78 | 19 | 59 | 70 | 51 |
+| 2 | 31 | 57 | 46 | 13 | 90 | 67 | 78 | 35 | 95 | 55 | 10 | 78 |
+| 3 | 80 | 36 | 16 | 94 | 57 | 60 | 75 | 83 | 38 | 36 | 88 | 89 |
+| 4 | 20 | 86 | 34 | 90 | 91 | 97 | 46 | 58 | 99 | 52 | 66 | 85 |
+| 5 | 95 | 86 | 63 | 42 | 26 | 81 | 21 | 49 | 33 | 59 | 71 | 41 |
+| 6 | 51 | 64 | 6 | 21 | 34 | 67 | 11 | 30 | 69 | 93 | 73 | 74 |
+| 7 | 93 | 69 | 93 | 61 | 62 | 85 | 80 | 90 | 18 | 54 | 99 | 67 |
+| 8 | 23 | 78 | 90 | 43 | 38 | 18 | 16 | 89 | 38 | 80 | 22 | 33 |
+| 9 | 81 | 65 | 97 | 14 | 29 | 10 | 14 | 98 | 77 | 65 | 12 | 2 |
+| 10 | 52 | 73 | 78 | 58 | 62 | 33 | 75 | 3 | 45 | 63 | 67 | 56 |
+| 11 | 11 | 61 | 68 | 85 | 12 | 99 | 53 | 61 | 30 | 91 | 39 | 50 |
+| 12 | 30 | 41 | 22 | 27 | 3 | 30 | 12 | 55 | 1 | 6 | 4 | 54 |
+
+## table_id=3
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 90 | 87 | 10 | 83 | 74 | 62 | 17 | 98 | 90 | 89 | 50 | 77 |
+| 2 | 29 | 39 | 89 | 96 | 56 | 10 | 23 | 27 | 79 | 93 | 13 | 46 |
+| 3 | 84 | 60 | 70 | 43 | 84 | 68 | 55 | 28 | 10 | 52 | 14 | 56 |
+| 4 | 17 | 4 | 72 | 37 | 13 | 53 | 18 | 81 | 78 | 87 | 15 | 35 |
+| 5 | 17 | 39 | 70 | 61 | 79 | 47 | 43 | 19 | 65 | 57 | 63 | 53 |
+| 6 | 75 | 82 | 63 | 67 | 54 | 53 | 24 | 62 | 47 | 94 | 88 | 3 |
+| 7 | 18 | 49 | 47 | 48 | 35 | 54 | 7 | 5 | 28 | 83 | 31 | 82 |
+| 8 | 49 | 10 | 23 | 87 | 25 | 31 | 87 | 1 | 18 | 68 | 12 | 62 |
+| 9 | 49 | 39 | 10 | 20 | 45 | 84 | 50 | 60 | 0 | 50 | 68 | 32 |
+| 10 | 14 | 8 | 45 | 57 | 50 | 78 | 78 | 75 | 70 | 42 | 7 | 47 |
+| 11 | 73 | 74 | 53 | 78 | 18 | 59 | 24 | 56 | 71 | 13 | 7 | 81 |
+| 12 | 95 | 13 | 2 | 29 | 40 | 29 | 70 | 79 | 0 | 67 | 90 | 62 |
+
+## table_id=4
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 94 | 16 | 59 | 25 | 68 | 12 | 91 | 89 | 43 | 48 | 20 | 56 |
+| 2 | 43 | 18 | 30 | 6 | 66 | 59 | 65 | 72 | 19 | 72 | 2 | 98 |
+| 3 | 84 | 26 | 91 | 96 | 13 | 31 | 47 | 47 | 84 | 48 | 5 | 63 |
+| 4 | 18 | 37 | 81 | 55 | 29 | 40 | 1 | 92 | 41 | 28 | 76 | 13 |
+| 5 | 79 | 49 | 67 | 55 | 47 | 41 | 65 | 94 | 49 | 79 | 79 | 60 |
+| 6 | 61 | 75 | 12 | 62 | 27 | 75 | 74 | 78 | 21 | 28 | 94 | 40 |
+| 7 | 12 | 44 | 80 | 65 | 79 | 79 | 70 | 1 | 73 | 73 | 52 | 40 |
+| 8 | 39 | 27 | 47 | 89 | 96 | 17 | 19 | 39 | 13 | 88 | 73 | 47 |
+| 9 | 48 | 66 | 81 | 33 | 96 | 94 | 82 | 53 | 89 | 84 | 50 | 5 |
+| 10 | 29 | 83 | 92 | 58 | 87 | 10 | 69 | 78 | 29 | 40 | 30 | 44 |
+| 11 | 24 | 70 | 42 | 68 | 36 | 66 | 16 | 35 | 43 | 39 | 44 | 33 |
+| 12 | 39 | 25 | 91 | 99 | 55 | 40 | 55 | 87 | 28 | 47 | 73 | 18 |
+
+## table_id=5
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 19 | 50 | 78 | 42 | 38 | 81 | 20 | 2 | 7 | 94 | 75 | 44 |
+| 2 | 23 | 59 | 52 | 48 | 43 | 74 | 77 | 61 | 98 | 58 | 55 | 35 |
+| 3 | 21 | 47 | 25 | 37 | 85 | 65 | 82 | 25 | 75 | 18 | 70 | 43 |
+| 4 | 35 | 12 | 77 | 14 | 23 | 5 | 33 | 5 | 19 | 43 | 91 | 25 |
+| 5 | 97 | 17 | 95 | 90 | 93 | 58 | 87 | 39 | 86 | 16 | 13 | 73 |
+| 6 | 44 | 86 | 0 | 49 | 16 | 21 | 4 | 63 | 52 | 10 | 61 | 22 |
+| 7 | 98 | 62 | 2 | 67 | 62 | 62 | 7 | 83 | 37 | 29 | 31 | 89 |
+| 8 | 94 | 74 | 0 | 21 | 58 | 61 | 0 | 0 | 42 | 17 | 41 | 77 |
+| 9 | 47 | 56 | 94 | 72 | 56 | 1 | 84 | 30 | 69 | 12 | 71 | 91 |
+| 10 | 64 | 7 | 92 | 55 | 42 | 39 | 19 | 75 | 1 | 86 | 35 | 57 |
+| 11 | 27 | 79 | 14 | 20 | 95 | 55 | 55 | 94 | 41 | 60 | 38 | 66 |
+| 12 | 4 | 16 | 39 | 26 | 75 | 31 | 95 | 59 | 8 | 84 | 47 | 6 |
+
+## table_id=6
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 15 | 76 | 76 | 55 | 35 | 23 | 40 | 16 | 75 | 13 | 39 | 15 |
+| 2 | 52 | 1 | 78 | 72 | 66 | 49 | 14 | 41 | 47 | 28 | 55 | 22 |
+| 3 | 78 | 13 | 11 | 27 | 67 | 51 | 43 | 82 | 46 | 76 | 93 | 7 |
+| 4 | 14 | 30 | 49 | 82 | 44 | 37 | 75 | 43 | 3 | 36 | 10 | 65 |
+| 5 | 32 | 65 | 92 | 11 | 33 | 24 | 70 | 92 | 38 | 40 | 36 | 68 |
+| 6 | 57 | 6 | 21 | 58 | 2 | 27 | 81 | 70 | 95 | 99 | 36 | 97 |
+| 7 | 38 | 23 | 3 | 14 | 51 | 13 | 62 | 19 | 39 | 95 | 5 | 70 |
+| 8 | 85 | 25 | 11 | 50 | 70 | 17 | 92 | 11 | 5 | 67 | 41 | 46 |
+| 9 | 84 | 2 | 23 | 4 | 36 | 85 | 18 | 74 | 88 | 83 | 90 | 37 |
+| 10 | 45 | 32 | 97 | 90 | 20 | 97 | 8 | 56 | 90 | 42 | 13 | 18 |
+| 11 | 20 | 3 | 79 | 49 | 88 | 25 | 98 | 83 | 36 | 29 | 96 | 91 |
+| 12 | 10 | 43 | 50 | 47 | 91 | 8 | 53 | 4 | 70 | 4 | 11 | 22 |
+
+## table_id=7
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 51 | 60 | 55 | 79 | 58 | 48 | 74 | 31 | 52 | 34 | 16 | 49 |
+| 2 | 36 | 28 | 99 | 24 | 54 | 58 | 41 | 35 | 89 | 0 | 10 | 82 |
+| 3 | 85 | 55 | 37 | 6 | 45 | 60 | 91 | 37 | 52 | 1 | 13 | 80 |
+| 4 | 75 | 39 | 44 | 36 | 0 | 85 | 75 | 98 | 32 | 9 | 75 | 91 |
+| 5 | 36 | 64 | 34 | 55 | 31 | 26 | 97 | 97 | 3 | 41 | 8 | 30 |
+| 6 | 81 | 86 | 42 | 14 | 69 | 67 | 98 | 94 | 56 | 32 | 28 | 67 |
+| 7 | 30 | 66 | 20 | 19 | 94 | 70 | 89 | 1 | 91 | 52 | 36 | 24 |
+| 8 | 1 | 41 | 39 | 74 | 46 | 15 | 45 | 29 | 96 | 14 | 67 | 8 |
+| 9 | 77 | 42 | 11 | 14 | 72 | 74 | 17 | 4 | 72 | 44 | 54 | 2 |
+| 10 | 94 | 53 | 68 | 53 | 55 | 82 | 7 | 48 | 66 | 91 | 36 | 53 |
+| 11 | 96 | 18 | 4 | 49 | 72 | 24 | 60 | 72 | 46 | 33 | 99 | 1 |
+| 12 | 45 | 79 | 34 | 0 | 91 | 19 | 29 | 34 | 11 | 60 | 46 | 15 |
+
+## table_id=8
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 85 | 73 | 59 | 95 | 60 | 26 | 2 | 90 | 11 | 58 | 35 | 97 |
+| 2 | 2 | 13 | 49 | 21 | 71 | 88 | 46 | 92 | 39 | 77 | 60 | 87 |
+| 3 | 62 | 24 | 79 | 51 | 34 | 90 | 72 | 35 | 3 | 89 | 97 | 88 |
+| 4 | 55 | 51 | 35 | 39 | 31 | 72 | 64 | 12 | 33 | 6 | 48 | 36 |
+| 5 | 73 | 49 | 42 | 21 | 88 | 49 | 10 | 93 | 4 | 27 | 23 | 62 |
+| 6 | 93 | 53 | 98 | 4 | 65 | 62 | 5 | 49 | 0 | 15 | 8 | 68 |
+| 7 | 45 | 3 | 77 | 98 | 63 | 58 | 92 | 96 | 27 | 68 | 26 | 29 |
+| 8 | 66 | 28 | 95 | 81 | 46 | 46 | 84 | 41 | 93 | 74 | 66 | 55 |
+| 9 | 97 | 84 | 93 | 69 | 75 | 9 | 91 | 38 | 93 | 75 | 12 | 46 |
+| 10 | 69 | 6 | 73 | 27 | 87 | 9 | 42 | 53 | 5 | 87 | 42 | 23 |
+| 11 | 41 | 76 | 68 | 35 | 46 | 91 | 69 | 10 | 66 | 2 | 94 | 22 |
+| 12 | 11 | 54 | 81 | 86 | 42 | 49 | 72 | 50 | 73 | 71 | 31 | 30 |
+
+## table_id=9
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 29 | 60 | 88 | 48 | 81 | 60 | 90 | 82 | 72 | 17 | 17 | 39 |
+| 2 | 70 | 78 | 84 | 59 | 47 | 70 | 78 | 53 | 71 | 59 | 3 | 12 |
+| 3 | 11 | 65 | 39 | 94 | 58 | 78 | 52 | 52 | 12 | 51 | 85 | 5 |
+| 4 | 37 | 73 | 66 | 44 | 82 | 74 | 5 | 39 | 40 | 26 | 54 | 99 |
+| 5 | 2 | 9 | 84 | 39 | 15 | 80 | 76 | 19 | 1 | 26 | 87 | 36 |
+| 6 | 89 | 6 | 49 | 46 | 18 | 17 | 96 | 83 | 93 | 93 | 31 | 99 |
+| 7 | 90 | 80 | 26 | 71 | 62 | 88 | 25 | 38 | 24 | 49 | 5 | 60 |
+| 8 | 81 | 11 | 37 | 79 | 79 | 73 | 77 | 86 | 16 | 90 | 53 | 33 |
+| 9 | 52 | 5 | 22 | 61 | 81 | 25 | 89 | 19 | 47 | 98 | 39 | 38 |
+| 10 | 51 | 76 | 86 | 57 | 79 | 69 | 42 | 65 | 50 | 79 | 9 | 95 |
+| 11 | 74 | 64 | 19 | 95 | 54 | 26 | 80 | 89 | 54 | 63 | 75 | 60 |
+| 12 | 84 | 76 | 42 | 89 | 41 | 95 | 75 | 42 | 79 | 88 | 86 | 64 |
+
+## table_id=10
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 54 | 4 | 99 | 33 | 88 | 15 | 63 | 97 | 23 | 43 | 48 | 37 |
+| 2 | 95 | 61 | 67 | 16 | 6 | 52 | 68 | 89 | 27 | 8 | 31 | 99 |
+| 3 | 52 | 31 | 93 | 76 | 53 | 32 | 74 | 21 | 35 | 11 | 79 | 34 |
+| 4 | 19 | 14 | 21 | 69 | 45 | 81 | 51 | 93 | 66 | 23 | 5 | 67 |
+| 5 | 3 | 9 | 50 | 11 | 60 | 93 | 54 | 72 | 60 | 27 | 14 | 19 |
+| 6 | 91 | 76 | 0 | 86 | 46 | 50 | 47 | 36 | 70 | 48 | 30 | 73 |
+| 7 | 31 | 99 | 95 | 29 | 78 | 24 | 83 | 9 | 86 | 69 | 24 | 72 |
+| 8 | 97 | 49 | 95 | 38 | 89 | 36 | 24 | 29 | 28 | 71 | 87 | 77 |
+| 9 | 73 | 22 | 37 | 40 | 87 | 48 | 17 | 90 | 52 | 51 | 3 | 94 |
+| 10 | 49 | 33 | 50 | 75 | 88 | 65 | 19 | 11 | 75 | 35 | 10 | 65 |
+| 11 | 88 | 9 | 7 | 44 | 8 | 15 | 12 | 18 | 38 | 16 | 21 | 93 |
+| 12 | 37 | 26 | 73 | 4 | 54 | 24 | 63 | 98 | 14 | 42 | 97 | 76 |
+
+## table_id=11
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 84 | 38 | 0 | 96 | 99 | 9 | 97 | 72 | 99 | 16 | 62 | 0 |
+| 2 | 81 | 52 | 11 | 18 | 22 | 33 | 97 | 19 | 99 | 37 | 85 | 41 |
+| 3 | 49 | 24 | 65 | 83 | 5 | 15 | 33 | 24 | 77 | 44 | 34 | 29 |
+| 4 | 50 | 32 | 30 | 86 | 63 | 37 | 0 | 37 | 71 | 4 | 59 | 76 |
+| 5 | 4 | 64 | 76 | 88 | 23 | 10 | 50 | 95 | 99 | 65 | 72 | 28 |
+| 6 | 72 | 48 | 9 | 18 | 18 | 28 | 84 | 96 | 19 | 11 | 91 | 49 |
+| 7 | 85 | 12 | 57 | 10 | 46 | 74 | 8 | 42 | 69 | 54 | 90 | 69 |
+| 8 | 10 | 50 | 51 | 79 | 68 | 28 | 76 | 85 | 40 | 70 | 78 | 74 |
+| 9 | 37 | 98 | 26 | 8 | 44 | 49 | 31 | 47 | 78 | 21 | 19 | 82 |
+| 10 | 24 | 98 | 59 | 64 | 17 | 52 | 36 | 65 | 4 | 74 | 67 | 84 |
+| 11 | 24 | 87 | 33 | 46 | 68 | 95 | 34 | 54 | 1 | 10 | 61 | 52 |
+| 12 | 95 | 39 | 81 | 77 | 0 | 54 | 12 | 59 | 17 | 15 | 97 | 78 |
+
+## table_id=12
+| waiter_id\wine_pairing_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 92 | 46 | 45 | 31 | 82 | 9 | 16 | 98 | 88 | 69 | 45 | 90 |
+| 2 | 81 | 92 | 79 | 41 | 19 | 61 | 99 | 14 | 32 | 8 | 55 | 80 |
+| 3 | 22 | 95 | 33 | 56 | 52 | 37 | 73 | 94 | 93 | 75 | 54 | 96 |
+| 4 | 28 | 36 | 75 | 14 | 29 | 32 | 5 | 85 | 67 | 26 | 27 | 12 |
+| 5 | 87 | 38 | 52 | 72 | 51 | 5 | 21 | 84 | 86 | 28 | 76 | 30 |
+| 6 | 56 | 54 | 83 | 88 | 51 | 67 | 83 | 3 | 75 | 62 | 48 | 40 |
+| 7 | 19 | 22 | 39 | 3 | 54 | 0 | 96 | 19 | 77 | 79 | 54 | 5 |
+| 8 | 69 | 73 | 38 | 71 | 59 | 91 | 32 | 15 | 14 | 95 | 85 | 60 |
+| 9 | 75 | 49 | 27 | 17 | 50 | 53 | 40 | 35 | 40 | 46 | 53 | 19 |
+| 10 | 88 | 42 | 59 | 57 | 24 | 35 | 8 | 55 | 10 | 64 | 53 | 48 |
+| 11 | 74 | 28 | 48 | 13 | 47 | 50 | 66 | 4 | 72 | 46 | 74 | 16 |
+| 12 | 29 | 98 | 22 | 3 | 46 | 51 | 48 | 11 | 73 | 36 | 72 | 31 |
+
+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': [[[34, 56, 70, 17, 22, 6, 19, 21, 78, 74, 41, 32], [88, 26, 68, 37, 36, 28, 61, 99, 16, 22, 64, 28], [91, 24, 82, 71, 35, 44, 48, 43, 80, 17, 95, 71], [78, 32, 93, 71, 50, 93, 6, 70, 10, 95, 8, 92], [25, 64, 29, 65, 95, 14, 57, 13, 0, 57, 12, 50], [17, 22, 35, 30, 1, 18, 47, 87, 42, 14, 44, 9], [77, 30, 72, 63, 12, 68, 76, 55, 94, 14, 31, 52], [40, 97, 66, 11, 85, 57, 27, 37, 79, 49, 24, 69], [3, 39, 28, 69, 15, 50, 47, 88, 58, 89, 54, 62], [33, 21, 21, 45, 49, 62, 86, 29, 82, 95, 54, 15], [65, 40, 22, 3, 51, 25, 85, 78, 51, 46, 0, 63], [11, 64, 67, 55, 96, 58, 39, 9, 8, 12, 82, 30]], [[9, 66, 48, 0, 94, 0, 82, 78, 19, 59, 70, 51], [31, 57, 46, 13, 90, 67, 78, 35, 95, 55, 10, 78], [80, 36, 16, 94, 57, 60, 75, 83, 38, 36, 88, 89], [20, 86, 34, 90, 91, 97, 46, 58, 99, 52, 66, 85], [95, 86, 63, 42, 26, 81, 21, 49, 33, 59, 71, 41], [51, 64, 6, 21, 34, 67, 11, 30, 69, 93, 73, 74], [93, 69, 93, 61, 62, 85, 80, 90, 18, 54, 99, 67], [23, 78, 90, 43, 38, 18, 16, 89, 38, 80, 22, 33], [81, 65, 97, 14, 29, 10, 14, 98, 77, 65, 12, 2], [52, 73, 78, 58, 62, 33, 75, 3, 45, 63, 67, 56], [11, 61, 68, 85, 12, 99, 53, 61, 30, 91, 39, 50], [30, 41, 22, 27, 3, 30, 12, 55, 1, 6, 4, 54]], [[90, 87, 10, 83, 74, 62, 17, 98, 90, 89, 50, 77], [29, 39, 89, 96, 56, 10, 23, 27, 79, 93, 13, 46], [84, 60, 70, 43, 84, 68, 55, 28, 10, 52, 14, 56], [17, 4, 72, 37, 13, 53, 18, 81, 78, 87, 15, 35], [17, 39, 70, 61, 79, 47, 43, 19, 65, 57, 63, 53], [75, 82, 63, 67, 54, 53, 24, 62, 47, 94, 88, 3], [18, 49, 47, 48, 35, 54, 7, 5, 28, 83, 31, 82], [49, 10, 23, 87, 25, 31, 87, 1, 18, 68, 12, 62], [49, 39, 10, 20, 45, 84, 50, 60, 0, 50, 68, 32], [14, 8, 45, 57, 50, 78, 78, 75, 70, 42, 7, 47], [73, 74, 53, 78, 18, 59, 24, 56, 71, 13, 7, 81], [95, 13, 2, 29, 40, 29, 70, 79, 0, 67, 90, 62]], [[94, 16, 59, 25, 68, 12, 91, 89, 43, 48, 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'cost': 64}, {'i': 11, 'j': 5, 'k': 3, 'cost': 76}, {'i': 11, 'j': 5, 'k': 4, 'cost': 88}, {'i': 11, 'j': 5, 'k': 5, 'cost': 23}, {'i': 11, 'j': 5, 'k': 6, 'cost': 10}, {'i': 11, 'j': 5, 'k': 7, 'cost': 50}, {'i': 11, 'j': 5, 'k': 8, 'cost': 95}, {'i': 11, 'j': 5, 'k': 9, 'cost': 99}, {'i': 11, 'j': 5, 'k': 10, 'cost': 65}, {'i': 11, 'j': 5, 'k': 11, 'cost': 72}, {'i': 11, 'j': 5, 'k': 12, 'cost': 28}, {'i': 11, 'j': 6, 'k': 1, 'cost': 72}, {'i': 11, 'j': 6, 'k': 2, 'cost': 48}, {'i': 11, 'j': 6, 'k': 3, 'cost': 9}, {'i': 11, 'j': 6, 'k': 4, 'cost': 18}, {'i': 11, 'j': 6, 'k': 5, 'cost': 18}, {'i': 11, 'j': 6, 'k': 6, 'cost': 28}, {'i': 11, 'j': 6, 'k': 7, 'cost': 84}, {'i': 11, 'j': 6, 'k': 8, 'cost': 96}, {'i': 11, 'j': 6, 'k': 9, 'cost': 19}, {'i': 11, 'j': 6, 'k': 10, 'cost': 11}, {'i': 11, 'j': 6, 'k': 11, 'cost': 91}, {'i': 11, 'j': 6, 'k': 12, 'cost': 49}, {'i': 11, 'j': 7, 'k': 1, 'cost': 85}, {'i': 11, 'j': 7, 'k': 2, 'cost': 12}, {'i': 11, 'j': 7, 'k': 3, 'cost': 57}, {'i': 11, 'j': 7, 'k': 4, 'cost': 10}, {'i': 11, 'j': 7, 'k': 5, 'cost': 46}, {'i': 11, 'j': 7, 'k': 6, 'cost': 74}, {'i': 11, 'j': 7, 'k': 7, 'cost': 8}, {'i': 11, 'j': 7, 'k': 8, 'cost': 42}, {'i': 11, 'j': 7, 'k': 9, 'cost': 69}, {'i': 11, 'j': 7, 'k': 10, 'cost': 54}, {'i': 11, 'j': 7, 'k': 11, 'cost': 90}, {'i': 11, 'j': 7, 'k': 12, 'cost': 69}, {'i': 11, 'j': 8, 'k': 1, 'cost': 10}, {'i': 11, 'j': 8, 'k': 2, 'cost': 50}, {'i': 11, 'j': 8, 'k': 3, 'cost': 51}, {'i': 11, 'j': 8, 'k': 4, 'cost': 79}, {'i': 11, 'j': 8, 'k': 5, 'cost': 68}, {'i': 11, 'j': 8, 'k': 6, 'cost': 28}, {'i': 11, 'j': 8, 'k': 7, 'cost': 76}, {'i': 11, 'j': 8, 'k': 8, 'cost': 85}, {'i': 11, 'j': 8, 'k': 9, 'cost': 40}, {'i': 11, 'j': 8, 'k': 10, 'cost': 70}, {'i': 11, 'j': 8, 'k': 11, 'cost': 78}, {'i': 11, 'j': 8, 'k': 12, 'cost': 74}, {'i': 11, 'j': 9, 'k': 1, 'cost': 37}, {'i': 11, 'j': 9, 'k': 2, 'cost': 98}, {'i': 11, 'j': 9, 'k': 3, 'cost': 26}, {'i': 11, 'j': 9, 'k': 4, 'cost': 8}, {'i': 11, 'j': 9, 'k': 5, 'cost': 44}, {'i': 11, 'j': 9, 'k': 6, 'cost': 49}, {'i': 11, 'j': 9, 'k': 7, 'cost': 31}, {'i': 11, 'j': 9, 'k': 8, 'cost': 47}, {'i': 11, 'j': 9, 'k': 9, 'cost': 78}, {'i': 11, 'j': 9, 'k': 10, 'cost': 21}, {'i': 11, 'j': 9, 'k': 11, 'cost': 19}, {'i': 11, 'j': 9, 'k': 12, 'cost': 82}, {'i': 11, 'j': 10, 'k': 1, 'cost': 24}, {'i': 11, 'j': 10, 'k': 2, 'cost': 98}, {'i': 11, 'j': 10, 'k': 3, 'cost': 59}, {'i': 11, 'j': 10, 'k': 4, 'cost': 64}, {'i': 11, 'j': 10, 'k': 5, 'cost': 17}, {'i': 11, 'j': 10, 'k': 6, 'cost': 52}, {'i': 11, 'j': 10, 'k': 7, 'cost': 36}, {'i': 11, 'j': 10, 'k': 8, 'cost': 65}, {'i': 11, 'j': 10, 'k': 9, 'cost': 4}, {'i': 11, 'j': 10, 'k': 10, 'cost': 74}, {'i': 11, 'j': 10, 'k': 11, 'cost': 67}, {'i': 11, 'j': 10, 'k': 12, 'cost': 84}, {'i': 11, 'j': 11, 'k': 1, 'cost': 24}, {'i': 11, 'j': 11, 'k': 2, 'cost': 87}, {'i': 11, 'j': 11, 'k': 3, 'cost': 33}, {'i': 11, 'j': 11, 'k': 4, 'cost': 46}, {'i': 11, 'j': 11, 'k': 5, 'cost': 68}, {'i': 11, 'j': 11, 'k': 6, 'cost': 95}, {'i': 11, 'j': 11, 'k': 7, 'cost': 34}, {'i': 11, 'j': 11, 'k': 8, 'cost': 54}, {'i': 11, 'j': 11, 'k': 9, 'cost': 1}, {'i': 11, 'j': 11, 'k': 10, 'cost': 10}, {'i': 11, 'j': 11, 'k': 11, 'cost': 61}, {'i': 11, 'j': 11, 'k': 12, 'cost': 52}, {'i': 11, 'j': 12, 'k': 1, 'cost': 95}, {'i': 11, 'j': 12, 'k': 2, 'cost': 39}, {'i': 11, 'j': 12, 'k': 3, 'cost': 81}, {'i': 11, 'j': 12, 'k': 4, 'cost': 77}, {'i': 11, 'j': 12, 'k': 5, 'cost': 0}, {'i': 11, 'j': 12, 'k': 6, 'cost': 54}, {'i': 11, 'j': 12, 'k': 7, 'cost': 12}, {'i': 11, 'j': 12, 'k': 8, 'cost': 59}, {'i': 11, 'j': 12, 'k': 9, 'cost': 17}, {'i': 11, 'j': 12, 'k': 10, 'cost': 15}, {'i': 11, 'j': 12, 'k': 11, 'cost': 97}, {'i': 11, 'j': 12, 'k': 12, 'cost': 78}, {'i': 12, 'j': 1, 'k': 1, 'cost': 92}, {'i': 12, 'j': 1, 'k': 2, 'cost': 46}, {'i': 12, 'j': 1, 'k': 3, 'cost': 45}, {'i': 12, 'j': 1, 'k': 4, 'cost': 31}, {'i': 12, 'j': 1, 'k': 5, 'cost': 82}, {'i': 12, 'j': 1, 'k': 6, 'cost': 9}, {'i': 12, 'j': 1, 'k': 7, 'cost': 16}, {'i': 12, 'j': 1, 'k': 8, 'cost': 98}, {'i': 12, 'j': 1, 'k': 9, 'cost': 88}, {'i': 12, 'j': 1, 'k': 10, 'cost': 69}, {'i': 12, 'j': 1, 'k': 11, 'cost': 45}, {'i': 12, 'j': 1, 'k': 12, 'cost': 90}, {'i': 12, 'j': 2, 'k': 1, 'cost': 81}, {'i': 12, 'j': 2, 'k': 2, 'cost': 92}, {'i': 12, 'j': 2, 'k': 3, 'cost': 79}, {'i': 12, 'j': 2, 'k': 4, 'cost': 41}, {'i': 12, 'j': 2, 'k': 5, 'cost': 19}, {'i': 12, 'j': 2, 'k': 6, 'cost': 61}, {'i': 12, 'j': 2, 'k': 7, 'cost': 99}, {'i': 12, 'j': 2, 'k': 8, 'cost': 14}, {'i': 12, 'j': 2, 'k': 9, 'cost': 32}, {'i': 12, 'j': 2, 'k': 10, 'cost': 8}, {'i': 12, 'j': 2, 'k': 11, 'cost': 55}, {'i': 12, 'j': 2, 'k': 12, 'cost': 80}, {'i': 12, 'j': 3, 'k': 1, 'cost': 22}, {'i': 12, 'j': 3, 'k': 2, 'cost': 95}, {'i': 12, 'j': 3, 'k': 3, 'cost': 33}, {'i': 12, 'j': 3, 'k': 4, 'cost': 56}, {'i': 12, 'j': 3, 'k': 5, 'cost': 52}, {'i': 12, 'j': 3, 'k': 6, 'cost': 37}, {'i': 12, 'j': 3, 'k': 7, 'cost': 73}, {'i': 12, 'j': 3, 'k': 8, 'cost': 94}, {'i': 12, 'j': 3, 'k': 9, 'cost': 93}, {'i': 12, 'j': 3, 'k': 10, 'cost': 75}, {'i': 12, 'j': 3, 'k': 11, 'cost': 54}, {'i': 12, 'j': 3, 'k': 12, 'cost': 96}, {'i': 12, 'j': 4, 'k': 1, 'cost': 28}, {'i': 12, 'j': 4, 'k': 2, 'cost': 36}, {'i': 12, 'j': 4, 'k': 3, 'cost': 75}, {'i': 12, 'j': 4, 'k': 4, 'cost': 14}, {'i': 12, 'j': 4, 'k': 5, 'cost': 29}, {'i': 12, 'j': 4, 'k': 6, 'cost': 32}, {'i': 12, 'j': 4, 'k': 7, 'cost': 5}, {'i': 12, 'j': 4, 'k': 8, 'cost': 85}, {'i': 12, 'j': 4, 'k': 9, 'cost': 67}, {'i': 12, 'j': 4, 'k': 10, 'cost': 26}, {'i': 12, 'j': 4, 'k': 11, 'cost': 27}, {'i': 12, 'j': 4, 'k': 12, 'cost': 12}, {'i': 12, 'j': 5, 'k': 1, 'cost': 87}, {'i': 12, 'j': 5, 'k': 2, 'cost': 38}, {'i': 12, 'j': 5, 'k': 3, 'cost': 52}, {'i': 12, 'j': 5, 'k': 4, 'cost': 72}, {'i': 12, 'j': 5, 'k': 5, 'cost': 51}, {'i': 12, 'j': 5, 'k': 6, 'cost': 5}, {'i': 12, 'j': 5, 'k': 7, 'cost': 21}, {'i': 12, 'j': 5, 'k': 8, 'cost': 84}, {'i': 12, 'j': 5, 'k': 9, 'cost': 86}, {'i': 12, 'j': 5, 'k': 10, 'cost': 28}, {'i': 12, 'j': 5, 'k': 11, 'cost': 76}, {'i': 12, 'j': 5, 'k': 12, 'cost': 30}, {'i': 12, 'j': 6, 'k': 1, 'cost': 56}, {'i': 12, 'j': 6, 'k': 2, 'cost': 54}, {'i': 12, 'j': 6, 'k': 3, 'cost': 83}, {'i': 12, 'j': 6, 'k': 4, 'cost': 88}, {'i': 12, 'j': 6, 'k': 5, 'cost': 51}, {'i': 12, 'j': 6, 'k': 6, 'cost': 67}, {'i': 12, 'j': 6, 'k': 7, 'cost': 83}, {'i': 12, 'j': 6, 'k': 8, 'cost': 3}, {'i': 12, 'j': 6, 'k': 9, 'cost': 75}, {'i': 12, 'j': 6, 'k': 10, 'cost': 62}, {'i': 12, 'j': 6, 'k': 11, 'cost': 48}, {'i': 12, 'j': 6, 'k': 12, 'cost': 40}, {'i': 12, 'j': 7, 'k': 1, 'cost': 19}, {'i': 12, 'j': 7, 'k': 2, 'cost': 22}, {'i': 12, 'j': 7, 'k': 3, 'cost': 39}, {'i': 12, 'j': 7, 'k': 4, 'cost': 3}, {'i': 12, 'j': 7, 'k': 5, 'cost': 54}, {'i': 12, 'j': 7, 'k': 6, 'cost': 0}, {'i': 12, 'j': 7, 'k': 7, 'cost': 96}, {'i': 12, 'j': 7, 'k': 8, 'cost': 19}, {'i': 12, 'j': 7, 'k': 9, 'cost': 77}, {'i': 12, 'j': 7, 'k': 10, 'cost': 79}, {'i': 12, 'j': 7, 'k': 11, 'cost': 54}, {'i': 12, 'j': 7, 'k': 12, 'cost': 5}, {'i': 12, 'j': 8, 'k': 1, 'cost': 69}, {'i': 12, 'j': 8, 'k': 2, 'cost': 73}, {'i': 12, 'j': 8, 'k': 3, 'cost': 38}, {'i': 12, 'j': 8, 'k': 4, 'cost': 71}, {'i': 12, 'j': 8, 'k': 5, 'cost': 59}, {'i': 12, 'j': 8, 'k': 6, 'cost': 91}, {'i': 12, 'j': 8, 'k': 7, 'cost': 32}, {'i': 12, 'j': 8, 'k': 8, 'cost': 15}, {'i': 12, 'j': 8, 'k': 9, 'cost': 14}, {'i': 12, 'j': 8, 'k': 10, 'cost': 95}, {'i': 12, 'j': 8, 'k': 11, 'cost': 85}, {'i': 12, 'j': 8, 'k': 12, 'cost': 60}, {'i': 12, 'j': 9, 'k': 1, 'cost': 75}, {'i': 12, 'j': 9, 'k': 2, 'cost': 49}, {'i': 12, 'j': 9, 'k': 3, 'cost': 27}, {'i': 12, 'j': 9, 'k': 4, 'cost': 17}, {'i': 12, 'j': 9, 'k': 5, 'cost': 50}, {'i': 12, 'j': 9, 'k': 6, 'cost': 53}, {'i': 12, 'j': 9, 'k': 7, 'cost': 40}, {'i': 12, 'j': 9, 'k': 8, 'cost': 35}, {'i': 12, 'j': 9, 'k': 9, 'cost': 40}, {'i': 12, 'j': 9, 'k': 10, 'cost': 46}, {'i': 12, 'j': 9, 'k': 11, 'cost': 53}, {'i': 12, 'j': 9, 'k': 12, 'cost': 19}, {'i': 12, 'j': 10, 'k': 1, 'cost': 88}, {'i': 12, 'j': 10, 'k': 2, 'cost': 42}, {'i': 12, 'j': 10, 'k': 3, 'cost': 59}, {'i': 12, 'j': 10, 'k': 4, 'cost': 57}, {'i': 12, 'j': 10, 'k': 5, 'cost': 24}, {'i': 12, 'j': 10, 'k': 6, 'cost': 35}, {'i': 12, 'j': 10, 'k': 7, 'cost': 8}, {'i': 12, 'j': 10, 'k': 8, 'cost': 55}, {'i': 12, 'j': 10, 'k': 9, 'cost': 10}, {'i': 12, 'j': 10, 'k': 10, 'cost': 64}, {'i': 12, 'j': 10, 'k': 11, 'cost': 53}, {'i': 12, 'j': 10, 'k': 12, 'cost': 48}, {'i': 12, 'j': 11, 'k': 1, 'cost': 74}, {'i': 12, 'j': 11, 'k': 2, 'cost': 28}, {'i': 12, 'j': 11, 'k': 3, 'cost': 48}, {'i': 12, 'j': 11, 'k': 4, 'cost': 13}, {'i': 12, 'j': 11, 'k': 5, 'cost': 47}, {'i': 12, 'j': 11, 'k': 6, 'cost': 50}, {'i': 12, 'j': 11, 'k': 7, 'cost': 66}, {'i': 12, 'j': 11, 'k': 8, 'cost': 4}, {'i': 12, 'j': 11, 'k': 9, 'cost': 72}, {'i': 12, 'j': 11, 'k': 10, 'cost': 46}, {'i': 12, 'j': 11, 'k': 11, 'cost': 74}, {'i': 12, 'j': 11, 'k': 12, 'cost': 16}, {'i': 12, 'j': 12, 'k': 1, 'cost': 29}, {'i': 12, 'j': 12, 'k': 2, 'cost': 98}, {'i': 12, 'j': 12, 'k': 3, 'cost': 22}, {'i': 12, 'j': 12, 'k': 4, 'cost': 3}, {'i': 12, 'j': 12, 'k': 5, 'cost': 46}, {'i': 12, 'j': 12, 'k': 6, 'cost': 51}, {'i': 12, 'j': 12, 'k': 7, 'cost': 48}, {'i': 12, 'j': 12, 'k': 8, 'cost': 11}, {'i': 12, 'j': 12, 'k': 9, 'cost': 73}, {'i': 12, 'j': 12, 'k': 10, 'cost': 36}, {'i': 12, 'j': 12, 'k': 11, 'cost': 72}, {'i': 12, 'j': 12, 'k': 12, 'cost': 31}]}","[[1, 11, 11], [2, 1, 4], [3, 9, 9], [4, 4, 7], [5, 8, 8], [6, 3, 12], [7, 2, 10], [8, 10, 2], [9, 5, 1], [10, 6, 3], [11, 12, 5], [12, 7, 6]]",14,csv,1
+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=12
+# course_ids=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
+
+# 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=0
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 89 | 99 | 9 | 90 | 88 | 16 | 12 | 79 | 1 | 40 | 75 | 85 |
+| 1 | 77 | 41 | 5 | 80 | 36 | 97 | 6 | 49 | 24 | 3 | 7 | 21 |
+| 2 | 68 | 76 | 22 | 2 | 63 | 58 | 52 | 12 | 26 | 0 | 41 | 62 |
+| 3 | 48 | 54 | 94 | 80 | 85 | 30 | 62 | 27 | 10 | 51 | 11 | 97 |
+| 4 | 84 | 80 | 82 | 51 | 46 | 24 | 42 | 92 | 91 | 16 | 56 | 99 |
+| 5 | 48 | 58 | 62 | 58 | 98 | 43 | 90 | 94 | 71 | 28 | 99 | 40 |
+| 6 | 56 | 79 | 77 | 54 | 40 | 67 | 83 | 13 | 51 | 19 | 63 | 8 |
+| 7 | 86 | 24 | 33 | 47 | 13 | 81 | 54 | 11 | 30 | 4 | 87 | 61 |
+| 8 | 63 | 49 | 65 | 37 | 96 | 3 | 63 | 60 | 1 | 89 | 1 | 63 |
+| 9 | 70 | 22 | 63 | 68 | 25 | 71 | 74 | 42 | 89 | 76 | 6 | 38 |
+| 10 | 99 | 61 | 63 | 61 | 67 | 88 | 11 | 58 | 40 | 11 | 9 | 87 |
+| 11 | 70 | 64 | 6 | 40 | 65 | 35 | 47 | 2 | 13 | 70 | 80 | 98 |
+
+## course_id=1
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 56 | 66 | 76 | 24 | 5 | 80 | 74 | 13 | 74 | 14 | 65 | 18 |
+| 1 | 28 | 25 | 5 | 86 | 8 | 95 | 0 | 87 | 51 | 20 | 30 | 77 |
+| 2 | 55 | 60 | 65 | 62 | 92 | 87 | 46 | 37 | 51 | 5 | 64 | 71 |
+| 3 | 99 | 53 | 33 | 17 | 25 | 72 | 76 | 98 | 88 | 52 | 24 | 74 |
+| 4 | 2 | 37 | 50 | 28 | 6 | 2 | 24 | 64 | 34 | 82 | 38 | 84 |
+| 5 | 36 | 71 | 59 | 14 | 76 | 58 | 68 | 47 | 40 | 37 | 63 | 90 |
+| 6 | 96 | 37 | 47 | 64 | 34 | 29 | 7 | 52 | 22 | 45 | 5 | 47 |
+| 7 | 10 | 60 | 62 | 90 | 28 | 90 | 84 | 53 | 89 | 42 | 99 | 55 |
+| 8 | 59 | 73 | 52 | 62 | 9 | 94 | 29 | 72 | 90 | 85 | 62 | 27 |
+| 9 | 61 | 36 | 78 | 44 | 21 | 1 | 47 | 28 | 49 | 69 | 0 | 43 |
+| 10 | 19 | 46 | 55 | 4 | 98 | 42 | 33 | 85 | 85 | 63 | 13 | 74 |
+| 11 | 97 | 10 | 81 | 98 | 70 | 62 | 40 | 42 | 75 | 76 | 44 | 73 |
+
+## course_id=2
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 16 | 55 | 91 | 3 | 17 | 24 | 80 | 6 | 50 | 81 | 36 | 17 |
+| 1 | 26 | 34 | 10 | 23 | 0 | 19 | 83 | 87 | 4 | 90 | 52 | 99 |
+| 2 | 59 | 88 | 36 | 15 | 89 | 74 | 97 | 57 | 82 | 33 | 87 | 49 |
+| 3 | 20 | 44 | 28 | 60 | 24 | 0 | 49 | 18 | 40 | 5 | 66 | 88 |
+| 4 | 8 | 99 | 31 | 53 | 37 | 65 | 60 | 6 | 39 | 52 | 37 | 94 |
+| 5 | 28 | 75 | 15 | 12 | 54 | 30 | 18 | 91 | 70 | 66 | 53 | 82 |
+| 6 | 2 | 81 | 50 | 82 | 18 | 61 | 17 | 93 | 72 | 37 | 57 | 70 |
+| 7 | 16 | 82 | 7 | 44 | 51 | 18 | 66 | 79 | 24 | 49 | 58 | 52 |
+| 8 | 23 | 15 | 3 | 1 | 90 | 54 | 51 | 47 | 5 | 71 | 27 | 29 |
+| 9 | 49 | 31 | 69 | 50 | 17 | 35 | 96 | 83 | 67 | 16 | 81 | 35 |
+| 10 | 96 | 19 | 78 | 12 | 21 | 86 | 71 | 84 | 45 | 28 | 95 | 97 |
+| 11 | 13 | 89 | 0 | 26 | 13 | 91 | 4 | 28 | 30 | 68 | 8 | 67 |
+
+## course_id=3
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 24 | 71 | 19 | 85 | 28 | 60 | 53 | 1 | 34 | 61 | 66 | 86 |
+| 1 | 69 | 97 | 85 | 17 | 30 | 79 | 81 | 44 | 81 | 77 | 64 | 88 |
+| 2 | 66 | 33 | 40 | 93 | 67 | 43 | 7 | 47 | 37 | 90 | 30 | 13 |
+| 3 | 46 | 31 | 78 | 56 | 84 | 24 | 55 | 38 | 30 | 16 | 14 | 53 |
+| 4 | 51 | 52 | 83 | 56 | 43 | 45 | 91 | 97 | 64 | 60 | 28 | 85 |
+| 5 | 76 | 52 | 21 | 94 | 55 | 13 | 68 | 53 | 75 | 65 | 95 | 15 |
+| 6 | 25 | 57 | 4 | 54 | 75 | 0 | 56 | 92 | 39 | 4 | 56 | 90 |
+| 7 | 62 | 42 | 12 | 14 | 65 | 10 | 94 | 13 | 83 | 11 | 92 | 6 |
+| 8 | 42 | 31 | 5 | 39 | 82 | 23 | 30 | 87 | 96 | 81 | 8 | 64 |
+| 9 | 83 | 26 | 93 | 31 | 85 | 61 | 92 | 54 | 6 | 38 | 45 | 0 |
+| 10 | 86 | 89 | 99 | 32 | 21 | 60 | 45 | 78 | 15 | 8 | 50 | 50 |
+| 11 | 40 | 86 | 92 | 81 | 93 | 91 | 96 | 48 | 44 | 94 | 94 | 65 |
+
+## course_id=4
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 38 | 23 | 13 | 99 | 55 | 26 | 89 | 10 | 4 | 77 | 41 | 44 |
+| 1 | 36 | 58 | 88 | 2 | 56 | 79 | 45 | 12 | 33 | 58 | 72 | 0 |
+| 2 | 73 | 52 | 30 | 32 | 57 | 25 | 10 | 83 | 7 | 60 | 81 | 26 |
+| 3 | 98 | 20 | 30 | 95 | 57 | 26 | 48 | 98 | 80 | 89 | 16 | 69 |
+| 4 | 2 | 49 | 65 | 98 | 55 | 65 | 48 | 46 | 54 | 2 | 7 | 87 |
+| 5 | 29 | 62 | 76 | 75 | 61 | 16 | 87 | 82 | 31 | 57 | 39 | 6 |
+| 6 | 41 | 60 | 85 | 90 | 16 | 56 | 8 | 63 | 53 | 0 | 21 | 28 |
+| 7 | 8 | 53 | 83 | 15 | 10 | 49 | 60 | 33 | 79 | 71 | 14 | 24 |
+| 8 | 29 | 5 | 60 | 60 | 63 | 94 | 68 | 88 | 10 | 73 | 51 | 63 |
+| 9 | 17 | 85 | 24 | 68 | 65 | 80 | 58 | 69 | 5 | 91 | 22 | 3 |
+| 10 | 77 | 75 | 54 | 37 | 32 | 39 | 28 | 12 | 97 | 14 | 62 | 0 |
+| 11 | 11 | 13 | 56 | 85 | 79 | 32 | 80 | 7 | 64 | 25 | 14 | 64 |
+
+## course_id=5
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 57 | 14 | 55 | 36 | 66 | 71 | 96 | 1 | 49 | 34 | 91 | 10 |
+| 1 | 26 | 74 | 7 | 16 | 12 | 1 | 90 | 90 | 99 | 14 | 26 | 38 |
+| 2 | 23 | 78 | 39 | 57 | 47 | 45 | 7 | 27 | 4 | 94 | 27 | 89 |
+| 3 | 22 | 6 | 20 | 98 | 80 | 50 | 4 | 14 | 5 | 9 | 25 | 13 |
+| 4 | 81 | 98 | 74 | 63 | 65 | 21 | 85 | 82 | 75 | 19 | 30 | 98 |
+| 5 | 67 | 38 | 20 | 32 | 42 | 89 | 21 | 35 | 14 | 30 | 93 | 78 |
+| 6 | 83 | 20 | 63 | 55 | 25 | 94 | 39 | 74 | 69 | 6 | 80 | 2 |
+| 7 | 52 | 82 | 24 | 51 | 28 | 41 | 89 | 59 | 34 | 16 | 52 | 48 |
+| 8 | 67 | 35 | 20 | 28 | 91 | 99 | 99 | 25 | 30 | 13 | 72 | 87 |
+| 9 | 50 | 5 | 92 | 68 | 1 | 99 | 8 | 33 | 15 | 61 | 20 | 77 |
+| 10 | 34 | 96 | 88 | 18 | 67 | 15 | 88 | 43 | 33 | 44 | 41 | 72 |
+| 11 | 12 | 93 | 6 | 18 | 54 | 69 | 68 | 10 | 54 | 39 | 10 | 61 |
+
+## course_id=6
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 60 | 25 | 91 | 31 | 16 | 50 | 32 | 86 | 5 | 13 | 32 | 98 |
+| 1 | 94 | 94 | 98 | 81 | 53 | 96 | 35 | 12 | 44 | 11 | 66 | 31 |
+| 2 | 45 | 1 | 25 | 72 | 20 | 13 | 5 | 16 | 91 | 99 | 98 | 19 |
+| 3 | 30 | 60 | 5 | 3 | 11 | 88 | 59 | 71 | 52 | 30 | 33 | 24 |
+| 4 | 2 | 47 | 87 | 45 | 67 | 77 | 16 | 39 | 55 | 93 | 48 | 67 |
+| 5 | 39 | 68 | 71 | 92 | 97 | 14 | 32 | 64 | 39 | 23 | 69 | 50 |
+| 6 | 83 | 92 | 44 | 54 | 90 | 26 | 32 | 29 | 12 | 21 | 18 | 13 |
+| 7 | 66 | 33 | 77 | 10 | 93 | 2 | 78 | 36 | 15 | 66 | 90 | 46 |
+| 8 | 40 | 29 | 30 | 83 | 34 | 95 | 36 | 44 | 11 | 68 | 95 | 12 |
+| 9 | 63 | 4 | 17 | 51 | 75 | 17 | 82 | 4 | 37 | 46 | 56 | 12 |
+| 10 | 29 | 55 | 92 | 68 | 59 | 91 | 24 | 30 | 42 | 79 | 63 | 37 |
+| 11 | 16 | 53 | 4 | 1 | 43 | 30 | 55 | 57 | 38 | 9 | 93 | 41 |
+
+## course_id=7
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 42 | 4 | 68 | 55 | 88 | 5 | 40 | 8 | 91 | 52 | 99 | 96 |
+| 1 | 90 | 49 | 22 | 96 | 84 | 69 | 38 | 35 | 95 | 96 | 55 | 32 |
+| 2 | 89 | 63 | 1 | 46 | 89 | 8 | 53 | 50 | 25 | 23 | 98 | 47 |
+| 3 | 33 | 17 | 6 | 58 | 69 | 66 | 43 | 4 | 39 | 68 | 17 | 90 |
+| 4 | 6 | 76 | 95 | 34 | 92 | 43 | 57 | 46 | 16 | 25 | 44 | 86 |
+| 5 | 2 | 89 | 70 | 21 | 93 | 87 | 31 | 10 | 95 | 16 | 12 | 19 |
+| 6 | 8 | 41 | 2 | 19 | 45 | 96 | 27 | 55 | 9 | 50 | 8 | 37 |
+| 7 | 35 | 38 | 58 | 49 | 51 | 46 | 30 | 27 | 70 | 63 | 4 | 98 |
+| 8 | 76 | 82 | 58 | 20 | 10 | 55 | 0 | 45 | 17 | 90 | 91 | 18 |
+| 9 | 57 | 6 | 52 | 34 | 51 | 12 | 86 | 92 | 64 | 46 | 96 | 43 |
+| 10 | 81 | 27 | 39 | 70 | 97 | 63 | 99 | 19 | 63 | 65 | 5 | 2 |
+| 11 | 21 | 9 | 98 | 88 | 61 | 3 | 56 | 22 | 33 | 90 | 80 | 63 |
+
+## course_id=8
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 51 | 54 | 74 | 98 | 26 | 52 | 89 | 28 | 53 | 43 | 86 | 60 |
+| 1 | 95 | 43 | 83 | 20 | 2 | 65 | 34 | 24 | 79 | 75 | 19 | 95 |
+| 2 | 67 | 39 | 78 | 2 | 40 | 65 | 80 | 77 | 88 | 42 | 48 | 97 |
+| 3 | 78 | 64 | 42 | 0 | 70 | 37 | 20 | 89 | 87 | 78 | 69 | 36 |
+| 4 | 2 | 81 | 38 | 4 | 48 | 73 | 57 | 11 | 18 | 28 | 75 | 72 |
+| 5 | 56 | 67 | 8 | 7 | 98 | 12 | 21 | 80 | 87 | 13 | 42 | 51 |
+| 6 | 98 | 28 | 23 | 98 | 4 | 68 | 54 | 95 | 28 | 88 | 48 | 5 |
+| 7 | 98 | 43 | 94 | 78 | 61 | 74 | 96 | 97 | 66 | 55 | 1 | 83 |
+| 8 | 78 | 73 | 40 | 84 | 29 | 51 | 63 | 73 | 61 | 4 | 14 | 73 |
+| 9 | 87 | 31 | 18 | 24 | 8 | 29 | 27 | 39 | 10 | 48 | 94 | 33 |
+| 10 | 97 | 51 | 26 | 86 | 66 | 10 | 85 | 28 | 85 | 5 | 85 | 94 |
+| 11 | 90 | 52 | 62 | 52 | 43 | 27 | 44 | 47 | 87 | 9 | 29 | 47 |
+
+## course_id=9
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 27 | 21 | 74 | 63 | 74 | 74 | 8 | 13 | 91 | 8 | 84 | 97 |
+| 1 | 61 | 34 | 66 | 65 | 34 | 60 | 72 | 39 | 64 | 10 | 79 | 72 |
+| 2 | 86 | 28 | 0 | 0 | 62 | 67 | 35 | 84 | 31 | 52 | 20 | 81 |
+| 3 | 90 | 26 | 67 | 49 | 65 | 62 | 25 | 32 | 65 | 53 | 37 | 13 |
+| 4 | 0 | 63 | 50 | 99 | 55 | 44 | 42 | 13 | 93 | 13 | 3 | 61 |
+| 5 | 83 | 90 | 71 | 53 | 23 | 82 | 32 | 45 | 67 | 33 | 92 | 71 |
+| 6 | 1 | 3 | 35 | 42 | 3 | 13 | 75 | 88 | 17 | 10 | 4 | 98 |
+| 7 | 78 | 93 | 60 | 53 | 25 | 58 | 8 | 1 | 27 | 84 | 57 | 68 |
+| 8 | 69 | 44 | 13 | 53 | 22 | 46 | 83 | 4 | 41 | 96 | 38 | 25 |
+| 9 | 6 | 81 | 40 | 2 | 78 | 68 | 52 | 7 | 54 | 19 | 27 | 66 |
+| 10 | 3 | 12 | 5 | 44 | 82 | 81 | 95 | 40 | 91 | 40 | 97 | 50 |
+| 11 | 84 | 36 | 28 | 71 | 84 | 73 | 90 | 25 | 18 | 49 | 78 | 65 |
+
+## course_id=10
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 38 | 78 | 46 | 46 | 17 | 4 | 24 | 24 | 8 | 95 | 16 | 55 |
+| 1 | 45 | 29 | 72 | 77 | 72 | 48 | 55 | 28 | 90 | 99 | 98 | 93 |
+| 2 | 91 | 41 | 82 | 33 | 91 | 28 | 19 | 83 | 7 | 51 | 75 | 79 |
+| 3 | 8 | 54 | 12 | 95 | 79 | 99 | 1 | 51 | 23 | 3 | 62 | 84 |
+| 4 | 54 | 14 | 91 | 26 | 85 | 49 | 48 | 85 | 82 | 78 | 40 | 87 |
+| 5 | 85 | 52 | 77 | 60 | 58 | 71 | 58 | 20 | 78 | 95 | 41 | 43 |
+| 6 | 15 | 89 | 53 | 92 | 32 | 98 | 19 | 63 | 39 | 57 | 43 | 29 |
+| 7 | 25 | 25 | 19 | 61 | 34 | 34 | 23 | 73 | 71 | 78 | 51 | 96 |
+| 8 | 23 | 93 | 54 | 26 | 87 | 77 | 41 | 31 | 75 | 99 | 97 | 86 |
+| 9 | 97 | 30 | 85 | 11 | 86 | 71 | 85 | 71 | 77 | 86 | 34 | 32 |
+| 10 | 87 | 32 | 25 | 22 | 30 | 82 | 22 | 88 | 90 | 45 | 50 | 4 |
+| 11 | 5 | 70 | 30 | 17 | 76 | 38 | 96 | 90 | 52 | 38 | 85 | 26 |
+
+## course_id=11
+| room_id\time_slot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 18 | 17 | 24 | 30 | 13 | 15 | 3 | 4 | 38 | 64 | 76 | 12 |
+| 1 | 49 | 65 | 60 | 29 | 12 | 25 | 74 | 7 | 12 | 66 | 8 | 57 |
+| 2 | 97 | 85 | 46 | 5 | 43 | 82 | 29 | 98 | 12 | 30 | 2 | 33 |
+| 3 | 19 | 14 | 18 | 82 | 44 | 96 | 38 | 70 | 29 | 47 | 14 | 11 |
+| 4 | 95 | 5 | 82 | 35 | 95 | 81 | 61 | 4 | 73 | 93 | 76 | 80 |
+| 5 | 21 | 45 | 10 | 18 | 9 | 19 | 96 | 54 | 86 | 9 | 57 | 66 |
+| 6 | 20 | 66 | 9 | 67 | 78 | 73 | 22 | 22 | 10 | 28 | 70 | 34 |
+| 7 | 54 | 49 | 58 | 7 | 0 | 84 | 51 | 11 | 50 | 31 | 6 | 71 |
+| 8 | 5 | 61 | 15 | 12 | 19 | 47 | 81 | 55 | 44 | 83 | 20 | 23 |
+| 9 | 12 | 7 | 3 | 45 | 85 | 8 | 64 | 99 | 95 | 31 | 53 | 12 |
+| 10 | 35 | 54 | 71 | 40 | 2 | 66 | 79 | 40 | 60 | 8 | 6 | 74 |
+| 11 | 28 | 98 | 38 | 43 | 49 | 29 | 37 | 5 | 58 | 37 | 62 | 62 |
+
+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': [[[89, 99, 9, 90, 88, 16, 12, 79, 1, 40, 75, 85], [77, 41, 5, 80, 36, 97, 6, 49, 24, 3, 7, 21], [68, 76, 22, 2, 63, 58, 52, 12, 26, 0, 41, 62], [48, 54, 94, 80, 85, 30, 62, 27, 10, 51, 11, 97], [84, 80, 82, 51, 46, 24, 42, 92, 91, 16, 56, 99], [48, 58, 62, 58, 98, 43, 90, 94, 71, 28, 99, 40], [56, 79, 77, 54, 40, 67, 83, 13, 51, 19, 63, 8], [86, 24, 33, 47, 13, 81, 54, 11, 30, 4, 87, 61], [63, 49, 65, 37, 96, 3, 63, 60, 1, 89, 1, 63], [70, 22, 63, 68, 25, 71, 74, 42, 89, 76, 6, 38], [99, 61, 63, 61, 67, 88, 11, 58, 40, 11, 9, 87], [70, 64, 6, 40, 65, 35, 47, 2, 13, 70, 80, 98]], [[56, 66, 76, 24, 5, 80, 74, 13, 74, 14, 65, 18], [28, 25, 5, 86, 8, 95, 0, 87, 51, 20, 30, 77], [55, 60, 65, 62, 92, 87, 46, 37, 51, 5, 64, 71], [99, 53, 33, 17, 25, 72, 76, 98, 88, 52, 24, 74], [2, 37, 50, 28, 6, 2, 24, 64, 34, 82, 38, 84], [36, 71, 59, 14, 76, 58, 68, 47, 40, 37, 63, 90], [96, 37, 47, 64, 34, 29, 7, 52, 22, 45, 5, 47], [10, 60, 62, 90, 28, 90, 84, 53, 89, 42, 99, 55], [59, 73, 52, 62, 9, 94, 29, 72, 90, 85, 62, 27], [61, 36, 78, 44, 21, 1, 47, 28, 49, 69, 0, 43], [19, 46, 55, 4, 98, 42, 33, 85, 85, 63, 13, 74], [97, 10, 81, 98, 70, 62, 40, 42, 75, 76, 44, 73]], [[16, 55, 91, 3, 17, 24, 80, 6, 50, 81, 36, 17], [26, 34, 10, 23, 0, 19, 83, 87, 4, 90, 52, 99], [59, 88, 36, 15, 89, 74, 97, 57, 82, 33, 87, 49], [20, 44, 28, 60, 24, 0, 49, 18, 40, 5, 66, 88], [8, 99, 31, 53, 37, 65, 60, 6, 39, 52, 37, 94], [28, 75, 15, 12, 54, 30, 18, 91, 70, 66, 53, 82], [2, 81, 50, 82, 18, 61, 17, 93, 72, 37, 57, 70], [16, 82, 7, 44, 51, 18, 66, 79, 24, 49, 58, 52], [23, 15, 3, 1, 90, 54, 51, 47, 5, 71, 27, 29], [49, 31, 69, 50, 17, 35, 96, 83, 67, 16, 81, 35], [96, 19, 78, 12, 21, 86, 71, 84, 45, 28, 95, 97], [13, 89, 0, 26, 13, 91, 4, 28, 30, 68, 8, 67]], [[24, 71, 19, 85, 28, 60, 53, 1, 34, 61, 66, 86], [69, 97, 85, 17, 30, 79, 81, 44, 81, 77, 64, 88], [66, 33, 40, 93, 67, 43, 7, 47, 37, 90, 30, 13], [46, 31, 78, 56, 84, 24, 55, 38, 30, 16, 14, 53], [51, 52, 83, 56, 43, 45, 91, 97, 64, 60, 28, 85], [76, 52, 21, 94, 55, 13, 68, 53, 75, 65, 95, 15], [25, 57, 4, 54, 75, 0, 56, 92, 39, 4, 56, 90], [62, 42, 12, 14, 65, 10, 94, 13, 83, 11, 92, 6], [42, 31, 5, 39, 82, 23, 30, 87, 96, 81, 8, 64], [83, 26, 93, 31, 85, 61, 92, 54, 6, 38, 45, 0], [86, 89, 99, 32, 21, 60, 45, 78, 15, 8, 50, 50], [40, 86, 92, 81, 93, 91, 96, 48, 44, 94, 94, 65]], [[38, 23, 13, 99, 55, 26, 89, 10, 4, 77, 41, 44], [36, 58, 88, 2, 56, 79, 45, 12, 33, 58, 72, 0], [73, 52, 30, 32, 57, 25, 10, 83, 7, 60, 81, 26], [98, 20, 30, 95, 57, 26, 48, 98, 80, 89, 16, 69], [2, 49, 65, 98, 55, 65, 48, 46, 54, 2, 7, 87], [29, 62, 76, 75, 61, 16, 87, 82, 31, 57, 39, 6], [41, 60, 85, 90, 16, 56, 8, 63, 53, 0, 21, 28], [8, 53, 83, 15, 10, 49, 60, 33, 79, 71, 14, 24], [29, 5, 60, 60, 63, 94, 68, 88, 10, 73, 51, 63], [17, 85, 24, 68, 65, 80, 58, 69, 5, 91, 22, 3], [77, 75, 54, 37, 32, 39, 28, 12, 97, 14, 62, 0], [11, 13, 56, 85, 79, 32, 80, 7, 64, 25, 14, 64]], [[57, 14, 55, 36, 66, 71, 96, 1, 49, 34, 91, 10], [26, 74, 7, 16, 12, 1, 90, 90, 99, 14, 26, 38], [23, 78, 39, 57, 47, 45, 7, 27, 4, 94, 27, 89], [22, 6, 20, 98, 80, 50, 4, 14, 5, 9, 25, 13], [81, 98, 74, 63, 65, 21, 85, 82, 75, 19, 30, 98], [67, 38, 20, 32, 42, 89, 21, 35, 14, 30, 93, 78], [83, 20, 63, 55, 25, 94, 39, 74, 69, 6, 80, 2], [52, 82, 24, 51, 28, 41, 89, 59, 34, 16, 52, 48], [67, 35, 20, 28, 91, 99, 99, 25, 30, 13, 72, 87], [50, 5, 92, 68, 1, 99, 8, 33, 15, 61, 20, 77], [34, 96, 88, 18, 67, 15, 88, 43, 33, 44, 41, 72], [12, 93, 6, 18, 54, 69, 68, 10, 54, 39, 10, 61]], [[60, 25, 91, 31, 16, 50, 32, 86, 5, 13, 32, 98], [94, 94, 98, 81, 53, 96, 35, 12, 44, 11, 66, 31], [45, 1, 25, 72, 20, 13, 5, 16, 91, 99, 98, 19], [30, 60, 5, 3, 11, 88, 59, 71, 52, 30, 33, 24], [2, 47, 87, 45, 67, 77, 16, 39, 55, 93, 48, 67], [39, 68, 71, 92, 97, 14, 32, 64, 39, 23, 69, 50], [83, 92, 44, 54, 90, 26, 32, 29, 12, 21, 18, 13], [66, 33, 77, 10, 93, 2, 78, 36, 15, 66, 90, 46], [40, 29, 30, 83, 34, 95, 36, 44, 11, 68, 95, 12], [63, 4, 17, 51, 75, 17, 82, 4, 37, 46, 56, 12], [29, 55, 92, 68, 59, 91, 24, 30, 42, 79, 63, 37], [16, 53, 4, 1, 43, 30, 55, 57, 38, 9, 93, 41]], [[42, 4, 68, 55, 88, 5, 40, 8, 91, 52, 99, 96], [90, 49, 22, 96, 84, 69, 38, 35, 95, 96, 55, 32], [89, 63, 1, 46, 89, 8, 53, 50, 25, 23, 98, 47], [33, 17, 6, 58, 69, 66, 43, 4, 39, 68, 17, 90], [6, 76, 95, 34, 92, 43, 57, 46, 16, 25, 44, 86], [2, 89, 70, 21, 93, 87, 31, 10, 95, 16, 12, 19], [8, 41, 2, 19, 45, 96, 27, 55, 9, 50, 8, 37], [35, 38, 58, 49, 51, 46, 30, 27, 70, 63, 4, 98], [76, 82, 58, 20, 10, 55, 0, 45, 17, 90, 91, 18], [57, 6, 52, 34, 51, 12, 86, 92, 64, 46, 96, 43], [81, 27, 39, 70, 97, 63, 99, 19, 63, 65, 5, 2], [21, 9, 98, 88, 61, 3, 56, 22, 33, 90, 80, 63]], [[51, 54, 74, 98, 26, 52, 89, 28, 53, 43, 86, 60], [95, 43, 83, 20, 2, 65, 34, 24, 79, 75, 19, 95], [67, 39, 78, 2, 40, 65, 80, 77, 88, 42, 48, 97], [78, 64, 42, 0, 70, 37, 20, 89, 87, 78, 69, 36], [2, 81, 38, 4, 48, 73, 57, 11, 18, 28, 75, 72], [56, 67, 8, 7, 98, 12, 21, 80, 87, 13, 42, 51], [98, 28, 23, 98, 4, 68, 54, 95, 28, 88, 48, 5], [98, 43, 94, 78, 61, 74, 96, 97, 66, 55, 1, 83], [78, 73, 40, 84, 29, 51, 63, 73, 61, 4, 14, 73], [87, 31, 18, 24, 8, 29, 27, 39, 10, 48, 94, 33], [97, 51, 26, 86, 66, 10, 85, 28, 85, 5, 85, 94], [90, 52, 62, 52, 43, 27, 44, 47, 87, 9, 29, 47]], [[27, 21, 74, 63, 74, 74, 8, 13, 91, 8, 84, 97], [61, 34, 66, 65, 34, 60, 72, 39, 64, 10, 79, 72], [86, 28, 0, 0, 62, 67, 35, 84, 31, 52, 20, 81], [90, 26, 67, 49, 65, 62, 25, 32, 65, 53, 37, 13], [0, 63, 50, 99, 55, 44, 42, 13, 93, 13, 3, 61], [83, 90, 71, 53, 23, 82, 32, 45, 67, 33, 92, 71], [1, 3, 35, 42, 3, 13, 75, 88, 17, 10, 4, 98], [78, 93, 60, 53, 25, 58, 8, 1, 27, 84, 57, 68], [69, 44, 13, 53, 22, 46, 83, 4, 41, 96, 38, 25], [6, 81, 40, 2, 78, 68, 52, 7, 54, 19, 27, 66], [3, 12, 5, 44, 82, 81, 95, 40, 91, 40, 97, 50], [84, 36, 28, 71, 84, 73, 90, 25, 18, 49, 78, 65]], [[38, 78, 46, 46, 17, 4, 24, 24, 8, 95, 16, 55], [45, 29, 72, 77, 72, 48, 55, 28, 90, 99, 98, 93], [91, 41, 82, 33, 91, 28, 19, 83, 7, 51, 75, 79], [8, 54, 12, 95, 79, 99, 1, 51, 23, 3, 62, 84], [54, 14, 91, 26, 85, 49, 48, 85, 82, 78, 40, 87], [85, 52, 77, 60, 58, 71, 58, 20, 78, 95, 41, 43], [15, 89, 53, 92, 32, 98, 19, 63, 39, 57, 43, 29], [25, 25, 19, 61, 34, 34, 23, 73, 71, 78, 51, 96], [23, 93, 54, 26, 87, 77, 41, 31, 75, 99, 97, 86], [97, 30, 85, 11, 86, 71, 85, 71, 77, 86, 34, 32], [87, 32, 25, 22, 30, 82, 22, 88, 90, 45, 50, 4], [5, 70, 30, 17, 76, 38, 96, 90, 52, 38, 85, 26]], [[18, 17, 24, 30, 13, 15, 3, 4, 38, 64, 76, 12], [49, 65, 60, 29, 12, 25, 74, 7, 12, 66, 8, 57], [97, 85, 46, 5, 43, 82, 29, 98, 12, 30, 2, 33], [19, 14, 18, 82, 44, 96, 38, 70, 29, 47, 14, 11], [95, 5, 82, 35, 95, 81, 61, 4, 73, 93, 76, 80], [21, 45, 10, 18, 9, 19, 96, 54, 86, 9, 57, 66], [20, 66, 9, 67, 78, 73, 22, 22, 10, 28, 70, 34], [54, 49, 58, 7, 0, 84, 51, 11, 50, 31, 6, 71], [5, 61, 15, 12, 19, 47, 81, 55, 44, 83, 20, 23], [12, 7, 3, 45, 85, 8, 64, 99, 95, 31, 53, 12], [35, 54, 71, 40, 2, 66, 79, 40, 60, 8, 6, 74], [28, 98, 38, 43, 49, 29, 37, 5, 58, 37, 62, 62]]], 'objective': 14.0}","[[0, 8, 8], [1, 9, 10], [2, 11, 2], [3, 0, 7], [4, 6, 9], [5, 1, 5], [6, 2, 1], [7, 10, 11], [8, 5, 3], [9, 4, 0], [10, 3, 6], [11, 7, 4]]",14.0,"{'problem_type': 'AP3', 'n': 12, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 89}, {'i': 0, 'j': 0, 'k': 1, 'cost': 99}, {'i': 0, 'j': 0, 'k': 2, 'cost': 9}, {'i': 0, 'j': 0, 'k': 3, 'cost': 90}, {'i': 0, 'j': 0, 'k': 4, 'cost': 88}, {'i': 0, 'j': 0, 'k': 5, 'cost': 16}, {'i': 0, 'j': 0, 'k': 6, 'cost': 12}, {'i': 0, 'j': 0, 'k': 7, 'cost': 79}, {'i': 0, 'j': 0, 'k': 8, 'cost': 1}, {'i': 0, 'j': 0, 'k': 9, 'cost': 40}, {'i': 0, 'j': 0, 'k': 10, 'cost': 75}, {'i': 0, 'j': 0, 'k': 11, 'cost': 85}, {'i': 0, 'j': 1, 'k': 0, 'cost': 77}, {'i': 0, 'j': 1, 'k': 1, 'cost': 41}, {'i': 0, 'j': 1, 'k': 2, 'cost': 5}, {'i': 0, 'j': 1, 'k': 3, 'cost': 80}, {'i': 0, 'j': 1, 'k': 4, 'cost': 36}, {'i': 0, 'j': 1, 'k': 5, 'cost': 97}, {'i': 0, 'j': 1, 'k': 6, 'cost': 6}, {'i': 0, 'j': 1, 'k': 7, 'cost': 49}, {'i': 0, 'j': 1, 'k': 8, 'cost': 24}, {'i': 0, 'j': 1, 'k': 9, 'cost': 3}, {'i': 0, 'j': 1, 'k': 10, 'cost': 7}, {'i': 0, 'j': 1, 'k': 11, 'cost': 21}, {'i': 0, 'j': 2, 'k': 0, 'cost': 68}, {'i': 0, 'j': 2, 'k': 1, 'cost': 76}, {'i': 0, 'j': 2, 'k': 2, 'cost': 22}, {'i': 0, 'j': 2, 'k': 3, 'cost': 2}, {'i': 0, 'j': 2, 'k': 4, 'cost': 63}, {'i': 0, 'j': 2, 'k': 5, 'cost': 58}, {'i': 0, 'j': 2, 'k': 6, 'cost': 52}, {'i': 0, 'j': 2, 'k': 7, 'cost': 12}, {'i': 0, 'j': 2, 'k': 8, 'cost': 26}, {'i': 0, 'j': 2, 'k': 9, 'cost': 0}, {'i': 0, 'j': 2, 'k': 10, 'cost': 41}, {'i': 0, 'j': 2, 'k': 11, 'cost': 62}, {'i': 0, 'j': 3, 'k': 0, 'cost': 48}, {'i': 0, 'j': 3, 'k': 1, 'cost': 54}, {'i': 0, 'j': 3, 'k': 2, 'cost': 94}, {'i': 0, 'j': 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'k': 6, 'cost': 83}, {'i': 9, 'j': 8, 'k': 7, 'cost': 4}, {'i': 9, 'j': 8, 'k': 8, 'cost': 41}, {'i': 9, 'j': 8, 'k': 9, 'cost': 96}, {'i': 9, 'j': 8, 'k': 10, 'cost': 38}, {'i': 9, 'j': 8, 'k': 11, 'cost': 25}, {'i': 9, 'j': 9, 'k': 0, 'cost': 6}, {'i': 9, 'j': 9, 'k': 1, 'cost': 81}, {'i': 9, 'j': 9, 'k': 2, 'cost': 40}, {'i': 9, 'j': 9, 'k': 3, 'cost': 2}, {'i': 9, 'j': 9, 'k': 4, 'cost': 78}, {'i': 9, 'j': 9, 'k': 5, 'cost': 68}, {'i': 9, 'j': 9, 'k': 6, 'cost': 52}, {'i': 9, 'j': 9, 'k': 7, 'cost': 7}, {'i': 9, 'j': 9, 'k': 8, 'cost': 54}, {'i': 9, 'j': 9, 'k': 9, 'cost': 19}, {'i': 9, 'j': 9, 'k': 10, 'cost': 27}, {'i': 9, 'j': 9, 'k': 11, 'cost': 66}, {'i': 9, 'j': 10, 'k': 0, 'cost': 3}, {'i': 9, 'j': 10, 'k': 1, 'cost': 12}, {'i': 9, 'j': 10, 'k': 2, 'cost': 5}, {'i': 9, 'j': 10, 'k': 3, 'cost': 44}, {'i': 9, 'j': 10, 'k': 4, 'cost': 82}, {'i': 9, 'j': 10, 'k': 5, 'cost': 81}, {'i': 9, 'j': 10, 'k': 6, 'cost': 95}, {'i': 9, 'j': 10, 'k': 7, 'cost': 40}, {'i': 9, 'j': 10, 'k': 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10, 'j': 0, 'k': 10, 'cost': 16}, {'i': 10, 'j': 0, 'k': 11, 'cost': 55}, {'i': 10, 'j': 1, 'k': 0, 'cost': 45}, {'i': 10, 'j': 1, 'k': 1, 'cost': 29}, {'i': 10, 'j': 1, 'k': 2, 'cost': 72}, {'i': 10, 'j': 1, 'k': 3, 'cost': 77}, {'i': 10, 'j': 1, 'k': 4, 'cost': 72}, {'i': 10, 'j': 1, 'k': 5, 'cost': 48}, {'i': 10, 'j': 1, 'k': 6, 'cost': 55}, {'i': 10, 'j': 1, 'k': 7, 'cost': 28}, {'i': 10, 'j': 1, 'k': 8, 'cost': 90}, {'i': 10, 'j': 1, 'k': 9, 'cost': 99}, {'i': 10, 'j': 1, 'k': 10, 'cost': 98}, {'i': 10, 'j': 1, 'k': 11, 'cost': 93}, {'i': 10, 'j': 2, 'k': 0, 'cost': 91}, {'i': 10, 'j': 2, 'k': 1, 'cost': 41}, {'i': 10, 'j': 2, 'k': 2, 'cost': 82}, {'i': 10, 'j': 2, 'k': 3, 'cost': 33}, {'i': 10, 'j': 2, 'k': 4, 'cost': 91}, {'i': 10, 'j': 2, 'k': 5, 'cost': 28}, {'i': 10, 'j': 2, 'k': 6, 'cost': 19}, {'i': 10, 'j': 2, 'k': 7, 'cost': 83}, {'i': 10, 'j': 2, 'k': 8, 'cost': 7}, {'i': 10, 'j': 2, 'k': 9, 'cost': 51}, {'i': 10, 'j': 2, 'k': 10, 'cost': 75}, {'i': 10, 'j': 2, 'k': 11, 'cost': 79}, {'i': 10, 'j': 3, 'k': 0, 'cost': 8}, {'i': 10, 'j': 3, 'k': 1, 'cost': 54}, {'i': 10, 'j': 3, 'k': 2, 'cost': 12}, {'i': 10, 'j': 3, 'k': 3, 'cost': 95}, {'i': 10, 'j': 3, 'k': 4, 'cost': 79}, {'i': 10, 'j': 3, 'k': 5, 'cost': 99}, {'i': 10, 'j': 3, 'k': 6, 'cost': 1}, {'i': 10, 'j': 3, 'k': 7, 'cost': 51}, {'i': 10, 'j': 3, 'k': 8, 'cost': 23}, {'i': 10, 'j': 3, 'k': 9, 'cost': 3}, {'i': 10, 'j': 3, 'k': 10, 'cost': 62}, {'i': 10, 'j': 3, 'k': 11, 'cost': 84}, {'i': 10, 'j': 4, 'k': 0, 'cost': 54}, {'i': 10, 'j': 4, 'k': 1, 'cost': 14}, {'i': 10, 'j': 4, 'k': 2, 'cost': 91}, {'i': 10, 'j': 4, 'k': 3, 'cost': 26}, {'i': 10, 'j': 4, 'k': 4, 'cost': 85}, {'i': 10, 'j': 4, 'k': 5, 'cost': 49}, {'i': 10, 'j': 4, 'k': 6, 'cost': 48}, {'i': 10, 'j': 4, 'k': 7, 'cost': 85}, {'i': 10, 'j': 4, 'k': 8, 'cost': 82}, {'i': 10, 'j': 4, 'k': 9, 'cost': 78}, {'i': 10, 'j': 4, 'k': 10, 'cost': 40}, {'i': 10, 'j': 4, 'k': 11, 'cost': 87}, {'i': 10, 'j': 5, 'k': 0, 'cost': 85}, {'i': 10, 'j': 5, 'k': 1, 'cost': 52}, {'i': 10, 'j': 5, 'k': 2, 'cost': 77}, {'i': 10, 'j': 5, 'k': 3, 'cost': 60}, {'i': 10, 'j': 5, 'k': 4, 'cost': 58}, {'i': 10, 'j': 5, 'k': 5, 'cost': 71}, {'i': 10, 'j': 5, 'k': 6, 'cost': 58}, {'i': 10, 'j': 5, 'k': 7, 'cost': 20}, {'i': 10, 'j': 5, 'k': 8, 'cost': 78}, {'i': 10, 'j': 5, 'k': 9, 'cost': 95}, {'i': 10, 'j': 5, 'k': 10, 'cost': 41}, {'i': 10, 'j': 5, 'k': 11, 'cost': 43}, {'i': 10, 'j': 6, 'k': 0, 'cost': 15}, {'i': 10, 'j': 6, 'k': 1, 'cost': 89}, {'i': 10, 'j': 6, 'k': 2, 'cost': 53}, {'i': 10, 'j': 6, 'k': 3, 'cost': 92}, {'i': 10, 'j': 6, 'k': 4, 'cost': 32}, {'i': 10, 'j': 6, 'k': 5, 'cost': 98}, {'i': 10, 'j': 6, 'k': 6, 'cost': 19}, {'i': 10, 'j': 6, 'k': 7, 'cost': 63}, {'i': 10, 'j': 6, 'k': 8, 'cost': 39}, {'i': 10, 'j': 6, 'k': 9, 'cost': 57}, {'i': 10, 'j': 6, 'k': 10, 'cost': 43}, {'i': 10, 'j': 6, 'k': 11, 'cost': 29}, {'i': 10, 'j': 7, 'k': 0, 'cost': 25}, {'i': 10, 'j': 7, 'k': 1, 'cost': 25}, {'i': 10, 'j': 7, 'k': 2, 'cost': 19}, {'i': 10, 'j': 7, 'k': 3, 'cost': 61}, {'i': 10, 'j': 7, 'k': 4, 'cost': 34}, {'i': 10, 'j': 7, 'k': 5, 'cost': 34}, {'i': 10, 'j': 7, 'k': 6, 'cost': 23}, {'i': 10, 'j': 7, 'k': 7, 'cost': 73}, {'i': 10, 'j': 7, 'k': 8, 'cost': 71}, {'i': 10, 'j': 7, 'k': 9, 'cost': 78}, {'i': 10, 'j': 7, 'k': 10, 'cost': 51}, {'i': 10, 'j': 7, 'k': 11, 'cost': 96}, {'i': 10, 'j': 8, 'k': 0, 'cost': 23}, {'i': 10, 'j': 8, 'k': 1, 'cost': 93}, {'i': 10, 'j': 8, 'k': 2, 'cost': 54}, {'i': 10, 'j': 8, 'k': 3, 'cost': 26}, {'i': 10, 'j': 8, 'k': 4, 'cost': 87}, {'i': 10, 'j': 8, 'k': 5, 'cost': 77}, {'i': 10, 'j': 8, 'k': 6, 'cost': 41}, {'i': 10, 'j': 8, 'k': 7, 'cost': 31}, {'i': 10, 'j': 8, 'k': 8, 'cost': 75}, {'i': 10, 'j': 8, 'k': 9, 'cost': 99}, {'i': 10, 'j': 8, 'k': 10, 'cost': 97}, {'i': 10, 'j': 8, 'k': 11, 'cost': 86}, {'i': 10, 'j': 9, 'k': 0, 'cost': 97}, {'i': 10, 'j': 9, 'k': 1, 'cost': 30}, {'i': 10, 'j': 9, 'k': 2, 'cost': 85}, {'i': 10, 'j': 9, 'k': 3, 'cost': 11}, {'i': 10, 'j': 9, 'k': 4, 'cost': 86}, {'i': 10, 'j': 9, 'k': 5, 'cost': 71}, {'i': 10, 'j': 9, 'k': 6, 'cost': 85}, {'i': 10, 'j': 9, 'k': 7, 'cost': 71}, {'i': 10, 'j': 9, 'k': 8, 'cost': 77}, {'i': 10, 'j': 9, 'k': 9, 'cost': 86}, {'i': 10, 'j': 9, 'k': 10, 'cost': 34}, {'i': 10, 'j': 9, 'k': 11, 'cost': 32}, {'i': 10, 'j': 10, 'k': 0, 'cost': 87}, {'i': 10, 'j': 10, 'k': 1, 'cost': 32}, {'i': 10, 'j': 10, 'k': 2, 'cost': 25}, {'i': 10, 'j': 10, 'k': 3, 'cost': 22}, {'i': 10, 'j': 10, 'k': 4, 'cost': 30}, {'i': 10, 'j': 10, 'k': 5, 'cost': 82}, {'i': 10, 'j': 10, 'k': 6, 'cost': 22}, {'i': 10, 'j': 10, 'k': 7, 'cost': 88}, {'i': 10, 'j': 10, 'k': 8, 'cost': 90}, {'i': 10, 'j': 10, 'k': 9, 'cost': 45}, {'i': 10, 'j': 10, 'k': 10, 'cost': 50}, {'i': 10, 'j': 10, 'k': 11, 'cost': 4}, {'i': 10, 'j': 11, 'k': 0, 'cost': 5}, {'i': 10, 'j': 11, 'k': 1, 'cost': 70}, {'i': 10, 'j': 11, 'k': 2, 'cost': 30}, {'i': 10, 'j': 11, 'k': 3, 'cost': 17}, {'i': 10, 'j': 11, 'k': 4, 'cost': 76}, {'i': 10, 'j': 11, 'k': 5, 'cost': 38}, {'i': 10, 'j': 11, 'k': 6, 'cost': 96}, {'i': 10, 'j': 11, 'k': 7, 'cost': 90}, {'i': 10, 'j': 11, 'k': 8, 'cost': 52}, {'i': 10, 'j': 11, 'k': 9, 'cost': 38}, {'i': 10, 'j': 11, 'k': 10, 'cost': 85}, {'i': 10, 'j': 11, 'k': 11, 'cost': 26}, {'i': 11, 'j': 0, 'k': 0, 'cost': 18}, {'i': 11, 'j': 0, 'k': 1, 'cost': 17}, {'i': 11, 'j': 0, 'k': 2, 'cost': 24}, {'i': 11, 'j': 0, 'k': 3, 'cost': 30}, {'i': 11, 'j': 0, 'k': 4, 'cost': 13}, {'i': 11, 'j': 0, 'k': 5, 'cost': 15}, {'i': 11, 'j': 0, 'k': 6, 'cost': 3}, {'i': 11, 'j': 0, 'k': 7, 'cost': 4}, {'i': 11, 'j': 0, 'k': 8, 'cost': 38}, {'i': 11, 'j': 0, 'k': 9, 'cost': 64}, {'i': 11, 'j': 0, 'k': 10, 'cost': 76}, {'i': 11, 'j': 0, 'k': 11, 'cost': 12}, {'i': 11, 'j': 1, 'k': 0, 'cost': 49}, {'i': 11, 'j': 1, 'k': 1, 'cost': 65}, {'i': 11, 'j': 1, 'k': 2, 'cost': 60}, {'i': 11, 'j': 1, 'k': 3, 'cost': 29}, {'i': 11, 'j': 1, 'k': 4, 'cost': 12}, {'i': 11, 'j': 1, 'k': 5, 'cost': 25}, {'i': 11, 'j': 1, 'k': 6, 'cost': 74}, {'i': 11, 'j': 1, 'k': 7, 'cost': 7}, {'i': 11, 'j': 1, 'k': 8, 'cost': 12}, {'i': 11, 'j': 1, 'k': 9, 'cost': 66}, {'i': 11, 'j': 1, 'k': 10, 'cost': 8}, {'i': 11, 'j': 1, 'k': 11, 'cost': 57}, {'i': 11, 'j': 2, 'k': 0, 'cost': 97}, {'i': 11, 'j': 2, 'k': 1, 'cost': 85}, {'i': 11, 'j': 2, 'k': 2, 'cost': 46}, {'i': 11, 'j': 2, 'k': 3, 'cost': 5}, {'i': 11, 'j': 2, 'k': 4, 'cost': 43}, {'i': 11, 'j': 2, 'k': 5, 'cost': 82}, {'i': 11, 'j': 2, 'k': 6, 'cost': 29}, {'i': 11, 'j': 2, 'k': 7, 'cost': 98}, {'i': 11, 'j': 2, 'k': 8, 'cost': 12}, {'i': 11, 'j': 2, 'k': 9, 'cost': 30}, {'i': 11, 'j': 2, 'k': 10, 'cost': 2}, {'i': 11, 'j': 2, 'k': 11, 'cost': 33}, {'i': 11, 'j': 3, 'k': 0, 'cost': 19}, {'i': 11, 'j': 3, 'k': 1, 'cost': 14}, {'i': 11, 'j': 3, 'k': 2, 'cost': 18}, {'i': 11, 'j': 3, 'k': 3, 'cost': 82}, {'i': 11, 'j': 3, 'k': 4, 'cost': 44}, {'i': 11, 'j': 3, 'k': 5, 'cost': 96}, {'i': 11, 'j': 3, 'k': 6, 'cost': 38}, {'i': 11, 'j': 3, 'k': 7, 'cost': 70}, {'i': 11, 'j': 3, 'k': 8, 'cost': 29}, {'i': 11, 'j': 3, 'k': 9, 'cost': 47}, {'i': 11, 'j': 3, 'k': 10, 'cost': 14}, {'i': 11, 'j': 3, 'k': 11, 'cost': 11}, {'i': 11, 'j': 4, 'k': 0, 'cost': 95}, {'i': 11, 'j': 4, 'k': 1, 'cost': 5}, {'i': 11, 'j': 4, 'k': 2, 'cost': 82}, {'i': 11, 'j': 4, 'k': 3, 'cost': 35}, {'i': 11, 'j': 4, 'k': 4, 'cost': 95}, {'i': 11, 'j': 4, 'k': 5, 'cost': 81}, {'i': 11, 'j': 4, 'k': 6, 'cost': 61}, {'i': 11, 'j': 4, 'k': 7, 'cost': 4}, {'i': 11, 'j': 4, 'k': 8, 'cost': 73}, {'i': 11, 'j': 4, 'k': 9, 'cost': 93}, {'i': 11, 'j': 4, 'k': 10, 'cost': 76}, {'i': 11, 'j': 4, 'k': 11, 'cost': 80}, {'i': 11, 'j': 5, 'k': 0, 'cost': 21}, {'i': 11, 'j': 5, 'k': 1, 'cost': 45}, {'i': 11, 'j': 5, 'k': 2, 'cost': 10}, {'i': 11, 'j': 5, 'k': 3, 'cost': 18}, {'i': 11, 'j': 5, 'k': 4, 'cost': 9}, {'i': 11, 'j': 5, 'k': 5, 'cost': 19}, {'i': 11, 'j': 5, 'k': 6, 'cost': 96}, {'i': 11, 'j': 5, 'k': 7, 'cost': 54}, {'i': 11, 'j': 5, 'k': 8, 'cost': 86}, {'i': 11, 'j': 5, 'k': 9, 'cost': 9}, {'i': 11, 'j': 5, 'k': 10, 'cost': 57}, {'i': 11, 'j': 5, 'k': 11, 'cost': 66}, {'i': 11, 'j': 6, 'k': 0, 'cost': 20}, {'i': 11, 'j': 6, 'k': 1, 'cost': 66}, {'i': 11, 'j': 6, 'k': 2, 'cost': 9}, {'i': 11, 'j': 6, 'k': 3, 'cost': 67}, {'i': 11, 'j': 6, 'k': 4, 'cost': 78}, {'i': 11, 'j': 6, 'k': 5, 'cost': 73}, {'i': 11, 'j': 6, 'k': 6, 'cost': 22}, {'i': 11, 'j': 6, 'k': 7, 'cost': 22}, {'i': 11, 'j': 6, 'k': 8, 'cost': 10}, {'i': 11, 'j': 6, 'k': 9, 'cost': 28}, {'i': 11, 'j': 6, 'k': 10, 'cost': 70}, {'i': 11, 'j': 6, 'k': 11, 'cost': 34}, {'i': 11, 'j': 7, 'k': 0, 'cost': 54}, {'i': 11, 'j': 7, 'k': 1, 'cost': 49}, {'i': 11, 'j': 7, 'k': 2, 'cost': 58}, {'i': 11, 'j': 7, 'k': 3, 'cost': 7}, {'i': 11, 'j': 7, 'k': 4, 'cost': 0}, {'i': 11, 'j': 7, 'k': 5, 'cost': 84}, {'i': 11, 'j': 7, 'k': 6, 'cost': 51}, {'i': 11, 'j': 7, 'k': 7, 'cost': 11}, {'i': 11, 'j': 7, 'k': 8, 'cost': 50}, {'i': 11, 'j': 7, 'k': 9, 'cost': 31}, {'i': 11, 'j': 7, 'k': 10, 'cost': 6}, {'i': 11, 'j': 7, 'k': 11, 'cost': 71}, {'i': 11, 'j': 8, 'k': 0, 'cost': 5}, {'i': 11, 'j': 8, 'k': 1, 'cost': 61}, {'i': 11, 'j': 8, 'k': 2, 'cost': 15}, {'i': 11, 'j': 8, 'k': 3, 'cost': 12}, {'i': 11, 'j': 8, 'k': 4, 'cost': 19}, {'i': 11, 'j': 8, 'k': 5, 'cost': 47}, {'i': 11, 'j': 8, 'k': 6, 'cost': 81}, {'i': 11, 'j': 8, 'k': 7, 'cost': 55}, {'i': 11, 'j': 8, 'k': 8, 'cost': 44}, {'i': 11, 'j': 8, 'k': 9, 'cost': 83}, {'i': 11, 'j': 8, 'k': 10, 'cost': 20}, {'i': 11, 'j': 8, 'k': 11, 'cost': 23}, {'i': 11, 'j': 9, 'k': 0, 'cost': 12}, {'i': 11, 'j': 9, 'k': 1, 'cost': 7}, {'i': 11, 'j': 9, 'k': 2, 'cost': 3}, {'i': 11, 'j': 9, 'k': 3, 'cost': 45}, {'i': 11, 'j': 9, 'k': 4, 'cost': 85}, {'i': 11, 'j': 9, 'k': 5, 'cost': 8}, {'i': 11, 'j': 9, 'k': 6, 'cost': 64}, {'i': 11, 'j': 9, 'k': 7, 'cost': 99}, {'i': 11, 'j': 9, 'k': 8, 'cost': 95}, {'i': 11, 'j': 9, 'k': 9, 'cost': 31}, {'i': 11, 'j': 9, 'k': 10, 'cost': 53}, {'i': 11, 'j': 9, 'k': 11, 'cost': 12}, {'i': 11, 'j': 10, 'k': 0, 'cost': 35}, {'i': 11, 'j': 10, 'k': 1, 'cost': 54}, {'i': 11, 'j': 10, 'k': 2, 'cost': 71}, {'i': 11, 'j': 10, 'k': 3, 'cost': 40}, {'i': 11, 'j': 10, 'k': 4, 'cost': 2}, {'i': 11, 'j': 10, 'k': 5, 'cost': 66}, {'i': 11, 'j': 10, 'k': 6, 'cost': 79}, {'i': 11, 'j': 10, 'k': 7, 'cost': 40}, {'i': 11, 'j': 10, 'k': 8, 'cost': 60}, {'i': 11, 'j': 10, 'k': 9, 'cost': 8}, {'i': 11, 'j': 10, 'k': 10, 'cost': 6}, {'i': 11, 'j': 10, 'k': 11, 'cost': 74}, {'i': 11, 'j': 11, 'k': 0, 'cost': 28}, {'i': 11, 'j': 11, 'k': 1, 'cost': 98}, {'i': 11, 'j': 11, 'k': 2, 'cost': 38}, {'i': 11, 'j': 11, 'k': 3, 'cost': 43}, {'i': 11, 'j': 11, 'k': 4, 'cost': 49}, {'i': 11, 'j': 11, 'k': 5, 'cost': 29}, {'i': 11, 'j': 11, 'k': 6, 'cost': 37}, {'i': 11, 'j': 11, 'k': 7, 'cost': 5}, {'i': 11, 'j': 11, 'k': 8, 'cost': 58}, {'i': 11, 'j': 11, 'k': 9, 'cost': 37}, {'i': 11, 'j': 11, 'k': 10, 'cost': 62}, {'i': 11, 'j': 11, 'k': 11, 'cost': 62}]}","[[0, 8, 8], [1, 9, 10], [2, 11, 2], [3, 0, 7], [4, 6, 9], [5, 1, 5], [6, 2, 1], [7, 10, 11], [8, 5, 3], [9, 4, 0], [10, 3, 6], [11, 7, 4]]",15,csv,0
+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 10 scenes, identified as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
+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 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 98 | 40 | 1 | 98 | 24 | 30 | 59 | 51 | 67 | 28 |
+| 1 | 5 | 64 | 32 | 49 | 41 | 56 | 53 | 3 | 54 | 44 |
+| 2 | 16 | 27 | 70 | 49 | 61 | 62 | 43 | 38 | 64 | 64 |
+| 3 | 52 | 42 | 82 | 49 | 54 | 82 | 78 | 13 | 27 | 1 |
+| 4 | 62 | 78 | 74 | 94 | 38 | 69 | 98 | 83 | 17 | 71 |
+| 5 | 34 | 10 | 37 | 56 | 61 | 60 | 95 | 26 | 74 | 41 |
+| 6 | 75 | 9 | 63 | 85 | 73 | 54 | 29 | 70 | 21 | 20 |
+| 7 | 82 | 6 | 56 | 44 | 87 | 47 | 60 | 98 | 43 | 0 |
+| 8 | 65 | 22 | 25 | 46 | 33 | 30 | 49 | 44 | 36 | 32 |
+| 9 | 30 | 26 | 41 | 23 | 7 | 48 | 88 | 44 | 66 | 40 |
+
+## scene_id=1
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 61 | 4 | 40 | 74 | 88 | 0 | 24 | 36 | 59 | 42 |
+| 1 | 95 | 59 | 75 | 33 | 60 | 60 | 28 | 38 | 74 | 13 |
+| 2 | 29 | 85 | 12 | 59 | 44 | 57 | 93 | 22 | 99 | 90 |
+| 3 | 27 | 61 | 84 | 75 | 14 | 3 | 36 | 83 | 85 | 21 |
+| 4 | 9 | 66 | 45 | 80 | 28 | 63 | 2 | 85 | 14 | 17 |
+| 5 | 18 | 95 | 93 | 73 | 7 | 5 | 70 | 33 | 32 | 8 |
+| 6 | 54 | 24 | 63 | 24 | 95 | 19 | 66 | 99 | 24 | 72 |
+| 7 | 35 | 52 | 51 | 42 | 98 | 18 | 94 | 36 | 97 | 44 |
+| 8 | 72 | 12 | 43 | 43 | 36 | 51 | 52 | 31 | 78 | 60 |
+| 9 | 56 | 66 | 74 | 48 | 2 | 49 | 53 | 11 | 83 | 47 |
+
+## scene_id=2
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 85 | 16 | 15 | 90 | 48 | 59 | 64 | 60 | 40 | 45 |
+| 1 | 95 | 82 | 5 | 12 | 13 | 74 | 45 | 8 | 71 | 78 |
+| 2 | 11 | 48 | 55 | 70 | 76 | 98 | 46 | 87 | 41 | 64 |
+| 3 | 53 | 50 | 61 | 54 | 50 | 95 | 17 | 62 | 38 | 77 |
+| 4 | 83 | 34 | 11 | 48 | 45 | 30 | 28 | 0 | 38 | 21 |
+| 5 | 5 | 96 | 41 | 99 | 23 | 54 | 56 | 97 | 50 | 77 |
+| 6 | 58 | 0 | 47 | 80 | 44 | 60 | 32 | 46 | 53 | 64 |
+| 7 | 20 | 78 | 72 | 18 | 13 | 19 | 31 | 34 | 63 | 38 |
+| 8 | 48 | 5 | 30 | 30 | 64 | 15 | 97 | 75 | 39 | 80 |
+| 9 | 60 | 43 | 83 | 66 | 71 | 34 | 77 | 16 | 19 | 36 |
+
+## scene_id=3
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 4 | 89 | 9 | 13 | 60 | 10 | 97 | 61 | 60 | 79 |
+| 1 | 94 | 65 | 18 | 84 | 44 | 13 | 78 | 37 | 23 | 7 |
+| 2 | 10 | 32 | 25 | 38 | 55 | 55 | 49 | 55 | 59 | 71 |
+| 3 | 66 | 74 | 7 | 79 | 72 | 30 | 19 | 94 | 83 | 19 |
+| 4 | 22 | 5 | 41 | 74 | 62 | 90 | 67 | 42 | 25 | 28 |
+| 5 | 57 | 3 | 14 | 25 | 79 | 93 | 61 | 33 | 49 | 26 |
+| 6 | 83 | 75 | 21 | 99 | 59 | 45 | 95 | 93 | 49 | 19 |
+| 7 | 94 | 25 | 0 | 66 | 0 | 37 | 85 | 79 | 61 | 5 |
+| 8 | 30 | 73 | 96 | 17 | 8 | 36 | 11 | 48 | 28 | 72 |
+| 9 | 37 | 0 | 22 | 53 | 89 | 62 | 49 | 58 | 35 | 27 |
+
+## scene_id=4
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 68 | 10 | 81 | 10 | 11 | 24 | 83 | 15 | 8 | 35 |
+| 1 | 7 | 14 | 53 | 22 | 58 | 83 | 58 | 39 | 71 | 51 |
+| 2 | 7 | 43 | 88 | 20 | 40 | 27 | 97 | 53 | 8 | 40 |
+| 3 | 47 | 43 | 90 | 11 | 43 | 49 | 60 | 76 | 26 | 17 |
+| 4 | 97 | 40 | 53 | 0 | 72 | 5 | 38 | 53 | 81 | 86 |
+| 5 | 29 | 33 | 40 | 99 | 50 | 70 | 95 | 97 | 50 | 72 |
+| 6 | 12 | 34 | 21 | 12 | 10 | 52 | 83 | 28 | 83 | 16 |
+| 7 | 57 | 13 | 25 | 55 | 45 | 62 | 61 | 70 | 31 | 62 |
+| 8 | 70 | 3 | 3 | 40 | 55 | 32 | 42 | 86 | 57 | 47 |
+| 9 | 56 | 77 | 73 | 21 | 31 | 49 | 33 | 24 | 25 | 47 |
+
+## scene_id=5
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 23 | 82 | 28 | 42 | 20 | 86 | 40 | 5 | 99 | 14 |
+| 1 | 50 | 46 | 35 | 85 | 16 | 61 | 35 | 73 | 13 | 10 |
+| 2 | 62 | 15 | 99 | 72 | 28 | 38 | 5 | 58 | 88 | 42 |
+| 3 | 56 | 88 | 14 | 99 | 90 | 72 | 38 | 92 | 54 | 18 |
+| 4 | 66 | 13 | 46 | 45 | 55 | 63 | 4 | 3 | 15 | 51 |
+| 5 | 92 | 88 | 80 | 10 | 34 | 66 | 67 | 20 | 21 | 87 |
+| 6 | 22 | 63 | 11 | 11 | 81 | 45 | 30 | 9 | 57 | 87 |
+| 7 | 29 | 42 | 17 | 85 | 83 | 71 | 27 | 27 | 86 | 19 |
+| 8 | 43 | 46 | 41 | 47 | 61 | 64 | 57 | 86 | 43 | 47 |
+| 9 | 88 | 5 | 48 | 18 | 30 | 9 | 23 | 61 | 80 | 51 |
+
+## scene_id=6
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 78 | 79 | 32 | 79 | 2 | 1 | 23 | 21 | 84 | 12 |
+| 1 | 34 | 31 | 9 | 27 | 57 | 84 | 85 | 12 | 16 | 11 |
+| 2 | 3 | 80 | 45 | 15 | 30 | 16 | 88 | 83 | 88 | 71 |
+| 3 | 95 | 57 | 10 | 51 | 63 | 53 | 38 | 8 | 69 | 70 |
+| 4 | 7 | 39 | 46 | 28 | 74 | 72 | 40 | 32 | 4 | 92 |
+| 5 | 22 | 86 | 20 | 21 | 35 | 84 | 58 | 88 | 54 | 13 |
+| 6 | 46 | 75 | 45 | 21 | 98 | 81 | 96 | 50 | 53 | 57 |
+| 7 | 10 | 44 | 46 | 87 | 48 | 94 | 60 | 8 | 71 | 10 |
+| 8 | 67 | 92 | 51 | 99 | 4 | 3 | 88 | 90 | 26 | 6 |
+| 9 | 18 | 75 | 38 | 72 | 98 | 96 | 30 | 16 | 90 | 99 |
+
+## scene_id=7
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 68 | 38 | 80 | 10 | 44 | 7 | 19 | 1 | 0 | 15 |
+| 1 | 97 | 8 | 65 | 36 | 68 | 91 | 98 | 94 | 18 | 40 |
+| 2 | 69 | 77 | 15 | 37 | 34 | 97 | 31 | 65 | 45 | 16 |
+| 3 | 1 | 87 | 66 | 55 | 47 | 30 | 47 | 62 | 9 | 61 |
+| 4 | 58 | 56 | 42 | 36 | 17 | 70 | 34 | 79 | 85 | 95 |
+| 5 | 58 | 65 | 48 | 19 | 40 | 61 | 56 | 39 | 89 | 39 |
+| 6 | 21 | 7 | 10 | 30 | 50 | 98 | 68 | 87 | 8 | 12 |
+| 7 | 38 | 56 | 0 | 49 | 28 | 68 | 49 | 51 | 25 | 24 |
+| 8 | 82 | 79 | 21 | 85 | 74 | 86 | 24 | 35 | 45 | 11 |
+| 9 | 84 | 25 | 31 | 72 | 22 | 48 | 39 | 27 | 94 | 80 |
+
+## scene_id=8
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 9 | 93 | 60 | 2 | 57 | 40 | 2 | 99 | 79 | 86 |
+| 1 | 8 | 88 | 67 | 4 | 54 | 2 | 59 | 37 | 70 | 35 |
+| 2 | 26 | 16 | 75 | 65 | 94 | 21 | 51 | 54 | 83 | 3 |
+| 3 | 62 | 82 | 5 | 68 | 4 | 23 | 45 | 31 | 14 | 11 |
+| 4 | 35 | 13 | 69 | 77 | 21 | 80 | 46 | 74 | 73 | 39 |
+| 5 | 94 | 16 | 19 | 26 | 10 | 45 | 24 | 35 | 9 | 38 |
+| 6 | 74 | 85 | 84 | 93 | 5 | 23 | 82 | 2 | 46 | 31 |
+| 7 | 87 | 61 | 29 | 5 | 82 | 21 | 43 | 71 | 85 | 69 |
+| 8 | 29 | 22 | 92 | 10 | 39 | 32 | 57 | 0 | 36 | 9 |
+| 9 | 72 | 15 | 76 | 59 | 87 | 97 | 18 | 68 | 33 | 91 |
+
+## scene_id=9
+| dp_id\location_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 33 | 63 | 67 | 37 | 4 | 42 | 63 | 93 | 17 | 30 |
+| 1 | 31 | 66 | 88 | 38 | 4 | 82 | 82 | 73 | 94 | 75 |
+| 2 | 91 | 33 | 40 | 47 | 27 | 39 | 2 | 34 | 39 | 19 |
+| 3 | 93 | 21 | 63 | 53 | 50 | 14 | 8 | 21 | 53 | 44 |
+| 4 | 37 | 28 | 75 | 86 | 58 | 67 | 39 | 97 | 55 | 54 |
+| 5 | 69 | 63 | 38 | 9 | 51 | 25 | 68 | 56 | 70 | 86 |
+| 6 | 28 | 4 | 68 | 23 | 84 | 6 | 99 | 55 | 4 | 68 |
+| 7 | 82 | 30 | 80 | 74 | 31 | 75 | 23 | 24 | 67 | 76 |
+| 8 | 37 | 54 | 68 | 23 | 9 | 71 | 29 | 94 | 85 | 77 |
+| 9 | 69 | 30 | 3 | 21 | 4 | 68 | 62 | 72 | 43 | 95 |
+Select exactly one line for each of the 10 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': [[[98, 40, 1, 98, 24, 30, 59, 51, 67, 28], [5, 64, 32, 49, 41, 56, 53, 3, 54, 44], [16, 27, 70, 49, 61, 62, 43, 38, 64, 64], [52, 42, 82, 49, 54, 82, 78, 13, 27, 1], [62, 78, 74, 94, 38, 69, 98, 83, 17, 71], [34, 10, 37, 56, 61, 60, 95, 26, 74, 41], [75, 9, 63, 85, 73, 54, 29, 70, 21, 20], [82, 6, 56, 44, 87, 47, 60, 98, 43, 0], [65, 22, 25, 46, 33, 30, 49, 44, 36, 32], [30, 26, 41, 23, 7, 48, 88, 44, 66, 40]], [[61, 4, 40, 74, 88, 0, 24, 36, 59, 42], [95, 59, 75, 33, 60, 60, 28, 38, 74, 13], [29, 85, 12, 59, 44, 57, 93, 22, 99, 90], [27, 61, 84, 75, 14, 3, 36, 83, 85, 21], [9, 66, 45, 80, 28, 63, 2, 85, 14, 17], [18, 95, 93, 73, 7, 5, 70, 33, 32, 8], [54, 24, 63, 24, 95, 19, 66, 99, 24, 72], [35, 52, 51, 42, 98, 18, 94, 36, 97, 44], [72, 12, 43, 43, 36, 51, 52, 31, 78, 60], [56, 66, 74, 48, 2, 49, 53, 11, 83, 47]], [[85, 16, 15, 90, 48, 59, 64, 60, 40, 45], [95, 82, 5, 12, 13, 74, 45, 8, 71, 78], [11, 48, 55, 70, 76, 98, 46, 87, 41, 64], [53, 50, 61, 54, 50, 95, 17, 62, 38, 77], [83, 34, 11, 48, 45, 30, 28, 0, 38, 21], [5, 96, 41, 99, 23, 54, 56, 97, 50, 77], [58, 0, 47, 80, 44, 60, 32, 46, 53, 64], [20, 78, 72, 18, 13, 19, 31, 34, 63, 38], [48, 5, 30, 30, 64, 15, 97, 75, 39, 80], [60, 43, 83, 66, 71, 34, 77, 16, 19, 36]], [[4, 89, 9, 13, 60, 10, 97, 61, 60, 79], [94, 65, 18, 84, 44, 13, 78, 37, 23, 7], [10, 32, 25, 38, 55, 55, 49, 55, 59, 71], [66, 74, 7, 79, 72, 30, 19, 94, 83, 19], [22, 5, 41, 74, 62, 90, 67, 42, 25, 28], [57, 3, 14, 25, 79, 93, 61, 33, 49, 26], [83, 75, 21, 99, 59, 45, 95, 93, 49, 19], [94, 25, 0, 66, 0, 37, 85, 79, 61, 5], [30, 73, 96, 17, 8, 36, 11, 48, 28, 72], [37, 0, 22, 53, 89, 62, 49, 58, 35, 27]], [[68, 10, 81, 10, 11, 24, 83, 15, 8, 35], [7, 14, 53, 22, 58, 83, 58, 39, 71, 51], [7, 43, 88, 20, 40, 27, 97, 53, 8, 40], [47, 43, 90, 11, 43, 49, 60, 76, 26, 17], [97, 40, 53, 0, 72, 5, 38, 53, 81, 86], [29, 33, 40, 99, 50, 70, 95, 97, 50, 72], [12, 34, 21, 12, 10, 52, 83, 28, 83, 16], [57, 13, 25, 55, 45, 62, 61, 70, 31, 62], [70, 3, 3, 40, 55, 32, 42, 86, 57, 47], [56, 77, 73, 21, 31, 49, 33, 24, 25, 47]], [[23, 82, 28, 42, 20, 86, 40, 5, 99, 14], [50, 46, 35, 85, 16, 61, 35, 73, 13, 10], [62, 15, 99, 72, 28, 38, 5, 58, 88, 42], [56, 88, 14, 99, 90, 72, 38, 92, 54, 18], [66, 13, 46, 45, 55, 63, 4, 3, 15, 51], [92, 88, 80, 10, 34, 66, 67, 20, 21, 87], [22, 63, 11, 11, 81, 45, 30, 9, 57, 87], [29, 42, 17, 85, 83, 71, 27, 27, 86, 19], [43, 46, 41, 47, 61, 64, 57, 86, 43, 47], [88, 5, 48, 18, 30, 9, 23, 61, 80, 51]], [[78, 79, 32, 79, 2, 1, 23, 21, 84, 12], [34, 31, 9, 27, 57, 84, 85, 12, 16, 11], [3, 80, 45, 15, 30, 16, 88, 83, 88, 71], [95, 57, 10, 51, 63, 53, 38, 8, 69, 70], [7, 39, 46, 28, 74, 72, 40, 32, 4, 92], [22, 86, 20, 21, 35, 84, 58, 88, 54, 13], [46, 75, 45, 21, 98, 81, 96, 50, 53, 57], [10, 44, 46, 87, 48, 94, 60, 8, 71, 10], [67, 92, 51, 99, 4, 3, 88, 90, 26, 6], [18, 75, 38, 72, 98, 96, 30, 16, 90, 99]], [[68, 38, 80, 10, 44, 7, 19, 1, 0, 15], [97, 8, 65, 36, 68, 91, 98, 94, 18, 40], [69, 77, 15, 37, 34, 97, 31, 65, 45, 16], [1, 87, 66, 55, 47, 30, 47, 62, 9, 61], [58, 56, 42, 36, 17, 70, 34, 79, 85, 95], [58, 65, 48, 19, 40, 61, 56, 39, 89, 39], [21, 7, 10, 30, 50, 98, 68, 87, 8, 12], [38, 56, 0, 49, 28, 68, 49, 51, 25, 24], [82, 79, 21, 85, 74, 86, 24, 35, 45, 11], [84, 25, 31, 72, 22, 48, 39, 27, 94, 80]], [[9, 93, 60, 2, 57, 40, 2, 99, 79, 86], [8, 88, 67, 4, 54, 2, 59, 37, 70, 35], [26, 16, 75, 65, 94, 21, 51, 54, 83, 3], [62, 82, 5, 68, 4, 23, 45, 31, 14, 11], [35, 13, 69, 77, 21, 80, 46, 74, 73, 39], [94, 16, 19, 26, 10, 45, 24, 35, 9, 38], [74, 85, 84, 93, 5, 23, 82, 2, 46, 31], [87, 61, 29, 5, 82, 21, 43, 71, 85, 69], [29, 22, 92, 10, 39, 32, 57, 0, 36, 9], [72, 15, 76, 59, 87, 97, 18, 68, 33, 91]], [[33, 63, 67, 37, 4, 42, 63, 93, 17, 30], [31, 66, 88, 38, 4, 82, 82, 73, 94, 75], [91, 33, 40, 47, 27, 39, 2, 34, 39, 19], [93, 21, 63, 53, 50, 14, 8, 21, 53, 44], [37, 28, 75, 86, 58, 67, 39, 97, 55, 54], [69, 63, 38, 9, 51, 25, 68, 56, 70, 86], [28, 4, 68, 23, 84, 6, 99, 55, 4, 68], [82, 30, 80, 74, 31, 75, 23, 24, 67, 76], [37, 54, 68, 23, 9, 71, 29, 94, 85, 77], [69, 30, 3, 21, 4, 68, 62, 72, 43, 95]]], 'objective': 21.0}","[[0, 7, 9], [1, 9, 4], [2, 1, 2], [3, 5, 1], [4, 4, 3], [5, 2, 6], [6, 0, 5], [7, 3, 0], [8, 8, 7], [9, 6, 8]]",21.0,"{'problem_type': 'AP3', 'n': 10, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 98}, {'i': 0, 'j': 0, 'k': 1, 'cost': 40}, {'i': 0, 'j': 0, 'k': 2, 'cost': 1}, {'i': 0, 'j': 0, 'k': 3, 'cost': 98}, {'i': 0, 'j': 0, 'k': 4, 'cost': 24}, {'i': 0, 'j': 0, 'k': 5, 'cost': 30}, {'i': 0, 'j': 0, 'k': 6, 'cost': 59}, {'i': 0, 'j': 0, 'k': 7, 'cost': 51}, {'i': 0, 'j': 0, 'k': 8, 'cost': 67}, {'i': 0, 'j': 0, 'k': 9, 'cost': 28}, {'i': 0, 'j': 1, 'k': 0, 'cost': 5}, {'i': 0, 'j': 1, 'k': 1, 'cost': 64}, {'i': 0, 'j': 1, 'k': 2, 'cost': 32}, {'i': 0, 'j': 1, 'k': 3, 'cost': 49}, {'i': 0, 'j': 1, 'k': 4, 'cost': 41}, {'i': 0, 'j': 1, 'k': 5, 'cost': 56}, {'i': 0, 'j': 1, 'k': 6, 'cost': 53}, {'i': 0, 'j': 1, 'k': 7, 'cost': 3}, {'i': 0, 'j': 1, 'k': 8, 'cost': 54}, {'i': 0, 'j': 1, 'k': 9, 'cost': 44}, {'i': 0, 'j': 2, 'k': 0, 'cost': 16}, {'i': 0, 'j': 2, 'k': 1, 'cost': 27}, {'i': 0, 'j': 2, 'k': 2, 'cost': 70}, {'i': 0, 'j': 2, 'k': 3, 'cost': 49}, {'i': 0, 'j': 2, 'k': 4, 'cost': 61}, {'i': 0, 'j': 2, 'k': 5, 'cost': 62}, {'i': 0, 'j': 2, 'k': 6, 'cost': 43}, {'i': 0, 'j': 2, 'k': 7, 'cost': 38}, {'i': 0, 'j': 2, 'k': 8, 'cost': 64}, {'i': 0, 'j': 2, 'k': 9, 'cost': 64}, {'i': 0, 'j': 3, 'k': 0, 'cost': 52}, {'i': 0, 'j': 3, 'k': 1, 'cost': 42}, {'i': 0, 'j': 3, 'k': 2, 'cost': 82}, {'i': 0, 'j': 3, 'k': 3, 'cost': 49}, {'i': 0, 'j': 3, 'k': 4, 'cost': 54}, {'i': 0, 'j': 3, 'k': 5, 'cost': 82}, {'i': 0, 'j': 3, 'k': 6, 'cost': 78}, {'i': 0, 'j': 3, 'k': 7, 'cost': 13}, {'i': 0, 'j': 3, 'k': 8, 'cost': 27}, {'i': 0, 'j': 3, 'k': 9, 'cost': 1}, {'i': 0, 'j': 4, 'k': 0, 'cost': 62}, {'i': 0, 'j': 4, 'k': 1, 'cost': 78}, {'i': 0, 'j': 4, 'k': 2, 'cost': 74}, {'i': 0, 'j': 4, 'k': 3, 'cost': 94}, {'i': 0, 'j': 4, 'k': 4, 'cost': 38}, {'i': 0, 'j': 4, 'k': 5, 'cost': 69}, {'i': 0, 'j': 4, 'k': 6, 'cost': 98}, {'i': 0, 'j': 4, 'k': 7, 'cost': 83}, {'i': 0, 'j': 4, 'k': 8, 'cost': 17}, {'i': 0, 'j': 4, 'k': 9, 'cost': 71}, {'i': 0, 'j': 5, 'k': 0, 'cost': 34}, {'i': 0, 'j': 5, 'k': 1, 'cost': 10}, {'i': 0, 'j': 5, 'k': 2, 'cost': 37}, {'i': 0, 'j': 5, 'k': 3, 'cost': 56}, {'i': 0, 'j': 5, 'k': 4, 'cost': 61}, {'i': 0, 'j': 5, 'k': 5, 'cost': 60}, {'i': 0, 'j': 5, 'k': 6, 'cost': 95}, {'i': 0, 'j': 5, 'k': 7, 'cost': 26}, {'i': 0, 'j': 5, 'k': 8, 'cost': 74}, {'i': 0, 'j': 5, 'k': 9, 'cost': 41}, {'i': 0, 'j': 6, 'k': 0, 'cost': 75}, {'i': 0, 'j': 6, 'k': 1, 'cost': 9}, {'i': 0, 'j': 6, 'k': 2, 'cost': 63}, {'i': 0, 'j': 6, 'k': 3, 'cost': 85}, {'i': 0, 'j': 6, 'k': 4, 'cost': 73}, {'i': 0, 'j': 6, 'k': 5, 'cost': 54}, {'i': 0, 'j': 6, 'k': 6, 'cost': 29}, {'i': 0, 'j': 6, 'k': 7, 'cost': 70}, {'i': 0, 'j': 6, 'k': 8, 'cost': 21}, {'i': 0, 'j': 6, 'k': 9, 'cost': 20}, {'i': 0, 'j': 7, 'k': 0, 'cost': 82}, {'i': 0, 'j': 7, 'k': 1, 'cost': 6}, {'i': 0, 'j': 7, 'k': 2, 'cost': 56}, {'i': 0, 'j': 7, 'k': 3, 'cost': 44}, {'i': 0, 'j': 7, 'k': 4, 'cost': 87}, {'i': 0, 'j': 7, 'k': 5, 'cost': 47}, {'i': 0, 'j': 7, 'k': 6, 'cost': 60}, {'i': 0, 'j': 7, 'k': 7, 'cost': 98}, {'i': 0, 'j': 7, 'k': 8, 'cost': 43}, {'i': 0, 'j': 7, 'k': 9, 'cost': 0}, {'i': 0, 'j': 8, 'k': 0, 'cost': 65}, {'i': 0, 'j': 8, 'k': 1, 'cost': 22}, {'i': 0, 'j': 8, 'k': 2, 'cost': 25}, {'i': 0, 'j': 8, 'k': 3, 'cost': 46}, {'i': 0, 'j': 8, 'k': 4, 'cost': 33}, {'i': 0, 'j': 8, 'k': 5, 'cost': 30}, {'i': 0, 'j': 8, 'k': 6, 'cost': 49}, {'i': 0, 'j': 8, 'k': 7, 'cost': 44}, {'i': 0, 'j': 8, 'k': 8, 'cost': 36}, {'i': 0, 'j': 8, 'k': 9, 'cost': 32}, {'i': 0, 'j': 9, 'k': 0, 'cost': 30}, {'i': 0, 'j': 9, 'k': 1, 'cost': 26}, {'i': 0, 'j': 9, 'k': 2, 'cost': 41}, {'i': 0, 'j': 9, 'k': 3, 'cost': 23}, {'i': 0, 'j': 9, 'k': 4, 'cost': 7}, {'i': 0, 'j': 9, 'k': 5, 'cost': 48}, {'i': 0, 'j': 9, 'k': 6, 'cost': 88}, {'i': 0, 'j': 9, 'k': 7, 'cost': 44}, {'i': 0, 'j': 9, 'k': 8, 'cost': 66}, {'i': 0, 'j': 9, 'k': 9, 'cost': 40}, {'i': 1, 'j': 0, 'k': 0, 'cost': 61}, {'i': 1, 'j': 0, 'k': 1, 'cost': 4}, {'i': 1, 'j': 0, 'k': 2, 'cost': 40}, {'i': 1, 'j': 0, 'k': 3, 'cost': 74}, {'i': 1, 'j': 0, 'k': 4, 'cost': 88}, {'i': 1, 'j': 0, 'k': 5, 'cost': 0}, {'i': 1, 'j': 0, 'k': 6, 'cost': 24}, {'i': 1, 'j': 0, 'k': 7, 'cost': 36}, {'i': 1, 'j': 0, 'k': 8, 'cost': 59}, {'i': 1, 'j': 0, 'k': 9, 'cost': 42}, {'i': 1, 'j': 1, 'k': 0, 'cost': 95}, {'i': 1, 'j': 1, 'k': 1, 'cost': 59}, {'i': 1, 'j': 1, 'k': 2, 'cost': 75}, {'i': 1, 'j': 1, 'k': 3, 'cost': 33}, {'i': 1, 'j': 1, 'k': 4, 'cost': 60}, {'i': 1, 'j': 1, 'k': 5, 'cost': 60}, {'i': 1, 'j': 1, 'k': 6, 'cost': 28}, {'i': 1, 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{'i': 8, 'j': 0, 'k': 2, 'cost': 60}, {'i': 8, 'j': 0, 'k': 3, 'cost': 2}, {'i': 8, 'j': 0, 'k': 4, 'cost': 57}, {'i': 8, 'j': 0, 'k': 5, 'cost': 40}, {'i': 8, 'j': 0, 'k': 6, 'cost': 2}, {'i': 8, 'j': 0, 'k': 7, 'cost': 99}, {'i': 8, 'j': 0, 'k': 8, 'cost': 79}, {'i': 8, 'j': 0, 'k': 9, 'cost': 86}, {'i': 8, 'j': 1, 'k': 0, 'cost': 8}, {'i': 8, 'j': 1, 'k': 1, 'cost': 88}, {'i': 8, 'j': 1, 'k': 2, 'cost': 67}, {'i': 8, 'j': 1, 'k': 3, 'cost': 4}, {'i': 8, 'j': 1, 'k': 4, 'cost': 54}, {'i': 8, 'j': 1, 'k': 5, 'cost': 2}, {'i': 8, 'j': 1, 'k': 6, 'cost': 59}, {'i': 8, 'j': 1, 'k': 7, 'cost': 37}, {'i': 8, 'j': 1, 'k': 8, 'cost': 70}, {'i': 8, 'j': 1, 'k': 9, 'cost': 35}, {'i': 8, 'j': 2, 'k': 0, 'cost': 26}, {'i': 8, 'j': 2, 'k': 1, 'cost': 16}, {'i': 8, 'j': 2, 'k': 2, 'cost': 75}, {'i': 8, 'j': 2, 'k': 3, 'cost': 65}, {'i': 8, 'j': 2, 'k': 4, 'cost': 94}, {'i': 8, 'j': 2, 'k': 5, 'cost': 21}, {'i': 8, 'j': 2, 'k': 6, 'cost': 51}, {'i': 8, 'j': 2, 'k': 7, 'cost': 54}, {'i': 8, 'j': 2, 'k': 8, 'cost': 83}, {'i': 8, 'j': 2, 'k': 9, 'cost': 3}, {'i': 8, 'j': 3, 'k': 0, 'cost': 62}, {'i': 8, 'j': 3, 'k': 1, 'cost': 82}, {'i': 8, 'j': 3, 'k': 2, 'cost': 5}, {'i': 8, 'j': 3, 'k': 3, 'cost': 68}, {'i': 8, 'j': 3, 'k': 4, 'cost': 4}, {'i': 8, 'j': 3, 'k': 5, 'cost': 23}, {'i': 8, 'j': 3, 'k': 6, 'cost': 45}, {'i': 8, 'j': 3, 'k': 7, 'cost': 31}, {'i': 8, 'j': 3, 'k': 8, 'cost': 14}, {'i': 8, 'j': 3, 'k': 9, 'cost': 11}, {'i': 8, 'j': 4, 'k': 0, 'cost': 35}, {'i': 8, 'j': 4, 'k': 1, 'cost': 13}, {'i': 8, 'j': 4, 'k': 2, 'cost': 69}, {'i': 8, 'j': 4, 'k': 3, 'cost': 77}, {'i': 8, 'j': 4, 'k': 4, 'cost': 21}, {'i': 8, 'j': 4, 'k': 5, 'cost': 80}, {'i': 8, 'j': 4, 'k': 6, 'cost': 46}, {'i': 8, 'j': 4, 'k': 7, 'cost': 74}, {'i': 8, 'j': 4, 'k': 8, 'cost': 73}, {'i': 8, 'j': 4, 'k': 9, 'cost': 39}, {'i': 8, 'j': 5, 'k': 0, 'cost': 94}, {'i': 8, 'j': 5, 'k': 1, 'cost': 16}, {'i': 8, 'j': 5, 'k': 2, 'cost': 19}, {'i': 8, 'j': 5, 'k': 3, 'cost': 26}, {'i': 8, 'j': 5, 'k': 4, 'cost': 10}, {'i': 8, 'j': 5, 'k': 5, 'cost': 45}, {'i': 8, 'j': 5, 'k': 6, 'cost': 24}, {'i': 8, 'j': 5, 'k': 7, 'cost': 35}, {'i': 8, 'j': 5, 'k': 8, 'cost': 9}, {'i': 8, 'j': 5, 'k': 9, 'cost': 38}, {'i': 8, 'j': 6, 'k': 0, 'cost': 74}, {'i': 8, 'j': 6, 'k': 1, 'cost': 85}, {'i': 8, 'j': 6, 'k': 2, 'cost': 84}, {'i': 8, 'j': 6, 'k': 3, 'cost': 93}, {'i': 8, 'j': 6, 'k': 4, 'cost': 5}, {'i': 8, 'j': 6, 'k': 5, 'cost': 23}, {'i': 8, 'j': 6, 'k': 6, 'cost': 82}, {'i': 8, 'j': 6, 'k': 7, 'cost': 2}, {'i': 8, 'j': 6, 'k': 8, 'cost': 46}, {'i': 8, 'j': 6, 'k': 9, 'cost': 31}, {'i': 8, 'j': 7, 'k': 0, 'cost': 87}, {'i': 8, 'j': 7, 'k': 1, 'cost': 61}, {'i': 8, 'j': 7, 'k': 2, 'cost': 29}, {'i': 8, 'j': 7, 'k': 3, 'cost': 5}, {'i': 8, 'j': 7, 'k': 4, 'cost': 82}, {'i': 8, 'j': 7, 'k': 5, 'cost': 21}, {'i': 8, 'j': 7, 'k': 6, 'cost': 43}, {'i': 8, 'j': 7, 'k': 7, 'cost': 71}, {'i': 8, 'j': 7, 'k': 8, 'cost': 85}, {'i': 8, 'j': 7, 'k': 9, 'cost': 69}, {'i': 8, 'j': 8, 'k': 0, 'cost': 29}, {'i': 8, 'j': 8, 'k': 1, 'cost': 22}, {'i': 8, 'j': 8, 'k': 2, 'cost': 92}, {'i': 8, 'j': 8, 'k': 3, 'cost': 10}, {'i': 8, 'j': 8, 'k': 4, 'cost': 39}, {'i': 8, 'j': 8, 'k': 5, 'cost': 32}, {'i': 8, 'j': 8, 'k': 6, 'cost': 57}, {'i': 8, 'j': 8, 'k': 7, 'cost': 0}, {'i': 8, 'j': 8, 'k': 8, 'cost': 36}, {'i': 8, 'j': 8, 'k': 9, 'cost': 9}, {'i': 8, 'j': 9, 'k': 0, 'cost': 72}, {'i': 8, 'j': 9, 'k': 1, 'cost': 15}, {'i': 8, 'j': 9, 'k': 2, 'cost': 76}, {'i': 8, 'j': 9, 'k': 3, 'cost': 59}, {'i': 8, 'j': 9, 'k': 4, 'cost': 87}, {'i': 8, 'j': 9, 'k': 5, 'cost': 97}, {'i': 8, 'j': 9, 'k': 6, 'cost': 18}, {'i': 8, 'j': 9, 'k': 7, 'cost': 68}, {'i': 8, 'j': 9, 'k': 8, 'cost': 33}, {'i': 8, 'j': 9, 'k': 9, 'cost': 91}, {'i': 9, 'j': 0, 'k': 0, 'cost': 33}, {'i': 9, 'j': 0, 'k': 1, 'cost': 63}, {'i': 9, 'j': 0, 'k': 2, 'cost': 67}, {'i': 9, 'j': 0, 'k': 3, 'cost': 37}, {'i': 9, 'j': 0, 'k': 4, 'cost': 4}, {'i': 9, 'j': 0, 'k': 5, 'cost': 42}, {'i': 9, 'j': 0, 'k': 6, 'cost': 63}, {'i': 9, 'j': 0, 'k': 7, 'cost': 93}, {'i': 9, 'j': 0, 'k': 8, 'cost': 17}, {'i': 9, 'j': 0, 'k': 9, 'cost': 30}, {'i': 9, 'j': 1, 'k': 0, 'cost': 31}, {'i': 9, 'j': 1, 'k': 1, 'cost': 66}, {'i': 9, 'j': 1, 'k': 2, 'cost': 88}, {'i': 9, 'j': 1, 'k': 3, 'cost': 38}, {'i': 9, 'j': 1, 'k': 4, 'cost': 4}, {'i': 9, 'j': 1, 'k': 5, 'cost': 82}, {'i': 9, 'j': 1, 'k': 6, 'cost': 82}, {'i': 9, 'j': 1, 'k': 7, 'cost': 73}, {'i': 9, 'j': 1, 'k': 8, 'cost': 94}, {'i': 9, 'j': 1, 'k': 9, 'cost': 75}, {'i': 9, 'j': 2, 'k': 0, 'cost': 91}, {'i': 9, 'j': 2, 'k': 1, 'cost': 33}, {'i': 9, 'j': 2, 'k': 2, 'cost': 40}, {'i': 9, 'j': 2, 'k': 3, 'cost': 47}, {'i': 9, 'j': 2, 'k': 4, 'cost': 27}, {'i': 9, 'j': 2, 'k': 5, 'cost': 39}, {'i': 9, 'j': 2, 'k': 6, 'cost': 2}, {'i': 9, 'j': 2, 'k': 7, 'cost': 34}, {'i': 9, 'j': 2, 'k': 8, 'cost': 39}, {'i': 9, 'j': 2, 'k': 9, 'cost': 19}, {'i': 9, 'j': 3, 'k': 0, 'cost': 93}, {'i': 9, 'j': 3, 'k': 1, 'cost': 21}, {'i': 9, 'j': 3, 'k': 2, 'cost': 63}, {'i': 9, 'j': 3, 'k': 3, 'cost': 53}, {'i': 9, 'j': 3, 'k': 4, 'cost': 50}, {'i': 9, 'j': 3, 'k': 5, 'cost': 14}, {'i': 9, 'j': 3, 'k': 6, 'cost': 8}, {'i': 9, 'j': 3, 'k': 7, 'cost': 21}, {'i': 9, 'j': 3, 'k': 8, 'cost': 53}, {'i': 9, 'j': 3, 'k': 9, 'cost': 44}, {'i': 9, 'j': 4, 'k': 0, 'cost': 37}, {'i': 9, 'j': 4, 'k': 1, 'cost': 28}, {'i': 9, 'j': 4, 'k': 2, 'cost': 75}, {'i': 9, 'j': 4, 'k': 3, 'cost': 86}, {'i': 9, 'j': 4, 'k': 4, 'cost': 58}, {'i': 9, 'j': 4, 'k': 5, 'cost': 67}, {'i': 9, 'j': 4, 'k': 6, 'cost': 39}, {'i': 9, 'j': 4, 'k': 7, 'cost': 97}, {'i': 9, 'j': 4, 'k': 8, 'cost': 55}, {'i': 9, 'j': 4, 'k': 9, 'cost': 54}, {'i': 9, 'j': 5, 'k': 0, 'cost': 69}, {'i': 9, 'j': 5, 'k': 1, 'cost': 63}, {'i': 9, 'j': 5, 'k': 2, 'cost': 38}, {'i': 9, 'j': 5, 'k': 3, 'cost': 9}, {'i': 9, 'j': 5, 'k': 4, 'cost': 51}, {'i': 9, 'j': 5, 'k': 5, 'cost': 25}, {'i': 9, 'j': 5, 'k': 6, 'cost': 68}, {'i': 9, 'j': 5, 'k': 7, 'cost': 56}, {'i': 9, 'j': 5, 'k': 8, 'cost': 70}, {'i': 9, 'j': 5, 'k': 9, 'cost': 86}, {'i': 9, 'j': 6, 'k': 0, 'cost': 28}, {'i': 9, 'j': 6, 'k': 1, 'cost': 4}, {'i': 9, 'j': 6, 'k': 2, 'cost': 68}, {'i': 9, 'j': 6, 'k': 3, 'cost': 23}, {'i': 9, 'j': 6, 'k': 4, 'cost': 84}, {'i': 9, 'j': 6, 'k': 5, 'cost': 6}, {'i': 9, 'j': 6, 'k': 6, 'cost': 99}, {'i': 9, 'j': 6, 'k': 7, 'cost': 55}, {'i': 9, 'j': 6, 'k': 8, 'cost': 4}, {'i': 9, 'j': 6, 'k': 9, 'cost': 68}, {'i': 9, 'j': 7, 'k': 0, 'cost': 82}, {'i': 9, 'j': 7, 'k': 1, 'cost': 30}, {'i': 9, 'j': 7, 'k': 2, 'cost': 80}, {'i': 9, 'j': 7, 'k': 3, 'cost': 74}, {'i': 9, 'j': 7, 'k': 4, 'cost': 31}, {'i': 9, 'j': 7, 'k': 5, 'cost': 75}, {'i': 9, 'j': 7, 'k': 6, 'cost': 23}, {'i': 9, 'j': 7, 'k': 7, 'cost': 24}, {'i': 9, 'j': 7, 'k': 8, 'cost': 67}, {'i': 9, 'j': 7, 'k': 9, 'cost': 76}, {'i': 9, 'j': 8, 'k': 0, 'cost': 37}, {'i': 9, 'j': 8, 'k': 1, 'cost': 54}, {'i': 9, 'j': 8, 'k': 2, 'cost': 68}, {'i': 9, 'j': 8, 'k': 3, 'cost': 23}, {'i': 9, 'j': 8, 'k': 4, 'cost': 9}, {'i': 9, 'j': 8, 'k': 5, 'cost': 71}, {'i': 9, 'j': 8, 'k': 6, 'cost': 29}, {'i': 9, 'j': 8, 'k': 7, 'cost': 94}, {'i': 9, 'j': 8, 'k': 8, 'cost': 85}, {'i': 9, 'j': 8, 'k': 9, 'cost': 77}, {'i': 9, 'j': 9, 'k': 0, 'cost': 69}, {'i': 9, 'j': 9, 'k': 1, 'cost': 30}, {'i': 9, 'j': 9, 'k': 2, 'cost': 3}, {'i': 9, 'j': 9, 'k': 3, 'cost': 21}, {'i': 9, 'j': 9, 'k': 4, 'cost': 4}, {'i': 9, 'j': 9, 'k': 5, 'cost': 68}, {'i': 9, 'j': 9, 'k': 6, 'cost': 62}, {'i': 9, 'j': 9, 'k': 7, 'cost': 72}, {'i': 9, 'j': 9, 'k': 8, 'cost': 43}, {'i': 9, 'j': 9, 'k': 9, 'cost': 95}]}","[[0, 7, 9], [1, 9, 4], [2, 1, 2], [3, 5, 1], [4, 4, 3], [5, 2, 6], [6, 0, 5], [7, 3, 0], [8, 8, 7], [9, 6, 8]]",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 9 menus are listed as 0, 1, 2, 3, 4, 5, 6, 7, 8.
+
+*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=0
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 98 | 21 | 40 | 1 | 81 | 98 | 24 | 30 | 84 |
+| 1 | 82 | 71 | 95 | 68 | 93 | 16 | 99 | 33 | 25 |
+| 2 | 5 | 68 | 64 | 32 | 46 | 49 | 41 | 56 | 21 |
+| 3 | 16 | 74 | 27 | 70 | 34 | 49 | 61 | 62 | 92 |
+| 4 | 26 | 65 | 13 | 43 | 26 | 10 | 46 | 47 | 13 |
+| 5 | 52 | 25 | 42 | 82 | 6 | 49 | 54 | 82 | 50 |
+| 6 | 62 | 22 | 78 | 74 | 48 | 94 | 38 | 69 | 36 |
+| 7 | 34 | 34 | 10 | 37 | 78 | 56 | 61 | 60 | 20 |
+| 8 | 12 | 68 | 69 | 78 | 9 | 69 | 47 | 91 | 94 |
+
+## menu_id=1
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 12 | 48 | 91 | 98 | 60 | 39 | 76 | 70 | 0 |
+| 1 | 47 | 85 | 70 | 94 | 75 | 7 | 58 | 11 | 71 |
+| 2 | 11 | 76 | 66 | 14 | 5 | 7 | 65 | 67 | 43 |
+| 3 | 10 | 54 | 90 | 80 | 52 | 15 | 2 | 57 | 20 |
+| 4 | 17 | 67 | 7 | 0 | 94 | 45 | 55 | 40 | 60 |
+| 5 | 6 | 70 | 71 | 53 | 24 | 36 | 78 | 45 | 16 |
+| 6 | 81 | 8 | 27 | 62 | 5 | 24 | 22 | 22 | 72 |
+| 7 | 73 | 60 | 12 | 21 | 43 | 21 | 82 | 53 | 77 |
+| 8 | 45 | 47 | 67 | 18 | 50 | 97 | 15 | 95 | 84 |
+
+## menu_id=2
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 61 | 70 | 4 | 40 | 47 | 74 | 88 | 0 | 6 |
+| 1 | 94 | 18 | 48 | 8 | 51 | 3 | 8 | 2 | 60 |
+| 2 | 95 | 77 | 59 | 75 | 91 | 33 | 60 | 60 | 11 |
+| 3 | 29 | 51 | 85 | 12 | 79 | 59 | 44 | 57 | 45 |
+| 4 | 28 | 61 | 22 | 73 | 5 | 20 | 45 | 8 | 8 |
+| 5 | 27 | 32 | 61 | 84 | 69 | 75 | 14 | 3 | 34 |
+| 6 | 9 | 8 | 66 | 45 | 7 | 80 | 28 | 63 | 15 |
+| 7 | 18 | 75 | 95 | 93 | 87 | 73 | 7 | 5 | 43 |
+| 8 | 10 | 11 | 35 | 53 | 20 | 33 | 20 | 34 | 48 |
+
+## menu_id=3
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 85 | 74 | 16 | 15 | 80 | 90 | 48 | 59 | 41 |
+| 1 | 62 | 59 | 65 | 97 | 56 | 92 | 36 | 41 | 30 |
+| 2 | 95 | 60 | 82 | 5 | 39 | 12 | 13 | 74 | 60 |
+| 3 | 11 | 54 | 48 | 55 | 54 | 70 | 76 | 98 | 5 |
+| 4 | 98 | 34 | 97 | 50 | 96 | 22 | 6 | 89 | 92 |
+| 5 | 53 | 97 | 50 | 61 | 78 | 54 | 50 | 95 | 42 |
+| 6 | 83 | 10 | 34 | 11 | 90 | 48 | 45 | 30 | 2 |
+| 7 | 5 | 66 | 96 | 41 | 45 | 99 | 23 | 54 | 55 |
+| 8 | 44 | 46 | 11 | 73 | 57 | 64 | 50 | 48 | 21 |
+
+## menu_id=4
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 20 | 49 | 65 | 8 | 98 | 74 | 43 | 83 | 40 |
+| 1 | 87 | 93 | 58 | 48 | 28 | 61 | 30 | 67 | 17 |
+| 2 | 49 | 11 | 71 | 90 | 89 | 33 | 12 | 46 | 30 |
+| 3 | 92 | 49 | 18 | 97 | 13 | 33 | 84 | 18 | 38 |
+| 4 | 64 | 73 | 67 | 18 | 6 | 40 | 23 | 20 | 52 |
+| 5 | 20 | 53 | 75 | 73 | 88 | 59 | 74 | 58 | 77 |
+| 6 | 42 | 2 | 68 | 47 | 92 | 17 | 61 | 60 | 71 |
+| 7 | 72 | 21 | 53 | 52 | 56 | 87 | 18 | 38 | 51 |
+| 8 | 84 | 40 | 31 | 63 | 98 | 77 | 90 | 72 | 43 |
+
+## menu_id=5
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 4 | 80 | 89 | 9 | 36 | 13 | 60 | 10 | 43 |
+| 1 | 7 | 10 | 67 | 49 | 5 | 97 | 76 | 18 | 59 |
+| 2 | 94 | 18 | 65 | 18 | 78 | 84 | 44 | 13 | 58 |
+| 3 | 10 | 25 | 32 | 25 | 94 | 38 | 55 | 55 | 80 |
+| 4 | 62 | 68 | 72 | 66 | 72 | 60 | 84 | 38 | 23 |
+| 5 | 66 | 87 | 74 | 7 | 38 | 79 | 72 | 30 | 76 |
+| 6 | 22 | 71 | 5 | 41 | 50 | 74 | 62 | 90 | 59 |
+| 7 | 57 | 26 | 3 | 14 | 56 | 25 | 79 | 93 | 69 |
+| 8 | 69 | 80 | 34 | 12 | 80 | 60 | 30 | 44 | 51 |
+
+## menu_id=6
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 68 | 67 | 10 | 81 | 27 | 10 | 11 | 24 | 6 |
+| 1 | 81 | 37 | 76 | 52 | 25 | 21 | 78 | 41 | 59 |
+| 2 | 7 | 50 | 14 | 53 | 20 | 22 | 58 | 83 | 35 |
+| 3 | 7 | 67 | 43 | 88 | 74 | 20 | 40 | 27 | 45 |
+| 4 | 10 | 69 | 33 | 47 | 20 | 59 | 89 | 88 | 53 |
+| 5 | 47 | 43 | 43 | 90 | 6 | 11 | 43 | 49 | 19 |
+| 6 | 97 | 89 | 40 | 53 | 86 | 0 | 72 | 5 | 43 |
+| 7 | 29 | 42 | 33 | 40 | 78 | 99 | 50 | 70 | 20 |
+| 8 | 21 | 51 | 36 | 35 | 20 | 85 | 57 | 85 | 73 |
+
+## menu_id=7
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 23 | 96 | 82 | 28 | 55 | 42 | 20 | 86 | 42 |
+| 1 | 11 | 24 | 53 | 28 | 42 | 85 | 8 | 89 | 92 |
+| 2 | 50 | 49 | 46 | 35 | 49 | 85 | 16 | 61 | 60 |
+| 3 | 62 | 8 | 15 | 99 | 46 | 72 | 28 | 38 | 42 |
+| 4 | 33 | 52 | 64 | 56 | 77 | 12 | 9 | 94 | 86 |
+| 5 | 56 | 38 | 88 | 14 | 99 | 99 | 90 | 72 | 37 |
+| 6 | 66 | 14 | 13 | 46 | 39 | 45 | 55 | 63 | 14 |
+| 7 | 92 | 27 | 88 | 80 | 75 | 10 | 34 | 66 | 28 |
+| 8 | 63 | 57 | 11 | 85 | 53 | 2 | 18 | 28 | 63 |
+
+## menu_id=8
+| chef_id\supplier_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 44 | 92 | 45 | 68 | 31 | 16 | 61 | 86 | 82 |
+| 1 | 47 | 71 | 76 | 48 | 10 | 94 | 12 | 50 | 11 |
+| 2 | 83 | 35 | 85 | 40 | 95 | 88 | 74 | 94 | 82 |
+| 3 | 31 | 50 | 31 | 79 | 9 | 57 | 11 | 11 | 95 |
+| 4 | 35 | 1 | 27 | 79 | 55 | 99 | 68 | 30 | 6 |
+| 5 | 41 | 75 | 71 | 31 | 45 | 39 | 59 | 51 | 65 |
+| 6 | 98 | 93 | 84 | 27 | 5 | 70 | 69 | 93 | 8 |
+| 7 | 0 | 24 | 40 | 94 | 5 | 30 | 45 | 15 | 92 |
+| 8 | 6 | 79 | 51 | 25 | 85 | 84 | 80 | 66 | 63 |
+
+Select one triple for each of the 9 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': [[[98, 21, 40, 1, 81, 98, 24, 30, 84], [82, 71, 95, 68, 93, 16, 99, 33, 25], [5, 68, 64, 32, 46, 49, 41, 56, 21], [16, 74, 27, 70, 34, 49, 61, 62, 92], [26, 65, 13, 43, 26, 10, 46, 47, 13], [52, 25, 42, 82, 6, 49, 54, 82, 50], [62, 22, 78, 74, 48, 94, 38, 69, 36], [34, 34, 10, 37, 78, 56, 61, 60, 20], [12, 68, 69, 78, 9, 69, 47, 91, 94]], [[12, 48, 91, 98, 60, 39, 76, 70, 0], [47, 85, 70, 94, 75, 7, 58, 11, 71], [11, 76, 66, 14, 5, 7, 65, 67, 43], [10, 54, 90, 80, 52, 15, 2, 57, 20], [17, 67, 7, 0, 94, 45, 55, 40, 60], [6, 70, 71, 53, 24, 36, 78, 45, 16], [81, 8, 27, 62, 5, 24, 22, 22, 72], [73, 60, 12, 21, 43, 21, 82, 53, 77], [45, 47, 67, 18, 50, 97, 15, 95, 84]], [[61, 70, 4, 40, 47, 74, 88, 0, 6], [94, 18, 48, 8, 51, 3, 8, 2, 60], [95, 77, 59, 75, 91, 33, 60, 60, 11], [29, 51, 85, 12, 79, 59, 44, 57, 45], [28, 61, 22, 73, 5, 20, 45, 8, 8], [27, 32, 61, 84, 69, 75, 14, 3, 34], [9, 8, 66, 45, 7, 80, 28, 63, 15], [18, 75, 95, 93, 87, 73, 7, 5, 43], [10, 11, 35, 53, 20, 33, 20, 34, 48]], [[85, 74, 16, 15, 80, 90, 48, 59, 41], [62, 59, 65, 97, 56, 92, 36, 41, 30], [95, 60, 82, 5, 39, 12, 13, 74, 60], [11, 54, 48, 55, 54, 70, 76, 98, 5], [98, 34, 97, 50, 96, 22, 6, 89, 92], [53, 97, 50, 61, 78, 54, 50, 95, 42], [83, 10, 34, 11, 90, 48, 45, 30, 2], [5, 66, 96, 41, 45, 99, 23, 54, 55], [44, 46, 11, 73, 57, 64, 50, 48, 21]], [[20, 49, 65, 8, 98, 74, 43, 83, 40], [87, 93, 58, 48, 28, 61, 30, 67, 17], [49, 11, 71, 90, 89, 33, 12, 46, 30], [92, 49, 18, 97, 13, 33, 84, 18, 38], [64, 73, 67, 18, 6, 40, 23, 20, 52], [20, 53, 75, 73, 88, 59, 74, 58, 77], [42, 2, 68, 47, 92, 17, 61, 60, 71], [72, 21, 53, 52, 56, 87, 18, 38, 51], [84, 40, 31, 63, 98, 77, 90, 72, 43]], [[4, 80, 89, 9, 36, 13, 60, 10, 43], [7, 10, 67, 49, 5, 97, 76, 18, 59], [94, 18, 65, 18, 78, 84, 44, 13, 58], [10, 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'j': 3, 'k': 0, 'cost': 62}, {'i': 7, 'j': 3, 'k': 1, 'cost': 8}, {'i': 7, 'j': 3, 'k': 2, 'cost': 15}, {'i': 7, 'j': 3, 'k': 3, 'cost': 99}, {'i': 7, 'j': 3, 'k': 4, 'cost': 46}, {'i': 7, 'j': 3, 'k': 5, 'cost': 72}, {'i': 7, 'j': 3, 'k': 6, 'cost': 28}, {'i': 7, 'j': 3, 'k': 7, 'cost': 38}, {'i': 7, 'j': 3, 'k': 8, 'cost': 42}, {'i': 7, 'j': 4, 'k': 0, 'cost': 33}, {'i': 7, 'j': 4, 'k': 1, 'cost': 52}, {'i': 7, 'j': 4, 'k': 2, 'cost': 64}, {'i': 7, 'j': 4, 'k': 3, 'cost': 56}, {'i': 7, 'j': 4, 'k': 4, 'cost': 77}, {'i': 7, 'j': 4, 'k': 5, 'cost': 12}, {'i': 7, 'j': 4, 'k': 6, 'cost': 9}, {'i': 7, 'j': 4, 'k': 7, 'cost': 94}, {'i': 7, 'j': 4, 'k': 8, 'cost': 86}, {'i': 7, 'j': 5, 'k': 0, 'cost': 56}, {'i': 7, 'j': 5, 'k': 1, 'cost': 38}, {'i': 7, 'j': 5, 'k': 2, 'cost': 88}, {'i': 7, 'j': 5, 'k': 3, 'cost': 14}, {'i': 7, 'j': 5, 'k': 4, 'cost': 99}, {'i': 7, 'j': 5, 'k': 5, 'cost': 99}, {'i': 7, 'j': 5, 'k': 6, 'cost': 90}, {'i': 7, 'j': 5, 'k': 7, 'cost': 72}, {'i': 7, 'j': 5, 'k': 8, 'cost': 37}, {'i': 7, 'j': 6, 'k': 0, 'cost': 66}, {'i': 7, 'j': 6, 'k': 1, 'cost': 14}, {'i': 7, 'j': 6, 'k': 2, 'cost': 13}, {'i': 7, 'j': 6, 'k': 3, 'cost': 46}, {'i': 7, 'j': 6, 'k': 4, 'cost': 39}, {'i': 7, 'j': 6, 'k': 5, 'cost': 45}, {'i': 7, 'j': 6, 'k': 6, 'cost': 55}, {'i': 7, 'j': 6, 'k': 7, 'cost': 63}, {'i': 7, 'j': 6, 'k': 8, 'cost': 14}, {'i': 7, 'j': 7, 'k': 0, 'cost': 92}, {'i': 7, 'j': 7, 'k': 1, 'cost': 27}, {'i': 7, 'j': 7, 'k': 2, 'cost': 88}, {'i': 7, 'j': 7, 'k': 3, 'cost': 80}, {'i': 7, 'j': 7, 'k': 4, 'cost': 75}, {'i': 7, 'j': 7, 'k': 5, 'cost': 10}, {'i': 7, 'j': 7, 'k': 6, 'cost': 34}, {'i': 7, 'j': 7, 'k': 7, 'cost': 66}, {'i': 7, 'j': 7, 'k': 8, 'cost': 28}, {'i': 7, 'j': 8, 'k': 0, 'cost': 63}, {'i': 7, 'j': 8, 'k': 1, 'cost': 57}, {'i': 7, 'j': 8, 'k': 2, 'cost': 11}, {'i': 7, 'j': 8, 'k': 3, 'cost': 85}, {'i': 7, 'j': 8, 'k': 4, 'cost': 53}, {'i': 7, 'j': 8, 'k': 5, 'cost': 2}, {'i': 7, 'j': 8, 'k': 6, 'cost': 18}, {'i': 7, 'j': 8, 'k': 7, 'cost': 28}, {'i': 7, 'j': 8, 'k': 8, 'cost': 63}, {'i': 8, 'j': 0, 'k': 0, 'cost': 44}, {'i': 8, 'j': 0, 'k': 1, 'cost': 92}, {'i': 8, 'j': 0, 'k': 2, 'cost': 45}, {'i': 8, 'j': 0, 'k': 3, 'cost': 68}, {'i': 8, 'j': 0, 'k': 4, 'cost': 31}, {'i': 8, 'j': 0, 'k': 5, 'cost': 16}, {'i': 8, 'j': 0, 'k': 6, 'cost': 61}, {'i': 8, 'j': 0, 'k': 7, 'cost': 86}, {'i': 8, 'j': 0, 'k': 8, 'cost': 82}, {'i': 8, 'j': 1, 'k': 0, 'cost': 47}, {'i': 8, 'j': 1, 'k': 1, 'cost': 71}, {'i': 8, 'j': 1, 'k': 2, 'cost': 76}, {'i': 8, 'j': 1, 'k': 3, 'cost': 48}, {'i': 8, 'j': 1, 'k': 4, 'cost': 10}, {'i': 8, 'j': 1, 'k': 5, 'cost': 94}, {'i': 8, 'j': 1, 'k': 6, 'cost': 12}, {'i': 8, 'j': 1, 'k': 7, 'cost': 50}, {'i': 8, 'j': 1, 'k': 8, 'cost': 11}, {'i': 8, 'j': 2, 'k': 0, 'cost': 83}, {'i': 8, 'j': 2, 'k': 1, 'cost': 35}, {'i': 8, 'j': 2, 'k': 2, 'cost': 85}, {'i': 8, 'j': 2, 'k': 3, 'cost': 40}, {'i': 8, 'j': 2, 'k': 4, 'cost': 95}, {'i': 8, 'j': 2, 'k': 5, 'cost': 88}, {'i': 8, 'j': 2, 'k': 6, 'cost': 74}, {'i': 8, 'j': 2, 'k': 7, 'cost': 94}, {'i': 8, 'j': 2, 'k': 8, 'cost': 82}, {'i': 8, 'j': 3, 'k': 0, 'cost': 31}, {'i': 8, 'j': 3, 'k': 1, 'cost': 50}, {'i': 8, 'j': 3, 'k': 2, 'cost': 31}, {'i': 8, 'j': 3, 'k': 3, 'cost': 79}, {'i': 8, 'j': 3, 'k': 4, 'cost': 9}, {'i': 8, 'j': 3, 'k': 5, 'cost': 57}, {'i': 8, 'j': 3, 'k': 6, 'cost': 11}, {'i': 8, 'j': 3, 'k': 7, 'cost': 11}, {'i': 8, 'j': 3, 'k': 8, 'cost': 95}, {'i': 8, 'j': 4, 'k': 0, 'cost': 35}, {'i': 8, 'j': 4, 'k': 1, 'cost': 1}, {'i': 8, 'j': 4, 'k': 2, 'cost': 27}, {'i': 8, 'j': 4, 'k': 3, 'cost': 79}, {'i': 8, 'j': 4, 'k': 4, 'cost': 55}, {'i': 8, 'j': 4, 'k': 5, 'cost': 99}, {'i': 8, 'j': 4, 'k': 6, 'cost': 68}, {'i': 8, 'j': 4, 'k': 7, 'cost': 30}, {'i': 8, 'j': 4, 'k': 8, 'cost': 6}, {'i': 8, 'j': 5, 'k': 0, 'cost': 41}, {'i': 8, 'j': 5, 'k': 1, 'cost': 75}, {'i': 8, 'j': 5, 'k': 2, 'cost': 71}, {'i': 8, 'j': 5, 'k': 3, 'cost': 31}, {'i': 8, 'j': 5, 'k': 4, 'cost': 45}, {'i': 8, 'j': 5, 'k': 5, 'cost': 39}, {'i': 8, 'j': 5, 'k': 6, 'cost': 59}, {'i': 8, 'j': 5, 'k': 7, 'cost': 51}, {'i': 8, 'j': 5, 'k': 8, 'cost': 65}, {'i': 8, 'j': 6, 'k': 0, 'cost': 98}, {'i': 8, 'j': 6, 'k': 1, 'cost': 93}, {'i': 8, 'j': 6, 'k': 2, 'cost': 84}, {'i': 8, 'j': 6, 'k': 3, 'cost': 27}, {'i': 8, 'j': 6, 'k': 4, 'cost': 5}, {'i': 8, 'j': 6, 'k': 5, 'cost': 70}, {'i': 8, 'j': 6, 'k': 6, 'cost': 69}, {'i': 8, 'j': 6, 'k': 7, 'cost': 93}, {'i': 8, 'j': 6, 'k': 8, 'cost': 8}, {'i': 8, 'j': 7, 'k': 0, 'cost': 0}, {'i': 8, 'j': 7, 'k': 1, 'cost': 24}, {'i': 8, 'j': 7, 'k': 2, 'cost': 40}, {'i': 8, 'j': 7, 'k': 3, 'cost': 94}, {'i': 8, 'j': 7, 'k': 4, 'cost': 5}, {'i': 8, 'j': 7, 'k': 5, 'cost': 30}, {'i': 8, 'j': 7, 'k': 6, 'cost': 45}, {'i': 8, 'j': 7, 'k': 7, 'cost': 15}, {'i': 8, 'j': 7, 'k': 8, 'cost': 92}, {'i': 8, 'j': 8, 'k': 0, 'cost': 6}, {'i': 8, 'j': 8, 'k': 1, 'cost': 79}, {'i': 8, 'j': 8, 'k': 2, 'cost': 51}, {'i': 8, 'j': 8, 'k': 3, 'cost': 25}, {'i': 8, 'j': 8, 'k': 4, 'cost': 85}, {'i': 8, 'j': 8, 'k': 5, 'cost': 84}, {'i': 8, 'j': 8, 'k': 6, 'cost': 80}, {'i': 8, 'j': 8, 'k': 7, 'cost': 66}, {'i': 8, 'j': 8, 'k': 8, 'cost': 63}]}","[[0, 2, 0], [1, 3, 6], [2, 1, 7], [3, 6, 8], [4, 0, 3], [5, 7, 2], [6, 5, 4], [7, 8, 5], [8, 4, 1]]",17,markdown_table,0
+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.
+
+There are 10 patients listed by ID: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
+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 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 24 | 1 | 54 | 69 | 4 | 4 | 0 | 37 | 33 | 32 |
+| 1 | 42 | 62 | 72 | 18 | 76 | 1 | 63 | 58 | 13 | 47 |
+| 2 | 40 | 17 | 91 | 29 | 71 | 98 | 1 | 82 | 16 | 51 |
+| 3 | 42 | 49 | 66 | 90 | 55 | 36 | 99 | 74 | 66 | 81 |
+| 4 | 16 | 57 | 6 | 90 | 44 | 72 | 52 | 3 | 57 | 3 |
+| 5 | 91 | 31 | 60 | 99 | 92 | 41 | 38 | 77 | 39 | 39 |
+| 6 | 74 | 78 | 90 | 70 | 38 | 45 | 27 | 14 | 41 | 56 |
+| 7 | 65 | 18 | 47 | 38 | 36 | 69 | 19 | 97 | 84 | 62 |
+| 8 | 66 | 12 | 46 | 68 | 91 | 4 | 25 | 56 | 60 | 96 |
+| 9 | 75 | 23 | 0 | 1 | 64 | 27 | 40 | 24 | 32 | 5 |
+
+## patient_id=1
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 54 | 74 | 44 | 16 | 58 | 25 | 45 | 61 | 13 | 58 |
+| 1 | 82 | 65 | 58 | 13 | 19 | 49 | 96 | 94 | 0 | 91 |
+| 2 | 35 | 46 | 90 | 15 | 93 | 17 | 43 | 98 | 44 | 3 |
+| 3 | 63 | 24 | 33 | 71 | 24 | 54 | 67 | 73 | 29 | 86 |
+| 4 | 1 | 99 | 51 | 13 | 11 | 8 | 30 | 62 | 61 | 16 |
+| 5 | 11 | 65 | 41 | 20 | 66 | 6 | 57 | 16 | 63 | 67 |
+| 6 | 88 | 92 | 5 | 24 | 6 | 3 | 35 | 59 | 87 | 90 |
+| 7 | 57 | 91 | 62 | 24 | 3 | 32 | 91 | 57 | 18 | 82 |
+| 8 | 95 | 28 | 7 | 76 | 66 | 89 | 28 | 69 | 14 | 17 |
+| 9 | 33 | 92 | 60 | 82 | 66 | 56 | 43 | 76 | 89 | 95 |
+
+## patient_id=2
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 58 | 57 | 21 | 43 | 36 | 46 | 41 | 40 | 51 | 89 |
+| 1 | 43 | 28 | 47 | 13 | 14 | 84 | 51 | 15 | 71 | 34 |
+| 2 | 62 | 9 | 36 | 39 | 88 | 38 | 54 | 11 | 58 | 44 |
+| 3 | 37 | 74 | 91 | 50 | 1 | 18 | 66 | 35 | 5 | 16 |
+| 4 | 30 | 87 | 50 | 66 | 60 | 97 | 84 | 34 | 56 | 94 |
+| 5 | 14 | 40 | 15 | 87 | 75 | 52 | 20 | 8 | 27 | 30 |
+| 6 | 63 | 69 | 69 | 91 | 81 | 67 | 53 | 25 | 52 | 44 |
+| 7 | 75 | 93 | 44 | 46 | 67 | 2 | 88 | 66 | 83 | 38 |
+| 8 | 34 | 71 | 0 | 63 | 72 | 55 | 97 | 35 | 94 | 32 |
+| 9 | 83 | 89 | 42 | 27 | 6 | 97 | 50 | 82 | 28 | 70 |
+
+## patient_id=3
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 22 | 10 | 53 | 96 | 25 | 20 | 28 | 39 | 23 | 67 |
+| 1 | 45 | 85 | 91 | 70 | 90 | 97 | 97 | 34 | 33 | 6 |
+| 2 | 77 | 91 | 27 | 88 | 41 | 32 | 68 | 97 | 79 | 82 |
+| 3 | 28 | 73 | 24 | 86 | 47 | 94 | 23 | 97 | 4 | 18 |
+| 4 | 80 | 27 | 0 | 36 | 52 | 64 | 9 | 62 | 20 | 56 |
+| 5 | 59 | 71 | 19 | 1 | 43 | 57 | 72 | 18 | 36 | 9 |
+| 6 | 18 | 44 | 58 | 33 | 29 | 65 | 51 | 87 | 3 | 43 |
+| 7 | 48 | 78 | 98 | 18 | 39 | 31 | 8 | 31 | 39 | 99 |
+| 8 | 64 | 90 | 18 | 42 | 17 | 58 | 84 | 39 | 57 | 98 |
+| 9 | 42 | 83 | 82 | 21 | 73 | 77 | 3 | 69 | 86 | 65 |
+
+## patient_id=4
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 86 | 67 | 3 | 88 | 15 | 6 | 87 | 31 | 26 | 56 |
+| 1 | 13 | 90 | 66 | 20 | 78 | 33 | 81 | 29 | 18 | 1 |
+| 2 | 55 | 86 | 4 | 16 | 68 | 27 | 27 | 81 | 94 | 58 |
+| 3 | 60 | 23 | 57 | 71 | 10 | 54 | 62 | 34 | 59 | 94 |
+| 4 | 78 | 41 | 21 | 94 | 51 | 51 | 22 | 65 | 33 | 58 |
+| 5 | 55 | 66 | 94 | 64 | 31 | 0 | 80 | 59 | 0 | 17 |
+| 6 | 76 | 3 | 54 | 50 | 57 | 7 | 74 | 32 | 34 | 5 |
+| 7 | 66 | 10 | 79 | 48 | 91 | 87 | 61 | 72 | 13 | 60 |
+| 8 | 44 | 40 | 75 | 37 | 23 | 18 | 58 | 87 | 46 | 27 |
+| 9 | 65 | 79 | 97 | 0 | 92 | 62 | 30 | 85 | 36 | 90 |
+
+## patient_id=5
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 24 | 97 | 91 | 46 | 30 | 61 | 35 | 70 | 75 | 21 |
+| 1 | 7 | 8 | 61 | 80 | 48 | 65 | 55 | 73 | 51 | 28 |
+| 2 | 75 | 77 | 13 | 47 | 63 | 59 | 3 | 68 | 3 | 80 |
+| 3 | 61 | 24 | 60 | 21 | 8 | 52 | 52 | 15 | 12 | 60 |
+| 4 | 22 | 27 | 73 | 6 | 19 | 81 | 3 | 68 | 98 | 61 |
+| 5 | 94 | 24 | 96 | 45 | 76 | 94 | 72 | 18 | 21 | 87 |
+| 6 | 26 | 2 | 73 | 90 | 73 | 74 | 94 | 78 | 85 | 3 |
+| 7 | 63 | 1 | 16 | 66 | 3 | 79 | 33 | 64 | 68 | 24 |
+| 8 | 11 | 86 | 88 | 2 | 73 | 95 | 12 | 32 | 51 | 24 |
+| 9 | 21 | 59 | 96 | 21 | 84 | 34 | 18 | 95 | 90 | 80 |
+
+## patient_id=6
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 38 | 92 | 79 | 22 | 90 | 26 | 40 | 33 | 97 | 10 |
+| 1 | 94 | 83 | 53 | 83 | 41 | 54 | 79 | 34 | 63 | 89 |
+| 2 | 23 | 49 | 31 | 14 | 3 | 39 | 48 | 36 | 6 | 60 |
+| 3 | 86 | 79 | 92 | 1 | 26 | 14 | 42 | 89 | 70 | 85 |
+| 4 | 61 | 15 | 14 | 70 | 99 | 26 | 9 | 98 | 67 | 76 |
+| 5 | 63 | 53 | 95 | 45 | 91 | 57 | 12 | 85 | 58 | 78 |
+| 6 | 5 | 11 | 64 | 53 | 75 | 76 | 3 | 86 | 76 | 5 |
+| 7 | 1 | 2 | 89 | 76 | 30 | 16 | 62 | 62 | 42 | 41 |
+| 8 | 15 | 43 | 28 | 25 | 13 | 13 | 66 | 80 | 40 | 7 |
+| 9 | 6 | 5 | 79 | 34 | 82 | 79 | 90 | 6 | 1 | 24 |
+
+## patient_id=7
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 53 | 81 | 8 | 48 | 55 | 15 | 90 | 56 | 68 | 93 |
+| 1 | 28 | 56 | 42 | 81 | 51 | 16 | 18 | 23 | 5 | 85 |
+| 2 | 55 | 17 | 6 | 2 | 55 | 12 | 41 | 87 | 39 | 51 |
+| 3 | 95 | 32 | 13 | 31 | 73 | 63 | 20 | 75 | 48 | 41 |
+| 4 | 18 | 57 | 3 | 35 | 20 | 99 | 31 | 66 | 45 | 22 |
+| 5 | 8 | 21 | 72 | 99 | 18 | 34 | 33 | 14 | 46 | 96 |
+| 6 | 80 | 49 | 77 | 54 | 14 | 9 | 23 | 70 | 80 | 66 |
+| 7 | 98 | 14 | 98 | 73 | 56 | 66 | 53 | 43 | 83 | 45 |
+| 8 | 56 | 23 | 65 | 58 | 87 | 97 | 61 | 29 | 70 | 50 |
+| 9 | 42 | 95 | 21 | 40 | 34 | 66 | 42 | 88 | 90 | 70 |
+
+## patient_id=8
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 68 | 5 | 38 | 7 | 63 | 76 | 76 | 58 | 55 | 85 |
+| 1 | 23 | 74 | 25 | 55 | 46 | 12 | 31 | 95 | 12 | 67 |
+| 2 | 1 | 61 | 19 | 19 | 57 | 79 | 38 | 25 | 81 | 96 |
+| 3 | 29 | 4 | 53 | 37 | 88 | 78 | 47 | 32 | 41 | 41 |
+| 4 | 83 | 79 | 65 | 26 | 69 | 78 | 99 | 34 | 0 | 75 |
+| 5 | 48 | 58 | 63 | 12 | 95 | 90 | 87 | 64 | 84 | 6 |
+| 6 | 47 | 95 | 71 | 79 | 47 | 28 | 67 | 96 | 65 | 68 |
+| 7 | 45 | 93 | 87 | 47 | 75 | 84 | 34 | 76 | 85 | 59 |
+| 8 | 59 | 34 | 41 | 79 | 85 | 42 | 85 | 82 | 89 | 96 |
+| 9 | 86 | 91 | 4 | 79 | 73 | 52 | 21 | 67 | 78 | 36 |
+
+## patient_id=9
+| specialist_id\room_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 62 | 89 | 29 | 7 | 95 | 93 | 12 | 85 | 77 | 89 |
+| 1 | 75 | 96 | 4 | 99 | 24 | 64 | 34 | 57 | 1 | 5 |
+| 2 | 38 | 37 | 96 | 86 | 4 | 73 | 25 | 24 | 31 | 83 |
+| 3 | 13 | 80 | 99 | 80 | 35 | 99 | 36 | 72 | 95 | 80 |
+| 4 | 23 | 50 | 3 | 60 | 78 | 75 | 97 | 33 | 44 | 82 |
+| 5 | 45 | 18 | 85 | 8 | 53 | 11 | 35 | 87 | 3 | 47 |
+| 6 | 74 | 31 | 55 | 42 | 43 | 37 | 69 | 86 | 3 | 67 |
+| 7 | 32 | 51 | 13 | 61 | 94 | 29 | 32 | 2 | 55 | 92 |
+| 8 | 74 | 9 | 57 | 88 | 85 | 7 | 8 | 11 | 92 | 22 |
+| 9 | 99 | 23 | 70 | 93 | 3 | 39 | 68 | 44 | 3 | 82 |
+Choose one triple for each of the 10 patients to form a conflict-free plan that minimizes the summed expected penalties.
+
+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': [[[24, 1, 54, 69, 4, 4, 0, 37, 33, 32], [42, 62, 72, 18, 76, 1, 63, 58, 13, 47], [40, 17, 91, 29, 71, 98, 1, 82, 16, 51], [42, 49, 66, 90, 55, 36, 99, 74, 66, 81], [16, 57, 6, 90, 44, 72, 52, 3, 57, 3], [91, 31, 60, 99, 92, 41, 38, 77, 39, 39], [74, 78, 90, 70, 38, 45, 27, 14, 41, 56], [65, 18, 47, 38, 36, 69, 19, 97, 84, 62], [66, 12, 46, 68, 91, 4, 25, 56, 60, 96], [75, 23, 0, 1, 64, 27, 40, 24, 32, 5]], [[54, 74, 44, 16, 58, 25, 45, 61, 13, 58], [82, 65, 58, 13, 19, 49, 96, 94, 0, 91], [35, 46, 90, 15, 93, 17, 43, 98, 44, 3], [63, 24, 33, 71, 24, 54, 67, 73, 29, 86], [1, 99, 51, 13, 11, 8, 30, 62, 61, 16], [11, 65, 41, 20, 66, 6, 57, 16, 63, 67], [88, 92, 5, 24, 6, 3, 35, 59, 87, 90], [57, 91, 62, 24, 3, 32, 91, 57, 18, 82], [95, 28, 7, 76, 66, 89, 28, 69, 14, 17], [33, 92, 60, 82, 66, 56, 43, 76, 89, 95]], [[58, 57, 21, 43, 36, 46, 41, 40, 51, 89], [43, 28, 47, 13, 14, 84, 51, 15, 71, 34], [62, 9, 36, 39, 88, 38, 54, 11, 58, 44], [37, 74, 91, 50, 1, 18, 66, 35, 5, 16], [30, 87, 50, 66, 60, 97, 84, 34, 56, 94], [14, 40, 15, 87, 75, 52, 20, 8, 27, 30], [63, 69, 69, 91, 81, 67, 53, 25, 52, 44], [75, 93, 44, 46, 67, 2, 88, 66, 83, 38], [34, 71, 0, 63, 72, 55, 97, 35, 94, 32], [83, 89, 42, 27, 6, 97, 50, 82, 28, 70]], [[22, 10, 53, 96, 25, 20, 28, 39, 23, 67], [45, 85, 91, 70, 90, 97, 97, 34, 33, 6], [77, 91, 27, 88, 41, 32, 68, 97, 79, 82], [28, 73, 24, 86, 47, 94, 23, 97, 4, 18], [80, 27, 0, 36, 52, 64, 9, 62, 20, 56], [59, 71, 19, 1, 43, 57, 72, 18, 36, 9], [18, 44, 58, 33, 29, 65, 51, 87, 3, 43], [48, 78, 98, 18, 39, 31, 8, 31, 39, 99], [64, 90, 18, 42, 17, 58, 84, 39, 57, 98], [42, 83, 82, 21, 73, 77, 3, 69, 86, 65]], [[86, 67, 3, 88, 15, 6, 87, 31, 26, 56], [13, 90, 66, 20, 78, 33, 81, 29, 18, 1], [55, 86, 4, 16, 68, 27, 27, 81, 94, 58], [60, 23, 57, 71, 10, 54, 62, 34, 59, 94], [78, 41, 21, 94, 51, 51, 22, 65, 33, 58], [55, 66, 94, 64, 31, 0, 80, 59, 0, 17], [76, 3, 54, 50, 57, 7, 74, 32, 34, 5], [66, 10, 79, 48, 91, 87, 61, 72, 13, 60], [44, 40, 75, 37, 23, 18, 58, 87, 46, 27], [65, 79, 97, 0, 92, 62, 30, 85, 36, 90]], [[24, 97, 91, 46, 30, 61, 35, 70, 75, 21], [7, 8, 61, 80, 48, 65, 55, 73, 51, 28], [75, 77, 13, 47, 63, 59, 3, 68, 3, 80], [61, 24, 60, 21, 8, 52, 52, 15, 12, 60], [22, 27, 73, 6, 19, 81, 3, 68, 98, 61], [94, 24, 96, 45, 76, 94, 72, 18, 21, 87], [26, 2, 73, 90, 73, 74, 94, 78, 85, 3], [63, 1, 16, 66, 3, 79, 33, 64, 68, 24], [11, 86, 88, 2, 73, 95, 12, 32, 51, 24], [21, 59, 96, 21, 84, 34, 18, 95, 90, 80]], [[38, 92, 79, 22, 90, 26, 40, 33, 97, 10], [94, 83, 53, 83, 41, 54, 79, 34, 63, 89], [23, 49, 31, 14, 3, 39, 48, 36, 6, 60], [86, 79, 92, 1, 26, 14, 42, 89, 70, 85], [61, 15, 14, 70, 99, 26, 9, 98, 67, 76], [63, 53, 95, 45, 91, 57, 12, 85, 58, 78], [5, 11, 64, 53, 75, 76, 3, 86, 76, 5], [1, 2, 89, 76, 30, 16, 62, 62, 42, 41], [15, 43, 28, 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{'i': 9, 'j': 3, 'k': 4, 'cost': 35}, {'i': 9, 'j': 3, 'k': 5, 'cost': 99}, {'i': 9, 'j': 3, 'k': 6, 'cost': 36}, {'i': 9, 'j': 3, 'k': 7, 'cost': 72}, {'i': 9, 'j': 3, 'k': 8, 'cost': 95}, {'i': 9, 'j': 3, 'k': 9, 'cost': 80}, {'i': 9, 'j': 4, 'k': 0, 'cost': 23}, {'i': 9, 'j': 4, 'k': 1, 'cost': 50}, {'i': 9, 'j': 4, 'k': 2, 'cost': 3}, {'i': 9, 'j': 4, 'k': 3, 'cost': 60}, {'i': 9, 'j': 4, 'k': 4, 'cost': 78}, {'i': 9, 'j': 4, 'k': 5, 'cost': 75}, {'i': 9, 'j': 4, 'k': 6, 'cost': 97}, {'i': 9, 'j': 4, 'k': 7, 'cost': 33}, {'i': 9, 'j': 4, 'k': 8, 'cost': 44}, {'i': 9, 'j': 4, 'k': 9, 'cost': 82}, {'i': 9, 'j': 5, 'k': 0, 'cost': 45}, {'i': 9, 'j': 5, 'k': 1, 'cost': 18}, {'i': 9, 'j': 5, 'k': 2, 'cost': 85}, {'i': 9, 'j': 5, 'k': 3, 'cost': 8}, {'i': 9, 'j': 5, 'k': 4, 'cost': 53}, {'i': 9, 'j': 5, 'k': 5, 'cost': 11}, {'i': 9, 'j': 5, 'k': 6, 'cost': 35}, {'i': 9, 'j': 5, 'k': 7, 'cost': 87}, {'i': 9, 'j': 5, 'k': 8, 'cost': 3}, {'i': 9, 'j': 5, 'k': 9, 'cost': 47}, {'i': 9, 'j': 6, 'k': 0, 'cost': 74}, {'i': 9, 'j': 6, 'k': 1, 'cost': 31}, {'i': 9, 'j': 6, 'k': 2, 'cost': 55}, {'i': 9, 'j': 6, 'k': 3, 'cost': 42}, {'i': 9, 'j': 6, 'k': 4, 'cost': 43}, {'i': 9, 'j': 6, 'k': 5, 'cost': 37}, {'i': 9, 'j': 6, 'k': 6, 'cost': 69}, {'i': 9, 'j': 6, 'k': 7, 'cost': 86}, {'i': 9, 'j': 6, 'k': 8, 'cost': 3}, {'i': 9, 'j': 6, 'k': 9, 'cost': 67}, {'i': 9, 'j': 7, 'k': 0, 'cost': 32}, {'i': 9, 'j': 7, 'k': 1, 'cost': 51}, {'i': 9, 'j': 7, 'k': 2, 'cost': 13}, {'i': 9, 'j': 7, 'k': 3, 'cost': 61}, {'i': 9, 'j': 7, 'k': 4, 'cost': 94}, {'i': 9, 'j': 7, 'k': 5, 'cost': 29}, {'i': 9, 'j': 7, 'k': 6, 'cost': 32}, {'i': 9, 'j': 7, 'k': 7, 'cost': 2}, {'i': 9, 'j': 7, 'k': 8, 'cost': 55}, {'i': 9, 'j': 7, 'k': 9, 'cost': 92}, {'i': 9, 'j': 8, 'k': 0, 'cost': 74}, {'i': 9, 'j': 8, 'k': 1, 'cost': 9}, {'i': 9, 'j': 8, 'k': 2, 'cost': 57}, {'i': 9, 'j': 8, 'k': 3, 'cost': 88}, {'i': 9, 'j': 8, 'k': 4, 'cost': 85}, {'i': 9, 'j': 8, 'k': 5, 'cost': 7}, {'i': 9, 'j': 8, 'k': 6, 'cost': 8}, {'i': 9, 'j': 8, 'k': 7, 'cost': 11}, {'i': 9, 'j': 8, 'k': 8, 'cost': 92}, {'i': 9, 'j': 8, 'k': 9, 'cost': 22}, {'i': 9, 'j': 9, 'k': 0, 'cost': 99}, {'i': 9, 'j': 9, 'k': 1, 'cost': 23}, {'i': 9, 'j': 9, 'k': 2, 'cost': 70}, {'i': 9, 'j': 9, 'k': 3, 'cost': 93}, {'i': 9, 'j': 9, 'k': 4, 'cost': 3}, {'i': 9, 'j': 9, 'k': 5, 'cost': 39}, {'i': 9, 'j': 9, 'k': 6, 'cost': 68}, {'i': 9, 'j': 9, 'k': 7, 'cost': 44}, {'i': 9, 'j': 9, 'k': 8, 'cost': 3}, {'i': 9, 'j': 9, 'k': 9, 'cost': 82}]}","[[0, 0, 1], [1, 1, 8], [2, 3, 4], [3, 9, 6], [4, 5, 5], [5, 8, 3], [6, 6, 9], [7, 4, 2], [8, 2, 0], [9, 7, 7]]",18,nl,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"": 12,
+  ""index_identifiers"": [
+    ""A"",
+    ""B"",
+    ""C"",
+    ""D"",
+    ""E"",
+    ""F"",
+    ""G"",
+    ""H"",
+    ""I"",
+    ""J"",
+    ""K"",
+    ""L""
+  ]
+}
+
+# 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=A
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 43 | 44 | 15 | 80 | 30 | 93 | 8 | 70 | 52 | 21 | 70 | 30 |
+| B | 86 | 20 | 51 | 51 | 38 | 51 | 44 | 16 | 30 | 81 | 23 | 8 |
+| C | 30 | 48 | 91 | 57 | 46 | 23 | 13 | 54 | 14 | 38 | 57 | 16 |
+| D | 28 | 40 | 57 | 67 | 35 | 54 | 63 | 2 | 11 | 68 | 76 | 28 |
+| E | 67 | 71 | 74 | 1 | 72 | 8 | 4 | 57 | 76 | 22 | 47 | 6 |
+| F | 56 | 64 | 15 | 96 | 12 | 28 | 32 | 23 | 8 | 7 | 87 | 41 |
+| G | 12 | 21 | 46 | 47 | 90 | 25 | 37 | 58 | 38 | 89 | 6 | 94 |
+| H | 84 | 35 | 53 | 59 | 64 | 75 | 56 | 78 | 92 | 87 | 45 | 5 |
+| I | 82 | 59 | 44 | 86 | 80 | 94 | 72 | 84 | 22 | 62 | 48 | 47 |
+| J | 68 | 58 | 98 | 84 | 30 | 46 | 47 | 31 | 30 | 48 | 31 | 62 |
+| K | 79 | 98 | 17 | 92 | 55 | 67 | 71 | 42 | 7 | 88 | 33 | 72 |
+| L | 99 | 70 | 65 | 33 | 78 | 89 | 81 | 76 | 52 | 4 | 2 | 48 |
+
+## creator_id=B
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 83 | 41 | 88 | 98 | 98 | 74 | 77 | 60 | 38 | 4 | 54 | 53 |
+| B | 91 | 4 | 0 | 56 | 46 | 32 | 46 | 51 | 29 | 9 | 0 | 61 |
+| C | 77 | 20 | 94 | 41 | 26 | 1 | 69 | 88 | 9 | 52 | 92 | 37 |
+| D | 71 | 63 | 49 | 9 | 34 | 41 | 31 | 61 | 44 | 15 | 9 | 65 |
+| E | 79 | 7 | 46 | 10 | 6 | 16 | 46 | 65 | 82 | 46 | 67 | 99 |
+| F | 15 | 34 | 38 | 60 | 76 | 48 | 32 | 55 | 68 | 73 | 22 | 94 |
+| G | 16 | 20 | 23 | 95 | 13 | 60 | 43 | 30 | 71 | 78 | 70 | 45 |
+| H | 90 | 35 | 87 | 72 | 2 | 27 | 69 | 13 | 79 | 43 | 66 | 36 |
+| I | 65 | 88 | 37 | 18 | 3 | 33 | 58 | 59 | 88 | 28 | 0 | 51 |
+| J | 38 | 89 | 80 | 20 | 62 | 87 | 87 | 49 | 58 | 45 | 81 | 68 |
+| K | 89 | 54 | 69 | 38 | 28 | 19 | 72 | 42 | 93 | 76 | 88 | 4 |
+| L | 13 | 49 | 22 | 81 | 47 | 13 | 23 | 19 | 51 | 67 | 58 | 77 |
+
+## creator_id=C
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 40 | 5 | 88 | 21 | 82 | 56 | 82 | 92 | 39 | 83 | 41 | 77 |
+| B | 77 | 23 | 50 | 2 | 10 | 9 | 90 | 67 | 60 | 84 | 41 | 54 |
+| C | 3 | 46 | 62 | 31 | 3 | 99 | 87 | 51 | 20 | 80 | 83 | 18 |
+| D | 72 | 5 | 29 | 72 | 68 | 0 | 11 | 84 | 80 | 79 | 98 | 9 |
+| E | 47 | 43 | 9 | 3 | 90 | 11 | 0 | 19 | 74 | 50 | 57 | 38 |
+| F | 28 | 49 | 41 | 88 | 80 | 42 | 80 | 20 | 64 | 3 | 24 | 70 |
+| G | 93 | 76 | 9 | 97 | 2 | 37 | 79 | 54 | 79 | 12 | 64 | 7 |
+| H | 51 | 60 | 79 | 56 | 2 | 49 | 49 | 45 | 41 | 21 | 10 | 30 |
+| I | 52 | 54 | 76 | 43 | 8 | 34 | 29 | 22 | 34 | 71 | 70 | 41 |
+| J | 70 | 61 | 92 | 55 | 2 | 53 | 11 | 87 | 79 | 11 | 68 | 9 |
+| K | 91 | 44 | 37 | 85 | 1 | 50 | 84 | 94 | 41 | 43 | 76 | 93 |
+| L | 69 | 20 | 80 | 22 | 95 | 8 | 60 | 6 | 93 | 64 | 39 | 99 |
+
+## creator_id=D
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 65 | 53 | 92 | 66 | 76 | 31 | 90 | 38 | 67 | 59 | 80 | 93 |
+| B | 47 | 8 | 3 | 65 | 14 | 80 | 93 | 76 | 12 | 6 | 19 | 50 |
+| C | 48 | 23 | 54 | 56 | 91 | 6 | 73 | 75 | 51 | 5 | 61 | 16 |
+| D | 74 | 52 | 38 | 95 | 48 | 13 | 44 | 33 | 29 | 88 | 80 | 95 |
+| E | 97 | 70 | 16 | 81 | 85 | 45 | 65 | 46 | 21 | 43 | 92 | 0 |
+| F | 33 | 6 | 35 | 50 | 47 | 18 | 46 | 42 | 89 | 48 | 38 | 53 |
+| G | 67 | 91 | 25 | 91 | 30 | 60 | 89 | 5 | 14 | 19 | 21 | 35 |
+| H | 69 | 20 | 12 | 82 | 42 | 78 | 17 | 28 | 37 | 38 | 76 | 42 |
+| I | 28 | 36 | 45 | 40 | 56 | 50 | 36 | 64 | 71 | 61 | 5 | 2 |
+| J | 20 | 25 | 25 | 84 | 22 | 35 | 63 | 34 | 40 | 96 | 81 | 61 |
+| K | 15 | 94 | 95 | 35 | 18 | 86 | 20 | 73 | 86 | 76 | 74 | 94 |
+| L | 39 | 72 | 60 | 23 | 97 | 48 | 83 | 54 | 86 | 60 | 48 | 78 |
+
+## creator_id=E
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 25 | 33 | 50 | 9 | 61 | 46 | 42 | 87 | 14 | 91 | 29 | 16 |
+| B | 42 | 47 | 83 | 64 | 27 | 67 | 26 | 67 | 74 | 46 | 81 | 81 |
+| C | 20 | 40 | 15 | 88 | 69 | 59 | 80 | 61 | 12 | 92 | 92 | 7 |
+| D | 19 | 98 | 52 | 84 | 32 | 56 | 77 | 43 | 12 | 4 | 76 | 13 |
+| E | 22 | 61 | 22 | 48 | 29 | 20 | 89 | 14 | 7 | 1 | 41 | 16 |
+| F | 91 | 51 | 47 | 96 | 90 | 38 | 92 | 44 | 40 | 73 | 54 | 88 |
+| G | 16 | 74 | 80 | 47 | 78 | 77 | 16 | 48 | 0 | 65 | 25 | 64 |
+| H | 9 | 20 | 61 | 59 | 55 | 56 | 56 | 34 | 43 | 34 | 20 | 73 |
+| I | 28 | 50 | 56 | 8 | 38 | 78 | 72 | 66 | 0 | 35 | 53 | 54 |
+| J | 80 | 58 | 59 | 28 | 35 | 90 | 87 | 64 | 86 | 2 | 49 | 63 |
+| K | 26 | 98 | 13 | 97 | 14 | 71 | 28 | 16 | 88 | 82 | 26 | 78 |
+| L | 44 | 22 | 4 | 97 | 87 | 65 | 85 | 21 | 2 | 85 | 96 | 32 |
+
+## creator_id=F
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 66 | 18 | 77 | 35 | 83 | 12 | 89 | 46 | 98 | 72 | 30 | 83 |
+| B | 45 | 60 | 1 | 47 | 63 | 78 | 65 | 27 | 70 | 88 | 70 | 79 |
+| C | 14 | 90 | 78 | 99 | 53 | 31 | 94 | 19 | 25 | 1 | 55 | 59 |
+| D | 22 | 92 | 60 | 92 | 27 | 68 | 12 | 69 | 0 | 44 | 56 | 0 |
+| E | 85 | 53 | 38 | 54 | 48 | 78 | 13 | 41 | 74 | 29 | 36 | 45 |
+| F | 40 | 85 | 44 | 31 | 20 | 59 | 40 | 95 | 55 | 73 | 77 | 23 |
+| G | 74 | 16 | 32 | 52 | 50 | 2 | 86 | 77 | 49 | 14 | 74 | 89 |
+| H | 47 | 17 | 13 | 38 | 69 | 18 | 57 | 56 | 53 | 22 | 29 | 48 |
+| I | 90 | 59 | 40 | 74 | 75 | 75 | 72 | 37 | 27 | 4 | 8 | 87 |
+| J | 90 | 47 | 63 | 67 | 75 | 79 | 61 | 25 | 38 | 80 | 85 | 91 |
+| K | 68 | 18 | 54 | 10 | 82 | 52 | 97 | 7 | 96 | 43 | 46 | 22 |
+| L | 65 | 13 | 12 | 44 | 14 | 4 | 42 | 16 | 34 | 60 | 95 | 50 |
+
+## creator_id=G
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 34 | 55 | 25 | 67 | 78 | 44 | 70 | 94 | 37 | 86 | 64 | 24 |
+| B | 53 | 22 | 6 | 53 | 93 | 53 | 18 | 24 | 9 | 58 | 58 | 43 |
+| C | 77 | 78 | 83 | 89 | 90 | 32 | 2 | 46 | 79 | 68 | 79 | 9 |
+| D | 29 | 30 | 11 | 89 | 61 | 17 | 88 | 37 | 25 | 95 | 43 | 44 |
+| E | 51 | 68 | 0 | 97 | 48 | 31 | 17 | 41 | 12 | 16 | 70 | 52 |
+| F | 45 | 24 | 57 | 24 | 11 | 72 | 65 | 60 | 3 | 82 | 30 | 87 |
+| G | 52 | 47 | 36 | 53 | 17 | 79 | 23 | 28 | 34 | 73 | 99 | 25 |
+| H | 83 | 28 | 45 | 7 | 60 | 60 | 62 | 7 | 0 | 60 | 27 | 50 |
+| I | 57 | 68 | 62 | 20 | 22 | 88 | 98 | 15 | 52 | 33 | 65 | 18 |
+| J | 91 | 12 | 86 | 8 | 29 | 95 | 27 | 66 | 57 | 36 | 60 | 70 |
+| K | 92 | 14 | 1 | 22 | 33 | 37 | 20 | 24 | 82 | 7 | 6 | 20 |
+| L | 64 | 39 | 65 | 8 | 15 | 23 | 5 | 97 | 47 | 81 | 3 | 21 |
+
+## creator_id=H
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 15 | 29 | 91 | 70 | 49 | 83 | 52 | 77 | 9 | 50 | 73 | 34 |
+| B | 86 | 33 | 42 | 50 | 69 | 69 | 61 | 92 | 93 | 9 | 33 | 94 |
+| C | 43 | 17 | 87 | 25 | 37 | 30 | 50 | 79 | 53 | 28 | 33 | 65 |
+| D | 88 | 48 | 93 | 72 | 29 | 94 | 69 | 18 | 15 | 84 | 41 | 88 |
+| E | 3 | 67 | 26 | 35 | 51 | 57 | 42 | 89 | 99 | 4 | 85 | 44 |
+| F | 59 | 15 | 34 | 11 | 16 | 81 | 83 | 92 | 64 | 26 | 39 | 46 |
+| G | 29 | 41 | 89 | 33 | 1 | 54 | 62 | 20 | 61 | 64 | 51 | 64 |
+| H | 84 | 60 | 4 | 49 | 68 | 47 | 95 | 86 | 72 | 35 | 82 | 5 |
+| I | 92 | 11 | 36 | 32 | 97 | 3 | 75 | 43 | 8 | 68 | 36 | 59 |
+| J | 5 | 92 | 59 | 19 | 95 | 90 | 79 | 47 | 98 | 84 | 29 | 5 |
+| K | 11 | 18 | 55 | 19 | 61 | 82 | 30 | 95 | 1 | 70 | 35 | 13 |
+| L | 15 | 92 | 37 | 3 | 73 | 61 | 38 | 67 | 67 | 27 | 95 | 91 |
+
+## creator_id=I
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 8 | 7 | 39 | 94 | 17 | 41 | 78 | 12 | 19 | 67 | 72 | 94 |
+| B | 3 | 9 | 12 | 92 | 6 | 79 | 94 | 78 | 73 | 99 | 98 | 28 |
+| C | 12 | 78 | 32 | 5 | 70 | 14 | 35 | 55 | 69 | 96 | 33 | 64 |
+| D | 43 | 70 | 13 | 13 | 44 | 96 | 56 | 72 | 13 | 29 | 98 | 1 |
+| E | 91 | 31 | 94 | 52 | 2 | 86 | 17 | 42 | 55 | 6 | 79 | 81 |
+| F | 92 | 60 | 91 | 88 | 53 | 32 | 55 | 32 | 19 | 0 | 63 | 15 |
+| G | 12 | 1 | 47 | 90 | 59 | 83 | 43 | 15 | 70 | 93 | 76 | 95 |
+| H | 67 | 80 | 55 | 92 | 9 | 40 | 51 | 60 | 25 | 18 | 56 | 30 |
+| I | 1 | 34 | 26 | 64 | 66 | 3 | 79 | 60 | 45 | 86 | 52 | 20 |
+| J | 18 | 61 | 58 | 50 | 19 | 45 | 41 | 92 | 73 | 92 | 58 | 7 |
+| K | 21 | 24 | 0 | 88 | 84 | 35 | 18 | 27 | 4 | 59 | 75 | 0 |
+| L | 45 | 21 | 73 | 2 | 87 | 36 | 24 | 30 | 75 | 38 | 94 | 68 |
+
+## creator_id=J
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 3 | 94 | 90 | 59 | 74 | 50 | 94 | 16 | 0 | 98 | 91 | 97 |
+| B | 99 | 21 | 85 | 41 | 84 | 90 | 14 | 78 | 91 | 54 | 73 | 7 |
+| C | 39 | 36 | 56 | 36 | 68 | 74 | 81 | 31 | 27 | 77 | 15 | 46 |
+| D | 45 | 77 | 98 | 19 | 1 | 48 | 62 | 26 | 77 | 94 | 82 | 94 |
+| E | 93 | 14 | 71 | 70 | 43 | 67 | 42 | 26 | 10 | 0 | 8 | 57 |
+| F | 76 | 46 | 16 | 91 | 41 | 85 | 16 | 15 | 52 | 10 | 40 | 76 |
+| G | 64 | 58 | 91 | 90 | 13 | 88 | 64 | 95 | 28 | 14 | 23 | 11 |
+| H | 86 | 25 | 53 | 11 | 14 | 43 | 86 | 21 | 26 | 35 | 16 | 39 |
+| I | 78 | 10 | 76 | 25 | 65 | 72 | 64 | 82 | 26 | 22 | 34 | 20 |
+| J | 25 | 74 | 33 | 21 | 48 | 11 | 87 | 98 | 97 | 41 | 39 | 18 |
+| K | 81 | 44 | 72 | 71 | 42 | 80 | 93 | 71 | 73 | 70 | 24 | 71 |
+| L | 32 | 20 | 23 | 13 | 5 | 57 | 55 | 99 | 56 | 0 | 72 | 56 |
+
+## creator_id=K
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 54 | 90 | 47 | 55 | 90 | 83 | 61 | 69 | 67 | 2 | 40 | 96 |
+| B | 77 | 64 | 25 | 92 | 65 | 68 | 66 | 40 | 1 | 35 | 6 | 69 |
+| C | 69 | 36 | 15 | 39 | 22 | 44 | 55 | 73 | 38 | 27 | 78 | 34 |
+| D | 60 | 49 | 36 | 93 | 18 | 59 | 16 | 83 | 87 | 41 | 1 | 2 |
+| E | 93 | 98 | 10 | 14 | 38 | 76 | 10 | 96 | 71 | 18 | 54 | 66 |
+| F | 92 | 65 | 15 | 14 | 26 | 48 | 21 | 51 | 50 | 9 | 49 | 78 |
+| G | 81 | 20 | 71 | 48 | 41 | 87 | 57 | 2 | 66 | 60 | 42 | 58 |
+| H | 99 | 33 | 13 | 99 | 46 | 6 | 73 | 96 | 22 | 63 | 69 | 31 |
+| I | 94 | 5 | 70 | 97 | 44 | 31 | 53 | 98 | 69 | 85 | 37 | 41 |
+| J | 16 | 10 | 61 | 47 | 97 | 57 | 52 | 17 | 34 | 22 | 78 | 99 |
+| K | 69 | 63 | 48 | 6 | 24 | 33 | 94 | 97 | 50 | 68 | 82 | 42 |
+| L | 35 | 18 | 65 | 30 | 39 | 42 | 76 | 45 | 94 | 95 | 23 | 96 |
+
+## creator_id=L
+| camera_kit_id\editing_slot_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 62 | 89 | 50 | 10 | 13 | 46 | 42 | 85 | 72 | 80 | 24 |
+| B | 23 | 92 | 46 | 58 | 31 | 82 | 55 | 35 | 15 | 75 | 28 | 2 |
+| C | 46 | 27 | 25 | 29 | 88 | 51 | 12 | 91 | 5 | 21 | 46 | 77 |
+| D | 88 | 80 | 14 | 25 | 47 | 38 | 49 | 22 | 9 | 27 | 68 | 19 |
+| E | 90 | 81 | 8 | 86 | 25 | 62 | 48 | 37 | 94 | 74 | 50 | 91 |
+| F | 59 | 11 | 31 | 49 | 50 | 40 | 54 | 35 | 95 | 27 | 57 | 4 |
+| G | 82 | 48 | 46 | 11 | 57 | 26 | 12 | 71 | 39 | 26 | 36 | 3 |
+| H | 45 | 29 | 91 | 48 | 89 | 12 | 35 | 2 | 0 | 37 | 40 | 35 |
+| I | 26 | 18 | 75 | 27 | 5 | 14 | 56 | 63 | 83 | 2 | 79 | 44 |
+| J | 83 | 79 | 76 | 30 | 72 | 94 | 63 | 55 | 80 | 64 | 39 | 87 |
+| K | 68 | 62 | 76 | 51 | 54 | 49 | 64 | 6 | 83 | 32 | 77 | 39 |
+| L | 22 | 15 | 40 | 34 | 91 | 48 | 62 | 92 | 78 | 96 | 66 | 28 |
+
+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': [[[43, 44, 15, 80, 30, 93, 8, 70, 52, 21, 70, 30], [86, 20, 51, 51, 38, 51, 44, 16, 30, 81, 23, 8], [30, 48, 91, 57, 46, 23, 13, 54, 14, 38, 57, 16], [28, 40, 57, 67, 35, 54, 63, 2, 11, 68, 76, 28], [67, 71, 74, 1, 72, 8, 4, 57, 76, 22, 47, 6], [56, 64, 15, 96, 12, 28, 32, 23, 8, 7, 87, 41], [12, 21, 46, 47, 90, 25, 37, 58, 38, 89, 6, 94], [84, 35, 53, 59, 64, 75, 56, 78, 92, 87, 45, 5], [82, 59, 44, 86, 80, 94, 72, 84, 22, 62, 48, 47], [68, 58, 98, 84, 30, 46, 47, 31, 30, 48, 31, 62], [79, 98, 17, 92, 55, 67, 71, 42, 7, 88, 33, 72], [99, 70, 65, 33, 78, 89, 81, 76, 52, 4, 2, 48]], [[83, 41, 88, 98, 98, 74, 77, 60, 38, 4, 54, 53], [91, 4, 0, 56, 46, 32, 46, 51, 29, 9, 0, 61], [77, 20, 94, 41, 26, 1, 69, 88, 9, 52, 92, 37], [71, 63, 49, 9, 34, 41, 31, 61, 44, 15, 9, 65], [79, 7, 46, 10, 6, 16, 46, 65, 82, 46, 67, 99], [15, 34, 38, 60, 76, 48, 32, 55, 68, 73, 22, 94], [16, 20, 23, 95, 13, 60, 43, 30, 71, 78, 70, 45], [90, 35, 87, 72, 2, 27, 69, 13, 79, 43, 66, 36], [65, 88, 37, 18, 3, 33, 58, 59, 88, 28, 0, 51], [38, 89, 80, 20, 62, 87, 87, 49, 58, 45, 81, 68], [89, 54, 69, 38, 28, 19, 72, 42, 93, 76, 88, 4], [13, 49, 22, 81, 47, 13, 23, 19, 51, 67, 58, 77]], [[40, 5, 88, 21, 82, 56, 82, 92, 39, 83, 41, 77], [77, 23, 50, 2, 10, 9, 90, 67, 60, 84, 41, 54], [3, 46, 62, 31, 3, 99, 87, 51, 20, 80, 83, 18], [72, 5, 29, 72, 68, 0, 11, 84, 80, 79, 98, 9], [47, 43, 9, 3, 90, 11, 0, 19, 74, 50, 57, 38], [28, 49, 41, 88, 80, 42, 80, 20, 64, 3, 24, 70], [93, 76, 9, 97, 2, 37, 79, 54, 79, 12, 64, 7], [51, 60, 79, 56, 2, 49, 49, 45, 41, 21, 10, 30], [52, 54, 76, 43, 8, 34, 29, 22, 34, 71, 70, 41], [70, 61, 92, 55, 2, 53, 11, 87, 79, 11, 68, 9], [91, 44, 37, 85, 1, 50, 84, 94, 41, 43, 76, 93], [69, 20, 80, 22, 95, 8, 60, 6, 93, 64, 39, 99]], [[65, 53, 92, 66, 76, 31, 90, 38, 67, 59, 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'j': 'F', 'k': 'E', 'cost': 50}, {'i': 'L', 'j': 'F', 'k': 'F', 'cost': 40}, {'i': 'L', 'j': 'F', 'k': 'G', 'cost': 54}, {'i': 'L', 'j': 'F', 'k': 'H', 'cost': 35}, {'i': 'L', 'j': 'F', 'k': 'I', 'cost': 95}, {'i': 'L', 'j': 'F', 'k': 'J', 'cost': 27}, {'i': 'L', 'j': 'F', 'k': 'K', 'cost': 57}, {'i': 'L', 'j': 'F', 'k': 'L', 'cost': 4}, {'i': 'L', 'j': 'G', 'k': 'A', 'cost': 82}, {'i': 'L', 'j': 'G', 'k': 'B', 'cost': 48}, {'i': 'L', 'j': 'G', 'k': 'C', 'cost': 46}, {'i': 'L', 'j': 'G', 'k': 'D', 'cost': 11}, {'i': 'L', 'j': 'G', 'k': 'E', 'cost': 57}, {'i': 'L', 'j': 'G', 'k': 'F', 'cost': 26}, {'i': 'L', 'j': 'G', 'k': 'G', 'cost': 12}, {'i': 'L', 'j': 'G', 'k': 'H', 'cost': 71}, {'i': 'L', 'j': 'G', 'k': 'I', 'cost': 39}, {'i': 'L', 'j': 'G', 'k': 'J', 'cost': 26}, {'i': 'L', 'j': 'G', 'k': 'K', 'cost': 36}, {'i': 'L', 'j': 'G', 'k': 'L', 'cost': 3}, {'i': 'L', 'j': 'H', 'k': 'A', 'cost': 45}, {'i': 'L', 'j': 'H', 'k': 'B', 'cost': 29}, {'i': 'L', 'j': 'H', 'k': 'C', 'cost': 91}, {'i': 'L', 'j': 'H', 'k': 'D', 'cost': 48}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 89}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 12}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 35}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 2}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 0}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 37}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 40}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 35}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 26}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 18}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 75}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 27}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 5}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 14}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 56}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 63}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 83}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 2}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 79}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 44}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 83}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 79}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 76}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 30}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 72}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 94}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 63}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 55}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 80}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 64}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 39}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 87}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 68}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 62}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 76}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 51}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 54}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 49}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 64}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 6}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 83}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 32}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 77}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 39}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 22}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 15}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 40}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 34}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 91}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 48}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 62}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 92}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 78}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 96}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 66}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 28}]}","[['A', 'E', 'D'], ['B', 'B', 'B'], ['C', 'J', 'E'], ['D', 'I', 'L'], ['E', 'L', 'C'], ['F', 'G', 'F'], ['G', 'C', 'G'], ['H', 'K', 'I'], ['I', 'F', 'J'], ['J', 'A', 'A'], ['K', 'D', 'K'], ['L', 'H', 'H']]",19,json,names
+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.
+
+The concrete cost table follows for 9 prototypes: 1, 2, 3, 4, 5, 6, 7, 8, 9.
+
+*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 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 29 | 3 | 95 | 85 | 14 | 24 | 24 | 2 | 47 |
+| 2 | 91 | 17 | 27 | 13 | 9 | 89 | 81 | 81 | 6 |
+| 3 | 80 | 73 | 54 | 72 | 27 | 5 | 9 | 27 | 91 |
+| 4 | 21 | 74 | 50 | 34 | 89 | 53 | 65 | 76 | 17 |
+| 5 | 67 | 37 | 12 | 30 | 92 | 29 | 77 | 45 | 32 |
+| 6 | 7 | 52 | 27 | 16 | 9 | 20 | 9 | 85 | 97 |
+| 7 | 27 | 19 | 26 | 78 | 69 | 52 | 83 | 80 | 8 |
+| 8 | 16 | 49 | 39 | 43 | 47 | 23 | 71 | 51 | 88 |
+| 9 | 73 | 67 | 61 | 70 | 67 | 32 | 95 | 94 | 56 |
+
+## prototype_id=2
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 19 | 20 | 60 | 18 | 1 | 63 | 87 | 84 | 81 |
+| 2 | 60 | 35 | 55 | 69 | 63 | 93 | 62 | 45 | 43 |
+| 3 | 97 | 12 | 36 | 98 | 96 | 86 | 77 | 44 | 6 |
+| 4 | 80 | 3 | 53 | 77 | 29 | 62 | 97 | 51 | 97 |
+| 5 | 90 | 28 | 98 | 89 | 81 | 9 | 82 | 42 | 92 |
+| 6 | 1 | 12 | 27 | 77 | 85 | 20 | 41 | 12 | 99 |
+| 7 | 19 | 1 | 30 | 93 | 0 | 4 | 3 | 43 | 72 |
+| 8 | 52 | 98 | 64 | 41 | 84 | 87 | 12 | 72 | 7 |
+| 9 | 49 | 57 | 40 | 93 | 45 | 52 | 25 | 57 | 2 |
+
+## prototype_id=3
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 76 | 93 | 27 | 2 | 34 | 60 | 84 | 39 | 83 |
+| 2 | 35 | 52 | 68 | 53 | 92 | 76 | 94 | 41 | 54 |
+| 3 | 10 | 43 | 37 | 78 | 22 | 18 | 63 | 3 | 51 |
+| 4 | 66 | 59 | 91 | 79 | 38 | 14 | 34 | 34 | 66 |
+| 5 | 80 | 89 | 4 | 85 | 68 | 52 | 9 | 5 | 47 |
+| 6 | 50 | 36 | 79 | 1 | 39 | 54 | 65 | 15 | 51 |
+| 7 | 37 | 24 | 87 | 54 | 50 | 3 | 19 | 7 | 52 |
+| 8 | 3 | 82 | 75 | 12 | 22 | 70 | 16 | 3 | 98 |
+| 9 | 11 | 61 | 7 | 71 | 64 | 3 | 22 | 55 | 88 |
+
+## prototype_id=4
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 41 | 54 | 12 | 70 | 88 | 78 | 26 | 22 | 37 |
+| 2 | 56 | 30 | 98 | 52 | 30 | 30 | 62 | 82 | 44 |
+| 3 | 76 | 29 | 44 | 52 | 95 | 80 | 43 | 94 | 73 |
+| 4 | 66 | 3 | 23 | 12 | 7 | 95 | 74 | 75 | 23 |
+| 5 | 6 | 73 | 22 | 38 | 87 | 78 | 84 | 84 | 92 |
+| 6 | 67 | 23 | 90 | 93 | 33 | 75 | 35 | 98 | 56 |
+| 7 | 98 | 48 | 11 | 65 | 61 | 95 | 85 | 90 | 12 |
+| 8 | 99 | 6 | 9 | 26 | 48 | 42 | 62 | 44 | 46 |
+| 9 | 37 | 61 | 53 | 45 | 78 | 52 | 66 | 10 | 24 |
+
+## prototype_id=5
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 23 | 17 | 6 | 29 | 83 | 74 | 47 | 24 | 66 |
+| 2 | 76 | 67 | 90 | 43 | 13 | 75 | 73 | 2 | 99 |
+| 3 | 4 | 58 | 25 | 22 | 17 | 87 | 12 | 1 | 27 |
+| 4 | 56 | 67 | 92 | 17 | 44 | 99 | 51 | 8 | 85 |
+| 5 | 18 | 70 | 10 | 70 | 94 | 37 | 5 | 74 | 56 |
+| 6 | 9 | 61 | 25 | 35 | 48 | 38 | 57 | 52 | 84 |
+| 7 | 17 | 23 | 52 | 90 | 97 | 62 | 11 | 84 | 66 |
+| 8 | 21 | 21 | 7 | 44 | 12 | 7 | 80 | 30 | 78 |
+| 9 | 77 | 33 | 8 | 16 | 48 | 25 | 88 | 41 | 49 |
+
+## prototype_id=6
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 22 | 86 | 51 | 88 | 75 | 78 | 51 | 51 | 12 |
+| 2 | 52 | 52 | 16 | 11 | 23 | 49 | 85 | 4 | 76 |
+| 3 | 78 | 30 | 73 | 96 | 45 | 93 | 50 | 0 | 60 |
+| 4 | 21 | 7 | 46 | 32 | 98 | 95 | 84 | 99 | 86 |
+| 5 | 46 | 87 | 66 | 88 | 49 | 8 | 0 | 81 | 65 |
+| 6 | 57 | 13 | 62 | 92 | 92 | 85 | 20 | 33 | 12 |
+| 7 | 11 | 91 | 98 | 11 | 3 | 27 | 81 | 29 | 88 |
+| 8 | 7 | 21 | 41 | 84 | 27 | 40 | 10 | 76 | 32 |
+| 9 | 52 | 68 | 1 | 92 | 10 | 79 | 27 | 58 | 64 |
+
+## prototype_id=7
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 94 | 2 | 68 | 42 | 0 | 11 | 38 | 50 | 28 |
+| 2 | 97 | 74 | 78 | 56 | 86 | 19 | 3 | 82 | 19 |
+| 3 | 54 | 67 | 4 | 23 | 47 | 88 | 54 | 18 | 1 |
+| 4 | 49 | 67 | 97 | 10 | 42 | 11 | 86 | 0 | 0 |
+| 5 | 0 | 36 | 25 | 40 | 79 | 77 | 97 | 78 | 35 |
+| 6 | 10 | 22 | 65 | 21 | 71 | 6 | 29 | 3 | 72 |
+| 7 | 20 | 21 | 29 | 26 | 16 | 83 | 37 | 48 | 26 |
+| 8 | 32 | 6 | 41 | 23 | 50 | 27 | 53 | 48 | 2 |
+| 9 | 61 | 33 | 80 | 28 | 23 | 11 | 20 | 99 | 12 |
+
+## prototype_id=8
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 35 | 68 | 92 | 76 | 50 | 21 | 50 | 48 | 18 |
+| 2 | 75 | 28 | 18 | 9 | 76 | 84 | 94 | 89 | 63 |
+| 3 | 89 | 79 | 0 | 92 | 78 | 70 | 43 | 57 | 22 |
+| 4 | 93 | 92 | 68 | 38 | 42 | 50 | 14 | 0 | 34 |
+| 5 | 67 | 9 | 32 | 81 | 2 | 77 | 59 | 28 | 98 |
+| 6 | 56 | 2 | 87 | 9 | 4 | 66 | 31 | 61 | 76 |
+| 7 | 91 | 32 | 62 | 7 | 77 | 14 | 62 | 73 | 89 |
+| 8 | 54 | 22 | 98 | 33 | 42 | 10 | 10 | 9 | 20 |
+| 9 | 50 | 0 | 98 | 2 | 28 | 68 | 1 | 34 | 55 |
+
+## prototype_id=9
+| tester_id\rig_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 73 | 46 | 56 | 51 | 73 | 60 | 61 | 69 |
+| 2 | 24 | 56 | 20 | 8 | 80 | 27 | 51 | 84 | 5 |
+| 3 | 47 | 38 | 74 | 2 | 86 | 90 | 2 | 95 | 28 |
+| 4 | 59 | 6 | 68 | 54 | 25 | 98 | 3 | 27 | 44 |
+| 5 | 38 | 27 | 43 | 0 | 36 | 31 | 58 | 55 | 30 |
+| 6 | 4 | 95 | 46 | 34 | 52 | 25 | 57 | 63 | 63 |
+| 7 | 29 | 93 | 59 | 3 | 57 | 67 | 81 | 34 | 52 |
+| 8 | 86 | 54 | 67 | 80 | 96 | 47 | 33 | 27 | 80 |
+| 9 | 99 | 59 | 55 | 31 | 70 | 10 | 20 | 28 | 90 |
+
+Assign one tester and one rig to each of the 9 prototypes so the total testing cost is minimized.
+
+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': [[[29, 3, 95, 85, 14, 24, 24, 2, 47], [91, 17, 27, 13, 9, 89, 81, 81, 6], [80, 73, 54, 72, 27, 5, 9, 27, 91], [21, 74, 50, 34, 89, 53, 65, 76, 17], [67, 37, 12, 30, 92, 29, 77, 45, 32], [7, 52, 27, 16, 9, 20, 9, 85, 97], [27, 19, 26, 78, 69, 52, 83, 80, 8], [16, 49, 39, 43, 47, 23, 71, 51, 88], [73, 67, 61, 70, 67, 32, 95, 94, 56]], [[19, 20, 60, 18, 1, 63, 87, 84, 81], [60, 35, 55, 69, 63, 93, 62, 45, 43], [97, 12, 36, 98, 96, 86, 77, 44, 6], [80, 3, 53, 77, 29, 62, 97, 51, 97], [90, 28, 98, 89, 81, 9, 82, 42, 92], [1, 12, 27, 77, 85, 20, 41, 12, 99], [19, 1, 30, 93, 0, 4, 3, 43, 72], [52, 98, 64, 41, 84, 87, 12, 72, 7], [49, 57, 40, 93, 45, 52, 25, 57, 2]], [[76, 93, 27, 2, 34, 60, 84, 39, 83], [35, 52, 68, 53, 92, 76, 94, 41, 54], [10, 43, 37, 78, 22, 18, 63, 3, 51], [66, 59, 91, 79, 38, 14, 34, 34, 66], [80, 89, 4, 85, 68, 52, 9, 5, 47], [50, 36, 79, 1, 39, 54, 65, 15, 51], [37, 24, 87, 54, 50, 3, 19, 7, 52], [3, 82, 75, 12, 22, 70, 16, 3, 98], [11, 61, 7, 71, 64, 3, 22, 55, 88]], [[41, 54, 12, 70, 88, 78, 26, 22, 37], [56, 30, 98, 52, 30, 30, 62, 82, 44], [76, 29, 44, 52, 95, 80, 43, 94, 73], [66, 3, 23, 12, 7, 95, 74, 75, 23], [6, 73, 22, 38, 87, 78, 84, 84, 92], [67, 23, 90, 93, 33, 75, 35, 98, 56], [98, 48, 11, 65, 61, 95, 85, 90, 12], [99, 6, 9, 26, 48, 42, 62, 44, 46], [37, 61, 53, 45, 78, 52, 66, 10, 24]], [[23, 17, 6, 29, 83, 74, 47, 24, 66], [76, 67, 90, 43, 13, 75, 73, 2, 99], [4, 58, 25, 22, 17, 87, 12, 1, 27], [56, 67, 92, 17, 44, 99, 51, 8, 85], [18, 70, 10, 70, 94, 37, 5, 74, 56], [9, 61, 25, 35, 48, 38, 57, 52, 84], [17, 23, 52, 90, 97, 62, 11, 84, 66], [21, 21, 7, 44, 12, 7, 80, 30, 78], [77, 33, 8, 16, 48, 25, 88, 41, 49]], [[22, 86, 51, 88, 75, 78, 51, 51, 12], [52, 52, 16, 11, 23, 49, 85, 4, 76], [78, 30, 73, 96, 45, 93, 50, 0, 60], [21, 7, 46, 32, 98, 95, 84, 99, 86], [46, 87, 66, 88, 49, 8, 0, 81, 65], [57, 13, 62, 92, 92, 85, 20, 33, 12], [11, 91, 98, 11, 3, 27, 81, 29, 88], [7, 21, 41, 84, 27, 40, 10, 76, 32], [52, 68, 1, 92, 10, 79, 27, 58, 64]], [[94, 2, 68, 42, 0, 11, 38, 50, 28], [97, 74, 78, 56, 86, 19, 3, 82, 19], [54, 67, 4, 23, 47, 88, 54, 18, 1], [49, 67, 97, 10, 42, 11, 86, 0, 0], [0, 36, 25, 40, 79, 77, 97, 78, 35], [10, 22, 65, 21, 71, 6, 29, 3, 72], [20, 21, 29, 26, 16, 83, 37, 48, 26], [32, 6, 41, 23, 50, 27, 53, 48, 2], [61, 33, 80, 28, 23, 11, 20, 99, 12]], [[35, 68, 92, 76, 50, 21, 50, 48, 18], [75, 28, 18, 9, 76, 84, 94, 89, 63], [89, 79, 0, 92, 78, 70, 43, 57, 22], [93, 92, 68, 38, 42, 50, 14, 0, 34], [67, 9, 32, 81, 2, 77, 59, 28, 98], [56, 2, 87, 9, 4, 66, 31, 61, 76], [91, 32, 62, 7, 77, 14, 62, 73, 89], [54, 22, 98, 33, 42, 10, 10, 9, 20], [50, 0, 98, 2, 28, 68, 1, 34, 55]], [[34, 73, 46, 56, 51, 73, 60, 61, 69], [24, 56, 20, 8, 80, 27, 51, 84, 5], [47, 38, 74, 2, 86, 90, 2, 95, 28], [59, 6, 68, 54, 25, 98, 3, 27, 44], [38, 27, 43, 0, 36, 31, 58, 55, 30], [4, 95, 46, 34, 52, 25, 57, 63, 63], [29, 93, 59, 3, 57, 67, 81, 34, 52], [86, 54, 67, 80, 96, 47, 33, 27, 80], [99, 59, 55, 31, 70, 10, 20, 28, 90]]], 'objective': 21.0}","[[0, 1, 8], [1, 5, 0], [2, 6, 5], [3, 3, 1], [4, 7, 2], [5, 2, 7], [6, 0, 4], [7, 8, 6], [8, 4, 3]]",21.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 29}, {'i': 1, 'j': 1, 'k': 2, 'cost': 3}, {'i': 1, 'j': 1, 'k': 3, 'cost': 95}, {'i': 1, 'j': 1, 'k': 4, 'cost': 85}, {'i': 1, 'j': 1, 'k': 5, 'cost': 14}, {'i': 1, 'j': 1, 'k': 6, 'cost': 24}, {'i': 1, 'j': 1, 'k': 7, 'cost': 24}, {'i': 1, 'j': 1, 'k': 8, 'cost': 2}, {'i': 1, 'j': 1, 'k': 9, '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': 27}, {'i': 1, 'j': 2, 'k': 4, 'cost': 13}, {'i': 1, 'j': 2, 'k': 5, 'cost': 9}, {'i': 1, 'j': 2, 'k': 6, 'cost': 89}, {'i': 1, 'j': 2, 'k': 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'k': 1, 'cost': 34}, {'i': 9, 'j': 1, 'k': 2, 'cost': 73}, {'i': 9, 'j': 1, 'k': 3, 'cost': 46}, {'i': 9, 'j': 1, 'k': 4, 'cost': 56}, {'i': 9, 'j': 1, 'k': 5, 'cost': 51}, {'i': 9, 'j': 1, 'k': 6, 'cost': 73}, {'i': 9, 'j': 1, 'k': 7, 'cost': 60}, {'i': 9, 'j': 1, 'k': 8, 'cost': 61}, {'i': 9, 'j': 1, 'k': 9, 'cost': 69}, {'i': 9, 'j': 2, 'k': 1, 'cost': 24}, {'i': 9, 'j': 2, 'k': 2, 'cost': 56}, {'i': 9, 'j': 2, 'k': 3, 'cost': 20}, {'i': 9, 'j': 2, 'k': 4, 'cost': 8}, {'i': 9, 'j': 2, 'k': 5, 'cost': 80}, {'i': 9, 'j': 2, 'k': 6, 'cost': 27}, {'i': 9, 'j': 2, 'k': 7, 'cost': 51}, {'i': 9, 'j': 2, 'k': 8, 'cost': 84}, {'i': 9, 'j': 2, 'k': 9, 'cost': 5}, {'i': 9, 'j': 3, 'k': 1, 'cost': 47}, {'i': 9, 'j': 3, 'k': 2, 'cost': 38}, {'i': 9, 'j': 3, 'k': 3, 'cost': 74}, {'i': 9, 'j': 3, 'k': 4, 'cost': 2}, {'i': 9, 'j': 3, 'k': 5, 'cost': 86}, {'i': 9, 'j': 3, 'k': 6, 'cost': 90}, {'i': 9, 'j': 3, 'k': 7, 'cost': 2}, {'i': 9, 'j': 3, 'k': 8, 'cost': 95}, {'i': 9, 'j': 3, 'k': 9, 'cost': 28}, {'i': 9, 'j': 4, 'k': 1, 'cost': 59}, {'i': 9, 'j': 4, 'k': 2, 'cost': 6}, {'i': 9, 'j': 4, 'k': 3, 'cost': 68}, {'i': 9, 'j': 4, 'k': 4, 'cost': 54}, {'i': 9, 'j': 4, 'k': 5, 'cost': 25}, {'i': 9, 'j': 4, 'k': 6, 'cost': 98}, {'i': 9, 'j': 4, 'k': 7, 'cost': 3}, {'i': 9, 'j': 4, 'k': 8, 'cost': 27}, {'i': 9, 'j': 4, 'k': 9, 'cost': 44}, {'i': 9, 'j': 5, 'k': 1, 'cost': 38}, {'i': 9, 'j': 5, 'k': 2, 'cost': 27}, {'i': 9, 'j': 5, 'k': 3, 'cost': 43}, {'i': 9, 'j': 5, 'k': 4, 'cost': 0}, {'i': 9, 'j': 5, 'k': 5, 'cost': 36}, {'i': 9, 'j': 5, 'k': 6, 'cost': 31}, {'i': 9, 'j': 5, 'k': 7, 'cost': 58}, {'i': 9, 'j': 5, 'k': 8, 'cost': 55}, {'i': 9, 'j': 5, 'k': 9, 'cost': 30}, {'i': 9, 'j': 6, 'k': 1, 'cost': 4}, {'i': 9, 'j': 6, 'k': 2, 'cost': 95}, {'i': 9, 'j': 6, 'k': 3, 'cost': 46}, {'i': 9, 'j': 6, 'k': 4, 'cost': 34}, {'i': 9, 'j': 6, 'k': 5, 'cost': 52}, {'i': 9, 'j': 6, 'k': 6, 'cost': 25}, {'i': 9, 'j': 6, 'k': 7, 'cost': 57}, {'i': 9, 'j': 6, 'k': 8, 'cost': 63}, {'i': 9, 'j': 6, 'k': 9, 'cost': 63}, {'i': 9, 'j': 7, 'k': 1, 'cost': 29}, {'i': 9, 'j': 7, 'k': 2, 'cost': 93}, {'i': 9, 'j': 7, 'k': 3, 'cost': 59}, {'i': 9, 'j': 7, 'k': 4, 'cost': 3}, {'i': 9, 'j': 7, 'k': 5, 'cost': 57}, {'i': 9, 'j': 7, 'k': 6, 'cost': 67}, {'i': 9, 'j': 7, 'k': 7, 'cost': 81}, {'i': 9, 'j': 7, 'k': 8, 'cost': 34}, {'i': 9, 'j': 7, 'k': 9, 'cost': 52}, {'i': 9, 'j': 8, 'k': 1, 'cost': 86}, {'i': 9, 'j': 8, 'k': 2, 'cost': 54}, {'i': 9, 'j': 8, 'k': 3, 'cost': 67}, {'i': 9, 'j': 8, 'k': 4, 'cost': 80}, {'i': 9, 'j': 8, 'k': 5, 'cost': 96}, {'i': 9, 'j': 8, 'k': 6, 'cost': 47}, {'i': 9, 'j': 8, 'k': 7, 'cost': 33}, {'i': 9, 'j': 8, 'k': 8, 'cost': 27}, {'i': 9, 'j': 8, 'k': 9, 'cost': 80}, {'i': 9, 'j': 9, 'k': 1, 'cost': 99}, {'i': 9, 'j': 9, 'k': 2, 'cost': 59}, {'i': 9, 'j': 9, 'k': 3, 'cost': 55}, {'i': 9, 'j': 9, 'k': 4, 'cost': 31}, {'i': 9, 'j': 9, 'k': 5, 'cost': 70}, {'i': 9, 'j': 9, 'k': 6, 'cost': 10}, {'i': 9, 'j': 9, 'k': 7, 'cost': 20}, {'i': 9, 'j': 9, 'k': 8, 'cost': 28}, {'i': 9, 'j': 9, 'k': 9, 'cost': 90}]}","[[1, 2, 9], [2, 6, 1], [3, 7, 6], [4, 4, 2], [5, 8, 3], [6, 3, 8], [7, 1, 5], [8, 9, 7], [9, 5, 4]]",20,markdown_table,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.
+
+{
+  ""num_shoots"": 9,
+  ""index_ids"": [
+    0,
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8
+  ]
+}
+
+# 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 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 26 | 46 | 47 | 2 | 58 | 17 | 21 | 0 | 57 |
+| 1 | 43 | 37 | 96 | 27 | 5 | 22 | 37 | 93 | 49 |
+| 2 | 0 | 58 | 70 | 33 | 93 | 52 | 69 | 17 | 25 |
+| 3 | 44 | 73 | 45 | 65 | 55 | 26 | 36 | 71 | 35 |
+| 4 | 3 | 0 | 2 | 21 | 79 | 62 | 39 | 51 | 3 |
+| 5 | 81 | 39 | 81 | 38 | 99 | 70 | 81 | 94 | 7 |
+| 6 | 93 | 80 | 85 | 26 | 82 | 56 | 46 | 53 | 72 |
+| 7 | 29 | 91 | 7 | 32 | 65 | 5 | 94 | 19 | 82 |
+| 8 | 3 | 18 | 7 | 73 | 12 | 93 | 19 | 31 | 82 |
+
+## shoot_id=1
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 5 | 40 | 22 | 90 | 68 | 62 | 4 | 92 | 71 |
+| 1 | 85 | 22 | 63 | 12 | 72 | 83 | 89 | 34 | 90 |
+| 2 | 25 | 40 | 95 | 24 | 12 | 48 | 55 | 31 | 55 |
+| 3 | 27 | 79 | 83 | 75 | 14 | 14 | 47 | 11 | 31 |
+| 4 | 48 | 95 | 82 | 74 | 71 | 72 | 56 | 68 | 15 |
+| 5 | 56 | 94 | 0 | 87 | 63 | 50 | 41 | 69 | 54 |
+| 6 | 65 | 58 | 78 | 75 | 65 | 29 | 91 | 0 | 60 |
+| 7 | 87 | 20 | 73 | 64 | 92 | 3 | 72 | 71 | 74 |
+| 8 | 2 | 25 | 44 | 71 | 54 | 31 | 84 | 67 | 83 |
+
+## shoot_id=2
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 88 | 5 | 52 | 1 | 3 | 59 | 21 | 6 | 71 |
+| 1 | 75 | 95 | 72 | 6 | 68 | 24 | 95 | 73 | 51 |
+| 2 | 99 | 71 | 40 | 47 | 62 | 36 | 6 | 83 | 20 |
+| 3 | 69 | 93 | 66 | 53 | 36 | 65 | 5 | 8 | 57 |
+| 4 | 34 | 41 | 42 | 69 | 58 | 34 | 24 | 82 | 91 |
+| 5 | 95 | 86 | 61 | 12 | 4 | 37 | 77 | 92 | 51 |
+| 6 | 56 | 57 | 64 | 61 | 92 | 22 | 87 | 49 | 55 |
+| 7 | 71 | 2 | 84 | 17 | 92 | 83 | 99 | 28 | 94 |
+| 8 | 67 | 12 | 80 | 62 | 51 | 57 | 40 | 53 | 89 |
+
+## shoot_id=3
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 38 | 99 | 22 | 72 | 5 | 45 | 78 | 71 | 47 |
+| 1 | 43 | 16 | 11 | 71 | 2 | 78 | 58 | 89 | 97 |
+| 2 | 61 | 13 | 25 | 74 | 22 | 60 | 80 | 63 | 71 |
+| 3 | 47 | 62 | 49 | 11 | 50 | 70 | 39 | 58 | 86 |
+| 4 | 60 | 7 | 21 | 38 | 66 | 49 | 96 | 37 | 81 |
+| 5 | 9 | 0 | 15 | 43 | 28 | 47 | 72 | 5 | 3 |
+| 6 | 15 | 20 | 21 | 0 | 93 | 16 | 82 | 76 | 90 |
+| 7 | 36 | 35 | 8 | 40 | 63 | 52 | 37 | 6 | 27 |
+| 8 | 30 | 66 | 94 | 92 | 34 | 17 | 47 | 19 | 94 |
+
+## shoot_id=4
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 18 | 27 | 85 | 12 | 69 | 38 | 88 | 75 | 89 |
+| 1 | 98 | 38 | 22 | 90 | 55 | 32 | 58 | 96 | 4 |
+| 2 | 23 | 15 | 60 | 17 | 80 | 16 | 77 | 62 | 40 |
+| 3 | 82 | 18 | 45 | 9 | 21 | 65 | 32 | 30 | 99 |
+| 4 | 44 | 61 | 43 | 24 | 86 | 60 | 78 | 43 | 88 |
+| 5 | 56 | 98 | 0 | 38 | 0 | 42 | 49 | 17 | 30 |
+| 6 | 0 | 99 | 23 | 1 | 50 | 25 | 68 | 61 | 92 |
+| 7 | 83 | 84 | 86 | 37 | 32 | 39 | 57 | 69 | 35 |
+| 8 | 85 | 83 | 95 | 40 | 77 | 15 | 27 | 35 | 6 |
+
+## shoot_id=5
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 58 | 24 | 13 | 83 | 56 | 52 | 71 | 24 | 84 |
+| 1 | 81 | 55 | 67 | 74 | 45 | 53 | 15 | 81 | 55 |
+| 2 | 21 | 83 | 23 | 99 | 98 | 94 | 6 | 29 | 16 |
+| 3 | 65 | 90 | 44 | 94 | 44 | 16 | 56 | 26 | 97 |
+| 4 | 21 | 93 | 56 | 85 | 14 | 39 | 67 | 22 | 86 |
+| 5 | 81 | 31 | 27 | 88 | 40 | 78 | 48 | 55 | 27 |
+| 6 | 34 | 60 | 34 | 92 | 75 | 94 | 18 | 80 | 47 |
+| 7 | 84 | 91 | 33 | 5 | 84 | 46 | 64 | 1 | 54 |
+| 8 | 69 | 22 | 90 | 32 | 14 | 52 | 80 | 29 | 23 |
+
+## shoot_id=6
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 49 | 86 | 39 | 85 | 96 | 52 | 74 | 46 | 13 |
+| 1 | 36 | 99 | 53 | 74 | 47 | 94 | 31 | 76 | 68 |
+| 2 | 0 | 57 | 11 | 58 | 29 | 62 | 19 | 48 | 24 |
+| 3 | 77 | 84 | 40 | 71 | 5 | 72 | 92 | 38 | 19 |
+| 4 | 20 | 61 | 75 | 13 | 36 | 70 | 5 | 9 | 89 |
+| 5 | 62 | 3 | 70 | 5 | 61 | 50 | 20 | 36 | 62 |
+| 6 | 38 | 72 | 65 | 5 | 62 | 11 | 57 | 25 | 15 |
+| 7 | 96 | 73 | 0 | 63 | 69 | 90 | 28 | 52 | 0 |
+| 8 | 55 | 57 | 56 | 72 | 29 | 25 | 13 | 85 | 14 |
+
+## shoot_id=7
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 68 | 49 | 67 | 0 | 30 | 66 | 49 | 50 | 46 |
+| 1 | 53 | 43 | 57 | 73 | 77 | 6 | 85 | 75 | 21 |
+| 2 | 68 | 45 | 70 | 97 | 61 | 66 | 52 | 15 | 45 |
+| 3 | 97 | 59 | 63 | 90 | 79 | 62 | 43 | 54 | 81 |
+| 4 | 16 | 57 | 67 | 28 | 84 | 63 | 89 | 44 | 55 |
+| 5 | 25 | 63 | 96 | 43 | 67 | 67 | 24 | 25 | 60 |
+| 6 | 82 | 11 | 10 | 20 | 20 | 2 | 62 | 52 | 35 |
+| 7 | 67 | 32 | 74 | 76 | 32 | 97 | 81 | 86 | 87 |
+| 8 | 64 | 9 | 47 | 91 | 71 | 31 | 6 | 37 | 71 |
+
+## shoot_id=8
+| photographer_id\kit_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 59 | 65 | 40 | 27 | 67 | 73 | 22 | 26 | 56 |
+| 1 | 3 | 30 | 49 | 19 | 93 | 27 | 28 | 21 | 87 |
+| 2 | 4 | 14 | 60 | 49 | 28 | 17 | 89 | 33 | 57 |
+| 3 | 84 | 64 | 28 | 10 | 70 | 51 | 49 | 1 | 94 |
+| 4 | 72 | 26 | 2 | 93 | 53 | 11 | 56 | 6 | 60 |
+| 5 | 48 | 55 | 32 | 50 | 69 | 22 | 68 | 61 | 86 |
+| 6 | 26 | 5 | 6 | 54 | 15 | 82 | 60 | 57 | 84 |
+| 7 | 91 | 47 | 56 | 19 | 82 | 91 | 32 | 52 | 11 |
+| 8 | 17 | 8 | 59 | 10 | 74 | 87 | 67 | 42 | 73 |
+
+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': [[[26, 46, 47, 2, 58, 17, 21, 0, 57], [43, 37, 96, 27, 5, 22, 37, 93, 49], [0, 58, 70, 33, 93, 52, 69, 17, 25], [44, 73, 45, 65, 55, 26, 36, 71, 35], [3, 0, 2, 21, 79, 62, 39, 51, 3], [81, 39, 81, 38, 99, 70, 81, 94, 7], [93, 80, 85, 26, 82, 56, 46, 53, 72], [29, 91, 7, 32, 65, 5, 94, 19, 82], [3, 18, 7, 73, 12, 93, 19, 31, 82]], [[5, 40, 22, 90, 68, 62, 4, 92, 71], [85, 22, 63, 12, 72, 83, 89, 34, 90], [25, 40, 95, 24, 12, 48, 55, 31, 55], [27, 79, 83, 75, 14, 14, 47, 11, 31], [48, 95, 82, 74, 71, 72, 56, 68, 15], [56, 94, 0, 87, 63, 50, 41, 69, 54], [65, 58, 78, 75, 65, 29, 91, 0, 60], [87, 20, 73, 64, 92, 3, 72, 71, 74], [2, 25, 44, 71, 54, 31, 84, 67, 83]], [[88, 5, 52, 1, 3, 59, 21, 6, 71], [75, 95, 72, 6, 68, 24, 95, 73, 51], [99, 71, 40, 47, 62, 36, 6, 83, 20], [69, 93, 66, 53, 36, 65, 5, 8, 57], [34, 41, 42, 69, 58, 34, 24, 82, 91], [95, 86, 61, 12, 4, 37, 77, 92, 51], [56, 57, 64, 61, 92, 22, 87, 49, 55], [71, 2, 84, 17, 92, 83, 99, 28, 94], [67, 12, 80, 62, 51, 57, 40, 53, 89]], [[38, 99, 22, 72, 5, 45, 78, 71, 47], [43, 16, 11, 71, 2, 78, 58, 89, 97], [61, 13, 25, 74, 22, 60, 80, 63, 71], [47, 62, 49, 11, 50, 70, 39, 58, 86], [60, 7, 21, 38, 66, 49, 96, 37, 81], [9, 0, 15, 43, 28, 47, 72, 5, 3], [15, 20, 21, 0, 93, 16, 82, 76, 90], [36, 35, 8, 40, 63, 52, 37, 6, 27], [30, 66, 94, 92, 34, 17, 47, 19, 94]], [[18, 27, 85, 12, 69, 38, 88, 75, 89], [98, 38, 22, 90, 55, 32, 58, 96, 4], [23, 15, 60, 17, 80, 16, 77, 62, 40], [82, 18, 45, 9, 21, 65, 32, 30, 99], [44, 61, 43, 24, 86, 60, 78, 43, 88], [56, 98, 0, 38, 0, 42, 49, 17, 30], [0, 99, 23, 1, 50, 25, 68, 61, 92], [83, 84, 86, 37, 32, 39, 57, 69, 35], [85, 83, 95, 40, 77, 15, 27, 35, 6]], [[58, 24, 13, 83, 56, 52, 71, 24, 84], [81, 55, 67, 74, 45, 53, 15, 81, 55], [21, 83, 23, 99, 98, 94, 6, 29, 16], [65, 90, 44, 94, 44, 16, 56, 26, 97], [21, 93, 56, 85, 14, 39, 67, 22, 86], [81, 31, 27, 88, 40, 78, 48, 55, 27], [34, 60, 34, 92, 75, 94, 18, 80, 47], [84, 91, 33, 5, 84, 46, 64, 1, 54], [69, 22, 90, 32, 14, 52, 80, 29, 23]], [[49, 86, 39, 85, 96, 52, 74, 46, 13], [36, 99, 53, 74, 47, 94, 31, 76, 68], [0, 57, 11, 58, 29, 62, 19, 48, 24], [77, 84, 40, 71, 5, 72, 92, 38, 19], [20, 61, 75, 13, 36, 70, 5, 9, 89], [62, 3, 70, 5, 61, 50, 20, 36, 62], [38, 72, 65, 5, 62, 11, 57, 25, 15], [96, 73, 0, 63, 69, 90, 28, 52, 0], [55, 57, 56, 72, 29, 25, 13, 85, 14]], [[68, 49, 67, 0, 30, 66, 49, 50, 46], [53, 43, 57, 73, 77, 6, 85, 75, 21], [68, 45, 70, 97, 61, 66, 52, 15, 45], [97, 59, 63, 90, 79, 62, 43, 54, 81], [16, 57, 67, 28, 84, 63, 89, 44, 55], [25, 63, 96, 43, 67, 67, 24, 25, 60], [82, 11, 10, 20, 20, 2, 62, 52, 35], [67, 32, 74, 76, 32, 97, 81, 86, 87], [64, 9, 47, 91, 71, 31, 6, 37, 71]], [[59, 65, 40, 27, 67, 73, 22, 26, 56], [3, 30, 49, 19, 93, 27, 28, 21, 87], [4, 14, 60, 49, 28, 17, 89, 33, 57], [84, 64, 28, 10, 70, 51, 49, 1, 94], [72, 26, 2, 93, 53, 11, 56, 6, 60], [48, 55, 32, 50, 69, 22, 68, 61, 86], [26, 5, 6, 54, 15, 82, 60, 57, 84], [91, 47, 56, 19, 82, 91, 32, 52, 11], [17, 8, 59, 10, 74, 87, 67, 42, 73]]], 'objective': 14.0}","[[0, 4, 1], [1, 8, 0], [2, 0, 3], [3, 1, 4], [4, 5, 2], [5, 2, 6], [6, 7, 8], [7, 6, 5], [8, 3, 7]]",14.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 26}, {'i': 0, 'j': 0, 'k': 1, 'cost': 46}, {'i': 0, 'j': 0, 'k': 2, 'cost': 47}, {'i': 0, 'j': 0, 'k': 3, 'cost': 2}, {'i': 0, 'j': 0, 'k': 4, 'cost': 58}, {'i': 0, 'j': 0, 'k': 5, 'cost': 17}, {'i': 0, 'j': 0, 'k': 6, 'cost': 21}, {'i': 0, 'j': 0, 'k': 7, 'cost': 0}, {'i': 0, 'j': 0, 'k': 8, 'cost': 57}, {'i': 0, 'j': 1, 'k': 0, 'cost': 43}, {'i': 0, 'j': 1, 'k': 1, 'cost': 37}, {'i': 0, 'j': 1, 'k': 2, 'cost': 96}, {'i': 0, 'j': 1, 'k': 3, 'cost': 27}, {'i': 0, 'j': 1, 'k': 4, 'cost': 5}, {'i': 0, 'j': 1, 'k': 5, 'cost': 22}, {'i': 0, 'j': 1, 'k': 6, 'cost': 37}, {'i': 0, 'j': 1, 'k': 7, 'cost': 93}, {'i': 0, 'j': 1, 'k': 8, 'cost': 49}, {'i': 0, 'j': 2, 'k': 0, 'cost': 0}, {'i': 0, 'j': 2, 'k': 1, 'cost': 58}, {'i': 0, 'j': 2, 'k': 2, 'cost': 70}, {'i': 0, 'j': 2, 'k': 3, 'cost': 33}, {'i': 0, 'j': 2, 'k': 4, 'cost': 93}, {'i': 0, 'j': 2, 'k': 5, 'cost': 52}, {'i': 0, 'j': 2, 'k': 6, 'cost': 69}, {'i': 0, 'j': 2, 'k': 7, 'cost': 17}, {'i': 0, 'j': 2, 'k': 8, 'cost': 25}, {'i': 0, 'j': 3, 'k': 0, 'cost': 44}, {'i': 0, 'j': 3, 'k': 1, 'cost': 73}, {'i': 0, 'j': 3, 'k': 2, 'cost': 45}, {'i': 0, 'j': 3, 'k': 3, 'cost': 65}, {'i': 0, 'j': 3, 'k': 4, 'cost': 55}, {'i': 0, 'j': 3, 'k': 5, 'cost': 26}, {'i': 0, 'j': 3, 'k': 6, 'cost': 36}, {'i': 0, 'j': 3, 'k': 7, 'cost': 71}, {'i': 0, 'j': 3, 'k': 8, 'cost': 35}, {'i': 0, 'j': 4, 'k': 0, 'cost': 3}, {'i': 0, 'j': 4, 'k': 1, 'cost': 0}, {'i': 0, 'j': 4, 'k': 2, 'cost': 2}, {'i': 0, 'j': 4, 'k': 3, 'cost': 21}, {'i': 0, 'j': 4, 'k': 4, 'cost': 79}, {'i': 0, 'j': 4, 'k': 5, 'cost': 62}, {'i': 0, 'j': 4, 'k': 6, 'cost': 39}, {'i': 0, 'j': 4, 'k': 7, 'cost': 51}, {'i': 0, 'j': 4, 'k': 8, 'cost': 3}, {'i': 0, 'j': 5, 'k': 0, 'cost': 81}, {'i': 0, 'j': 5, 'k': 1, 'cost': 39}, {'i': 0, 'j': 5, 'k': 2, 'cost': 81}, {'i': 0, 'j': 5, 'k': 3, 'cost': 38}, {'i': 0, 'j': 5, 'k': 4, 'cost': 99}, {'i': 0, 'j': 5, 'k': 5, 'cost': 70}, {'i': 0, 'j': 5, 'k': 6, 'cost': 81}, {'i': 0, 'j': 5, 'k': 7, 'cost': 94}, {'i': 0, 'j': 5, 'k': 8, 'cost': 7}, {'i': 0, 'j': 6, 'k': 0, 'cost': 93}, {'i': 0, 'j': 6, 'k': 1, 'cost': 80}, {'i': 0, 'j': 6, 'k': 2, 'cost': 85}, {'i': 0, 'j': 6, 'k': 3, 'cost': 26}, {'i': 0, 'j': 6, 'k': 4, 'cost': 82}, {'i': 0, 'j': 6, 'k': 5, 'cost': 56}, {'i': 0, 'j': 6, 'k': 6, 'cost': 46}, {'i': 0, 'j': 6, 'k': 7, 'cost': 53}, {'i': 0, 'j': 6, 'k': 8, 'cost': 72}, {'i': 0, 'j': 7, 'k': 0, 'cost': 29}, {'i': 0, 'j': 7, 'k': 1, 'cost': 91}, {'i': 0, 'j': 7, 'k': 2, 'cost': 7}, {'i': 0, 'j': 7, 'k': 3, 'cost': 32}, {'i': 0, 'j': 7, 'k': 4, 'cost': 65}, {'i': 0, 'j': 7, 'k': 5, 'cost': 5}, {'i': 0, 'j': 7, 'k': 6, 'cost': 94}, {'i': 0, 'j': 7, 'k': 7, 'cost': 19}, {'i': 0, 'j': 7, 'k': 8, 'cost': 82}, {'i': 0, 'j': 8, 'k': 0, 'cost': 3}, {'i': 0, 'j': 8, 'k': 1, 'cost': 18}, {'i': 0, 'j': 8, 'k': 2, 'cost': 7}, {'i': 0, 'j': 8, 'k': 3, 'cost': 73}, {'i': 0, 'j': 8, 'k': 4, 'cost': 12}, {'i': 0, 'j': 8, 'k': 5, 'cost': 93}, {'i': 0, 'j': 8, 'k': 6, 'cost': 19}, {'i': 0, 'j': 8, 'k': 7, 'cost': 31}, {'i': 0, 'j': 8, 'k': 8, 'cost': 82}, {'i': 1, 'j': 0, 'k': 0, 'cost': 5}, {'i': 1, 'j': 0, 'k': 1, 'cost': 40}, {'i': 1, 'j': 0, 'k': 2, 'cost': 22}, {'i': 1, 'j': 0, 'k': 3, 'cost': 90}, {'i': 1, 'j': 0, 'k': 4, 'cost': 68}, {'i': 1, 'j': 0, 'k': 5, 'cost': 62}, {'i': 1, 'j': 0, 'k': 6, 'cost': 4}, {'i': 1, 'j': 0, 'k': 7, 'cost': 92}, {'i': 1, 'j': 0, 'k': 8, 'cost': 71}, {'i': 1, 'j': 1, 'k': 0, 'cost': 85}, {'i': 1, 'j': 1, 'k': 1, 'cost': 22}, {'i': 1, 'j': 1, 'k': 2, 'cost': 63}, {'i': 1, 'j': 1, 'k': 3, 'cost': 12}, {'i': 1, 'j': 1, 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'k': 6, 'cost': 68}, {'i': 4, 'j': 6, 'k': 7, 'cost': 61}, {'i': 4, 'j': 6, 'k': 8, 'cost': 92}, {'i': 4, 'j': 7, 'k': 0, 'cost': 83}, {'i': 4, 'j': 7, 'k': 1, 'cost': 84}, {'i': 4, 'j': 7, 'k': 2, 'cost': 86}, {'i': 4, 'j': 7, 'k': 3, 'cost': 37}, {'i': 4, 'j': 7, 'k': 4, 'cost': 32}, {'i': 4, 'j': 7, 'k': 5, 'cost': 39}, {'i': 4, 'j': 7, 'k': 6, 'cost': 57}, {'i': 4, 'j': 7, 'k': 7, 'cost': 69}, {'i': 4, 'j': 7, 'k': 8, 'cost': 35}, {'i': 4, 'j': 8, 'k': 0, 'cost': 85}, {'i': 4, 'j': 8, 'k': 1, 'cost': 83}, {'i': 4, 'j': 8, 'k': 2, 'cost': 95}, {'i': 4, 'j': 8, 'k': 3, 'cost': 40}, {'i': 4, 'j': 8, 'k': 4, 'cost': 77}, {'i': 4, 'j': 8, 'k': 5, 'cost': 15}, {'i': 4, 'j': 8, 'k': 6, 'cost': 27}, {'i': 4, 'j': 8, 'k': 7, 'cost': 35}, {'i': 4, 'j': 8, 'k': 8, 'cost': 6}, {'i': 5, 'j': 0, 'k': 0, 'cost': 58}, {'i': 5, 'j': 0, 'k': 1, 'cost': 24}, {'i': 5, 'j': 0, 'k': 2, 'cost': 13}, {'i': 5, 'j': 0, 'k': 3, 'cost': 83}, {'i': 5, 'j': 0, 'k': 4, 'cost': 56}, {'i': 5, 'j': 0, 'k': 5, 'cost': 52}, {'i': 5, 'j': 0, 'k': 6, 'cost': 71}, {'i': 5, 'j': 0, 'k': 7, 'cost': 24}, {'i': 5, 'j': 0, 'k': 8, 'cost': 84}, {'i': 5, 'j': 1, 'k': 0, 'cost': 81}, {'i': 5, 'j': 1, 'k': 1, 'cost': 55}, {'i': 5, 'j': 1, 'k': 2, 'cost': 67}, {'i': 5, 'j': 1, 'k': 3, 'cost': 74}, {'i': 5, 'j': 1, 'k': 4, 'cost': 45}, {'i': 5, 'j': 1, 'k': 5, 'cost': 53}, {'i': 5, 'j': 1, 'k': 6, 'cost': 15}, {'i': 5, 'j': 1, 'k': 7, 'cost': 81}, {'i': 5, 'j': 1, 'k': 8, 'cost': 55}, {'i': 5, 'j': 2, 'k': 0, 'cost': 21}, {'i': 5, 'j': 2, 'k': 1, 'cost': 83}, {'i': 5, 'j': 2, 'k': 2, 'cost': 23}, {'i': 5, 'j': 2, 'k': 3, 'cost': 99}, {'i': 5, 'j': 2, 'k': 4, 'cost': 98}, {'i': 5, 'j': 2, 'k': 5, 'cost': 94}, {'i': 5, 'j': 2, 'k': 6, 'cost': 6}, {'i': 5, 'j': 2, 'k': 7, 'cost': 29}, {'i': 5, 'j': 2, 'k': 8, 'cost': 16}, {'i': 5, 'j': 3, 'k': 0, 'cost': 65}, {'i': 5, 'j': 3, 'k': 1, 'cost': 90}, {'i': 5, 'j': 3, 'k': 2, 'cost': 44}, {'i': 5, 'j': 3, 'k': 3, 'cost': 94}, {'i': 5, 'j': 3, 'k': 4, 'cost': 44}, {'i': 5, 'j': 3, 'k': 5, 'cost': 16}, {'i': 5, 'j': 3, 'k': 6, 'cost': 56}, {'i': 5, 'j': 3, 'k': 7, 'cost': 26}, {'i': 5, 'j': 3, 'k': 8, 'cost': 97}, {'i': 5, 'j': 4, 'k': 0, 'cost': 21}, {'i': 5, 'j': 4, 'k': 1, 'cost': 93}, {'i': 5, 'j': 4, 'k': 2, 'cost': 56}, {'i': 5, 'j': 4, 'k': 3, 'cost': 85}, {'i': 5, 'j': 4, 'k': 4, 'cost': 14}, {'i': 5, 'j': 4, 'k': 5, 'cost': 39}, {'i': 5, 'j': 4, 'k': 6, 'cost': 67}, {'i': 5, 'j': 4, 'k': 7, 'cost': 22}, {'i': 5, 'j': 4, 'k': 8, 'cost': 86}, {'i': 5, 'j': 5, 'k': 0, 'cost': 81}, {'i': 5, 'j': 5, 'k': 1, 'cost': 31}, {'i': 5, 'j': 5, 'k': 2, 'cost': 27}, {'i': 5, 'j': 5, 'k': 3, 'cost': 88}, {'i': 5, 'j': 5, 'k': 4, 'cost': 40}, {'i': 5, 'j': 5, 'k': 5, 'cost': 78}, {'i': 5, 'j': 5, 'k': 6, 'cost': 48}, {'i': 5, 'j': 5, 'k': 7, 'cost': 55}, {'i': 5, 'j': 5, 'k': 8, 'cost': 27}, {'i': 5, 'j': 6, 'k': 0, 'cost': 34}, {'i': 5, 'j': 6, 'k': 1, 'cost': 60}, {'i': 5, 'j': 6, 'k': 2, 'cost': 34}, {'i': 5, 'j': 6, 'k': 3, 'cost': 92}, {'i': 5, 'j': 6, 'k': 4, 'cost': 75}, {'i': 5, 'j': 6, 'k': 5, 'cost': 94}, {'i': 5, 'j': 6, 'k': 6, 'cost': 18}, {'i': 5, 'j': 6, 'k': 7, 'cost': 80}, {'i': 5, 'j': 6, 'k': 8, 'cost': 47}, {'i': 5, 'j': 7, 'k': 0, 'cost': 84}, {'i': 5, 'j': 7, 'k': 1, 'cost': 91}, {'i': 5, 'j': 7, 'k': 2, 'cost': 33}, {'i': 5, 'j': 7, 'k': 3, 'cost': 5}, {'i': 5, 'j': 7, 'k': 4, 'cost': 84}, {'i': 5, 'j': 7, 'k': 5, 'cost': 46}, {'i': 5, 'j': 7, 'k': 6, 'cost': 64}, {'i': 5, 'j': 7, 'k': 7, 'cost': 1}, {'i': 5, 'j': 7, 'k': 8, 'cost': 54}, {'i': 5, 'j': 8, 'k': 0, 'cost': 69}, {'i': 5, 'j': 8, 'k': 1, 'cost': 22}, {'i': 5, 'j': 8, 'k': 2, 'cost': 90}, {'i': 5, 'j': 8, 'k': 3, 'cost': 32}, {'i': 5, 'j': 8, 'k': 4, 'cost': 14}, {'i': 5, 'j': 8, 'k': 5, 'cost': 52}, {'i': 5, 'j': 8, 'k': 6, 'cost': 80}, {'i': 5, 'j': 8, 'k': 7, 'cost': 29}, {'i': 5, 'j': 8, 'k': 8, 'cost': 23}, {'i': 6, 'j': 0, 'k': 0, 'cost': 49}, {'i': 6, 'j': 0, 'k': 1, 'cost': 86}, {'i': 6, 'j': 0, 'k': 2, 'cost': 39}, {'i': 6, 'j': 0, 'k': 3, 'cost': 85}, {'i': 6, 'j': 0, 'k': 4, 'cost': 96}, {'i': 6, 'j': 0, 'k': 5, 'cost': 52}, {'i': 6, 'j': 0, 'k': 6, 'cost': 74}, {'i': 6, 'j': 0, 'k': 7, 'cost': 46}, {'i': 6, 'j': 0, 'k': 8, 'cost': 13}, {'i': 6, 'j': 1, 'k': 0, 'cost': 36}, {'i': 6, 'j': 1, 'k': 1, 'cost': 99}, {'i': 6, 'j': 1, 'k': 2, 'cost': 53}, {'i': 6, 'j': 1, 'k': 3, 'cost': 74}, {'i': 6, 'j': 1, 'k': 4, 'cost': 47}, {'i': 6, 'j': 1, 'k': 5, 'cost': 94}, {'i': 6, 'j': 1, 'k': 6, 'cost': 31}, {'i': 6, 'j': 1, 'k': 7, 'cost': 76}, {'i': 6, 'j': 1, 'k': 8, 'cost': 68}, {'i': 6, 'j': 2, 'k': 0, 'cost': 0}, {'i': 6, 'j': 2, 'k': 1, 'cost': 57}, {'i': 6, 'j': 2, 'k': 2, 'cost': 11}, {'i': 6, 'j': 2, 'k': 3, 'cost': 58}, {'i': 6, 'j': 2, 'k': 4, 'cost': 29}, {'i': 6, 'j': 2, 'k': 5, 'cost': 62}, {'i': 6, 'j': 2, 'k': 6, 'cost': 19}, {'i': 6, 'j': 2, 'k': 7, 'cost': 48}, {'i': 6, 'j': 2, 'k': 8, 'cost': 24}, {'i': 6, 'j': 3, 'k': 0, 'cost': 77}, {'i': 6, 'j': 3, 'k': 1, 'cost': 84}, {'i': 6, 'j': 3, 'k': 2, 'cost': 40}, {'i': 6, 'j': 3, 'k': 3, 'cost': 71}, {'i': 6, 'j': 3, 'k': 4, 'cost': 5}, {'i': 6, 'j': 3, 'k': 5, 'cost': 72}, {'i': 6, 'j': 3, 'k': 6, 'cost': 92}, {'i': 6, 'j': 3, 'k': 7, 'cost': 38}, {'i': 6, 'j': 3, 'k': 8, 'cost': 19}, {'i': 6, 'j': 4, 'k': 0, 'cost': 20}, {'i': 6, 'j': 4, 'k': 1, 'cost': 61}, {'i': 6, 'j': 4, 'k': 2, 'cost': 75}, {'i': 6, 'j': 4, 'k': 3, 'cost': 13}, {'i': 6, 'j': 4, 'k': 4, 'cost': 36}, {'i': 6, 'j': 4, 'k': 5, 'cost': 70}, {'i': 6, 'j': 4, 'k': 6, 'cost': 5}, {'i': 6, 'j': 4, 'k': 7, 'cost': 9}, {'i': 6, 'j': 4, 'k': 8, 'cost': 89}, {'i': 6, 'j': 5, 'k': 0, 'cost': 62}, {'i': 6, 'j': 5, 'k': 1, 'cost': 3}, {'i': 6, 'j': 5, 'k': 2, 'cost': 70}, {'i': 6, 'j': 5, 'k': 3, 'cost': 5}, {'i': 6, 'j': 5, 'k': 4, 'cost': 61}, {'i': 6, 'j': 5, 'k': 5, 'cost': 50}, {'i': 6, 'j': 5, 'k': 6, 'cost': 20}, {'i': 6, 'j': 5, 'k': 7, 'cost': 36}, {'i': 6, 'j': 5, 'k': 8, 'cost': 62}, {'i': 6, 'j': 6, 'k': 0, 'cost': 38}, {'i': 6, 'j': 6, 'k': 1, 'cost': 72}, {'i': 6, 'j': 6, 'k': 2, 'cost': 65}, {'i': 6, 'j': 6, 'k': 3, 'cost': 5}, {'i': 6, 'j': 6, 'k': 4, 'cost': 62}, {'i': 6, 'j': 6, 'k': 5, 'cost': 11}, {'i': 6, 'j': 6, 'k': 6, 'cost': 57}, {'i': 6, 'j': 6, 'k': 7, 'cost': 25}, {'i': 6, 'j': 6, 'k': 8, 'cost': 15}, {'i': 6, 'j': 7, 'k': 0, 'cost': 96}, {'i': 6, 'j': 7, 'k': 1, 'cost': 73}, {'i': 6, 'j': 7, 'k': 2, 'cost': 0}, {'i': 6, 'j': 7, 'k': 3, 'cost': 63}, {'i': 6, 'j': 7, 'k': 4, 'cost': 69}, {'i': 6, 'j': 7, 'k': 5, 'cost': 90}, {'i': 6, 'j': 7, 'k': 6, 'cost': 28}, {'i': 6, 'j': 7, 'k': 7, 'cost': 52}, {'i': 6, 'j': 7, 'k': 8, 'cost': 0}, {'i': 6, 'j': 8, 'k': 0, 'cost': 55}, {'i': 6, 'j': 8, 'k': 1, 'cost': 57}, {'i': 6, 'j': 8, 'k': 2, 'cost': 56}, {'i': 6, 'j': 8, 'k': 3, 'cost': 72}, {'i': 6, 'j': 8, 'k': 4, 'cost': 29}, {'i': 6, 'j': 8, 'k': 5, 'cost': 25}, {'i': 6, 'j': 8, 'k': 6, 'cost': 13}, {'i': 6, 'j': 8, 'k': 7, 'cost': 85}, {'i': 6, 'j': 8, 'k': 8, 'cost': 14}, {'i': 7, 'j': 0, 'k': 0, 'cost': 68}, {'i': 7, 'j': 0, 'k': 1, 'cost': 49}, {'i': 7, 'j': 0, 'k': 2, 'cost': 67}, {'i': 7, 'j': 0, 'k': 3, 'cost': 0}, {'i': 7, 'j': 0, 'k': 4, 'cost': 30}, {'i': 7, 'j': 0, 'k': 5, 'cost': 66}, {'i': 7, 'j': 0, 'k': 6, 'cost': 49}, {'i': 7, 'j': 0, 'k': 7, 'cost': 50}, {'i': 7, 'j': 0, 'k': 8, 'cost': 46}, {'i': 7, 'j': 1, 'k': 0, 'cost': 53}, {'i': 7, 'j': 1, 'k': 1, 'cost': 43}, {'i': 7, 'j': 1, 'k': 2, 'cost': 57}, {'i': 7, 'j': 1, 'k': 3, 'cost': 73}, {'i': 7, 'j': 1, 'k': 4, 'cost': 77}, {'i': 7, 'j': 1, 'k': 5, 'cost': 6}, {'i': 7, 'j': 1, 'k': 6, 'cost': 85}, {'i': 7, 'j': 1, 'k': 7, 'cost': 75}, {'i': 7, 'j': 1, 'k': 8, 'cost': 21}, {'i': 7, 'j': 2, 'k': 0, 'cost': 68}, {'i': 7, 'j': 2, 'k': 1, 'cost': 45}, {'i': 7, 'j': 2, 'k': 2, 'cost': 70}, {'i': 7, 'j': 2, 'k': 3, 'cost': 97}, {'i': 7, 'j': 2, 'k': 4, 'cost': 61}, {'i': 7, 'j': 2, 'k': 5, 'cost': 66}, {'i': 7, 'j': 2, 'k': 6, 'cost': 52}, {'i': 7, 'j': 2, 'k': 7, 'cost': 15}, {'i': 7, 'j': 2, 'k': 8, 'cost': 45}, {'i': 7, 'j': 3, 'k': 0, 'cost': 97}, {'i': 7, 'j': 3, 'k': 1, 'cost': 59}, {'i': 7, 'j': 3, 'k': 2, 'cost': 63}, {'i': 7, 'j': 3, 'k': 3, 'cost': 90}, {'i': 7, 'j': 3, 'k': 4, 'cost': 79}, {'i': 7, 'j': 3, 'k': 5, 'cost': 62}, {'i': 7, 'j': 3, 'k': 6, 'cost': 43}, {'i': 7, 'j': 3, 'k': 7, 'cost': 54}, {'i': 7, 'j': 3, 'k': 8, 'cost': 81}, {'i': 7, 'j': 4, 'k': 0, 'cost': 16}, {'i': 7, 'j': 4, 'k': 1, 'cost': 57}, {'i': 7, 'j': 4, 'k': 2, 'cost': 67}, {'i': 7, 'j': 4, 'k': 3, 'cost': 28}, {'i': 7, 'j': 4, 'k': 4, 'cost': 84}, {'i': 7, 'j': 4, 'k': 5, 'cost': 63}, {'i': 7, 'j': 4, 'k': 6, 'cost': 89}, {'i': 7, 'j': 4, 'k': 7, 'cost': 44}, {'i': 7, 'j': 4, 'k': 8, 'cost': 55}, {'i': 7, 'j': 5, 'k': 0, 'cost': 25}, {'i': 7, 'j': 5, 'k': 1, 'cost': 63}, {'i': 7, 'j': 5, 'k': 2, 'cost': 96}, {'i': 7, 'j': 5, 'k': 3, 'cost': 43}, {'i': 7, 'j': 5, 'k': 4, 'cost': 67}, {'i': 7, 'j': 5, 'k': 5, 'cost': 67}, {'i': 7, 'j': 5, 'k': 6, 'cost': 24}, {'i': 7, 'j': 5, 'k': 7, 'cost': 25}, {'i': 7, 'j': 5, 'k': 8, 'cost': 60}, {'i': 7, 'j': 6, 'k': 0, 'cost': 82}, {'i': 7, 'j': 6, 'k': 1, 'cost': 11}, {'i': 7, 'j': 6, 'k': 2, 'cost': 10}, {'i': 7, 'j': 6, 'k': 3, 'cost': 20}, {'i': 7, 'j': 6, 'k': 4, 'cost': 20}, {'i': 7, 'j': 6, 'k': 5, 'cost': 2}, {'i': 7, 'j': 6, 'k': 6, 'cost': 62}, {'i': 7, 'j': 6, 'k': 7, 'cost': 52}, {'i': 7, 'j': 6, 'k': 8, 'cost': 35}, {'i': 7, 'j': 7, 'k': 0, 'cost': 67}, {'i': 7, 'j': 7, 'k': 1, 'cost': 32}, {'i': 7, 'j': 7, 'k': 2, 'cost': 74}, {'i': 7, 'j': 7, 'k': 3, 'cost': 76}, {'i': 7, 'j': 7, 'k': 4, 'cost': 32}, {'i': 7, 'j': 7, 'k': 5, 'cost': 97}, {'i': 7, 'j': 7, 'k': 6, 'cost': 81}, {'i': 7, 'j': 7, 'k': 7, 'cost': 86}, {'i': 7, 'j': 7, 'k': 8, 'cost': 87}, {'i': 7, 'j': 8, 'k': 0, 'cost': 64}, {'i': 7, 'j': 8, 'k': 1, 'cost': 9}, {'i': 7, 'j': 8, 'k': 2, 'cost': 47}, {'i': 7, 'j': 8, 'k': 3, 'cost': 91}, {'i': 7, 'j': 8, 'k': 4, 'cost': 71}, {'i': 7, 'j': 8, 'k': 5, 'cost': 31}, {'i': 7, 'j': 8, 'k': 6, 'cost': 6}, {'i': 7, 'j': 8, 'k': 7, 'cost': 37}, {'i': 7, 'j': 8, 'k': 8, 'cost': 71}, {'i': 8, 'j': 0, 'k': 0, 'cost': 59}, {'i': 8, 'j': 0, 'k': 1, 'cost': 65}, {'i': 8, 'j': 0, 'k': 2, 'cost': 40}, {'i': 8, 'j': 0, 'k': 3, 'cost': 27}, {'i': 8, 'j': 0, 'k': 4, 'cost': 67}, {'i': 8, 'j': 0, 'k': 5, 'cost': 73}, {'i': 8, 'j': 0, 'k': 6, 'cost': 22}, {'i': 8, 'j': 0, 'k': 7, 'cost': 26}, {'i': 8, 'j': 0, 'k': 8, 'cost': 56}, {'i': 8, 'j': 1, 'k': 0, 'cost': 3}, {'i': 8, 'j': 1, 'k': 1, 'cost': 30}, {'i': 8, 'j': 1, 'k': 2, 'cost': 49}, {'i': 8, 'j': 1, 'k': 3, 'cost': 19}, {'i': 8, 'j': 1, 'k': 4, 'cost': 93}, {'i': 8, 'j': 1, 'k': 5, 'cost': 27}, {'i': 8, 'j': 1, 'k': 6, 'cost': 28}, {'i': 8, 'j': 1, 'k': 7, 'cost': 21}, {'i': 8, 'j': 1, 'k': 8, 'cost': 87}, {'i': 8, 'j': 2, 'k': 0, 'cost': 4}, {'i': 8, 'j': 2, 'k': 1, 'cost': 14}, {'i': 8, 'j': 2, 'k': 2, 'cost': 60}, {'i': 8, 'j': 2, 'k': 3, 'cost': 49}, {'i': 8, 'j': 2, 'k': 4, 'cost': 28}, {'i': 8, 'j': 2, 'k': 5, 'cost': 17}, {'i': 8, 'j': 2, 'k': 6, 'cost': 89}, {'i': 8, 'j': 2, 'k': 7, 'cost': 33}, {'i': 8, 'j': 2, 'k': 8, 'cost': 57}, {'i': 8, 'j': 3, 'k': 0, 'cost': 84}, {'i': 8, 'j': 3, 'k': 1, 'cost': 64}, {'i': 8, 'j': 3, 'k': 2, 'cost': 28}, {'i': 8, 'j': 3, 'k': 3, 'cost': 10}, {'i': 8, 'j': 3, 'k': 4, 'cost': 70}, {'i': 8, 'j': 3, 'k': 5, 'cost': 51}, {'i': 8, 'j': 3, 'k': 6, 'cost': 49}, {'i': 8, 'j': 3, 'k': 7, 'cost': 1}, {'i': 8, 'j': 3, 'k': 8, 'cost': 94}, {'i': 8, 'j': 4, 'k': 0, 'cost': 72}, {'i': 8, 'j': 4, 'k': 1, 'cost': 26}, {'i': 8, 'j': 4, 'k': 2, 'cost': 2}, {'i': 8, 'j': 4, 'k': 3, 'cost': 93}, {'i': 8, 'j': 4, 'k': 4, 'cost': 53}, {'i': 8, 'j': 4, 'k': 5, 'cost': 11}, {'i': 8, 'j': 4, 'k': 6, 'cost': 56}, {'i': 8, 'j': 4, 'k': 7, 'cost': 6}, {'i': 8, 'j': 4, 'k': 8, 'cost': 60}, {'i': 8, 'j': 5, 'k': 0, 'cost': 48}, {'i': 8, 'j': 5, 'k': 1, 'cost': 55}, {'i': 8, 'j': 5, 'k': 2, 'cost': 32}, {'i': 8, 'j': 5, 'k': 3, 'cost': 50}, {'i': 8, 'j': 5, 'k': 4, 'cost': 69}, {'i': 8, 'j': 5, 'k': 5, 'cost': 22}, {'i': 8, 'j': 5, 'k': 6, 'cost': 68}, {'i': 8, 'j': 5, 'k': 7, 'cost': 61}, {'i': 8, 'j': 5, 'k': 8, 'cost': 86}, {'i': 8, 'j': 6, 'k': 0, 'cost': 26}, {'i': 8, 'j': 6, 'k': 1, 'cost': 5}, {'i': 8, 'j': 6, 'k': 2, 'cost': 6}, {'i': 8, 'j': 6, 'k': 3, 'cost': 54}, {'i': 8, 'j': 6, 'k': 4, 'cost': 15}, {'i': 8, 'j': 6, 'k': 5, 'cost': 82}, {'i': 8, 'j': 6, 'k': 6, 'cost': 60}, {'i': 8, 'j': 6, 'k': 7, 'cost': 57}, {'i': 8, 'j': 6, 'k': 8, 'cost': 84}, {'i': 8, 'j': 7, 'k': 0, 'cost': 91}, {'i': 8, 'j': 7, 'k': 1, 'cost': 47}, {'i': 8, 'j': 7, 'k': 2, 'cost': 56}, {'i': 8, 'j': 7, 'k': 3, 'cost': 19}, {'i': 8, 'j': 7, 'k': 4, 'cost': 82}, {'i': 8, 'j': 7, 'k': 5, 'cost': 91}, {'i': 8, 'j': 7, 'k': 6, 'cost': 32}, {'i': 8, 'j': 7, 'k': 7, 'cost': 52}, {'i': 8, 'j': 7, 'k': 8, 'cost': 11}, {'i': 8, 'j': 8, 'k': 0, 'cost': 17}, {'i': 8, 'j': 8, 'k': 1, 'cost': 8}, {'i': 8, 'j': 8, 'k': 2, 'cost': 59}, {'i': 8, 'j': 8, 'k': 3, 'cost': 10}, {'i': 8, 'j': 8, 'k': 4, 'cost': 74}, {'i': 8, 'j': 8, 'k': 5, 'cost': 87}, {'i': 8, 'j': 8, 'k': 6, 'cost': 67}, {'i': 8, 'j': 8, 'k': 7, 'cost': 42}, {'i': 8, 'j': 8, 'k': 8, 'cost': 73}]}","[[0, 4, 1], [1, 8, 0], [2, 0, 3], [3, 1, 4], [4, 5, 2], [5, 2, 6], [6, 7, 8], [7, 6, 5], [8, 3, 7]]",21,json,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"": 9,
+  ""index_identifiers"": [
+    ""A"",
+    ""B"",
+    ""C"",
+    ""D"",
+    ""E"",
+    ""F"",
+    ""G"",
+    ""H"",
+    ""I""
+  ]
+}
+
+# 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=A
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 46 | 74 | 88 | 80 | 56 | 22 | 91 | 15 | 1 |
+| B | 22 | 45 | 21 | 60 | 45 | 89 | 88 | 89 | 59 |
+| C | 8 | 45 | 72 | 26 | 50 | 83 | 55 | 72 | 22 |
+| D | 59 | 30 | 51 | 33 | 49 | 26 | 67 | 38 | 61 |
+| E | 38 | 63 | 20 | 48 | 85 | 91 | 59 | 69 | 54 |
+| F | 28 | 86 | 56 | 39 | 45 | 86 | 60 | 21 | 9 |
+| G | 66 | 31 | 98 | 25 | 91 | 69 | 21 | 26 | 81 |
+| H | 7 | 24 | 98 | 61 | 7 | 98 | 95 | 14 | 74 |
+| I | 32 | 89 | 29 | 76 | 68 | 46 | 37 | 59 | 45 |
+
+## order_id=B
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 47 | 93 | 6 | 37 | 24 | 15 | 82 | 57 | 72 |
+| B | 82 | 44 | 45 | 40 | 22 | 22 | 20 | 3 | 7 |
+| C | 0 | 28 | 79 | 74 | 65 | 33 | 54 | 80 | 62 |
+| D | 67 | 66 | 65 | 46 | 71 | 58 | 36 | 90 | 55 |
+| E | 60 | 79 | 32 | 85 | 8 | 57 | 87 | 81 | 92 |
+| F | 0 | 55 | 7 | 67 | 48 | 61 | 15 | 33 | 17 |
+| G | 75 | 87 | 40 | 70 | 82 | 65 | 92 | 43 | 39 |
+| H | 23 | 29 | 32 | 96 | 36 | 94 | 90 | 17 | 91 |
+| I | 30 | 79 | 8 | 72 | 1 | 33 | 49 | 84 | 34 |
+
+## order_id=C
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 42 | 30 | 33 | 7 | 69 | 67 | 81 | 0 | 31 |
+| B | 4 | 6 | 83 | 57 | 40 | 86 | 62 | 61 | 68 |
+| C | 35 | 31 | 10 | 12 | 16 | 67 | 34 | 98 | 66 |
+| D | 92 | 30 | 55 | 6 | 52 | 65 | 55 | 57 | 31 |
+| E | 21 | 75 | 22 | 62 | 93 | 37 | 82 | 2 | 74 |
+| F | 81 | 84 | 58 | 55 | 7 | 60 | 46 | 11 | 12 |
+| G | 39 | 80 | 39 | 1 | 66 | 15 | 80 | 38 | 27 |
+| H | 78 | 81 | 48 | 12 | 97 | 9 | 57 | 70 | 13 |
+| I | 69 | 88 | 13 | 61 | 39 | 55 | 39 | 93 | 37 |
+
+## order_id=D
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 63 | 19 | 94 | 6 | 79 | 64 | 88 | 6 | 91 |
+| B | 19 | 95 | 8 | 84 | 26 | 21 | 93 | 38 | 21 |
+| C | 44 | 96 | 81 | 44 | 15 | 61 | 4 | 81 | 34 |
+| D | 51 | 9 | 71 | 22 | 97 | 33 | 39 | 30 | 79 |
+| E | 66 | 13 | 47 | 96 | 2 | 66 | 63 | 36 | 68 |
+| F | 39 | 45 | 86 | 18 | 57 | 33 | 44 | 84 | 34 |
+| G | 67 | 9 | 26 | 15 | 67 | 6 | 13 | 91 | 32 |
+| H | 45 | 1 | 48 | 52 | 62 | 14 | 9 | 14 | 14 |
+| I | 75 | 32 | 50 | 55 | 71 | 85 | 13 | 22 | 89 |
+
+## order_id=E
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 9 | 29 | 20 | 9 | 56 | 61 | 89 | 93 | 71 |
+| B | 88 | 84 | 59 | 59 | 94 | 72 | 98 | 34 | 74 |
+| C | 46 | 77 | 1 | 13 | 23 | 31 | 41 | 47 | 34 |
+| D | 75 | 71 | 94 | 12 | 2 | 2 | 73 | 48 | 73 |
+| E | 61 | 7 | 71 | 41 | 1 | 92 | 10 | 42 | 42 |
+| F | 15 | 34 | 21 | 56 | 57 | 25 | 75 | 50 | 73 |
+| G | 86 | 7 | 63 | 7 | 81 | 92 | 14 | 36 | 73 |
+| H | 87 | 94 | 25 | 50 | 25 | 37 | 5 | 96 | 28 |
+| I | 89 | 6 | 27 | 77 | 45 | 53 | 3 | 61 | 42 |
+
+## order_id=F
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 89 | 34 | 80 | 30 | 79 | 82 | 42 | 37 | 8 |
+| B | 21 | 20 | 46 | 53 | 68 | 28 | 19 | 65 | 94 |
+| C | 53 | 78 | 81 | 66 | 65 | 3 | 57 | 83 | 24 |
+| D | 16 | 29 | 24 | 13 | 93 | 53 | 68 | 7 | 53 |
+| E | 8 | 35 | 52 | 85 | 80 | 22 | 37 | 75 | 28 |
+| F | 3 | 84 | 8 | 38 | 56 | 85 | 9 | 80 | 7 |
+| G | 20 | 74 | 54 | 63 | 96 | 44 | 22 | 33 | 45 |
+| H | 85 | 99 | 51 | 17 | 78 | 50 | 6 | 12 | 91 |
+| I | 95 | 80 | 19 | 92 | 0 | 86 | 28 | 24 | 11 |
+
+## order_id=G
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 56 | 73 | 30 | 2 | 73 | 89 | 95 | 25 | 5 |
+| B | 66 | 25 | 14 | 35 | 88 | 99 | 89 | 10 | 69 |
+| C | 80 | 64 | 89 | 49 | 81 | 98 | 20 | 80 | 37 |
+| D | 72 | 19 | 79 | 27 | 4 | 34 | 37 | 95 | 93 |
+| E | 50 | 56 | 94 | 62 | 28 | 38 | 83 | 63 | 98 |
+| F | 71 | 56 | 50 | 18 | 48 | 5 | 90 | 6 | 13 |
+| G | 86 | 93 | 60 | 0 | 37 | 88 | 79 | 70 | 59 |
+| H | 5 | 24 | 51 | 46 | 43 | 48 | 92 | 65 | 21 |
+| I | 65 | 71 | 35 | 81 | 23 | 71 | 67 | 59 | 41 |
+
+## order_id=H
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 41 | 16 | 93 | 48 | 74 | 46 | 38 | 35 | 57 |
+| B | 45 | 93 | 53 | 8 | 16 | 91 | 54 | 38 | 15 |
+| C | 69 | 61 | 14 | 15 | 63 | 0 | 44 | 79 | 95 |
+| D | 40 | 54 | 0 | 93 | 71 | 21 | 74 | 21 | 31 |
+| E | 76 | 19 | 38 | 9 | 7 | 90 | 85 | 63 | 7 |
+| F | 62 | 58 | 18 | 81 | 71 | 79 | 22 | 23 | 18 |
+| G | 12 | 25 | 24 | 12 | 30 | 41 | 42 | 94 | 84 |
+| H | 76 | 20 | 20 | 81 | 48 | 69 | 19 | 15 | 52 |
+| I | 20 | 54 | 74 | 76 | 52 | 16 | 12 | 83 | 33 |
+
+## order_id=I
+| driver_id\van_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 74 | 3 | 14 | 10 | 10 | 67 | 19 | 93 | 35 |
+| B | 59 | 24 | 73 | 23 | 47 | 64 | 72 | 68 | 44 |
+| C | 87 | 55 | 40 | 75 | 80 | 72 | 71 | 27 | 4 |
+| D | 69 | 92 | 1 | 77 | 98 | 68 | 65 | 48 | 85 |
+| E | 1 | 52 | 17 | 20 | 60 | 66 | 68 | 86 | 0 |
+| F | 55 | 74 | 53 | 92 | 38 | 22 | 19 | 95 | 54 |
+| G | 39 | 95 | 0 | 63 | 70 | 58 | 5 | 14 | 49 |
+| H | 67 | 25 | 14 | 24 | 43 | 7 | 89 | 93 | 97 |
+| I | 38 | 1 | 97 | 9 | 32 | 5 | 56 | 99 | 73 |
+
+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': [[[46, 74, 88, 80, 56, 22, 91, 15, 1], [22, 45, 21, 60, 45, 89, 88, 89, 59], [8, 45, 72, 26, 50, 83, 55, 72, 22], [59, 30, 51, 33, 49, 26, 67, 38, 61], [38, 63, 20, 48, 85, 91, 59, 69, 54], [28, 86, 56, 39, 45, 86, 60, 21, 9], [66, 31, 98, 25, 91, 69, 21, 26, 81], [7, 24, 98, 61, 7, 98, 95, 14, 74], [32, 89, 29, 76, 68, 46, 37, 59, 45]], [[47, 93, 6, 37, 24, 15, 82, 57, 72], [82, 44, 45, 40, 22, 22, 20, 3, 7], [0, 28, 79, 74, 65, 33, 54, 80, 62], [67, 66, 65, 46, 71, 58, 36, 90, 55], [60, 79, 32, 85, 8, 57, 87, 81, 92], [0, 55, 7, 67, 48, 61, 15, 33, 17], [75, 87, 40, 70, 82, 65, 92, 43, 39], [23, 29, 32, 96, 36, 94, 90, 17, 91], [30, 79, 8, 72, 1, 33, 49, 84, 34]], [[42, 30, 33, 7, 69, 67, 81, 0, 31], [4, 6, 83, 57, 40, 86, 62, 61, 68], [35, 31, 10, 12, 16, 67, 34, 98, 66], [92, 30, 55, 6, 52, 65, 55, 57, 31], [21, 75, 22, 62, 93, 37, 82, 2, 74], [81, 84, 58, 55, 7, 60, 46, 11, 12], [39, 80, 39, 1, 66, 15, 80, 38, 27], [78, 81, 48, 12, 97, 9, 57, 70, 13], [69, 88, 13, 61, 39, 55, 39, 93, 37]], [[63, 19, 94, 6, 79, 64, 88, 6, 91], [19, 95, 8, 84, 26, 21, 93, 38, 21], [44, 96, 81, 44, 15, 61, 4, 81, 34], [51, 9, 71, 22, 97, 33, 39, 30, 79], [66, 13, 47, 96, 2, 66, 63, 36, 68], [39, 45, 86, 18, 57, 33, 44, 84, 34], [67, 9, 26, 15, 67, 6, 13, 91, 32], [45, 1, 48, 52, 62, 14, 9, 14, 14], [75, 32, 50, 55, 71, 85, 13, 22, 89]], [[9, 29, 20, 9, 56, 61, 89, 93, 71], [88, 84, 59, 59, 94, 72, 98, 34, 74], [46, 77, 1, 13, 23, 31, 41, 47, 34], [75, 71, 94, 12, 2, 2, 73, 48, 73], [61, 7, 71, 41, 1, 92, 10, 42, 42], [15, 34, 21, 56, 57, 25, 75, 50, 73], [86, 7, 63, 7, 81, 92, 14, 36, 73], [87, 94, 25, 50, 25, 37, 5, 96, 28], [89, 6, 27, 77, 45, 53, 3, 61, 42]], [[89, 34, 80, 30, 79, 82, 42, 37, 8], [21, 20, 46, 53, 68, 28, 19, 65, 94], [53, 78, 81, 66, 65, 3, 57, 83, 24], [16, 29, 24, 13, 93, 53, 68, 7, 53], [8, 35, 52, 85, 80, 22, 37, 75, 28], [3, 84, 8, 38, 56, 85, 9, 80, 7], [20, 74, 54, 63, 96, 44, 22, 33, 45], [85, 99, 51, 17, 78, 50, 6, 12, 91], [95, 80, 19, 92, 0, 86, 28, 24, 11]], [[56, 73, 30, 2, 73, 89, 95, 25, 5], [66, 25, 14, 35, 88, 99, 89, 10, 69], [80, 64, 89, 49, 81, 98, 20, 80, 37], [72, 19, 79, 27, 4, 34, 37, 95, 93], [50, 56, 94, 62, 28, 38, 83, 63, 98], [71, 56, 50, 18, 48, 5, 90, 6, 13], [86, 93, 60, 0, 37, 88, 79, 70, 59], [5, 24, 51, 46, 43, 48, 92, 65, 21], [65, 71, 35, 81, 23, 71, 67, 59, 41]], [[41, 16, 93, 48, 74, 46, 38, 35, 57], [45, 93, 53, 8, 16, 91, 54, 38, 15], [69, 61, 14, 15, 63, 0, 44, 79, 95], [40, 54, 0, 93, 71, 21, 74, 21, 31], [76, 19, 38, 9, 7, 90, 85, 63, 7], [62, 58, 18, 81, 71, 79, 22, 23, 18], [12, 25, 24, 12, 30, 41, 42, 94, 84], [76, 20, 20, 81, 48, 69, 19, 15, 52], [20, 54, 74, 76, 52, 16, 12, 83, 33]], [[74, 3, 14, 10, 10, 67, 19, 93, 35], [59, 24, 73, 23, 47, 64, 72, 68, 44], [87, 55, 40, 75, 80, 72, 71, 27, 4], [69, 92, 1, 77, 98, 68, 65, 48, 85], [1, 52, 17, 20, 60, 66, 68, 86, 0], [55, 74, 53, 92, 38, 22, 19, 95, 54], [39, 95, 0, 63, 70, 58, 5, 14, 49], [67, 25, 14, 24, 43, 7, 89, 93, 97], [38, 1, 97, 9, 32, 5, 56, 99, 73]]], 'objective': 19.0}","[[0, 0, 8], [1, 1, 7], [2, 5, 4], [3, 7, 1], [4, 8, 6], [5, 2, 5], [6, 6, 3], [7, 3, 2], [8, 4, 0]]",19.0,"{'problem_type': 'AP3', 'n': 9, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 46}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 74}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 88}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 80}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 56}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 22}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 91}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 15}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 1}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 22}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 45}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 21}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 60}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 45}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 89}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 88}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 89}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 59}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 8}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 45}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 72}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 26}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 50}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 83}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 55}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 72}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 22}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 59}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 30}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 51}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 33}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 49}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 26}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 67}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 38}, {'i': 'A', 'j': 'D', 'k': 'I', 'cost': 61}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 38}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 63}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 20}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 48}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 85}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 91}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 59}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 69}, {'i': 'A', 'j': 'E', 'k': 'I', 'cost': 54}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 28}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 86}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 56}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 39}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 45}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 86}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 60}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 21}, {'i': 'A', 'j': 'F', 'k': 'I', 'cost': 9}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 66}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 31}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 98}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 25}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 91}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 69}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 21}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 26}, {'i': 'A', 'j': 'G', 'k': 'I', 'cost': 81}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 7}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 24}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 98}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 61}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 7}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 98}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 95}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 14}, {'i': 'A', 'j': 'H', 'k': 'I', 'cost': 74}, {'i': 'A', 'j': 'I', 'k': 'A', 'cost': 32}, {'i': 'A', 'j': 'I', 'k': 'B', 'cost': 89}, {'i': 'A', 'j': 'I', 'k': 'C', 'cost': 29}, {'i': 'A', 'j': 'I', 'k': 'D', 'cost': 76}, {'i': 'A', 'j': 'I', 'k': 'E', 'cost': 68}, {'i': 'A', 'j': 'I', 'k': 'F', 'cost': 46}, {'i': 'A', 'j': 'I', 'k': 'G', 'cost': 37}, {'i': 'A', 'j': 'I', 'k': 'H', 'cost': 59}, {'i': 'A', 'j': 'I', 'k': 'I', 'cost': 45}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 47}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 93}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 6}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 37}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 24}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 15}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 82}, {'i': 'B', 'j': 'A', 'k': 'H', 'cost': 57}, {'i': 'B', 'j': 'A', 'k': 'I', 'cost': 72}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 82}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 44}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 45}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 40}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 22}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 22}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 20}, {'i': 'B', 'j': 'B', 'k': 'H', 'cost': 3}, {'i': 'B', 'j': 'B', 'k': 'I', 'cost': 7}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 0}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 28}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 79}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 74}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 65}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 33}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 54}, {'i': 'B', 'j': 'C', 'k': 'H', 'cost': 80}, {'i': 'B', 'j': 'C', 'k': 'I', 'cost': 62}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 67}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 66}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 65}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 46}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 71}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 58}, {'i': 'B', 'j': 'D', 'k': 'G', 'cost': 36}, {'i': 'B', 'j': 'D', 'k': 'H', 'cost': 90}, {'i': 'B', 'j': 'D', 'k': 'I', 'cost': 55}, {'i': 'B', 'j': 'E', 'k': 'A', 'cost': 60}, {'i': 'B', 'j': 'E', 'k': 'B', 'cost': 79}, {'i': 'B', 'j': 'E', 'k': 'C', 'cost': 32}, {'i': 'B', 'j': 'E', 'k': 'D', 'cost': 85}, {'i': 'B', 'j': 'E', 'k': 'E', 'cost': 8}, {'i': 'B', 'j': 'E', 'k': 'F', 'cost': 57}, {'i': 'B', 'j': 'E', 'k': 'G', 'cost': 87}, {'i': 'B', 'j': 'E', 'k': 'H', 'cost': 81}, {'i': 'B', 'j': 'E', 'k': 'I', 'cost': 92}, {'i': 'B', 'j': 'F', 'k': 'A', 'cost': 0}, {'i': 'B', 'j': 'F', 'k': 'B', 'cost': 55}, {'i': 'B', 'j': 'F', 'k': 'C', 'cost': 7}, {'i': 'B', 'j': 'F', 'k': 'D', 'cost': 67}, {'i': 'B', 'j': 'F', 'k': 'E', 'cost': 48}, {'i': 'B', 'j': 'F', 'k': 'F', 'cost': 61}, {'i': 'B', 'j': 'F', 'k': 'G', 'cost': 15}, {'i': 'B', 'j': 'F', 'k': 'H', 'cost': 33}, {'i': 'B', 'j': 'F', 'k': 'I', 'cost': 17}, {'i': 'B', 'j': 'G', 'k': 'A', 'cost': 75}, {'i': 'B', 'j': 'G', 'k': 'B', 'cost': 87}, {'i': 'B', 'j': 'G', 'k': 'C', 'cost': 40}, {'i': 'B', 'j': 'G', 'k': 'D', 'cost': 70}, {'i': 'B', 'j': 'G', 'k': 'E', 'cost': 82}, {'i': 'B', 'j': 'G', 'k': 'F', 'cost': 65}, {'i': 'B', 'j': 'G', 'k': 'G', 'cost': 92}, {'i': 'B', 'j': 'G', 'k': 'H', 'cost': 43}, {'i': 'B', 'j': 'G', 'k': 'I', 'cost': 39}, {'i': 'B', 'j': 'H', 'k': 'A', 'cost': 23}, {'i': 'B', 'j': 'H', 'k': 'B', 'cost': 29}, {'i': 'B', 'j': 'H', 'k': 'C', 'cost': 32}, {'i': 'B', 'j': 'H', 'k': 'D', 'cost': 96}, {'i': 'B', 'j': 'H', 'k': 'E', 'cost': 36}, {'i': 'B', 'j': 'H', 'k': 'F', 'cost': 94}, {'i': 'B', 'j': 'H', 'k': 'G', 'cost': 90}, {'i': 'B', 'j': 'H', 'k': 'H', 'cost': 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'j': 'A', 'k': 'H', 'cost': 25}, {'i': 'G', 'j': 'A', 'k': 'I', 'cost': 5}, {'i': 'G', 'j': 'B', 'k': 'A', 'cost': 66}, {'i': 'G', 'j': 'B', 'k': 'B', 'cost': 25}, {'i': 'G', 'j': 'B', 'k': 'C', 'cost': 14}, {'i': 'G', 'j': 'B', 'k': 'D', 'cost': 35}, {'i': 'G', 'j': 'B', 'k': 'E', 'cost': 88}, {'i': 'G', 'j': 'B', 'k': 'F', 'cost': 99}, {'i': 'G', 'j': 'B', 'k': 'G', 'cost': 89}, {'i': 'G', 'j': 'B', 'k': 'H', 'cost': 10}, {'i': 'G', 'j': 'B', 'k': 'I', 'cost': 69}, {'i': 'G', 'j': 'C', 'k': 'A', 'cost': 80}, {'i': 'G', 'j': 'C', 'k': 'B', 'cost': 64}, {'i': 'G', 'j': 'C', 'k': 'C', 'cost': 89}, {'i': 'G', 'j': 'C', 'k': 'D', 'cost': 49}, {'i': 'G', 'j': 'C', 'k': 'E', 'cost': 81}, {'i': 'G', 'j': 'C', 'k': 'F', 'cost': 98}, {'i': 'G', 'j': 'C', 'k': 'G', 'cost': 20}, {'i': 'G', 'j': 'C', 'k': 'H', 'cost': 80}, {'i': 'G', 'j': 'C', 'k': 'I', 'cost': 37}, {'i': 'G', 'j': 'D', 'k': 'A', 'cost': 72}, {'i': 'G', 'j': 'D', 'k': 'B', 'cost': 19}, {'i': 'G', 'j': 'D', 'k': 'C', 'cost': 79}, {'i': 'G', 'j': 'D', 'k': 'D', 'cost': 27}, {'i': 'G', 'j': 'D', 'k': 'E', 'cost': 4}, {'i': 'G', 'j': 'D', 'k': 'F', 'cost': 34}, {'i': 'G', 'j': 'D', 'k': 'G', 'cost': 37}, {'i': 'G', 'j': 'D', 'k': 'H', 'cost': 95}, {'i': 'G', 'j': 'D', 'k': 'I', 'cost': 93}, {'i': 'G', 'j': 'E', 'k': 'A', 'cost': 50}, {'i': 'G', 'j': 'E', 'k': 'B', 'cost': 56}, {'i': 'G', 'j': 'E', 'k': 'C', 'cost': 94}, {'i': 'G', 'j': 'E', 'k': 'D', 'cost': 62}, {'i': 'G', 'j': 'E', 'k': 'E', 'cost': 28}, {'i': 'G', 'j': 'E', 'k': 'F', 'cost': 38}, {'i': 'G', 'j': 'E', 'k': 'G', 'cost': 83}, {'i': 'G', 'j': 'E', 'k': 'H', 'cost': 63}, {'i': 'G', 'j': 'E', 'k': 'I', 'cost': 98}, {'i': 'G', 'j': 'F', 'k': 'A', 'cost': 71}, {'i': 'G', 'j': 'F', 'k': 'B', 'cost': 56}, {'i': 'G', 'j': 'F', 'k': 'C', 'cost': 50}, {'i': 'G', 'j': 'F', 'k': 'D', 'cost': 18}, {'i': 'G', 'j': 'F', 'k': 'E', 'cost': 48}, {'i': 'G', 'j': 'F', 'k': 'F', 'cost': 5}, {'i': 'G', 'j': 'F', 'k': 'G', 'cost': 90}, {'i': 'G', 'j': 'F', 'k': 'H', 'cost': 6}, {'i': 'G', 'j': 'F', 'k': 'I', 'cost': 13}, {'i': 'G', 'j': 'G', 'k': 'A', 'cost': 86}, {'i': 'G', 'j': 'G', 'k': 'B', 'cost': 93}, {'i': 'G', 'j': 'G', 'k': 'C', 'cost': 60}, {'i': 'G', 'j': 'G', 'k': 'D', 'cost': 0}, {'i': 'G', 'j': 'G', 'k': 'E', 'cost': 37}, {'i': 'G', 'j': 'G', 'k': 'F', 'cost': 88}, {'i': 'G', 'j': 'G', 'k': 'G', 'cost': 79}, {'i': 'G', 'j': 'G', 'k': 'H', 'cost': 70}, {'i': 'G', 'j': 'G', 'k': 'I', 'cost': 59}, {'i': 'G', 'j': 'H', 'k': 'A', 'cost': 5}, {'i': 'G', 'j': 'H', 'k': 'B', 'cost': 24}, {'i': 'G', 'j': 'H', 'k': 'C', 'cost': 51}, {'i': 'G', 'j': 'H', 'k': 'D', 'cost': 46}, {'i': 'G', 'j': 'H', 'k': 'E', 'cost': 43}, {'i': 'G', 'j': 'H', 'k': 'F', 'cost': 48}, {'i': 'G', 'j': 'H', 'k': 'G', 'cost': 92}, {'i': 'G', 'j': 'H', 'k': 'H', 'cost': 65}, {'i': 'G', 'j': 'H', 'k': 'I', 'cost': 21}, {'i': 'G', 'j': 'I', 'k': 'A', 'cost': 65}, {'i': 'G', 'j': 'I', 'k': 'B', 'cost': 71}, {'i': 'G', 'j': 'I', 'k': 'C', 'cost': 35}, {'i': 'G', 'j': 'I', 'k': 'D', 'cost': 81}, {'i': 'G', 'j': 'I', 'k': 'E', 'cost': 23}, {'i': 'G', 'j': 'I', 'k': 'F', 'cost': 71}, {'i': 'G', 'j': 'I', 'k': 'G', 'cost': 67}, {'i': 'G', 'j': 'I', 'k': 'H', 'cost': 59}, {'i': 'G', 'j': 'I', 'k': 'I', 'cost': 41}, {'i': 'H', 'j': 'A', 'k': 'A', 'cost': 41}, {'i': 'H', 'j': 'A', 'k': 'B', 'cost': 16}, {'i': 'H', 'j': 'A', 'k': 'C', 'cost': 93}, {'i': 'H', 'j': 'A', 'k': 'D', 'cost': 48}, {'i': 'H', 'j': 'A', 'k': 'E', 'cost': 74}, {'i': 'H', 'j': 'A', 'k': 'F', 'cost': 46}, {'i': 'H', 'j': 'A', 'k': 'G', 'cost': 38}, {'i': 'H', 'j': 'A', 'k': 'H', 'cost': 35}, {'i': 'H', 'j': 'A', 'k': 'I', 'cost': 57}, {'i': 'H', 'j': 'B', 'k': 'A', 'cost': 45}, {'i': 'H', 'j': 'B', 'k': 'B', 'cost': 93}, {'i': 'H', 'j': 'B', 'k': 'C', 'cost': 53}, {'i': 'H', 'j': 'B', 'k': 'D', 'cost': 8}, {'i': 'H', 'j': 'B', 'k': 'E', 'cost': 16}, {'i': 'H', 'j': 'B', 'k': 'F', 'cost': 91}, {'i': 'H', 'j': 'B', 'k': 'G', 'cost': 54}, {'i': 'H', 'j': 'B', 'k': 'H', 'cost': 38}, {'i': 'H', 'j': 'B', 'k': 'I', 'cost': 15}, {'i': 'H', 'j': 'C', 'k': 'A', 'cost': 69}, {'i': 'H', 'j': 'C', 'k': 'B', 'cost': 61}, {'i': 'H', 'j': 'C', 'k': 'C', 'cost': 14}, {'i': 'H', 'j': 'C', 'k': 'D', 'cost': 15}, {'i': 'H', 'j': 'C', 'k': 'E', 'cost': 63}, {'i': 'H', 'j': 'C', 'k': 'F', 'cost': 0}, {'i': 'H', 'j': 'C', 'k': 'G', 'cost': 44}, {'i': 'H', 'j': 'C', 'k': 'H', 'cost': 79}, {'i': 'H', 'j': 'C', 'k': 'I', 'cost': 95}, {'i': 'H', 'j': 'D', 'k': 'A', 'cost': 40}, {'i': 'H', 'j': 'D', 'k': 'B', 'cost': 54}, {'i': 'H', 'j': 'D', 'k': 'C', 'cost': 0}, {'i': 'H', 'j': 'D', 'k': 'D', 'cost': 93}, {'i': 'H', 'j': 'D', 'k': 'E', 'cost': 71}, {'i': 'H', 'j': 'D', 'k': 'F', 'cost': 21}, {'i': 'H', 'j': 'D', 'k': 'G', 'cost': 74}, {'i': 'H', 'j': 'D', 'k': 'H', 'cost': 21}, {'i': 'H', 'j': 'D', 'k': 'I', 'cost': 31}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 76}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 19}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 38}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 9}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 7}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 90}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 85}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 63}, {'i': 'H', 'j': 'E', 'k': 'I', 'cost': 7}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 62}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 58}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 18}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 81}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 71}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 79}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 22}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 23}, {'i': 'H', 'j': 'F', 'k': 'I', 'cost': 18}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 12}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 25}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 24}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 12}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 30}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 41}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 42}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 94}, {'i': 'H', 'j': 'G', 'k': 'I', 'cost': 84}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 76}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 20}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 20}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 81}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 48}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 69}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 19}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 15}, {'i': 'H', 'j': 'H', 'k': 'I', 'cost': 52}, {'i': 'H', 'j': 'I', 'k': 'A', 'cost': 20}, {'i': 'H', 'j': 'I', 'k': 'B', 'cost': 54}, {'i': 'H', 'j': 'I', 'k': 'C', 'cost': 74}, {'i': 'H', 'j': 'I', 'k': 'D', 'cost': 76}, {'i': 'H', 'j': 'I', 'k': 'E', 'cost': 52}, {'i': 'H', 'j': 'I', 'k': 'F', 'cost': 16}, {'i': 'H', 'j': 'I', 'k': 'G', 'cost': 12}, {'i': 'H', 'j': 'I', 'k': 'H', 'cost': 83}, {'i': 'H', 'j': 'I', 'k': 'I', 'cost': 33}, {'i': 'I', 'j': 'A', 'k': 'A', 'cost': 74}, {'i': 'I', 'j': 'A', 'k': 'B', 'cost': 3}, {'i': 'I', 'j': 'A', 'k': 'C', 'cost': 14}, {'i': 'I', 'j': 'A', 'k': 'D', 'cost': 10}, {'i': 'I', 'j': 'A', 'k': 'E', 'cost': 10}, {'i': 'I', 'j': 'A', 'k': 'F', 'cost': 67}, {'i': 'I', 'j': 'A', 'k': 'G', 'cost': 19}, {'i': 'I', 'j': 'A', 'k': 'H', 'cost': 93}, {'i': 'I', 'j': 'A', 'k': 'I', 'cost': 35}, {'i': 'I', 'j': 'B', 'k': 'A', 'cost': 59}, {'i': 'I', 'j': 'B', 'k': 'B', 'cost': 24}, {'i': 'I', 'j': 'B', 'k': 'C', 'cost': 73}, {'i': 'I', 'j': 'B', 'k': 'D', 'cost': 23}, {'i': 'I', 'j': 'B', 'k': 'E', 'cost': 47}, {'i': 'I', 'j': 'B', 'k': 'F', 'cost': 64}, {'i': 'I', 'j': 'B', 'k': 'G', 'cost': 72}, {'i': 'I', 'j': 'B', 'k': 'H', 'cost': 68}, {'i': 'I', 'j': 'B', 'k': 'I', 'cost': 44}, {'i': 'I', 'j': 'C', 'k': 'A', 'cost': 87}, {'i': 'I', 'j': 'C', 'k': 'B', 'cost': 55}, {'i': 'I', 'j': 'C', 'k': 'C', 'cost': 40}, {'i': 'I', 'j': 'C', 'k': 'D', 'cost': 75}, {'i': 'I', 'j': 'C', 'k': 'E', 'cost': 80}, {'i': 'I', 'j': 'C', 'k': 'F', 'cost': 72}, {'i': 'I', 'j': 'C', 'k': 'G', 'cost': 71}, {'i': 'I', 'j': 'C', 'k': 'H', 'cost': 27}, {'i': 'I', 'j': 'C', 'k': 'I', 'cost': 4}, {'i': 'I', 'j': 'D', 'k': 'A', 'cost': 69}, {'i': 'I', 'j': 'D', 'k': 'B', 'cost': 92}, {'i': 'I', 'j': 'D', 'k': 'C', 'cost': 1}, {'i': 'I', 'j': 'D', 'k': 'D', 'cost': 77}, {'i': 'I', 'j': 'D', 'k': 'E', 'cost': 98}, {'i': 'I', 'j': 'D', 'k': 'F', 'cost': 68}, {'i': 'I', 'j': 'D', 'k': 'G', 'cost': 65}, {'i': 'I', 'j': 'D', 'k': 'H', 'cost': 48}, {'i': 'I', 'j': 'D', 'k': 'I', 'cost': 85}, {'i': 'I', 'j': 'E', 'k': 'A', 'cost': 1}, {'i': 'I', 'j': 'E', 'k': 'B', 'cost': 52}, {'i': 'I', 'j': 'E', 'k': 'C', 'cost': 17}, {'i': 'I', 'j': 'E', 'k': 'D', 'cost': 20}, {'i': 'I', 'j': 'E', 'k': 'E', 'cost': 60}, {'i': 'I', 'j': 'E', 'k': 'F', 'cost': 66}, {'i': 'I', 'j': 'E', 'k': 'G', 'cost': 68}, {'i': 'I', 'j': 'E', 'k': 'H', 'cost': 86}, {'i': 'I', 'j': 'E', 'k': 'I', 'cost': 0}, {'i': 'I', 'j': 'F', 'k': 'A', 'cost': 55}, {'i': 'I', 'j': 'F', 'k': 'B', 'cost': 74}, {'i': 'I', 'j': 'F', 'k': 'C', 'cost': 53}, {'i': 'I', 'j': 'F', 'k': 'D', 'cost': 92}, {'i': 'I', 'j': 'F', 'k': 'E', 'cost': 38}, {'i': 'I', 'j': 'F', 'k': 'F', 'cost': 22}, {'i': 'I', 'j': 'F', 'k': 'G', 'cost': 19}, {'i': 'I', 'j': 'F', 'k': 'H', 'cost': 95}, {'i': 'I', 'j': 'F', 'k': 'I', 'cost': 54}, {'i': 'I', 'j': 'G', 'k': 'A', 'cost': 39}, {'i': 'I', 'j': 'G', 'k': 'B', 'cost': 95}, {'i': 'I', 'j': 'G', 'k': 'C', 'cost': 0}, {'i': 'I', 'j': 'G', 'k': 'D', 'cost': 63}, {'i': 'I', 'j': 'G', 'k': 'E', 'cost': 70}, {'i': 'I', 'j': 'G', 'k': 'F', 'cost': 58}, {'i': 'I', 'j': 'G', 'k': 'G', 'cost': 5}, {'i': 'I', 'j': 'G', 'k': 'H', 'cost': 14}, {'i': 'I', 'j': 'G', 'k': 'I', 'cost': 49}, {'i': 'I', 'j': 'H', 'k': 'A', 'cost': 67}, {'i': 'I', 'j': 'H', 'k': 'B', 'cost': 25}, {'i': 'I', 'j': 'H', 'k': 'C', 'cost': 14}, {'i': 'I', 'j': 'H', 'k': 'D', 'cost': 24}, {'i': 'I', 'j': 'H', 'k': 'E', 'cost': 43}, {'i': 'I', 'j': 'H', 'k': 'F', 'cost': 7}, {'i': 'I', 'j': 'H', 'k': 'G', 'cost': 89}, {'i': 'I', 'j': 'H', 'k': 'H', 'cost': 93}, {'i': 'I', 'j': 'H', 'k': 'I', 'cost': 97}, {'i': 'I', 'j': 'I', 'k': 'A', 'cost': 38}, {'i': 'I', 'j': 'I', 'k': 'B', 'cost': 1}, {'i': 'I', 'j': 'I', 'k': 'C', 'cost': 97}, {'i': 'I', 'j': 'I', 'k': 'D', 'cost': 9}, {'i': 'I', 'j': 'I', 'k': 'E', 'cost': 32}, {'i': 'I', 'j': 'I', 'k': 'F', 'cost': 5}, {'i': 'I', 'j': 'I', 'k': 'G', 'cost': 56}, {'i': 'I', 'j': 'I', 'k': 'H', 'cost': 99}, {'i': 'I', 'j': 'I', 'k': 'I', 'cost': 73}]}","[['A', 'A', 'I'], ['B', 'B', 'H'], ['C', 'F', 'E'], ['D', 'H', 'B'], ['E', 'I', 'G'], ['F', 'C', 'F'], ['G', 'G', 'D'], ['H', 'D', 'C'], ['I', 'E', 'A']]",22,json,names
+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.
+
+There are 12 activities, listed by identifier as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
+
+*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=1
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 15 | 59 | 64 | 87 | 82 | 93 | 89 | 33 | 93 | 26 | 58 | 93 |
+| 2 | 37 | 73 | 4 | 75 | 20 | 83 | 13 | 55 | 92 | 9 | 55 | 27 |
+| 3 | 31 | 11 | 91 | 94 | 38 | 32 | 6 | 74 | 45 | 55 | 38 | 49 |
+| 4 | 76 | 17 | 88 | 84 | 92 | 93 | 19 | 38 | 62 | 21 | 17 | 90 |
+| 5 | 71 | 86 | 81 | 39 | 91 | 97 | 88 | 89 | 22 | 78 | 84 | 7 |
+| 6 | 30 | 64 | 40 | 72 | 96 | 37 | 72 | 69 | 51 | 35 | 74 | 99 |
+| 7 | 94 | 26 | 3 | 28 | 95 | 24 | 18 | 43 | 55 | 30 | 58 | 89 |
+| 8 | 19 | 90 | 61 | 18 | 15 | 66 | 75 | 73 | 25 | 13 | 63 | 84 |
+| 9 | 97 | 16 | 87 | 58 | 40 | 41 | 80 | 12 | 48 | 28 | 70 | 8 |
+| 10 | 37 | 40 | 37 | 15 | 28 | 65 | 39 | 84 | 8 | 67 | 16 | 93 |
+| 11 | 16 | 81 | 6 | 51 | 32 | 61 | 61 | 87 | 38 | 18 | 2 | 92 |
+| 12 | 76 | 0 | 94 | 41 | 1 | 9 | 8 | 97 | 61 | 36 | 54 | 16 |
+
+## activity_id=2
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 48 | 98 | 36 | 49 | 10 | 10 | 41 | 76 | 81 | 87 | 21 | 63 |
+| 2 | 86 | 28 | 13 | 74 | 67 | 19 | 8 | 98 | 72 | 66 | 5 | 41 |
+| 3 | 50 | 64 | 35 | 21 | 32 | 5 | 62 | 43 | 31 | 52 | 21 | 41 |
+| 4 | 18 | 88 | 73 | 53 | 36 | 6 | 88 | 16 | 6 | 24 | 88 | 15 |
+| 5 | 84 | 64 | 86 | 3 | 31 | 52 | 15 | 15 | 56 | 34 | 5 | 33 |
+| 6 | 89 | 37 | 79 | 53 | 0 | 77 | 29 | 10 | 92 | 33 | 87 | 4 |
+| 7 | 18 | 49 | 98 | 32 | 91 | 66 | 97 | 0 | 32 | 53 | 43 | 44 |
+| 8 | 44 | 22 | 77 | 13 | 85 | 36 | 46 | 97 | 82 | 9 | 30 | 4 |
+| 9 | 54 | 56 | 58 | 41 | 75 | 17 | 98 | 63 | 66 | 85 | 24 | 4 |
+| 10 | 44 | 44 | 66 | 86 | 46 | 0 | 59 | 18 | 22 | 14 | 54 | 77 |
+| 11 | 52 | 97 | 89 | 13 | 27 | 37 | 94 | 70 | 18 | 80 | 4 | 12 |
+| 12 | 51 | 87 | 46 | 49 | 28 | 97 | 49 | 74 | 66 | 72 | 2 | 23 |
+
+## activity_id=3
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 74 | 9 | 8 | 61 | 32 | 72 | 77 | 55 | 68 | 30 | 65 | 82 |
+| 2 | 57 | 91 | 2 | 85 | 30 | 52 | 81 | 63 | 68 | 39 | 77 | 39 |
+| 3 | 11 | 0 | 38 | 84 | 72 | 77 | 9 | 41 | 39 | 24 | 44 | 57 |
+| 4 | 26 | 11 | 57 | 20 | 27 | 10 | 79 | 49 | 34 | 35 | 68 | 59 |
+| 5 | 19 | 94 | 50 | 56 | 60 | 62 | 58 | 61 | 82 | 14 | 76 | 77 |
+| 6 | 51 | 23 | 87 | 83 | 25 | 20 | 60 | 26 | 56 | 71 | 50 | 80 |
+| 7 | 32 | 47 | 19 | 72 | 46 | 29 | 32 | 22 | 43 | 1 | 49 | 3 |
+| 8 | 34 | 32 | 53 | 96 | 7 | 78 | 50 | 37 | 34 | 61 | 4 | 43 |
+| 9 | 20 | 82 | 79 | 4 | 82 | 30 | 32 | 88 | 68 | 18 | 53 | 33 |
+| 10 | 21 | 60 | 12 | 85 | 63 | 12 | 9 | 19 | 85 | 18 | 27 | 89 |
+| 11 | 3 | 75 | 81 | 91 | 99 | 42 | 30 | 26 | 0 | 0 | 38 | 16 |
+| 12 | 87 | 1 | 79 | 66 | 57 | 81 | 63 | 35 | 83 | 62 | 30 | 17 |
+
+## activity_id=4
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 20 | 51 | 33 | 36 | 51 | 2 | 34 | 35 | 32 | 76 | 25 | 38 |
+| 2 | 45 | 25 | 13 | 83 | 20 | 54 | 62 | 81 | 72 | 29 | 38 | 65 |
+| 3 | 78 | 57 | 13 | 70 | 12 | 38 | 71 | 56 | 24 | 39 | 21 | 81 |
+| 4 | 55 | 8 | 90 | 30 | 85 | 75 | 69 | 62 | 35 | 31 | 8 | 51 |
+| 5 | 37 | 45 | 3 | 99 | 71 | 10 | 84 | 46 | 30 | 53 | 14 | 33 |
+| 6 | 46 | 41 | 41 | 77 | 91 | 84 | 30 | 56 | 74 | 63 | 82 | 7 |
+| 7 | 47 | 97 | 51 | 90 | 60 | 60 | 21 | 24 | 90 | 78 | 18 | 84 |
+| 8 | 32 | 19 | 76 | 22 | 64 | 71 | 48 | 82 | 65 | 45 | 74 | 39 |
+| 9 | 53 | 30 | 52 | 0 | 42 | 40 | 55 | 38 | 51 | 46 | 73 | 34 |
+| 10 | 67 | 95 | 97 | 91 | 58 | 84 | 84 | 62 | 82 | 52 | 11 | 15 |
+| 11 | 25 | 97 | 6 | 91 | 93 | 69 | 87 | 6 | 86 | 61 | 71 | 10 |
+| 12 | 10 | 67 | 47 | 97 | 37 | 35 | 71 | 27 | 79 | 50 | 81 | 32 |
+
+## activity_id=5
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 91 | 38 | 58 | 79 | 78 | 86 | 58 | 75 | 76 | 17 | 10 | 30 |
+| 2 | 89 | 76 | 62 | 27 | 75 | 10 | 27 | 50 | 1 | 62 | 49 | 79 |
+| 3 | 99 | 97 | 59 | 18 | 14 | 56 | 79 | 82 | 92 | 65 | 70 | 35 |
+| 4 | 2 | 9 | 40 | 93 | 13 | 45 | 61 | 71 | 86 | 18 | 38 | 56 |
+| 5 | 82 | 59 | 91 | 62 | 63 | 20 | 12 | 69 | 31 | 88 | 70 | 35 |
+| 6 | 8 | 33 | 36 | 62 | 91 | 51 | 89 | 44 | 87 | 57 | 58 | 53 |
+| 7 | 33 | 3 | 50 | 36 | 96 | 54 | 24 | 34 | 89 | 92 | 74 | 72 |
+| 8 | 99 | 82 | 83 | 81 | 95 | 16 | 74 | 14 | 12 | 63 | 85 | 42 |
+| 9 | 17 | 36 | 93 | 10 | 65 | 65 | 60 | 50 | 8 | 97 | 30 | 39 |
+| 10 | 83 | 54 | 48 | 40 | 60 | 66 | 0 | 83 | 19 | 8 | 72 | 14 |
+| 11 | 58 | 48 | 16 | 26 | 93 | 64 | 19 | 70 | 48 | 54 | 72 | 62 |
+| 12 | 39 | 62 | 13 | 2 | 57 | 0 | 47 | 67 | 76 | 96 | 96 | 57 |
+
+## activity_id=6
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 54 | 33 | 68 | 17 | 2 | 72 | 14 | 11 | 78 | 96 | 61 | 81 |
+| 2 | 18 | 38 | 14 | 16 | 52 | 24 | 27 | 63 | 80 | 69 | 87 | 65 |
+| 3 | 74 | 91 | 53 | 92 | 69 | 41 | 6 | 93 | 37 | 85 | 89 | 15 |
+| 4 | 61 | 18 | 9 | 10 | 70 | 8 | 17 | 46 | 48 | 21 | 95 | 68 |
+| 5 | 89 | 64 | 24 | 57 | 97 | 49 | 78 | 28 | 50 | 36 | 43 | 24 |
+| 6 | 15 | 77 | 45 | 57 | 36 | 83 | 84 | 64 | 81 | 84 | 60 | 30 |
+| 7 | 21 | 21 | 9 | 70 | 66 | 11 | 98 | 38 | 77 | 32 | 40 | 78 |
+| 8 | 45 | 83 | 21 | 72 | 84 | 37 | 25 | 42 | 3 | 44 | 84 | 20 |
+| 9 | 28 | 34 | 6 | 56 | 68 | 58 | 68 | 32 | 62 | 55 | 45 | 51 |
+| 10 | 48 | 83 | 0 | 24 | 43 | 11 | 70 | 28 | 88 | 32 | 74 | 98 |
+| 11 | 84 | 41 | 59 | 14 | 45 | 94 | 59 | 89 | 77 | 61 | 64 | 48 |
+| 12 | 9 | 68 | 43 | 66 | 18 | 79 | 82 | 87 | 75 | 62 | 29 | 42 |
+
+## activity_id=7
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 84 | 0 | 12 | 45 | 22 | 22 | 88 | 56 | 65 | 96 | 12 | 94 |
+| 2 | 64 | 2 | 52 | 55 | 39 | 69 | 21 | 43 | 25 | 19 | 8 | 38 |
+| 3 | 97 | 27 | 4 | 31 | 66 | 50 | 43 | 19 | 54 | 13 | 57 | 40 |
+| 4 | 2 | 67 | 63 | 23 | 63 | 81 | 71 | 0 | 62 | 45 | 45 | 36 |
+| 5 | 96 | 17 | 10 | 87 | 40 | 28 | 90 | 89 | 91 | 10 | 67 | 65 |
+| 6 | 94 | 57 | 53 | 17 | 26 | 29 | 48 | 10 | 69 | 68 | 85 | 58 |
+| 7 | 68 | 75 | 30 | 55 | 82 | 35 | 49 | 44 | 14 | 66 | 46 | 85 |
+| 8 | 70 | 29 | 77 | 1 | 86 | 39 | 88 | 11 | 53 | 1 | 58 | 35 |
+| 9 | 3 | 83 | 24 | 66 | 37 | 18 | 52 | 29 | 8 | 27 | 26 | 94 |
+| 10 | 53 | 8 | 74 | 58 | 25 | 73 | 54 | 46 | 34 | 53 | 51 | 51 |
+| 11 | 66 | 78 | 4 | 60 | 14 | 12 | 26 | 12 | 63 | 52 | 5 | 77 |
+| 12 | 85 | 15 | 42 | 69 | 6 | 61 | 71 | 37 | 14 | 60 | 16 | 89 |
+
+## activity_id=8
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 74 | 29 | 11 | 34 | 70 | 30 | 65 | 17 | 71 | 34 | 80 | 8 |
+| 2 | 33 | 42 | 86 | 53 | 29 | 95 | 72 | 22 | 89 | 95 | 14 | 96 |
+| 3 | 81 | 18 | 82 | 52 | 71 | 50 | 22 | 17 | 5 | 73 | 5 | 52 |
+| 4 | 74 | 73 | 61 | 8 | 72 | 94 | 36 | 75 | 63 | 57 | 32 | 40 |
+| 5 | 70 | 1 | 4 | 96 | 83 | 91 | 29 | 1 | 88 | 80 | 60 | 6 |
+| 6 | 68 | 2 | 17 | 83 | 23 | 15 | 71 | 5 | 96 | 19 | 22 | 35 |
+| 7 | 19 | 73 | 23 | 39 | 21 | 85 | 80 | 57 | 39 | 76 | 41 | 44 |
+| 8 | 9 | 8 | 20 | 92 | 57 | 89 | 58 | 90 | 29 | 53 | 55 | 28 |
+| 9 | 50 | 33 | 21 | 22 | 84 | 67 | 58 | 66 | 37 | 35 | 74 | 18 |
+| 10 | 56 | 49 | 85 | 8 | 32 | 17 | 78 | 69 | 17 | 25 | 45 | 92 |
+| 11 | 77 | 94 | 70 | 26 | 94 | 84 | 53 | 7 | 1 | 80 | 32 | 63 |
+| 12 | 53 | 53 | 27 | 69 | 68 | 77 | 33 | 86 | 19 | 9 | 86 | 75 |
+
+## activity_id=9
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 35 | 86 | 4 | 99 | 55 | 96 | 96 | 90 | 24 | 88 | 94 | 54 |
+| 2 | 52 | 98 | 55 | 96 | 9 | 33 | 56 | 46 | 1 | 95 | 59 | 80 |
+| 3 | 92 | 18 | 21 | 5 | 7 | 0 | 39 | 80 | 78 | 54 | 60 | 61 |
+| 4 | 2 | 52 | 33 | 15 | 68 | 57 | 0 | 83 | 97 | 49 | 23 | 23 |
+| 5 | 40 | 56 | 40 | 6 | 98 | 86 | 2 | 24 | 69 | 20 | 87 | 95 |
+| 6 | 58 | 48 | 44 | 90 | 96 | 62 | 82 | 36 | 1 | 73 | 60 | 67 |
+| 7 | 22 | 96 | 38 | 14 | 3 | 12 | 0 | 28 | 36 | 66 | 7 | 24 |
+| 8 | 56 | 1 | 83 | 37 | 20 | 19 | 54 | 7 | 78 | 48 | 12 | 21 |
+| 9 | 95 | 5 | 74 | 26 | 36 | 88 | 36 | 35 | 48 | 69 | 40 | 67 |
+| 10 | 83 | 19 | 84 | 88 | 98 | 89 | 83 | 95 | 68 | 60 | 48 | 74 |
+| 11 | 77 | 7 | 13 | 24 | 15 | 57 | 5 | 6 | 12 | 99 | 95 | 91 |
+| 12 | 87 | 18 | 87 | 26 | 26 | 12 | 18 | 11 | 45 | 49 | 35 | 66 |
+
+## activity_id=10
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 24 | 61 | 32 | 95 | 93 | 79 | 95 | 34 | 98 | 55 | 11 | 0 |
+| 2 | 46 | 8 | 6 | 13 | 90 | 72 | 78 | 93 | 74 | 91 | 18 | 77 |
+| 3 | 78 | 11 | 90 | 3 | 84 | 69 | 10 | 55 | 54 | 14 | 85 | 82 |
+| 4 | 76 | 65 | 86 | 9 | 59 | 45 | 67 | 12 | 44 | 45 | 48 | 74 |
+| 5 | 61 | 38 | 84 | 29 | 19 | 24 | 32 | 19 | 49 | 67 | 6 | 81 |
+| 6 | 96 | 90 | 46 | 55 | 67 | 13 | 45 | 60 | 87 | 42 | 41 | 3 |
+| 7 | 68 | 49 | 23 | 93 | 17 | 20 | 23 | 43 | 2 | 78 | 98 | 70 |
+| 8 | 53 | 65 | 96 | 21 | 22 | 77 | 80 | 15 | 18 | 66 | 32 | 22 |
+| 9 | 77 | 80 | 89 | 66 | 62 | 92 | 70 | 74 | 86 | 45 | 89 | 37 |
+| 10 | 9 | 11 | 67 | 88 | 10 | 23 | 92 | 41 | 24 | 76 | 71 | 29 |
+| 11 | 55 | 73 | 63 | 65 | 5 | 14 | 56 | 90 | 95 | 6 | 17 | 17 |
+| 12 | 2 | 93 | 83 | 75 | 36 | 14 | 54 | 99 | 58 | 11 | 54 | 17 |
+
+## activity_id=11
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 21 | 89 | 26 | 95 | 57 | 34 | 7 | 2 | 92 | 46 | 25 | 0 |
+| 2 | 74 | 32 | 91 | 54 | 16 | 54 | 10 | 38 | 56 | 81 | 70 | 42 |
+| 3 | 71 | 77 | 78 | 91 | 84 | 54 | 37 | 34 | 53 | 95 | 29 | 66 |
+| 4 | 7 | 91 | 76 | 49 | 8 | 84 | 81 | 23 | 19 | 41 | 45 | 18 |
+| 5 | 13 | 52 | 95 | 96 | 30 | 58 | 39 | 11 | 34 | 98 | 71 | 53 |
+| 6 | 6 | 27 | 28 | 51 | 82 | 19 | 20 | 55 | 81 | 18 | 64 | 7 |
+| 7 | 1 | 54 | 77 | 32 | 48 | 62 | 48 | 92 | 31 | 22 | 39 | 25 |
+| 8 | 91 | 29 | 34 | 58 | 82 | 93 | 69 | 1 | 22 | 90 | 0 | 74 |
+| 9 | 33 | 71 | 18 | 14 | 43 | 17 | 91 | 20 | 55 | 72 | 62 | 63 |
+| 10 | 34 | 18 | 26 | 58 | 10 | 8 | 22 | 3 | 23 | 2 | 9 | 92 |
+| 11 | 13 | 44 | 26 | 68 | 50 | 73 | 4 | 84 | 69 | 42 | 5 | 32 |
+| 12 | 14 | 88 | 19 | 77 | 67 | 96 | 81 | 28 | 14 | 65 | 5 | 46 |
+
+## activity_id=12
+| volunteer_id\station_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 46 | 61 | 87 | 78 | 56 | 9 | 67 | 7 | 85 | 17 | 12 | 99 |
+| 2 | 38 | 19 | 85 | 58 | 55 | 4 | 62 | 17 | 15 | 66 | 43 | 85 |
+| 3 | 45 | 45 | 89 | 82 | 13 | 82 | 21 | 10 | 76 | 99 | 32 | 37 |
+| 4 | 99 | 59 | 15 | 53 | 74 | 61 | 24 | 15 | 90 | 94 | 39 | 38 |
+| 5 | 54 | 78 | 11 | 36 | 6 | 45 | 1 | 28 | 48 | 31 | 37 | 3 |
+| 6 | 51 | 66 | 37 | 16 | 37 | 35 | 55 | 1 | 90 | 86 | 13 | 91 |
+| 7 | 38 | 15 | 51 | 50 | 41 | 24 | 48 | 54 | 85 | 35 | 9 | 32 |
+| 8 | 85 | 52 | 45 | 14 | 41 | 82 | 14 | 27 | 58 | 64 | 34 | 68 |
+| 9 | 81 | 57 | 45 | 25 | 45 | 72 | 54 | 63 | 8 | 0 | 48 | 22 |
+| 10 | 95 | 30 | 77 | 55 | 56 | 37 | 13 | 95 | 66 | 59 | 7 | 7 |
+| 11 | 37 | 51 | 64 | 66 | 66 | 33 | 37 | 60 | 76 | 58 | 63 | 15 |
+| 12 | 7 | 42 | 71 | 31 | 43 | 58 | 47 | 11 | 54 | 56 | 12 | 11 |
+
+Choose one of these triples for each of the 12 activities so every identifier in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 is covered and each volunteer and station is used exactly once to minimize the total staffing cost.
+
+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': [[[15, 59, 64, 87, 82, 93, 89, 33, 93, 26, 58, 93], [37, 73, 4, 75, 20, 83, 13, 55, 92, 9, 55, 27], [31, 11, 91, 94, 38, 32, 6, 74, 45, 55, 38, 49], [76, 17, 88, 84, 92, 93, 19, 38, 62, 21, 17, 90], [71, 86, 81, 39, 91, 97, 88, 89, 22, 78, 84, 7], [30, 64, 40, 72, 96, 37, 72, 69, 51, 35, 74, 99], [94, 26, 3, 28, 95, 24, 18, 43, 55, 30, 58, 89], [19, 90, 61, 18, 15, 66, 75, 73, 25, 13, 63, 84], [97, 16, 87, 58, 40, 41, 80, 12, 48, 28, 70, 8], [37, 40, 37, 15, 28, 65, 39, 84, 8, 67, 16, 93], [16, 81, 6, 51, 32, 61, 61, 87, 38, 18, 2, 92], [76, 0, 94, 41, 1, 9, 8, 97, 61, 36, 54, 16]], [[48, 98, 36, 49, 10, 10, 41, 76, 81, 87, 21, 63], [86, 28, 13, 74, 67, 19, 8, 98, 72, 66, 5, 41], [50, 64, 35, 21, 32, 5, 62, 43, 31, 52, 21, 41], [18, 88, 73, 53, 36, 6, 88, 16, 6, 24, 88, 15], [84, 64, 86, 3, 31, 52, 15, 15, 56, 34, 5, 33], [89, 37, 79, 53, 0, 77, 29, 10, 92, 33, 87, 4], [18, 49, 98, 32, 91, 66, 97, 0, 32, 53, 43, 44], [44, 22, 77, 13, 85, 36, 46, 97, 82, 9, 30, 4], [54, 56, 58, 41, 75, 17, 98, 63, 66, 85, 24, 4], [44, 44, 66, 86, 46, 0, 59, 18, 22, 14, 54, 77], [52, 97, 89, 13, 27, 37, 94, 70, 18, 80, 4, 12], [51, 87, 46, 49, 28, 97, 49, 74, 66, 72, 2, 23]], [[74, 9, 8, 61, 32, 72, 77, 55, 68, 30, 65, 82], [57, 91, 2, 85, 30, 52, 81, 63, 68, 39, 77, 39], [11, 0, 38, 84, 72, 77, 9, 41, 39, 24, 44, 57], [26, 11, 57, 20, 27, 10, 79, 49, 34, 35, 68, 59], [19, 94, 50, 56, 60, 62, 58, 61, 82, 14, 76, 77], [51, 23, 87, 83, 25, 20, 60, 26, 56, 71, 50, 80], [32, 47, 19, 72, 46, 29, 32, 22, 43, 1, 49, 3], [34, 32, 53, 96, 7, 78, 50, 37, 34, 61, 4, 43], [20, 82, 79, 4, 82, 30, 32, 88, 68, 18, 53, 33], [21, 60, 12, 85, 63, 12, 9, 19, 85, 18, 27, 89], [3, 75, 81, 91, 99, 42, 30, 26, 0, 0, 38, 16], [87, 1, 79, 66, 57, 81, 63, 35, 83, 62, 30, 17]], [[20, 51, 33, 36, 51, 2, 34, 35, 32, 76, 25, 38], [45, 25, 13, 83, 20, 54, 62, 81, 72, 29, 38, 65], [78, 57, 13, 70, 12, 38, 71, 56, 24, 39, 21, 81], [55, 8, 90, 30, 85, 75, 69, 62, 35, 31, 8, 51], [37, 45, 3, 99, 71, 10, 84, 46, 30, 53, 14, 33], [46, 41, 41, 77, 91, 84, 30, 56, 74, 63, 82, 7], [47, 97, 51, 90, 60, 60, 21, 24, 90, 78, 18, 84], [32, 19, 76, 22, 64, 71, 48, 82, 65, 45, 74, 39], [53, 30, 52, 0, 42, 40, 55, 38, 51, 46, 73, 34], [67, 95, 97, 91, 58, 84, 84, 62, 82, 52, 11, 15], [25, 97, 6, 91, 93, 69, 87, 6, 86, 61, 71, 10], [10, 67, 47, 97, 37, 35, 71, 27, 79, 50, 81, 32]], [[91, 38, 58, 79, 78, 86, 58, 75, 76, 17, 10, 30], [89, 76, 62, 27, 75, 10, 27, 50, 1, 62, 49, 79], [99, 97, 59, 18, 14, 56, 79, 82, 92, 65, 70, 35], [2, 9, 40, 93, 13, 45, 61, 71, 86, 18, 38, 56], [82, 59, 91, 62, 63, 20, 12, 69, 31, 88, 70, 35], [8, 33, 36, 62, 91, 51, 89, 44, 87, 57, 58, 53], [33, 3, 50, 36, 96, 54, 24, 34, 89, 92, 74, 72], [99, 82, 83, 81, 95, 16, 74, 14, 12, 63, 85, 42], [17, 36, 93, 10, 65, 65, 60, 50, 8, 97, 30, 39], [83, 54, 48, 40, 60, 66, 0, 83, 19, 8, 72, 14], [58, 48, 16, 26, 93, 64, 19, 70, 48, 54, 72, 62], [39, 62, 13, 2, 57, 0, 47, 67, 76, 96, 96, 57]], [[54, 33, 68, 17, 2, 72, 14, 11, 78, 96, 61, 81], [18, 38, 14, 16, 52, 24, 27, 63, 80, 69, 87, 65], [74, 91, 53, 92, 69, 41, 6, 93, 37, 85, 89, 15], [61, 18, 9, 10, 70, 8, 17, 46, 48, 21, 95, 68], [89, 64, 24, 57, 97, 49, 78, 28, 50, 36, 43, 24], [15, 77, 45, 57, 36, 83, 84, 64, 81, 84, 60, 30], [21, 21, 9, 70, 66, 11, 98, 38, 77, 32, 40, 78], [45, 83, 21, 72, 84, 37, 25, 42, 3, 44, 84, 20], [28, 34, 6, 56, 68, 58, 68, 32, 62, 55, 45, 51], [48, 83, 0, 24, 43, 11, 70, 28, 88, 32, 74, 98], [84, 41, 59, 14, 45, 94, 59, 89, 77, 61, 64, 48], [9, 68, 43, 66, 18, 79, 82, 87, 75, 62, 29, 42]], [[84, 0, 12, 45, 22, 22, 88, 56, 65, 96, 12, 94], [64, 2, 52, 55, 39, 69, 21, 43, 25, 19, 8, 38], [97, 27, 4, 31, 66, 50, 43, 19, 54, 13, 57, 40], [2, 67, 63, 23, 63, 81, 71, 0, 62, 45, 45, 36], [96, 17, 10, 87, 40, 28, 90, 89, 91, 10, 67, 65], [94, 57, 53, 17, 26, 29, 48, 10, 69, 68, 85, 58], [68, 75, 30, 55, 82, 35, 49, 44, 14, 66, 46, 85], [70, 29, 77, 1, 86, 39, 88, 11, 53, 1, 58, 35], [3, 83, 24, 66, 37, 18, 52, 29, 8, 27, 26, 94], [53, 8, 74, 58, 25, 73, 54, 46, 34, 53, 51, 51], [66, 78, 4, 60, 14, 12, 26, 12, 63, 52, 5, 77], [85, 15, 42, 69, 6, 61, 71, 37, 14, 60, 16, 89]], [[74, 29, 11, 34, 70, 30, 65, 17, 71, 34, 80, 8], [33, 42, 86, 53, 29, 95, 72, 22, 89, 95, 14, 96], [81, 18, 82, 52, 71, 50, 22, 17, 5, 73, 5, 52], [74, 73, 61, 8, 72, 94, 36, 75, 63, 57, 32, 40], [70, 1, 4, 96, 83, 91, 29, 1, 88, 80, 60, 6], [68, 2, 17, 83, 23, 15, 71, 5, 96, 19, 22, 35], [19, 73, 23, 39, 21, 85, 80, 57, 39, 76, 41, 44], [9, 8, 20, 92, 57, 89, 58, 90, 29, 53, 55, 28], [50, 33, 21, 22, 84, 67, 58, 66, 37, 35, 74, 18], [56, 49, 85, 8, 32, 17, 78, 69, 17, 25, 45, 92], [77, 94, 70, 26, 94, 84, 53, 7, 1, 80, 32, 63], [53, 53, 27, 69, 68, 77, 33, 86, 19, 9, 86, 75]], [[35, 86, 4, 99, 55, 96, 96, 90, 24, 88, 94, 54], [52, 98, 55, 96, 9, 33, 56, 46, 1, 95, 59, 80], [92, 18, 21, 5, 7, 0, 39, 80, 78, 54, 60, 61], [2, 52, 33, 15, 68, 57, 0, 83, 97, 49, 23, 23], [40, 56, 40, 6, 98, 86, 2, 24, 69, 20, 87, 95], [58, 48, 44, 90, 96, 62, 82, 36, 1, 73, 60, 67], [22, 96, 38, 14, 3, 12, 0, 28, 36, 66, 7, 24], [56, 1, 83, 37, 20, 19, 54, 7, 78, 48, 12, 21], [95, 5, 74, 26, 36, 88, 36, 35, 48, 69, 40, 67], [83, 19, 84, 88, 98, 89, 83, 95, 68, 60, 48, 74], [77, 7, 13, 24, 15, 57, 5, 6, 12, 99, 95, 91], [87, 18, 87, 26, 26, 12, 18, 11, 45, 49, 35, 66]], [[24, 61, 32, 95, 93, 79, 95, 34, 98, 55, 11, 0], [46, 8, 6, 13, 90, 72, 78, 93, 74, 91, 18, 77], [78, 11, 90, 3, 84, 69, 10, 55, 54, 14, 85, 82], [76, 65, 86, 9, 59, 45, 67, 12, 44, 45, 48, 74], [61, 38, 84, 29, 19, 24, 32, 19, 49, 67, 6, 81], [96, 90, 46, 55, 67, 13, 45, 60, 87, 42, 41, 3], [68, 49, 23, 93, 17, 20, 23, 43, 2, 78, 98, 70], [53, 65, 96, 21, 22, 77, 80, 15, 18, 66, 32, 22], [77, 80, 89, 66, 62, 92, 70, 74, 86, 45, 89, 37], [9, 11, 67, 88, 10, 23, 92, 41, 24, 76, 71, 29], [55, 73, 63, 65, 5, 14, 56, 90, 95, 6, 17, 17], [2, 93, 83, 75, 36, 14, 54, 99, 58, 11, 54, 17]], [[21, 89, 26, 95, 57, 34, 7, 2, 92, 46, 25, 0], [74, 32, 91, 54, 16, 54, 10, 38, 56, 81, 70, 42], [71, 77, 78, 91, 84, 54, 37, 34, 53, 95, 29, 66], [7, 91, 76, 49, 8, 84, 81, 23, 19, 41, 45, 18], [13, 52, 95, 96, 30, 58, 39, 11, 34, 98, 71, 53], [6, 27, 28, 51, 82, 19, 20, 55, 81, 18, 64, 7], [1, 54, 77, 32, 48, 62, 48, 92, 31, 22, 39, 25], [91, 29, 34, 58, 82, 93, 69, 1, 22, 90, 0, 74], [33, 71, 18, 14, 43, 17, 91, 20, 55, 72, 62, 63], [34, 18, 26, 58, 10, 8, 22, 3, 23, 2, 9, 92], [13, 44, 26, 68, 50, 73, 4, 84, 69, 42, 5, 32], [14, 88, 19, 77, 67, 96, 81, 28, 14, 65, 5, 46]], [[46, 61, 87, 78, 56, 9, 67, 7, 85, 17, 12, 99], [38, 19, 85, 58, 55, 4, 62, 17, 15, 66, 43, 85], [45, 45, 89, 82, 13, 82, 21, 10, 76, 99, 32, 37], [99, 59, 15, 53, 74, 61, 24, 15, 90, 94, 39, 38], [54, 78, 11, 36, 6, 45, 1, 28, 48, 31, 37, 3], [51, 66, 37, 16, 37, 35, 55, 1, 90, 86, 13, 91], [38, 15, 51, 50, 41, 24, 48, 54, 85, 35, 9, 32], [85, 52, 45, 14, 41, 82, 14, 27, 58, 64, 34, 68], [81, 57, 45, 25, 45, 72, 54, 63, 8, 0, 48, 22], [95, 30, 77, 55, 56, 37, 13, 95, 66, 59, 7, 7], [37, 51, 64, 66, 66, 33, 37, 60, 76, 58, 63, 15], [7, 42, 71, 31, 43, 58, 47, 11, 54, 56, 12, 11]]], 'objective': 7.0}","[[0, 11, 4], [1, 6, 7], [2, 10, 9], [3, 8, 3], [4, 1, 8], [5, 9, 2], [6, 3, 0], [7, 5, 1], [8, 2, 5], [9, 0, 11], [10, 7, 10], [11, 4, 6]]",7.0,"{'problem_type': 'AP3', 'n': 12, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 15}, {'i': 1, 'j': 1, 'k': 2, 'cost': 59}, {'i': 1, 'j': 1, 'k': 3, 'cost': 64}, {'i': 1, 'j': 1, 'k': 4, 'cost': 87}, {'i': 1, 'j': 1, 'k': 5, 'cost': 82}, {'i': 1, 'j': 1, 'k': 6, 'cost': 93}, {'i': 1, 'j': 1, 'k': 7, 'cost': 89}, {'i': 1, 'j': 1, 'k': 8, 'cost': 33}, {'i': 1, 'j': 1, 'k': 9, 'cost': 93}, {'i': 1, 'j': 1, 'k': 10, 'cost': 26}, {'i': 1, 'j': 1, 'k': 11, 'cost': 58}, {'i': 1, 'j': 1, 'k': 12, 'cost': 93}, {'i': 1, 'j': 2, 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12, 'j': 8, 'k': 1, 'cost': 85}, {'i': 12, 'j': 8, 'k': 2, 'cost': 52}, {'i': 12, 'j': 8, 'k': 3, 'cost': 45}, {'i': 12, 'j': 8, 'k': 4, 'cost': 14}, {'i': 12, 'j': 8, 'k': 5, 'cost': 41}, {'i': 12, 'j': 8, 'k': 6, 'cost': 82}, {'i': 12, 'j': 8, 'k': 7, 'cost': 14}, {'i': 12, 'j': 8, 'k': 8, 'cost': 27}, {'i': 12, 'j': 8, 'k': 9, 'cost': 58}, {'i': 12, 'j': 8, 'k': 10, 'cost': 64}, {'i': 12, 'j': 8, 'k': 11, 'cost': 34}, {'i': 12, 'j': 8, 'k': 12, 'cost': 68}, {'i': 12, 'j': 9, 'k': 1, 'cost': 81}, {'i': 12, 'j': 9, 'k': 2, 'cost': 57}, {'i': 12, 'j': 9, 'k': 3, 'cost': 45}, {'i': 12, 'j': 9, 'k': 4, 'cost': 25}, {'i': 12, 'j': 9, 'k': 5, 'cost': 45}, {'i': 12, 'j': 9, 'k': 6, 'cost': 72}, {'i': 12, 'j': 9, 'k': 7, 'cost': 54}, {'i': 12, 'j': 9, 'k': 8, 'cost': 63}, {'i': 12, 'j': 9, 'k': 9, 'cost': 8}, {'i': 12, 'j': 9, 'k': 10, 'cost': 0}, {'i': 12, 'j': 9, 'k': 11, 'cost': 48}, {'i': 12, 'j': 9, 'k': 12, 'cost': 22}, {'i': 12, 'j': 10, 'k': 1, 'cost': 95}, {'i': 12, 'j': 10, 'k': 2, 'cost': 30}, {'i': 12, 'j': 10, 'k': 3, 'cost': 77}, {'i': 12, 'j': 10, 'k': 4, 'cost': 55}, {'i': 12, 'j': 10, 'k': 5, 'cost': 56}, {'i': 12, 'j': 10, 'k': 6, 'cost': 37}, {'i': 12, 'j': 10, 'k': 7, 'cost': 13}, {'i': 12, 'j': 10, 'k': 8, 'cost': 95}, {'i': 12, 'j': 10, 'k': 9, 'cost': 66}, {'i': 12, 'j': 10, 'k': 10, 'cost': 59}, {'i': 12, 'j': 10, 'k': 11, 'cost': 7}, {'i': 12, 'j': 10, 'k': 12, 'cost': 7}, {'i': 12, 'j': 11, 'k': 1, 'cost': 37}, {'i': 12, 'j': 11, 'k': 2, 'cost': 51}, {'i': 12, 'j': 11, 'k': 3, 'cost': 64}, {'i': 12, 'j': 11, 'k': 4, 'cost': 66}, {'i': 12, 'j': 11, 'k': 5, 'cost': 66}, {'i': 12, 'j': 11, 'k': 6, 'cost': 33}, {'i': 12, 'j': 11, 'k': 7, 'cost': 37}, {'i': 12, 'j': 11, 'k': 8, 'cost': 60}, {'i': 12, 'j': 11, 'k': 9, 'cost': 76}, {'i': 12, 'j': 11, 'k': 10, 'cost': 58}, {'i': 12, 'j': 11, 'k': 11, 'cost': 63}, {'i': 12, 'j': 11, 'k': 12, 'cost': 15}, {'i': 12, 'j': 12, 'k': 1, 'cost': 7}, {'i': 12, 'j': 12, 'k': 2, 'cost': 42}, {'i': 12, 'j': 12, 'k': 3, 'cost': 71}, {'i': 12, 'j': 12, 'k': 4, 'cost': 31}, {'i': 12, 'j': 12, 'k': 5, 'cost': 43}, {'i': 12, 'j': 12, 'k': 6, 'cost': 58}, {'i': 12, 'j': 12, 'k': 7, 'cost': 47}, {'i': 12, 'j': 12, 'k': 8, 'cost': 11}, {'i': 12, 'j': 12, 'k': 9, 'cost': 54}, {'i': 12, 'j': 12, 'k': 10, 'cost': 56}, {'i': 12, 'j': 12, 'k': 11, 'cost': 12}, {'i': 12, 'j': 12, 'k': 12, 'cost': 11}]}","[[1, 12, 5], [2, 7, 8], [3, 11, 10], [4, 9, 4], [5, 2, 9], [6, 10, 3], [7, 4, 1], [8, 6, 2], [9, 3, 6], [10, 1, 12], [11, 8, 11], [12, 5, 7]]",23,markdown_table,1
+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=12
+# package_ids=A, B, C, D, E, F, G, H, I, J, K, L
+
+# 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 | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 2 | 2 | 19 | 89 | 13 | 28 | 95 | 86 | 23 | 56 | 25 |
+| B | 40 | 96 | 39 | 13 | 70 | 94 | 52 | 46 | 10 | 83 | 61 | 52 |
+| C | 22 | 93 | 90 | 2 | 98 | 33 | 65 | 30 | 0 | 93 | 10 | 43 |
+| D | 89 | 22 | 29 | 95 | 23 | 64 | 66 | 32 | 4 | 86 | 3 | 77 |
+| E | 81 | 16 | 50 | 71 | 47 | 29 | 79 | 37 | 55 | 36 | 29 | 83 |
+| F | 12 | 8 | 33 | 46 | 15 | 17 | 53 | 90 | 54 | 99 | 91 | 53 |
+| G | 72 | 52 | 32 | 82 | 95 | 20 | 32 | 36 | 52 | 51 | 27 | 18 |
+| H | 93 | 26 | 71 | 9 | 53 | 48 | 4 | 22 | 28 | 59 | 34 | 2 |
+| I | 24 | 78 | 51 | 49 | 72 | 17 | 52 | 65 | 59 | 68 | 84 | 66 |
+| J | 5 | 78 | 32 | 67 | 98 | 77 | 86 | 24 | 46 | 79 | 44 | 18 |
+| K | 65 | 48 | 31 | 10 | 34 | 72 | 59 | 51 | 31 | 4 | 56 | 34 |
+| L | 74 | 85 | 57 | 52 | 77 | 26 | 13 | 34 | 84 | 7 | 92 | 48 |
+
+## package_id=B
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 13 | 63 | 32 | 16 | 48 | 84 | 93 | 90 | 74 | 75 | 77 | 21 |
+| B | 67 | 89 | 5 | 80 | 61 | 58 | 5 | 86 | 76 | 29 | 75 | 26 |
+| C | 38 | 94 | 24 | 41 | 27 | 37 | 40 | 86 | 78 | 22 | 23 | 4 |
+| D | 31 | 70 | 16 | 59 | 82 | 23 | 22 | 97 | 22 | 85 | 84 | 81 |
+| E | 82 | 1 | 73 | 92 | 89 | 5 | 93 | 45 | 20 | 61 | 85 | 27 |
+| F | 81 | 83 | 73 | 65 | 86 | 98 | 72 | 76 | 92 | 51 | 11 | 52 |
+| G | 92 | 73 | 11 | 57 | 63 | 52 | 55 | 99 | 77 | 9 | 14 | 68 |
+| H | 85 | 9 | 21 | 55 | 0 | 86 | 88 | 3 | 14 | 48 | 30 | 72 |
+| I | 40 | 59 | 59 | 74 | 65 | 0 | 10 | 21 | 14 | 93 | 82 | 44 |
+| J | 63 | 79 | 77 | 3 | 36 | 92 | 88 | 16 | 36 | 74 | 64 | 16 |
+| K | 40 | 3 | 1 | 75 | 64 | 36 | 35 | 10 | 1 | 17 | 48 | 21 |
+| L | 79 | 60 | 8 | 98 | 72 | 54 | 95 | 79 | 59 | 45 | 90 | 96 |
+
+## package_id=C
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 91 | 25 | 74 | 26 | 75 | 70 | 49 | 82 | 10 | 64 | 91 | 7 |
+| B | 29 | 81 | 34 | 26 | 51 | 19 | 89 | 70 | 76 | 46 | 29 | 15 |
+| C | 17 | 49 | 39 | 0 | 33 | 34 | 26 | 69 | 70 | 19 | 35 | 48 |
+| D | 71 | 44 | 57 | 49 | 7 | 15 | 58 | 86 | 83 | 62 | 49 | 59 |
+| E | 48 | 23 | 78 | 0 | 87 | 86 | 94 | 84 | 17 | 27 | 95 | 10 |
+| F | 11 | 52 | 52 | 81 | 28 | 71 | 39 | 10 | 33 | 40 | 62 | 86 |
+| G | 51 | 98 | 99 | 77 | 3 | 30 | 97 | 70 | 8 | 37 | 49 | 86 |
+| H | 95 | 85 | 40 | 92 | 30 | 29 | 99 | 55 | 40 | 75 | 35 | 4 |
+| I | 22 | 94 | 81 | 45 | 14 | 35 | 11 | 49 | 59 | 36 | 70 | 66 |
+| J | 17 | 63 | 96 | 12 | 1 | 83 | 77 | 47 | 19 | 36 | 86 | 9 |
+| K | 62 | 87 | 13 | 86 | 89 | 92 | 2 | 77 | 20 | 83 | 25 | 19 |
+| L | 36 | 57 | 64 | 79 | 32 | 60 | 76 | 78 | 57 | 78 | 98 | 11 |
+
+## package_id=D
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 65 | 33 | 18 | 21 | 68 | 9 | 71 | 38 | 99 | 99 | 77 | 51 |
+| B | 74 | 27 | 87 | 98 | 67 | 58 | 68 | 45 | 55 | 74 | 19 | 8 |
+| C | 38 | 97 | 7 | 51 | 68 | 76 | 79 | 14 | 72 | 16 | 36 | 65 |
+| D | 80 | 87 | 54 | 71 | 51 | 91 | 83 | 75 | 62 | 19 | 14 | 79 |
+| E | 81 | 59 | 30 | 94 | 26 | 10 | 33 | 30 | 49 | 96 | 8 | 72 |
+| F | 5 | 43 | 46 | 47 | 3 | 49 | 83 | 17 | 5 | 0 | 68 | 29 |
+| G | 13 | 56 | 12 | 97 | 16 | 11 | 50 | 4 | 78 | 15 | 19 | 20 |
+| H | 34 | 55 | 60 | 72 | 13 | 28 | 9 | 20 | 86 | 89 | 97 | 42 |
+| I | 5 | 18 | 88 | 17 | 31 | 30 | 37 | 57 | 65 | 18 | 60 | 76 |
+| J | 19 | 75 | 17 | 97 | 66 | 43 | 20 | 10 | 1 | 15 | 94 | 97 |
+| K | 31 | 81 | 2 | 8 | 23 | 93 | 4 | 23 | 7 | 5 | 26 | 24 |
+| L | 94 | 35 | 39 | 19 | 49 | 40 | 81 | 15 | 95 | 67 | 56 | 16 |
+
+## package_id=E
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 24 | 23 | 92 | 38 | 30 | 66 | 36 | 96 | 24 | 92 | 58 | 73 |
+| B | 95 | 29 | 53 | 40 | 21 | 57 | 95 | 73 | 24 | 64 | 63 | 66 |
+| C | 21 | 96 | 3 | 26 | 79 | 24 | 63 | 12 | 83 | 2 | 8 | 76 |
+| D | 40 | 4 | 43 | 8 | 39 | 86 | 93 | 23 | 27 | 32 | 64 | 22 |
+| E | 46 | 97 | 56 | 18 | 67 | 13 | 53 | 96 | 60 | 5 | 2 | 47 |
+| F | 38 | 22 | 65 | 37 | 75 | 16 | 67 | 48 | 4 | 42 | 70 | 32 |
+| G | 74 | 26 | 92 | 81 | 58 | 35 | 15 | 85 | 23 | 32 | 24 | 37 |
+| H | 67 | 37 | 52 | 7 | 5 | 69 | 67 | 1 | 52 | 71 | 84 | 96 |
+| I | 38 | 7 | 1 | 73 | 77 | 57 | 47 | 90 | 23 | 23 | 98 | 67 |
+| J | 92 | 7 | 12 | 42 | 83 | 37 | 90 | 65 | 27 | 17 | 54 | 15 |
+| K | 39 | 8 | 27 | 55 | 9 | 24 | 86 | 32 | 80 | 7 | 53 | 71 |
+| L | 47 | 57 | 26 | 43 | 62 | 68 | 86 | 47 | 74 | 24 | 87 | 58 |
+
+## package_id=F
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 14 | 63 | 6 | 12 | 96 | 64 | 91 | 39 | 70 | 73 | 49 | 92 |
+| B | 43 | 10 | 41 | 4 | 85 | 12 | 35 | 30 | 76 | 8 | 1 | 42 |
+| C | 38 | 81 | 46 | 1 | 96 | 48 | 20 | 19 | 95 | 72 | 0 | 44 |
+| D | 18 | 96 | 2 | 48 | 43 | 92 | 19 | 37 | 25 | 75 | 71 | 40 |
+| E | 77 | 74 | 19 | 73 | 69 | 62 | 16 | 56 | 30 | 69 | 92 | 94 |
+| F | 12 | 31 | 85 | 48 | 42 | 7 | 95 | 85 | 24 | 71 | 58 | 40 |
+| G | 21 | 76 | 40 | 86 | 62 | 98 | 16 | 46 | 32 | 96 | 35 | 65 |
+| H | 72 | 3 | 54 | 8 | 5 | 85 | 85 | 60 | 95 | 45 | 54 | 3 |
+| I | 62 | 79 | 41 | 15 | 92 | 76 | 45 | 17 | 79 | 35 | 13 | 45 |
+| J | 75 | 58 | 47 | 96 | 9 | 61 | 47 | 94 | 79 | 25 | 65 | 44 |
+| K | 54 | 57 | 64 | 95 | 91 | 40 | 80 | 47 | 8 | 13 | 5 | 61 |
+| L | 52 | 21 | 17 | 64 | 92 | 7 | 4 | 99 | 61 | 33 | 71 | 8 |
+
+## package_id=G
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 31 | 96 | 38 | 88 | 70 | 43 | 38 | 42 | 74 | 56 | 70 | 82 |
+| B | 88 | 5 | 96 | 68 | 56 | 94 | 38 | 90 | 90 | 53 | 74 | 60 |
+| C | 49 | 20 | 90 | 51 | 50 | 54 | 1 | 91 | 34 | 34 | 51 | 99 |
+| D | 10 | 9 | 46 | 82 | 88 | 45 | 0 | 70 | 63 | 72 | 54 | 45 |
+| E | 4 | 55 | 43 | 46 | 52 | 51 | 65 | 23 | 7 | 99 | 83 | 9 |
+| F | 10 | 44 | 66 | 78 | 89 | 18 | 57 | 28 | 16 | 38 | 78 | 59 |
+| G | 20 | 16 | 19 | 44 | 66 | 90 | 65 | 10 | 74 | 86 | 42 | 60 |
+| H | 94 | 26 | 72 | 37 | 6 | 32 | 49 | 83 | 10 | 29 | 15 | 22 |
+| I | 10 | 83 | 84 | 45 | 44 | 22 | 11 | 65 | 60 | 9 | 15 | 77 |
+| J | 82 | 97 | 85 | 26 | 25 | 94 | 85 | 55 | 72 | 90 | 60 | 98 |
+| K | 65 | 39 | 53 | 39 | 49 | 19 | 19 | 77 | 9 | 84 | 20 | 15 |
+| L | 9 | 20 | 23 | 90 | 54 | 41 | 79 | 11 | 94 | 41 | 32 | 46 |
+
+## package_id=H
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 40 | 10 | 34 | 44 | 83 | 8 | 44 | 7 | 1 | 18 | 87 | 94 |
+| B | 14 | 89 | 74 | 21 | 24 | 90 | 59 | 33 | 48 | 91 | 8 | 53 |
+| C | 43 | 59 | 39 | 14 | 29 | 76 | 95 | 30 | 74 | 85 | 76 | 55 |
+| D | 97 | 67 | 49 | 88 | 2 | 36 | 44 | 50 | 91 | 81 | 76 | 17 |
+| E | 81 | 36 | 40 | 32 | 65 | 33 | 2 | 0 | 57 | 39 | 10 | 16 |
+| F | 50 | 98 | 21 | 70 | 89 | 47 | 94 | 56 | 6 | 48 | 73 | 17 |
+| G | 20 | 50 | 25 | 62 | 8 | 13 | 86 | 55 | 78 | 52 | 10 | 58 |
+| H | 52 | 74 | 23 | 49 | 8 | 71 | 9 | 57 | 38 | 47 | 13 | 60 |
+| I | 76 | 11 | 85 | 89 | 70 | 1 | 5 | 51 | 99 | 18 | 10 | 61 |
+| J | 24 | 75 | 89 | 31 | 33 | 41 | 70 | 0 | 53 | 45 | 94 | 45 |
+| K | 19 | 79 | 39 | 57 | 92 | 8 | 74 | 22 | 56 | 61 | 64 | 58 |
+| L | 63 | 95 | 40 | 12 | 65 | 30 | 76 | 81 | 74 | 43 | 29 | 92 |
+
+## package_id=I
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 31 | 44 | 58 | 84 | 60 | 69 | 15 | 60 | 85 | 11 | 49 | 3 |
+| B | 24 | 69 | 35 | 23 | 87 | 62 | 85 | 58 | 56 | 58 | 11 | 47 |
+| C | 65 | 41 | 19 | 89 | 23 | 22 | 28 | 3 | 2 | 6 | 81 | 74 |
+| D | 69 | 16 | 59 | 24 | 81 | 99 | 69 | 3 | 1 | 8 | 61 | 36 |
+| E | 79 | 0 | 80 | 62 | 12 | 3 | 91 | 68 | 72 | 30 | 62 | 87 |
+| F | 96 | 26 | 52 | 41 | 82 | 47 | 87 | 3 | 10 | 21 | 99 | 60 |
+| G | 34 | 37 | 74 | 64 | 87 | 31 | 20 | 8 | 48 | 93 | 80 | 70 |
+| H | 6 | 34 | 27 | 67 | 28 | 61 | 92 | 75 | 45 | 33 | 58 | 52 |
+| I | 82 | 25 | 13 | 99 | 40 | 85 | 74 | 64 | 81 | 23 | 49 | 14 |
+| J | 2 | 51 | 6 | 29 | 54 | 67 | 87 | 19 | 27 | 24 | 86 | 95 |
+| K | 30 | 44 | 78 | 30 | 49 | 4 | 14 | 51 | 82 | 21 | 38 | 88 |
+| L | 13 | 64 | 59 | 18 | 68 | 30 | 76 | 84 | 85 | 45 | 50 | 78 |
+
+## package_id=J
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 98 | 41 | 38 | 65 | 38 | 96 | 21 | 63 | 29 | 49 | 87 | 49 |
+| B | 41 | 17 | 38 | 67 | 30 | 81 | 55 | 39 | 5 | 9 | 73 | 19 |
+| C | 71 | 24 | 61 | 12 | 20 | 93 | 15 | 49 | 76 | 97 | 1 | 27 |
+| D | 90 | 44 | 96 | 6 | 89 | 62 | 57 | 0 | 24 | 32 | 4 | 24 |
+| E | 3 | 83 | 11 | 21 | 6 | 77 | 87 | 3 | 98 | 22 | 42 | 64 |
+| F | 72 | 0 | 25 | 55 | 35 | 39 | 35 | 36 | 37 | 48 | 9 | 33 |
+| G | 35 | 96 | 19 | 46 | 22 | 38 | 25 | 84 | 31 | 63 | 25 | 33 |
+| H | 36 | 83 | 13 | 35 | 73 | 76 | 1 | 21 | 13 | 2 | 33 | 22 |
+| I | 55 | 5 | 87 | 32 | 17 | 6 | 89 | 40 | 40 | 83 | 11 | 58 |
+| J | 99 | 68 | 65 | 96 | 86 | 6 | 60 | 32 | 18 | 96 | 34 | 35 |
+| K | 60 | 95 | 24 | 92 | 85 | 21 | 11 | 66 | 65 | 20 | 99 | 14 |
+| L | 40 | 17 | 34 | 19 | 43 | 36 | 31 | 88 | 55 | 58 | 84 | 86 |
+
+## package_id=K
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 32 | 91 | 62 | 32 | 87 | 70 | 78 | 67 | 53 | 29 | 10 | 47 |
+| B | 56 | 7 | 83 | 63 | 69 | 58 | 7 | 89 | 38 | 95 | 55 | 1 |
+| C | 54 | 27 | 14 | 69 | 79 | 55 | 91 | 79 | 63 | 53 | 96 | 57 |
+| D | 26 | 82 | 15 | 97 | 4 | 37 | 8 | 79 | 97 | 81 | 35 | 54 |
+| E | 55 | 20 | 21 | 90 | 21 | 95 | 74 | 41 | 18 | 50 | 97 | 48 |
+| F | 21 | 72 | 70 | 27 | 56 | 73 | 93 | 59 | 12 | 2 | 69 | 82 |
+| G | 98 | 93 | 40 | 58 | 65 | 77 | 36 | 28 | 39 | 32 | 27 | 84 |
+| H | 5 | 35 | 24 | 69 | 4 | 47 | 41 | 20 | 56 | 23 | 50 | 17 |
+| I | 74 | 26 | 77 | 98 | 59 | 77 | 45 | 20 | 5 | 87 | 53 | 16 |
+| J | 78 | 54 | 75 | 5 | 24 | 96 | 65 | 57 | 55 | 74 | 90 | 31 |
+| K | 97 | 91 | 44 | 62 | 10 | 93 | 34 | 42 | 5 | 93 | 54 | 37 |
+| L | 3 | 27 | 47 | 22 | 57 | 34 | 95 | 36 | 77 | 96 | 12 | 97 |
+
+## package_id=L
+| courier_id\route_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 81 | 34 | 69 | 98 | 88 | 45 | 15 | 46 | 75 | 97 | 23 |
+| B | 84 | 70 | 31 | 45 | 94 | 14 | 55 | 13 | 20 | 98 | 10 | 77 |
+| C | 14 | 29 | 51 | 73 | 27 | 93 | 24 | 95 | 92 | 2 | 11 | 99 |
+| D | 53 | 81 | 26 | 22 | 27 | 61 | 81 | 27 | 48 | 92 | 4 | 80 |
+| E | 8 | 80 | 59 | 72 | 78 | 2 | 66 | 86 | 74 | 54 | 19 | 67 |
+| F | 41 | 23 | 77 | 72 | 47 | 14 | 9 | 74 | 74 | 10 | 66 | 81 |
+| G | 28 | 4 | 81 | 33 | 95 | 35 | 57 | 50 | 80 | 99 | 47 | 85 |
+| H | 80 | 5 | 17 | 94 | 67 | 73 | 93 | 72 | 38 | 10 | 71 | 12 |
+| I | 43 | 78 | 88 | 37 | 26 | 26 | 28 | 36 | 19 | 85 | 16 | 63 |
+| J | 70 | 90 | 62 | 45 | 93 | 22 | 75 | 60 | 27 | 9 | 50 | 58 |
+| K | 37 | 26 | 17 | 24 | 81 | 71 | 79 | 90 | 45 | 7 | 25 | 55 |
+| L | 44 | 30 | 98 | 51 | 71 | 27 | 6 | 29 | 86 | 65 | 61 | 39 |
+
+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': [[[12, 2, 2, 19, 89, 13, 28, 95, 86, 23, 56, 25], [40, 96, 39, 13, 70, 94, 52, 46, 10, 83, 61, 52], [22, 93, 90, 2, 98, 33, 65, 30, 0, 93, 10, 43], [89, 22, 29, 95, 23, 64, 66, 32, 4, 86, 3, 77], [81, 16, 50, 71, 47, 29, 79, 37, 55, 36, 29, 83], [12, 8, 33, 46, 15, 17, 53, 90, 54, 99, 91, 53], [72, 52, 32, 82, 95, 20, 32, 36, 52, 51, 27, 18], [93, 26, 71, 9, 53, 48, 4, 22, 28, 59, 34, 2], [24, 78, 51, 49, 72, 17, 52, 65, 59, 68, 84, 66], [5, 78, 32, 67, 98, 77, 86, 24, 46, 79, 44, 18], [65, 48, 31, 10, 34, 72, 59, 51, 31, 4, 56, 34], [74, 85, 57, 52, 77, 26, 13, 34, 84, 7, 92, 48]], [[13, 63, 32, 16, 48, 84, 93, 90, 74, 75, 77, 21], [67, 89, 5, 80, 61, 58, 5, 86, 76, 29, 75, 26], [38, 94, 24, 41, 27, 37, 40, 86, 78, 22, 23, 4], [31, 70, 16, 59, 82, 23, 22, 97, 22, 85, 84, 81], [82, 1, 73, 92, 89, 5, 93, 45, 20, 61, 85, 27], [81, 83, 73, 65, 86, 98, 72, 76, 92, 51, 11, 52], [92, 73, 11, 57, 63, 52, 55, 99, 77, 9, 14, 68], [85, 9, 21, 55, 0, 86, 88, 3, 14, 48, 30, 72], [40, 59, 59, 74, 65, 0, 10, 21, 14, 93, 82, 44], [63, 79, 77, 3, 36, 92, 88, 16, 36, 74, 64, 16], [40, 3, 1, 75, 64, 36, 35, 10, 1, 17, 48, 21], [79, 60, 8, 98, 72, 54, 95, 79, 59, 45, 90, 96]], [[91, 25, 74, 26, 75, 70, 49, 82, 10, 64, 91, 7], [29, 81, 34, 26, 51, 19, 89, 70, 76, 46, 29, 15], [17, 49, 39, 0, 33, 34, 26, 69, 70, 19, 35, 48], [71, 44, 57, 49, 7, 15, 58, 86, 83, 62, 49, 59], [48, 23, 78, 0, 87, 86, 94, 84, 17, 27, 95, 10], [11, 52, 52, 81, 28, 71, 39, 10, 33, 40, 62, 86], [51, 98, 99, 77, 3, 30, 97, 70, 8, 37, 49, 86], [95, 85, 40, 92, 30, 29, 99, 55, 40, 75, 35, 4], [22, 94, 81, 45, 14, 35, 11, 49, 59, 36, 70, 66], [17, 63, 96, 12, 1, 83, 77, 47, 19, 36, 86, 9], [62, 87, 13, 86, 89, 92, 2, 77, 20, 83, 25, 19], [36, 57, 64, 79, 32, 60, 76, 78, 57, 78, 98, 11]], [[65, 33, 18, 21, 68, 9, 71, 38, 99, 99, 77, 51], [74, 27, 87, 98, 67, 58, 68, 45, 55, 74, 19, 8], [38, 97, 7, 51, 68, 76, 79, 14, 72, 16, 36, 65], [80, 87, 54, 71, 51, 91, 83, 75, 62, 19, 14, 79], [81, 59, 30, 94, 26, 10, 33, 30, 49, 96, 8, 72], [5, 43, 46, 47, 3, 49, 83, 17, 5, 0, 68, 29], [13, 56, 12, 97, 16, 11, 50, 4, 78, 15, 19, 20], [34, 55, 60, 72, 13, 28, 9, 20, 86, 89, 97, 42], [5, 18, 88, 17, 31, 30, 37, 57, 65, 18, 60, 76], [19, 75, 17, 97, 66, 43, 20, 10, 1, 15, 94, 97], [31, 81, 2, 8, 23, 93, 4, 23, 7, 5, 26, 24], [94, 35, 39, 19, 49, 40, 81, 15, 95, 67, 56, 16]], [[24, 23, 92, 38, 30, 66, 36, 96, 24, 92, 58, 73], [95, 29, 53, 40, 21, 57, 95, 73, 24, 64, 63, 66], [21, 96, 3, 26, 79, 24, 63, 12, 83, 2, 8, 76], [40, 4, 43, 8, 39, 86, 93, 23, 27, 32, 64, 22], [46, 97, 56, 18, 67, 13, 53, 96, 60, 5, 2, 47], [38, 22, 65, 37, 75, 16, 67, 48, 4, 42, 70, 32], [74, 26, 92, 81, 58, 35, 15, 85, 23, 32, 24, 37], [67, 37, 52, 7, 5, 69, 67, 1, 52, 71, 84, 96], [38, 7, 1, 73, 77, 57, 47, 90, 23, 23, 98, 67], [92, 7, 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'k': 'D', 'cost': 94}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 67}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 73}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 93}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 72}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 38}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 10}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 71}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 12}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 43}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 78}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 88}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 37}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 26}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 26}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 28}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 36}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 19}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 85}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 16}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 63}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 70}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 90}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 62}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 45}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 93}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 22}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 75}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 60}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 27}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 9}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 50}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 58}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 37}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 26}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 17}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 24}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 81}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 71}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 79}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 90}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 45}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 7}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 25}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 55}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 44}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 30}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 98}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 51}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 71}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 27}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 6}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 29}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 86}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 65}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 61}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 39}]}","[['A', 'C', 'D'], ['B', 'I', 'F'], ['C', 'J', 'E'], ['D', 'K', 'C'], ['E', 'F', 'I'], ['F', 'B', 'K'], ['G', 'D', 'G'], ['H', 'E', 'H'], ['I', 'A', 'L'], ['J', 'H', 'J'], ['K', 'L', 'A'], ['L', 'G', 'B']]",24,csv,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 10 repair request identifiers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
+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 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 16 | 52 | 11 | 10 | 74 | 57 | 72 | 54 | 51 | 67 |
+| 2 | 8 | 10 | 0 | 59 | 67 | 16 | 61 | 13 | 61 | 22 |
+| 3 | 90 | 95 | 39 | 21 | 48 | 85 | 23 | 70 | 95 | 85 |
+| 4 | 11 | 93 | 4 | 62 | 38 | 27 | 25 | 97 | 54 | 81 |
+| 5 | 30 | 26 | 36 | 2 | 54 | 87 | 73 | 25 | 72 | 10 |
+| 6 | 73 | 21 | 62 | 3 | 90 | 27 | 8 | 87 | 49 | 52 |
+| 7 | 26 | 53 | 37 | 18 | 44 | 97 | 61 | 85 | 70 | 4 |
+| 8 | 90 | 13 | 97 | 28 | 22 | 97 | 37 | 32 | 18 | 17 |
+| 9 | 70 | 19 | 65 | 51 | 4 | 39 | 11 | 25 | 31 | 49 |
+| 10 | 73 | 75 | 40 | 64 | 82 | 1 | 23 | 46 | 51 | 45 |
+
+## request_id=2
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 30 | 89 | 65 | 10 | 79 | 18 | 55 | 41 | 33 | 83 |
+| 2 | 83 | 95 | 31 | 62 | 53 | 88 | 84 | 73 | 6 | 43 |
+| 3 | 58 | 56 | 38 | 33 | 79 | 86 | 44 | 62 | 96 | 67 |
+| 4 | 68 | 24 | 82 | 3 | 48 | 2 | 57 | 56 | 58 | 31 |
+| 5 | 55 | 48 | 32 | 76 | 80 | 50 | 93 | 36 | 96 | 38 |
+| 6 | 71 | 15 | 69 | 76 | 76 | 96 | 17 | 2 | 89 | 40 |
+| 7 | 60 | 61 | 62 | 55 | 84 | 96 | 52 | 89 | 24 | 10 |
+| 8 | 0 | 97 | 48 | 96 | 83 | 27 | 94 | 57 | 97 | 99 |
+| 9 | 72 | 0 | 55 | 91 | 22 | 97 | 83 | 35 | 83 | 89 |
+| 10 | 3 | 96 | 12 | 62 | 0 | 80 | 9 | 82 | 42 | 9 |
+
+## request_id=3
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 51 | 89 | 73 | 7 | 50 | 48 | 60 | 94 | 50 | 0 |
+| 2 | 62 | 18 | 75 | 94 | 93 | 9 | 68 | 25 | 67 | 78 |
+| 3 | 25 | 44 | 28 | 2 | 41 | 82 | 36 | 36 | 60 | 30 |
+| 4 | 73 | 24 | 78 | 57 | 97 | 87 | 50 | 98 | 54 | 8 |
+| 5 | 37 | 34 | 58 | 93 | 93 | 39 | 43 | 78 | 15 | 74 |
+| 6 | 96 | 40 | 21 | 68 | 6 | 85 | 6 | 71 | 99 | 38 |
+| 7 | 58 | 76 | 83 | 29 | 10 | 43 | 86 | 26 | 11 | 1 |
+| 8 | 68 | 22 | 95 | 68 | 14 | 7 | 1 | 2 | 0 | 35 |
+| 9 | 17 | 47 | 5 | 1 | 24 | 36 | 52 | 94 | 92 | 38 |
+| 10 | 6 | 38 | 81 | 52 | 59 | 80 | 92 | 27 | 8 | 57 |
+
+## request_id=4
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 20 | 79 | 85 | 71 | 6 | 4 | 43 | 9 | 96 | 64 |
+| 2 | 29 | 96 | 40 | 25 | 69 | 93 | 44 | 85 | 5 | 6 |
+| 3 | 34 | 51 | 65 | 55 | 53 | 27 | 19 | 31 | 10 | 9 |
+| 4 | 94 | 64 | 36 | 52 | 16 | 58 | 85 | 78 | 78 | 7 |
+| 5 | 57 | 82 | 33 | 89 | 81 | 21 | 35 | 27 | 79 | 78 |
+| 6 | 99 | 3 | 35 | 65 | 45 | 48 | 79 | 95 | 44 | 42 |
+| 7 | 17 | 33 | 4 | 56 | 46 | 26 | 1 | 8 | 67 | 77 |
+| 8 | 12 | 67 | 25 | 34 | 85 | 62 | 7 | 57 | 71 | 56 |
+| 9 | 52 | 69 | 6 | 49 | 42 | 91 | 0 | 5 | 10 | 46 |
+| 10 | 42 | 15 | 94 | 5 | 95 | 22 | 84 | 49 | 51 | 68 |
+
+## request_id=5
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 84 | 77 | 22 | 94 | 12 | 20 | 74 | 93 | 99 | 13 |
+| 2 | 59 | 57 | 42 | 35 | 3 | 35 | 42 | 55 | 53 | 80 |
+| 3 | 81 | 54 | 87 | 7 | 91 | 60 | 67 | 77 | 5 | 51 |
+| 4 | 36 | 19 | 91 | 21 | 19 | 1 | 40 | 40 | 78 | 24 |
+| 5 | 25 | 67 | 66 | 84 | 40 | 13 | 12 | 38 | 21 | 35 |
+| 6 | 98 | 13 | 11 | 42 | 52 | 38 | 87 | 16 | 54 | 26 |
+| 7 | 90 | 79 | 89 | 45 | 45 | 22 | 47 | 84 | 42 | 16 |
+| 8 | 38 | 79 | 16 | 5 | 9 | 4 | 92 | 84 | 10 | 44 |
+| 9 | 8 | 25 | 68 | 49 | 56 | 32 | 31 | 79 | 42 | 8 |
+| 10 | 20 | 87 | 92 | 77 | 92 | 35 | 68 | 4 | 52 | 34 |
+
+## request_id=6
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 49 | 98 | 98 | 0 | 94 | 37 | 26 | 62 | 6 | 55 |
+| 2 | 83 | 93 | 60 | 49 | 98 | 81 | 24 | 60 | 72 | 54 |
+| 3 | 36 | 37 | 62 | 33 | 86 | 46 | 88 | 41 | 51 | 88 |
+| 4 | 29 | 24 | 91 | 40 | 55 | 71 | 53 | 57 | 68 | 82 |
+| 5 | 77 | 17 | 79 | 96 | 46 | 68 | 55 | 73 | 49 | 70 |
+| 6 | 99 | 53 | 62 | 31 | 7 | 45 | 15 | 81 | 62 | 16 |
+| 7 | 67 | 90 | 0 | 7 | 40 | 74 | 84 | 84 | 30 | 61 |
+| 8 | 20 | 18 | 90 | 77 | 9 | 92 | 14 | 40 | 77 | 85 |
+| 9 | 46 | 94 | 34 | 45 | 17 | 77 | 68 | 80 | 10 | 29 |
+| 10 | 22 | 97 | 97 | 6 | 67 | 54 | 49 | 91 | 68 | 90 |
+
+## request_id=7
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 31 | 66 | 3 | 35 | 10 | 34 | 37 | 18 | 39 | 51 |
+| 2 | 46 | 11 | 29 | 98 | 82 | 84 | 34 | 53 | 22 | 87 |
+| 3 | 45 | 69 | 73 | 62 | 33 | 22 | 44 | 74 | 44 | 86 |
+| 4 | 19 | 1 | 46 | 52 | 64 | 6 | 7 | 86 | 40 | 79 |
+| 5 | 90 | 39 | 43 | 6 | 89 | 0 | 95 | 0 | 70 | 66 |
+| 6 | 16 | 77 | 82 | 75 | 20 | 27 | 37 | 42 | 31 | 55 |
+| 7 | 26 | 77 | 29 | 38 | 68 | 72 | 44 | 12 | 25 | 9 |
+| 8 | 35 | 71 | 64 | 62 | 43 | 26 | 55 | 39 | 48 | 38 |
+| 9 | 19 | 83 | 72 | 59 | 12 | 90 | 68 | 45 | 88 | 53 |
+| 10 | 0 | 88 | 76 | 27 | 66 | 78 | 68 | 60 | 28 | 4 |
+
+## request_id=8
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 1 | 81 | 23 | 11 | 47 | 31 | 92 | 89 | 39 |
+| 2 | 76 | 94 | 13 | 79 | 8 | 28 | 13 | 22 | 81 | 96 |
+| 3 | 42 | 16 | 2 | 29 | 98 | 50 | 29 | 67 | 3 | 46 |
+| 4 | 68 | 74 | 55 | 19 | 30 | 19 | 46 | 94 | 75 | 43 |
+| 5 | 0 | 75 | 22 | 75 | 69 | 84 | 57 | 37 | 89 | 74 |
+| 6 | 65 | 17 | 48 | 70 | 64 | 49 | 12 | 45 | 35 | 2 |
+| 7 | 47 | 70 | 34 | 28 | 58 | 29 | 77 | 62 | 0 | 11 |
+| 8 | 44 | 61 | 67 | 10 | 15 | 52 | 28 | 22 | 29 | 92 |
+| 9 | 7 | 39 | 73 | 80 | 9 | 8 | 44 | 22 | 14 | 65 |
+| 10 | 80 | 24 | 95 | 71 | 59 | 13 | 98 | 82 | 6 | 28 |
+
+## request_id=9
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 40 | 78 | 88 | 11 | 66 | 94 | 75 | 74 | 11 | 79 |
+| 2 | 52 | 27 | 45 | 58 | 79 | 22 | 5 | 62 | 60 | 99 |
+| 3 | 5 | 87 | 57 | 40 | 76 | 61 | 36 | 27 | 86 | 11 |
+| 4 | 74 | 80 | 14 | 47 | 81 | 44 | 49 | 70 | 14 | 1 |
+| 5 | 19 | 0 | 2 | 43 | 41 | 36 | 18 | 96 | 91 | 94 |
+| 6 | 86 | 11 | 47 | 8 | 20 | 92 | 44 | 34 | 97 | 46 |
+| 7 | 87 | 20 | 83 | 80 | 14 | 7 | 25 | 62 | 96 | 97 |
+| 8 | 90 | 53 | 34 | 37 | 33 | 85 | 48 | 11 | 81 | 27 |
+| 9 | 28 | 26 | 20 | 38 | 83 | 42 | 34 | 23 | 75 | 46 |
+| 10 | 29 | 69 | 43 | 60 | 5 | 54 | 3 | 33 | 7 | 16 |
+
+## request_id=10
+| technician_id\kit_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 21 | 90 | 53 | 19 | 4 | 82 | 31 | 89 | 1 | 33 |
+| 2 | 11 | 32 | 22 | 74 | 77 | 40 | 65 | 91 | 95 | 53 |
+| 3 | 9 | 56 | 16 | 84 | 98 | 1 | 78 | 63 | 34 | 13 |
+| 4 | 50 | 37 | 93 | 37 | 7 | 43 | 6 | 99 | 1 | 51 |
+| 5 | 78 | 38 | 37 | 37 | 75 | 26 | 45 | 91 | 11 | 62 |
+| 6 | 19 | 74 | 86 | 38 | 38 | 85 | 18 | 52 | 93 | 90 |
+| 7 | 46 | 44 | 18 | 18 | 15 | 84 | 74 | 1 | 28 | 38 |
+| 8 | 86 | 28 | 81 | 94 | 81 | 48 | 1 | 25 | 91 | 2 |
+| 9 | 93 | 69 | 54 | 97 | 27 | 43 | 62 | 84 | 90 | 82 |
+| 10 | 98 | 85 | 46 | 66 | 6 | 85 | 93 | 99 | 58 | 35 |
+Aim to minimize the sum of these costs across all 10 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': [[[16, 52, 11, 10, 74, 57, 72, 54, 51, 67], [8, 10, 0, 59, 67, 16, 61, 13, 61, 22], [90, 95, 39, 21, 48, 85, 23, 70, 95, 85], [11, 93, 4, 62, 38, 27, 25, 97, 54, 81], [30, 26, 36, 2, 54, 87, 73, 25, 72, 10], [73, 21, 62, 3, 90, 27, 8, 87, 49, 52], [26, 53, 37, 18, 44, 97, 61, 85, 70, 4], [90, 13, 97, 28, 22, 97, 37, 32, 18, 17], [70, 19, 65, 51, 4, 39, 11, 25, 31, 49], [73, 75, 40, 64, 82, 1, 23, 46, 51, 45]], [[30, 89, 65, 10, 79, 18, 55, 41, 33, 83], [83, 95, 31, 62, 53, 88, 84, 73, 6, 43], [58, 56, 38, 33, 79, 86, 44, 62, 96, 67], [68, 24, 82, 3, 48, 2, 57, 56, 58, 31], [55, 48, 32, 76, 80, 50, 93, 36, 96, 38], [71, 15, 69, 76, 76, 96, 17, 2, 89, 40], [60, 61, 62, 55, 84, 96, 52, 89, 24, 10], [0, 97, 48, 96, 83, 27, 94, 57, 97, 99], [72, 0, 55, 91, 22, 97, 83, 35, 83, 89], [3, 96, 12, 62, 0, 80, 9, 82, 42, 9]], [[51, 89, 73, 7, 50, 48, 60, 94, 50, 0], [62, 18, 75, 94, 93, 9, 68, 25, 67, 78], [25, 44, 28, 2, 41, 82, 36, 36, 60, 30], [73, 24, 78, 57, 97, 87, 50, 98, 54, 8], [37, 34, 58, 93, 93, 39, 43, 78, 15, 74], [96, 40, 21, 68, 6, 85, 6, 71, 99, 38], [58, 76, 83, 29, 10, 43, 86, 26, 11, 1], [68, 22, 95, 68, 14, 7, 1, 2, 0, 35], [17, 47, 5, 1, 24, 36, 52, 94, 92, 38], [6, 38, 81, 52, 59, 80, 92, 27, 8, 57]], [[20, 79, 85, 71, 6, 4, 43, 9, 96, 64], [29, 96, 40, 25, 69, 93, 44, 85, 5, 6], [34, 51, 65, 55, 53, 27, 19, 31, 10, 9], [94, 64, 36, 52, 16, 58, 85, 78, 78, 7], [57, 82, 33, 89, 81, 21, 35, 27, 79, 78], [99, 3, 35, 65, 45, 48, 79, 95, 44, 42], [17, 33, 4, 56, 46, 26, 1, 8, 67, 77], [12, 67, 25, 34, 85, 62, 7, 57, 71, 56], [52, 69, 6, 49, 42, 91, 0, 5, 10, 46], [42, 15, 94, 5, 95, 22, 84, 49, 51, 68]], [[84, 77, 22, 94, 12, 20, 74, 93, 99, 13], [59, 57, 42, 35, 3, 35, 42, 55, 53, 80], [81, 54, 87, 7, 91, 60, 67, 77, 5, 51], [36, 19, 91, 21, 19, 1, 40, 40, 78, 24], [25, 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{'i': 7, 'j': 7, 'k': 9, 'cost': 25}, {'i': 7, 'j': 7, 'k': 10, 'cost': 9}, {'i': 7, 'j': 8, 'k': 1, 'cost': 35}, {'i': 7, 'j': 8, 'k': 2, 'cost': 71}, {'i': 7, 'j': 8, 'k': 3, 'cost': 64}, {'i': 7, 'j': 8, 'k': 4, 'cost': 62}, {'i': 7, 'j': 8, 'k': 5, 'cost': 43}, {'i': 7, 'j': 8, 'k': 6, 'cost': 26}, {'i': 7, 'j': 8, 'k': 7, 'cost': 55}, {'i': 7, 'j': 8, 'k': 8, 'cost': 39}, {'i': 7, 'j': 8, 'k': 9, 'cost': 48}, {'i': 7, 'j': 8, 'k': 10, 'cost': 38}, {'i': 7, 'j': 9, 'k': 1, 'cost': 19}, {'i': 7, 'j': 9, 'k': 2, 'cost': 83}, {'i': 7, 'j': 9, 'k': 3, 'cost': 72}, {'i': 7, 'j': 9, 'k': 4, 'cost': 59}, {'i': 7, 'j': 9, 'k': 5, 'cost': 12}, {'i': 7, 'j': 9, 'k': 6, 'cost': 90}, {'i': 7, 'j': 9, 'k': 7, 'cost': 68}, {'i': 7, 'j': 9, 'k': 8, 'cost': 45}, {'i': 7, 'j': 9, 'k': 9, 'cost': 88}, {'i': 7, 'j': 9, 'k': 10, 'cost': 53}, {'i': 7, 'j': 10, 'k': 1, 'cost': 0}, {'i': 7, 'j': 10, 'k': 2, 'cost': 88}, {'i': 7, 'j': 10, 'k': 3, 'cost': 76}, {'i': 7, 'j': 10, 'k': 4, 'cost': 27}, {'i': 7, 'j': 10, 'k': 5, 'cost': 66}, {'i': 7, 'j': 10, 'k': 6, 'cost': 78}, {'i': 7, 'j': 10, 'k': 7, 'cost': 68}, {'i': 7, 'j': 10, 'k': 8, 'cost': 60}, {'i': 7, 'j': 10, 'k': 9, 'cost': 28}, {'i': 7, 'j': 10, 'k': 10, 'cost': 4}, {'i': 8, 'j': 1, 'k': 1, 'cost': 34}, {'i': 8, 'j': 1, 'k': 2, 'cost': 1}, {'i': 8, 'j': 1, 'k': 3, 'cost': 81}, {'i': 8, 'j': 1, 'k': 4, 'cost': 23}, {'i': 8, 'j': 1, 'k': 5, 'cost': 11}, {'i': 8, 'j': 1, 'k': 6, 'cost': 47}, {'i': 8, 'j': 1, 'k': 7, 'cost': 31}, {'i': 8, 'j': 1, 'k': 8, 'cost': 92}, {'i': 8, 'j': 1, 'k': 9, 'cost': 89}, {'i': 8, 'j': 1, 'k': 10, 'cost': 39}, {'i': 8, 'j': 2, 'k': 1, 'cost': 76}, {'i': 8, 'j': 2, 'k': 2, 'cost': 94}, {'i': 8, 'j': 2, 'k': 3, 'cost': 13}, {'i': 8, 'j': 2, 'k': 4, 'cost': 79}, {'i': 8, 'j': 2, 'k': 5, 'cost': 8}, {'i': 8, 'j': 2, 'k': 6, 'cost': 28}, {'i': 8, 'j': 2, 'k': 7, 'cost': 13}, {'i': 8, 'j': 2, 'k': 8, 'cost': 22}, {'i': 8, 'j': 2, 'k': 9, 'cost': 81}, {'i': 8, 'j': 2, 'k': 10, 'cost': 96}, {'i': 8, 'j': 3, 'k': 1, 'cost': 42}, {'i': 8, 'j': 3, 'k': 2, 'cost': 16}, {'i': 8, 'j': 3, 'k': 3, 'cost': 2}, {'i': 8, 'j': 3, 'k': 4, 'cost': 29}, {'i': 8, 'j': 3, 'k': 5, 'cost': 98}, {'i': 8, 'j': 3, 'k': 6, 'cost': 50}, {'i': 8, 'j': 3, 'k': 7, 'cost': 29}, {'i': 8, 'j': 3, 'k': 8, 'cost': 67}, {'i': 8, 'j': 3, 'k': 9, 'cost': 3}, {'i': 8, 'j': 3, 'k': 10, 'cost': 46}, {'i': 8, 'j': 4, 'k': 1, 'cost': 68}, {'i': 8, 'j': 4, 'k': 2, 'cost': 74}, {'i': 8, 'j': 4, 'k': 3, 'cost': 55}, {'i': 8, 'j': 4, 'k': 4, 'cost': 19}, {'i': 8, 'j': 4, 'k': 5, 'cost': 30}, {'i': 8, 'j': 4, 'k': 6, 'cost': 19}, {'i': 8, 'j': 4, 'k': 7, 'cost': 46}, {'i': 8, 'j': 4, 'k': 8, 'cost': 94}, {'i': 8, 'j': 4, 'k': 9, 'cost': 75}, {'i': 8, 'j': 4, 'k': 10, 'cost': 43}, {'i': 8, 'j': 5, 'k': 1, 'cost': 0}, {'i': 8, 'j': 5, 'k': 2, 'cost': 75}, {'i': 8, 'j': 5, 'k': 3, 'cost': 22}, {'i': 8, 'j': 5, 'k': 4, 'cost': 75}, {'i': 8, 'j': 5, 'k': 5, 'cost': 69}, {'i': 8, 'j': 5, 'k': 6, 'cost': 84}, {'i': 8, 'j': 5, 'k': 7, 'cost': 57}, {'i': 8, 'j': 5, 'k': 8, 'cost': 37}, {'i': 8, 'j': 5, 'k': 9, 'cost': 89}, {'i': 8, 'j': 5, 'k': 10, 'cost': 74}, {'i': 8, 'j': 6, 'k': 1, 'cost': 65}, {'i': 8, 'j': 6, 'k': 2, 'cost': 17}, {'i': 8, 'j': 6, 'k': 3, 'cost': 48}, {'i': 8, 'j': 6, 'k': 4, 'cost': 70}, {'i': 8, 'j': 6, 'k': 5, 'cost': 64}, {'i': 8, 'j': 6, 'k': 6, 'cost': 49}, {'i': 8, 'j': 6, 'k': 7, 'cost': 12}, {'i': 8, 'j': 6, 'k': 8, 'cost': 45}, {'i': 8, 'j': 6, 'k': 9, 'cost': 35}, {'i': 8, 'j': 6, 'k': 10, 'cost': 2}, {'i': 8, 'j': 7, 'k': 1, 'cost': 47}, {'i': 8, 'j': 7, 'k': 2, 'cost': 70}, {'i': 8, 'j': 7, 'k': 3, 'cost': 34}, {'i': 8, 'j': 7, 'k': 4, 'cost': 28}, {'i': 8, 'j': 7, 'k': 5, 'cost': 58}, {'i': 8, 'j': 7, 'k': 6, 'cost': 29}, {'i': 8, 'j': 7, 'k': 7, 'cost': 77}, {'i': 8, 'j': 7, 'k': 8, 'cost': 62}, {'i': 8, 'j': 7, 'k': 9, 'cost': 0}, {'i': 8, 'j': 7, 'k': 10, 'cost': 11}, {'i': 8, 'j': 8, 'k': 1, 'cost': 44}, {'i': 8, 'j': 8, 'k': 2, 'cost': 61}, {'i': 8, 'j': 8, 'k': 3, 'cost': 67}, {'i': 8, 'j': 8, 'k': 4, 'cost': 10}, {'i': 8, 'j': 8, 'k': 5, 'cost': 15}, {'i': 8, 'j': 8, 'k': 6, 'cost': 52}, {'i': 8, 'j': 8, 'k': 7, 'cost': 28}, {'i': 8, 'j': 8, 'k': 8, 'cost': 22}, {'i': 8, 'j': 8, 'k': 9, 'cost': 29}, {'i': 8, 'j': 8, 'k': 10, 'cost': 92}, {'i': 8, 'j': 9, 'k': 1, 'cost': 7}, {'i': 8, 'j': 9, 'k': 2, 'cost': 39}, {'i': 8, 'j': 9, 'k': 3, 'cost': 73}, {'i': 8, 'j': 9, 'k': 4, 'cost': 80}, {'i': 8, 'j': 9, 'k': 5, 'cost': 9}, {'i': 8, 'j': 9, 'k': 6, 'cost': 8}, {'i': 8, 'j': 9, 'k': 7, 'cost': 44}, {'i': 8, 'j': 9, 'k': 8, 'cost': 22}, {'i': 8, 'j': 9, 'k': 9, 'cost': 14}, {'i': 8, 'j': 9, 'k': 10, 'cost': 65}, {'i': 8, 'j': 10, 'k': 1, 'cost': 80}, {'i': 8, 'j': 10, 'k': 2, 'cost': 24}, {'i': 8, 'j': 10, 'k': 3, 'cost': 95}, {'i': 8, 'j': 10, 'k': 4, 'cost': 71}, {'i': 8, 'j': 10, 'k': 5, 'cost': 59}, {'i': 8, 'j': 10, 'k': 6, 'cost': 13}, {'i': 8, 'j': 10, 'k': 7, 'cost': 98}, {'i': 8, 'j': 10, 'k': 8, 'cost': 82}, {'i': 8, 'j': 10, 'k': 9, 'cost': 6}, {'i': 8, 'j': 10, 'k': 10, 'cost': 28}, {'i': 9, 'j': 1, 'k': 1, 'cost': 40}, {'i': 9, 'j': 1, 'k': 2, 'cost': 78}, {'i': 9, 'j': 1, 'k': 3, 'cost': 88}, {'i': 9, 'j': 1, 'k': 4, 'cost': 11}, {'i': 9, 'j': 1, 'k': 5, 'cost': 66}, {'i': 9, 'j': 1, 'k': 6, 'cost': 94}, {'i': 9, 'j': 1, 'k': 7, 'cost': 75}, {'i': 9, 'j': 1, 'k': 8, 'cost': 74}, {'i': 9, 'j': 1, 'k': 9, 'cost': 11}, {'i': 9, 'j': 1, 'k': 10, 'cost': 79}, {'i': 9, 'j': 2, 'k': 1, 'cost': 52}, {'i': 9, 'j': 2, 'k': 2, 'cost': 27}, {'i': 9, 'j': 2, 'k': 3, 'cost': 45}, {'i': 9, 'j': 2, 'k': 4, 'cost': 58}, {'i': 9, 'j': 2, 'k': 5, 'cost': 79}, {'i': 9, 'j': 2, 'k': 6, 'cost': 22}, {'i': 9, 'j': 2, 'k': 7, 'cost': 5}, {'i': 9, 'j': 2, 'k': 8, 'cost': 62}, {'i': 9, 'j': 2, 'k': 9, 'cost': 60}, {'i': 9, 'j': 2, 'k': 10, 'cost': 99}, {'i': 9, 'j': 3, 'k': 1, 'cost': 5}, {'i': 9, 'j': 3, 'k': 2, 'cost': 87}, {'i': 9, 'j': 3, 'k': 3, 'cost': 57}, {'i': 9, 'j': 3, 'k': 4, 'cost': 40}, {'i': 9, 'j': 3, 'k': 5, 'cost': 76}, {'i': 9, 'j': 3, 'k': 6, 'cost': 61}, {'i': 9, 'j': 3, 'k': 7, 'cost': 36}, {'i': 9, 'j': 3, 'k': 8, 'cost': 27}, {'i': 9, 'j': 3, 'k': 9, 'cost': 86}, {'i': 9, 'j': 3, 'k': 10, 'cost': 11}, {'i': 9, 'j': 4, 'k': 1, 'cost': 74}, {'i': 9, 'j': 4, 'k': 2, 'cost': 80}, {'i': 9, 'j': 4, 'k': 3, 'cost': 14}, {'i': 9, 'j': 4, 'k': 4, 'cost': 47}, {'i': 9, 'j': 4, 'k': 5, 'cost': 81}, {'i': 9, 'j': 4, 'k': 6, 'cost': 44}, {'i': 9, 'j': 4, 'k': 7, 'cost': 49}, {'i': 9, 'j': 4, 'k': 8, 'cost': 70}, {'i': 9, 'j': 4, 'k': 9, 'cost': 14}, {'i': 9, 'j': 4, 'k': 10, 'cost': 1}, {'i': 9, 'j': 5, 'k': 1, 'cost': 19}, {'i': 9, 'j': 5, 'k': 2, 'cost': 0}, {'i': 9, 'j': 5, 'k': 3, 'cost': 2}, {'i': 9, 'j': 5, 'k': 4, 'cost': 43}, {'i': 9, 'j': 5, 'k': 5, 'cost': 41}, {'i': 9, 'j': 5, 'k': 6, 'cost': 36}, {'i': 9, 'j': 5, 'k': 7, 'cost': 18}, {'i': 9, 'j': 5, 'k': 8, 'cost': 96}, {'i': 9, 'j': 5, 'k': 9, 'cost': 91}, {'i': 9, 'j': 5, 'k': 10, 'cost': 94}, {'i': 9, 'j': 6, 'k': 1, 'cost': 86}, {'i': 9, 'j': 6, 'k': 2, 'cost': 11}, {'i': 9, 'j': 6, 'k': 3, 'cost': 47}, {'i': 9, 'j': 6, 'k': 4, 'cost': 8}, {'i': 9, 'j': 6, 'k': 5, 'cost': 20}, {'i': 9, 'j': 6, 'k': 6, 'cost': 92}, {'i': 9, 'j': 6, 'k': 7, 'cost': 44}, {'i': 9, 'j': 6, 'k': 8, 'cost': 34}, {'i': 9, 'j': 6, 'k': 9, 'cost': 97}, {'i': 9, 'j': 6, 'k': 10, 'cost': 46}, {'i': 9, 'j': 7, 'k': 1, 'cost': 87}, {'i': 9, 'j': 7, 'k': 2, 'cost': 20}, {'i': 9, 'j': 7, 'k': 3, 'cost': 83}, {'i': 9, 'j': 7, 'k': 4, 'cost': 80}, {'i': 9, 'j': 7, 'k': 5, 'cost': 14}, {'i': 9, 'j': 7, 'k': 6, 'cost': 7}, {'i': 9, 'j': 7, 'k': 7, 'cost': 25}, {'i': 9, 'j': 7, 'k': 8, 'cost': 62}, {'i': 9, 'j': 7, 'k': 9, 'cost': 96}, {'i': 9, 'j': 7, 'k': 10, 'cost': 97}, {'i': 9, 'j': 8, 'k': 1, 'cost': 90}, {'i': 9, 'j': 8, 'k': 2, 'cost': 53}, {'i': 9, 'j': 8, 'k': 3, 'cost': 34}, {'i': 9, 'j': 8, 'k': 4, 'cost': 37}, {'i': 9, 'j': 8, 'k': 5, 'cost': 33}, {'i': 9, 'j': 8, 'k': 6, 'cost': 85}, {'i': 9, 'j': 8, 'k': 7, 'cost': 48}, {'i': 9, 'j': 8, 'k': 8, 'cost': 11}, {'i': 9, 'j': 8, 'k': 9, 'cost': 81}, {'i': 9, 'j': 8, 'k': 10, 'cost': 27}, {'i': 9, 'j': 9, 'k': 1, 'cost': 28}, {'i': 9, 'j': 9, 'k': 2, 'cost': 26}, {'i': 9, 'j': 9, 'k': 3, 'cost': 20}, {'i': 9, 'j': 9, 'k': 4, 'cost': 38}, {'i': 9, 'j': 9, 'k': 5, 'cost': 83}, {'i': 9, 'j': 9, 'k': 6, 'cost': 42}, {'i': 9, 'j': 9, 'k': 7, 'cost': 34}, {'i': 9, 'j': 9, 'k': 8, 'cost': 23}, {'i': 9, 'j': 9, 'k': 9, 'cost': 75}, {'i': 9, 'j': 9, 'k': 10, 'cost': 46}, {'i': 9, 'j': 10, 'k': 1, 'cost': 29}, {'i': 9, 'j': 10, 'k': 2, 'cost': 69}, {'i': 9, 'j': 10, 'k': 3, 'cost': 43}, {'i': 9, 'j': 10, 'k': 4, 'cost': 60}, {'i': 9, 'j': 10, 'k': 5, 'cost': 5}, {'i': 9, 'j': 10, 'k': 6, 'cost': 54}, {'i': 9, 'j': 10, 'k': 7, 'cost': 3}, {'i': 9, 'j': 10, 'k': 8, 'cost': 33}, {'i': 9, 'j': 10, 'k': 9, 'cost': 7}, {'i': 9, 'j': 10, 'k': 10, 'cost': 16}, {'i': 10, 'j': 1, 'k': 1, 'cost': 21}, {'i': 10, 'j': 1, 'k': 2, 'cost': 90}, {'i': 10, 'j': 1, 'k': 3, 'cost': 53}, {'i': 10, 'j': 1, 'k': 4, 'cost': 19}, {'i': 10, 'j': 1, 'k': 5, 'cost': 4}, {'i': 10, 'j': 1, 'k': 6, 'cost': 82}, {'i': 10, 'j': 1, 'k': 7, 'cost': 31}, {'i': 10, 'j': 1, 'k': 8, 'cost': 89}, {'i': 10, 'j': 1, 'k': 9, 'cost': 1}, {'i': 10, 'j': 1, 'k': 10, 'cost': 33}, {'i': 10, 'j': 2, 'k': 1, 'cost': 11}, {'i': 10, 'j': 2, 'k': 2, 'cost': 32}, {'i': 10, 'j': 2, 'k': 3, 'cost': 22}, {'i': 10, 'j': 2, 'k': 4, 'cost': 74}, {'i': 10, 'j': 2, 'k': 5, 'cost': 77}, {'i': 10, 'j': 2, 'k': 6, 'cost': 40}, {'i': 10, 'j': 2, 'k': 7, 'cost': 65}, {'i': 10, 'j': 2, 'k': 8, 'cost': 91}, {'i': 10, 'j': 2, 'k': 9, 'cost': 95}, {'i': 10, 'j': 2, 'k': 10, 'cost': 53}, {'i': 10, 'j': 3, 'k': 1, 'cost': 9}, {'i': 10, 'j': 3, 'k': 2, 'cost': 56}, {'i': 10, 'j': 3, 'k': 3, 'cost': 16}, {'i': 10, 'j': 3, 'k': 4, 'cost': 84}, {'i': 10, 'j': 3, 'k': 5, 'cost': 98}, {'i': 10, 'j': 3, 'k': 6, 'cost': 1}, {'i': 10, 'j': 3, 'k': 7, 'cost': 78}, {'i': 10, 'j': 3, 'k': 8, 'cost': 63}, {'i': 10, 'j': 3, 'k': 9, 'cost': 34}, {'i': 10, 'j': 3, 'k': 10, 'cost': 13}, {'i': 10, 'j': 4, 'k': 1, 'cost': 50}, {'i': 10, 'j': 4, 'k': 2, 'cost': 37}, {'i': 10, 'j': 4, 'k': 3, 'cost': 93}, {'i': 10, 'j': 4, 'k': 4, 'cost': 37}, {'i': 10, 'j': 4, 'k': 5, 'cost': 7}, {'i': 10, 'j': 4, 'k': 6, 'cost': 43}, {'i': 10, 'j': 4, 'k': 7, 'cost': 6}, {'i': 10, 'j': 4, 'k': 8, 'cost': 99}, {'i': 10, 'j': 4, 'k': 9, 'cost': 1}, {'i': 10, 'j': 4, 'k': 10, 'cost': 51}, {'i': 10, 'j': 5, 'k': 1, 'cost': 78}, {'i': 10, 'j': 5, 'k': 2, 'cost': 38}, {'i': 10, 'j': 5, 'k': 3, 'cost': 37}, {'i': 10, 'j': 5, 'k': 4, 'cost': 37}, {'i': 10, 'j': 5, 'k': 5, 'cost': 75}, {'i': 10, 'j': 5, 'k': 6, 'cost': 26}, {'i': 10, 'j': 5, 'k': 7, 'cost': 45}, {'i': 10, 'j': 5, 'k': 8, 'cost': 91}, {'i': 10, 'j': 5, 'k': 9, 'cost': 11}, {'i': 10, 'j': 5, 'k': 10, 'cost': 62}, {'i': 10, 'j': 6, 'k': 1, 'cost': 19}, {'i': 10, 'j': 6, 'k': 2, 'cost': 74}, {'i': 10, 'j': 6, 'k': 3, 'cost': 86}, {'i': 10, 'j': 6, 'k': 4, 'cost': 38}, {'i': 10, 'j': 6, 'k': 5, 'cost': 38}, {'i': 10, 'j': 6, 'k': 6, 'cost': 85}, {'i': 10, 'j': 6, 'k': 7, 'cost': 18}, {'i': 10, 'j': 6, 'k': 8, 'cost': 52}, {'i': 10, 'j': 6, 'k': 9, 'cost': 93}, {'i': 10, 'j': 6, 'k': 10, 'cost': 90}, {'i': 10, 'j': 7, 'k': 1, 'cost': 46}, {'i': 10, 'j': 7, 'k': 2, 'cost': 44}, {'i': 10, 'j': 7, 'k': 3, 'cost': 18}, {'i': 10, 'j': 7, 'k': 4, 'cost': 18}, {'i': 10, 'j': 7, 'k': 5, 'cost': 15}, {'i': 10, 'j': 7, 'k': 6, 'cost': 84}, {'i': 10, 'j': 7, 'k': 7, 'cost': 74}, {'i': 10, 'j': 7, 'k': 8, 'cost': 1}, {'i': 10, 'j': 7, 'k': 9, 'cost': 28}, {'i': 10, 'j': 7, 'k': 10, 'cost': 38}, {'i': 10, 'j': 8, 'k': 1, 'cost': 86}, {'i': 10, 'j': 8, 'k': 2, 'cost': 28}, {'i': 10, 'j': 8, 'k': 3, 'cost': 81}, {'i': 10, 'j': 8, 'k': 4, 'cost': 94}, {'i': 10, 'j': 8, 'k': 5, 'cost': 81}, {'i': 10, 'j': 8, 'k': 6, 'cost': 48}, {'i': 10, 'j': 8, 'k': 7, 'cost': 1}, {'i': 10, 'j': 8, 'k': 8, 'cost': 25}, {'i': 10, 'j': 8, 'k': 9, 'cost': 91}, {'i': 10, 'j': 8, 'k': 10, 'cost': 2}, {'i': 10, 'j': 9, 'k': 1, 'cost': 93}, {'i': 10, 'j': 9, 'k': 2, 'cost': 69}, {'i': 10, 'j': 9, 'k': 3, 'cost': 54}, {'i': 10, 'j': 9, 'k': 4, 'cost': 97}, {'i': 10, 'j': 9, 'k': 5, 'cost': 27}, {'i': 10, 'j': 9, 'k': 6, 'cost': 43}, {'i': 10, 'j': 9, 'k': 7, 'cost': 62}, {'i': 10, 'j': 9, 'k': 8, 'cost': 84}, {'i': 10, 'j': 9, 'k': 9, 'cost': 90}, {'i': 10, 'j': 9, 'k': 10, 'cost': 82}, {'i': 10, 'j': 10, 'k': 1, 'cost': 98}, {'i': 10, 'j': 10, 'k': 2, 'cost': 85}, {'i': 10, 'j': 10, 'k': 3, 'cost': 46}, {'i': 10, 'j': 10, 'k': 4, 'cost': 66}, {'i': 10, 'j': 10, 'k': 5, 'cost': 6}, {'i': 10, 'j': 10, 'k': 6, 'cost': 85}, {'i': 10, 'j': 10, 'k': 7, 'cost': 93}, {'i': 10, 'j': 10, 'k': 8, 'cost': 99}, {'i': 10, 'j': 10, 'k': 9, 'cost': 58}, {'i': 10, 'j': 10, 'k': 10, 'cost': 35}]}","[[1, 5, 4], [2, 6, 8], [3, 8, 9], [4, 9, 7], [5, 2, 5], [6, 7, 3], [7, 10, 1], [8, 1, 2], [9, 4, 10], [10, 3, 6]]",25,nl,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=11
+# meeting_ids=A, B, C, D, E, F, G, H, I, J, K
+
+# 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=A
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 76 | 51 | 96 | 4 | 94 | 53 | 12 | 54 | 44 | 5 | 70 |
+| B | 18 | 8 | 32 | 88 | 6 | 71 | 71 | 3 | 98 | 49 | 15 |
+| C | 22 | 11 | 98 | 86 | 18 | 89 | 18 | 27 | 68 | 88 | 12 |
+| D | 85 | 73 | 23 | 26 | 74 | 12 | 34 | 82 | 67 | 73 | 1 |
+| E | 68 | 19 | 85 | 18 | 93 | 82 | 36 | 9 | 42 | 24 | 66 |
+| F | 38 | 82 | 55 | 45 | 8 | 67 | 17 | 14 | 13 | 68 | 71 |
+| G | 2 | 87 | 29 | 49 | 1 | 50 | 78 | 61 | 10 | 80 | 3 |
+| H | 48 | 36 | 69 | 17 | 45 | 14 | 72 | 59 | 9 | 18 | 3 |
+| I | 77 | 0 | 37 | 72 | 36 | 33 | 38 | 45 | 74 | 61 | 7 |
+| J | 3 | 13 | 49 | 28 | 99 | 93 | 96 | 15 | 97 | 2 | 69 |
+| K | 47 | 55 | 41 | 6 | 0 | 15 | 18 | 26 | 1 | 75 | 90 |
+
+## meeting_id=B
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 71 | 98 | 39 | 14 | 13 | 87 | 26 | 65 | 34 | 77 | 60 |
+| B | 3 | 30 | 38 | 14 | 67 | 42 | 12 | 10 | 64 | 4 | 57 |
+| C | 85 | 14 | 68 | 54 | 94 | 15 | 64 | 85 | 4 | 21 | 58 |
+| D | 73 | 35 | 91 | 10 | 45 | 33 | 47 | 45 | 26 | 10 | 12 |
+| E | 90 | 91 | 22 | 37 | 52 | 59 | 64 | 27 | 36 | 27 | 13 |
+| F | 61 | 85 | 65 | 66 | 54 | 84 | 91 | 35 | 13 | 34 | 35 |
+| G | 53 | 15 | 49 | 85 | 46 | 12 | 14 | 29 | 48 | 39 | 73 |
+| H | 11 | 54 | 73 | 29 | 6 | 49 | 70 | 14 | 75 | 35 | 78 |
+| I | 98 | 46 | 32 | 68 | 43 | 90 | 82 | 25 | 17 | 34 | 95 |
+| J | 12 | 14 | 84 | 1 | 20 | 29 | 25 | 47 | 83 | 26 | 47 |
+| K | 38 | 25 | 59 | 48 | 64 | 88 | 81 | 24 | 40 | 60 | 3 |
+
+## meeting_id=C
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 2 | 40 | 44 | 69 | 42 | 14 | 11 | 36 | 15 | 12 | 81 |
+| B | 70 | 71 | 45 | 27 | 21 | 17 | 1 | 7 | 43 | 38 | 89 |
+| C | 26 | 11 | 29 | 3 | 95 | 7 | 85 | 14 | 24 | 96 | 2 |
+| D | 87 | 15 | 91 | 17 | 27 | 32 | 13 | 9 | 89 | 5 | 81 |
+| E | 34 | 55 | 80 | 73 | 54 | 76 | 72 | 27 | 5 | 53 | 27 |
+| F | 51 | 5 | 35 | 47 | 28 | 53 | 22 | 68 | 10 | 36 | 24 |
+| G | 66 | 33 | 21 | 74 | 50 | 88 | 34 | 89 | 53 | 0 | 76 |
+| H | 84 | 87 | 67 | 37 | 12 | 9 | 30 | 92 | 29 | 68 | 45 |
+| I | 25 | 80 | 7 | 52 | 27 | 33 | 16 | 9 | 20 | 90 | 85 |
+| J | 69 | 3 | 30 | 98 | 36 | 25 | 48 | 94 | 20 | 12 | 92 |
+| K | 19 | 79 | 16 | 49 | 39 | 96 | 43 | 47 | 23 | 86 | 51 |
+
+## meeting_id=D
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 8 | 65 | 49 | 55 | 16 | 21 | 3 | 55 | 24 | 48 | 72 |
+| B | 56 | 19 | 93 | 16 | 5 | 85 | 74 | 81 | 70 | 87 | 49 |
+| C | 83 | 89 | 19 | 20 | 60 | 54 | 18 | 1 | 63 | 52 | 84 |
+| D | 63 | 1 | 60 | 35 | 55 | 96 | 69 | 63 | 93 | 95 | 45 |
+| E | 35 | 98 | 97 | 12 | 36 | 20 | 98 | 96 | 86 | 38 | 44 |
+| F | 46 | 27 | 4 | 74 | 65 | 61 | 48 | 0 | 40 | 14 | 75 |
+| G | 80 | 29 | 80 | 3 | 53 | 65 | 77 | 29 | 62 | 0 | 51 |
+| H | 3 | 21 | 90 | 28 | 98 | 82 | 89 | 81 | 9 | 57 | 42 |
+| I | 94 | 91 | 1 | 12 | 27 | 52 | 77 | 85 | 20 | 66 | 12 |
+| J | 11 | 67 | 25 | 6 | 85 | 69 | 2 | 44 | 46 | 97 | 44 |
+| K | 26 | 8 | 52 | 98 | 64 | 24 | 41 | 84 | 87 | 90 | 72 |
+
+## meeting_id=E
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 25 | 59 | 91 | 61 | 75 | 97 | 41 | 9 | 99 | 22 | 70 |
+| B | 1 | 61 | 17 | 67 | 56 | 33 | 71 | 21 | 84 | 90 | 74 |
+| C | 94 | 35 | 76 | 93 | 27 | 42 | 2 | 34 | 60 | 26 | 39 |
+| D | 38 | 79 | 35 | 52 | 68 | 14 | 53 | 92 | 76 | 17 | 41 |
+| E | 33 | 8 | 10 | 43 | 37 | 80 | 78 | 22 | 18 | 22 | 3 |
+| F | 82 | 41 | 9 | 36 | 5 | 95 | 6 | 21 | 41 | 5 | 26 |
+| G | 32 | 90 | 66 | 59 | 91 | 30 | 79 | 38 | 14 | 78 | 34 |
+| H | 5 | 46 | 80 | 89 | 4 | 56 | 85 | 68 | 52 | 37 | 5 |
+| I | 43 | 66 | 50 | 36 | 79 | 32 | 1 | 39 | 54 | 98 | 15 |
+| J | 75 | 92 | 4 | 14 | 3 | 48 | 24 | 82 | 99 | 19 | 37 |
+| K | 98 | 96 | 3 | 82 | 75 | 62 | 12 | 22 | 70 | 12 | 3 |
+
+## meeting_id=F
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 90 | 11 | 8 | 74 | 55 | 29 | 62 | 85 | 77 | 72 | 13 |
+| B | 40 | 85 | 55 | 68 | 12 | 49 | 28 | 14 | 23 | 83 | 3 |
+| C | 96 | 37 | 38 | 8 | 31 | 59 | 73 | 0 | 53 | 55 | 6 |
+| D | 50 | 37 | 54 | 54 | 3 | 73 | 1 | 85 | 76 | 10 | 8 |
+| E | 63 | 72 | 58 | 52 | 94 | 43 | 50 | 93 | 36 | 40 | 40 |
+| F | 98 | 33 | 89 | 19 | 84 | 45 | 34 | 16 | 51 | 45 | 14 |
+| G | 59 | 4 | 16 | 30 | 1 | 72 | 78 | 1 | 46 | 71 | 62 |
+| H | 30 | 47 | 72 | 8 | 66 | 17 | 56 | 41 | 96 | 47 | 74 |
+| I | 9 | 92 | 93 | 10 | 21 | 62 | 28 | 59 | 60 | 25 | 31 |
+| J | 99 | 67 | 7 | 9 | 28 | 50 | 54 | 98 | 15 | 15 | 12 |
+| K | 71 | 33 | 6 | 89 | 11 | 96 | 95 | 47 | 9 | 87 | 81 |
+
+## meeting_id=G
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 42 | 8 | 36 | 81 | 93 | 4 | 3 | 71 | 95 | 35 | 37 |
+| B | 12 | 78 | 46 | 7 | 10 | 19 | 83 | 48 | 23 | 4 | 72 |
+| C | 26 | 82 | 41 | 54 | 12 | 93 | 70 | 88 | 78 | 77 | 22 |
+| D | 37 | 63 | 56 | 30 | 98 | 61 | 52 | 30 | 30 | 11 | 82 |
+| E | 65 | 78 | 76 | 29 | 44 | 95 | 52 | 95 | 80 | 31 | 94 |
+| F | 31 | 92 | 79 | 12 | 39 | 96 | 69 | 73 | 7 | 72 | 77 |
+| G | 99 | 58 | 66 | 3 | 23 | 77 | 12 | 7 | 95 | 16 | 75 |
+| H | 13 | 13 | 6 | 73 | 22 | 53 | 38 | 87 | 78 | 24 | 84 |
+| I | 31 | 57 | 67 | 23 | 90 | 29 | 93 | 33 | 75 | 84 | 98 |
+| J | 20 | 80 | 70 | 78 | 99 | 63 | 27 | 79 | 34 | 22 | 4 |
+| K | 85 | 6 | 99 | 6 | 9 | 14 | 26 | 48 | 42 | 53 | 44 |
+
+## meeting_id=H
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 18 | 37 | 15 | 71 | 28 | 9 | 2 | 55 | 92 | 49 | 80 |
+| B | 54 | 28 | 25 | 70 | 89 | 32 | 73 | 9 | 23 | 90 | 19 |
+| C | 22 | 59 | 23 | 17 | 6 | 32 | 29 | 83 | 74 | 30 | 24 |
+| D | 36 | 44 | 76 | 67 | 90 | 64 | 43 | 13 | 75 | 57 | 2 |
+| E | 74 | 14 | 4 | 58 | 25 | 25 | 22 | 17 | 87 | 32 | 1 |
+| F | 18 | 4 | 18 | 2 | 9 | 36 | 49 | 80 | 46 | 25 | 53 |
+| G | 90 | 41 | 56 | 67 | 92 | 33 | 17 | 44 | 99 | 50 | 8 |
+| H | 93 | 31 | 18 | 70 | 10 | 52 | 70 | 94 | 37 | 6 | 74 |
+| I | 45 | 48 | 9 | 61 | 25 | 20 | 35 | 48 | 38 | 12 | 52 |
+| J | 76 | 17 | 30 | 8 | 51 | 74 | 81 | 12 | 91 | 79 | 51 |
+| K | 75 | 1 | 21 | 21 | 7 | 3 | 44 | 12 | 7 | 48 | 30 |
+
+## meeting_id=I
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 55 | 87 | 80 | 30 | 97 | 33 | 97 | 23 | 5 | 51 | 81 |
+| B | 3 | 22 | 32 | 46 | 85 | 75 | 35 | 86 | 59 | 80 | 81 |
+| C | 22 | 54 | 22 | 86 | 51 | 62 | 88 | 75 | 78 | 50 | 51 |
+| D | 85 | 68 | 52 | 52 | 16 | 71 | 11 | 23 | 49 | 85 | 4 |
+| E | 29 | 67 | 78 | 30 | 73 | 20 | 96 | 45 | 93 | 81 | 0 |
+| F | 96 | 57 | 44 | 76 | 31 | 53 | 11 | 24 | 7 | 40 | 78 |
+| G | 68 | 38 | 21 | 7 | 46 | 27 | 32 | 98 | 95 | 12 | 99 |
+| H | 7 | 88 | 46 | 87 | 66 | 1 | 88 | 49 | 8 | 30 | 81 |
+| I | 90 | 53 | 57 | 13 | 62 | 23 | 92 | 92 | 85 | 47 | 33 |
+| J | 4 | 67 | 27 | 88 | 24 | 70 | 54 | 84 | 26 | 22 | 91 |
+| K | 80 | 8 | 7 | 21 | 41 | 51 | 84 | 27 | 40 | 10 | 76 |
+
+## meeting_id=J
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 64 | 96 | 21 | 6 | 86 | 86 | 23 | 65 | 26 | 70 | 2 |
+| B | 73 | 93 | 76 | 86 | 79 | 1 | 29 | 36 | 92 | 18 | 3 |
+| C | 83 | 49 | 20 | 91 | 45 | 47 | 57 | 96 | 59 | 44 | 26 |
+| D | 82 | 93 | 26 | 18 | 23 | 45 | 30 | 72 | 33 | 41 | 6 |
+| E | 27 | 72 | 16 | 47 | 25 | 56 | 9 | 73 | 56 | 71 | 21 |
+| F | 79 | 37 | 4 | 27 | 79 | 68 | 31 | 75 | 42 | 7 | 28 |
+| G | 39 | 29 | 30 | 70 | 61 | 82 | 41 | 10 | 13 | 68 | 8 |
+| H | 87 | 72 | 0 | 32 | 36 | 1 | 36 | 54 | 41 | 54 | 95 |
+| I | 19 | 54 | 20 | 6 | 95 | 16 | 97 | 16 | 81 | 88 | 20 |
+| J | 27 | 52 | 76 | 45 | 77 | 68 | 8 | 97 | 74 | 19 | 0 |
+| K | 83 | 2 | 25 | 26 | 71 | 74 | 87 | 58 | 62 | 82 | 98 |
+
+## meeting_id=K
+| presenter_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 68 | 35 | 61 | 11 | 61 | 61 | 80 | 97 | 61 | 91 | 1 |
+| B | 24 | 90 | 78 | 25 | 92 | 97 | 65 | 97 | 22 | 19 | 36 |
+| C | 7 | 68 | 35 | 68 | 92 | 48 | 76 | 50 | 21 | 60 | 48 |
+| D | 27 | 39 | 75 | 28 | 18 | 82 | 9 | 76 | 84 | 77 | 89 |
+| E | 58 | 96 | 89 | 79 | 0 | 2 | 92 | 78 | 70 | 1 | 57 |
+| F | 80 | 31 | 58 | 66 | 85 | 41 | 30 | 24 | 11 | 74 | 28 |
+| G | 12 | 31 | 93 | 92 | 68 | 42 | 38 | 42 | 50 | 83 | 0 |
+| H | 53 | 63 | 67 | 9 | 32 | 52 | 81 | 2 | 77 | 97 | 28 |
+| I | 19 | 60 | 56 | 2 | 87 | 6 | 9 | 4 | 66 | 7 | 61 |
+| J | 90 | 36 | 18 | 49 | 60 | 58 | 87 | 20 | 78 | 12 | 30 |
+| K | 94 | 89 | 54 | 22 | 98 | 82 | 33 | 42 | 10 | 69 | 9 |
+
+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': [[[76, 51, 96, 4, 94, 53, 12, 54, 44, 5, 70], [18, 8, 32, 88, 6, 71, 71, 3, 98, 49, 15], [22, 11, 98, 86, 18, 89, 18, 27, 68, 88, 12], [85, 73, 23, 26, 74, 12, 34, 82, 67, 73, 1], [68, 19, 85, 18, 93, 82, 36, 9, 42, 24, 66], [38, 82, 55, 45, 8, 67, 17, 14, 13, 68, 71], [2, 87, 29, 49, 1, 50, 78, 61, 10, 80, 3], [48, 36, 69, 17, 45, 14, 72, 59, 9, 18, 3], [77, 0, 37, 72, 36, 33, 38, 45, 74, 61, 7], [3, 13, 49, 28, 99, 93, 96, 15, 97, 2, 69], [47, 55, 41, 6, 0, 15, 18, 26, 1, 75, 90]], [[71, 98, 39, 14, 13, 87, 26, 65, 34, 77, 60], [3, 30, 38, 14, 67, 42, 12, 10, 64, 4, 57], [85, 14, 68, 54, 94, 15, 64, 85, 4, 21, 58], [73, 35, 91, 10, 45, 33, 47, 45, 26, 10, 12], [90, 91, 22, 37, 52, 59, 64, 27, 36, 27, 13], [61, 85, 65, 66, 54, 84, 91, 35, 13, 34, 35], [53, 15, 49, 85, 46, 12, 14, 29, 48, 39, 73], [11, 54, 73, 29, 6, 49, 70, 14, 75, 35, 78], [98, 46, 32, 68, 43, 90, 82, 25, 17, 34, 95], [12, 14, 84, 1, 20, 29, 25, 47, 83, 26, 47], [38, 25, 59, 48, 64, 88, 81, 24, 40, 60, 3]], [[2, 40, 44, 69, 42, 14, 11, 36, 15, 12, 81], [70, 71, 45, 27, 21, 17, 1, 7, 43, 38, 89], [26, 11, 29, 3, 95, 7, 85, 14, 24, 96, 2], [87, 15, 91, 17, 27, 32, 13, 9, 89, 5, 81], [34, 55, 80, 73, 54, 76, 72, 27, 5, 53, 27], [51, 5, 35, 47, 28, 53, 22, 68, 10, 36, 24], [66, 33, 21, 74, 50, 88, 34, 89, 53, 0, 76], [84, 87, 67, 37, 12, 9, 30, 92, 29, 68, 45], [25, 80, 7, 52, 27, 33, 16, 9, 20, 90, 85], [69, 3, 30, 98, 36, 25, 48, 94, 20, 12, 92], [19, 79, 16, 49, 39, 96, 43, 47, 23, 86, 51]], [[8, 65, 49, 55, 16, 21, 3, 55, 24, 48, 72], [56, 19, 93, 16, 5, 85, 74, 81, 70, 87, 49], [83, 89, 19, 20, 60, 54, 18, 1, 63, 52, 84], [63, 1, 60, 35, 55, 96, 69, 63, 93, 95, 45], [35, 98, 97, 12, 36, 20, 98, 96, 86, 38, 44], [46, 27, 4, 74, 65, 61, 48, 0, 40, 14, 75], [80, 29, 80, 3, 53, 65, 77, 29, 62, 0, 51], [3, 21, 90, 28, 98, 82, 89, 81, 9, 57, 42], [94, 91, 1, 12, 27, 52, 77, 85, 20, 66, 12], [11, 67, 25, 6, 85, 69, 2, 44, 46, 97, 44], [26, 8, 52, 98, 64, 24, 41, 84, 87, 90, 72]], [[25, 59, 91, 61, 75, 97, 41, 9, 99, 22, 70], [1, 61, 17, 67, 56, 33, 71, 21, 84, 90, 74], [94, 35, 76, 93, 27, 42, 2, 34, 60, 26, 39], [38, 79, 35, 52, 68, 14, 53, 92, 76, 17, 41], [33, 8, 10, 43, 37, 80, 78, 22, 18, 22, 3], [82, 41, 9, 36, 5, 95, 6, 21, 41, 5, 26], [32, 90, 66, 59, 91, 30, 79, 38, 14, 78, 34], [5, 46, 80, 89, 4, 56, 85, 68, 52, 37, 5], [43, 66, 50, 36, 79, 32, 1, 39, 54, 98, 15], [75, 92, 4, 14, 3, 48, 24, 82, 99, 19, 37], [98, 96, 3, 82, 75, 62, 12, 22, 70, 12, 3]], [[90, 11, 8, 74, 55, 29, 62, 85, 77, 72, 13], [40, 85, 55, 68, 12, 49, 28, 14, 23, 83, 3], [96, 37, 38, 8, 31, 59, 73, 0, 53, 55, 6], [50, 37, 54, 54, 3, 73, 1, 85, 76, 10, 8], [63, 72, 58, 52, 94, 43, 50, 93, 36, 40, 40], [98, 33, 89, 19, 84, 45, 34, 16, 51, 45, 14], [59, 4, 16, 30, 1, 72, 78, 1, 46, 71, 62], [30, 47, 72, 8, 66, 17, 56, 41, 96, 47, 74], [9, 92, 93, 10, 21, 62, 28, 59, 60, 25, 31], [99, 67, 7, 9, 28, 50, 54, 98, 15, 15, 12], [71, 33, 6, 89, 11, 96, 95, 47, 9, 87, 81]], [[42, 8, 36, 81, 93, 4, 3, 71, 95, 35, 37], [12, 78, 46, 7, 10, 19, 83, 48, 23, 4, 72], [26, 82, 41, 54, 12, 93, 70, 88, 78, 77, 22], [37, 63, 56, 30, 98, 61, 52, 30, 30, 11, 82], [65, 78, 76, 29, 44, 95, 52, 95, 80, 31, 94], [31, 92, 79, 12, 39, 96, 69, 73, 7, 72, 77], [99, 58, 66, 3, 23, 77, 12, 7, 95, 16, 75], [13, 13, 6, 73, 22, 53, 38, 87, 78, 24, 84], [31, 57, 67, 23, 90, 29, 93, 33, 75, 84, 98], [20, 80, 70, 78, 99, 63, 27, 79, 34, 22, 4], [85, 6, 99, 6, 9, 14, 26, 48, 42, 53, 44]], [[18, 37, 15, 71, 28, 9, 2, 55, 92, 49, 80], [54, 28, 25, 70, 89, 32, 73, 9, 23, 90, 19], [22, 59, 23, 17, 6, 32, 29, 83, 74, 30, 24], [36, 44, 76, 67, 90, 64, 43, 13, 75, 57, 2], [74, 14, 4, 58, 25, 25, 22, 17, 87, 32, 1], [18, 4, 18, 2, 9, 36, 49, 80, 46, 25, 53], [90, 41, 56, 67, 92, 33, 17, 44, 99, 50, 8], [93, 31, 18, 70, 10, 52, 70, 94, 37, 6, 74], [45, 48, 9, 61, 25, 20, 35, 48, 38, 12, 52], [76, 17, 30, 8, 51, 74, 81, 12, 91, 79, 51], [75, 1, 21, 21, 7, 3, 44, 12, 7, 48, 30]], [[55, 87, 80, 30, 97, 33, 97, 23, 5, 51, 81], [3, 22, 32, 46, 85, 75, 35, 86, 59, 80, 81], [22, 54, 22, 86, 51, 62, 88, 75, 78, 50, 51], [85, 68, 52, 52, 16, 71, 11, 23, 49, 85, 4], [29, 67, 78, 30, 73, 20, 96, 45, 93, 81, 0], [96, 57, 44, 76, 31, 53, 11, 24, 7, 40, 78], [68, 38, 21, 7, 46, 27, 32, 98, 95, 12, 99], [7, 88, 46, 87, 66, 1, 88, 49, 8, 30, 81], [90, 53, 57, 13, 62, 23, 92, 92, 85, 47, 33], [4, 67, 27, 88, 24, 70, 54, 84, 26, 22, 91], [80, 8, 7, 21, 41, 51, 84, 27, 40, 10, 76]], [[64, 96, 21, 6, 86, 86, 23, 65, 26, 70, 2], [73, 93, 76, 86, 79, 1, 29, 36, 92, 18, 3], [83, 49, 20, 91, 45, 47, 57, 96, 59, 44, 26], [82, 93, 26, 18, 23, 45, 30, 72, 33, 41, 6], [27, 72, 16, 47, 25, 56, 9, 73, 56, 71, 21], [79, 37, 4, 27, 79, 68, 31, 75, 42, 7, 28], [39, 29, 30, 70, 61, 82, 41, 10, 13, 68, 8], [87, 72, 0, 32, 36, 1, 36, 54, 41, 54, 95], [19, 54, 20, 6, 95, 16, 97, 16, 81, 88, 20], [27, 52, 76, 45, 77, 68, 8, 97, 74, 19, 0], [83, 2, 25, 26, 71, 74, 87, 58, 62, 82, 98]], [[68, 35, 61, 11, 61, 61, 80, 97, 61, 91, 1], [24, 90, 78, 25, 92, 97, 65, 97, 22, 19, 36], [7, 68, 35, 68, 92, 48, 76, 50, 21, 60, 48], [27, 39, 75, 28, 18, 82, 9, 76, 84, 77, 89], [58, 96, 89, 79, 0, 2, 92, 78, 70, 1, 57], [80, 31, 58, 66, 85, 41, 30, 24, 11, 74, 28], [12, 31, 93, 92, 68, 42, 38, 42, 50, 83, 0], [53, 63, 67, 9, 32, 52, 81, 2, 77, 97, 28], [19, 60, 56, 2, 87, 6, 9, 4, 66, 7, 61], [90, 36, 18, 49, 60, 58, 87, 20, 78, 12, 30], [94, 89, 54, 22, 98, 82, 33, 42, 10, 69, 9]]], 'objective': 16.0}","[[0, 10, 8], [1, 9, 3], [2, 6, 9], [3, 8, 2], [4, 1, 0], [5, 2, 7], [6, 0, 6], [7, 5, 1], [8, 3, 10], [9, 7, 5], [10, 4, 4]]",16.0,"{'problem_type': 'AP3', 'n': 11, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 76}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 51}, {'i': 'A', 'j': 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'j': 'B', 'k': 'K', 'cost': 36}, {'i': 'K', 'j': 'C', 'k': 'A', 'cost': 7}, {'i': 'K', 'j': 'C', 'k': 'B', 'cost': 68}, {'i': 'K', 'j': 'C', 'k': 'C', 'cost': 35}, {'i': 'K', 'j': 'C', 'k': 'D', 'cost': 68}, {'i': 'K', 'j': 'C', 'k': 'E', 'cost': 92}, {'i': 'K', 'j': 'C', 'k': 'F', 'cost': 48}, {'i': 'K', 'j': 'C', 'k': 'G', 'cost': 76}, {'i': 'K', 'j': 'C', 'k': 'H', 'cost': 50}, {'i': 'K', 'j': 'C', 'k': 'I', 'cost': 21}, {'i': 'K', 'j': 'C', 'k': 'J', 'cost': 60}, {'i': 'K', 'j': 'C', 'k': 'K', 'cost': 48}, {'i': 'K', 'j': 'D', 'k': 'A', 'cost': 27}, {'i': 'K', 'j': 'D', 'k': 'B', 'cost': 39}, {'i': 'K', 'j': 'D', 'k': 'C', 'cost': 75}, {'i': 'K', 'j': 'D', 'k': 'D', 'cost': 28}, {'i': 'K', 'j': 'D', 'k': 'E', 'cost': 18}, {'i': 'K', 'j': 'D', 'k': 'F', 'cost': 82}, {'i': 'K', 'j': 'D', 'k': 'G', 'cost': 9}, {'i': 'K', 'j': 'D', 'k': 'H', 'cost': 76}, {'i': 'K', 'j': 'D', 'k': 'I', 'cost': 84}, {'i': 'K', 'j': 'D', 'k': 'J', 'cost': 77}, {'i': 'K', 'j': 'D', 'k': 'K', 'cost': 89}, {'i': 'K', 'j': 'E', 'k': 'A', 'cost': 58}, {'i': 'K', 'j': 'E', 'k': 'B', 'cost': 96}, {'i': 'K', 'j': 'E', 'k': 'C', 'cost': 89}, {'i': 'K', 'j': 'E', 'k': 'D', 'cost': 79}, {'i': 'K', 'j': 'E', 'k': 'E', 'cost': 0}, {'i': 'K', 'j': 'E', 'k': 'F', 'cost': 2}, {'i': 'K', 'j': 'E', 'k': 'G', 'cost': 92}, {'i': 'K', 'j': 'E', 'k': 'H', 'cost': 78}, {'i': 'K', 'j': 'E', 'k': 'I', 'cost': 70}, {'i': 'K', 'j': 'E', 'k': 'J', 'cost': 1}, {'i': 'K', 'j': 'E', 'k': 'K', 'cost': 57}, {'i': 'K', 'j': 'F', 'k': 'A', 'cost': 80}, {'i': 'K', 'j': 'F', 'k': 'B', 'cost': 31}, {'i': 'K', 'j': 'F', 'k': 'C', 'cost': 58}, {'i': 'K', 'j': 'F', 'k': 'D', 'cost': 66}, {'i': 'K', 'j': 'F', 'k': 'E', 'cost': 85}, {'i': 'K', 'j': 'F', 'k': 'F', 'cost': 41}, {'i': 'K', 'j': 'F', 'k': 'G', 'cost': 30}, {'i': 'K', 'j': 'F', 'k': 'H', 'cost': 24}, {'i': 'K', 'j': 'F', 'k': 'I', 'cost': 11}, {'i': 'K', 'j': 'F', 'k': 'J', 'cost': 74}, {'i': 'K', 'j': 'F', 'k': 'K', 'cost': 28}, {'i': 'K', 'j': 'G', 'k': 'A', 'cost': 12}, {'i': 'K', 'j': 'G', 'k': 'B', 'cost': 31}, {'i': 'K', 'j': 'G', 'k': 'C', 'cost': 93}, {'i': 'K', 'j': 'G', 'k': 'D', 'cost': 92}, {'i': 'K', 'j': 'G', 'k': 'E', 'cost': 68}, {'i': 'K', 'j': 'G', 'k': 'F', 'cost': 42}, {'i': 'K', 'j': 'G', 'k': 'G', 'cost': 38}, {'i': 'K', 'j': 'G', 'k': 'H', 'cost': 42}, {'i': 'K', 'j': 'G', 'k': 'I', 'cost': 50}, {'i': 'K', 'j': 'G', 'k': 'J', 'cost': 83}, {'i': 'K', 'j': 'G', 'k': 'K', 'cost': 0}, {'i': 'K', 'j': 'H', 'k': 'A', 'cost': 53}, {'i': 'K', 'j': 'H', 'k': 'B', 'cost': 63}, {'i': 'K', 'j': 'H', 'k': 'C', 'cost': 67}, {'i': 'K', 'j': 'H', 'k': 'D', 'cost': 9}, {'i': 'K', 'j': 'H', 'k': 'E', 'cost': 32}, {'i': 'K', 'j': 'H', 'k': 'F', 'cost': 52}, {'i': 'K', 'j': 'H', 'k': 'G', 'cost': 81}, {'i': 'K', 'j': 'H', 'k': 'H', 'cost': 2}, {'i': 'K', 'j': 'H', 'k': 'I', 'cost': 77}, {'i': 'K', 'j': 'H', 'k': 'J', 'cost': 97}, {'i': 'K', 'j': 'H', 'k': 'K', 'cost': 28}, {'i': 'K', 'j': 'I', 'k': 'A', 'cost': 19}, {'i': 'K', 'j': 'I', 'k': 'B', 'cost': 60}, {'i': 'K', 'j': 'I', 'k': 'C', 'cost': 56}, {'i': 'K', 'j': 'I', 'k': 'D', 'cost': 2}, {'i': 'K', 'j': 'I', 'k': 'E', 'cost': 87}, {'i': 'K', 'j': 'I', 'k': 'F', 'cost': 6}, {'i': 'K', 'j': 'I', 'k': 'G', 'cost': 9}, {'i': 'K', 'j': 'I', 'k': 'H', 'cost': 4}, {'i': 'K', 'j': 'I', 'k': 'I', 'cost': 66}, {'i': 'K', 'j': 'I', 'k': 'J', 'cost': 7}, {'i': 'K', 'j': 'I', 'k': 'K', 'cost': 61}, {'i': 'K', 'j': 'J', 'k': 'A', 'cost': 90}, {'i': 'K', 'j': 'J', 'k': 'B', 'cost': 36}, {'i': 'K', 'j': 'J', 'k': 'C', 'cost': 18}, {'i': 'K', 'j': 'J', 'k': 'D', 'cost': 49}, {'i': 'K', 'j': 'J', 'k': 'E', 'cost': 60}, {'i': 'K', 'j': 'J', 'k': 'F', 'cost': 58}, {'i': 'K', 'j': 'J', 'k': 'G', 'cost': 87}, {'i': 'K', 'j': 'J', 'k': 'H', 'cost': 20}, {'i': 'K', 'j': 'J', 'k': 'I', 'cost': 78}, {'i': 'K', 'j': 'J', 'k': 'J', 'cost': 12}, {'i': 'K', 'j': 'J', 'k': 'K', 'cost': 30}, {'i': 'K', 'j': 'K', 'k': 'A', 'cost': 94}, {'i': 'K', 'j': 'K', 'k': 'B', 'cost': 89}, {'i': 'K', 'j': 'K', 'k': 'C', 'cost': 54}, {'i': 'K', 'j': 'K', 'k': 'D', 'cost': 22}, {'i': 'K', 'j': 'K', 'k': 'E', 'cost': 98}, {'i': 'K', 'j': 'K', 'k': 'F', 'cost': 82}, {'i': 'K', 'j': 'K', 'k': 'G', 'cost': 33}, {'i': 'K', 'j': 'K', 'k': 'H', 'cost': 42}, {'i': 'K', 'j': 'K', 'k': 'I', 'cost': 10}, {'i': 'K', 'j': 'K', 'k': 'J', 'cost': 69}, {'i': 'K', 'j': 'K', 'k': 'K', 'cost': 9}]}","[['A', 'K', 'I'], ['B', 'J', 'D'], ['C', 'G', 'J'], ['D', 'I', 'C'], ['E', 'B', 'A'], ['F', 'C', 'H'], ['G', 'A', 'G'], ['H', 'F', 'B'], ['I', 'D', 'K'], ['J', 'H', 'F'], ['K', 'E', 'E']]",26,csv,names
+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.
+
+{
+  ""num_scenes"": 9,
+  ""index_identifiers"": [
+    0,
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8
+  ]
+}
+
+# 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 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 39 | 95 | 27 | 30 | 0 | 24 | 5 | 36 | 11 |
+| 1 | 93 | 22 | 4 | 21 | 5 | 51 | 60 | 8 | 15 |
+| 2 | 17 | 94 | 53 | 96 | 70 | 33 | 48 | 10 | 62 |
+| 3 | 90 | 95 | 31 | 75 | 87 | 52 | 13 | 19 | 73 |
+| 4 | 29 | 62 | 0 | 84 | 41 | 1 | 57 | 60 | 52 |
+| 5 | 25 | 15 | 75 | 51 | 71 | 9 | 9 | 91 | 92 |
+| 6 | 67 | 5 | 34 | 70 | 91 | 10 | 80 | 1 | 13 |
+| 7 | 84 | 26 | 49 | 41 | 79 | 70 | 97 | 18 | 32 |
+| 8 | 26 | 88 | 18 | 64 | 93 | 93 | 7 | 97 | 14 |
+
+## scene_id=1
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 72 | 46 | 46 | 25 | 2 | 72 | 37 | 68 | 12 |
+| 1 | 63 | 25 | 16 | 32 | 31 | 83 | 50 | 56 | 40 |
+| 2 | 36 | 64 | 13 | 76 | 69 | 4 | 65 | 9 | 49 |
+| 3 | 89 | 62 | 46 | 95 | 87 | 64 | 13 | 33 | 99 |
+| 4 | 18 | 80 | 33 | 45 | 18 | 51 | 23 | 93 | 84 |
+| 5 | 40 | 96 | 89 | 82 | 84 | 37 | 18 | 65 | 75 |
+| 6 | 69 | 88 | 58 | 11 | 70 | 48 | 23 | 95 | 43 |
+| 7 | 17 | 42 | 31 | 62 | 64 | 64 | 99 | 13 | 34 |
+| 8 | 85 | 29 | 84 | 32 | 50 | 43 | 32 | 41 | 36 |
+
+## scene_id=2
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 46 | 66 | 53 | 50 | 14 | 96 | 68 | 1 | 4 |
+| 1 | 25 | 40 | 25 | 60 | 87 | 61 | 78 | 67 | 72 |
+| 2 | 55 | 31 | 8 | 87 | 29 | 25 | 88 | 33 | 17 |
+| 3 | 69 | 17 | 57 | 14 | 63 | 36 | 65 | 13 | 49 |
+| 4 | 74 | 70 | 19 | 56 | 0 | 73 | 52 | 91 | 55 |
+| 5 | 60 | 59 | 68 | 97 | 24 | 58 | 19 | 68 | 70 |
+| 6 | 83 | 12 | 24 | 7 | 80 | 10 | 40 | 51 | 89 |
+| 7 | 79 | 16 | 66 | 64 | 18 | 71 | 61 | 93 | 28 |
+| 8 | 30 | 68 | 59 | 20 | 25 | 62 | 33 | 6 | 70 |
+
+## scene_id=3
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 57 | 74 | 60 | 60 | 44 | 30 | 50 | 6 | 10 |
+| 1 | 8 | 45 | 29 | 62 | 82 | 6 | 83 | 95 | 70 |
+| 2 | 77 | 54 | 67 | 30 | 42 | 87 | 76 | 40 | 79 |
+| 3 | 68 | 90 | 75 | 87 | 85 | 11 | 36 | 50 | 68 |
+| 4 | 39 | 84 | 12 | 90 | 44 | 71 | 81 | 29 | 90 |
+| 5 | 1 | 91 | 4 | 63 | 2 | 48 | 96 | 29 | 33 |
+| 6 | 19 | 4 | 38 | 22 | 20 | 15 | 25 | 92 | 90 |
+| 7 | 95 | 18 | 87 | 26 | 88 | 1 | 92 | 74 | 28 |
+| 8 | 86 | 13 | 79 | 89 | 82 | 78 | 17 | 85 | 31 |
+
+## scene_id=4
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 57 | 43 | 18 | 27 | 63 | 31 | 51 | 78 | 17 |
+| 1 | 67 | 86 | 73 | 55 | 13 | 19 | 11 | 94 | 98 |
+| 2 | 64 | 31 | 14 | 61 | 68 | 56 | 34 | 16 | 43 |
+| 3 | 62 | 63 | 5 | 59 | 21 | 69 | 37 | 46 | 40 |
+| 4 | 23 | 86 | 19 | 3 | 84 | 85 | 26 | 18 | 39 |
+| 5 | 56 | 75 | 93 | 60 | 8 | 79 | 50 | 19 | 82 |
+| 6 | 43 | 4 | 15 | 76 | 0 | 27 | 77 | 62 | 82 |
+| 7 | 74 | 92 | 94 | 75 | 8 | 16 | 42 | 19 | 36 |
+| 8 | 42 | 53 | 6 | 18 | 8 | 81 | 60 | 5 | 99 |
+
+## scene_id=5
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 12 | 55 | 19 | 71 | 95 | 3 | 6 | 39 | 39 |
+| 1 | 36 | 45 | 88 | 27 | 64 | 52 | 2 | 51 | 57 |
+| 2 | 9 | 33 | 76 | 94 | 71 | 19 | 65 | 83 | 20 |
+| 3 | 50 | 18 | 60 | 84 | 18 | 34 | 91 | 72 | 88 |
+| 4 | 42 | 34 | 85 | 44 | 93 | 26 | 62 | 90 | 52 |
+| 5 | 55 | 46 | 93 | 74 | 10 | 34 | 66 | 94 | 18 |
+| 6 | 79 | 85 | 6 | 86 | 83 | 84 | 10 | 87 | 16 |
+| 7 | 61 | 72 | 10 | 98 | 97 | 10 | 56 | 23 | 60 |
+| 8 | 45 | 69 | 75 | 97 | 51 | 13 | 66 | 49 | 9 |
+
+## scene_id=6
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 73 | 3 | 1 | 91 | 3 | 46 | 79 | 68 | 45 |
+| 1 | 58 | 97 | 97 | 40 | 75 | 94 | 95 | 60 | 34 |
+| 2 | 29 | 17 | 56 | 58 | 54 | 90 | 88 | 26 | 21 |
+| 3 | 24 | 8 | 33 | 84 | 39 | 3 | 52 | 74 | 5 |
+| 4 | 64 | 85 | 55 | 92 | 45 | 53 | 80 | 7 | 46 |
+| 5 | 81 | 79 | 78 | 16 | 35 | 99 | 74 | 63 | 20 |
+| 6 | 9 | 3 | 47 | 48 | 92 | 25 | 89 | 65 | 20 |
+| 7 | 14 | 56 | 77 | 47 | 13 | 92 | 30 | 83 | 20 |
+| 8 | 22 | 88 | 97 | 87 | 91 | 47 | 92 | 21 | 9 |
+
+## scene_id=7
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 9 | 0 | 87 | 35 | 65 | 73 | 83 | 17 | 7 |
+| 1 | 58 | 27 | 96 | 91 | 81 | 21 | 44 | 14 | 8 |
+| 2 | 14 | 47 | 32 | 7 | 34 | 96 | 59 | 16 | 76 |
+| 3 | 24 | 88 | 92 | 58 | 70 | 50 | 34 | 52 | 32 |
+| 4 | 56 | 10 | 37 | 40 | 34 | 71 | 42 | 16 | 88 |
+| 5 | 59 | 29 | 44 | 18 | 24 | 64 | 27 | 2 | 12 |
+| 6 | 34 | 81 | 80 | 39 | 24 | 38 | 4 | 90 | 13 |
+| 7 | 92 | 46 | 22 | 5 | 46 | 41 | 18 | 88 | 51 |
+| 8 | 32 | 63 | 62 | 93 | 23 | 53 | 75 | 2 | 6 |
+
+## scene_id=8
+| actor_id\costume_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 4 | 49 | 58 | 86 | 49 | 35 | 33 | 57 | 50 |
+| 1 | 51 | 59 | 98 | 14 | 62 | 33 | 58 | 13 | 28 |
+| 2 | 67 | 80 | 33 | 66 | 63 | 17 | 2 | 93 | 99 |
+| 3 | 26 | 51 | 99 | 65 | 47 | 68 | 57 | 9 | 95 |
+| 4 | 69 | 66 | 71 | 13 | 11 | 61 | 62 | 15 | 96 |
+| 5 | 79 | 52 | 51 | 66 | 85 | 54 | 48 | 98 | 78 |
+| 6 | 79 | 70 | 20 | 97 | 77 | 72 | 47 | 46 | 37 |
+| 7 | 60 | 35 | 55 | 11 | 16 | 69 | 30 | 11 | 3 |
+| 8 | 5 | 20 | 46 | 69 | 58 | 77 | 39 | 97 | 31 |
+
+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': [[[39, 95, 27, 30, 0, 24, 5, 36, 11], [93, 22, 4, 21, 5, 51, 60, 8, 15], [17, 94, 53, 96, 70, 33, 48, 10, 62], [90, 95, 31, 75, 87, 52, 13, 19, 73], [29, 62, 0, 84, 41, 1, 57, 60, 52], [25, 15, 75, 51, 71, 9, 9, 91, 92], [67, 5, 34, 70, 91, 10, 80, 1, 13], [84, 26, 49, 41, 79, 70, 97, 18, 32], [26, 88, 18, 64, 93, 93, 7, 97, 14]], [[72, 46, 46, 25, 2, 72, 37, 68, 12], [63, 25, 16, 32, 31, 83, 50, 56, 40], [36, 64, 13, 76, 69, 4, 65, 9, 49], [89, 62, 46, 95, 87, 64, 13, 33, 99], [18, 80, 33, 45, 18, 51, 23, 93, 84], [40, 96, 89, 82, 84, 37, 18, 65, 75], [69, 88, 58, 11, 70, 48, 23, 95, 43], [17, 42, 31, 62, 64, 64, 99, 13, 34], [85, 29, 84, 32, 50, 43, 32, 41, 36]], [[46, 66, 53, 50, 14, 96, 68, 1, 4], [25, 40, 25, 60, 87, 61, 78, 67, 72], [55, 31, 8, 87, 29, 25, 88, 33, 17], [69, 17, 57, 14, 63, 36, 65, 13, 49], [74, 70, 19, 56, 0, 73, 52, 91, 55], [60, 59, 68, 97, 24, 58, 19, 68, 70], [83, 12, 24, 7, 80, 10, 40, 51, 89], [79, 16, 66, 64, 18, 71, 61, 93, 28], [30, 68, 59, 20, 25, 62, 33, 6, 70]], [[57, 74, 60, 60, 44, 30, 50, 6, 10], [8, 45, 29, 62, 82, 6, 83, 95, 70], [77, 54, 67, 30, 42, 87, 76, 40, 79], [68, 90, 75, 87, 85, 11, 36, 50, 68], [39, 84, 12, 90, 44, 71, 81, 29, 90], [1, 91, 4, 63, 2, 48, 96, 29, 33], [19, 4, 38, 22, 20, 15, 25, 92, 90], [95, 18, 87, 26, 88, 1, 92, 74, 28], [86, 13, 79, 89, 82, 78, 17, 85, 31]], [[57, 43, 18, 27, 63, 31, 51, 78, 17], [67, 86, 73, 55, 13, 19, 11, 94, 98], [64, 31, 14, 61, 68, 56, 34, 16, 43], [62, 63, 5, 59, 21, 69, 37, 46, 40], [23, 86, 19, 3, 84, 85, 26, 18, 39], [56, 75, 93, 60, 8, 79, 50, 19, 82], [43, 4, 15, 76, 0, 27, 77, 62, 82], [74, 92, 94, 75, 8, 16, 42, 19, 36], [42, 53, 6, 18, 8, 81, 60, 5, 99]], [[12, 55, 19, 71, 95, 3, 6, 39, 39], [36, 45, 88, 27, 64, 52, 2, 51, 57], [9, 33, 76, 94, 71, 19, 65, 83, 20], [50, 18, 60, 84, 18, 34, 91, 72, 88], [42, 34, 85, 44, 93, 26, 62, 90, 52], [55, 46, 93, 74, 10, 34, 66, 94, 18], [79, 85, 6, 86, 83, 84, 10, 87, 16], [61, 72, 10, 98, 97, 10, 56, 23, 60], [45, 69, 75, 97, 51, 13, 66, 49, 9]], [[73, 3, 1, 91, 3, 46, 79, 68, 45], [58, 97, 97, 40, 75, 94, 95, 60, 34], [29, 17, 56, 58, 54, 90, 88, 26, 21], [24, 8, 33, 84, 39, 3, 52, 74, 5], [64, 85, 55, 92, 45, 53, 80, 7, 46], [81, 79, 78, 16, 35, 99, 74, 63, 20], [9, 3, 47, 48, 92, 25, 89, 65, 20], [14, 56, 77, 47, 13, 92, 30, 83, 20], [22, 88, 97, 87, 91, 47, 92, 21, 9]], [[9, 0, 87, 35, 65, 73, 83, 17, 7], [58, 27, 96, 91, 81, 21, 44, 14, 8], [14, 47, 32, 7, 34, 96, 59, 16, 76], [24, 88, 92, 58, 70, 50, 34, 52, 32], [56, 10, 37, 40, 34, 71, 42, 16, 88], [59, 29, 44, 18, 24, 64, 27, 2, 12], [34, 81, 80, 39, 24, 38, 4, 90, 13], [92, 46, 22, 5, 46, 41, 18, 88, 51], [32, 63, 62, 93, 23, 53, 75, 2, 6]], [[4, 49, 58, 86, 49, 35, 33, 57, 50], [51, 59, 98, 14, 62, 33, 58, 13, 28], [67, 80, 33, 66, 63, 17, 2, 93, 99], [26, 51, 99, 65, 47, 68, 57, 9, 95], [69, 66, 71, 13, 11, 61, 62, 15, 96], [79, 52, 51, 66, 85, 54, 48, 98, 78], [79, 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{'i': 7, 'j': 6, 'k': 3, 'cost': 39}, {'i': 7, 'j': 6, 'k': 4, 'cost': 24}, {'i': 7, 'j': 6, 'k': 5, 'cost': 38}, {'i': 7, 'j': 6, 'k': 6, 'cost': 4}, {'i': 7, 'j': 6, 'k': 7, 'cost': 90}, {'i': 7, 'j': 6, 'k': 8, 'cost': 13}, {'i': 7, 'j': 7, 'k': 0, 'cost': 92}, {'i': 7, 'j': 7, 'k': 1, 'cost': 46}, {'i': 7, 'j': 7, 'k': 2, 'cost': 22}, {'i': 7, 'j': 7, 'k': 3, 'cost': 5}, {'i': 7, 'j': 7, 'k': 4, 'cost': 46}, {'i': 7, 'j': 7, 'k': 5, 'cost': 41}, {'i': 7, 'j': 7, 'k': 6, 'cost': 18}, {'i': 7, 'j': 7, 'k': 7, 'cost': 88}, {'i': 7, 'j': 7, 'k': 8, 'cost': 51}, {'i': 7, 'j': 8, 'k': 0, 'cost': 32}, {'i': 7, 'j': 8, 'k': 1, 'cost': 63}, {'i': 7, 'j': 8, 'k': 2, 'cost': 62}, {'i': 7, 'j': 8, 'k': 3, 'cost': 93}, {'i': 7, 'j': 8, 'k': 4, 'cost': 23}, {'i': 7, 'j': 8, 'k': 5, 'cost': 53}, {'i': 7, 'j': 8, 'k': 6, 'cost': 75}, {'i': 7, 'j': 8, 'k': 7, 'cost': 2}, {'i': 7, 'j': 8, 'k': 8, 'cost': 6}, {'i': 8, 'j': 0, 'k': 0, 'cost': 4}, {'i': 8, 'j': 0, 'k': 1, 'cost': 49}, {'i': 8, 'j': 0, 'k': 2, 'cost': 58}, {'i': 8, 'j': 0, 'k': 3, 'cost': 86}, {'i': 8, 'j': 0, 'k': 4, 'cost': 49}, {'i': 8, 'j': 0, 'k': 5, 'cost': 35}, {'i': 8, 'j': 0, 'k': 6, 'cost': 33}, {'i': 8, 'j': 0, 'k': 7, 'cost': 57}, {'i': 8, 'j': 0, 'k': 8, 'cost': 50}, {'i': 8, 'j': 1, 'k': 0, 'cost': 51}, {'i': 8, 'j': 1, 'k': 1, 'cost': 59}, {'i': 8, 'j': 1, 'k': 2, 'cost': 98}, {'i': 8, 'j': 1, 'k': 3, 'cost': 14}, {'i': 8, 'j': 1, 'k': 4, 'cost': 62}, {'i': 8, 'j': 1, 'k': 5, 'cost': 33}, {'i': 8, 'j': 1, 'k': 6, 'cost': 58}, {'i': 8, 'j': 1, 'k': 7, 'cost': 13}, {'i': 8, 'j': 1, 'k': 8, 'cost': 28}, {'i': 8, 'j': 2, 'k': 0, 'cost': 67}, {'i': 8, 'j': 2, 'k': 1, 'cost': 80}, {'i': 8, 'j': 2, 'k': 2, 'cost': 33}, {'i': 8, 'j': 2, 'k': 3, 'cost': 66}, {'i': 8, 'j': 2, 'k': 4, 'cost': 63}, {'i': 8, 'j': 2, 'k': 5, 'cost': 17}, {'i': 8, 'j': 2, 'k': 6, 'cost': 2}, {'i': 8, 'j': 2, 'k': 7, 'cost': 93}, {'i': 8, 'j': 2, 'k': 8, 'cost': 99}, {'i': 8, 'j': 3, 'k': 0, 'cost': 26}, {'i': 8, 'j': 3, 'k': 1, 'cost': 51}, {'i': 8, 'j': 3, 'k': 2, 'cost': 99}, {'i': 8, 'j': 3, 'k': 3, 'cost': 65}, {'i': 8, 'j': 3, 'k': 4, 'cost': 47}, {'i': 8, 'j': 3, 'k': 5, 'cost': 68}, {'i': 8, 'j': 3, 'k': 6, 'cost': 57}, {'i': 8, 'j': 3, 'k': 7, 'cost': 9}, {'i': 8, 'j': 3, 'k': 8, 'cost': 95}, {'i': 8, 'j': 4, 'k': 0, 'cost': 69}, {'i': 8, 'j': 4, 'k': 1, 'cost': 66}, {'i': 8, 'j': 4, 'k': 2, 'cost': 71}, {'i': 8, 'j': 4, 'k': 3, 'cost': 13}, {'i': 8, 'j': 4, 'k': 4, 'cost': 11}, {'i': 8, 'j': 4, 'k': 5, 'cost': 61}, {'i': 8, 'j': 4, 'k': 6, 'cost': 62}, {'i': 8, 'j': 4, 'k': 7, 'cost': 15}, {'i': 8, 'j': 4, 'k': 8, 'cost': 96}, {'i': 8, 'j': 5, 'k': 0, 'cost': 79}, {'i': 8, 'j': 5, 'k': 1, 'cost': 52}, {'i': 8, 'j': 5, 'k': 2, 'cost': 51}, {'i': 8, 'j': 5, 'k': 3, 'cost': 66}, {'i': 8, 'j': 5, 'k': 4, 'cost': 85}, {'i': 8, 'j': 5, 'k': 5, 'cost': 54}, {'i': 8, 'j': 5, 'k': 6, 'cost': 48}, {'i': 8, 'j': 5, 'k': 7, 'cost': 98}, {'i': 8, 'j': 5, 'k': 8, 'cost': 78}, {'i': 8, 'j': 6, 'k': 0, 'cost': 79}, {'i': 8, 'j': 6, 'k': 1, 'cost': 70}, {'i': 8, 'j': 6, 'k': 2, 'cost': 20}, {'i': 8, 'j': 6, 'k': 3, 'cost': 97}, {'i': 8, 'j': 6, 'k': 4, 'cost': 77}, {'i': 8, 'j': 6, 'k': 5, 'cost': 72}, {'i': 8, 'j': 6, 'k': 6, 'cost': 47}, {'i': 8, 'j': 6, 'k': 7, 'cost': 46}, {'i': 8, 'j': 6, 'k': 8, 'cost': 37}, {'i': 8, 'j': 7, 'k': 0, 'cost': 60}, {'i': 8, 'j': 7, 'k': 1, 'cost': 35}, {'i': 8, 'j': 7, 'k': 2, 'cost': 55}, {'i': 8, 'j': 7, 'k': 3, 'cost': 11}, {'i': 8, 'j': 7, 'k': 4, 'cost': 16}, {'i': 8, 'j': 7, 'k': 5, 'cost': 69}, {'i': 8, 'j': 7, 'k': 6, 'cost': 30}, {'i': 8, 'j': 7, 'k': 7, 'cost': 11}, {'i': 8, 'j': 7, 'k': 8, 'cost': 3}, {'i': 8, 'j': 8, 'k': 0, 'cost': 5}, {'i': 8, 'j': 8, 'k': 1, 'cost': 20}, {'i': 8, 'j': 8, 'k': 2, 'cost': 46}, {'i': 8, 'j': 8, 'k': 3, 'cost': 69}, {'i': 8, 'j': 8, 'k': 4, 'cost': 58}, {'i': 8, 'j': 8, 'k': 5, 'cost': 77}, {'i': 8, 'j': 8, 'k': 6, 'cost': 39}, {'i': 8, 'j': 8, 'k': 7, 'cost': 97}, {'i': 8, 'j': 8, 'k': 8, 'cost': 31}]}","[[0, 4, 2], [1, 2, 5], [2, 0, 7], [3, 5, 4], [4, 6, 1], [5, 1, 6], [6, 3, 8], [7, 7, 3], [8, 8, 0]]",27,json,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.
+
+There are 11 of each, labeled 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
+
+*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=0
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 46 | 52 | 74 | 88 | 56 | 48 | 22 | 91 | 15 | 30 | 1 |
+| 1 | 69 | 13 | 17 | 86 | 86 | 60 | 44 | 37 | 38 | 0 | 86 |
+| 2 | 22 | 49 | 45 | 21 | 45 | 78 | 89 | 88 | 89 | 53 | 59 |
+| 3 | 8 | 41 | 45 | 72 | 50 | 71 | 83 | 55 | 72 | 10 | 22 |
+| 4 | 38 | 20 | 63 | 20 | 85 | 63 | 91 | 59 | 69 | 91 | 54 |
+| 5 | 35 | 45 | 45 | 29 | 31 | 78 | 85 | 43 | 19 | 7 | 71 |
+| 6 | 28 | 35 | 86 | 56 | 45 | 56 | 86 | 60 | 21 | 78 | 9 |
+| 7 | 66 | 45 | 31 | 98 | 91 | 49 | 69 | 21 | 26 | 33 | 81 |
+| 8 | 7 | 26 | 24 | 98 | 7 | 82 | 98 | 95 | 14 | 28 | 74 |
+| 9 | 72 | 38 | 24 | 44 | 84 | 68 | 38 | 66 | 17 | 12 | 17 |
+| 10 | 32 | 22 | 89 | 29 | 68 | 21 | 46 | 37 | 59 | 12 | 45 |
+
+## client_id=1
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 76 | 39 | 18 | 49 | 98 | 55 | 72 | 85 | 63 | 10 | 23 |
+| 1 | 28 | 51 | 3 | 21 | 30 | 47 | 83 | 28 | 69 | 8 | 94 |
+| 2 | 82 | 82 | 47 | 22 | 83 | 73 | 20 | 87 | 20 | 34 | 15 |
+| 3 | 50 | 91 | 43 | 26 | 90 | 95 | 12 | 7 | 63 | 92 | 56 |
+| 4 | 18 | 48 | 46 | 46 | 97 | 35 | 79 | 89 | 19 | 58 | 64 |
+| 5 | 53 | 26 | 92 | 57 | 72 | 18 | 53 | 95 | 40 | 19 | 25 |
+| 6 | 19 | 65 | 74 | 13 | 81 | 19 | 66 | 76 | 66 | 52 | 32 |
+| 7 | 82 | 27 | 42 | 35 | 20 | 83 | 16 | 27 | 68 | 73 | 67 |
+| 8 | 24 | 61 | 92 | 88 | 89 | 14 | 68 | 84 | 22 | 52 | 45 |
+| 9 | 91 | 23 | 55 | 68 | 13 | 13 | 37 | 37 | 38 | 4 | 79 |
+| 10 | 3 | 54 | 85 | 27 | 84 | 30 | 17 | 89 | 73 | 33 | 10 |
+
+## client_id=2
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 47 | 7 | 93 | 6 | 24 | 63 | 15 | 82 | 57 | 95 | 72 |
+| 1 | 43 | 98 | 92 | 14 | 10 | 62 | 67 | 98 | 71 | 22 | 61 |
+| 2 | 82 | 49 | 44 | 45 | 22 | 0 | 22 | 20 | 3 | 14 | 7 |
+| 3 | 0 | 85 | 28 | 79 | 65 | 47 | 33 | 54 | 80 | 88 | 62 |
+| 4 | 60 | 97 | 79 | 32 | 8 | 17 | 57 | 87 | 81 | 48 | 92 |
+| 5 | 59 | 93 | 39 | 61 | 61 | 63 | 62 | 47 | 54 | 26 | 50 |
+| 6 | 0 | 82 | 55 | 7 | 48 | 57 | 61 | 15 | 33 | 78 | 17 |
+| 7 | 75 | 30 | 87 | 40 | 82 | 30 | 65 | 92 | 43 | 95 | 39 |
+| 8 | 23 | 99 | 29 | 32 | 36 | 48 | 94 | 90 | 17 | 42 | 91 |
+| 9 | 27 | 1 | 43 | 83 | 14 | 69 | 30 | 29 | 83 | 60 | 22 |
+| 10 | 30 | 44 | 79 | 8 | 1 | 6 | 33 | 49 | 84 | 16 | 34 |
+
+## client_id=3
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 42 | 24 | 30 | 33 | 69 | 7 | 67 | 81 | 0 | 92 | 31 |
+| 1 | 10 | 71 | 6 | 86 | 47 | 95 | 63 | 54 | 74 | 90 | 7 |
+| 2 | 4 | 51 | 6 | 83 | 40 | 77 | 86 | 62 | 61 | 51 | 68 |
+| 3 | 35 | 28 | 31 | 10 | 16 | 14 | 67 | 34 | 98 | 66 | 66 |
+| 4 | 21 | 89 | 75 | 22 | 93 | 53 | 37 | 82 | 2 | 87 | 74 |
+| 5 | 16 | 90 | 6 | 28 | 69 | 92 | 2 | 80 | 38 | 8 | 76 |
+| 6 | 81 | 63 | 84 | 58 | 7 | 35 | 60 | 46 | 11 | 62 | 12 |
+| 7 | 39 | 8 | 80 | 39 | 66 | 32 | 15 | 80 | 38 | 45 | 27 |
+| 8 | 78 | 66 | 81 | 48 | 97 | 62 | 9 | 57 | 70 | 10 | 13 |
+| 9 | 41 | 52 | 69 | 59 | 54 | 4 | 62 | 53 | 24 | 9 | 29 |
+| 10 | 69 | 56 | 88 | 13 | 39 | 41 | 55 | 39 | 93 | 54 | 37 |
+
+## client_id=4
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 9 | 84 | 29 | 20 | 56 | 70 | 61 | 89 | 93 | 58 | 71 |
+| 1 | 10 | 1 | 54 | 67 | 46 | 27 | 15 | 0 | 46 | 64 | 23 |
+| 2 | 88 | 21 | 84 | 59 | 94 | 90 | 72 | 98 | 34 | 36 | 74 |
+| 3 | 46 | 30 | 77 | 1 | 23 | 3 | 31 | 41 | 47 | 54 | 34 |
+| 4 | 61 | 33 | 7 | 71 | 1 | 15 | 92 | 10 | 42 | 4 | 42 |
+| 5 | 69 | 4 | 68 | 18 | 49 | 60 | 36 | 25 | 48 | 31 | 60 |
+| 6 | 15 | 68 | 34 | 21 | 57 | 76 | 25 | 75 | 50 | 66 | 73 |
+| 7 | 86 | 46 | 7 | 63 | 81 | 28 | 92 | 14 | 36 | 92 | 73 |
+| 8 | 87 | 84 | 94 | 25 | 25 | 24 | 37 | 5 | 96 | 83 | 28 |
+| 9 | 22 | 97 | 92 | 4 | 7 | 35 | 86 | 63 | 82 | 35 | 70 |
+| 10 | 89 | 10 | 6 | 27 | 45 | 51 | 53 | 3 | 61 | 24 | 42 |
+
+## client_id=5
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 34 | 89 | 81 | 66 | 71 | 38 | 17 | 85 | 13 | 42 | 97 |
+| 1 | 19 | 12 | 61 | 0 | 31 | 59 | 97 | 88 | 68 | 91 | 18 |
+| 2 | 97 | 39 | 2 | 78 | 18 | 62 | 11 | 28 | 23 | 75 | 57 |
+| 3 | 5 | 81 | 31 | 7 | 51 | 26 | 15 | 88 | 1 | 23 | 99 |
+| 4 | 57 | 55 | 14 | 81 | 16 | 34 | 29 | 59 | 32 | 92 | 57 |
+| 5 | 36 | 1 | 54 | 88 | 14 | 15 | 91 | 1 | 49 | 24 | 47 |
+| 6 | 43 | 81 | 82 | 20 | 33 | 5 | 56 | 75 | 58 | 42 | 0 |
+| 7 | 52 | 81 | 6 | 36 | 13 | 91 | 39 | 98 | 79 | 77 | 48 |
+| 8 | 80 | 16 | 44 | 17 | 69 | 38 | 97 | 62 | 90 | 50 | 11 |
+| 9 | 34 | 85 | 8 | 13 | 83 | 31 | 35 | 61 | 2 | 76 | 70 |
+| 10 | 85 | 4 | 11 | 39 | 84 | 86 | 64 | 87 | 81 | 93 | 88 |
+
+## client_id=6
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 89 | 9 | 34 | 80 | 79 | 70 | 82 | 42 | 37 | 5 | 8 |
+| 1 | 66 | 52 | 81 | 2 | 49 | 0 | 36 | 74 | 95 | 93 | 53 |
+| 2 | 21 | 10 | 20 | 46 | 68 | 12 | 28 | 19 | 65 | 17 | 94 |
+| 3 | 53 | 40 | 78 | 81 | 65 | 57 | 3 | 57 | 83 | 83 | 24 |
+| 4 | 8 | 29 | 35 | 52 | 80 | 77 | 22 | 37 | 75 | 57 | 28 |
+| 5 | 21 | 58 | 44 | 76 | 41 | 62 | 73 | 98 | 19 | 74 | 65 |
+| 6 | 3 | 33 | 84 | 8 | 56 | 23 | 85 | 9 | 80 | 8 | 7 |
+| 7 | 20 | 19 | 74 | 54 | 96 | 6 | 44 | 22 | 33 | 7 | 45 |
+| 8 | 85 | 35 | 99 | 51 | 78 | 29 | 50 | 6 | 12 | 53 | 91 |
+| 9 | 5 | 84 | 7 | 9 | 51 | 73 | 12 | 20 | 88 | 93 | 53 |
+| 10 | 95 | 60 | 80 | 19 | 0 | 33 | 86 | 28 | 24 | 6 | 11 |
+
+## client_id=7
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 56 | 98 | 73 | 30 | 73 | 47 | 89 | 95 | 25 | 83 | 5 |
+| 1 | 87 | 64 | 69 | 42 | 21 | 24 | 56 | 45 | 82 | 47 | 35 |
+| 2 | 66 | 85 | 25 | 14 | 88 | 84 | 99 | 89 | 10 | 77 | 69 |
+| 3 | 80 | 77 | 64 | 89 | 81 | 88 | 98 | 20 | 80 | 46 | 37 |
+| 4 | 50 | 62 | 56 | 94 | 28 | 46 | 38 | 83 | 63 | 60 | 98 |
+| 5 | 18 | 98 | 9 | 26 | 66 | 39 | 15 | 51 | 10 | 0 | 94 |
+| 6 | 71 | 84 | 56 | 50 | 48 | 10 | 5 | 90 | 6 | 56 | 13 |
+| 7 | 86 | 59 | 93 | 60 | 37 | 76 | 88 | 79 | 70 | 92 | 59 |
+| 8 | 5 | 45 | 24 | 51 | 43 | 50 | 48 | 92 | 65 | 60 | 21 |
+| 9 | 6 | 6 | 70 | 81 | 82 | 92 | 90 | 11 | 39 | 27 | 94 |
+| 10 | 65 | 4 | 71 | 35 | 23 | 66 | 71 | 67 | 59 | 9 | 41 |
+
+## client_id=8
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 41 | 11 | 16 | 93 | 74 | 59 | 46 | 38 | 35 | 25 | 57 |
+| 1 | 83 | 46 | 32 | 96 | 46 | 85 | 64 | 63 | 92 | 82 | 71 |
+| 2 | 45 | 19 | 93 | 53 | 16 | 42 | 91 | 54 | 38 | 36 | 15 |
+| 3 | 69 | 82 | 61 | 14 | 63 | 27 | 0 | 44 | 79 | 86 | 95 |
+| 4 | 76 | 54 | 19 | 38 | 7 | 7 | 90 | 85 | 63 | 72 | 7 |
+| 5 | 41 | 30 | 32 | 89 | 22 | 19 | 17 | 81 | 67 | 76 | 82 |
+| 6 | 62 | 67 | 58 | 18 | 71 | 99 | 79 | 22 | 23 | 16 | 18 |
+| 7 | 12 | 45 | 25 | 24 | 30 | 0 | 41 | 42 | 94 | 53 | 84 |
+| 8 | 76 | 39 | 20 | 20 | 48 | 26 | 69 | 19 | 15 | 29 | 52 |
+| 9 | 89 | 22 | 1 | 0 | 8 | 5 | 64 | 50 | 56 | 29 | 26 |
+| 10 | 20 | 80 | 54 | 74 | 52 | 32 | 16 | 12 | 83 | 91 | 33 |
+
+## client_id=9
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 29 | 65 | 91 | 76 | 99 | 15 | 29 | 81 | 52 | 98 | 40 |
+| 1 | 81 | 47 | 34 | 14 | 38 | 13 | 51 | 83 | 77 | 79 | 12 |
+| 2 | 5 | 27 | 22 | 11 | 91 | 13 | 39 | 47 | 40 | 54 | 86 |
+| 3 | 29 | 74 | 80 | 50 | 18 | 47 | 71 | 82 | 60 | 90 | 3 |
+| 4 | 75 | 20 | 53 | 48 | 17 | 88 | 36 | 86 | 28 | 77 | 21 |
+| 5 | 56 | 30 | 24 | 82 | 73 | 24 | 88 | 9 | 37 | 95 | 48 |
+| 6 | 75 | 11 | 73 | 34 | 47 | 12 | 47 | 87 | 6 | 41 | 79 |
+| 7 | 5 | 19 | 90 | 40 | 52 | 1 | 98 | 75 | 86 | 22 | 3 |
+| 8 | 57 | 38 | 29 | 29 | 35 | 69 | 96 | 1 | 86 | 46 | 54 |
+| 9 | 67 | 13 | 71 | 82 | 73 | 21 | 48 | 43 | 68 | 10 | 50 |
+| 10 | 85 | 46 | 85 | 26 | 96 | 14 | 18 | 55 | 95 | 23 | 93 |
+
+## client_id=10
+| interpreter_id\timeslot_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 74 | 80 | 3 | 14 | 10 | 56 | 67 | 19 | 93 | 48 | 35 |
+| 1 | 88 | 31 | 93 | 73 | 74 | 75 | 32 | 76 | 4 | 46 | 54 |
+| 2 | 59 | 60 | 24 | 73 | 47 | 10 | 64 | 72 | 68 | 22 | 44 |
+| 3 | 87 | 33 | 55 | 40 | 80 | 20 | 72 | 71 | 27 | 98 | 4 |
+| 4 | 1 | 41 | 52 | 17 | 60 | 7 | 66 | 68 | 86 | 37 | 0 |
+| 5 | 97 | 83 | 90 | 24 | 38 | 92 | 88 | 33 | 59 | 48 | 36 |
+| 6 | 55 | 99 | 74 | 53 | 38 | 17 | 22 | 19 | 95 | 83 | 54 |
+| 7 | 39 | 14 | 95 | 0 | 70 | 80 | 58 | 5 | 14 | 77 | 49 |
+| 8 | 67 | 7 | 25 | 14 | 43 | 39 | 7 | 89 | 93 | 61 | 97 |
+| 9 | 51 | 12 | 85 | 68 | 71 | 2 | 24 | 27 | 55 | 87 | 65 |
+| 10 | 38 | 71 | 1 | 97 | 32 | 45 | 5 | 56 | 99 | 27 | 73 |
+
+Matches from this list should be chosen so that every client gets exactly one session, no interpreter or time is used more than once, and the total cost is minimized.
+
+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': [[[46, 52, 74, 88, 56, 48, 22, 91, 15, 30, 1], [69, 13, 17, 86, 86, 60, 44, 37, 38, 0, 86], [22, 49, 45, 21, 45, 78, 89, 88, 89, 53, 59], [8, 41, 45, 72, 50, 71, 83, 55, 72, 10, 22], [38, 20, 63, 20, 85, 63, 91, 59, 69, 91, 54], [35, 45, 45, 29, 31, 78, 85, 43, 19, 7, 71], [28, 35, 86, 56, 45, 56, 86, 60, 21, 78, 9], [66, 45, 31, 98, 91, 49, 69, 21, 26, 33, 81], [7, 26, 24, 98, 7, 82, 98, 95, 14, 28, 74], [72, 38, 24, 44, 84, 68, 38, 66, 17, 12, 17], [32, 22, 89, 29, 68, 21, 46, 37, 59, 12, 45]], [[76, 39, 18, 49, 98, 55, 72, 85, 63, 10, 23], [28, 51, 3, 21, 30, 47, 83, 28, 69, 8, 94], [82, 82, 47, 22, 83, 73, 20, 87, 20, 34, 15], [50, 91, 43, 26, 90, 95, 12, 7, 63, 92, 56], [18, 48, 46, 46, 97, 35, 79, 89, 19, 58, 64], [53, 26, 92, 57, 72, 18, 53, 95, 40, 19, 25], [19, 65, 74, 13, 81, 19, 66, 76, 66, 52, 32], [82, 27, 42, 35, 20, 83, 16, 27, 68, 73, 67], [24, 61, 92, 88, 89, 14, 68, 84, 22, 52, 45], [91, 23, 55, 68, 13, 13, 37, 37, 38, 4, 79], [3, 54, 85, 27, 84, 30, 17, 89, 73, 33, 10]], [[47, 7, 93, 6, 24, 63, 15, 82, 57, 95, 72], [43, 98, 92, 14, 10, 62, 67, 98, 71, 22, 61], [82, 49, 44, 45, 22, 0, 22, 20, 3, 14, 7], [0, 85, 28, 79, 65, 47, 33, 54, 80, 88, 62], [60, 97, 79, 32, 8, 17, 57, 87, 81, 48, 92], [59, 93, 39, 61, 61, 63, 62, 47, 54, 26, 50], [0, 82, 55, 7, 48, 57, 61, 15, 33, 78, 17], [75, 30, 87, 40, 82, 30, 65, 92, 43, 95, 39], [23, 99, 29, 32, 36, 48, 94, 90, 17, 42, 91], [27, 1, 43, 83, 14, 69, 30, 29, 83, 60, 22], [30, 44, 79, 8, 1, 6, 33, 49, 84, 16, 34]], [[42, 24, 30, 33, 69, 7, 67, 81, 0, 92, 31], [10, 71, 6, 86, 47, 95, 63, 54, 74, 90, 7], [4, 51, 6, 83, 40, 77, 86, 62, 61, 51, 68], [35, 28, 31, 10, 16, 14, 67, 34, 98, 66, 66], [21, 89, 75, 22, 93, 53, 37, 82, 2, 87, 74], [16, 90, 6, 28, 69, 92, 2, 80, 38, 8, 76], [81, 63, 84, 58, 7, 35, 60, 46, 11, 62, 12], [39, 8, 80, 39, 66, 32, 15, 80, 38, 45, 27], [78, 66, 81, 48, 97, 62, 9, 57, 70, 10, 13], [41, 52, 69, 59, 54, 4, 62, 53, 24, 9, 29], [69, 56, 88, 13, 39, 41, 55, 39, 93, 54, 37]], [[9, 84, 29, 20, 56, 70, 61, 89, 93, 58, 71], [10, 1, 54, 67, 46, 27, 15, 0, 46, 64, 23], [88, 21, 84, 59, 94, 90, 72, 98, 34, 36, 74], [46, 30, 77, 1, 23, 3, 31, 41, 47, 54, 34], [61, 33, 7, 71, 1, 15, 92, 10, 42, 4, 42], [69, 4, 68, 18, 49, 60, 36, 25, 48, 31, 60], [15, 68, 34, 21, 57, 76, 25, 75, 50, 66, 73], [86, 46, 7, 63, 81, 28, 92, 14, 36, 92, 73], [87, 84, 94, 25, 25, 24, 37, 5, 96, 83, 28], [22, 97, 92, 4, 7, 35, 86, 63, 82, 35, 70], [89, 10, 6, 27, 45, 51, 53, 3, 61, 24, 42]], [[34, 89, 81, 66, 71, 38, 17, 85, 13, 42, 97], [19, 12, 61, 0, 31, 59, 97, 88, 68, 91, 18], [97, 39, 2, 78, 18, 62, 11, 28, 23, 75, 57], [5, 81, 31, 7, 51, 26, 15, 88, 1, 23, 99], [57, 55, 14, 81, 16, 34, 29, 59, 32, 92, 57], [36, 1, 54, 88, 14, 15, 91, 1, 49, 24, 47], [43, 81, 82, 20, 33, 5, 56, 75, 58, 42, 0], [52, 81, 6, 36, 13, 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'cost': 73}, {'i': 10, 'j': 2, 'k': 4, 'cost': 47}, {'i': 10, 'j': 2, 'k': 5, 'cost': 10}, {'i': 10, 'j': 2, 'k': 6, 'cost': 64}, {'i': 10, 'j': 2, 'k': 7, 'cost': 72}, {'i': 10, 'j': 2, 'k': 8, 'cost': 68}, {'i': 10, 'j': 2, 'k': 9, 'cost': 22}, {'i': 10, 'j': 2, 'k': 10, 'cost': 44}, {'i': 10, 'j': 3, 'k': 0, 'cost': 87}, {'i': 10, 'j': 3, 'k': 1, 'cost': 33}, {'i': 10, 'j': 3, 'k': 2, 'cost': 55}, {'i': 10, 'j': 3, 'k': 3, 'cost': 40}, {'i': 10, 'j': 3, 'k': 4, 'cost': 80}, {'i': 10, 'j': 3, 'k': 5, 'cost': 20}, {'i': 10, 'j': 3, 'k': 6, 'cost': 72}, {'i': 10, 'j': 3, 'k': 7, 'cost': 71}, {'i': 10, 'j': 3, 'k': 8, 'cost': 27}, {'i': 10, 'j': 3, 'k': 9, 'cost': 98}, {'i': 10, 'j': 3, 'k': 10, 'cost': 4}, {'i': 10, 'j': 4, 'k': 0, 'cost': 1}, {'i': 10, 'j': 4, 'k': 1, 'cost': 41}, {'i': 10, 'j': 4, 'k': 2, 'cost': 52}, {'i': 10, 'j': 4, 'k': 3, 'cost': 17}, {'i': 10, 'j': 4, 'k': 4, 'cost': 60}, {'i': 10, 'j': 4, 'k': 5, 'cost': 7}, {'i': 10, 'j': 4, 'k': 6, 'cost': 66}, {'i': 10, 'j': 4, 'k': 7, 'cost': 68}, {'i': 10, 'j': 4, 'k': 8, 'cost': 86}, {'i': 10, 'j': 4, 'k': 9, 'cost': 37}, {'i': 10, 'j': 4, 'k': 10, 'cost': 0}, {'i': 10, 'j': 5, 'k': 0, 'cost': 97}, {'i': 10, 'j': 5, 'k': 1, 'cost': 83}, {'i': 10, 'j': 5, 'k': 2, 'cost': 90}, {'i': 10, 'j': 5, 'k': 3, 'cost': 24}, {'i': 10, 'j': 5, 'k': 4, 'cost': 38}, {'i': 10, 'j': 5, 'k': 5, 'cost': 92}, {'i': 10, 'j': 5, 'k': 6, 'cost': 88}, {'i': 10, 'j': 5, 'k': 7, 'cost': 33}, {'i': 10, 'j': 5, 'k': 8, 'cost': 59}, {'i': 10, 'j': 5, 'k': 9, 'cost': 48}, {'i': 10, 'j': 5, 'k': 10, 'cost': 36}, {'i': 10, 'j': 6, 'k': 0, 'cost': 55}, {'i': 10, 'j': 6, 'k': 1, 'cost': 99}, {'i': 10, 'j': 6, 'k': 2, 'cost': 74}, {'i': 10, 'j': 6, 'k': 3, 'cost': 53}, {'i': 10, 'j': 6, 'k': 4, 'cost': 38}, {'i': 10, 'j': 6, 'k': 5, 'cost': 17}, {'i': 10, 'j': 6, 'k': 6, 'cost': 22}, {'i': 10, 'j': 6, 'k': 7, 'cost': 19}, {'i': 10, 'j': 6, 'k': 8, 'cost': 95}, {'i': 10, 'j': 6, 'k': 9, 'cost': 83}, {'i': 10, 'j': 6, 'k': 10, 'cost': 54}, {'i': 10, 'j': 7, 'k': 0, 'cost': 39}, {'i': 10, 'j': 7, 'k': 1, 'cost': 14}, {'i': 10, 'j': 7, 'k': 2, 'cost': 95}, {'i': 10, 'j': 7, 'k': 3, 'cost': 0}, {'i': 10, 'j': 7, 'k': 4, 'cost': 70}, {'i': 10, 'j': 7, 'k': 5, 'cost': 80}, {'i': 10, 'j': 7, 'k': 6, 'cost': 58}, {'i': 10, 'j': 7, 'k': 7, 'cost': 5}, {'i': 10, 'j': 7, 'k': 8, 'cost': 14}, {'i': 10, 'j': 7, 'k': 9, 'cost': 77}, {'i': 10, 'j': 7, 'k': 10, 'cost': 49}, {'i': 10, 'j': 8, 'k': 0, 'cost': 67}, {'i': 10, 'j': 8, 'k': 1, 'cost': 7}, {'i': 10, 'j': 8, 'k': 2, 'cost': 25}, {'i': 10, 'j': 8, 'k': 3, 'cost': 14}, {'i': 10, 'j': 8, 'k': 4, 'cost': 43}, {'i': 10, 'j': 8, 'k': 5, 'cost': 39}, {'i': 10, 'j': 8, 'k': 6, 'cost': 7}, {'i': 10, 'j': 8, 'k': 7, 'cost': 89}, {'i': 10, 'j': 8, 'k': 8, 'cost': 93}, {'i': 10, 'j': 8, 'k': 9, 'cost': 61}, {'i': 10, 'j': 8, 'k': 10, 'cost': 97}, {'i': 10, 'j': 9, 'k': 0, 'cost': 51}, {'i': 10, 'j': 9, 'k': 1, 'cost': 12}, {'i': 10, 'j': 9, 'k': 2, 'cost': 85}, {'i': 10, 'j': 9, 'k': 3, 'cost': 68}, {'i': 10, 'j': 9, 'k': 4, 'cost': 71}, {'i': 10, 'j': 9, 'k': 5, 'cost': 2}, {'i': 10, 'j': 9, 'k': 6, 'cost': 24}, {'i': 10, 'j': 9, 'k': 7, 'cost': 27}, {'i': 10, 'j': 9, 'k': 8, 'cost': 55}, {'i': 10, 'j': 9, 'k': 9, 'cost': 87}, {'i': 10, 'j': 9, 'k': 10, 'cost': 65}, {'i': 10, 'j': 10, 'k': 0, 'cost': 38}, {'i': 10, 'j': 10, 'k': 1, 'cost': 71}, {'i': 10, 'j': 10, 'k': 2, 'cost': 1}, {'i': 10, 'j': 10, 'k': 3, 'cost': 97}, {'i': 10, 'j': 10, 'k': 4, 'cost': 32}, {'i': 10, 'j': 10, 'k': 5, 'cost': 45}, {'i': 10, 'j': 10, 'k': 6, 'cost': 5}, {'i': 10, 'j': 10, 'k': 7, 'cost': 56}, {'i': 10, 'j': 10, 'k': 8, 'cost': 99}, {'i': 10, 'j': 10, 'k': 9, 'cost': 27}, {'i': 10, 'j': 10, 'k': 10, 'cost': 73}]}","[[0, 6, 10], [1, 10, 0], [2, 9, 1], [3, 0, 8], [4, 4, 4], [5, 2, 2], [6, 1, 5], [7, 5, 9], [8, 3, 6], [9, 8, 7], [10, 7, 3]]",28,markdown_table,0
+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.
+
+# num_exams=10
+# index_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10
+
+# 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=1
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 96 | 90 | 30 | 18 | 48 | 27 | 84 | 73 | 7 | 0 |
+| 2 | 75 | 54 | 92 | 41 | 94 | 52 | 96 | 71 | 42 | 43 |
+| 3 | 39 | 76 | 37 | 99 | 22 | 4 | 21 | 82 | 36 | 35 |
+| 4 | 37 | 21 | 72 | 69 | 45 | 41 | 90 | 40 | 49 | 11 |
+| 5 | 23 | 43 | 76 | 44 | 4 | 92 | 27 | 93 | 31 | 18 |
+| 6 | 53 | 35 | 12 | 1 | 30 | 91 | 28 | 67 | 1 | 10 |
+| 7 | 81 | 6 | 83 | 90 | 25 | 50 | 33 | 48 | 53 | 14 |
+| 8 | 19 | 35 | 82 | 44 | 40 | 96 | 6 | 73 | 55 | 14 |
+| 9 | 76 | 95 | 15 | 48 | 72 | 6 | 62 | 80 | 2 | 60 |
+| 10 | 53 | 77 | 5 | 20 | 76 | 52 | 16 | 71 | 69 | 10 |
+
+## exam_id=2
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 45 | 28 | 43 | 51 | 3 | 93 | 57 | 6 | 63 | 73 |
+| 2 | 67 | 83 | 28 | 59 | 54 | 96 | 42 | 19 | 51 | 75 |
+| 3 | 1 | 81 | 19 | 34 | 76 | 30 | 79 | 18 | 78 | 53 |
+| 4 | 70 | 22 | 70 | 62 | 4 | 11 | 71 | 82 | 88 | 39 |
+| 5 | 99 | 93 | 6 | 46 | 2 | 26 | 14 | 6 | 16 | 76 |
+| 6 | 7 | 4 | 8 | 27 | 66 | 45 | 47 | 52 | 58 | 52 |
+| 7 | 85 | 84 | 48 | 20 | 53 | 49 | 7 | 34 | 94 | 38 |
+| 8 | 86 | 45 | 84 | 85 | 3 | 0 | 90 | 5 | 60 | 14 |
+| 9 | 30 | 98 | 25 | 51 | 42 | 97 | 84 | 98 | 7 | 6 |
+| 10 | 21 | 61 | 94 | 52 | 24 | 90 | 24 | 90 | 46 | 21 |
+
+## exam_id=3
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 1 | 5 | 32 | 13 | 50 | 9 | 30 | 16 | 99 | 70 |
+| 2 | 39 | 41 | 32 | 41 | 67 | 61 | 37 | 14 | 43 | 87 |
+| 3 | 69 | 55 | 12 | 16 | 95 | 97 | 86 | 18 | 55 | 56 |
+| 4 | 84 | 82 | 71 | 36 | 91 | 92 | 49 | 56 | 64 | 8 |
+| 5 | 80 | 43 | 84 | 12 | 39 | 94 | 97 | 68 | 91 | 81 |
+| 6 | 39 | 90 | 81 | 68 | 76 | 95 | 61 | 41 | 62 | 57 |
+| 7 | 89 | 20 | 31 | 49 | 67 | 66 | 75 | 41 | 34 | 30 |
+| 8 | 51 | 43 | 40 | 42 | 25 | 15 | 16 | 44 | 18 | 42 |
+| 9 | 55 | 9 | 19 | 20 | 7 | 61 | 45 | 78 | 22 | 98 |
+| 10 | 85 | 93 | 9 | 35 | 78 | 22 | 71 | 89 | 86 | 83 |
+
+## exam_id=4
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 50 | 59 | 83 | 43 | 78 | 11 | 91 | 92 | 53 | 79 |
+| 2 | 81 | 66 | 92 | 23 | 22 | 84 | 69 | 41 | 54 | 66 |
+| 3 | 30 | 36 | 3 | 82 | 67 | 44 | 28 | 69 | 4 | 33 |
+| 4 | 64 | 38 | 64 | 28 | 92 | 24 | 13 | 48 | 15 | 5 |
+| 5 | 51 | 28 | 95 | 80 | 4 | 34 | 65 | 67 | 92 | 19 |
+| 6 | 33 | 33 | 17 | 61 | 48 | 80 | 56 | 20 | 50 | 12 |
+| 7 | 82 | 52 | 21 | 14 | 55 | 38 | 25 | 57 | 11 | 78 |
+| 8 | 4 | 66 | 38 | 53 | 95 | 77 | 72 | 78 | 68 | 88 |
+| 9 | 40 | 65 | 84 | 93 | 54 | 36 | 34 | 7 | 86 | 22 |
+| 10 | 32 | 9 | 38 | 5 | 26 | 86 | 45 | 54 | 27 | 84 |
+
+## exam_id=5
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 28 | 83 | 78 | 73 | 38 | 26 | 20 | 62 | 88 |
+| 2 | 78 | 95 | 95 | 44 | 7 | 2 | 25 | 89 | 24 | 0 |
+| 3 | 71 | 61 | 81 | 71 | 81 | 6 | 94 | 58 | 63 | 69 |
+| 4 | 98 | 28 | 36 | 76 | 97 | 44 | 50 | 47 | 79 | 17 |
+| 5 | 1 | 88 | 28 | 88 | 82 | 81 | 5 | 91 | 59 | 78 |
+| 6 | 80 | 68 | 3 | 44 | 70 | 36 | 22 | 79 | 60 | 5 |
+| 7 | 49 | 17 | 5 | 53 | 4 | 3 | 44 | 69 | 62 | 69 |
+| 8 | 30 | 52 | 66 | 54 | 99 | 24 | 45 | 95 | 46 | 37 |
+| 9 | 70 | 3 | 7 | 8 | 71 | 60 | 38 | 72 | 36 | 67 |
+| 10 | 50 | 48 | 68 | 1 | 56 | 20 | 33 | 74 | 6 | 11 |
+
+## exam_id=6
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 42 | 96 | 61 | 87 | 38 | 38 | 59 | 97 | 95 | 85 |
+| 2 | 80 | 83 | 35 | 13 | 10 | 4 | 15 | 33 | 51 | 7 |
+| 3 | 50 | 75 | 3 | 45 | 42 | 68 | 8 | 34 | 75 | 16 |
+| 4 | 3 | 77 | 0 | 29 | 0 | 3 | 71 | 59 | 17 | 25 |
+| 5 | 98 | 84 | 34 | 21 | 79 | 52 | 32 | 86 | 20 | 60 |
+| 6 | 1 | 10 | 43 | 9 | 8 | 13 | 10 | 99 | 94 | 85 |
+| 7 | 80 | 86 | 93 | 86 | 94 | 32 | 87 | 61 | 32 | 77 |
+| 8 | 27 | 61 | 4 | 79 | 95 | 53 | 42 | 15 | 27 | 86 |
+| 9 | 18 | 86 | 4 | 78 | 15 | 97 | 14 | 59 | 73 | 1 |
+| 10 | 3 | 72 | 44 | 14 | 9 | 15 | 57 | 34 | 45 | 22 |
+
+## exam_id=7
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 75 | 97 | 37 | 16 | 78 | 37 | 70 | 11 | 0 | 66 |
+| 2 | 76 | 4 | 85 | 63 | 86 | 79 | 43 | 39 | 26 | 35 |
+| 3 | 86 | 51 | 99 | 98 | 94 | 72 | 43 | 53 | 49 | 69 |
+| 4 | 30 | 78 | 63 | 75 | 90 | 47 | 73 | 60 | 5 | 76 |
+| 5 | 37 | 13 | 30 | 61 | 90 | 9 | 34 | 83 | 19 | 80 |
+| 6 | 27 | 94 | 7 | 28 | 2 | 32 | 29 | 47 | 66 | 3 |
+| 7 | 25 | 59 | 27 | 95 | 63 | 44 | 56 | 34 | 54 | 15 |
+| 8 | 24 | 73 | 26 | 19 | 13 | 16 | 60 | 36 | 95 | 26 |
+| 9 | 10 | 29 | 37 | 35 | 86 | 89 | 53 | 44 | 40 | 3 |
+| 10 | 79 | 75 | 55 | 85 | 40 | 2 | 76 | 46 | 51 | 27 |
+
+## exam_id=8
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 87 | 43 | 38 | 90 | 60 | 7 | 17 | 98 | 76 | 27 |
+| 2 | 35 | 58 | 12 | 78 | 26 | 14 | 73 | 13 | 47 | 57 |
+| 3 | 0 | 35 | 49 | 68 | 21 | 28 | 84 | 7 | 26 | 56 |
+| 4 | 47 | 81 | 25 | 33 | 78 | 99 | 97 | 81 | 16 | 26 |
+| 5 | 52 | 94 | 87 | 58 | 56 | 50 | 56 | 52 | 12 | 83 |
+| 6 | 33 | 41 | 89 | 35 | 40 | 86 | 76 | 77 | 73 | 54 |
+| 7 | 40 | 3 | 75 | 33 | 84 | 48 | 0 | 70 | 19 | 22 |
+| 8 | 40 | 86 | 58 | 71 | 53 | 99 | 46 | 26 | 17 | 20 |
+| 9 | 34 | 61 | 78 | 73 | 38 | 20 | 75 | 24 | 32 | 69 |
+| 10 | 43 | 46 | 83 | 4 | 46 | 86 | 58 | 32 | 76 | 16 |
+
+## exam_id=9
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 81 | 82 | 78 | 0 | 2 | 56 | 63 | 86 | 15 | 76 |
+| 2 | 7 | 35 | 89 | 53 | 17 | 45 | 63 | 92 | 24 | 14 |
+| 3 | 83 | 55 | 81 | 53 | 81 | 98 | 84 | 41 | 29 | 51 |
+| 4 | 94 | 53 | 71 | 1 | 91 | 46 | 90 | 75 | 88 | 81 |
+| 5 | 25 | 30 | 49 | 11 | 73 | 88 | 40 | 51 | 48 | 10 |
+| 6 | 39 | 75 | 5 | 35 | 31 | 69 | 80 | 73 | 9 | 74 |
+| 7 | 92 | 81 | 14 | 5 | 38 | 63 | 45 | 61 | 33 | 69 |
+| 8 | 30 | 39 | 92 | 43 | 35 | 73 | 17 | 91 | 26 | 5 |
+| 9 | 82 | 40 | 92 | 5 | 1 | 42 | 82 | 28 | 24 | 34 |
+| 10 | 33 | 83 | 49 | 84 | 30 | 45 | 98 | 32 | 13 | 57 |
+
+## exam_id=10
+| proctor_id\hall_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 42 | 57 | 91 | 46 | 84 | 88 | 62 | 54 | 39 | 91 |
+| 2 | 76 | 69 | 33 | 21 | 6 | 79 | 75 | 60 | 31 | 9 |
+| 3 | 38 | 83 | 30 | 25 | 16 | 88 | 98 | 30 | 50 | 3 |
+| 4 | 84 | 45 | 45 | 68 | 34 | 3 | 66 | 53 | 36 | 64 |
+| 5 | 74 | 90 | 14 | 74 | 8 | 85 | 12 | 34 | 23 | 95 |
+| 6 | 10 | 6 | 11 | 81 | 60 | 8 | 54 | 29 | 97 | 56 |
+| 7 | 27 | 40 | 47 | 42 | 12 | 21 | 64 | 50 | 86 | 4 |
+| 8 | 8 | 16 | 30 | 16 | 98 | 35 | 75 | 44 | 54 | 8 |
+| 9 | 91 | 64 | 14 | 99 | 29 | 13 | 48 | 68 | 93 | 97 |
+| 10 | 71 | 6 | 8 | 95 | 87 | 37 | 40 | 7 | 34 | 56 |
+
+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': [[[96, 90, 30, 18, 48, 27, 84, 73, 7, 0], [75, 54, 92, 41, 94, 52, 96, 71, 42, 43], [39, 76, 37, 99, 22, 4, 21, 82, 36, 35], [37, 21, 72, 69, 45, 41, 90, 40, 49, 11], [23, 43, 76, 44, 4, 92, 27, 93, 31, 18], [53, 35, 12, 1, 30, 91, 28, 67, 1, 10], [81, 6, 83, 90, 25, 50, 33, 48, 53, 14], [19, 35, 82, 44, 40, 96, 6, 73, 55, 14], [76, 95, 15, 48, 72, 6, 62, 80, 2, 60], [53, 77, 5, 20, 76, 52, 16, 71, 69, 10]], [[45, 28, 43, 51, 3, 93, 57, 6, 63, 73], [67, 83, 28, 59, 54, 96, 42, 19, 51, 75], [1, 81, 19, 34, 76, 30, 79, 18, 78, 53], [70, 22, 70, 62, 4, 11, 71, 82, 88, 39], [99, 93, 6, 46, 2, 26, 14, 6, 16, 76], [7, 4, 8, 27, 66, 45, 47, 52, 58, 52], [85, 84, 48, 20, 53, 49, 7, 34, 94, 38], [86, 45, 84, 85, 3, 0, 90, 5, 60, 14], [30, 98, 25, 51, 42, 97, 84, 98, 7, 6], [21, 61, 94, 52, 24, 90, 24, 90, 46, 21]], [[1, 5, 32, 13, 50, 9, 30, 16, 99, 70], [39, 41, 32, 41, 67, 61, 37, 14, 43, 87], [69, 55, 12, 16, 95, 97, 86, 18, 55, 56], [84, 82, 71, 36, 91, 92, 49, 56, 64, 8], [80, 43, 84, 12, 39, 94, 97, 68, 91, 81], [39, 90, 81, 68, 76, 95, 61, 41, 62, 57], [89, 20, 31, 49, 67, 66, 75, 41, 34, 30], [51, 43, 40, 42, 25, 15, 16, 44, 18, 42], [55, 9, 19, 20, 7, 61, 45, 78, 22, 98], [85, 93, 9, 35, 78, 22, 71, 89, 86, 83]], [[50, 59, 83, 43, 78, 11, 91, 92, 53, 79], [81, 66, 92, 23, 22, 84, 69, 41, 54, 66], [30, 36, 3, 82, 67, 44, 28, 69, 4, 33], [64, 38, 64, 28, 92, 24, 13, 48, 15, 5], [51, 28, 95, 80, 4, 34, 65, 67, 92, 19], [33, 33, 17, 61, 48, 80, 56, 20, 50, 12], [82, 52, 21, 14, 55, 38, 25, 57, 11, 78], [4, 66, 38, 53, 95, 77, 72, 78, 68, 88], [40, 65, 84, 93, 54, 36, 34, 7, 86, 22], [32, 9, 38, 5, 26, 86, 45, 54, 27, 84]], [[82, 28, 83, 78, 73, 38, 26, 20, 62, 88], [78, 95, 95, 44, 7, 2, 25, 89, 24, 0], [71, 61, 81, 71, 81, 6, 94, 58, 63, 69], [98, 28, 36, 76, 97, 44, 50, 47, 79, 17], [1, 88, 28, 88, 82, 81, 5, 91, 59, 78], [80, 68, 3, 44, 70, 36, 22, 79, 60, 5], [49, 17, 5, 53, 4, 3, 44, 69, 62, 69], [30, 52, 66, 54, 99, 24, 45, 95, 46, 37], [70, 3, 7, 8, 71, 60, 38, 72, 36, 67], [50, 48, 68, 1, 56, 20, 33, 74, 6, 11]], [[42, 96, 61, 87, 38, 38, 59, 97, 95, 85], [80, 83, 35, 13, 10, 4, 15, 33, 51, 7], [50, 75, 3, 45, 42, 68, 8, 34, 75, 16], [3, 77, 0, 29, 0, 3, 71, 59, 17, 25], [98, 84, 34, 21, 79, 52, 32, 86, 20, 60], [1, 10, 43, 9, 8, 13, 10, 99, 94, 85], [80, 86, 93, 86, 94, 32, 87, 61, 32, 77], [27, 61, 4, 79, 95, 53, 42, 15, 27, 86], [18, 86, 4, 78, 15, 97, 14, 59, 73, 1], [3, 72, 44, 14, 9, 15, 57, 34, 45, 22]], [[75, 97, 37, 16, 78, 37, 70, 11, 0, 66], [76, 4, 85, 63, 86, 79, 43, 39, 26, 35], [86, 51, 99, 98, 94, 72, 43, 53, 49, 69], [30, 78, 63, 75, 90, 47, 73, 60, 5, 76], [37, 13, 30, 61, 90, 9, 34, 83, 19, 80], [27, 94, 7, 28, 2, 32, 29, 47, 66, 3], [25, 59, 27, 95, 63, 44, 56, 34, 54, 15], [24, 73, 26, 19, 13, 16, 60, 36, 95, 26], [10, 29, 37, 35, 86, 89, 53, 44, 40, 3], [79, 75, 55, 85, 40, 2, 76, 46, 51, 27]], [[87, 43, 38, 90, 60, 7, 17, 98, 76, 27], [35, 58, 12, 78, 26, 14, 73, 13, 47, 57], [0, 35, 49, 68, 21, 28, 84, 7, 26, 56], [47, 81, 25, 33, 78, 99, 97, 81, 16, 26], [52, 94, 87, 58, 56, 50, 56, 52, 12, 83], [33, 41, 89, 35, 40, 86, 76, 77, 73, 54], [40, 3, 75, 33, 84, 48, 0, 70, 19, 22], [40, 86, 58, 71, 53, 99, 46, 26, 17, 20], [34, 61, 78, 73, 38, 20, 75, 24, 32, 69], [43, 46, 83, 4, 46, 86, 58, 32, 76, 16]], [[81, 82, 78, 0, 2, 56, 63, 86, 15, 76], [7, 35, 89, 53, 17, 45, 63, 92, 24, 14], [83, 55, 81, 53, 81, 98, 84, 41, 29, 51], [94, 53, 71, 1, 91, 46, 90, 75, 88, 81], [25, 30, 49, 11, 73, 88, 40, 51, 48, 10], [39, 75, 5, 35, 31, 69, 80, 73, 9, 74], [92, 81, 14, 5, 38, 63, 45, 61, 33, 69], [30, 39, 92, 43, 35, 73, 17, 91, 26, 5], [82, 40, 92, 5, 1, 42, 82, 28, 24, 34], [33, 83, 49, 84, 30, 45, 98, 32, 13, 57]], [[42, 57, 91, 46, 84, 88, 62, 54, 39, 91], [76, 69, 33, 21, 6, 79, 75, 60, 31, 9], [38, 83, 30, 25, 16, 88, 98, 30, 50, 3], [84, 45, 45, 68, 34, 3, 66, 53, 36, 64], [74, 90, 14, 74, 8, 85, 12, 34, 23, 95], [10, 6, 11, 81, 60, 8, 54, 29, 97, 56], [27, 40, 47, 42, 12, 21, 64, 50, 86, 4], [8, 16, 30, 16, 98, 35, 75, 44, 54, 8], [91, 64, 14, 99, 29, 13, 48, 68, 93, 97], [71, 6, 8, 95, 87, 37, 40, 7, 34, 56]]], 'objective': 24.0}","[[0, 8, 8], [1, 7, 7], [2, 0, 0], [3, 4, 4], [4, 1, 9], [5, 2, 2], [6, 9, 5], [7, 6, 6], [8, 3, 3], [9, 5, 1]]",24.0,"{'problem_type': 'AP3', 'n': 10, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 96}, {'i': 1, 'j': 1, 'k': 2, 'cost': 90}, {'i': 1, 'j': 1, 'k': 3, 'cost': 30}, {'i': 1, 'j': 1, 'k': 4, 'cost': 18}, {'i': 1, 'j': 1, 'k': 5, 'cost': 48}, {'i': 1, 'j': 1, 'k': 6, 'cost': 27}, {'i': 1, 'j': 1, 'k': 7, 'cost': 84}, {'i': 1, 'j': 1, 'k': 8, 'cost': 73}, {'i': 1, 'j': 1, 'k': 9, 'cost': 7}, {'i': 1, 'j': 1, 'k': 10, 'cost': 0}, {'i': 1, 'j': 2, 'k': 1, 'cost': 75}, {'i': 1, 'j': 2, 'k': 2, 'cost': 54}, {'i': 1, 'j': 2, 'k': 3, 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'cost': 40}, {'i': 7, 'j': 10, 'k': 6, 'cost': 2}, {'i': 7, 'j': 10, 'k': 7, 'cost': 76}, {'i': 7, 'j': 10, 'k': 8, 'cost': 46}, {'i': 7, 'j': 10, 'k': 9, 'cost': 51}, {'i': 7, 'j': 10, 'k': 10, 'cost': 27}, {'i': 8, 'j': 1, 'k': 1, 'cost': 87}, {'i': 8, 'j': 1, 'k': 2, 'cost': 43}, {'i': 8, 'j': 1, 'k': 3, 'cost': 38}, {'i': 8, 'j': 1, 'k': 4, 'cost': 90}, {'i': 8, 'j': 1, 'k': 5, 'cost': 60}, {'i': 8, 'j': 1, 'k': 6, 'cost': 7}, {'i': 8, 'j': 1, 'k': 7, 'cost': 17}, {'i': 8, 'j': 1, 'k': 8, 'cost': 98}, {'i': 8, 'j': 1, 'k': 9, 'cost': 76}, {'i': 8, 'j': 1, 'k': 10, 'cost': 27}, {'i': 8, 'j': 2, 'k': 1, 'cost': 35}, {'i': 8, 'j': 2, 'k': 2, 'cost': 58}, {'i': 8, 'j': 2, 'k': 3, 'cost': 12}, {'i': 8, 'j': 2, 'k': 4, 'cost': 78}, {'i': 8, 'j': 2, 'k': 5, 'cost': 26}, {'i': 8, 'j': 2, 'k': 6, 'cost': 14}, {'i': 8, 'j': 2, 'k': 7, 'cost': 73}, {'i': 8, 'j': 2, 'k': 8, 'cost': 13}, {'i': 8, 'j': 2, 'k': 9, 'cost': 47}, {'i': 8, 'j': 2, 'k': 10, 'cost': 57}, {'i': 8, 'j': 3, 'k': 1, 'cost': 0}, {'i': 8, 'j': 3, 'k': 2, 'cost': 35}, {'i': 8, 'j': 3, 'k': 3, 'cost': 49}, {'i': 8, 'j': 3, 'k': 4, 'cost': 68}, {'i': 8, 'j': 3, 'k': 5, 'cost': 21}, {'i': 8, 'j': 3, 'k': 6, 'cost': 28}, {'i': 8, 'j': 3, 'k': 7, 'cost': 84}, {'i': 8, 'j': 3, 'k': 8, 'cost': 7}, {'i': 8, 'j': 3, 'k': 9, 'cost': 26}, {'i': 8, 'j': 3, 'k': 10, 'cost': 56}, {'i': 8, 'j': 4, 'k': 1, 'cost': 47}, {'i': 8, 'j': 4, 'k': 2, 'cost': 81}, {'i': 8, 'j': 4, 'k': 3, 'cost': 25}, {'i': 8, 'j': 4, 'k': 4, 'cost': 33}, {'i': 8, 'j': 4, 'k': 5, 'cost': 78}, {'i': 8, 'j': 4, 'k': 6, 'cost': 99}, {'i': 8, 'j': 4, 'k': 7, 'cost': 97}, {'i': 8, 'j': 4, 'k': 8, 'cost': 81}, {'i': 8, 'j': 4, 'k': 9, 'cost': 16}, {'i': 8, 'j': 4, 'k': 10, 'cost': 26}, {'i': 8, 'j': 5, 'k': 1, 'cost': 52}, {'i': 8, 'j': 5, 'k': 2, 'cost': 94}, {'i': 8, 'j': 5, 'k': 3, 'cost': 87}, {'i': 8, 'j': 5, 'k': 4, 'cost': 58}, {'i': 8, 'j': 5, 'k': 5, 'cost': 56}, {'i': 8, 'j': 5, 'k': 6, 'cost': 50}, {'i': 8, 'j': 5, 'k': 7, 'cost': 56}, {'i': 8, 'j': 5, 'k': 8, 'cost': 52}, {'i': 8, 'j': 5, 'k': 9, 'cost': 12}, {'i': 8, 'j': 5, 'k': 10, 'cost': 83}, {'i': 8, 'j': 6, 'k': 1, 'cost': 33}, {'i': 8, 'j': 6, 'k': 2, 'cost': 41}, {'i': 8, 'j': 6, 'k': 3, 'cost': 89}, {'i': 8, 'j': 6, 'k': 4, 'cost': 35}, {'i': 8, 'j': 6, 'k': 5, 'cost': 40}, {'i': 8, 'j': 6, 'k': 6, 'cost': 86}, {'i': 8, 'j': 6, 'k': 7, 'cost': 76}, {'i': 8, 'j': 6, 'k': 8, 'cost': 77}, {'i': 8, 'j': 6, 'k': 9, 'cost': 73}, {'i': 8, 'j': 6, 'k': 10, 'cost': 54}, {'i': 8, 'j': 7, 'k': 1, 'cost': 40}, {'i': 8, 'j': 7, 'k': 2, 'cost': 3}, {'i': 8, 'j': 7, 'k': 3, 'cost': 75}, {'i': 8, 'j': 7, 'k': 4, 'cost': 33}, {'i': 8, 'j': 7, 'k': 5, 'cost': 84}, {'i': 8, 'j': 7, 'k': 6, 'cost': 48}, {'i': 8, 'j': 7, 'k': 7, 'cost': 0}, {'i': 8, 'j': 7, 'k': 8, 'cost': 70}, {'i': 8, 'j': 7, 'k': 9, 'cost': 19}, {'i': 8, 'j': 7, 'k': 10, 'cost': 22}, {'i': 8, 'j': 8, 'k': 1, 'cost': 40}, {'i': 8, 'j': 8, 'k': 2, 'cost': 86}, {'i': 8, 'j': 8, 'k': 3, 'cost': 58}, {'i': 8, 'j': 8, 'k': 4, 'cost': 71}, {'i': 8, 'j': 8, 'k': 5, 'cost': 53}, {'i': 8, 'j': 8, 'k': 6, 'cost': 99}, {'i': 8, 'j': 8, 'k': 7, 'cost': 46}, {'i': 8, 'j': 8, 'k': 8, 'cost': 26}, {'i': 8, 'j': 8, 'k': 9, 'cost': 17}, {'i': 8, 'j': 8, 'k': 10, 'cost': 20}, {'i': 8, 'j': 9, 'k': 1, 'cost': 34}, {'i': 8, 'j': 9, 'k': 2, 'cost': 61}, {'i': 8, 'j': 9, 'k': 3, 'cost': 78}, {'i': 8, 'j': 9, 'k': 4, 'cost': 73}, {'i': 8, 'j': 9, 'k': 5, 'cost': 38}, {'i': 8, 'j': 9, 'k': 6, 'cost': 20}, {'i': 8, 'j': 9, 'k': 7, 'cost': 75}, {'i': 8, 'j': 9, 'k': 8, 'cost': 24}, {'i': 8, 'j': 9, 'k': 9, 'cost': 32}, {'i': 8, 'j': 9, 'k': 10, 'cost': 69}, {'i': 8, 'j': 10, 'k': 1, 'cost': 43}, {'i': 8, 'j': 10, 'k': 2, 'cost': 46}, {'i': 8, 'j': 10, 'k': 3, 'cost': 83}, {'i': 8, 'j': 10, 'k': 4, 'cost': 4}, {'i': 8, 'j': 10, 'k': 5, 'cost': 46}, {'i': 8, 'j': 10, 'k': 6, 'cost': 86}, {'i': 8, 'j': 10, 'k': 7, 'cost': 58}, {'i': 8, 'j': 10, 'k': 8, 'cost': 32}, {'i': 8, 'j': 10, 'k': 9, 'cost': 76}, {'i': 8, 'j': 10, 'k': 10, 'cost': 16}, {'i': 9, 'j': 1, 'k': 1, 'cost': 81}, {'i': 9, 'j': 1, 'k': 2, 'cost': 82}, {'i': 9, 'j': 1, 'k': 3, 'cost': 78}, {'i': 9, 'j': 1, 'k': 4, 'cost': 0}, {'i': 9, 'j': 1, 'k': 5, 'cost': 2}, {'i': 9, 'j': 1, 'k': 6, 'cost': 56}, {'i': 9, 'j': 1, 'k': 7, 'cost': 63}, {'i': 9, 'j': 1, 'k': 8, 'cost': 86}, {'i': 9, 'j': 1, 'k': 9, 'cost': 15}, {'i': 9, 'j': 1, 'k': 10, 'cost': 76}, {'i': 9, 'j': 2, 'k': 1, 'cost': 7}, {'i': 9, 'j': 2, 'k': 2, 'cost': 35}, {'i': 9, 'j': 2, 'k': 3, 'cost': 89}, {'i': 9, 'j': 2, 'k': 4, 'cost': 53}, {'i': 9, 'j': 2, 'k': 5, 'cost': 17}, {'i': 9, 'j': 2, 'k': 6, 'cost': 45}, {'i': 9, 'j': 2, 'k': 7, 'cost': 63}, {'i': 9, 'j': 2, 'k': 8, 'cost': 92}, {'i': 9, 'j': 2, 'k': 9, 'cost': 24}, {'i': 9, 'j': 2, 'k': 10, 'cost': 14}, {'i': 9, 'j': 3, 'k': 1, 'cost': 83}, {'i': 9, 'j': 3, 'k': 2, 'cost': 55}, {'i': 9, 'j': 3, 'k': 3, 'cost': 81}, {'i': 9, 'j': 3, 'k': 4, 'cost': 53}, {'i': 9, 'j': 3, 'k': 5, 'cost': 81}, {'i': 9, 'j': 3, 'k': 6, 'cost': 98}, {'i': 9, 'j': 3, 'k': 7, 'cost': 84}, {'i': 9, 'j': 3, 'k': 8, 'cost': 41}, {'i': 9, 'j': 3, 'k': 9, 'cost': 29}, {'i': 9, 'j': 3, 'k': 10, 'cost': 51}, {'i': 9, 'j': 4, 'k': 1, 'cost': 94}, {'i': 9, 'j': 4, 'k': 2, 'cost': 53}, {'i': 9, 'j': 4, 'k': 3, 'cost': 71}, {'i': 9, 'j': 4, 'k': 4, 'cost': 1}, {'i': 9, 'j': 4, 'k': 5, 'cost': 91}, {'i': 9, 'j': 4, 'k': 6, 'cost': 46}, {'i': 9, 'j': 4, 'k': 7, 'cost': 90}, {'i': 9, 'j': 4, 'k': 8, 'cost': 75}, {'i': 9, 'j': 4, 'k': 9, 'cost': 88}, {'i': 9, 'j': 4, 'k': 10, 'cost': 81}, {'i': 9, 'j': 5, 'k': 1, 'cost': 25}, {'i': 9, 'j': 5, 'k': 2, 'cost': 30}, {'i': 9, 'j': 5, 'k': 3, 'cost': 49}, {'i': 9, 'j': 5, 'k': 4, 'cost': 11}, {'i': 9, 'j': 5, 'k': 5, 'cost': 73}, {'i': 9, 'j': 5, 'k': 6, 'cost': 88}, {'i': 9, 'j': 5, 'k': 7, 'cost': 40}, {'i': 9, 'j': 5, 'k': 8, 'cost': 51}, {'i': 9, 'j': 5, 'k': 9, 'cost': 48}, {'i': 9, 'j': 5, 'k': 10, 'cost': 10}, {'i': 9, 'j': 6, 'k': 1, 'cost': 39}, {'i': 9, 'j': 6, 'k': 2, 'cost': 75}, {'i': 9, 'j': 6, 'k': 3, 'cost': 5}, {'i': 9, 'j': 6, 'k': 4, 'cost': 35}, {'i': 9, 'j': 6, 'k': 5, 'cost': 31}, {'i': 9, 'j': 6, 'k': 6, 'cost': 69}, {'i': 9, 'j': 6, 'k': 7, 'cost': 80}, {'i': 9, 'j': 6, 'k': 8, 'cost': 73}, {'i': 9, 'j': 6, 'k': 9, 'cost': 9}, {'i': 9, 'j': 6, 'k': 10, 'cost': 74}, {'i': 9, 'j': 7, 'k': 1, 'cost': 92}, {'i': 9, 'j': 7, 'k': 2, 'cost': 81}, {'i': 9, 'j': 7, 'k': 3, 'cost': 14}, {'i': 9, 'j': 7, 'k': 4, 'cost': 5}, {'i': 9, 'j': 7, 'k': 5, 'cost': 38}, {'i': 9, 'j': 7, 'k': 6, 'cost': 63}, {'i': 9, 'j': 7, 'k': 7, 'cost': 45}, {'i': 9, 'j': 7, 'k': 8, 'cost': 61}, {'i': 9, 'j': 7, 'k': 9, 'cost': 33}, {'i': 9, 'j': 7, 'k': 10, 'cost': 69}, {'i': 9, 'j': 8, 'k': 1, 'cost': 30}, {'i': 9, 'j': 8, 'k': 2, 'cost': 39}, {'i': 9, 'j': 8, 'k': 3, 'cost': 92}, {'i': 9, 'j': 8, 'k': 4, 'cost': 43}, {'i': 9, 'j': 8, 'k': 5, 'cost': 35}, {'i': 9, 'j': 8, 'k': 6, 'cost': 73}, {'i': 9, 'j': 8, 'k': 7, 'cost': 17}, {'i': 9, 'j': 8, 'k': 8, 'cost': 91}, {'i': 9, 'j': 8, 'k': 9, 'cost': 26}, {'i': 9, 'j': 8, 'k': 10, 'cost': 5}, {'i': 9, 'j': 9, 'k': 1, 'cost': 82}, {'i': 9, 'j': 9, 'k': 2, 'cost': 40}, {'i': 9, 'j': 9, 'k': 3, 'cost': 92}, {'i': 9, 'j': 9, 'k': 4, 'cost': 5}, {'i': 9, 'j': 9, 'k': 5, 'cost': 1}, {'i': 9, 'j': 9, 'k': 6, 'cost': 42}, {'i': 9, 'j': 9, 'k': 7, 'cost': 82}, {'i': 9, 'j': 9, 'k': 8, 'cost': 28}, {'i': 9, 'j': 9, 'k': 9, 'cost': 24}, {'i': 9, 'j': 9, 'k': 10, 'cost': 34}, {'i': 9, 'j': 10, 'k': 1, 'cost': 33}, {'i': 9, 'j': 10, 'k': 2, 'cost': 83}, {'i': 9, 'j': 10, 'k': 3, 'cost': 49}, {'i': 9, 'j': 10, 'k': 4, 'cost': 84}, {'i': 9, 'j': 10, 'k': 5, 'cost': 30}, {'i': 9, 'j': 10, 'k': 6, 'cost': 45}, {'i': 9, 'j': 10, 'k': 7, 'cost': 98}, {'i': 9, 'j': 10, 'k': 8, 'cost': 32}, {'i': 9, 'j': 10, 'k': 9, 'cost': 13}, {'i': 9, 'j': 10, 'k': 10, 'cost': 57}, {'i': 10, 'j': 1, 'k': 1, 'cost': 42}, {'i': 10, 'j': 1, 'k': 2, 'cost': 57}, {'i': 10, 'j': 1, 'k': 3, 'cost': 91}, {'i': 10, 'j': 1, 'k': 4, 'cost': 46}, {'i': 10, 'j': 1, 'k': 5, 'cost': 84}, {'i': 10, 'j': 1, 'k': 6, 'cost': 88}, {'i': 10, 'j': 1, 'k': 7, 'cost': 62}, {'i': 10, 'j': 1, 'k': 8, 'cost': 54}, {'i': 10, 'j': 1, 'k': 9, 'cost': 39}, {'i': 10, 'j': 1, 'k': 10, 'cost': 91}, {'i': 10, 'j': 2, 'k': 1, 'cost': 76}, {'i': 10, 'j': 2, 'k': 2, 'cost': 69}, {'i': 10, 'j': 2, 'k': 3, 'cost': 33}, {'i': 10, 'j': 2, 'k': 4, 'cost': 21}, {'i': 10, 'j': 2, 'k': 5, 'cost': 6}, {'i': 10, 'j': 2, 'k': 6, 'cost': 79}, {'i': 10, 'j': 2, 'k': 7, 'cost': 75}, {'i': 10, 'j': 2, 'k': 8, 'cost': 60}, {'i': 10, 'j': 2, 'k': 9, 'cost': 31}, {'i': 10, 'j': 2, 'k': 10, 'cost': 9}, {'i': 10, 'j': 3, 'k': 1, 'cost': 38}, {'i': 10, 'j': 3, 'k': 2, 'cost': 83}, {'i': 10, 'j': 3, 'k': 3, 'cost': 30}, {'i': 10, 'j': 3, 'k': 4, 'cost': 25}, {'i': 10, 'j': 3, 'k': 5, 'cost': 16}, {'i': 10, 'j': 3, 'k': 6, 'cost': 88}, {'i': 10, 'j': 3, 'k': 7, 'cost': 98}, {'i': 10, 'j': 3, 'k': 8, 'cost': 30}, {'i': 10, 'j': 3, 'k': 9, 'cost': 50}, {'i': 10, 'j': 3, 'k': 10, 'cost': 3}, {'i': 10, 'j': 4, 'k': 1, 'cost': 84}, {'i': 10, 'j': 4, 'k': 2, 'cost': 45}, {'i': 10, 'j': 4, 'k': 3, 'cost': 45}, {'i': 10, 'j': 4, 'k': 4, 'cost': 68}, {'i': 10, 'j': 4, 'k': 5, 'cost': 34}, {'i': 10, 'j': 4, 'k': 6, 'cost': 3}, {'i': 10, 'j': 4, 'k': 7, 'cost': 66}, {'i': 10, 'j': 4, 'k': 8, 'cost': 53}, {'i': 10, 'j': 4, 'k': 9, 'cost': 36}, {'i': 10, 'j': 4, 'k': 10, 'cost': 64}, {'i': 10, 'j': 5, 'k': 1, 'cost': 74}, {'i': 10, 'j': 5, 'k': 2, 'cost': 90}, {'i': 10, 'j': 5, 'k': 3, 'cost': 14}, {'i': 10, 'j': 5, 'k': 4, 'cost': 74}, {'i': 10, 'j': 5, 'k': 5, 'cost': 8}, {'i': 10, 'j': 5, 'k': 6, 'cost': 85}, {'i': 10, 'j': 5, 'k': 7, 'cost': 12}, {'i': 10, 'j': 5, 'k': 8, 'cost': 34}, {'i': 10, 'j': 5, 'k': 9, 'cost': 23}, {'i': 10, 'j': 5, 'k': 10, 'cost': 95}, {'i': 10, 'j': 6, 'k': 1, 'cost': 10}, {'i': 10, 'j': 6, 'k': 2, 'cost': 6}, {'i': 10, 'j': 6, 'k': 3, 'cost': 11}, {'i': 10, 'j': 6, 'k': 4, 'cost': 81}, {'i': 10, 'j': 6, 'k': 5, 'cost': 60}, {'i': 10, 'j': 6, 'k': 6, 'cost': 8}, {'i': 10, 'j': 6, 'k': 7, 'cost': 54}, {'i': 10, 'j': 6, 'k': 8, 'cost': 29}, {'i': 10, 'j': 6, 'k': 9, 'cost': 97}, {'i': 10, 'j': 6, 'k': 10, 'cost': 56}, {'i': 10, 'j': 7, 'k': 1, 'cost': 27}, {'i': 10, 'j': 7, 'k': 2, 'cost': 40}, {'i': 10, 'j': 7, 'k': 3, 'cost': 47}, {'i': 10, 'j': 7, 'k': 4, 'cost': 42}, {'i': 10, 'j': 7, 'k': 5, 'cost': 12}, {'i': 10, 'j': 7, 'k': 6, 'cost': 21}, {'i': 10, 'j': 7, 'k': 7, 'cost': 64}, {'i': 10, 'j': 7, 'k': 8, 'cost': 50}, {'i': 10, 'j': 7, 'k': 9, 'cost': 86}, {'i': 10, 'j': 7, 'k': 10, 'cost': 4}, {'i': 10, 'j': 8, 'k': 1, 'cost': 8}, {'i': 10, 'j': 8, 'k': 2, 'cost': 16}, {'i': 10, 'j': 8, 'k': 3, 'cost': 30}, {'i': 10, 'j': 8, 'k': 4, 'cost': 16}, {'i': 10, 'j': 8, 'k': 5, 'cost': 98}, {'i': 10, 'j': 8, 'k': 6, 'cost': 35}, {'i': 10, 'j': 8, 'k': 7, 'cost': 75}, {'i': 10, 'j': 8, 'k': 8, 'cost': 44}, {'i': 10, 'j': 8, 'k': 9, 'cost': 54}, {'i': 10, 'j': 8, 'k': 10, 'cost': 8}, {'i': 10, 'j': 9, 'k': 1, 'cost': 91}, {'i': 10, 'j': 9, 'k': 2, 'cost': 64}, {'i': 10, 'j': 9, 'k': 3, 'cost': 14}, {'i': 10, 'j': 9, 'k': 4, 'cost': 99}, {'i': 10, 'j': 9, 'k': 5, 'cost': 29}, {'i': 10, 'j': 9, 'k': 6, 'cost': 13}, {'i': 10, 'j': 9, 'k': 7, 'cost': 48}, {'i': 10, 'j': 9, 'k': 8, 'cost': 68}, {'i': 10, 'j': 9, 'k': 9, 'cost': 93}, {'i': 10, 'j': 9, 'k': 10, 'cost': 97}, {'i': 10, 'j': 10, 'k': 1, 'cost': 71}, {'i': 10, 'j': 10, 'k': 2, 'cost': 6}, {'i': 10, 'j': 10, 'k': 3, 'cost': 8}, {'i': 10, 'j': 10, 'k': 4, 'cost': 95}, {'i': 10, 'j': 10, 'k': 5, 'cost': 87}, {'i': 10, 'j': 10, 'k': 6, 'cost': 37}, {'i': 10, 'j': 10, 'k': 7, 'cost': 40}, {'i': 10, 'j': 10, 'k': 8, 'cost': 7}, {'i': 10, 'j': 10, 'k': 9, 'cost': 34}, {'i': 10, 'j': 10, 'k': 10, 'cost': 56}]}","[[1, 9, 9], [2, 8, 8], [3, 1, 1], [4, 5, 5], [5, 2, 10], [6, 3, 3], [7, 10, 6], [8, 7, 7], [9, 4, 4], [10, 6, 2]]",29,csv,1
+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.
+
+# number_of_patients=11
+# patient_nurse_room_ids=A, B, C, D, E, F, G, H, I, J, K
+
+# 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 | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 50 | 58 | 65 | 3 | 58 | 37 | 43 | 64 | 43 | 92 | 85 |
+| B | 8 | 24 | 81 | 75 | 50 | 24 | 26 | 67 | 29 | 4 | 16 |
+| C | 22 | 94 | 2 | 81 | 30 | 40 | 21 | 55 | 36 | 56 | 67 |
+| D | 14 | 97 | 15 | 52 | 60 | 46 | 35 | 14 | 25 | 35 | 35 |
+| E | 75 | 24 | 37 | 81 | 25 | 3 | 46 | 69 | 80 | 3 | 88 |
+| F | 27 | 70 | 92 | 75 | 80 | 45 | 3 | 91 | 73 | 86 | 23 |
+| G | 42 | 69 | 53 | 0 | 14 | 73 | 98 | 26 | 25 | 0 | 11 |
+| H | 43 | 72 | 42 | 93 | 23 | 91 | 1 | 72 | 5 | 28 | 57 |
+| I | 84 | 97 | 19 | 6 | 38 | 58 | 89 | 69 | 81 | 10 | 18 |
+| J | 76 | 55 | 12 | 20 | 76 | 94 | 4 | 20 | 3 | 3 | 18 |
+| K | 20 | 15 | 28 | 97 | 24 | 60 | 25 | 49 | 70 | 85 | 12 |
+
+## patient_id=B
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 84 | 79 | 12 | 72 | 82 | 47 | 85 | 8 | 30 | 27 | 21 |
+| B | 88 | 70 | 87 | 43 | 25 | 0 | 20 | 80 | 51 | 1 | 81 |
+| C | 52 | 6 | 52 | 49 | 10 | 18 | 90 | 88 | 86 | 82 | 14 |
+| D | 66 | 65 | 59 | 96 | 90 | 5 | 19 | 69 | 11 | 31 | 82 |
+| E | 97 | 69 | 51 | 40 | 34 | 53 | 42 | 24 | 1 | 62 | 85 |
+| F | 95 | 17 | 47 | 66 | 14 | 54 | 34 | 3 | 74 | 27 | 90 |
+| G | 55 | 45 | 32 | 74 | 64 | 9 | 98 | 4 | 4 | 97 | 25 |
+| H | 85 | 86 | 4 | 52 | 75 | 58 | 53 | 53 | 61 | 97 | 97 |
+| I | 59 | 12 | 8 | 3 | 9 | 3 | 34 | 64 | 55 | 87 | 26 |
+| J | 73 | 31 | 35 | 58 | 65 | 69 | 47 | 33 | 22 | 20 | 96 |
+| K | 26 | 11 | 20 | 66 | 1 | 9 | 34 | 85 | 14 | 3 | 24 |
+
+## patient_id=C
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 66 | 77 | 27 | 11 | 88 | 92 | 48 | 49 | 31 | 91 | 75 |
+| B | 15 | 81 | 37 | 76 | 21 | 26 | 64 | 11 | 24 | 72 | 87 |
+| C | 52 | 74 | 14 | 69 | 83 | 50 | 83 | 45 | 67 | 45 | 8 |
+| D | 43 | 36 | 90 | 86 | 18 | 9 | 43 | 79 | 7 | 68 | 19 |
+| E | 86 | 85 | 43 | 5 | 18 | 99 | 42 | 8 | 63 | 3 | 34 |
+| F | 42 | 7 | 81 | 27 | 2 | 53 | 91 | 5 | 1 | 27 | 23 |
+| G | 72 | 10 | 64 | 77 | 33 | 3 | 76 | 84 | 9 | 66 | 48 |
+| H | 58 | 59 | 66 | 30 | 76 | 33 | 31 | 14 | 54 | 72 | 85 |
+| I | 88 | 54 | 80 | 7 | 80 | 4 | 53 | 27 | 80 | 78 | 21 |
+| J | 66 | 47 | 70 | 61 | 42 | 45 | 55 | 80 | 37 | 87 | 77 |
+| K | 30 | 2 | 31 | 22 | 69 | 42 | 17 | 49 | 28 | 16 | 4 |
+
+## patient_id=D
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 46 | 29 | 39 | 90 | 77 | 35 | 68 | 16 | 81 | 69 | 25 |
+| B | 71 | 75 | 8 | 28 | 97 | 96 | 9 | 84 | 91 | 55 | 23 |
+| C | 4 | 46 | 70 | 28 | 23 | 78 | 78 | 52 | 68 | 38 | 7 |
+| D | 5 | 77 | 15 | 15 | 77 | 51 | 16 | 34 | 27 | 88 | 47 |
+| E | 78 | 63 | 35 | 41 | 44 | 71 | 74 | 29 | 25 | 50 | 20 |
+| F | 85 | 83 | 30 | 66 | 33 | 80 | 70 | 58 | 67 | 14 | 41 |
+| G | 99 | 47 | 26 | 69 | 59 | 39 | 48 | 72 | 68 | 33 | 45 |
+| H | 94 | 39 | 58 | 23 | 83 | 23 | 43 | 20 | 89 | 59 | 21 |
+| I | 29 | 61 | 12 | 57 | 21 | 78 | 66 | 43 | 9 | 0 | 6 |
+| J | 66 | 52 | 8 | 39 | 47 | 57 | 63 | 4 | 64 | 34 | 88 |
+| K | 52 | 85 | 58 | 68 | 83 | 67 | 74 | 63 | 63 | 40 | 98 |
+
+## patient_id=E
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 75 | 46 | 94 | 15 | 77 | 67 | 8 | 56 | 53 | 10 | 89 |
+| B | 51 | 16 | 41 | 8 | 61 | 93 | 21 | 76 | 6 | 55 | 39 |
+| C | 71 | 46 | 3 | 41 | 5 | 2 | 22 | 61 | 95 | 8 | 96 |
+| D | 81 | 38 | 79 | 89 | 72 | 56 | 7 | 6 | 96 | 34 | 26 |
+| E | 25 | 1 | 12 | 23 | 63 | 37 | 15 | 70 | 70 | 5 | 82 |
+| F | 23 | 52 | 89 | 9 | 71 | 89 | 82 | 65 | 24 | 55 | 31 |
+| G | 92 | 30 | 17 | 10 | 21 | 49 | 87 | 8 | 74 | 22 | 99 |
+| H | 19 | 23 | 43 | 50 | 33 | 93 | 75 | 85 | 10 | 6 | 60 |
+| I | 23 | 10 | 76 | 40 | 54 | 58 | 94 | 48 | 61 | 52 | 45 |
+| J | 41 | 76 | 19 | 85 | 71 | 96 | 58 | 77 | 8 | 44 | 6 |
+| K | 58 | 84 | 71 | 21 | 41 | 13 | 79 | 45 | 55 | 48 | 37 |
+
+## patient_id=F
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 2 | 19 | 6 | 71 | 94 | 34 | 9 | 8 | 79 | 75 | 8 |
+| B | 90 | 17 | 14 | 32 | 69 | 36 | 19 | 35 | 73 | 51 | 51 |
+| C | 8 | 5 | 34 | 28 | 16 | 41 | 23 | 68 | 2 | 72 | 12 |
+| D | 61 | 55 | 56 | 80 | 57 | 59 | 74 | 51 | 55 | 1 | 17 |
+| E | 49 | 2 | 99 | 92 | 95 | 70 | 49 | 21 | 86 | 62 | 10 |
+| F | 79 | 80 | 68 | 85 | 94 | 23 | 47 | 63 | 80 | 25 | 86 |
+| G | 53 | 42 | 94 | 5 | 79 | 23 | 25 | 7 | 21 | 12 | 66 |
+| H | 20 | 26 | 93 | 1 | 24 | 86 | 5 | 79 | 24 | 14 | 11 |
+| I | 1 | 74 | 14 | 75 | 33 | 13 | 29 | 75 | 28 | 84 | 58 |
+| J | 2 | 71 | 72 | 53 | 43 | 75 | 72 | 65 | 94 | 43 | 90 |
+| K | 30 | 55 | 68 | 89 | 94 | 5 | 2 | 5 | 9 | 14 | 12 |
+
+## patient_id=G
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 32 | 67 | 74 | 43 | 78 | 57 | 90 | 50 | 87 | 1 | 58 |
+| B | 1 | 94 | 47 | 75 | 18 | 24 | 78 | 46 | 62 | 50 | 91 |
+| C | 22 | 53 | 53 | 37 | 53 | 35 | 30 | 6 | 35 | 81 | 97 |
+| D | 15 | 12 | 29 | 26 | 45 | 53 | 9 | 37 | 22 | 82 | 71 |
+| E | 74 | 47 | 67 | 42 | 36 | 58 | 43 | 71 | 80 | 47 | 49 |
+| F | 36 | 82 | 54 | 27 | 91 | 18 | 15 | 50 | 8 | 45 | 39 |
+| G | 18 | 97 | 73 | 99 | 84 | 66 | 10 | 69 | 14 | 59 | 73 |
+| H | 95 | 0 | 31 | 4 | 13 | 19 | 30 | 16 | 26 | 53 | 24 |
+| I | 9 | 38 | 30 | 89 | 21 | 85 | 69 | 41 | 39 | 44 | 14 |
+| J | 8 | 6 | 14 | 76 | 64 | 39 | 92 | 2 | 17 | 13 | 24 |
+| K | 17 | 18 | 20 | 25 | 62 | 31 | 31 | 6 | 92 | 96 | 29 |
+
+## patient_id=H
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 52 | 33 | 46 | 34 | 80 | 19 | 8 | 20 | 36 | 60 | 27 |
+| B | 75 | 59 | 67 | 80 | 76 | 7 | 54 | 54 | 89 | 41 | 68 |
+| C | 88 | 45 | 25 | 71 | 29 | 77 | 57 | 32 | 57 | 49 | 56 |
+| D | 48 | 54 | 43 | 21 | 12 | 39 | 74 | 47 | 27 | 34 | 76 |
+| E | 43 | 8 | 75 | 50 | 87 | 35 | 35 | 6 | 76 | 79 | 65 |
+| F | 35 | 80 | 15 | 78 | 89 | 42 | 62 | 89 | 41 | 81 | 13 |
+| G | 74 | 83 | 69 | 94 | 43 | 6 | 20 | 24 | 89 | 91 | 11 |
+| H | 14 | 99 | 31 | 7 | 65 | 13 | 2 | 98 | 49 | 92 | 89 |
+| I | 85 | 94 | 37 | 48 | 98 | 10 | 74 | 1 | 75 | 60 | 9 |
+| J | 1 | 64 | 40 | 15 | 78 | 78 | 40 | 3 | 54 | 86 | 62 |
+| K | 25 | 86 | 78 | 12 | 87 | 73 | 55 | 39 | 98 | 84 | 71 |
+
+## patient_id=I
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 31 | 21 | 41 | 20 | 42 | 91 | 20 | 79 | 66 | 30 | 22 |
+| B | 44 | 3 | 80 | 6 | 68 | 39 | 24 | 97 | 2 | 87 | 68 |
+| C | 48 | 36 | 87 | 67 | 78 | 29 | 35 | 97 | 48 | 98 | 21 |
+| D | 46 | 48 | 99 | 91 | 82 | 35 | 5 | 65 | 53 | 9 | 47 |
+| E | 75 | 23 | 2 | 71 | 32 | 16 | 18 | 72 | 3 | 36 | 96 |
+| F | 48 | 38 | 23 | 93 | 80 | 37 | 63 | 19 | 2 | 87 | 90 |
+| G | 24 | 85 | 21 | 59 | 69 | 31 | 89 | 63 | 28 | 98 | 54 |
+| H | 52 | 84 | 78 | 3 | 7 | 79 | 86 | 53 | 66 | 1 | 41 |
+| I | 86 | 93 | 79 | 72 | 14 | 40 | 72 | 9 | 64 | 44 | 10 |
+| J | 56 | 67 | 9 | 30 | 83 | 13 | 68 | 73 | 63 | 92 | 21 |
+| K | 15 | 2 | 2 | 80 | 95 | 77 | 17 | 15 | 73 | 33 | 89 |
+
+## patient_id=J
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 66 | 30 | 14 | 74 | 94 | 7 | 68 | 26 | 65 | 46 | 32 |
+| B | 82 | 92 | 40 | 14 | 2 | 60 | 8 | 40 | 39 | 25 | 51 |
+| C | 79 | 28 | 59 | 19 | 61 | 52 | 46 | 85 | 21 | 30 | 1 |
+| D | 99 | 89 | 47 | 27 | 54 | 59 | 57 | 60 | 19 | 82 | 51 |
+| E | 69 | 23 | 22 | 17 | 94 | 3 | 75 | 89 | 1 | 44 | 49 |
+| F | 60 | 61 | 13 | 45 | 19 | 46 | 10 | 48 | 80 | 82 | 61 |
+| G | 55 | 92 | 57 | 33 | 76 | 78 | 80 | 41 | 62 | 66 | 17 |
+| H | 46 | 77 | 3 | 16 | 32 | 88 | 36 | 51 | 10 | 50 | 93 |
+| I | 57 | 40 | 29 | 71 | 10 | 23 | 36 | 62 | 83 | 29 | 87 |
+| J | 67 | 95 | 32 | 18 | 68 | 80 | 6 | 92 | 96 | 8 | 21 |
+| K | 68 | 10 | 86 | 81 | 7 | 45 | 4 | 34 | 15 | 59 | 91 |
+
+## patient_id=K
+| nurse_id\room_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 96 | 24 | 49 | 19 | 68 | 15 | 64 | 27 | 34 | 31 | 47 |
+| B | 79 | 46 | 23 | 48 | 61 | 21 | 34 | 46 | 71 | 45 | 80 |
+| C | 58 | 15 | 78 | 98 | 42 | 32 | 52 | 77 | 14 | 64 | 94 |
+| D | 97 | 31 | 91 | 67 | 45 | 93 | 69 | 55 | 69 | 4 | 10 |
+| E | 52 | 52 | 91 | 90 | 55 | 30 | 8 | 4 | 59 | 69 | 17 |
+| F | 81 | 39 | 40 | 11 | 7 | 48 | 36 | 16 | 1 | 90 | 16 |
+| G | 80 | 15 | 60 | 72 | 44 | 10 | 23 | 50 | 2 | 38 | 61 |
+| H | 4 | 74 | 46 | 66 | 81 | 90 | 50 | 18 | 16 | 61 | 82 |
+| I | 98 | 25 | 64 | 80 | 49 | 45 | 32 | 75 | 89 | 41 | 41 |
+| J | 84 | 57 | 73 | 7 | 1 | 49 | 37 | 54 | 73 | 85 | 47 |
+| K | 39 | 55 | 92 | 23 | 3 | 87 | 69 | 37 | 20 | 28 | 99 |
+
+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': [[[50, 58, 65, 3, 58, 37, 43, 64, 43, 92, 85], [8, 24, 81, 75, 50, 24, 26, 67, 29, 4, 16], [22, 94, 2, 81, 30, 40, 21, 55, 36, 56, 67], [14, 97, 15, 52, 60, 46, 35, 14, 25, 35, 35], [75, 24, 37, 81, 25, 3, 46, 69, 80, 3, 88], [27, 70, 92, 75, 80, 45, 3, 91, 73, 86, 23], [42, 69, 53, 0, 14, 73, 98, 26, 25, 0, 11], [43, 72, 42, 93, 23, 91, 1, 72, 5, 28, 57], [84, 97, 19, 6, 38, 58, 89, 69, 81, 10, 18], [76, 55, 12, 20, 76, 94, 4, 20, 3, 3, 18], [20, 15, 28, 97, 24, 60, 25, 49, 70, 85, 12]], [[84, 79, 12, 72, 82, 47, 85, 8, 30, 27, 21], [88, 70, 87, 43, 25, 0, 20, 80, 51, 1, 81], [52, 6, 52, 49, 10, 18, 90, 88, 86, 82, 14], [66, 65, 59, 96, 90, 5, 19, 69, 11, 31, 82], [97, 69, 51, 40, 34, 53, 42, 24, 1, 62, 85], [95, 17, 47, 66, 14, 54, 34, 3, 74, 27, 90], [55, 45, 32, 74, 64, 9, 98, 4, 4, 97, 25], [85, 86, 4, 52, 75, 58, 53, 53, 61, 97, 97], [59, 12, 8, 3, 9, 3, 34, 64, 55, 87, 26], [73, 31, 35, 58, 65, 69, 47, 33, 22, 20, 96], [26, 11, 20, 66, 1, 9, 34, 85, 14, 3, 24]], [[66, 77, 27, 11, 88, 92, 48, 49, 31, 91, 75], [15, 81, 37, 76, 21, 26, 64, 11, 24, 72, 87], [52, 74, 14, 69, 83, 50, 83, 45, 67, 45, 8], [43, 36, 90, 86, 18, 9, 43, 79, 7, 68, 19], [86, 85, 43, 5, 18, 99, 42, 8, 63, 3, 34], [42, 7, 81, 27, 2, 53, 91, 5, 1, 27, 23], [72, 10, 64, 77, 33, 3, 76, 84, 9, 66, 48], [58, 59, 66, 30, 76, 33, 31, 14, 54, 72, 85], [88, 54, 80, 7, 80, 4, 53, 27, 80, 78, 21], [66, 47, 70, 61, 42, 45, 55, 80, 37, 87, 77], [30, 2, 31, 22, 69, 42, 17, 49, 28, 16, 4]], [[46, 29, 39, 90, 77, 35, 68, 16, 81, 69, 25], [71, 75, 8, 28, 97, 96, 9, 84, 91, 55, 23], [4, 46, 70, 28, 23, 78, 78, 52, 68, 38, 7], [5, 77, 15, 15, 77, 51, 16, 34, 27, 88, 47], [78, 63, 35, 41, 44, 71, 74, 29, 25, 50, 20], [85, 83, 30, 66, 33, 80, 70, 58, 67, 14, 41], [99, 47, 26, 69, 59, 39, 48, 72, 68, 33, 45], [94, 39, 58, 23, 83, 23, 43, 20, 89, 59, 21], [29, 61, 12, 57, 21, 78, 66, 43, 9, 0, 6], [66, 52, 8, 39, 47, 57, 63, 4, 64, 34, 88], [52, 85, 58, 68, 83, 67, 74, 63, 63, 40, 98]], [[75, 46, 94, 15, 77, 67, 8, 56, 53, 10, 89], [51, 16, 41, 8, 61, 93, 21, 76, 6, 55, 39], [71, 46, 3, 41, 5, 2, 22, 61, 95, 8, 96], [81, 38, 79, 89, 72, 56, 7, 6, 96, 34, 26], [25, 1, 12, 23, 63, 37, 15, 70, 70, 5, 82], [23, 52, 89, 9, 71, 89, 82, 65, 24, 55, 31], [92, 30, 17, 10, 21, 49, 87, 8, 74, 22, 99], [19, 23, 43, 50, 33, 93, 75, 85, 10, 6, 60], [23, 10, 76, 40, 54, 58, 94, 48, 61, 52, 45], [41, 76, 19, 85, 71, 96, 58, 77, 8, 44, 6], [58, 84, 71, 21, 41, 13, 79, 45, 55, 48, 37]], [[2, 19, 6, 71, 94, 34, 9, 8, 79, 75, 8], [90, 17, 14, 32, 69, 36, 19, 35, 73, 51, 51], [8, 5, 34, 28, 16, 41, 23, 68, 2, 72, 12], [61, 55, 56, 80, 57, 59, 74, 51, 55, 1, 17], [49, 2, 99, 92, 95, 70, 49, 21, 86, 62, 10], [79, 80, 68, 85, 94, 23, 47, 63, 80, 25, 86], [53, 42, 94, 5, 79, 23, 25, 7, 21, 12, 66], [20, 26, 93, 1, 24, 86, 5, 79, 24, 14, 11], [1, 74, 14, 75, 33, 13, 29, 75, 28, 84, 58], [2, 71, 72, 53, 43, 75, 72, 65, 94, 43, 90], [30, 55, 68, 89, 94, 5, 2, 5, 9, 14, 12]], [[32, 67, 74, 43, 78, 57, 90, 50, 87, 1, 58], [1, 94, 47, 75, 18, 24, 78, 46, 62, 50, 91], [22, 53, 53, 37, 53, 35, 30, 6, 35, 81, 97], [15, 12, 29, 26, 45, 53, 9, 37, 22, 82, 71], [74, 47, 67, 42, 36, 58, 43, 71, 80, 47, 49], [36, 82, 54, 27, 91, 18, 15, 50, 8, 45, 39], [18, 97, 73, 99, 84, 66, 10, 69, 14, 59, 73], [95, 0, 31, 4, 13, 19, 30, 16, 26, 53, 24], [9, 38, 30, 89, 21, 85, 69, 41, 39, 44, 14], [8, 6, 14, 76, 64, 39, 92, 2, 17, 13, 24], [17, 18, 20, 25, 62, 31, 31, 6, 92, 96, 29]], [[52, 33, 46, 34, 80, 19, 8, 20, 36, 60, 27], [75, 59, 67, 80, 76, 7, 54, 54, 89, 41, 68], [88, 45, 25, 71, 29, 77, 57, 32, 57, 49, 56], [48, 54, 43, 21, 12, 39, 74, 47, 27, 34, 76], [43, 8, 75, 50, 87, 35, 35, 6, 76, 79, 65], [35, 80, 15, 78, 89, 42, 62, 89, 41, 81, 13], [74, 83, 69, 94, 43, 6, 20, 24, 89, 91, 11], [14, 99, 31, 7, 65, 13, 2, 98, 49, 92, 89], [85, 94, 37, 48, 98, 10, 74, 1, 75, 60, 9], [1, 64, 40, 15, 78, 78, 40, 3, 54, 86, 62], [25, 86, 78, 12, 87, 73, 55, 39, 98, 84, 71]], [[31, 21, 41, 20, 42, 91, 20, 79, 66, 30, 22], [44, 3, 80, 6, 68, 39, 24, 97, 2, 87, 68], [48, 36, 87, 67, 78, 29, 35, 97, 48, 98, 21], [46, 48, 99, 91, 82, 35, 5, 65, 53, 9, 47], [75, 23, 2, 71, 32, 16, 18, 72, 3, 36, 96], [48, 38, 23, 93, 80, 37, 63, 19, 2, 87, 90], [24, 85, 21, 59, 69, 31, 89, 63, 28, 98, 54], [52, 84, 78, 3, 7, 79, 86, 53, 66, 1, 41], [86, 93, 79, 72, 14, 40, 72, 9, 64, 44, 10], [56, 67, 9, 30, 83, 13, 68, 73, 63, 92, 21], [15, 2, 2, 80, 95, 77, 17, 15, 73, 33, 89]], [[66, 30, 14, 74, 94, 7, 68, 26, 65, 46, 32], [82, 92, 40, 14, 2, 60, 8, 40, 39, 25, 51], [79, 28, 59, 19, 61, 52, 46, 85, 21, 30, 1], [99, 89, 47, 27, 54, 59, 57, 60, 19, 82, 51], [69, 23, 22, 17, 94, 3, 75, 89, 1, 44, 49], [60, 61, 13, 45, 19, 46, 10, 48, 80, 82, 61], [55, 92, 57, 33, 76, 78, 80, 41, 62, 66, 17], [46, 77, 3, 16, 32, 88, 36, 51, 10, 50, 93], [57, 40, 29, 71, 10, 23, 36, 62, 83, 29, 87], [67, 95, 32, 18, 68, 80, 6, 92, 96, 8, 21], [68, 10, 86, 81, 7, 45, 4, 34, 15, 59, 91]], [[96, 24, 49, 19, 68, 15, 64, 27, 34, 31, 47], [79, 46, 23, 48, 61, 21, 34, 46, 71, 45, 80], [58, 15, 78, 98, 42, 32, 52, 77, 14, 64, 94], [97, 31, 91, 67, 45, 93, 69, 55, 69, 4, 10], [52, 52, 91, 90, 55, 30, 8, 4, 59, 69, 17], [81, 39, 40, 11, 7, 48, 36, 16, 1, 90, 16], [80, 15, 60, 72, 44, 10, 23, 50, 2, 38, 61], [4, 74, 46, 66, 81, 90, 50, 18, 16, 61, 82], [98, 25, 64, 80, 49, 45, 32, 75, 89, 41, 41], [84, 57, 73, 7, 1, 49, 37, 54, 73, 85, 47], [39, 55, 92, 23, 3, 87, 69, 37, 20, 28, 99]]], 'objective': 18.0}","[[0, 6, 3], [1, 1, 5], [2, 5, 8], [3, 3, 0], [4, 4, 1], [5, 7, 6], [6, 0, 9], [7, 8, 7], [8, 10, 2], [9, 2, 10], [10, 9, 4]]",18.0,"{'problem_type': 'AP3', 'n': 11, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 50}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 58}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 65}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 3}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 58}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 37}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 43}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 64}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 43}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 92}, {'i': 'A', 'j': 'A', 'k': 'K', 'cost': 85}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 8}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 24}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 81}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 75}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 50}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 24}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 26}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 67}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 29}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 4}, {'i': 'A', 'j': 'B', 'k': 'K', 'cost': 16}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 22}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 94}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 2}, {'i': 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10}, {'i': 'K', 'j': 'E', 'k': 'A', 'cost': 52}, {'i': 'K', 'j': 'E', 'k': 'B', 'cost': 52}, {'i': 'K', 'j': 'E', 'k': 'C', 'cost': 91}, {'i': 'K', 'j': 'E', 'k': 'D', 'cost': 90}, {'i': 'K', 'j': 'E', 'k': 'E', 'cost': 55}, {'i': 'K', 'j': 'E', 'k': 'F', 'cost': 30}, {'i': 'K', 'j': 'E', 'k': 'G', 'cost': 8}, {'i': 'K', 'j': 'E', 'k': 'H', 'cost': 4}, {'i': 'K', 'j': 'E', 'k': 'I', 'cost': 59}, {'i': 'K', 'j': 'E', 'k': 'J', 'cost': 69}, {'i': 'K', 'j': 'E', 'k': 'K', 'cost': 17}, {'i': 'K', 'j': 'F', 'k': 'A', 'cost': 81}, {'i': 'K', 'j': 'F', 'k': 'B', 'cost': 39}, {'i': 'K', 'j': 'F', 'k': 'C', 'cost': 40}, {'i': 'K', 'j': 'F', 'k': 'D', 'cost': 11}, {'i': 'K', 'j': 'F', 'k': 'E', 'cost': 7}, {'i': 'K', 'j': 'F', 'k': 'F', 'cost': 48}, {'i': 'K', 'j': 'F', 'k': 'G', 'cost': 36}, {'i': 'K', 'j': 'F', 'k': 'H', 'cost': 16}, {'i': 'K', 'j': 'F', 'k': 'I', 'cost': 1}, {'i': 'K', 'j': 'F', 'k': 'J', 'cost': 90}, {'i': 'K', 'j': 'F', 'k': 'K', 'cost': 16}, {'i': 'K', 'j': 'G', 'k': 'A', 'cost': 80}, {'i': 'K', 'j': 'G', 'k': 'B', 'cost': 15}, {'i': 'K', 'j': 'G', 'k': 'C', 'cost': 60}, {'i': 'K', 'j': 'G', 'k': 'D', 'cost': 72}, {'i': 'K', 'j': 'G', 'k': 'E', 'cost': 44}, {'i': 'K', 'j': 'G', 'k': 'F', 'cost': 10}, {'i': 'K', 'j': 'G', 'k': 'G', 'cost': 23}, {'i': 'K', 'j': 'G', 'k': 'H', 'cost': 50}, {'i': 'K', 'j': 'G', 'k': 'I', 'cost': 2}, {'i': 'K', 'j': 'G', 'k': 'J', 'cost': 38}, {'i': 'K', 'j': 'G', 'k': 'K', 'cost': 61}, {'i': 'K', 'j': 'H', 'k': 'A', 'cost': 4}, {'i': 'K', 'j': 'H', 'k': 'B', 'cost': 74}, {'i': 'K', 'j': 'H', 'k': 'C', 'cost': 46}, {'i': 'K', 'j': 'H', 'k': 'D', 'cost': 66}, {'i': 'K', 'j': 'H', 'k': 'E', 'cost': 81}, {'i': 'K', 'j': 'H', 'k': 'F', 'cost': 90}, {'i': 'K', 'j': 'H', 'k': 'G', 'cost': 50}, {'i': 'K', 'j': 'H', 'k': 'H', 'cost': 18}, {'i': 'K', 'j': 'H', 'k': 'I', 'cost': 16}, {'i': 'K', 'j': 'H', 'k': 'J', 'cost': 61}, {'i': 'K', 'j': 'H', 'k': 'K', 'cost': 82}, {'i': 'K', 'j': 'I', 'k': 'A', 'cost': 98}, {'i': 'K', 'j': 'I', 'k': 'B', 'cost': 25}, {'i': 'K', 'j': 'I', 'k': 'C', 'cost': 64}, {'i': 'K', 'j': 'I', 'k': 'D', 'cost': 80}, {'i': 'K', 'j': 'I', 'k': 'E', 'cost': 49}, {'i': 'K', 'j': 'I', 'k': 'F', 'cost': 45}, {'i': 'K', 'j': 'I', 'k': 'G', 'cost': 32}, {'i': 'K', 'j': 'I', 'k': 'H', 'cost': 75}, {'i': 'K', 'j': 'I', 'k': 'I', 'cost': 89}, {'i': 'K', 'j': 'I', 'k': 'J', 'cost': 41}, {'i': 'K', 'j': 'I', 'k': 'K', 'cost': 41}, {'i': 'K', 'j': 'J', 'k': 'A', 'cost': 84}, {'i': 'K', 'j': 'J', 'k': 'B', 'cost': 57}, {'i': 'K', 'j': 'J', 'k': 'C', 'cost': 73}, {'i': 'K', 'j': 'J', 'k': 'D', 'cost': 7}, {'i': 'K', 'j': 'J', 'k': 'E', 'cost': 1}, {'i': 'K', 'j': 'J', 'k': 'F', 'cost': 49}, {'i': 'K', 'j': 'J', 'k': 'G', 'cost': 37}, {'i': 'K', 'j': 'J', 'k': 'H', 'cost': 54}, {'i': 'K', 'j': 'J', 'k': 'I', 'cost': 73}, {'i': 'K', 'j': 'J', 'k': 'J', 'cost': 85}, {'i': 'K', 'j': 'J', 'k': 'K', 'cost': 47}, {'i': 'K', 'j': 'K', 'k': 'A', 'cost': 39}, {'i': 'K', 'j': 'K', 'k': 'B', 'cost': 55}, {'i': 'K', 'j': 'K', 'k': 'C', 'cost': 92}, {'i': 'K', 'j': 'K', 'k': 'D', 'cost': 23}, {'i': 'K', 'j': 'K', 'k': 'E', 'cost': 3}, {'i': 'K', 'j': 'K', 'k': 'F', 'cost': 87}, {'i': 'K', 'j': 'K', 'k': 'G', 'cost': 69}, {'i': 'K', 'j': 'K', 'k': 'H', 'cost': 37}, {'i': 'K', 'j': 'K', 'k': 'I', 'cost': 20}, {'i': 'K', 'j': 'K', 'k': 'J', 'cost': 28}, {'i': 'K', 'j': 'K', 'k': 'K', 'cost': 99}]}","[['A', 'G', 'D'], ['B', 'B', 'F'], ['C', 'F', 'I'], ['D', 'D', 'A'], ['E', 'E', 'B'], ['F', 'H', 'G'], ['G', 'A', 'J'], ['H', 'I', 'H'], ['I', 'K', 'C'], ['J', 'C', 'K'], ['K', 'J', 'E']]",30,csv,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 9 songs, 9 musicians, and 9 instruments labeled 0, 1, 2, 3, 4, 5, 6, 7, 8.
+
+*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=0
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 80 | 36 | 82 | 34 | 2 | 9 | 23 | 73 | 15 |
+| 1 | 88 | 93 | 26 | 87 | 96 | 78 | 71 | 48 | 87 |
+| 2 | 34 | 92 | 66 | 16 | 95 | 71 | 47 | 2 | 35 |
+| 3 | 80 | 17 | 49 | 72 | 30 | 10 | 69 | 10 | 66 |
+| 4 | 41 | 94 | 41 | 57 | 89 | 53 | 26 | 64 | 82 |
+| 5 | 85 | 32 | 79 | 11 | 54 | 6 | 58 | 42 | 54 |
+| 6 | 85 | 96 | 92 | 41 | 68 | 43 | 77 | 0 | 63 |
+| 7 | 1 | 39 | 45 | 18 | 83 | 29 | 7 | 41 | 15 |
+| 8 | 25 | 86 | 58 | 28 | 35 | 7 | 74 | 70 | 30 |
+
+## song_id=1
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 46 | 60 | 43 | 12 | 74 | 30 | 96 | 46 | 14 |
+| 1 | 87 | 26 | 29 | 70 | 87 | 14 | 42 | 52 | 68 |
+| 2 | 26 | 3 | 18 | 14 | 70 | 2 | 30 | 61 | 97 |
+| 3 | 83 | 14 | 63 | 85 | 87 | 10 | 5 | 39 | 9 |
+| 4 | 75 | 39 | 52 | 48 | 56 | 76 | 39 | 90 | 69 |
+| 5 | 70 | 33 | 47 | 52 | 36 | 54 | 35 | 71 | 14 |
+| 6 | 14 | 22 | 43 | 51 | 92 | 58 | 30 | 33 | 56 |
+| 7 | 26 | 51 | 13 | 44 | 47 | 66 | 68 | 48 | 87 |
+| 8 | 33 | 89 | 36 | 72 | 59 | 82 | 47 | 70 | 23 |
+
+## song_id=2
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 48 | 58 | 29 | 21 | 92 | 70 | 85 | 36 | 76 |
+| 1 | 30 | 76 | 88 | 52 | 46 | 39 | 19 | 85 | 66 |
+| 2 | 96 | 39 | 62 | 79 | 43 | 13 | 87 | 54 | 9 |
+| 3 | 39 | 14 | 96 | 85 | 35 | 39 | 37 | 8 | 50 |
+| 4 | 0 | 30 | 96 | 55 | 66 | 55 | 54 | 61 | 59 |
+| 5 | 20 | 6 | 52 | 94 | 65 | 6 | 35 | 81 | 99 |
+| 6 | 99 | 75 | 88 | 82 | 64 | 0 | 68 | 63 | 20 |
+| 7 | 60 | 4 | 89 | 91 | 32 | 75 | 90 | 76 | 63 |
+| 8 | 6 | 95 | 26 | 73 | 41 | 85 | 4 | 1 | 3 |
+
+## song_id=3
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 67 | 93 | 98 | 77 | 4 | 91 | 60 | 79 | 19 |
+| 1 | 0 | 68 | 11 | 45 | 79 | 72 | 30 | 48 | 45 |
+| 2 | 11 | 92 | 9 | 0 | 98 | 32 | 24 | 12 | 78 |
+| 3 | 36 | 49 | 33 | 74 | 21 | 71 | 89 | 5 | 35 |
+| 4 | 41 | 58 | 30 | 22 | 53 | 45 | 46 | 66 | 27 |
+| 5 | 65 | 86 | 29 | 90 | 7 | 87 | 50 | 54 | 31 |
+| 6 | 15 | 69 | 73 | 57 | 40 | 6 | 36 | 47 | 57 |
+| 7 | 96 | 56 | 31 | 20 | 84 | 98 | 73 | 28 | 11 |
+| 8 | 54 | 77 | 30 | 94 | 59 | 75 | 91 | 43 | 72 |
+
+## song_id=4
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 56 | 39 | 0 | 55 | 13 | 12 | 39 | 78 | 27 |
+| 1 | 74 | 96 | 0 | 29 | 77 | 55 | 27 | 35 | 24 |
+| 2 | 60 | 19 | 73 | 32 | 2 | 50 | 37 | 78 | 51 |
+| 3 | 1 | 93 | 18 | 14 | 65 | 30 | 37 | 71 | 38 |
+| 4 | 39 | 95 | 17 | 2 | 40 | 80 | 94 | 14 | 61 |
+| 5 | 73 | 52 | 35 | 2 | 58 | 60 | 98 | 17 | 65 |
+| 6 | 87 | 16 | 51 | 89 | 38 | 60 | 65 | 48 | 37 |
+| 7 | 91 | 54 | 25 | 16 | 14 | 7 | 23 | 67 | 76 |
+| 8 | 50 | 67 | 22 | 46 | 90 | 85 | 64 | 23 | 42 |
+
+## song_id=5
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 87 | 72 | 74 | 84 | 53 | 33 | 1 | 18 | 61 |
+| 1 | 54 | 81 | 11 | 35 | 80 | 23 | 7 | 40 | 79 |
+| 2 | 37 | 90 | 89 | 98 | 83 | 38 | 50 | 54 | 93 |
+| 3 | 96 | 90 | 14 | 24 | 41 | 49 | 19 | 21 | 4 |
+| 4 | 26 | 69 | 3 | 21 | 24 | 2 | 25 | 70 | 93 |
+| 5 | 55 | 85 | 15 | 20 | 30 | 60 | 99 | 6 | 18 |
+| 6 | 75 | 94 | 8 | 10 | 45 | 46 | 27 | 33 | 22 |
+| 7 | 15 | 80 | 71 | 93 | 37 | 18 | 3 | 5 | 11 |
+| 8 | 38 | 78 | 56 | 35 | 40 | 2 | 13 | 71 | 83 |
+
+## song_id=6
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 80 | 93 | 36 | 12 | 74 | 41 | 98 | 6 | 90 |
+| 1 | 2 | 82 | 81 | 36 | 23 | 0 | 90 | 30 | 22 |
+| 2 | 9 | 66 | 60 | 82 | 62 | 9 | 83 | 40 | 31 |
+| 3 | 97 | 36 | 42 | 85 | 75 | 19 | 35 | 61 | 7 |
+| 4 | 13 | 63 | 55 | 77 | 53 | 62 | 21 | 23 | 62 |
+| 5 | 91 | 75 | 48 | 37 | 22 | 8 | 33 | 93 | 65 |
+| 6 | 18 | 95 | 89 | 83 | 92 | 23 | 75 | 36 | 0 |
+| 7 | 94 | 40 | 0 | 90 | 8 | 92 | 45 | 34 | 47 |
+| 8 | 36 | 90 | 75 | 1 | 20 | 71 | 5 | 20 | 97 |
+
+## song_id=7
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 29 | 79 | 38 | 89 | 88 | 17 | 52 | 82 | 29 |
+| 1 | 66 | 16 | 3 | 58 | 42 | 35 | 42 | 52 | 95 |
+| 2 | 3 | 30 | 33 | 35 | 32 | 47 | 8 | 74 | 4 |
+| 3 | 96 | 3 | 15 | 48 | 55 | 63 | 55 | 7 | 90 |
+| 4 | 3 | 50 | 7 | 91 | 79 | 75 | 73 | 71 | 67 |
+| 5 | 88 | 6 | 81 | 82 | 38 | 78 | 25 | 92 | 71 |
+| 6 | 89 | 61 | 70 | 38 | 97 | 97 | 69 | 85 | 67 |
+| 7 | 62 | 22 | 73 | 73 | 47 | 26 | 90 | 79 | 21 |
+| 8 | 99 | 56 | 29 | 74 | 9 | 62 | 72 | 88 | 89 |
+
+## song_id=8
+| musician_id\instrument_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+|---|---|---|---|---|---|---|---|---|---|
+| 0 | 8 | 9 | 66 | 88 | 13 | 61 | 52 | 92 | 42 |
+| 1 | 76 | 74 | 48 | 33 | 29 | 37 | 5 | 1 | 42 |
+| 2 | 31 | 89 | 31 | 3 | 23 | 47 | 30 | 84 | 77 |
+| 3 | 44 | 23 | 30 | 14 | 50 | 88 | 64 | 61 | 20 |
+| 4 | 33 | 16 | 82 | 49 | 22 | 98 | 89 | 97 | 85 |
+| 5 | 86 | 0 | 40 | 60 | 62 | 1 | 16 | 29 | 30 |
+| 6 | 84 | 13 | 48 | 38 | 9 | 43 | 85 | 3 | 62 |
+| 7 | 84 | 55 | 32 | 27 | 36 | 32 | 84 | 3 | 87 |
+| 8 | 79 | 13 | 46 | 44 | 92 | 47 | 63 | 16 | 64 |
+
+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': [[[80, 36, 82, 34, 2, 9, 23, 73, 15], [88, 93, 26, 87, 96, 78, 71, 48, 87], [34, 92, 66, 16, 95, 71, 47, 2, 35], [80, 17, 49, 72, 30, 10, 69, 10, 66], [41, 94, 41, 57, 89, 53, 26, 64, 82], [85, 32, 79, 11, 54, 6, 58, 42, 54], [85, 96, 92, 41, 68, 43, 77, 0, 63], [1, 39, 45, 18, 83, 29, 7, 41, 15], [25, 86, 58, 28, 35, 7, 74, 70, 30]], [[46, 60, 43, 12, 74, 30, 96, 46, 14], [87, 26, 29, 70, 87, 14, 42, 52, 68], [26, 3, 18, 14, 70, 2, 30, 61, 97], [83, 14, 63, 85, 87, 10, 5, 39, 9], [75, 39, 52, 48, 56, 76, 39, 90, 69], [70, 33, 47, 52, 36, 54, 35, 71, 14], [14, 22, 43, 51, 92, 58, 30, 33, 56], [26, 51, 13, 44, 47, 66, 68, 48, 87], [33, 89, 36, 72, 59, 82, 47, 70, 23]], [[48, 58, 29, 21, 92, 70, 85, 36, 76], [30, 76, 88, 52, 46, 39, 19, 85, 66], [96, 39, 62, 79, 43, 13, 87, 54, 9], [39, 14, 96, 85, 35, 39, 37, 8, 50], [0, 30, 96, 55, 66, 55, 54, 61, 59], [20, 6, 52, 94, 65, 6, 35, 81, 99], [99, 75, 88, 82, 64, 0, 68, 63, 20], [60, 4, 89, 91, 32, 75, 90, 76, 63], [6, 95, 26, 73, 41, 85, 4, 1, 3]], [[67, 93, 98, 77, 4, 91, 60, 79, 19], [0, 68, 11, 45, 79, 72, 30, 48, 45], [11, 92, 9, 0, 98, 32, 24, 12, 78], [36, 49, 33, 74, 21, 71, 89, 5, 35], [41, 58, 30, 22, 53, 45, 46, 66, 27], [65, 86, 29, 90, 7, 87, 50, 54, 31], [15, 69, 73, 57, 40, 6, 36, 47, 57], [96, 56, 31, 20, 84, 98, 73, 28, 11], [54, 77, 30, 94, 59, 75, 91, 43, 72]], [[56, 39, 0, 55, 13, 12, 39, 78, 27], [74, 96, 0, 29, 77, 55, 27, 35, 24], [60, 19, 73, 32, 2, 50, 37, 78, 51], [1, 93, 18, 14, 65, 30, 37, 71, 38], [39, 95, 17, 2, 40, 80, 94, 14, 61], [73, 52, 35, 2, 58, 60, 98, 17, 65], [87, 16, 51, 89, 38, 60, 65, 48, 37], [91, 54, 25, 16, 14, 7, 23, 67, 76], [50, 67, 22, 46, 90, 85, 64, 23, 42]], [[87, 72, 74, 84, 53, 33, 1, 18, 61], [54, 81, 11, 35, 80, 23, 7, 40, 79], [37, 90, 89, 98, 83, 38, 50, 54, 93], [96, 90, 14, 24, 41, 49, 19, 21, 4], [26, 69, 3, 21, 24, 2, 25, 70, 93], [55, 85, 15, 20, 30, 60, 99, 6, 18], [75, 94, 8, 10, 45, 46, 27, 33, 22], [15, 80, 71, 93, 37, 18, 3, 5, 11], [38, 78, 56, 35, 40, 2, 13, 71, 83]], [[80, 93, 36, 12, 74, 41, 98, 6, 90], [2, 82, 81, 36, 23, 0, 90, 30, 22], [9, 66, 60, 82, 62, 9, 83, 40, 31], [97, 36, 42, 85, 75, 19, 35, 61, 7], [13, 63, 55, 77, 53, 62, 21, 23, 62], [91, 75, 48, 37, 22, 8, 33, 93, 65], [18, 95, 89, 83, 92, 23, 75, 36, 0], [94, 40, 0, 90, 8, 92, 45, 34, 47], [36, 90, 75, 1, 20, 71, 5, 20, 97]], [[29, 79, 38, 89, 88, 17, 52, 82, 29], [66, 16, 3, 58, 42, 35, 42, 52, 95], [3, 30, 33, 35, 32, 47, 8, 74, 4], [96, 3, 15, 48, 55, 63, 55, 7, 90], [3, 50, 7, 91, 79, 75, 73, 71, 67], [88, 6, 81, 82, 38, 78, 25, 92, 71], [89, 61, 70, 38, 97, 97, 69, 85, 67], [62, 22, 73, 73, 47, 26, 90, 79, 21], [99, 56, 29, 74, 9, 62, 72, 88, 89]], [[8, 9, 66, 88, 13, 61, 52, 92, 42], [76, 74, 48, 33, 29, 37, 5, 1, 42], [31, 89, 31, 3, 23, 47, 30, 84, 77], [44, 23, 30, 14, 50, 88, 64, 61, 20], [33, 16, 82, 49, 22, 98, 89, 97, 85], [86, 0, 40, 60, 62, 1, 16, 29, 30], [84, 13, 48, 38, 9, 43, 85, 3, 62], [84, 55, 32, 27, 36, 32, 84, 3, 87], [79, 13, 46, 44, 92, 47, 63, 16, 64]]], 'objective': 18.0}","[[0, 0, 4], [1, 3, 6], [2, 4, 0], [3, 2, 3], [4, 1, 2], [5, 8, 5], [6, 6, 8], [7, 5, 1], [8, 7, 7]]",18.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 80}, {'i': 0, 'j': 0, 'k': 1, 'cost': 36}, {'i': 0, 'j': 0, 'k': 2, 'cost': 82}, {'i': 0, 'j': 0, 'k': 3, 'cost': 34}, {'i': 0, 'j': 0, 'k': 4, 'cost': 2}, {'i': 0, 'j': 0, 'k': 5, 'cost': 9}, {'i': 0, 'j': 0, 'k': 6, 'cost': 23}, {'i': 0, 'j': 0, 'k': 7, 'cost': 73}, {'i': 0, 'j': 0, 'k': 8, 'cost': 15}, {'i': 0, 'j': 1, 'k': 0, 'cost': 88}, {'i': 0, 'j': 1, 'k': 1, 'cost': 93}, {'i': 0, 'j': 1, 'k': 2, 'cost': 26}, {'i': 0, 'j': 1, 'k': 3, 'cost': 87}, {'i': 0, 'j': 1, 'k': 4, 'cost': 96}, {'i': 0, 'j': 1, 'k': 5, 'cost': 78}, {'i': 0, 'j': 1, 'k': 6, 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'j': 0, 'k': 0, 'cost': 8}, {'i': 8, 'j': 0, 'k': 1, 'cost': 9}, {'i': 8, 'j': 0, 'k': 2, 'cost': 66}, {'i': 8, 'j': 0, 'k': 3, 'cost': 88}, {'i': 8, 'j': 0, 'k': 4, 'cost': 13}, {'i': 8, 'j': 0, 'k': 5, 'cost': 61}, {'i': 8, 'j': 0, 'k': 6, 'cost': 52}, {'i': 8, 'j': 0, 'k': 7, 'cost': 92}, {'i': 8, 'j': 0, 'k': 8, 'cost': 42}, {'i': 8, 'j': 1, 'k': 0, 'cost': 76}, {'i': 8, 'j': 1, 'k': 1, 'cost': 74}, {'i': 8, 'j': 1, 'k': 2, 'cost': 48}, {'i': 8, 'j': 1, 'k': 3, 'cost': 33}, {'i': 8, 'j': 1, 'k': 4, 'cost': 29}, {'i': 8, 'j': 1, 'k': 5, 'cost': 37}, {'i': 8, 'j': 1, 'k': 6, 'cost': 5}, {'i': 8, 'j': 1, 'k': 7, 'cost': 1}, {'i': 8, 'j': 1, 'k': 8, 'cost': 42}, {'i': 8, 'j': 2, 'k': 0, 'cost': 31}, {'i': 8, 'j': 2, 'k': 1, 'cost': 89}, {'i': 8, 'j': 2, 'k': 2, 'cost': 31}, {'i': 8, 'j': 2, 'k': 3, 'cost': 3}, {'i': 8, 'j': 2, 'k': 4, 'cost': 23}, {'i': 8, 'j': 2, 'k': 5, 'cost': 47}, {'i': 8, 'j': 2, 'k': 6, 'cost': 30}, {'i': 8, 'j': 2, 'k': 7, 'cost': 84}, {'i': 8, 'j': 2, 'k': 8, 'cost': 77}, {'i': 8, 'j': 3, 'k': 0, 'cost': 44}, {'i': 8, 'j': 3, 'k': 1, 'cost': 23}, {'i': 8, 'j': 3, 'k': 2, 'cost': 30}, {'i': 8, 'j': 3, 'k': 3, 'cost': 14}, {'i': 8, 'j': 3, 'k': 4, 'cost': 50}, {'i': 8, 'j': 3, 'k': 5, 'cost': 88}, {'i': 8, 'j': 3, 'k': 6, 'cost': 64}, {'i': 8, 'j': 3, 'k': 7, 'cost': 61}, {'i': 8, 'j': 3, 'k': 8, 'cost': 20}, {'i': 8, 'j': 4, 'k': 0, 'cost': 33}, {'i': 8, 'j': 4, 'k': 1, 'cost': 16}, {'i': 8, 'j': 4, 'k': 2, 'cost': 82}, {'i': 8, 'j': 4, 'k': 3, 'cost': 49}, {'i': 8, 'j': 4, 'k': 4, 'cost': 22}, {'i': 8, 'j': 4, 'k': 5, 'cost': 98}, {'i': 8, 'j': 4, 'k': 6, 'cost': 89}, {'i': 8, 'j': 4, 'k': 7, 'cost': 97}, {'i': 8, 'j': 4, 'k': 8, 'cost': 85}, {'i': 8, 'j': 5, 'k': 0, 'cost': 86}, {'i': 8, 'j': 5, 'k': 1, 'cost': 0}, {'i': 8, 'j': 5, 'k': 2, 'cost': 40}, {'i': 8, 'j': 5, 'k': 3, 'cost': 60}, {'i': 8, 'j': 5, 'k': 4, 'cost': 62}, {'i': 8, 'j': 5, 'k': 5, 'cost': 1}, {'i': 8, 'j': 5, 'k': 6, 'cost': 16}, {'i': 8, 'j': 5, 'k': 7, 'cost': 29}, {'i': 8, 'j': 5, 'k': 8, 'cost': 30}, {'i': 8, 'j': 6, 'k': 0, 'cost': 84}, {'i': 8, 'j': 6, 'k': 1, 'cost': 13}, {'i': 8, 'j': 6, 'k': 2, 'cost': 48}, {'i': 8, 'j': 6, 'k': 3, 'cost': 38}, {'i': 8, 'j': 6, 'k': 4, 'cost': 9}, {'i': 8, 'j': 6, 'k': 5, 'cost': 43}, {'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': 0, 'cost': 84}, {'i': 8, 'j': 7, 'k': 1, 'cost': 55}, {'i': 8, 'j': 7, 'k': 2, 'cost': 32}, {'i': 8, 'j': 7, 'k': 3, 'cost': 27}, {'i': 8, 'j': 7, 'k': 4, 'cost': 36}, {'i': 8, 'j': 7, 'k': 5, 'cost': 32}, {'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': 0, 'cost': 79}, {'i': 8, 'j': 8, 'k': 1, 'cost': 13}, {'i': 8, 'j': 8, 'k': 2, 'cost': 46}, {'i': 8, 'j': 8, 'k': 3, 'cost': 44}, {'i': 8, 'j': 8, 'k': 4, 'cost': 92}, {'i': 8, 'j': 8, 'k': 5, 'cost': 47}, {'i': 8, 'j': 8, 'k': 6, 'cost': 63}, {'i': 8, 'j': 8, 'k': 7, 'cost': 16}, {'i': 8, 'j': 8, 'k': 8, 'cost': 64}]}","[[0, 0, 4], [1, 3, 6], [2, 4, 0], [3, 2, 3], [4, 1, 2], [5, 8, 5], [6, 6, 8], [7, 5, 1], [8, 7, 7]]",31,markdown_table,0
+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.
+
+There are 9 commissions, labeled A, B, C, D, E, F, G, H, I.
+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=A
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 39 | 95 | 27 | 30 | 0 | 28 | 24 | 36 | 11 |
+| B | 93 | 22 | 4 | 21 | 5 | 50 | 51 | 8 | 15 |
+| C | 17 | 94 | 53 | 96 | 70 | 30 | 33 | 10 | 62 |
+| D | 90 | 95 | 31 | 75 | 87 | 97 | 52 | 19 | 73 |
+| E | 29 | 62 | 0 | 84 | 41 | 63 | 1 | 60 | 52 |
+| F | 2 | 88 | 91 | 83 | 45 | 36 | 12 | 76 | 35 |
+| G | 25 | 15 | 75 | 51 | 71 | 77 | 9 | 91 | 92 |
+| H | 84 | 26 | 49 | 41 | 79 | 94 | 70 | 18 | 32 |
+| I | 26 | 88 | 18 | 64 | 93 | 83 | 93 | 97 | 14 |
+
+## commission_id=B
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 72 | 46 | 46 | 25 | 2 | 90 | 72 | 68 | 12 |
+| B | 63 | 25 | 16 | 32 | 31 | 91 | 83 | 56 | 40 |
+| C | 36 | 64 | 13 | 76 | 69 | 57 | 4 | 9 | 49 |
+| D | 89 | 62 | 46 | 95 | 87 | 29 | 64 | 33 | 99 |
+| E | 18 | 80 | 33 | 45 | 18 | 88 | 51 | 93 | 84 |
+| F | 61 | 71 | 9 | 63 | 21 | 71 | 97 | 22 | 34 |
+| G | 40 | 96 | 89 | 82 | 84 | 3 | 37 | 65 | 75 |
+| H | 17 | 42 | 31 | 62 | 64 | 52 | 64 | 13 | 34 |
+| I | 85 | 29 | 84 | 32 | 50 | 7 | 43 | 41 | 36 |
+
+## commission_id=C
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 46 | 66 | 53 | 50 | 14 | 40 | 96 | 1 | 4 |
+| B | 25 | 40 | 25 | 60 | 87 | 61 | 61 | 67 | 72 |
+| C | 55 | 31 | 8 | 87 | 29 | 24 | 25 | 33 | 17 |
+| D | 69 | 17 | 57 | 14 | 63 | 30 | 36 | 13 | 49 |
+| E | 74 | 70 | 19 | 56 | 0 | 64 | 73 | 91 | 55 |
+| F | 61 | 66 | 40 | 0 | 86 | 39 | 59 | 35 | 18 |
+| G | 60 | 59 | 68 | 97 | 24 | 63 | 58 | 68 | 70 |
+| H | 79 | 16 | 66 | 64 | 18 | 52 | 71 | 93 | 28 |
+| I | 30 | 68 | 59 | 20 | 25 | 59 | 62 | 6 | 70 |
+
+## commission_id=D
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 57 | 74 | 60 | 60 | 44 | 14 | 30 | 6 | 10 |
+| B | 8 | 45 | 29 | 62 | 82 | 35 | 6 | 95 | 70 |
+| C | 77 | 54 | 67 | 30 | 42 | 52 | 87 | 40 | 79 |
+| D | 68 | 90 | 75 | 87 | 85 | 50 | 11 | 50 | 68 |
+| E | 39 | 84 | 12 | 90 | 44 | 99 | 71 | 29 | 90 |
+| F | 35 | 52 | 59 | 14 | 6 | 6 | 74 | 34 | 95 |
+| G | 1 | 91 | 4 | 63 | 2 | 44 | 48 | 29 | 33 |
+| H | 95 | 18 | 87 | 26 | 88 | 63 | 1 | 74 | 28 |
+| I | 86 | 13 | 79 | 89 | 82 | 46 | 78 | 85 | 31 |
+
+## commission_id=E
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 57 | 43 | 18 | 27 | 63 | 26 | 31 | 78 | 17 |
+| B | 67 | 86 | 73 | 55 | 13 | 30 | 19 | 94 | 98 |
+| C | 64 | 31 | 14 | 61 | 68 | 26 | 56 | 16 | 43 |
+| D | 62 | 63 | 5 | 59 | 21 | 58 | 69 | 46 | 40 |
+| E | 23 | 86 | 19 | 3 | 84 | 41 | 85 | 18 | 39 |
+| F | 61 | 43 | 0 | 54 | 52 | 45 | 9 | 47 | 39 |
+| G | 56 | 75 | 93 | 60 | 8 | 58 | 79 | 19 | 82 |
+| H | 74 | 92 | 94 | 75 | 8 | 51 | 16 | 19 | 36 |
+| I | 42 | 53 | 6 | 18 | 8 | 27 | 81 | 5 | 99 |
+
+## commission_id=F
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 85 | 89 | 57 | 38 | 44 | 54 | 16 | 72 | 66 |
+| B | 32 | 69 | 78 | 9 | 10 | 93 | 12 | 56 | 14 |
+| C | 77 | 80 | 8 | 75 | 74 | 70 | 19 | 12 | 2 |
+| D | 1 | 57 | 94 | 59 | 73 | 36 | 57 | 45 | 73 |
+| E | 39 | 49 | 35 | 26 | 68 | 64 | 28 | 41 | 70 |
+| F | 96 | 72 | 86 | 79 | 37 | 21 | 57 | 55 | 80 |
+| G | 24 | 79 | 80 | 73 | 55 | 21 | 52 | 85 | 78 |
+| H | 37 | 54 | 88 | 71 | 37 | 75 | 62 | 78 | 31 |
+| I | 86 | 38 | 64 | 95 | 49 | 95 | 53 | 59 | 3 |
+
+## commission_id=G
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 55 | 19 | 71 | 95 | 25 | 3 | 39 | 39 |
+| B | 36 | 45 | 88 | 27 | 64 | 87 | 52 | 51 | 57 |
+| C | 9 | 33 | 76 | 94 | 71 | 46 | 19 | 83 | 20 |
+| D | 50 | 18 | 60 | 84 | 18 | 66 | 34 | 72 | 88 |
+| E | 42 | 34 | 85 | 44 | 93 | 53 | 26 | 90 | 52 |
+| F | 20 | 78 | 75 | 48 | 51 | 77 | 78 | 27 | 92 |
+| G | 55 | 46 | 93 | 74 | 10 | 44 | 34 | 94 | 18 |
+| H | 61 | 72 | 10 | 98 | 97 | 68 | 10 | 23 | 60 |
+| I | 45 | 69 | 75 | 97 | 51 | 66 | 13 | 49 | 9 |
+
+## commission_id=H
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 9 | 0 | 87 | 35 | 65 | 94 | 73 | 17 | 7 |
+| B | 58 | 27 | 96 | 91 | 81 | 28 | 21 | 14 | 8 |
+| C | 14 | 47 | 32 | 7 | 34 | 17 | 96 | 16 | 76 |
+| D | 24 | 88 | 92 | 58 | 70 | 14 | 50 | 52 | 32 |
+| E | 56 | 10 | 37 | 40 | 34 | 79 | 71 | 16 | 88 |
+| F | 68 | 47 | 56 | 83 | 51 | 28 | 15 | 99 | 71 |
+| G | 59 | 29 | 44 | 18 | 24 | 22 | 64 | 2 | 12 |
+| H | 92 | 46 | 22 | 5 | 46 | 3 | 41 | 88 | 51 |
+| I | 32 | 63 | 62 | 93 | 23 | 24 | 53 | 2 | 6 |
+
+## commission_id=I
+| artist_id\frame_id | A | B | C | D | E | F | G | H | I |
+|---|---|---|---|---|---|---|---|---|---|
+| A | 4 | 49 | 58 | 86 | 49 | 57 | 35 | 57 | 50 |
+| B | 51 | 59 | 98 | 14 | 62 | 38 | 33 | 13 | 28 |
+| C | 67 | 80 | 33 | 66 | 63 | 82 | 17 | 93 | 99 |
+| D | 26 | 51 | 99 | 65 | 47 | 81 | 68 | 9 | 95 |
+| E | 69 | 66 | 71 | 13 | 11 | 67 | 61 | 15 | 96 |
+| F | 84 | 44 | 29 | 54 | 85 | 88 | 47 | 21 | 96 |
+| G | 79 | 52 | 51 | 66 | 85 | 80 | 54 | 98 | 78 |
+| H | 60 | 35 | 55 | 11 | 16 | 18 | 69 | 11 | 3 |
+| I | 5 | 20 | 46 | 69 | 58 | 95 | 77 | 97 | 31 |
+The team will select one artist and one frame for each commission so the total of the listed costs is minimized.
+
+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': [[[39, 95, 27, 30, 0, 28, 24, 36, 11], [93, 22, 4, 21, 5, 50, 51, 8, 15], [17, 94, 53, 96, 70, 30, 33, 10, 62], [90, 95, 31, 75, 87, 97, 52, 19, 73], [29, 62, 0, 84, 41, 63, 1, 60, 52], [2, 88, 91, 83, 45, 36, 12, 76, 35], [25, 15, 75, 51, 71, 77, 9, 91, 92], [84, 26, 49, 41, 79, 94, 70, 18, 32], [26, 88, 18, 64, 93, 83, 93, 97, 14]], [[72, 46, 46, 25, 2, 90, 72, 68, 12], [63, 25, 16, 32, 31, 91, 83, 56, 40], [36, 64, 13, 76, 69, 57, 4, 9, 49], [89, 62, 46, 95, 87, 29, 64, 33, 99], [18, 80, 33, 45, 18, 88, 51, 93, 84], [61, 71, 9, 63, 21, 71, 97, 22, 34], [40, 96, 89, 82, 84, 3, 37, 65, 75], [17, 42, 31, 62, 64, 52, 64, 13, 34], [85, 29, 84, 32, 50, 7, 43, 41, 36]], [[46, 66, 53, 50, 14, 40, 96, 1, 4], [25, 40, 25, 60, 87, 61, 61, 67, 72], [55, 31, 8, 87, 29, 24, 25, 33, 17], [69, 17, 57, 14, 63, 30, 36, 13, 49], [74, 70, 19, 56, 0, 64, 73, 91, 55], [61, 66, 40, 0, 86, 39, 59, 35, 18], [60, 59, 68, 97, 24, 63, 58, 68, 70], [79, 16, 66, 64, 18, 52, 71, 93, 28], [30, 68, 59, 20, 25, 59, 62, 6, 70]], [[57, 74, 60, 60, 44, 14, 30, 6, 10], [8, 45, 29, 62, 82, 35, 6, 95, 70], [77, 54, 67, 30, 42, 52, 87, 40, 79], [68, 90, 75, 87, 85, 50, 11, 50, 68], [39, 84, 12, 90, 44, 99, 71, 29, 90], [35, 52, 59, 14, 6, 6, 74, 34, 95], [1, 91, 4, 63, 2, 44, 48, 29, 33], [95, 18, 87, 26, 88, 63, 1, 74, 28], [86, 13, 79, 89, 82, 46, 78, 85, 31]], [[57, 43, 18, 27, 63, 26, 31, 78, 17], [67, 86, 73, 55, 13, 30, 19, 94, 98], [64, 31, 14, 61, 68, 26, 56, 16, 43], [62, 63, 5, 59, 21, 58, 69, 46, 40], [23, 86, 19, 3, 84, 41, 85, 18, 39], [61, 43, 0, 54, 52, 45, 9, 47, 39], [56, 75, 93, 60, 8, 58, 79, 19, 82], [74, 92, 94, 75, 8, 51, 16, 19, 36], [42, 53, 6, 18, 8, 27, 81, 5, 99]], [[85, 89, 57, 38, 44, 54, 16, 72, 66], [32, 69, 78, 9, 10, 93, 12, 56, 14], [77, 80, 8, 75, 74, 70, 19, 12, 2], [1, 57, 94, 59, 73, 36, 57, 45, 73], [39, 49, 35, 26, 68, 64, 28, 41, 70], [96, 72, 86, 79, 37, 21, 57, 55, 80], [24, 79, 80, 73, 55, 21, 52, 85, 78], [37, 54, 88, 71, 37, 75, 62, 78, 31], [86, 38, 64, 95, 49, 95, 53, 59, 3]], [[12, 55, 19, 71, 95, 25, 3, 39, 39], [36, 45, 88, 27, 64, 87, 52, 51, 57], [9, 33, 76, 94, 71, 46, 19, 83, 20], [50, 18, 60, 84, 18, 66, 34, 72, 88], [42, 34, 85, 44, 93, 53, 26, 90, 52], [20, 78, 75, 48, 51, 77, 78, 27, 92], [55, 46, 93, 74, 10, 44, 34, 94, 18], [61, 72, 10, 98, 97, 68, 10, 23, 60], [45, 69, 75, 97, 51, 66, 13, 49, 9]], [[9, 0, 87, 35, 65, 94, 73, 17, 7], [58, 27, 96, 91, 81, 28, 21, 14, 8], [14, 47, 32, 7, 34, 17, 96, 16, 76], [24, 88, 92, 58, 70, 14, 50, 52, 32], [56, 10, 37, 40, 34, 79, 71, 16, 88], [68, 47, 56, 83, 51, 28, 15, 99, 71], [59, 29, 44, 18, 24, 22, 64, 2, 12], [92, 46, 22, 5, 46, 3, 41, 88, 51], [32, 63, 62, 93, 23, 24, 53, 2, 6]], [[4, 49, 58, 86, 49, 57, 35, 57, 50], [51, 59, 98, 14, 62, 38, 33, 13, 28], [67, 80, 33, 66, 63, 82, 17, 93, 99], [26, 51, 99, 65, 47, 81, 68, 9, 95], [69, 66, 71, 13, 11, 67, 61, 15, 96], [84, 44, 29, 54, 85, 88, 47, 21, 96], [79, 52, 51, 66, 85, 80, 54, 98, 78], [60, 35, 55, 11, 16, 18, 69, 11, 3], [5, 20, 46, 69, 58, 95, 77, 97, 31]]], 'objective': 37.0}","[[0, 1, 2], [1, 2, 6], [2, 8, 7], [3, 5, 5], [4, 4, 3], [5, 3, 0], [6, 6, 4], [7, 0, 1], [8, 7, 8]]",37.0,"{'problem_type': 'AP3', 'n': 9, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 39}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 95}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 27}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 30}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 0}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 28}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 24}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 36}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 11}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 93}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 22}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 4}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 21}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 5}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 50}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 51}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 8}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 15}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 17}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 94}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 53}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 96}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 70}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 30}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 33}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 10}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 62}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 90}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 95}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 31}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 75}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 87}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 97}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 52}, {'i': 'A', 'j': 'D', 'k': 'H', 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'cost': 82}, {'i': 'I', 'j': 'C', 'k': 'G', 'cost': 17}, {'i': 'I', 'j': 'C', 'k': 'H', 'cost': 93}, {'i': 'I', 'j': 'C', 'k': 'I', 'cost': 99}, {'i': 'I', 'j': 'D', 'k': 'A', 'cost': 26}, {'i': 'I', 'j': 'D', 'k': 'B', 'cost': 51}, {'i': 'I', 'j': 'D', 'k': 'C', 'cost': 99}, {'i': 'I', 'j': 'D', 'k': 'D', 'cost': 65}, {'i': 'I', 'j': 'D', 'k': 'E', 'cost': 47}, {'i': 'I', 'j': 'D', 'k': 'F', 'cost': 81}, {'i': 'I', 'j': 'D', 'k': 'G', 'cost': 68}, {'i': 'I', 'j': 'D', 'k': 'H', 'cost': 9}, {'i': 'I', 'j': 'D', 'k': 'I', 'cost': 95}, {'i': 'I', 'j': 'E', 'k': 'A', 'cost': 69}, {'i': 'I', 'j': 'E', 'k': 'B', 'cost': 66}, {'i': 'I', 'j': 'E', 'k': 'C', 'cost': 71}, {'i': 'I', 'j': 'E', 'k': 'D', 'cost': 13}, {'i': 'I', 'j': 'E', 'k': 'E', 'cost': 11}, {'i': 'I', 'j': 'E', 'k': 'F', 'cost': 67}, {'i': 'I', 'j': 'E', 'k': 'G', 'cost': 61}, {'i': 'I', 'j': 'E', 'k': 'H', 'cost': 15}, {'i': 'I', 'j': 'E', 'k': 'I', 'cost': 96}, {'i': 'I', 'j': 'F', 'k': 'A', 'cost': 84}, {'i': 'I', 'j': 'F', 'k': 'B', 'cost': 44}, {'i': 'I', 'j': 'F', 'k': 'C', 'cost': 29}, {'i': 'I', 'j': 'F', 'k': 'D', 'cost': 54}, {'i': 'I', 'j': 'F', 'k': 'E', 'cost': 85}, {'i': 'I', 'j': 'F', 'k': 'F', 'cost': 88}, {'i': 'I', 'j': 'F', 'k': 'G', 'cost': 47}, {'i': 'I', 'j': 'F', 'k': 'H', 'cost': 21}, {'i': 'I', 'j': 'F', 'k': 'I', 'cost': 96}, {'i': 'I', 'j': 'G', 'k': 'A', 'cost': 79}, {'i': 'I', 'j': 'G', 'k': 'B', 'cost': 52}, {'i': 'I', 'j': 'G', 'k': 'C', 'cost': 51}, {'i': 'I', 'j': 'G', 'k': 'D', 'cost': 66}, {'i': 'I', 'j': 'G', 'k': 'E', 'cost': 85}, {'i': 'I', 'j': 'G', 'k': 'F', 'cost': 80}, {'i': 'I', 'j': 'G', 'k': 'G', 'cost': 54}, {'i': 'I', 'j': 'G', 'k': 'H', 'cost': 98}, {'i': 'I', 'j': 'G', 'k': 'I', 'cost': 78}, {'i': 'I', 'j': 'H', 'k': 'A', 'cost': 60}, {'i': 'I', 'j': 'H', 'k': 'B', 'cost': 35}, {'i': 'I', 'j': 'H', 'k': 'C', 'cost': 55}, {'i': 'I', 'j': 'H', 'k': 'D', 'cost': 11}, {'i': 'I', 'j': 'H', 'k': 'E', 'cost': 16}, {'i': 'I', 'j': 'H', 'k': 'F', 'cost': 18}, {'i': 'I', 'j': 'H', 'k': 'G', 'cost': 69}, {'i': 'I', 'j': 'H', 'k': 'H', 'cost': 11}, {'i': 'I', 'j': 'H', 'k': 'I', 'cost': 3}, {'i': 'I', 'j': 'I', 'k': 'A', 'cost': 5}, {'i': 'I', 'j': 'I', 'k': 'B', 'cost': 20}, {'i': 'I', 'j': 'I', 'k': 'C', 'cost': 46}, {'i': 'I', 'j': 'I', 'k': 'D', 'cost': 69}, {'i': 'I', 'j': 'I', 'k': 'E', 'cost': 58}, {'i': 'I', 'j': 'I', 'k': 'F', 'cost': 95}, {'i': 'I', 'j': 'I', 'k': 'G', 'cost': 77}, {'i': 'I', 'j': 'I', 'k': 'H', 'cost': 97}, {'i': 'I', 'j': 'I', 'k': 'I', 'cost': 31}]}","[['A', 'B', 'C'], ['B', 'C', 'G'], ['C', 'I', 'H'], ['D', 'F', 'F'], ['E', 'E', 'D'], ['F', 'D', 'A'], ['G', 'G', 'E'], ['H', 'A', 'B'], ['I', 'H', 'I']]",32,nl,names
+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.
+
+# num_shipments=10
+# shipment_identifiers=1, 2, 3, 4, 5, 6, 7, 8, 9, 10
+
+# 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=1
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 96 | 93 | 36 | 43 | 6 | 68 | 21 | 30 | 37 | 76 |
+| 2 | 20 | 36 | 36 | 71 | 31 | 52 | 37 | 2 | 29 | 44 |
+| 3 | 17 | 57 | 92 | 93 | 26 | 94 | 42 | 51 | 94 | 3 |
+| 4 | 78 | 2 | 84 | 52 | 32 | 89 | 91 | 53 | 44 | 98 |
+| 5 | 54 | 7 | 75 | 38 | 84 | 63 | 54 | 28 | 81 | 53 |
+| 6 | 92 | 25 | 20 | 30 | 41 | 4 | 7 | 76 | 37 | 13 |
+| 7 | 72 | 11 | 13 | 34 | 90 | 63 | 12 | 63 | 27 | 31 |
+| 8 | 88 | 33 | 63 | 4 | 27 | 3 | 21 | 71 | 72 | 32 |
+| 9 | 36 | 77 | 93 | 67 | 2 | 57 | 72 | 59 | 28 | 23 |
+| 10 | 56 | 32 | 36 | 19 | 47 | 27 | 42 | 11 | 68 | 41 |
+
+## shipment_id=2
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 45 | 54 | 96 | 90 | 74 | 83 | 89 | 8 | 94 | 68 |
+| 2 | 88 | 5 | 63 | 94 | 41 | 18 | 0 | 2 | 20 | 62 |
+| 3 | 75 | 37 | 80 | 10 | 89 | 58 | 23 | 20 | 29 | 53 |
+| 4 | 25 | 46 | 91 | 99 | 96 | 20 | 50 | 32 | 9 | 75 |
+| 5 | 63 | 45 | 87 | 84 | 78 | 99 | 78 | 75 | 62 | 52 |
+| 6 | 5 | 12 | 95 | 91 | 22 | 90 | 46 | 83 | 69 | 51 |
+| 7 | 99 | 18 | 44 | 48 | 16 | 63 | 98 | 70 | 20 | 9 |
+| 8 | 68 | 73 | 95 | 18 | 40 | 6 | 62 | 55 | 84 | 82 |
+| 9 | 46 | 15 | 31 | 5 | 91 | 31 | 33 | 66 | 28 | 71 |
+| 10 | 98 | 52 | 61 | 6 | 21 | 64 | 82 | 64 | 0 | 85 |
+
+## shipment_id=3
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 66 | 46 | 82 | 19 | 66 | 25 | 1 | 99 | 50 | 0 |
+| 2 | 70 | 29 | 19 | 21 | 85 | 34 | 30 | 73 | 94 | 78 |
+| 3 | 66 | 18 | 7 | 52 | 81 | 90 | 84 | 58 | 60 | 44 |
+| 4 | 82 | 7 | 35 | 46 | 1 | 75 | 62 | 25 | 10 | 94 |
+| 5 | 39 | 41 | 83 | 54 | 55 | 22 | 41 | 89 | 36 | 6 |
+| 6 | 24 | 13 | 1 | 46 | 77 | 79 | 85 | 15 | 97 | 40 |
+| 7 | 32 | 65 | 8 | 75 | 29 | 85 | 11 | 52 | 80 | 97 |
+| 8 | 90 | 15 | 87 | 60 | 3 | 40 | 41 | 91 | 57 | 58 |
+| 9 | 91 | 93 | 75 | 2 | 84 | 95 | 75 | 56 | 61 | 98 |
+| 10 | 60 | 68 | 88 | 13 | 29 | 22 | 12 | 8 | 31 | 6 |
+
+## shipment_id=4
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 24 | 46 | 48 | 85 | 8 | 9 | 47 | 18 | 72 | 25 |
+| 2 | 72 | 24 | 39 | 64 | 33 | 28 | 74 | 30 | 49 | 4 |
+| 3 | 52 | 25 | 3 | 48 | 27 | 94 | 77 | 83 | 7 | 35 |
+| 4 | 14 | 41 | 9 | 95 | 78 | 21 | 76 | 12 | 63 | 67 |
+| 5 | 52 | 41 | 14 | 68 | 81 | 25 | 19 | 16 | 41 | 36 |
+| 6 | 35 | 39 | 63 | 58 | 94 | 29 | 57 | 36 | 71 | 85 |
+| 7 | 94 | 56 | 48 | 8 | 58 | 91 | 56 | 40 | 27 | 64 |
+| 8 | 36 | 12 | 94 | 78 | 92 | 66 | 80 | 53 | 88 | 41 |
+| 9 | 62 | 20 | 51 | 77 | 58 | 29 | 34 | 10 | 97 | 89 |
+| 10 | 13 | 55 | 16 | 34 | 56 | 3 | 4 | 2 | 43 | 55 |
+
+## shipment_id=5
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 54 | 35 | 83 | 23 | 21 | 98 | 1 | 94 | 57 | 96 |
+| 2 | 30 | 24 | 25 | 12 | 1 | 28 | 61 | 40 | 59 | 37 |
+| 3 | 76 | 27 | 91 | 15 | 73 | 3 | 94 | 72 | 91 | 18 |
+| 4 | 84 | 76 | 10 | 63 | 59 | 19 | 66 | 84 | 21 | 23 |
+| 5 | 91 | 74 | 68 | 33 | 28 | 63 | 72 | 0 | 55 | 69 |
+| 6 | 39 | 1 | 28 | 43 | 74 | 86 | 26 | 69 | 53 | 5 |
+| 7 | 68 | 53 | 9 | 7 | 8 | 61 | 50 | 67 | 70 | 40 |
+| 8 | 13 | 21 | 22 | 79 | 62 | 82 | 78 | 45 | 36 | 98 |
+| 9 | 80 | 63 | 78 | 41 | 2 | 53 | 19 | 84 | 93 | 11 |
+| 10 | 59 | 41 | 99 | 38 | 32 | 54 | 18 | 12 | 78 | 77 |
+
+## shipment_id=6
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 84 | 94 | 27 | 53 | 51 | 76 | 2 | 32 | 89 | 54 |
+| 2 | 49 | 24 | 40 | 41 | 15 | 43 | 53 | 95 | 66 | 22 |
+| 3 | 53 | 78 | 72 | 64 | 53 | 31 | 51 | 15 | 73 | 71 |
+| 4 | 99 | 10 | 68 | 95 | 94 | 81 | 34 | 0 | 17 | 92 |
+| 5 | 87 | 7 | 52 | 77 | 94 | 95 | 23 | 39 | 46 | 29 |
+| 6 | 39 | 10 | 45 | 92 | 86 | 6 | 11 | 9 | 51 | 89 |
+| 7 | 62 | 66 | 2 | 71 | 94 | 14 | 31 | 63 | 90 | 59 |
+| 8 | 68 | 18 | 7 | 42 | 71 | 51 | 62 | 87 | 9 | 10 |
+| 9 | 54 | 36 | 46 | 57 | 66 | 47 | 30 | 47 | 61 | 72 |
+| 10 | 97 | 69 | 37 | 96 | 13 | 13 | 39 | 42 | 38 | 56 |
+
+## shipment_id=7
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 96 | 32 | 51 | 11 | 93 | 19 | 13 | 40 | 25 | 54 |
+| 2 | 16 | 80 | 64 | 20 | 81 | 65 | 73 | 8 | 65 | 11 |
+| 3 | 2 | 41 | 41 | 46 | 5 | 32 | 91 | 36 | 92 | 94 |
+| 4 | 1 | 11 | 89 | 72 | 96 | 20 | 99 | 22 | 75 | 33 |
+| 5 | 22 | 1 | 19 | 24 | 66 | 6 | 21 | 36 | 82 | 14 |
+| 6 | 91 | 71 | 43 | 60 | 20 | 7 | 35 | 17 | 28 | 87 |
+| 7 | 51 | 7 | 90 | 79 | 65 | 2 | 66 | 42 | 86 | 54 |
+| 8 | 33 | 15 | 50 | 9 | 29 | 62 | 65 | 42 | 27 | 68 |
+| 9 | 69 | 73 | 38 | 46 | 1 | 93 | 54 | 37 | 56 | 66 |
+| 10 | 54 | 59 | 23 | 39 | 58 | 5 | 79 | 17 | 62 | 18 |
+
+## shipment_id=8
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 28 | 41 | 50 | 70 | 67 | 27 | 92 | 60 | 72 | 96 |
+| 2 | 47 | 55 | 69 | 67 | 73 | 2 | 3 | 27 | 47 | 17 |
+| 3 | 55 | 65 | 30 | 93 | 26 | 69 | 43 | 33 | 45 | 84 |
+| 4 | 17 | 39 | 5 | 32 | 73 | 77 | 90 | 78 | 87 | 32 |
+| 5 | 8 | 60 | 10 | 89 | 77 | 48 | 96 | 54 | 85 | 73 |
+| 6 | 90 | 26 | 78 | 74 | 52 | 76 | 85 | 0 | 69 | 2 |
+| 7 | 39 | 42 | 98 | 42 | 9 | 96 | 34 | 13 | 97 | 57 |
+| 8 | 26 | 39 | 5 | 46 | 32 | 59 | 46 | 42 | 41 | 59 |
+| 9 | 93 | 60 | 54 | 40 | 33 | 22 | 52 | 41 | 35 | 56 |
+| 10 | 43 | 49 | 92 | 2 | 7 | 9 | 40 | 25 | 48 | 52 |
+
+## shipment_id=9
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 21 | 31 | 59 | 90 | 1 | 89 | 12 | 49 | 89 | 45 |
+| 2 | 79 | 26 | 81 | 41 | 98 | 29 | 83 | 11 | 95 | 71 |
+| 3 | 22 | 82 | 55 | 9 | 99 | 47 | 81 | 70 | 7 | 34 |
+| 4 | 15 | 65 | 60 | 37 | 68 | 37 | 48 | 46 | 33 | 42 |
+| 5 | 79 | 27 | 12 | 8 | 13 | 92 | 65 | 63 | 55 | 17 |
+| 6 | 81 | 92 | 99 | 46 | 83 | 12 | 11 | 32 | 90 | 4 |
+| 7 | 30 | 56 | 19 | 18 | 67 | 85 | 70 | 83 | 3 | 95 |
+| 8 | 63 | 18 | 47 | 28 | 79 | 5 | 65 | 7 | 81 | 7 |
+| 9 | 32 | 85 | 43 | 81 | 31 | 37 | 85 | 85 | 40 | 83 |
+| 10 | 39 | 33 | 37 | 50 | 30 | 76 | 56 | 58 | 16 | 75 |
+
+## shipment_id=10
+| container_id\loading_dock_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 35 | 37 | 55 | 51 | 86 | 59 | 53 | 66 | 18 | 6 |
+| 2 | 57 | 25 | 58 | 33 | 51 | 57 | 89 | 67 | 8 | 53 |
+| 3 | 58 | 98 | 69 | 29 | 66 | 96 | 1 | 0 | 1 | 10 |
+| 4 | 92 | 9 | 22 | 94 | 46 | 15 | 45 | 7 | 38 | 83 |
+| 5 | 65 | 29 | 89 | 76 | 36 | 51 | 6 | 91 | 57 | 68 |
+| 6 | 79 | 37 | 93 | 48 | 52 | 10 | 63 | 93 | 69 | 48 |
+| 7 | 34 | 66 | 17 | 27 | 50 | 9 | 57 | 80 | 36 | 26 |
+| 8 | 78 | 99 | 8 | 38 | 55 | 17 | 29 | 0 | 46 | 97 |
+| 9 | 25 | 96 | 12 | 55 | 37 | 75 | 98 | 39 | 86 | 66 |
+| 10 | 57 | 75 | 48 | 23 | 46 | 18 | 15 | 50 | 93 | 11 |
+
+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': [[[96, 93, 36, 43, 6, 68, 21, 30, 37, 76], [20, 36, 36, 71, 31, 52, 37, 2, 29, 44], [17, 57, 92, 93, 26, 94, 42, 51, 94, 3], [78, 2, 84, 52, 32, 89, 91, 53, 44, 98], [54, 7, 75, 38, 84, 63, 54, 28, 81, 53], [92, 25, 20, 30, 41, 4, 7, 76, 37, 13], [72, 11, 13, 34, 90, 63, 12, 63, 27, 31], [88, 33, 63, 4, 27, 3, 21, 71, 72, 32], [36, 77, 93, 67, 2, 57, 72, 59, 28, 23], [56, 32, 36, 19, 47, 27, 42, 11, 68, 41]], [[45, 54, 96, 90, 74, 83, 89, 8, 94, 68], [88, 5, 63, 94, 41, 18, 0, 2, 20, 62], [75, 37, 80, 10, 89, 58, 23, 20, 29, 53], [25, 46, 91, 99, 96, 20, 50, 32, 9, 75], [63, 45, 87, 84, 78, 99, 78, 75, 62, 52], [5, 12, 95, 91, 22, 90, 46, 83, 69, 51], [99, 18, 44, 48, 16, 63, 98, 70, 20, 9], [68, 73, 95, 18, 40, 6, 62, 55, 84, 82], [46, 15, 31, 5, 91, 31, 33, 66, 28, 71], [98, 52, 61, 6, 21, 64, 82, 64, 0, 85]], [[66, 46, 82, 19, 66, 25, 1, 99, 50, 0], [70, 29, 19, 21, 85, 34, 30, 73, 94, 78], [66, 18, 7, 52, 81, 90, 84, 58, 60, 44], [82, 7, 35, 46, 1, 75, 62, 25, 10, 94], [39, 41, 83, 54, 55, 22, 41, 89, 36, 6], [24, 13, 1, 46, 77, 79, 85, 15, 97, 40], [32, 65, 8, 75, 29, 85, 11, 52, 80, 97], [90, 15, 87, 60, 3, 40, 41, 91, 57, 58], [91, 93, 75, 2, 84, 95, 75, 56, 61, 98], [60, 68, 88, 13, 29, 22, 12, 8, 31, 6]], [[24, 46, 48, 85, 8, 9, 47, 18, 72, 25], [72, 24, 39, 64, 33, 28, 74, 30, 49, 4], [52, 25, 3, 48, 27, 94, 77, 83, 7, 35], [14, 41, 9, 95, 78, 21, 76, 12, 63, 67], [52, 41, 14, 68, 81, 25, 19, 16, 41, 36], [35, 39, 63, 58, 94, 29, 57, 36, 71, 85], [94, 56, 48, 8, 58, 91, 56, 40, 27, 64], [36, 12, 94, 78, 92, 66, 80, 53, 88, 41], [62, 20, 51, 77, 58, 29, 34, 10, 97, 89], [13, 55, 16, 34, 56, 3, 4, 2, 43, 55]], [[54, 35, 83, 23, 21, 98, 1, 94, 57, 96], [30, 24, 25, 12, 1, 28, 61, 40, 59, 37], [76, 27, 91, 15, 73, 3, 94, 72, 91, 18], [84, 76, 10, 63, 59, 19, 66, 84, 21, 23], [91, 74, 68, 33, 28, 63, 72, 0, 55, 69], [39, 1, 28, 43, 74, 86, 26, 69, 53, 5], [68, 53, 9, 7, 8, 61, 50, 67, 70, 40], [13, 21, 22, 79, 62, 82, 78, 45, 36, 98], [80, 63, 78, 41, 2, 53, 19, 84, 93, 11], [59, 41, 99, 38, 32, 54, 18, 12, 78, 77]], [[84, 94, 27, 53, 51, 76, 2, 32, 89, 54], [49, 24, 40, 41, 15, 43, 53, 95, 66, 22], [53, 78, 72, 64, 53, 31, 51, 15, 73, 71], [99, 10, 68, 95, 94, 81, 34, 0, 17, 92], [87, 7, 52, 77, 94, 95, 23, 39, 46, 29], [39, 10, 45, 92, 86, 6, 11, 9, 51, 89], [62, 66, 2, 71, 94, 14, 31, 63, 90, 59], [68, 18, 7, 42, 71, 51, 62, 87, 9, 10], [54, 36, 46, 57, 66, 47, 30, 47, 61, 72], [97, 69, 37, 96, 13, 13, 39, 42, 38, 56]], [[96, 32, 51, 11, 93, 19, 13, 40, 25, 54], [16, 80, 64, 20, 81, 65, 73, 8, 65, 11], [2, 41, 41, 46, 5, 32, 91, 36, 92, 94], [1, 11, 89, 72, 96, 20, 99, 22, 75, 33], [22, 1, 19, 24, 66, 6, 21, 36, 82, 14], [91, 71, 43, 60, 20, 7, 35, 17, 28, 87], [51, 7, 90, 79, 65, 2, 66, 42, 86, 54], [33, 15, 50, 9, 29, 62, 65, 42, 27, 68], [69, 73, 38, 46, 1, 93, 54, 37, 56, 66], [54, 59, 23, 39, 58, 5, 79, 17, 62, 18]], [[28, 41, 50, 70, 67, 27, 92, 60, 72, 96], [47, 55, 69, 67, 73, 2, 3, 27, 47, 17], [55, 65, 30, 93, 26, 69, 43, 33, 45, 84], [17, 39, 5, 32, 73, 77, 90, 78, 87, 32], [8, 60, 10, 89, 77, 48, 96, 54, 85, 73], [90, 26, 78, 74, 52, 76, 85, 0, 69, 2], [39, 42, 98, 42, 9, 96, 34, 13, 97, 57], [26, 39, 5, 46, 32, 59, 46, 42, 41, 59], [93, 60, 54, 40, 33, 22, 52, 41, 35, 56], [43, 49, 92, 2, 7, 9, 40, 25, 48, 52]], [[21, 31, 59, 90, 1, 89, 12, 49, 89, 45], [79, 26, 81, 41, 98, 29, 83, 11, 95, 71], [22, 82, 55, 9, 99, 47, 81, 70, 7, 34], [15, 65, 60, 37, 68, 37, 48, 46, 33, 42], [79, 27, 12, 8, 13, 92, 65, 63, 55, 17], [81, 92, 99, 46, 83, 12, 11, 32, 90, 4], [30, 56, 19, 18, 67, 85, 70, 83, 3, 95], [63, 18, 47, 28, 79, 5, 65, 7, 81, 7], [32, 85, 43, 81, 31, 37, 85, 85, 40, 83], [39, 33, 37, 50, 30, 76, 56, 58, 16, 75]], [[35, 37, 55, 51, 86, 59, 53, 66, 18, 6], [57, 25, 58, 33, 51, 57, 89, 67, 8, 53], [58, 98, 69, 29, 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{'i': 7, 'j': 7, 'k': 9, 'cost': 86}, {'i': 7, 'j': 7, 'k': 10, 'cost': 54}, {'i': 7, 'j': 8, 'k': 1, 'cost': 33}, {'i': 7, 'j': 8, 'k': 2, 'cost': 15}, {'i': 7, 'j': 8, 'k': 3, 'cost': 50}, {'i': 7, 'j': 8, 'k': 4, 'cost': 9}, {'i': 7, 'j': 8, 'k': 5, 'cost': 29}, {'i': 7, 'j': 8, 'k': 6, 'cost': 62}, {'i': 7, 'j': 8, 'k': 7, 'cost': 65}, {'i': 7, 'j': 8, 'k': 8, 'cost': 42}, {'i': 7, 'j': 8, 'k': 9, 'cost': 27}, {'i': 7, 'j': 8, 'k': 10, 'cost': 68}, {'i': 7, 'j': 9, 'k': 1, 'cost': 69}, {'i': 7, 'j': 9, 'k': 2, 'cost': 73}, {'i': 7, 'j': 9, 'k': 3, 'cost': 38}, {'i': 7, 'j': 9, 'k': 4, 'cost': 46}, {'i': 7, 'j': 9, 'k': 5, 'cost': 1}, {'i': 7, 'j': 9, 'k': 6, 'cost': 93}, {'i': 7, 'j': 9, 'k': 7, 'cost': 54}, {'i': 7, 'j': 9, 'k': 8, 'cost': 37}, {'i': 7, 'j': 9, 'k': 9, 'cost': 56}, {'i': 7, 'j': 9, 'k': 10, 'cost': 66}, {'i': 7, 'j': 10, 'k': 1, 'cost': 54}, {'i': 7, 'j': 10, 'k': 2, 'cost': 59}, {'i': 7, 'j': 10, 'k': 3, 'cost': 23}, {'i': 7, 'j': 10, 'k': 4, 'cost': 39}, {'i': 7, 'j': 10, 'k': 5, 'cost': 58}, {'i': 7, 'j': 10, 'k': 6, 'cost': 5}, {'i': 7, 'j': 10, 'k': 7, 'cost': 79}, {'i': 7, 'j': 10, 'k': 8, 'cost': 17}, {'i': 7, 'j': 10, 'k': 9, 'cost': 62}, {'i': 7, 'j': 10, 'k': 10, 'cost': 18}, {'i': 8, 'j': 1, 'k': 1, 'cost': 28}, {'i': 8, 'j': 1, 'k': 2, 'cost': 41}, {'i': 8, 'j': 1, 'k': 3, 'cost': 50}, {'i': 8, 'j': 1, 'k': 4, 'cost': 70}, {'i': 8, 'j': 1, 'k': 5, 'cost': 67}, {'i': 8, 'j': 1, 'k': 6, 'cost': 27}, {'i': 8, 'j': 1, 'k': 7, 'cost': 92}, {'i': 8, 'j': 1, 'k': 8, 'cost': 60}, {'i': 8, 'j': 1, 'k': 9, 'cost': 72}, {'i': 8, 'j': 1, 'k': 10, 'cost': 96}, {'i': 8, 'j': 2, 'k': 1, 'cost': 47}, {'i': 8, 'j': 2, 'k': 2, 'cost': 55}, {'i': 8, 'j': 2, 'k': 3, 'cost': 69}, {'i': 8, 'j': 2, 'k': 4, 'cost': 67}, {'i': 8, 'j': 2, 'k': 5, 'cost': 73}, {'i': 8, 'j': 2, 'k': 6, 'cost': 2}, {'i': 8, 'j': 2, 'k': 7, 'cost': 3}, {'i': 8, 'j': 2, 'k': 8, 'cost': 27}, {'i': 8, 'j': 2, 'k': 9, 'cost': 47}, {'i': 8, 'j': 2, 'k': 10, 'cost': 17}, {'i': 8, 'j': 3, 'k': 1, 'cost': 55}, {'i': 8, 'j': 3, 'k': 2, 'cost': 65}, {'i': 8, 'j': 3, 'k': 3, 'cost': 30}, {'i': 8, 'j': 3, 'k': 4, 'cost': 93}, {'i': 8, 'j': 3, 'k': 5, 'cost': 26}, {'i': 8, 'j': 3, 'k': 6, 'cost': 69}, {'i': 8, 'j': 3, 'k': 7, 'cost': 43}, {'i': 8, 'j': 3, 'k': 8, 'cost': 33}, {'i': 8, 'j': 3, 'k': 9, 'cost': 45}, {'i': 8, 'j': 3, 'k': 10, 'cost': 84}, {'i': 8, 'j': 4, 'k': 1, 'cost': 17}, {'i': 8, 'j': 4, 'k': 2, 'cost': 39}, {'i': 8, 'j': 4, 'k': 3, 'cost': 5}, {'i': 8, 'j': 4, 'k': 4, 'cost': 32}, {'i': 8, 'j': 4, 'k': 5, 'cost': 73}, {'i': 8, 'j': 4, 'k': 6, 'cost': 77}, {'i': 8, 'j': 4, 'k': 7, 'cost': 90}, {'i': 8, 'j': 4, 'k': 8, 'cost': 78}, {'i': 8, 'j': 4, 'k': 9, 'cost': 87}, {'i': 8, 'j': 4, 'k': 10, 'cost': 32}, {'i': 8, 'j': 5, 'k': 1, 'cost': 8}, {'i': 8, 'j': 5, 'k': 2, 'cost': 60}, {'i': 8, 'j': 5, 'k': 3, 'cost': 10}, {'i': 8, 'j': 5, 'k': 4, 'cost': 89}, {'i': 8, 'j': 5, 'k': 5, 'cost': 77}, {'i': 8, 'j': 5, 'k': 6, 'cost': 48}, {'i': 8, 'j': 5, 'k': 7, 'cost': 96}, {'i': 8, 'j': 5, 'k': 8, 'cost': 54}, {'i': 8, 'j': 5, 'k': 9, 'cost': 85}, {'i': 8, 'j': 5, 'k': 10, 'cost': 73}, {'i': 8, 'j': 6, 'k': 1, 'cost': 90}, {'i': 8, 'j': 6, 'k': 2, 'cost': 26}, {'i': 8, 'j': 6, 'k': 3, 'cost': 78}, {'i': 8, 'j': 6, 'k': 4, 'cost': 74}, {'i': 8, 'j': 6, 'k': 5, 'cost': 52}, {'i': 8, 'j': 6, 'k': 6, 'cost': 76}, {'i': 8, 'j': 6, 'k': 7, 'cost': 85}, {'i': 8, 'j': 6, 'k': 8, 'cost': 0}, {'i': 8, 'j': 6, 'k': 9, 'cost': 69}, {'i': 8, 'j': 6, 'k': 10, 'cost': 2}, {'i': 8, 'j': 7, 'k': 1, 'cost': 39}, {'i': 8, 'j': 7, 'k': 2, 'cost': 42}, {'i': 8, 'j': 7, 'k': 3, 'cost': 98}, {'i': 8, 'j': 7, 'k': 4, 'cost': 42}, {'i': 8, 'j': 7, 'k': 5, 'cost': 9}, {'i': 8, 'j': 7, 'k': 6, 'cost': 96}, {'i': 8, 'j': 7, 'k': 7, 'cost': 34}, {'i': 8, 'j': 7, 'k': 8, 'cost': 13}, {'i': 8, 'j': 7, 'k': 9, 'cost': 97}, {'i': 8, 'j': 7, 'k': 10, 'cost': 57}, {'i': 8, 'j': 8, 'k': 1, 'cost': 26}, {'i': 8, 'j': 8, 'k': 2, 'cost': 39}, {'i': 8, 'j': 8, 'k': 3, 'cost': 5}, {'i': 8, 'j': 8, 'k': 4, 'cost': 46}, {'i': 8, 'j': 8, 'k': 5, 'cost': 32}, {'i': 8, 'j': 8, 'k': 6, 'cost': 59}, {'i': 8, 'j': 8, 'k': 7, 'cost': 46}, {'i': 8, 'j': 8, 'k': 8, 'cost': 42}, {'i': 8, 'j': 8, 'k': 9, 'cost': 41}, {'i': 8, 'j': 8, 'k': 10, 'cost': 59}, {'i': 8, 'j': 9, 'k': 1, 'cost': 93}, {'i': 8, 'j': 9, 'k': 2, 'cost': 60}, {'i': 8, 'j': 9, 'k': 3, 'cost': 54}, {'i': 8, 'j': 9, 'k': 4, 'cost': 40}, {'i': 8, 'j': 9, 'k': 5, 'cost': 33}, {'i': 8, 'j': 9, 'k': 6, 'cost': 22}, {'i': 8, 'j': 9, 'k': 7, 'cost': 52}, {'i': 8, 'j': 9, 'k': 8, 'cost': 41}, {'i': 8, 'j': 9, 'k': 9, 'cost': 35}, {'i': 8, 'j': 9, 'k': 10, 'cost': 56}, {'i': 8, 'j': 10, 'k': 1, 'cost': 43}, {'i': 8, 'j': 10, 'k': 2, 'cost': 49}, {'i': 8, 'j': 10, 'k': 3, 'cost': 92}, {'i': 8, 'j': 10, 'k': 4, 'cost': 2}, {'i': 8, 'j': 10, 'k': 5, 'cost': 7}, {'i': 8, 'j': 10, 'k': 6, 'cost': 9}, {'i': 8, 'j': 10, 'k': 7, 'cost': 40}, {'i': 8, 'j': 10, 'k': 8, 'cost': 25}, {'i': 8, 'j': 10, 'k': 9, 'cost': 48}, {'i': 8, 'j': 10, 'k': 10, 'cost': 52}, {'i': 9, 'j': 1, 'k': 1, 'cost': 21}, {'i': 9, 'j': 1, 'k': 2, 'cost': 31}, {'i': 9, 'j': 1, 'k': 3, 'cost': 59}, {'i': 9, 'j': 1, 'k': 4, 'cost': 90}, {'i': 9, 'j': 1, 'k': 5, 'cost': 1}, {'i': 9, 'j': 1, 'k': 6, 'cost': 89}, {'i': 9, 'j': 1, 'k': 7, 'cost': 12}, {'i': 9, 'j': 1, 'k': 8, 'cost': 49}, {'i': 9, 'j': 1, 'k': 9, 'cost': 89}, {'i': 9, 'j': 1, 'k': 10, 'cost': 45}, {'i': 9, 'j': 2, 'k': 1, 'cost': 79}, {'i': 9, 'j': 2, 'k': 2, 'cost': 26}, {'i': 9, 'j': 2, 'k': 3, 'cost': 81}, {'i': 9, 'j': 2, 'k': 4, 'cost': 41}, {'i': 9, 'j': 2, 'k': 5, 'cost': 98}, {'i': 9, 'j': 2, 'k': 6, 'cost': 29}, {'i': 9, 'j': 2, 'k': 7, 'cost': 83}, {'i': 9, 'j': 2, 'k': 8, 'cost': 11}, {'i': 9, 'j': 2, 'k': 9, 'cost': 95}, {'i': 9, 'j': 2, 'k': 10, 'cost': 71}, {'i': 9, 'j': 3, 'k': 1, 'cost': 22}, {'i': 9, 'j': 3, 'k': 2, 'cost': 82}, {'i': 9, 'j': 3, 'k': 3, 'cost': 55}, {'i': 9, 'j': 3, 'k': 4, 'cost': 9}, {'i': 9, 'j': 3, 'k': 5, 'cost': 99}, {'i': 9, 'j': 3, 'k': 6, 'cost': 47}, {'i': 9, 'j': 3, 'k': 7, 'cost': 81}, {'i': 9, 'j': 3, 'k': 8, 'cost': 70}, {'i': 9, 'j': 3, 'k': 9, 'cost': 7}, {'i': 9, 'j': 3, 'k': 10, 'cost': 34}, {'i': 9, 'j': 4, 'k': 1, 'cost': 15}, {'i': 9, 'j': 4, 'k': 2, 'cost': 65}, {'i': 9, 'j': 4, 'k': 3, 'cost': 60}, {'i': 9, 'j': 4, 'k': 4, 'cost': 37}, {'i': 9, 'j': 4, 'k': 5, 'cost': 68}, {'i': 9, 'j': 4, 'k': 6, 'cost': 37}, {'i': 9, 'j': 4, 'k': 7, 'cost': 48}, {'i': 9, 'j': 4, 'k': 8, 'cost': 46}, {'i': 9, 'j': 4, 'k': 9, 'cost': 33}, {'i': 9, 'j': 4, 'k': 10, 'cost': 42}, {'i': 9, 'j': 5, 'k': 1, 'cost': 79}, {'i': 9, 'j': 5, 'k': 2, 'cost': 27}, {'i': 9, 'j': 5, 'k': 3, 'cost': 12}, {'i': 9, 'j': 5, 'k': 4, 'cost': 8}, {'i': 9, 'j': 5, 'k': 5, 'cost': 13}, {'i': 9, 'j': 5, 'k': 6, 'cost': 92}, {'i': 9, 'j': 5, 'k': 7, 'cost': 65}, {'i': 9, 'j': 5, 'k': 8, 'cost': 63}, {'i': 9, 'j': 5, 'k': 9, 'cost': 55}, {'i': 9, 'j': 5, 'k': 10, 'cost': 17}, {'i': 9, 'j': 6, 'k': 1, 'cost': 81}, {'i': 9, 'j': 6, 'k': 2, 'cost': 92}, {'i': 9, 'j': 6, 'k': 3, 'cost': 99}, {'i': 9, 'j': 6, 'k': 4, 'cost': 46}, {'i': 9, 'j': 6, 'k': 5, 'cost': 83}, {'i': 9, 'j': 6, 'k': 6, 'cost': 12}, {'i': 9, 'j': 6, 'k': 7, 'cost': 11}, {'i': 9, 'j': 6, 'k': 8, 'cost': 32}, {'i': 9, 'j': 6, 'k': 9, 'cost': 90}, {'i': 9, 'j': 6, 'k': 10, 'cost': 4}, {'i': 9, 'j': 7, 'k': 1, 'cost': 30}, {'i': 9, 'j': 7, 'k': 2, 'cost': 56}, {'i': 9, 'j': 7, 'k': 3, 'cost': 19}, {'i': 9, 'j': 7, 'k': 4, 'cost': 18}, {'i': 9, 'j': 7, 'k': 5, 'cost': 67}, {'i': 9, 'j': 7, 'k': 6, 'cost': 85}, {'i': 9, 'j': 7, 'k': 7, 'cost': 70}, {'i': 9, 'j': 7, 'k': 8, 'cost': 83}, {'i': 9, 'j': 7, 'k': 9, 'cost': 3}, {'i': 9, 'j': 7, 'k': 10, 'cost': 95}, {'i': 9, 'j': 8, 'k': 1, 'cost': 63}, {'i': 9, 'j': 8, 'k': 2, 'cost': 18}, {'i': 9, 'j': 8, 'k': 3, 'cost': 47}, {'i': 9, 'j': 8, 'k': 4, 'cost': 28}, {'i': 9, 'j': 8, 'k': 5, 'cost': 79}, {'i': 9, 'j': 8, 'k': 6, 'cost': 5}, {'i': 9, 'j': 8, 'k': 7, 'cost': 65}, {'i': 9, 'j': 8, 'k': 8, 'cost': 7}, {'i': 9, 'j': 8, 'k': 9, 'cost': 81}, {'i': 9, 'j': 8, 'k': 10, 'cost': 7}, {'i': 9, 'j': 9, 'k': 1, 'cost': 32}, {'i': 9, 'j': 9, 'k': 2, 'cost': 85}, {'i': 9, 'j': 9, 'k': 3, 'cost': 43}, {'i': 9, 'j': 9, 'k': 4, 'cost': 81}, {'i': 9, 'j': 9, 'k': 5, 'cost': 31}, {'i': 9, 'j': 9, 'k': 6, 'cost': 37}, {'i': 9, 'j': 9, 'k': 7, 'cost': 85}, {'i': 9, 'j': 9, 'k': 8, 'cost': 85}, {'i': 9, 'j': 9, 'k': 9, 'cost': 40}, {'i': 9, 'j': 9, 'k': 10, 'cost': 83}, {'i': 9, 'j': 10, 'k': 1, 'cost': 39}, {'i': 9, 'j': 10, 'k': 2, 'cost': 33}, {'i': 9, 'j': 10, 'k': 3, 'cost': 37}, {'i': 9, 'j': 10, 'k': 4, 'cost': 50}, {'i': 9, 'j': 10, 'k': 5, 'cost': 30}, {'i': 9, 'j': 10, 'k': 6, 'cost': 76}, {'i': 9, 'j': 10, 'k': 7, 'cost': 56}, {'i': 9, 'j': 10, 'k': 8, 'cost': 58}, {'i': 9, 'j': 10, 'k': 9, 'cost': 16}, {'i': 9, 'j': 10, 'k': 10, 'cost': 75}, {'i': 10, 'j': 1, 'k': 1, 'cost': 35}, {'i': 10, 'j': 1, 'k': 2, 'cost': 37}, {'i': 10, 'j': 1, 'k': 3, 'cost': 55}, {'i': 10, 'j': 1, 'k': 4, 'cost': 51}, {'i': 10, 'j': 1, 'k': 5, 'cost': 86}, {'i': 10, 'j': 1, 'k': 6, 'cost': 59}, {'i': 10, 'j': 1, 'k': 7, 'cost': 53}, {'i': 10, 'j': 1, 'k': 8, 'cost': 66}, {'i': 10, 'j': 1, 'k': 9, 'cost': 18}, {'i': 10, 'j': 1, 'k': 10, 'cost': 6}, {'i': 10, 'j': 2, 'k': 1, 'cost': 57}, {'i': 10, 'j': 2, 'k': 2, 'cost': 25}, {'i': 10, 'j': 2, 'k': 3, 'cost': 58}, {'i': 10, 'j': 2, 'k': 4, 'cost': 33}, {'i': 10, 'j': 2, 'k': 5, 'cost': 51}, {'i': 10, 'j': 2, 'k': 6, 'cost': 57}, {'i': 10, 'j': 2, 'k': 7, 'cost': 89}, {'i': 10, 'j': 2, 'k': 8, 'cost': 67}, {'i': 10, 'j': 2, 'k': 9, 'cost': 8}, {'i': 10, 'j': 2, 'k': 10, 'cost': 53}, {'i': 10, 'j': 3, 'k': 1, 'cost': 58}, {'i': 10, 'j': 3, 'k': 2, 'cost': 98}, {'i': 10, 'j': 3, 'k': 3, 'cost': 69}, {'i': 10, 'j': 3, 'k': 4, 'cost': 29}, {'i': 10, 'j': 3, 'k': 5, 'cost': 66}, {'i': 10, 'j': 3, 'k': 6, 'cost': 96}, {'i': 10, 'j': 3, 'k': 7, 'cost': 1}, {'i': 10, 'j': 3, 'k': 8, 'cost': 0}, {'i': 10, 'j': 3, 'k': 9, 'cost': 1}, {'i': 10, 'j': 3, 'k': 10, 'cost': 10}, {'i': 10, 'j': 4, 'k': 1, 'cost': 92}, {'i': 10, 'j': 4, 'k': 2, 'cost': 9}, {'i': 10, 'j': 4, 'k': 3, 'cost': 22}, {'i': 10, 'j': 4, 'k': 4, 'cost': 94}, {'i': 10, 'j': 4, 'k': 5, 'cost': 46}, {'i': 10, 'j': 4, 'k': 6, 'cost': 15}, {'i': 10, 'j': 4, 'k': 7, 'cost': 45}, {'i': 10, 'j': 4, 'k': 8, 'cost': 7}, {'i': 10, 'j': 4, 'k': 9, 'cost': 38}, {'i': 10, 'j': 4, 'k': 10, 'cost': 83}, {'i': 10, 'j': 5, 'k': 1, 'cost': 65}, {'i': 10, 'j': 5, 'k': 2, 'cost': 29}, {'i': 10, 'j': 5, 'k': 3, 'cost': 89}, {'i': 10, 'j': 5, 'k': 4, 'cost': 76}, {'i': 10, 'j': 5, 'k': 5, 'cost': 36}, {'i': 10, 'j': 5, 'k': 6, 'cost': 51}, {'i': 10, 'j': 5, 'k': 7, 'cost': 6}, {'i': 10, 'j': 5, 'k': 8, 'cost': 91}, {'i': 10, 'j': 5, 'k': 9, 'cost': 57}, {'i': 10, 'j': 5, 'k': 10, 'cost': 68}, {'i': 10, 'j': 6, 'k': 1, 'cost': 79}, {'i': 10, 'j': 6, 'k': 2, 'cost': 37}, {'i': 10, 'j': 6, 'k': 3, 'cost': 93}, {'i': 10, 'j': 6, 'k': 4, 'cost': 48}, {'i': 10, 'j': 6, 'k': 5, 'cost': 52}, {'i': 10, 'j': 6, 'k': 6, 'cost': 10}, {'i': 10, 'j': 6, 'k': 7, 'cost': 63}, {'i': 10, 'j': 6, 'k': 8, 'cost': 93}, {'i': 10, 'j': 6, 'k': 9, 'cost': 69}, {'i': 10, 'j': 6, 'k': 10, 'cost': 48}, {'i': 10, 'j': 7, 'k': 1, 'cost': 34}, {'i': 10, 'j': 7, 'k': 2, 'cost': 66}, {'i': 10, 'j': 7, 'k': 3, 'cost': 17}, {'i': 10, 'j': 7, 'k': 4, 'cost': 27}, {'i': 10, 'j': 7, 'k': 5, 'cost': 50}, {'i': 10, 'j': 7, 'k': 6, 'cost': 9}, {'i': 10, 'j': 7, 'k': 7, 'cost': 57}, {'i': 10, 'j': 7, 'k': 8, 'cost': 80}, {'i': 10, 'j': 7, 'k': 9, 'cost': 36}, {'i': 10, 'j': 7, 'k': 10, 'cost': 26}, {'i': 10, 'j': 8, 'k': 1, 'cost': 78}, {'i': 10, 'j': 8, 'k': 2, 'cost': 99}, {'i': 10, 'j': 8, 'k': 3, 'cost': 8}, {'i': 10, 'j': 8, 'k': 4, 'cost': 38}, {'i': 10, 'j': 8, 'k': 5, 'cost': 55}, {'i': 10, 'j': 8, 'k': 6, 'cost': 17}, {'i': 10, 'j': 8, 'k': 7, 'cost': 29}, {'i': 10, 'j': 8, 'k': 8, 'cost': 0}, {'i': 10, 'j': 8, 'k': 9, 'cost': 46}, {'i': 10, 'j': 8, 'k': 10, 'cost': 97}, {'i': 10, 'j': 9, 'k': 1, 'cost': 25}, {'i': 10, 'j': 9, 'k': 2, 'cost': 96}, {'i': 10, 'j': 9, 'k': 3, 'cost': 12}, {'i': 10, 'j': 9, 'k': 4, 'cost': 55}, {'i': 10, 'j': 9, 'k': 5, 'cost': 37}, {'i': 10, 'j': 9, 'k': 6, 'cost': 75}, {'i': 10, 'j': 9, 'k': 7, 'cost': 98}, {'i': 10, 'j': 9, 'k': 8, 'cost': 39}, {'i': 10, 'j': 9, 'k': 9, 'cost': 86}, {'i': 10, 'j': 9, 'k': 10, 'cost': 66}, {'i': 10, 'j': 10, 'k': 1, 'cost': 57}, {'i': 10, 'j': 10, 'k': 2, 'cost': 75}, {'i': 10, 'j': 10, 'k': 3, 'cost': 48}, {'i': 10, 'j': 10, 'k': 4, 'cost': 23}, {'i': 10, 'j': 10, 'k': 5, 'cost': 46}, {'i': 10, 'j': 10, 'k': 6, 'cost': 18}, {'i': 10, 'j': 10, 'k': 7, 'cost': 15}, {'i': 10, 'j': 10, 'k': 8, 'cost': 50}, {'i': 10, 'j': 10, 'k': 9, 'cost': 93}, {'i': 10, 'j': 10, 'k': 10, 'cost': 11}]}","[[1, 8, 6], [2, 2, 2], [3, 9, 4], [4, 10, 7], [5, 5, 8], [6, 7, 3], [7, 4, 1], [8, 6, 10], [9, 1, 5], [10, 3, 9]]",33,csv,1
+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.
+
+They correspond to the 11 sessions labeled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
+
+*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=1
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 40 | 74 | 69 | 42 | 0 | 30 | 68 | 2 | 33 | 66 | 63 |
+| 2 | 71 | 59 | 51 | 3 | 93 | 31 | 88 | 64 | 17 | 48 | 97 |
+| 3 | 25 | 36 | 20 | 52 | 36 | 20 | 82 | 70 | 14 | 67 | 16 |
+| 4 | 13 | 96 | 21 | 43 | 5 | 81 | 29 | 27 | 39 | 75 | 18 |
+| 5 | 31 | 31 | 43 | 14 | 44 | 37 | 46 | 54 | 7 | 15 | 3 |
+| 6 | 72 | 68 | 13 | 33 | 66 | 6 | 51 | 20 | 73 | 61 | 87 |
+| 7 | 67 | 89 | 36 | 87 | 47 | 14 | 13 | 32 | 23 | 11 | 0 |
+| 8 | 5 | 94 | 60 | 13 | 65 | 72 | 97 | 96 | 19 | 10 | 89 |
+| 9 | 30 | 5 | 77 | 24 | 61 | 97 | 41 | 45 | 16 | 13 | 52 |
+| 10 | 88 | 78 | 10 | 94 | 92 | 66 | 6 | 94 | 62 | 69 | 43 |
+| 11 | 93 | 19 | 27 | 8 | 68 | 88 | 0 | 66 | 61 | 8 | 59 |
+
+## session_id=2
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 92 | 93 | 0 | 68 | 22 | 97 | 8 | 0 | 74 | 38 | 13 |
+| 2 | 0 | 54 | 71 | 5 | 49 | 32 | 59 | 18 | 41 | 93 | 87 |
+| 3 | 12 | 33 | 17 | 48 | 52 | 94 | 70 | 40 | 83 | 41 | 49 |
+| 4 | 85 | 97 | 86 | 52 | 27 | 48 | 25 | 30 | 43 | 93 | 75 |
+| 5 | 5 | 7 | 5 | 27 | 25 | 4 | 8 | 47 | 10 | 57 | 7 |
+| 6 | 37 | 35 | 12 | 65 | 42 | 29 | 33 | 15 | 57 | 94 | 27 |
+| 7 | 25 | 57 | 12 | 63 | 75 | 37 | 90 | 77 | 83 | 75 | 81 |
+| 8 | 38 | 89 | 78 | 88 | 69 | 74 | 49 | 90 | 55 | 4 | 6 |
+| 9 | 57 | 20 | 15 | 11 | 29 | 90 | 35 | 40 | 29 | 76 | 23 |
+| 10 | 18 | 49 | 75 | 36 | 37 | 73 | 88 | 62 | 72 | 17 | 78 |
+| 11 | 88 | 91 | 7 | 61 | 71 | 72 | 58 | 43 | 22 | 26 | 97 |
+
+## session_id=3
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 49 | 50 | 13 | 92 | 24 | 85 | 55 | 8 | 64 | 30 | 5 |
+| 2 | 15 | 0 | 87 | 24 | 11 | 90 | 28 | 42 | 98 | 86 | 0 |
+| 3 | 0 | 57 | 32 | 44 | 60 | 85 | 27 | 80 | 44 | 7 | 12 |
+| 4 | 3 | 47 | 15 | 54 | 99 | 5 | 19 | 12 | 44 | 57 | 32 |
+| 5 | 39 | 7 | 59 | 56 | 99 | 27 | 83 | 23 | 91 | 64 | 54 |
+| 6 | 14 | 67 | 17 | 7 | 65 | 4 | 85 | 9 | 1 | 91 | 54 |
+| 7 | 23 | 78 | 68 | 5 | 95 | 86 | 8 | 50 | 40 | 6 | 7 |
+| 8 | 11 | 9 | 23 | 60 | 16 | 75 | 94 | 82 | 30 | 24 | 58 |
+| 9 | 3 | 1 | 86 | 15 | 79 | 33 | 98 | 89 | 17 | 90 | 12 |
+| 10 | 87 | 57 | 3 | 71 | 65 | 89 | 84 | 63 | 97 | 60 | 78 |
+| 11 | 86 | 11 | 49 | 49 | 7 | 49 | 7 | 56 | 60 | 27 | 57 |
+
+## session_id=4
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 38 | 80 | 34 | 10 | 84 | 59 | 53 | 24 | 51 | 48 | 93 |
+| 2 | 86 | 79 | 54 | 5 | 16 | 3 | 32 | 23 | 39 | 43 | 44 |
+| 3 | 62 | 19 | 70 | 10 | 50 | 49 | 61 | 0 | 80 | 9 | 63 |
+| 4 | 30 | 48 | 76 | 76 | 53 | 57 | 23 | 20 | 11 | 36 | 99 |
+| 5 | 90 | 93 | 46 | 18 | 30 | 69 | 8 | 48 | 83 | 35 | 71 |
+| 6 | 63 | 79 | 95 | 30 | 21 | 69 | 16 | 8 | 64 | 47 | 8 |
+| 7 | 86 | 16 | 39 | 32 | 35 | 78 | 94 | 95 | 76 | 37 | 1 |
+| 8 | 17 | 62 | 28 | 91 | 1 | 98 | 9 | 93 | 84 | 38 | 98 |
+| 9 | 76 | 21 | 90 | 57 | 79 | 8 | 39 | 98 | 90 | 68 | 36 |
+| 10 | 73 | 98 | 93 | 14 | 88 | 6 | 72 | 22 | 81 | 97 | 25 |
+| 11 | 32 | 48 | 16 | 27 | 15 | 37 | 46 | 92 | 86 | 53 | 56 |
+
+## session_id=5
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 40 | 52 | 16 | 94 | 42 | 37 | 28 | 39 | 25 | 19 | 77 |
+| 2 | 61 | 48 | 34 | 50 | 57 | 28 | 78 | 29 | 24 | 96 | 54 |
+| 3 | 32 | 27 | 32 | 94 | 42 | 17 | 27 | 80 | 81 | 80 | 19 |
+| 4 | 33 | 63 | 71 | 8 | 78 | 42 | 73 | 70 | 76 | 80 | 2 |
+| 5 | 23 | 14 | 59 | 81 | 37 | 81 | 15 | 45 | 15 | 62 | 16 |
+| 6 | 92 | 78 | 25 | 45 | 89 | 95 | 88 | 28 | 3 | 82 | 91 |
+| 7 | 82 | 49 | 93 | 37 | 97 | 48 | 34 | 18 | 68 | 88 | 3 |
+| 8 | 83 | 97 | 48 | 56 | 9 | 2 | 94 | 16 | 99 | 35 | 89 |
+| 9 | 66 | 0 | 3 | 94 | 8 | 11 | 32 | 88 | 61 | 10 | 21 |
+| 10 | 66 | 25 | 1 | 41 | 72 | 97 | 8 | 71 | 37 | 82 | 9 |
+| 11 | 5 | 4 | 98 | 75 | 39 | 82 | 58 | 60 | 77 | 65 | 24 |
+
+## session_id=6
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 70 | 0 | 56 | 30 | 78 | 90 | 94 | 48 | 19 | 73 | 14 |
+| 2 | 85 | 9 | 16 | 73 | 90 | 9 | 62 | 67 | 84 | 5 | 99 |
+| 3 | 11 | 68 | 13 | 25 | 22 | 11 | 49 | 51 | 28 | 81 | 39 |
+| 4 | 43 | 10 | 92 | 93 | 63 | 65 | 59 | 44 | 11 | 40 | 9 |
+| 5 | 87 | 46 | 52 | 67 | 55 | 5 | 99 | 45 | 33 | 54 | 50 |
+| 6 | 5 | 21 | 33 | 17 | 70 | 95 | 74 | 68 | 25 | 27 | 9 |
+| 7 | 19 | 80 | 91 | 1 | 61 | 88 | 20 | 25 | 96 | 83 | 33 |
+| 8 | 97 | 84 | 81 | 53 | 23 | 15 | 55 | 9 | 30 | 90 | 75 |
+| 9 | 39 | 72 | 47 | 26 | 5 | 47 | 12 | 56 | 17 | 74 | 29 |
+| 10 | 82 | 60 | 29 | 61 | 43 | 64 | 15 | 85 | 32 | 64 | 24 |
+| 11 | 18 | 83 | 81 | 74 | 81 | 56 | 57 | 31 | 89 | 17 | 36 |
+
+## session_id=7
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 95 | 92 | 40 | 6 | 77 | 35 | 70 | 27 | 48 | 53 | 6 |
+| 2 | 91 | 51 | 53 | 26 | 21 | 75 | 45 | 60 | 65 | 29 | 16 |
+| 3 | 84 | 91 | 99 | 77 | 84 | 94 | 5 | 62 | 67 | 91 | 89 |
+| 4 | 34 | 37 | 80 | 42 | 63 | 61 | 96 | 38 | 36 | 70 | 19 |
+| 5 | 15 | 52 | 52 | 54 | 0 | 33 | 29 | 87 | 62 | 96 | 57 |
+| 6 | 37 | 56 | 56 | 13 | 44 | 33 | 80 | 10 | 28 | 38 | 68 |
+| 7 | 37 | 44 | 27 | 16 | 85 | 6 | 75 | 47 | 54 | 74 | 60 |
+| 8 | 49 | 25 | 3 | 60 | 7 | 43 | 87 | 27 | 84 | 78 | 42 |
+| 9 | 47 | 23 | 67 | 74 | 83 | 74 | 11 | 14 | 75 | 3 | 56 |
+| 10 | 86 | 99 | 80 | 61 | 18 | 90 | 95 | 74 | 31 | 31 | 83 |
+| 11 | 54 | 93 | 77 | 53 | 46 | 12 | 37 | 52 | 76 | 97 | 91 |
+
+## session_id=8
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 13 | 66 | 52 | 69 | 33 | 9 | 68 | 86 | 34 | 7 | 1 |
+| 2 | 50 | 95 | 89 | 57 | 32 | 39 | 89 | 21 | 28 | 28 | 75 |
+| 3 | 19 | 68 | 24 | 4 | 57 | 46 | 75 | 20 | 13 | 5 | 64 |
+| 4 | 40 | 63 | 25 | 13 | 32 | 41 | 60 | 45 | 2 | 51 | 77 |
+| 5 | 45 | 86 | 75 | 58 | 76 | 15 | 4 | 47 | 54 | 99 | 33 |
+| 6 | 53 | 22 | 94 | 39 | 66 | 32 | 69 | 13 | 49 | 87 | 65 |
+| 7 | 64 | 72 | 44 | 62 | 96 | 52 | 64 | 33 | 6 | 7 | 91 |
+| 8 | 41 | 82 | 35 | 17 | 5 | 88 | 1 | 3 | 6 | 72 | 54 |
+| 9 | 46 | 0 | 65 | 78 | 60 | 90 | 16 | 89 | 11 | 30 | 76 |
+| 10 | 78 | 49 | 61 | 45 | 54 | 78 | 55 | 5 | 56 | 76 | 59 |
+| 11 | 68 | 42 | 25 | 59 | 77 | 55 | 82 | 52 | 68 | 72 | 34 |
+
+## session_id=9
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 86 | 27 | 88 | 48 | 22 | 57 | 51 | 43 | 72 | 24 | 70 |
+| 2 | 80 | 15 | 61 | 15 | 78 | 9 | 69 | 71 | 73 | 95 | 23 |
+| 3 | 80 | 69 | 82 | 74 | 67 | 75 | 21 | 35 | 9 | 73 | 38 |
+| 4 | 75 | 29 | 87 | 43 | 39 | 98 | 19 | 94 | 74 | 1 | 51 |
+| 5 | 72 | 13 | 56 | 52 | 43 | 20 | 83 | 71 | 89 | 9 | 25 |
+| 6 | 17 | 85 | 31 | 23 | 92 | 41 | 71 | 22 | 6 | 15 | 5 |
+| 7 | 76 | 33 | 0 | 74 | 75 | 78 | 27 | 72 | 19 | 52 | 88 |
+| 8 | 86 | 53 | 87 | 86 | 21 | 88 | 1 | 98 | 65 | 3 | 68 |
+| 9 | 81 | 39 | 77 | 44 | 2 | 42 | 30 | 3 | 91 | 64 | 99 |
+| 10 | 7 | 21 | 17 | 21 | 47 | 54 | 49 | 80 | 32 | 15 | 75 |
+| 11 | 32 | 61 | 65 | 52 | 44 | 88 | 42 | 92 | 46 | 96 | 16 |
+
+## session_id=10
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 87 | 32 | 65 | 36 | 88 | 68 | 5 | 54 | 29 | 7 | 55 |
+| 2 | 93 | 48 | 31 | 15 | 75 | 83 | 80 | 45 | 7 | 40 | 86 |
+| 3 | 25 | 49 | 36 | 89 | 70 | 99 | 28 | 96 | 61 | 74 | 15 |
+| 4 | 14 | 66 | 96 | 49 | 49 | 91 | 94 | 40 | 56 | 93 | 63 |
+| 5 | 8 | 3 | 75 | 16 | 38 | 62 | 98 | 70 | 23 | 49 | 58 |
+| 6 | 51 | 68 | 38 | 58 | 70 | 45 | 26 | 98 | 41 | 53 | 59 |
+| 7 | 26 | 43 | 26 | 63 | 95 | 58 | 2 | 5 | 31 | 93 | 74 |
+| 8 | 88 | 32 | 35 | 1 | 49 | 9 | 20 | 58 | 4 | 66 | 28 |
+| 9 | 7 | 81 | 76 | 79 | 61 | 84 | 81 | 32 | 10 | 11 | 17 |
+| 10 | 13 | 53 | 85 | 84 | 21 | 12 | 43 | 22 | 62 | 55 | 0 |
+| 11 | 0 | 38 | 53 | 37 | 70 | 7 | 10 | 54 | 27 | 50 | 47 |
+
+## session_id=11
+| tutor_id\textbook_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 95 | 95 | 27 | 38 | 28 | 68 | 73 | 1 | 78 | 11 | 40 |
+| 2 | 58 | 86 | 33 | 67 | 94 | 88 | 39 | 92 | 36 | 4 | 41 |
+| 3 | 0 | 99 | 48 | 80 | 74 | 81 | 66 | 28 | 13 | 51 | 18 |
+| 4 | 85 | 40 | 93 | 82 | 22 | 72 | 61 | 11 | 14 | 0 | 33 |
+| 5 | 65 | 49 | 20 | 62 | 70 | 67 | 30 | 30 | 50 | 52 | 82 |
+| 6 | 70 | 9 | 15 | 3 | 30 | 81 | 80 | 35 | 55 | 45 | 61 |
+| 7 | 13 | 1 | 96 | 38 | 70 | 99 | 81 | 49 | 73 | 39 | 47 |
+| 8 | 30 | 82 | 98 | 7 | 66 | 47 | 36 | 68 | 80 | 90 | 80 |
+| 9 | 30 | 71 | 48 | 49 | 9 | 34 | 81 | 36 | 49 | 43 | 19 |
+| 10 | 5 | 60 | 11 | 86 | 58 | 13 | 48 | 87 | 14 | 41 | 23 |
+| 11 | 33 | 39 | 88 | 82 | 80 | 33 | 89 | 34 | 2 | 60 | 78 |
+
+The optimal plan is the selection of one triple per session that minimizes the total cost.
+
+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': [[[40, 74, 69, 42, 0, 30, 68, 2, 33, 66, 63], [71, 59, 51, 3, 93, 31, 88, 64, 17, 48, 97], [25, 36, 20, 52, 36, 20, 82, 70, 14, 67, 16], [13, 96, 21, 43, 5, 81, 29, 27, 39, 75, 18], [31, 31, 43, 14, 44, 37, 46, 54, 7, 15, 3], [72, 68, 13, 33, 66, 6, 51, 20, 73, 61, 87], [67, 89, 36, 87, 47, 14, 13, 32, 23, 11, 0], [5, 94, 60, 13, 65, 72, 97, 96, 19, 10, 89], [30, 5, 77, 24, 61, 97, 41, 45, 16, 13, 52], [88, 78, 10, 94, 92, 66, 6, 94, 62, 69, 43], [93, 19, 27, 8, 68, 88, 0, 66, 61, 8, 59]], [[92, 93, 0, 68, 22, 97, 8, 0, 74, 38, 13], [0, 54, 71, 5, 49, 32, 59, 18, 41, 93, 87], [12, 33, 17, 48, 52, 94, 70, 40, 83, 41, 49], [85, 97, 86, 52, 27, 48, 25, 30, 43, 93, 75], [5, 7, 5, 27, 25, 4, 8, 47, 10, 57, 7], [37, 35, 12, 65, 42, 29, 33, 15, 57, 94, 27], [25, 57, 12, 63, 75, 37, 90, 77, 83, 75, 81], [38, 89, 78, 88, 69, 74, 49, 90, 55, 4, 6], [57, 20, 15, 11, 29, 90, 35, 40, 29, 76, 23], [18, 49, 75, 36, 37, 73, 88, 62, 72, 17, 78], [88, 91, 7, 61, 71, 72, 58, 43, 22, 26, 97]], [[49, 50, 13, 92, 24, 85, 55, 8, 64, 30, 5], [15, 0, 87, 24, 11, 90, 28, 42, 98, 86, 0], [0, 57, 32, 44, 60, 85, 27, 80, 44, 7, 12], [3, 47, 15, 54, 99, 5, 19, 12, 44, 57, 32], [39, 7, 59, 56, 99, 27, 83, 23, 91, 64, 54], [14, 67, 17, 7, 65, 4, 85, 9, 1, 91, 54], [23, 78, 68, 5, 95, 86, 8, 50, 40, 6, 7], [11, 9, 23, 60, 16, 75, 94, 82, 30, 24, 58], [3, 1, 86, 15, 79, 33, 98, 89, 17, 90, 12], [87, 57, 3, 71, 65, 89, 84, 63, 97, 60, 78], [86, 11, 49, 49, 7, 49, 7, 56, 60, 27, 57]], [[38, 80, 34, 10, 84, 59, 53, 24, 51, 48, 93], [86, 79, 54, 5, 16, 3, 32, 23, 39, 43, 44], [62, 19, 70, 10, 50, 49, 61, 0, 80, 9, 63], [30, 48, 76, 76, 53, 57, 23, 20, 11, 36, 99], [90, 93, 46, 18, 30, 69, 8, 48, 83, 35, 71], [63, 79, 95, 30, 21, 69, 16, 8, 64, 47, 8], [86, 16, 39, 32, 35, 78, 94, 95, 76, 37, 1], [17, 62, 28, 91, 1, 98, 9, 93, 84, 38, 98], [76, 21, 90, 57, 79, 8, 39, 98, 90, 68, 36], [73, 98, 93, 14, 88, 6, 72, 22, 81, 97, 25], [32, 48, 16, 27, 15, 37, 46, 92, 86, 53, 56]], [[40, 52, 16, 94, 42, 37, 28, 39, 25, 19, 77], [61, 48, 34, 50, 57, 28, 78, 29, 24, 96, 54], [32, 27, 32, 94, 42, 17, 27, 80, 81, 80, 19], [33, 63, 71, 8, 78, 42, 73, 70, 76, 80, 2], [23, 14, 59, 81, 37, 81, 15, 45, 15, 62, 16], [92, 78, 25, 45, 89, 95, 88, 28, 3, 82, 91], [82, 49, 93, 37, 97, 48, 34, 18, 68, 88, 3], [83, 97, 48, 56, 9, 2, 94, 16, 99, 35, 89], [66, 0, 3, 94, 8, 11, 32, 88, 61, 10, 21], [66, 25, 1, 41, 72, 97, 8, 71, 37, 82, 9], [5, 4, 98, 75, 39, 82, 58, 60, 77, 65, 24]], [[70, 0, 56, 30, 78, 90, 94, 48, 19, 73, 14], [85, 9, 16, 73, 90, 9, 62, 67, 84, 5, 99], [11, 68, 13, 25, 22, 11, 49, 51, 28, 81, 39], [43, 10, 92, 93, 63, 65, 59, 44, 11, 40, 9], [87, 46, 52, 67, 55, 5, 99, 45, 33, 54, 50], [5, 21, 33, 17, 70, 95, 74, 68, 25, 27, 9], [19, 80, 91, 1, 61, 88, 20, 25, 96, 83, 33], [97, 84, 81, 53, 23, 15, 55, 9, 30, 90, 75], [39, 72, 47, 26, 5, 47, 12, 56, 17, 74, 29], [82, 60, 29, 61, 43, 64, 15, 85, 32, 64, 24], [18, 83, 81, 74, 81, 56, 57, 31, 89, 17, 36]], [[95, 92, 40, 6, 77, 35, 70, 27, 48, 53, 6], [91, 51, 53, 26, 21, 75, 45, 60, 65, 29, 16], [84, 91, 99, 77, 84, 94, 5, 62, 67, 91, 89], [34, 37, 80, 42, 63, 61, 96, 38, 36, 70, 19], [15, 52, 52, 54, 0, 33, 29, 87, 62, 96, 57], [37, 56, 56, 13, 44, 33, 80, 10, 28, 38, 68], [37, 44, 27, 16, 85, 6, 75, 47, 54, 74, 60], [49, 25, 3, 60, 7, 43, 87, 27, 84, 78, 42], [47, 23, 67, 74, 83, 74, 11, 14, 75, 3, 56], [86, 99, 80, 61, 18, 90, 95, 74, 31, 31, 83], [54, 93, 77, 53, 46, 12, 37, 52, 76, 97, 91]], [[13, 66, 52, 69, 33, 9, 68, 86, 34, 7, 1], [50, 95, 89, 57, 32, 39, 89, 21, 28, 28, 75], [19, 68, 24, 4, 57, 46, 75, 20, 13, 5, 64], [40, 63, 25, 13, 32, 41, 60, 45, 2, 51, 77], [45, 86, 75, 58, 76, 15, 4, 47, 54, 99, 33], [53, 22, 94, 39, 66, 32, 69, 13, 49, 87, 65], [64, 72, 44, 62, 96, 52, 64, 33, 6, 7, 91], [41, 82, 35, 17, 5, 88, 1, 3, 6, 72, 54], [46, 0, 65, 78, 60, 90, 16, 89, 11, 30, 76], [78, 49, 61, 45, 54, 78, 55, 5, 56, 76, 59], [68, 42, 25, 59, 77, 55, 82, 52, 68, 72, 34]], [[86, 27, 88, 48, 22, 57, 51, 43, 72, 24, 70], [80, 15, 61, 15, 78, 9, 69, 71, 73, 95, 23], [80, 69, 82, 74, 67, 75, 21, 35, 9, 73, 38], [75, 29, 87, 43, 39, 98, 19, 94, 74, 1, 51], [72, 13, 56, 52, 43, 20, 83, 71, 89, 9, 25], [17, 85, 31, 23, 92, 41, 71, 22, 6, 15, 5], [76, 33, 0, 74, 75, 78, 27, 72, 19, 52, 88], [86, 53, 87, 86, 21, 88, 1, 98, 65, 3, 68], [81, 39, 77, 44, 2, 42, 30, 3, 91, 64, 99], [7, 21, 17, 21, 47, 54, 49, 80, 32, 15, 75], [32, 61, 65, 52, 44, 88, 42, 92, 46, 96, 16]], [[87, 32, 65, 36, 88, 68, 5, 54, 29, 7, 55], [93, 48, 31, 15, 75, 83, 80, 45, 7, 40, 86], [25, 49, 36, 89, 70, 99, 28, 96, 61, 74, 15], [14, 66, 96, 49, 49, 91, 94, 40, 56, 93, 63], [8, 3, 75, 16, 38, 62, 98, 70, 23, 49, 58], [51, 68, 38, 58, 70, 45, 26, 98, 41, 53, 59], [26, 43, 26, 63, 95, 58, 2, 5, 31, 93, 74], [88, 32, 35, 1, 49, 9, 20, 58, 4, 66, 28], [7, 81, 76, 79, 61, 84, 81, 32, 10, 11, 17], [13, 53, 85, 84, 21, 12, 43, 22, 62, 55, 0], [0, 38, 53, 37, 70, 7, 10, 54, 27, 50, 47]], [[95, 95, 27, 38, 28, 68, 73, 1, 78, 11, 40], [58, 86, 33, 67, 94, 88, 39, 92, 36, 4, 41], [0, 99, 48, 80, 74, 81, 66, 28, 13, 51, 18], [85, 40, 93, 82, 22, 72, 61, 11, 14, 0, 33], [65, 49, 20, 62, 70, 67, 30, 30, 50, 52, 82], [70, 9, 15, 3, 30, 81, 80, 35, 55, 45, 61], [13, 1, 96, 38, 70, 99, 81, 49, 73, 39, 47], [30, 82, 98, 7, 66, 47, 36, 68, 80, 90, 80], [30, 71, 48, 49, 9, 34, 81, 36, 49, 43, 19], [5, 60, 11, 86, 58, 13, 48, 87, 14, 41, 23], [33, 39, 88, 82, 80, 33, 89, 34, 2, 60, 78]]], 'objective': 9.0}","[[0, 10, 6], [1, 0, 2], [2, 5, 8], [3, 1, 5], [4, 8, 1], [5, 6, 3], [6, 4, 4], [7, 7, 7], [8, 3, 9], [9, 9, 10], [10, 2, 0]]",9.0,"{'problem_type': 'AP3', 'n': 11, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 40}, {'i': 1, 'j': 1, 'k': 2, 'cost': 74}, {'i': 1, 'j': 1, 'k': 3, 'cost': 69}, {'i': 1, 'j': 1, 'k': 4, 'cost': 42}, {'i': 1, 'j': 1, 'k': 5, 'cost': 0}, {'i': 1, 'j': 1, 'k': 6, 'cost': 30}, {'i': 1, 'j': 1, 'k': 7, 'cost': 68}, {'i': 1, 'j': 1, 'k': 8, 'cost': 2}, {'i': 1, 'j': 1, 'k': 9, 'cost': 33}, {'i': 1, 'j': 1, 'k': 10, 'cost': 66}, {'i': 1, 'j': 1, 'k': 11, 'cost': 63}, {'i': 1, 'j': 2, 'k': 1, 'cost': 71}, {'i': 1, 'j': 2, 'k': 2, 'cost': 59}, {'i': 1, 'j': 2, 'k': 3, 'cost': 51}, {'i': 1, 'j': 2, 'k': 4, 'cost': 3}, {'i': 1, 'j': 2, 'k': 5, 'cost': 93}, {'i': 1, 'j': 2, 'k': 6, 'cost': 31}, {'i': 1, 'j': 2, 'k': 7, 'cost': 88}, {'i': 1, 'j': 2, 'k': 8, 'cost': 64}, {'i': 1, 'j': 2, 'k': 9, 'cost': 17}, {'i': 1, 'j': 2, 'k': 10, 'cost': 48}, {'i': 1, 'j': 2, 'k': 11, 'cost': 97}, {'i': 1, 'j': 3, 'k': 1, 'cost': 25}, {'i': 1, 'j': 3, 'k': 2, 'cost': 36}, {'i': 1, 'j': 3, 'k': 3, 'cost': 20}, {'i': 1, 'j': 3, 'k': 4, 'cost': 52}, {'i': 1, 'j': 3, 'k': 5, 'cost': 36}, {'i': 1, 'j': 3, 'k': 6, 'cost': 20}, {'i': 1, 'j': 3, 'k': 7, 'cost': 82}, {'i': 1, 'j': 3, 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'cost': 75}, {'i': 9, 'j': 3, 'k': 7, 'cost': 21}, {'i': 9, 'j': 3, 'k': 8, 'cost': 35}, {'i': 9, 'j': 3, 'k': 9, 'cost': 9}, {'i': 9, 'j': 3, 'k': 10, 'cost': 73}, {'i': 9, 'j': 3, 'k': 11, 'cost': 38}, {'i': 9, 'j': 4, 'k': 1, 'cost': 75}, {'i': 9, 'j': 4, 'k': 2, 'cost': 29}, {'i': 9, 'j': 4, 'k': 3, 'cost': 87}, {'i': 9, 'j': 4, 'k': 4, 'cost': 43}, {'i': 9, 'j': 4, 'k': 5, 'cost': 39}, {'i': 9, 'j': 4, 'k': 6, 'cost': 98}, {'i': 9, 'j': 4, 'k': 7, 'cost': 19}, {'i': 9, 'j': 4, 'k': 8, 'cost': 94}, {'i': 9, 'j': 4, 'k': 9, 'cost': 74}, {'i': 9, 'j': 4, 'k': 10, 'cost': 1}, {'i': 9, 'j': 4, 'k': 11, 'cost': 51}, {'i': 9, 'j': 5, 'k': 1, 'cost': 72}, {'i': 9, 'j': 5, 'k': 2, 'cost': 13}, {'i': 9, 'j': 5, 'k': 3, 'cost': 56}, {'i': 9, 'j': 5, 'k': 4, 'cost': 52}, {'i': 9, 'j': 5, 'k': 5, 'cost': 43}, {'i': 9, 'j': 5, 'k': 6, 'cost': 20}, {'i': 9, 'j': 5, 'k': 7, 'cost': 83}, {'i': 9, 'j': 5, 'k': 8, 'cost': 71}, {'i': 9, 'j': 5, 'k': 9, 'cost': 89}, {'i': 9, 'j': 5, 'k': 10, 'cost': 9}, {'i': 9, 'j': 5, 'k': 11, 'cost': 25}, {'i': 9, 'j': 6, 'k': 1, 'cost': 17}, {'i': 9, 'j': 6, 'k': 2, 'cost': 85}, {'i': 9, 'j': 6, 'k': 3, 'cost': 31}, {'i': 9, 'j': 6, 'k': 4, 'cost': 23}, {'i': 9, 'j': 6, 'k': 5, 'cost': 92}, {'i': 9, 'j': 6, 'k': 6, 'cost': 41}, {'i': 9, 'j': 6, 'k': 7, 'cost': 71}, {'i': 9, 'j': 6, 'k': 8, 'cost': 22}, {'i': 9, 'j': 6, 'k': 9, 'cost': 6}, {'i': 9, 'j': 6, 'k': 10, 'cost': 15}, {'i': 9, 'j': 6, 'k': 11, 'cost': 5}, {'i': 9, 'j': 7, 'k': 1, 'cost': 76}, {'i': 9, 'j': 7, 'k': 2, 'cost': 33}, {'i': 9, 'j': 7, 'k': 3, 'cost': 0}, {'i': 9, 'j': 7, 'k': 4, 'cost': 74}, {'i': 9, 'j': 7, 'k': 5, 'cost': 75}, {'i': 9, 'j': 7, 'k': 6, 'cost': 78}, {'i': 9, 'j': 7, 'k': 7, 'cost': 27}, {'i': 9, 'j': 7, 'k': 8, 'cost': 72}, {'i': 9, 'j': 7, 'k': 9, 'cost': 19}, {'i': 9, 'j': 7, 'k': 10, 'cost': 52}, {'i': 9, 'j': 7, 'k': 11, 'cost': 88}, {'i': 9, 'j': 8, 'k': 1, 'cost': 86}, {'i': 9, 'j': 8, 'k': 2, 'cost': 53}, {'i': 9, 'j': 8, 'k': 3, 'cost': 87}, {'i': 9, 'j': 8, 'k': 4, 'cost': 86}, {'i': 9, 'j': 8, 'k': 5, 'cost': 21}, {'i': 9, 'j': 8, 'k': 6, 'cost': 88}, {'i': 9, 'j': 8, 'k': 7, 'cost': 1}, {'i': 9, 'j': 8, 'k': 8, 'cost': 98}, {'i': 9, 'j': 8, 'k': 9, 'cost': 65}, {'i': 9, 'j': 8, 'k': 10, 'cost': 3}, {'i': 9, 'j': 8, 'k': 11, 'cost': 68}, {'i': 9, 'j': 9, 'k': 1, 'cost': 81}, {'i': 9, 'j': 9, 'k': 2, 'cost': 39}, {'i': 9, 'j': 9, 'k': 3, 'cost': 77}, {'i': 9, 'j': 9, 'k': 4, 'cost': 44}, {'i': 9, 'j': 9, 'k': 5, 'cost': 2}, {'i': 9, 'j': 9, 'k': 6, 'cost': 42}, {'i': 9, 'j': 9, 'k': 7, 'cost': 30}, {'i': 9, 'j': 9, 'k': 8, 'cost': 3}, {'i': 9, 'j': 9, 'k': 9, 'cost': 91}, {'i': 9, 'j': 9, 'k': 10, 'cost': 64}, {'i': 9, 'j': 9, 'k': 11, 'cost': 99}, {'i': 9, 'j': 10, 'k': 1, 'cost': 7}, {'i': 9, 'j': 10, 'k': 2, 'cost': 21}, {'i': 9, 'j': 10, 'k': 3, 'cost': 17}, {'i': 9, 'j': 10, 'k': 4, 'cost': 21}, {'i': 9, 'j': 10, 'k': 5, 'cost': 47}, {'i': 9, 'j': 10, 'k': 6, 'cost': 54}, {'i': 9, 'j': 10, 'k': 7, 'cost': 49}, {'i': 9, 'j': 10, 'k': 8, 'cost': 80}, {'i': 9, 'j': 10, 'k': 9, 'cost': 32}, {'i': 9, 'j': 10, 'k': 10, 'cost': 15}, {'i': 9, 'j': 10, 'k': 11, 'cost': 75}, {'i': 9, 'j': 11, 'k': 1, 'cost': 32}, {'i': 9, 'j': 11, 'k': 2, 'cost': 61}, {'i': 9, 'j': 11, 'k': 3, 'cost': 65}, {'i': 9, 'j': 11, 'k': 4, 'cost': 52}, {'i': 9, 'j': 11, 'k': 5, 'cost': 44}, {'i': 9, 'j': 11, 'k': 6, 'cost': 88}, {'i': 9, 'j': 11, 'k': 7, 'cost': 42}, {'i': 9, 'j': 11, 'k': 8, 'cost': 92}, {'i': 9, 'j': 11, 'k': 9, 'cost': 46}, {'i': 9, 'j': 11, 'k': 10, 'cost': 96}, {'i': 9, 'j': 11, 'k': 11, 'cost': 16}, {'i': 10, 'j': 1, 'k': 1, 'cost': 87}, {'i': 10, 'j': 1, 'k': 2, 'cost': 32}, {'i': 10, 'j': 1, 'k': 3, 'cost': 65}, {'i': 10, 'j': 1, 'k': 4, 'cost': 36}, {'i': 10, 'j': 1, 'k': 5, 'cost': 88}, {'i': 10, 'j': 1, 'k': 6, 'cost': 68}, {'i': 10, 'j': 1, 'k': 7, 'cost': 5}, {'i': 10, 'j': 1, 'k': 8, 'cost': 54}, {'i': 10, 'j': 1, 'k': 9, 'cost': 29}, {'i': 10, 'j': 1, 'k': 10, 'cost': 7}, {'i': 10, 'j': 1, 'k': 11, 'cost': 55}, {'i': 10, 'j': 2, 'k': 1, 'cost': 93}, {'i': 10, 'j': 2, 'k': 2, 'cost': 48}, {'i': 10, 'j': 2, 'k': 3, 'cost': 31}, {'i': 10, 'j': 2, 'k': 4, 'cost': 15}, {'i': 10, 'j': 2, 'k': 5, 'cost': 75}, {'i': 10, 'j': 2, 'k': 6, 'cost': 83}, {'i': 10, 'j': 2, 'k': 7, 'cost': 80}, {'i': 10, 'j': 2, 'k': 8, 'cost': 45}, {'i': 10, 'j': 2, 'k': 9, 'cost': 7}, {'i': 10, 'j': 2, 'k': 10, 'cost': 40}, {'i': 10, 'j': 2, 'k': 11, 'cost': 86}, {'i': 10, 'j': 3, 'k': 1, 'cost': 25}, {'i': 10, 'j': 3, 'k': 2, 'cost': 49}, {'i': 10, 'j': 3, 'k': 3, 'cost': 36}, {'i': 10, 'j': 3, 'k': 4, 'cost': 89}, {'i': 10, 'j': 3, 'k': 5, 'cost': 70}, {'i': 10, 'j': 3, 'k': 6, 'cost': 99}, {'i': 10, 'j': 3, 'k': 7, 'cost': 28}, {'i': 10, 'j': 3, 'k': 8, 'cost': 96}, {'i': 10, 'j': 3, 'k': 9, 'cost': 61}, {'i': 10, 'j': 3, 'k': 10, 'cost': 74}, {'i': 10, 'j': 3, 'k': 11, 'cost': 15}, {'i': 10, 'j': 4, 'k': 1, 'cost': 14}, {'i': 10, 'j': 4, 'k': 2, 'cost': 66}, {'i': 10, 'j': 4, 'k': 3, 'cost': 96}, {'i': 10, 'j': 4, 'k': 4, 'cost': 49}, {'i': 10, 'j': 4, 'k': 5, 'cost': 49}, {'i': 10, 'j': 4, 'k': 6, 'cost': 91}, {'i': 10, 'j': 4, 'k': 7, 'cost': 94}, {'i': 10, 'j': 4, 'k': 8, 'cost': 40}, {'i': 10, 'j': 4, 'k': 9, 'cost': 56}, {'i': 10, 'j': 4, 'k': 10, 'cost': 93}, {'i': 10, 'j': 4, 'k': 11, 'cost': 63}, {'i': 10, 'j': 5, 'k': 1, 'cost': 8}, {'i': 10, 'j': 5, 'k': 2, 'cost': 3}, {'i': 10, 'j': 5, 'k': 3, 'cost': 75}, {'i': 10, 'j': 5, 'k': 4, 'cost': 16}, {'i': 10, 'j': 5, 'k': 5, 'cost': 38}, {'i': 10, 'j': 5, 'k': 6, 'cost': 62}, {'i': 10, 'j': 5, 'k': 7, 'cost': 98}, {'i': 10, 'j': 5, 'k': 8, 'cost': 70}, {'i': 10, 'j': 5, 'k': 9, 'cost': 23}, {'i': 10, 'j': 5, 'k': 10, 'cost': 49}, {'i': 10, 'j': 5, 'k': 11, 'cost': 58}, {'i': 10, 'j': 6, 'k': 1, 'cost': 51}, {'i': 10, 'j': 6, 'k': 2, 'cost': 68}, {'i': 10, 'j': 6, 'k': 3, 'cost': 38}, {'i': 10, 'j': 6, 'k': 4, 'cost': 58}, {'i': 10, 'j': 6, 'k': 5, 'cost': 70}, {'i': 10, 'j': 6, 'k': 6, 'cost': 45}, {'i': 10, 'j': 6, 'k': 7, 'cost': 26}, {'i': 10, 'j': 6, 'k': 8, 'cost': 98}, {'i': 10, 'j': 6, 'k': 9, 'cost': 41}, {'i': 10, 'j': 6, 'k': 10, 'cost': 53}, {'i': 10, 'j': 6, 'k': 11, 'cost': 59}, {'i': 10, 'j': 7, 'k': 1, 'cost': 26}, {'i': 10, 'j': 7, 'k': 2, 'cost': 43}, {'i': 10, 'j': 7, 'k': 3, 'cost': 26}, {'i': 10, 'j': 7, 'k': 4, 'cost': 63}, {'i': 10, 'j': 7, 'k': 5, 'cost': 95}, {'i': 10, 'j': 7, 'k': 6, 'cost': 58}, {'i': 10, 'j': 7, 'k': 7, 'cost': 2}, {'i': 10, 'j': 7, 'k': 8, 'cost': 5}, {'i': 10, 'j': 7, 'k': 9, 'cost': 31}, {'i': 10, 'j': 7, 'k': 10, 'cost': 93}, {'i': 10, 'j': 7, 'k': 11, 'cost': 74}, {'i': 10, 'j': 8, 'k': 1, 'cost': 88}, {'i': 10, 'j': 8, 'k': 2, 'cost': 32}, {'i': 10, 'j': 8, 'k': 3, 'cost': 35}, {'i': 10, 'j': 8, 'k': 4, 'cost': 1}, {'i': 10, 'j': 8, 'k': 5, 'cost': 49}, {'i': 10, 'j': 8, 'k': 6, 'cost': 9}, {'i': 10, 'j': 8, 'k': 7, 'cost': 20}, {'i': 10, 'j': 8, 'k': 8, 'cost': 58}, {'i': 10, 'j': 8, 'k': 9, 'cost': 4}, {'i': 10, 'j': 8, 'k': 10, 'cost': 66}, {'i': 10, 'j': 8, 'k': 11, 'cost': 28}, {'i': 10, 'j': 9, 'k': 1, 'cost': 7}, {'i': 10, 'j': 9, 'k': 2, 'cost': 81}, {'i': 10, 'j': 9, 'k': 3, 'cost': 76}, {'i': 10, 'j': 9, 'k': 4, 'cost': 79}, {'i': 10, 'j': 9, 'k': 5, 'cost': 61}, {'i': 10, 'j': 9, 'k': 6, 'cost': 84}, {'i': 10, 'j': 9, 'k': 7, 'cost': 81}, {'i': 10, 'j': 9, 'k': 8, 'cost': 32}, {'i': 10, 'j': 9, 'k': 9, 'cost': 10}, {'i': 10, 'j': 9, 'k': 10, 'cost': 11}, {'i': 10, 'j': 9, 'k': 11, 'cost': 17}, {'i': 10, 'j': 10, 'k': 1, 'cost': 13}, {'i': 10, 'j': 10, 'k': 2, 'cost': 53}, {'i': 10, 'j': 10, 'k': 3, 'cost': 85}, {'i': 10, 'j': 10, 'k': 4, 'cost': 84}, {'i': 10, 'j': 10, 'k': 5, 'cost': 21}, {'i': 10, 'j': 10, 'k': 6, 'cost': 12}, {'i': 10, 'j': 10, 'k': 7, 'cost': 43}, {'i': 10, 'j': 10, 'k': 8, 'cost': 22}, {'i': 10, 'j': 10, 'k': 9, 'cost': 62}, {'i': 10, 'j': 10, 'k': 10, 'cost': 55}, {'i': 10, 'j': 10, 'k': 11, 'cost': 0}, {'i': 10, 'j': 11, 'k': 1, 'cost': 0}, {'i': 10, 'j': 11, 'k': 2, 'cost': 38}, {'i': 10, 'j': 11, 'k': 3, 'cost': 53}, {'i': 10, 'j': 11, 'k': 4, 'cost': 37}, {'i': 10, 'j': 11, 'k': 5, 'cost': 70}, {'i': 10, 'j': 11, 'k': 6, 'cost': 7}, {'i': 10, 'j': 11, 'k': 7, 'cost': 10}, {'i': 10, 'j': 11, 'k': 8, 'cost': 54}, {'i': 10, 'j': 11, 'k': 9, 'cost': 27}, {'i': 10, 'j': 11, 'k': 10, 'cost': 50}, {'i': 10, 'j': 11, 'k': 11, 'cost': 47}, {'i': 11, 'j': 1, 'k': 1, 'cost': 95}, {'i': 11, 'j': 1, 'k': 2, 'cost': 95}, {'i': 11, 'j': 1, 'k': 3, 'cost': 27}, {'i': 11, 'j': 1, 'k': 4, 'cost': 38}, {'i': 11, 'j': 1, 'k': 5, 'cost': 28}, {'i': 11, 'j': 1, 'k': 6, 'cost': 68}, {'i': 11, 'j': 1, 'k': 7, 'cost': 73}, {'i': 11, 'j': 1, 'k': 8, 'cost': 1}, {'i': 11, 'j': 1, 'k': 9, 'cost': 78}, {'i': 11, 'j': 1, 'k': 10, 'cost': 11}, {'i': 11, 'j': 1, 'k': 11, 'cost': 40}, {'i': 11, 'j': 2, 'k': 1, 'cost': 58}, {'i': 11, 'j': 2, 'k': 2, 'cost': 86}, {'i': 11, 'j': 2, 'k': 3, 'cost': 33}, {'i': 11, 'j': 2, 'k': 4, 'cost': 67}, {'i': 11, 'j': 2, 'k': 5, 'cost': 94}, {'i': 11, 'j': 2, 'k': 6, 'cost': 88}, {'i': 11, 'j': 2, 'k': 7, 'cost': 39}, {'i': 11, 'j': 2, 'k': 8, 'cost': 92}, {'i': 11, 'j': 2, 'k': 9, 'cost': 36}, {'i': 11, 'j': 2, 'k': 10, 'cost': 4}, {'i': 11, 'j': 2, 'k': 11, 'cost': 41}, {'i': 11, 'j': 3, 'k': 1, 'cost': 0}, {'i': 11, 'j': 3, 'k': 2, 'cost': 99}, {'i': 11, 'j': 3, 'k': 3, 'cost': 48}, {'i': 11, 'j': 3, 'k': 4, 'cost': 80}, {'i': 11, 'j': 3, 'k': 5, 'cost': 74}, {'i': 11, 'j': 3, 'k': 6, 'cost': 81}, {'i': 11, 'j': 3, 'k': 7, 'cost': 66}, {'i': 11, 'j': 3, 'k': 8, 'cost': 28}, {'i': 11, 'j': 3, 'k': 9, 'cost': 13}, {'i': 11, 'j': 3, 'k': 10, 'cost': 51}, {'i': 11, 'j': 3, 'k': 11, 'cost': 18}, {'i': 11, 'j': 4, 'k': 1, 'cost': 85}, {'i': 11, 'j': 4, 'k': 2, 'cost': 40}, {'i': 11, 'j': 4, 'k': 3, 'cost': 93}, {'i': 11, 'j': 4, 'k': 4, 'cost': 82}, {'i': 11, 'j': 4, 'k': 5, 'cost': 22}, {'i': 11, 'j': 4, 'k': 6, 'cost': 72}, {'i': 11, 'j': 4, 'k': 7, 'cost': 61}, {'i': 11, 'j': 4, 'k': 8, 'cost': 11}, {'i': 11, 'j': 4, 'k': 9, 'cost': 14}, {'i': 11, 'j': 4, 'k': 10, 'cost': 0}, {'i': 11, 'j': 4, 'k': 11, 'cost': 33}, {'i': 11, 'j': 5, 'k': 1, 'cost': 65}, {'i': 11, 'j': 5, 'k': 2, 'cost': 49}, {'i': 11, 'j': 5, 'k': 3, 'cost': 20}, {'i': 11, 'j': 5, 'k': 4, 'cost': 62}, {'i': 11, 'j': 5, 'k': 5, 'cost': 70}, {'i': 11, 'j': 5, 'k': 6, 'cost': 67}, {'i': 11, 'j': 5, 'k': 7, 'cost': 30}, {'i': 11, 'j': 5, 'k': 8, 'cost': 30}, {'i': 11, 'j': 5, 'k': 9, 'cost': 50}, {'i': 11, 'j': 5, 'k': 10, 'cost': 52}, {'i': 11, 'j': 5, 'k': 11, 'cost': 82}, {'i': 11, 'j': 6, 'k': 1, 'cost': 70}, {'i': 11, 'j': 6, 'k': 2, 'cost': 9}, {'i': 11, 'j': 6, 'k': 3, 'cost': 15}, {'i': 11, 'j': 6, 'k': 4, 'cost': 3}, {'i': 11, 'j': 6, 'k': 5, 'cost': 30}, {'i': 11, 'j': 6, 'k': 6, 'cost': 81}, {'i': 11, 'j': 6, 'k': 7, 'cost': 80}, {'i': 11, 'j': 6, 'k': 8, 'cost': 35}, {'i': 11, 'j': 6, 'k': 9, 'cost': 55}, {'i': 11, 'j': 6, 'k': 10, 'cost': 45}, {'i': 11, 'j': 6, 'k': 11, 'cost': 61}, {'i': 11, 'j': 7, 'k': 1, 'cost': 13}, {'i': 11, 'j': 7, 'k': 2, 'cost': 1}, {'i': 11, 'j': 7, 'k': 3, 'cost': 96}, {'i': 11, 'j': 7, 'k': 4, 'cost': 38}, {'i': 11, 'j': 7, 'k': 5, 'cost': 70}, {'i': 11, 'j': 7, 'k': 6, 'cost': 99}, {'i': 11, 'j': 7, 'k': 7, 'cost': 81}, {'i': 11, 'j': 7, 'k': 8, 'cost': 49}, {'i': 11, 'j': 7, 'k': 9, 'cost': 73}, {'i': 11, 'j': 7, 'k': 10, 'cost': 39}, {'i': 11, 'j': 7, 'k': 11, 'cost': 47}, {'i': 11, 'j': 8, 'k': 1, 'cost': 30}, {'i': 11, 'j': 8, 'k': 2, 'cost': 82}, {'i': 11, 'j': 8, 'k': 3, 'cost': 98}, {'i': 11, 'j': 8, 'k': 4, 'cost': 7}, {'i': 11, 'j': 8, 'k': 5, 'cost': 66}, {'i': 11, 'j': 8, 'k': 6, 'cost': 47}, {'i': 11, 'j': 8, 'k': 7, 'cost': 36}, {'i': 11, 'j': 8, 'k': 8, 'cost': 68}, {'i': 11, 'j': 8, 'k': 9, 'cost': 80}, {'i': 11, 'j': 8, 'k': 10, 'cost': 90}, {'i': 11, 'j': 8, 'k': 11, 'cost': 80}, {'i': 11, 'j': 9, 'k': 1, 'cost': 30}, {'i': 11, 'j': 9, 'k': 2, 'cost': 71}, {'i': 11, 'j': 9, 'k': 3, 'cost': 48}, {'i': 11, 'j': 9, 'k': 4, 'cost': 49}, {'i': 11, 'j': 9, 'k': 5, 'cost': 9}, {'i': 11, 'j': 9, 'k': 6, 'cost': 34}, {'i': 11, 'j': 9, 'k': 7, 'cost': 81}, {'i': 11, 'j': 9, 'k': 8, 'cost': 36}, {'i': 11, 'j': 9, 'k': 9, 'cost': 49}, {'i': 11, 'j': 9, 'k': 10, 'cost': 43}, {'i': 11, 'j': 9, 'k': 11, 'cost': 19}, {'i': 11, 'j': 10, 'k': 1, 'cost': 5}, {'i': 11, 'j': 10, 'k': 2, 'cost': 60}, {'i': 11, 'j': 10, 'k': 3, 'cost': 11}, {'i': 11, 'j': 10, 'k': 4, 'cost': 86}, {'i': 11, 'j': 10, 'k': 5, 'cost': 58}, {'i': 11, 'j': 10, 'k': 6, 'cost': 13}, {'i': 11, 'j': 10, 'k': 7, 'cost': 48}, {'i': 11, 'j': 10, 'k': 8, 'cost': 87}, {'i': 11, 'j': 10, 'k': 9, 'cost': 14}, {'i': 11, 'j': 10, 'k': 10, 'cost': 41}, {'i': 11, 'j': 10, 'k': 11, 'cost': 23}, {'i': 11, 'j': 11, 'k': 1, 'cost': 33}, {'i': 11, 'j': 11, 'k': 2, 'cost': 39}, {'i': 11, 'j': 11, 'k': 3, 'cost': 88}, {'i': 11, 'j': 11, 'k': 4, 'cost': 82}, {'i': 11, 'j': 11, 'k': 5, 'cost': 80}, {'i': 11, 'j': 11, 'k': 6, 'cost': 33}, {'i': 11, 'j': 11, 'k': 7, 'cost': 89}, {'i': 11, 'j': 11, 'k': 8, 'cost': 34}, {'i': 11, 'j': 11, 'k': 9, 'cost': 2}, {'i': 11, 'j': 11, 'k': 10, 'cost': 60}, {'i': 11, 'j': 11, 'k': 11, 'cost': 78}]}","[[1, 11, 7], [2, 1, 3], [3, 6, 9], [4, 2, 6], [5, 9, 2], [6, 7, 4], [7, 5, 5], [8, 8, 8], [9, 4, 10], [10, 10, 11], [11, 3, 1]]",34,markdown_table,1
+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.
+
+There are 10 houses to be painted (hence 10 crews and 10 paint colors), identified as A, B, C, D, E, F, G, H, I, J.
+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=A
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 58 | 77 | 2 | 80 | 2 | 54 | 0 | 91 | 53 | 92 |
+| B | 20 | 47 | 17 | 96 | 80 | 54 | 56 | 37 | 20 | 1 |
+| C | 50 | 36 | 27 | 54 | 93 | 66 | 7 | 20 | 52 | 23 |
+| D | 36 | 64 | 62 | 19 | 45 | 75 | 3 | 3 | 38 | 97 |
+| E | 31 | 74 | 77 | 68 | 48 | 28 | 63 | 82 | 28 | 97 |
+| F | 49 | 28 | 93 | 71 | 88 | 41 | 18 | 82 | 53 | 47 |
+| G | 92 | 95 | 32 | 2 | 5 | 54 | 30 | 25 | 50 | 59 |
+| H | 32 | 22 | 59 | 58 | 85 | 75 | 95 | 43 | 32 | 70 |
+| I | 40 | 48 | 60 | 67 | 36 | 52 | 70 | 2 | 75 | 70 |
+| J | 43 | 7 | 71 | 63 | 67 | 48 | 0 | 48 | 97 | 97 |
+
+## house_id=B
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 17 | 64 | 36 | 98 | 71 | 83 | 91 | 17 | 62 | 54 |
+| B | 43 | 85 | 43 | 26 | 50 | 53 | 99 | 23 | 57 | 31 |
+| C | 28 | 64 | 61 | 84 | 86 | 72 | 92 | 98 | 8 | 23 |
+| D | 98 | 82 | 83 | 95 | 48 | 89 | 79 | 47 | 96 | 58 |
+| E | 95 | 93 | 89 | 64 | 88 | 63 | 52 | 29 | 68 | 64 |
+| F | 0 | 12 | 55 | 15 | 65 | 40 | 10 | 40 | 73 | 33 |
+| G | 77 | 81 | 52 | 42 | 4 | 53 | 75 | 51 | 58 | 0 |
+| H | 80 | 60 | 68 | 4 | 99 | 71 | 90 | 73 | 49 | 4 |
+| I | 95 | 58 | 26 | 25 | 54 | 68 | 10 | 92 | 8 | 18 |
+| J | 46 | 85 | 35 | 91 | 94 | 8 | 32 | 87 | 1 | 3 |
+
+## house_id=C
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 82 | 11 | 26 | 0 | 56 | 10 | 83 | 71 | 15 | 81 |
+| B | 74 | 4 | 44 | 87 | 71 | 12 | 57 | 53 | 39 | 55 |
+| C | 94 | 60 | 85 | 65 | 66 | 76 | 11 | 71 | 31 | 57 |
+| D | 61 | 54 | 90 | 90 | 64 | 42 | 58 | 9 | 26 | 83 |
+| E | 50 | 87 | 56 | 84 | 60 | 1 | 69 | 0 | 85 | 12 |
+| F | 69 | 10 | 53 | 66 | 43 | 93 | 96 | 88 | 27 | 81 |
+| G | 99 | 8 | 46 | 73 | 7 | 49 | 80 | 37 | 14 | 67 |
+| H | 93 | 58 | 76 | 98 | 79 | 85 | 35 | 82 | 1 | 88 |
+| I | 10 | 22 | 26 | 29 | 22 | 66 | 60 | 23 | 17 | 40 |
+| J | 97 | 58 | 61 | 72 | 14 | 82 | 29 | 71 | 28 | 2 |
+
+## house_id=D
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 91 | 38 | 95 | 76 | 23 | 77 | 38 | 14 | 95 | 30 |
+| B | 35 | 1 | 96 | 69 | 83 | 31 | 62 | 44 | 83 | 47 |
+| C | 59 | 27 | 4 | 60 | 56 | 86 | 46 | 49 | 84 | 53 |
+| D | 90 | 91 | 34 | 92 | 9 | 43 | 21 | 20 | 55 | 64 |
+| E | 56 | 43 | 32 | 59 | 69 | 9 | 55 | 91 | 37 | 63 |
+| F | 74 | 66 | 33 | 18 | 68 | 40 | 36 | 28 | 48 | 78 |
+| G | 42 | 89 | 93 | 51 | 66 | 60 | 22 | 87 | 73 | 30 |
+| H | 79 | 2 | 52 | 81 | 44 | 81 | 71 | 70 | 59 | 10 |
+| I | 83 | 28 | 66 | 68 | 85 | 65 | 84 | 5 | 66 | 46 |
+| J | 90 | 70 | 99 | 35 | 38 | 80 | 86 | 78 | 29 | 32 |
+
+## house_id=E
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 7 | 75 | 27 | 35 | 19 | 81 | 58 | 76 | 39 | 93 |
+| B | 45 | 9 | 34 | 98 | 67 | 58 | 38 | 56 | 47 | 12 |
+| C | 35 | 18 | 29 | 57 | 86 | 74 | 26 | 83 | 3 | 6 |
+| D | 61 | 64 | 27 | 2 | 73 | 94 | 54 | 49 | 13 | 95 |
+| E | 10 | 87 | 80 | 98 | 7 | 84 | 55 | 63 | 19 | 83 |
+| F | 46 | 97 | 47 | 63 | 30 | 30 | 44 | 1 | 4 | 51 |
+| G | 28 | 94 | 30 | 1 | 86 | 52 | 39 | 67 | 60 | 42 |
+| H | 69 | 72 | 72 | 62 | 89 | 77 | 4 | 75 | 84 | 65 |
+| I | 60 | 40 | 8 | 70 | 70 | 85 | 18 | 9 | 49 | 99 |
+| J | 46 | 72 | 54 | 66 | 20 | 95 | 17 | 21 | 76 | 77 |
+
+## house_id=F
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 47 | 45 | 41 | 24 | 72 | 83 | 56 | 47 | 3 | 0 |
+| B | 26 | 74 | 97 | 70 | 86 | 13 | 14 | 96 | 88 | 7 |
+| C | 23 | 64 | 16 | 69 | 56 | 1 | 97 | 31 | 68 | 11 |
+| D | 87 | 92 | 16 | 1 | 82 | 94 | 69 | 79 | 83 | 1 |
+| E | 14 | 60 | 18 | 88 | 17 | 88 | 10 | 3 | 22 | 17 |
+| F | 14 | 80 | 93 | 72 | 41 | 80 | 28 | 60 | 38 | 24 |
+| G | 6 | 25 | 93 | 77 | 83 | 86 | 2 | 1 | 34 | 90 |
+| H | 39 | 92 | 97 | 52 | 93 | 56 | 98 | 37 | 22 | 68 |
+| I | 14 | 76 | 47 | 43 | 42 | 67 | 84 | 39 | 55 | 36 |
+| J | 26 | 21 | 49 | 81 | 65 | 3 | 1 | 8 | 4 | 92 |
+
+## house_id=G
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 47 | 34 | 24 | 32 | 21 | 70 | 70 | 15 | 23 | 37 |
+| B | 14 | 84 | 73 | 72 | 78 | 83 | 26 | 51 | 46 | 19 |
+| C | 60 | 53 | 51 | 85 | 4 | 54 | 97 | 80 | 15 | 58 |
+| D | 4 | 60 | 90 | 77 | 73 | 32 | 6 | 95 | 4 | 72 |
+| E | 6 | 48 | 33 | 17 | 36 | 11 | 57 | 97 | 83 | 51 |
+| F | 17 | 2 | 60 | 30 | 39 | 79 | 26 | 92 | 90 | 85 |
+| G | 14 | 70 | 70 | 64 | 93 | 48 | 50 | 76 | 35 | 62 |
+| H | 28 | 47 | 14 | 40 | 94 | 5 | 89 | 45 | 12 | 5 |
+| I | 82 | 23 | 71 | 75 | 37 | 0 | 18 | 81 | 21 | 44 |
+| J | 66 | 6 | 73 | 66 | 11 | 92 | 75 | 26 | 50 | 65 |
+
+## house_id=H
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 93 | 99 | 67 | 40 | 16 | 16 | 79 | 79 | 0 | 4 |
+| B | 97 | 52 | 49 | 33 | 66 | 61 | 59 | 83 | 86 | 33 |
+| C | 46 | 51 | 21 | 27 | 87 | 47 | 46 | 9 | 27 | 14 |
+| D | 83 | 87 | 92 | 42 | 15 | 44 | 18 | 41 | 38 | 43 |
+| E | 85 | 78 | 17 | 9 | 27 | 60 | 26 | 86 | 93 | 32 |
+| F | 4 | 83 | 58 | 82 | 28 | 38 | 74 | 0 | 22 | 66 |
+| G | 94 | 63 | 53 | 73 | 86 | 82 | 75 | 21 | 65 | 99 |
+| H | 80 | 8 | 93 | 61 | 47 | 49 | 23 | 12 | 66 | 95 |
+| I | 49 | 1 | 30 | 0 | 39 | 78 | 9 | 61 | 53 | 68 |
+| J | 24 | 43 | 88 | 19 | 31 | 21 | 12 | 39 | 77 | 5 |
+
+## house_id=I
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 15 | 43 | 4 | 96 | 22 | 17 | 30 | 11 | 23 | 37 |
+| B | 90 | 13 | 50 | 30 | 24 | 68 | 94 | 74 | 80 | 89 |
+| C | 57 | 86 | 25 | 32 | 19 | 80 | 37 | 38 | 80 | 98 |
+| D | 42 | 95 | 78 | 1 | 9 | 6 | 15 | 81 | 33 | 44 |
+| E | 4 | 2 | 16 | 67 | 59 | 29 | 17 | 76 | 64 | 44 |
+| F | 18 | 39 | 81 | 16 | 48 | 5 | 0 | 99 | 17 | 51 |
+| G | 98 | 38 | 57 | 83 | 28 | 34 | 36 | 35 | 42 | 43 |
+| H | 18 | 84 | 53 | 12 | 7 | 53 | 80 | 74 | 36 | 44 |
+| I | 51 | 65 | 70 | 42 | 3 | 88 | 93 | 30 | 34 | 34 |
+| J | 81 | 41 | 99 | 61 | 56 | 9 | 20 | 55 | 73 | 84 |
+
+## house_id=J
+| crew_id\paint_color_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 85 | 46 | 48 | 7 | 10 | 42 | 85 | 78 | 90 | 38 |
+| B | 77 | 56 | 1 | 94 | 43 | 28 | 52 | 18 | 77 | 99 |
+| C | 5 | 0 | 14 | 77 | 17 | 78 | 45 | 5 | 3 | 59 |
+| D | 82 | 81 | 86 | 74 | 74 | 42 | 20 | 45 | 65 | 47 |
+| E | 99 | 79 | 30 | 1 | 89 | 53 | 88 | 59 | 80 | 93 |
+| F | 53 | 71 | 62 | 38 | 43 | 57 | 26 | 9 | 17 | 61 |
+| G | 19 | 64 | 12 | 43 | 72 | 52 | 69 | 27 | 33 | 48 |
+| H | 61 | 34 | 44 | 98 | 51 | 65 | 23 | 18 | 46 | 65 |
+| I | 54 | 77 | 33 | 81 | 79 | 86 | 34 | 49 | 62 | 9 |
+| J | 86 | 12 | 76 | 12 | 69 | 16 | 6 | 39 | 75 | 58 |
+All crews and all paint colors are used exactly once across the 10 houses.
+
+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': [[[58, 77, 2, 80, 2, 54, 0, 91, 53, 92], [20, 47, 17, 96, 80, 54, 56, 37, 20, 1], [50, 36, 27, 54, 93, 66, 7, 20, 52, 23], [36, 64, 62, 19, 45, 75, 3, 3, 38, 97], [31, 74, 77, 68, 48, 28, 63, 82, 28, 97], [49, 28, 93, 71, 88, 41, 18, 82, 53, 47], [92, 95, 32, 2, 5, 54, 30, 25, 50, 59], [32, 22, 59, 58, 85, 75, 95, 43, 32, 70], [40, 48, 60, 67, 36, 52, 70, 2, 75, 70], [43, 7, 71, 63, 67, 48, 0, 48, 97, 97]], [[17, 64, 36, 98, 71, 83, 91, 17, 62, 54], [43, 85, 43, 26, 50, 53, 99, 23, 57, 31], [28, 64, 61, 84, 86, 72, 92, 98, 8, 23], [98, 82, 83, 95, 48, 89, 79, 47, 96, 58], [95, 93, 89, 64, 88, 63, 52, 29, 68, 64], [0, 12, 55, 15, 65, 40, 10, 40, 73, 33], [77, 81, 52, 42, 4, 53, 75, 51, 58, 0], [80, 60, 68, 4, 99, 71, 90, 73, 49, 4], [95, 58, 26, 25, 54, 68, 10, 92, 8, 18], [46, 85, 35, 91, 94, 8, 32, 87, 1, 3]], [[82, 11, 26, 0, 56, 10, 83, 71, 15, 81], [74, 4, 44, 87, 71, 12, 57, 53, 39, 55], [94, 60, 85, 65, 66, 76, 11, 71, 31, 57], [61, 54, 90, 90, 64, 42, 58, 9, 26, 83], [50, 87, 56, 84, 60, 1, 69, 0, 85, 12], [69, 10, 53, 66, 43, 93, 96, 88, 27, 81], [99, 8, 46, 73, 7, 49, 80, 37, 14, 67], [93, 58, 76, 98, 79, 85, 35, 82, 1, 88], [10, 22, 26, 29, 22, 66, 60, 23, 17, 40], [97, 58, 61, 72, 14, 82, 29, 71, 28, 2]], [[91, 38, 95, 76, 23, 77, 38, 14, 95, 30], [35, 1, 96, 69, 83, 31, 62, 44, 83, 47], [59, 27, 4, 60, 56, 86, 46, 49, 84, 53], [90, 91, 34, 92, 9, 43, 21, 20, 55, 64], [56, 43, 32, 59, 69, 9, 55, 91, 37, 63], [74, 66, 33, 18, 68, 40, 36, 28, 48, 78], [42, 89, 93, 51, 66, 60, 22, 87, 73, 30], [79, 2, 52, 81, 44, 81, 71, 70, 59, 10], [83, 28, 66, 68, 85, 65, 84, 5, 66, 46], [90, 70, 99, 35, 38, 80, 86, 78, 29, 32]], [[7, 75, 27, 35, 19, 81, 58, 76, 39, 93], [45, 9, 34, 98, 67, 58, 38, 56, 47, 12], [35, 18, 29, 57, 86, 74, 26, 83, 3, 6], [61, 64, 27, 2, 73, 94, 54, 49, 13, 95], [10, 87, 80, 98, 7, 84, 55, 63, 19, 83], [46, 97, 47, 63, 30, 30, 44, 1, 4, 51], [28, 94, 30, 1, 86, 52, 39, 67, 60, 42], [69, 72, 72, 62, 89, 77, 4, 75, 84, 65], [60, 40, 8, 70, 70, 85, 18, 9, 49, 99], [46, 72, 54, 66, 20, 95, 17, 21, 76, 77]], [[47, 45, 41, 24, 72, 83, 56, 47, 3, 0], [26, 74, 97, 70, 86, 13, 14, 96, 88, 7], [23, 64, 16, 69, 56, 1, 97, 31, 68, 11], [87, 92, 16, 1, 82, 94, 69, 79, 83, 1], [14, 60, 18, 88, 17, 88, 10, 3, 22, 17], [14, 80, 93, 72, 41, 80, 28, 60, 38, 24], [6, 25, 93, 77, 83, 86, 2, 1, 34, 90], [39, 92, 97, 52, 93, 56, 98, 37, 22, 68], [14, 76, 47, 43, 42, 67, 84, 39, 55, 36], [26, 21, 49, 81, 65, 3, 1, 8, 4, 92]], [[47, 34, 24, 32, 21, 70, 70, 15, 23, 37], [14, 84, 73, 72, 78, 83, 26, 51, 46, 19], [60, 53, 51, 85, 4, 54, 97, 80, 15, 58], [4, 60, 90, 77, 73, 32, 6, 95, 4, 72], [6, 48, 33, 17, 36, 11, 57, 97, 83, 51], [17, 2, 60, 30, 39, 79, 26, 92, 90, 85], [14, 70, 70, 64, 93, 48, 50, 76, 35, 62], [28, 47, 14, 40, 94, 5, 89, 45, 12, 5], [82, 23, 71, 75, 37, 0, 18, 81, 21, 44], [66, 6, 73, 66, 11, 92, 75, 26, 50, 65]], [[93, 99, 67, 40, 16, 16, 79, 79, 0, 4], [97, 52, 49, 33, 66, 61, 59, 83, 86, 33], [46, 51, 21, 27, 87, 47, 46, 9, 27, 14], [83, 87, 92, 42, 15, 44, 18, 41, 38, 43], [85, 78, 17, 9, 27, 60, 26, 86, 93, 32], [4, 83, 58, 82, 28, 38, 74, 0, 22, 66], [94, 63, 53, 73, 86, 82, 75, 21, 65, 99], [80, 8, 93, 61, 47, 49, 23, 12, 66, 95], [49, 1, 30, 0, 39, 78, 9, 61, 53, 68], [24, 43, 88, 19, 31, 21, 12, 39, 77, 5]], [[15, 43, 4, 96, 22, 17, 30, 11, 23, 37], [90, 13, 50, 30, 24, 68, 94, 74, 80, 89], [57, 86, 25, 32, 19, 80, 37, 38, 80, 98], [42, 95, 78, 1, 9, 6, 15, 81, 33, 44], [4, 2, 16, 67, 59, 29, 17, 76, 64, 44], [18, 39, 81, 16, 48, 5, 0, 99, 17, 51], [98, 38, 57, 83, 28, 34, 36, 35, 42, 43], [18, 84, 53, 12, 7, 53, 80, 74, 36, 44], [51, 65, 70, 42, 3, 88, 93, 30, 34, 34], [81, 41, 99, 61, 56, 9, 20, 55, 73, 84]], [[85, 46, 48, 7, 10, 42, 85, 78, 90, 38], [77, 56, 1, 94, 43, 28, 52, 18, 77, 99], [5, 0, 14, 77, 17, 78, 45, 5, 3, 59], [82, 81, 86, 74, 74, 42, 20, 45, 65, 47], [99, 79, 30, 1, 89, 53, 88, 59, 80, 93], [53, 71, 62, 38, 43, 57, 26, 9, 17, 61], [19, 64, 12, 43, 72, 52, 69, 27, 33, 48], [61, 34, 44, 98, 51, 65, 23, 18, 46, 65], [54, 77, 33, 81, 79, 86, 34, 49, 62, 9], [86, 12, 76, 12, 69, 16, 6, 39, 75, 58]]], 'objective': 14.0}","[[0, 0, 4], [1, 6, 9], [2, 4, 7], [3, 7, 1], [4, 2, 8], [5, 9, 6], [6, 8, 5], [7, 5, 0], [8, 3, 3], [9, 1, 2]]",14.0,"{'problem_type': 'AP3', 'n': 10, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 58}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 77}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 2}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 80}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 2}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 54}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 0}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 91}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 53}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 92}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 20}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 47}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 17}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 96}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 80}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 54}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 56}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 37}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 20}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 1}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 50}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 36}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 27}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 54}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 93}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 66}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 7}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 20}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 52}, {'i': 'A', 'j': 'C', 'k': 'J', 'cost': 23}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 36}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 64}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 62}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 19}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 45}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 75}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 3}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 3}, {'i': 'A', 'j': 'D', 'k': 'I', 'cost': 38}, {'i': 'A', 'j': 'D', 'k': 'J', 'cost': 97}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 31}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 74}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 77}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 68}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 48}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 28}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 63}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 82}, {'i': 'A', 'j': 'E', 'k': 'I', 'cost': 28}, {'i': 'A', 'j': 'E', 'k': 'J', 'cost': 97}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 49}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 28}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 93}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 71}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 88}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 41}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 18}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 82}, {'i': 'A', 'j': 'F', 'k': 'I', 'cost': 53}, {'i': 'A', 'j': 'F', 'k': 'J', 'cost': 47}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 92}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 95}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 32}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 2}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 5}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 54}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 30}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 25}, {'i': 'A', 'j': 'G', 'k': 'I', 'cost': 50}, {'i': 'A', 'j': 'G', 'k': 'J', 'cost': 59}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 32}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 22}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 59}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 58}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 85}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 75}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 95}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 43}, {'i': 'A', 'j': 'H', 'k': 'I', 'cost': 32}, {'i': 'A', 'j': 'H', 'k': 'J', 'cost': 70}, {'i': 'A', 'j': 'I', 'k': 'A', 'cost': 40}, {'i': 'A', 'j': 'I', 'k': 'B', 'cost': 48}, {'i': 'A', 'j': 'I', 'k': 'C', 'cost': 60}, {'i': 'A', 'j': 'I', 'k': 'D', 'cost': 67}, {'i': 'A', 'j': 'I', 'k': 'E', 'cost': 36}, {'i': 'A', 'j': 'I', 'k': 'F', 'cost': 52}, {'i': 'A', 'j': 'I', 'k': 'G', 'cost': 70}, {'i': 'A', 'j': 'I', 'k': 'H', 'cost': 2}, {'i': 'A', 'j': 'I', 'k': 'I', 'cost': 75}, {'i': 'A', 'j': 'I', 'k': 'J', 'cost': 70}, {'i': 'A', 'j': 'J', 'k': 'A', 'cost': 43}, {'i': 'A', 'j': 'J', 'k': 'B', 'cost': 7}, {'i': 'A', 'j': 'J', 'k': 'C', 'cost': 71}, {'i': 'A', 'j': 'J', 'k': 'D', 'cost': 63}, {'i': 'A', 'j': 'J', 'k': 'E', 'cost': 67}, {'i': 'A', 'j': 'J', 'k': 'F', 'cost': 48}, {'i': 'A', 'j': 'J', 'k': 'G', 'cost': 0}, {'i': 'A', 'j': 'J', 'k': 'H', 'cost': 48}, {'i': 'A', 'j': 'J', 'k': 'I', 'cost': 97}, {'i': 'A', 'j': 'J', 'k': 'J', 'cost': 97}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 17}, {'i': 'B', 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'I', 'j': 'C', 'k': 'J', 'cost': 98}, {'i': 'I', 'j': 'D', 'k': 'A', 'cost': 42}, {'i': 'I', 'j': 'D', 'k': 'B', 'cost': 95}, {'i': 'I', 'j': 'D', 'k': 'C', 'cost': 78}, {'i': 'I', 'j': 'D', 'k': 'D', 'cost': 1}, {'i': 'I', 'j': 'D', 'k': 'E', 'cost': 9}, {'i': 'I', 'j': 'D', 'k': 'F', 'cost': 6}, {'i': 'I', 'j': 'D', 'k': 'G', 'cost': 15}, {'i': 'I', 'j': 'D', 'k': 'H', 'cost': 81}, {'i': 'I', 'j': 'D', 'k': 'I', 'cost': 33}, {'i': 'I', 'j': 'D', 'k': 'J', 'cost': 44}, {'i': 'I', 'j': 'E', 'k': 'A', 'cost': 4}, {'i': 'I', 'j': 'E', 'k': 'B', 'cost': 2}, {'i': 'I', 'j': 'E', 'k': 'C', 'cost': 16}, {'i': 'I', 'j': 'E', 'k': 'D', 'cost': 67}, {'i': 'I', 'j': 'E', 'k': 'E', 'cost': 59}, {'i': 'I', 'j': 'E', 'k': 'F', 'cost': 29}, {'i': 'I', 'j': 'E', 'k': 'G', 'cost': 17}, {'i': 'I', 'j': 'E', 'k': 'H', 'cost': 76}, {'i': 'I', 'j': 'E', 'k': 'I', 'cost': 64}, {'i': 'I', 'j': 'E', 'k': 'J', 'cost': 44}, {'i': 'I', 'j': 'F', 'k': 'A', 'cost': 18}, {'i': 'I', 'j': 'F', 'k': 'B', 'cost': 39}, {'i': 'I', 'j': 'F', 'k': 'C', 'cost': 81}, {'i': 'I', 'j': 'F', 'k': 'D', 'cost': 16}, {'i': 'I', 'j': 'F', 'k': 'E', 'cost': 48}, {'i': 'I', 'j': 'F', 'k': 'F', 'cost': 5}, {'i': 'I', 'j': 'F', 'k': 'G', 'cost': 0}, {'i': 'I', 'j': 'F', 'k': 'H', 'cost': 99}, {'i': 'I', 'j': 'F', 'k': 'I', 'cost': 17}, {'i': 'I', 'j': 'F', 'k': 'J', 'cost': 51}, {'i': 'I', 'j': 'G', 'k': 'A', 'cost': 98}, {'i': 'I', 'j': 'G', 'k': 'B', 'cost': 38}, {'i': 'I', 'j': 'G', 'k': 'C', 'cost': 57}, {'i': 'I', 'j': 'G', 'k': 'D', 'cost': 83}, {'i': 'I', 'j': 'G', 'k': 'E', 'cost': 28}, {'i': 'I', 'j': 'G', 'k': 'F', 'cost': 34}, {'i': 'I', 'j': 'G', 'k': 'G', 'cost': 36}, {'i': 'I', 'j': 'G', 'k': 'H', 'cost': 35}, {'i': 'I', 'j': 'G', 'k': 'I', 'cost': 42}, {'i': 'I', 'j': 'G', 'k': 'J', 'cost': 43}, {'i': 'I', 'j': 'H', 'k': 'A', 'cost': 18}, {'i': 'I', 'j': 'H', 'k': 'B', 'cost': 84}, {'i': 'I', 'j': 'H', 'k': 'C', 'cost': 53}, {'i': 'I', 'j': 'H', 'k': 'D', 'cost': 12}, {'i': 'I', 'j': 'H', 'k': 'E', 'cost': 7}, {'i': 'I', 'j': 'H', 'k': 'F', 'cost': 53}, {'i': 'I', 'j': 'H', 'k': 'G', 'cost': 80}, {'i': 'I', 'j': 'H', 'k': 'H', 'cost': 74}, {'i': 'I', 'j': 'H', 'k': 'I', 'cost': 36}, {'i': 'I', 'j': 'H', 'k': 'J', 'cost': 44}, {'i': 'I', 'j': 'I', 'k': 'A', 'cost': 51}, {'i': 'I', 'j': 'I', 'k': 'B', 'cost': 65}, {'i': 'I', 'j': 'I', 'k': 'C', 'cost': 70}, {'i': 'I', 'j': 'I', 'k': 'D', 'cost': 42}, {'i': 'I', 'j': 'I', 'k': 'E', 'cost': 3}, {'i': 'I', 'j': 'I', 'k': 'F', 'cost': 88}, {'i': 'I', 'j': 'I', 'k': 'G', 'cost': 93}, {'i': 'I', 'j': 'I', 'k': 'H', 'cost': 30}, {'i': 'I', 'j': 'I', 'k': 'I', 'cost': 34}, {'i': 'I', 'j': 'I', 'k': 'J', 'cost': 34}, {'i': 'I', 'j': 'J', 'k': 'A', 'cost': 81}, {'i': 'I', 'j': 'J', 'k': 'B', 'cost': 41}, {'i': 'I', 'j': 'J', 'k': 'C', 'cost': 99}, {'i': 'I', 'j': 'J', 'k': 'D', 'cost': 61}, {'i': 'I', 'j': 'J', 'k': 'E', 'cost': 56}, {'i': 'I', 'j': 'J', 'k': 'F', 'cost': 9}, {'i': 'I', 'j': 'J', 'k': 'G', 'cost': 20}, {'i': 'I', 'j': 'J', 'k': 'H', 'cost': 55}, {'i': 'I', 'j': 'J', 'k': 'I', 'cost': 73}, {'i': 'I', 'j': 'J', 'k': 'J', 'cost': 84}, {'i': 'J', 'j': 'A', 'k': 'A', 'cost': 85}, {'i': 'J', 'j': 'A', 'k': 'B', 'cost': 46}, {'i': 'J', 'j': 'A', 'k': 'C', 'cost': 48}, {'i': 'J', 'j': 'A', 'k': 'D', 'cost': 7}, {'i': 'J', 'j': 'A', 'k': 'E', 'cost': 10}, {'i': 'J', 'j': 'A', 'k': 'F', 'cost': 42}, {'i': 'J', 'j': 'A', 'k': 'G', 'cost': 85}, {'i': 'J', 'j': 'A', 'k': 'H', 'cost': 78}, {'i': 'J', 'j': 'A', 'k': 'I', 'cost': 90}, {'i': 'J', 'j': 'A', 'k': 'J', 'cost': 38}, {'i': 'J', 'j': 'B', 'k': 'A', 'cost': 77}, {'i': 'J', 'j': 'B', 'k': 'B', 'cost': 56}, {'i': 'J', 'j': 'B', 'k': 'C', 'cost': 1}, {'i': 'J', 'j': 'B', 'k': 'D', 'cost': 94}, {'i': 'J', 'j': 'B', 'k': 'E', 'cost': 43}, {'i': 'J', 'j': 'B', 'k': 'F', 'cost': 28}, {'i': 'J', 'j': 'B', 'k': 'G', 'cost': 52}, {'i': 'J', 'j': 'B', 'k': 'H', 'cost': 18}, {'i': 'J', 'j': 'B', 'k': 'I', 'cost': 77}, {'i': 'J', 'j': 'B', 'k': 'J', 'cost': 99}, {'i': 'J', 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'I', 'k': 'I', 'cost': 62}, {'i': 'J', 'j': 'I', 'k': 'J', 'cost': 9}, {'i': 'J', 'j': 'J', 'k': 'A', 'cost': 86}, {'i': 'J', 'j': 'J', 'k': 'B', 'cost': 12}, {'i': 'J', 'j': 'J', 'k': 'C', 'cost': 76}, {'i': 'J', 'j': 'J', 'k': 'D', 'cost': 12}, {'i': 'J', 'j': 'J', 'k': 'E', 'cost': 69}, {'i': 'J', 'j': 'J', 'k': 'F', 'cost': 16}, {'i': 'J', 'j': 'J', 'k': 'G', 'cost': 6}, {'i': 'J', 'j': 'J', 'k': 'H', 'cost': 39}, {'i': 'J', 'j': 'J', 'k': 'I', 'cost': 75}, {'i': 'J', 'j': 'J', 'k': 'J', 'cost': 58}]}","[['A', 'A', 'E'], ['B', 'G', 'J'], ['C', 'E', 'H'], ['D', 'H', 'B'], ['E', 'C', 'I'], ['F', 'J', 'G'], ['G', 'I', 'F'], ['H', 'F', 'A'], ['I', 'D', 'D'], ['J', 'B', 'C']]",35,nl,names
+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 12 orders, identified as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
+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=0
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 43 | 44 | 54 | 47 | 35 | 15 | 80 | 52 | 9 | 30 | 70 | 30 |
+| 1 | 86 | 20 | 76 | 4 | 31 | 51 | 51 | 84 | 14 | 38 | 23 | 8 |
+| 2 | 50 | 67 | 29 | 68 | 45 | 18 | 70 | 95 | 76 | 64 | 30 | 2 |
+| 3 | 30 | 52 | 65 | 22 | 44 | 67 | 88 | 83 | 0 | 71 | 38 | 13 |
+| 4 | 96 | 51 | 53 | 73 | 3 | 72 | 52 | 84 | 74 | 50 | 53 | 90 |
+| 5 | 30 | 48 | 79 | 94 | 42 | 91 | 57 | 25 | 5 | 46 | 57 | 16 |
+| 6 | 28 | 40 | 79 | 45 | 90 | 57 | 67 | 33 | 65 | 35 | 76 | 28 |
+| 7 | 37 | 41 | 41 | 99 | 24 | 65 | 31 | 81 | 52 | 25 | 96 | 27 |
+| 8 | 18 | 94 | 89 | 65 | 6 | 70 | 20 | 43 | 82 | 40 | 1 | 80 |
+| 9 | 67 | 71 | 53 | 11 | 45 | 74 | 1 | 4 | 54 | 72 | 47 | 6 |
+| 10 | 79 | 98 | 25 | 94 | 98 | 17 | 92 | 29 | 5 | 55 | 33 | 72 |
+| 11 | 99 | 70 | 25 | 79 | 61 | 65 | 33 | 43 | 50 | 78 | 2 | 48 |
+
+## order_id=1
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 83 | 41 | 72 | 37 | 75 | 88 | 98 | 66 | 10 | 98 | 54 | 53 |
+| 1 | 91 | 4 | 65 | 94 | 52 | 0 | 56 | 80 | 22 | 46 | 0 | 61 |
+| 2 | 42 | 36 | 3 | 21 | 94 | 10 | 79 | 44 | 22 | 34 | 49 | 90 |
+| 3 | 58 | 69 | 6 | 40 | 80 | 29 | 86 | 29 | 14 | 19 | 53 | 42 |
+| 4 | 76 | 23 | 74 | 25 | 60 | 39 | 68 | 49 | 3 | 65 | 78 | 13 |
+| 5 | 77 | 20 | 59 | 11 | 24 | 94 | 41 | 48 | 5 | 26 | 92 | 37 |
+| 6 | 71 | 63 | 56 | 77 | 71 | 49 | 9 | 76 | 28 | 34 | 9 | 65 |
+| 7 | 89 | 96 | 96 | 11 | 41 | 93 | 29 | 83 | 60 | 6 | 47 | 97 |
+| 8 | 54 | 31 | 62 | 61 | 44 | 9 | 92 | 77 | 29 | 7 | 40 | 65 |
+| 9 | 79 | 7 | 78 | 96 | 67 | 46 | 10 | 83 | 3 | 6 | 67 | 99 |
+| 10 | 89 | 54 | 53 | 60 | 10 | 69 | 38 | 36 | 64 | 28 | 88 | 4 |
+| 11 | 13 | 49 | 22 | 37 | 35 | 22 | 81 | 49 | 24 | 47 | 58 | 77 |
+
+## order_id=2
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 99 | 6 | 36 | 73 | 34 | 16 | 6 | 8 | 17 | 70 | 65 | 94 |
+| 1 | 75 | 82 | 62 | 43 | 97 | 59 | 91 | 85 | 35 | 4 | 89 | 75 |
+| 2 | 73 | 94 | 8 | 94 | 73 | 7 | 62 | 85 | 70 | 43 | 39 | 9 |
+| 3 | 51 | 49 | 13 | 22 | 68 | 97 | 22 | 45 | 96 | 80 | 99 | 69 |
+| 4 | 43 | 8 | 91 | 66 | 86 | 44 | 41 | 15 | 50 | 74 | 90 | 61 |
+| 5 | 21 | 30 | 90 | 95 | 54 | 9 | 27 | 58 | 38 | 2 | 18 | 50 |
+| 6 | 85 | 57 | 12 | 42 | 20 | 80 | 59 | 84 | 22 | 7 | 1 | 12 |
+| 7 | 23 | 93 | 12 | 42 | 46 | 96 | 98 | 80 | 48 | 68 | 27 | 40 |
+| 8 | 55 | 15 | 35 | 72 | 50 | 24 | 21 | 56 | 57 | 6 | 24 | 45 |
+| 9 | 28 | 33 | 5 | 67 | 45 | 16 | 19 | 23 | 57 | 13 | 40 | 5 |
+| 10 | 49 | 2 | 97 | 33 | 72 | 53 | 20 | 36 | 88 | 56 | 72 | 94 |
+| 11 | 5 | 77 | 64 | 88 | 31 | 0 | 54 | 18 | 13 | 64 | 69 | 89 |
+
+## order_id=3
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 5 | 61 | 76 | 34 | 51 | 84 | 4 | 19 | 50 | 54 | 12 | 51 |
+| 1 | 9 | 71 | 69 | 58 | 42 | 90 | 72 | 30 | 9 | 37 | 23 | 26 |
+| 2 | 30 | 19 | 59 | 36 | 63 | 20 | 8 | 98 | 94 | 27 | 28 | 49 |
+| 3 | 58 | 85 | 6 | 22 | 42 | 25 | 45 | 1 | 35 | 82 | 89 | 63 |
+| 4 | 60 | 44 | 1 | 65 | 72 | 70 | 47 | 5 | 40 | 15 | 43 | 93 |
+| 5 | 74 | 80 | 11 | 48 | 45 | 65 | 2 | 11 | 41 | 72 | 59 | 6 |
+| 6 | 94 | 34 | 26 | 34 | 64 | 48 | 35 | 58 | 76 | 41 | 44 | 69 |
+| 7 | 45 | 40 | 42 | 37 | 50 | 80 | 1 | 1 | 66 | 72 | 73 | 8 |
+| 8 | 20 | 44 | 78 | 92 | 34 | 20 | 79 | 77 | 83 | 73 | 18 | 81 |
+| 9 | 62 | 91 | 97 | 46 | 95 | 34 | 5 | 62 | 19 | 10 | 84 | 31 |
+| 10 | 65 | 58 | 57 | 22 | 78 | 69 | 85 | 80 | 48 | 67 | 58 | 93 |
+| 11 | 84 | 24 | 52 | 12 | 65 | 37 | 98 | 83 | 28 | 4 | 53 | 8 |
+
+## order_id=4
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 99 | 92 | 8 | 87 | 28 | 31 | 92 | 16 | 16 | 70 | 32 | 20 |
+| 1 | 80 | 96 | 84 | 18 | 90 | 44 | 78 | 15 | 16 | 9 | 70 | 8 |
+| 2 | 89 | 53 | 52 | 45 | 92 | 32 | 10 | 66 | 73 | 95 | 95 | 16 |
+| 3 | 0 | 15 | 37 | 79 | 57 | 55 | 1 | 42 | 52 | 54 | 37 | 0 |
+| 4 | 22 | 2 | 22 | 54 | 24 | 19 | 39 | 74 | 86 | 23 | 26 | 59 |
+| 5 | 62 | 19 | 52 | 3 | 39 | 71 | 22 | 99 | 0 | 2 | 22 | 77 |
+| 6 | 55 | 22 | 90 | 19 | 92 | 60 | 43 | 43 | 92 | 9 | 57 | 14 |
+| 7 | 97 | 54 | 6 | 42 | 79 | 92 | 15 | 66 | 42 | 89 | 14 | 53 |
+| 8 | 59 | 41 | 55 | 65 | 87 | 0 | 52 | 86 | 14 | 18 | 73 | 42 |
+| 9 | 45 | 1 | 61 | 26 | 5 | 93 | 52 | 91 | 18 | 79 | 27 | 73 |
+| 10 | 78 | 91 | 24 | 63 | 13 | 50 | 54 | 60 | 43 | 15 | 69 | 39 |
+| 11 | 1 | 45 | 77 | 31 | 67 | 68 | 77 | 77 | 94 | 55 | 3 | 1 |
+
+## order_id=5
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 40 | 5 | 39 | 95 | 27 | 88 | 21 | 66 | 91 | 82 | 41 | 77 |
+| 1 | 77 | 23 | 27 | 10 | 33 | 50 | 2 | 68 | 22 | 10 | 41 | 54 |
+| 2 | 17 | 77 | 95 | 19 | 88 | 87 | 39 | 13 | 31 | 45 | 78 | 19 |
+| 3 | 14 | 7 | 6 | 12 | 17 | 59 | 64 | 5 | 18 | 34 | 63 | 95 |
+| 4 | 77 | 4 | 31 | 35 | 43 | 48 | 93 | 69 | 6 | 14 | 45 | 17 |
+| 5 | 3 | 46 | 10 | 39 | 43 | 62 | 31 | 32 | 85 | 3 | 83 | 18 |
+| 6 | 72 | 5 | 89 | 29 | 59 | 29 | 72 | 1 | 29 | 68 | 98 | 9 |
+| 7 | 24 | 51 | 30 | 65 | 89 | 71 | 94 | 20 | 88 | 63 | 76 | 53 |
+| 8 | 21 | 10 | 80 | 58 | 23 | 55 | 58 | 71 | 33 | 26 | 36 | 97 |
+| 9 | 47 | 43 | 8 | 90 | 22 | 9 | 3 | 40 | 15 | 90 | 57 | 38 |
+| 10 | 91 | 44 | 20 | 23 | 79 | 37 | 85 | 50 | 86 | 1 | 76 | 93 |
+| 11 | 69 | 20 | 76 | 83 | 58 | 80 | 22 | 4 | 88 | 95 | 39 | 99 |
+
+## order_id=6
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 65 | 53 | 9 | 46 | 37 | 92 | 66 | 71 | 43 | 76 | 80 | 93 |
+| 1 | 47 | 8 | 54 | 25 | 72 | 3 | 65 | 49 | 31 | 14 | 19 | 50 |
+| 2 | 91 | 53 | 29 | 5 | 35 | 26 | 58 | 81 | 24 | 2 | 65 | 92 |
+| 3 | 32 | 3 | 13 | 7 | 83 | 12 | 8 | 61 | 85 | 71 | 75 | 18 |
+| 4 | 23 | 52 | 2 | 93 | 76 | 28 | 41 | 90 | 44 | 10 | 25 | 29 |
+| 5 | 48 | 23 | 39 | 95 | 91 | 54 | 56 | 11 | 40 | 91 | 61 | 16 |
+| 6 | 74 | 52 | 38 | 38 | 7 | 38 | 95 | 13 | 69 | 48 | 80 | 95 |
+| 7 | 41 | 6 | 36 | 89 | 37 | 21 | 4 | 35 | 37 | 92 | 29 | 7 |
+| 8 | 38 | 0 | 19 | 91 | 22 | 62 | 80 | 77 | 21 | 70 | 5 | 95 |
+| 9 | 97 | 70 | 51 | 9 | 73 | 16 | 81 | 94 | 44 | 85 | 92 | 0 |
+| 10 | 15 | 94 | 65 | 99 | 66 | 95 | 35 | 44 | 21 | 18 | 74 | 94 |
+| 11 | 39 | 72 | 57 | 29 | 72 | 60 | 23 | 30 | 93 | 97 | 48 | 78 |
+
+## order_id=7
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 24 | 78 | 11 | 45 | 9 | 91 | 99 | 72 | 79 | 38 | 8 | 70 |
+| 1 | 66 | 0 | 99 | 45 | 89 | 68 | 36 | 57 | 13 | 11 | 26 | 92 |
+| 2 | 84 | 31 | 43 | 42 | 91 | 94 | 5 | 1 | 85 | 45 | 68 | 73 |
+| 3 | 82 | 56 | 6 | 9 | 75 | 40 | 38 | 18 | 51 | 98 | 9 | 66 |
+| 4 | 44 | 16 | 97 | 75 | 71 | 46 | 94 | 77 | 50 | 17 | 64 | 12 |
+| 5 | 89 | 29 | 71 | 28 | 30 | 83 | 48 | 37 | 62 | 56 | 11 | 84 |
+| 6 | 56 | 67 | 83 | 31 | 61 | 41 | 99 | 65 | 97 | 13 | 75 | 92 |
+| 7 | 96 | 82 | 46 | 13 | 14 | 48 | 26 | 15 | 91 | 94 | 63 | 79 |
+| 8 | 15 | 5 | 35 | 41 | 65 | 66 | 44 | 25 | 68 | 31 | 72 | 67 |
+| 9 | 28 | 84 | 25 | 15 | 79 | 39 | 16 | 88 | 7 | 94 | 68 | 0 |
+| 10 | 14 | 8 | 85 | 71 | 64 | 15 | 12 | 79 | 26 | 73 | 80 | 4 |
+| 11 | 67 | 14 | 9 | 21 | 87 | 5 | 15 | 49 | 37 | 98 | 53 | 75 |
+
+## order_id=8
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 50 | 65 | 96 | 11 | 86 | 12 | 5 | 70 | 60 | 36 | 88 | 69 |
+| 1 | 43 | 94 | 11 | 98 | 69 | 34 | 95 | 62 | 85 | 46 | 37 | 26 |
+| 2 | 13 | 3 | 59 | 61 | 1 | 70 | 79 | 93 | 69 | 75 | 50 | 94 |
+| 3 | 17 | 65 | 31 | 59 | 37 | 12 | 91 | 64 | 25 | 39 | 90 | 95 |
+| 4 | 78 | 89 | 50 | 30 | 90 | 23 | 86 | 28 | 25 | 39 | 96 | 98 |
+| 5 | 91 | 56 | 5 | 35 | 15 | 92 | 58 | 24 | 7 | 0 | 92 | 6 |
+| 6 | 1 | 19 | 49 | 35 | 8 | 33 | 81 | 64 | 48 | 81 | 40 | 24 |
+| 7 | 87 | 15 | 2 | 74 | 64 | 36 | 63 | 87 | 56 | 63 | 99 | 16 |
+| 8 | 67 | 92 | 76 | 20 | 54 | 30 | 29 | 44 | 36 | 94 | 52 | 76 |
+| 9 | 46 | 41 | 82 | 62 | 93 | 33 | 28 | 55 | 57 | 30 | 88 | 69 |
+| 10 | 16 | 11 | 25 | 2 | 20 | 37 | 2 | 65 | 49 | 7 | 93 | 17 |
+| 11 | 48 | 50 | 84 | 94 | 61 | 61 | 6 | 92 | 33 | 57 | 90 | 26 |
+
+## order_id=9
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 25 | 33 | 68 | 16 | 68 | 50 | 9 | 74 | 88 | 61 | 29 | 16 |
+| 1 | 42 | 47 | 65 | 84 | 14 | 83 | 64 | 6 | 83 | 27 | 81 | 81 |
+| 2 | 62 | 18 | 57 | 71 | 67 | 14 | 60 | 74 | 60 | 12 | 62 | 26 |
+| 3 | 52 | 44 | 67 | 31 | 40 | 23 | 16 | 12 | 80 | 72 | 52 | 88 |
+| 4 | 20 | 85 | 56 | 63 | 62 | 2 | 77 | 60 | 8 | 6 | 55 | 1 |
+| 5 | 20 | 40 | 81 | 28 | 67 | 15 | 88 | 54 | 2 | 69 | 92 | 7 |
+| 6 | 19 | 98 | 29 | 91 | 8 | 52 | 84 | 98 | 8 | 32 | 76 | 13 |
+| 7 | 11 | 21 | 46 | 96 | 3 | 50 | 8 | 42 | 25 | 21 | 71 | 15 |
+| 8 | 77 | 95 | 37 | 8 | 3 | 13 | 85 | 48 | 85 | 15 | 76 | 86 |
+| 9 | 22 | 61 | 29 | 43 | 11 | 22 | 48 | 88 | 87 | 29 | 41 | 16 |
+| 10 | 26 | 98 | 52 | 16 | 10 | 13 | 97 | 8 | 71 | 14 | 26 | 78 |
+| 11 | 44 | 22 | 26 | 15 | 75 | 4 | 97 | 0 | 8 | 87 | 96 | 32 |
+
+## order_id=10
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 54 | 90 | 67 | 84 | 48 | 47 | 55 | 69 | 93 | 90 | 40 | 96 |
+| 1 | 77 | 64 | 12 | 20 | 72 | 25 | 92 | 0 | 96 | 65 | 6 | 69 |
+| 2 | 74 | 52 | 71 | 56 | 36 | 15 | 50 | 99 | 24 | 54 | 47 | 84 |
+| 3 | 96 | 25 | 7 | 82 | 10 | 23 | 73 | 93 | 10 | 26 | 80 | 4 |
+| 4 | 18 | 36 | 65 | 56 | 54 | 42 | 41 | 61 | 93 | 8 | 59 | 90 |
+| 5 | 69 | 36 | 57 | 41 | 30 | 15 | 39 | 51 | 75 | 22 | 78 | 34 |
+| 6 | 60 | 49 | 62 | 34 | 13 | 36 | 93 | 36 | 25 | 18 | 1 | 2 |
+| 7 | 65 | 0 | 11 | 79 | 47 | 9 | 84 | 74 | 21 | 44 | 32 | 97 |
+| 8 | 94 | 82 | 47 | 23 | 27 | 1 | 42 | 71 | 14 | 86 | 73 | 70 |
+| 9 | 93 | 98 | 71 | 13 | 10 | 10 | 14 | 84 | 23 | 38 | 54 | 66 |
+| 10 | 69 | 63 | 70 | 39 | 10 | 48 | 6 | 20 | 50 | 24 | 82 | 42 |
+| 11 | 35 | 18 | 30 | 0 | 95 | 65 | 30 | 92 | 11 | 39 | 23 | 96 |
+
+## order_id=11
+| courier_id\window_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 12 | 62 | 18 | 65 | 23 | 89 | 50 | 87 | 49 | 10 | 80 | 24 |
+| 1 | 23 | 92 | 6 | 27 | 14 | 46 | 58 | 8 | 1 | 31 | 28 | 2 |
+| 2 | 47 | 61 | 65 | 5 | 79 | 0 | 4 | 68 | 70 | 87 | 66 | 96 |
+| 3 | 32 | 3 | 52 | 82 | 68 | 90 | 26 | 13 | 61 | 17 | 23 | 89 |
+| 4 | 26 | 76 | 24 | 51 | 94 | 51 | 92 | 43 | 2 | 20 | 90 | 51 |
+| 5 | 46 | 27 | 84 | 48 | 16 | 25 | 29 | 50 | 75 | 88 | 46 | 77 |
+| 6 | 88 | 80 | 83 | 63 | 26 | 14 | 25 | 41 | 26 | 47 | 68 | 19 |
+| 7 | 15 | 26 | 69 | 90 | 11 | 67 | 28 | 23 | 8 | 48 | 79 | 86 |
+| 8 | 97 | 60 | 96 | 34 | 6 | 84 | 98 | 19 | 10 | 82 | 21 | 13 |
+| 9 | 90 | 81 | 5 | 94 | 93 | 8 | 86 | 59 | 56 | 25 | 50 | 91 |
+| 10 | 68 | 62 | 27 | 94 | 30 | 76 | 51 | 8 | 32 | 54 | 77 | 39 |
+| 11 | 22 | 15 | 37 | 17 | 17 | 40 | 34 | 56 | 58 | 91 | 66 | 28 |
+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': [[[43, 44, 54, 47, 35, 15, 80, 52, 9, 30, 70, 30], [86, 20, 76, 4, 31, 51, 51, 84, 14, 38, 23, 8], [50, 67, 29, 68, 45, 18, 70, 95, 76, 64, 30, 2], [30, 52, 65, 22, 44, 67, 88, 83, 0, 71, 38, 13], [96, 51, 53, 73, 3, 72, 52, 84, 74, 50, 53, 90], [30, 48, 79, 94, 42, 91, 57, 25, 5, 46, 57, 16], [28, 40, 79, 45, 90, 57, 67, 33, 65, 35, 76, 28], [37, 41, 41, 99, 24, 65, 31, 81, 52, 25, 96, 27], [18, 94, 89, 65, 6, 70, 20, 43, 82, 40, 1, 80], [67, 71, 53, 11, 45, 74, 1, 4, 54, 72, 47, 6], [79, 98, 25, 94, 98, 17, 92, 29, 5, 55, 33, 72], [99, 70, 25, 79, 61, 65, 33, 43, 50, 78, 2, 48]], [[83, 41, 72, 37, 75, 88, 98, 66, 10, 98, 54, 53], [91, 4, 65, 94, 52, 0, 56, 80, 22, 46, 0, 61], [42, 36, 3, 21, 94, 10, 79, 44, 22, 34, 49, 90], [58, 69, 6, 40, 80, 29, 86, 29, 14, 19, 53, 42], [76, 23, 74, 25, 60, 39, 68, 49, 3, 65, 78, 13], [77, 20, 59, 11, 24, 94, 41, 48, 5, 26, 92, 37], [71, 63, 56, 77, 71, 49, 9, 76, 28, 34, 9, 65], [89, 96, 96, 11, 41, 93, 29, 83, 60, 6, 47, 97], [54, 31, 62, 61, 44, 9, 92, 77, 29, 7, 40, 65], [79, 7, 78, 96, 67, 46, 10, 83, 3, 6, 67, 99], [89, 54, 53, 60, 10, 69, 38, 36, 64, 28, 88, 4], [13, 49, 22, 37, 35, 22, 81, 49, 24, 47, 58, 77]], [[99, 6, 36, 73, 34, 16, 6, 8, 17, 70, 65, 94], [75, 82, 62, 43, 97, 59, 91, 85, 35, 4, 89, 75], [73, 94, 8, 94, 73, 7, 62, 85, 70, 43, 39, 9], [51, 49, 13, 22, 68, 97, 22, 45, 96, 80, 99, 69], [43, 8, 91, 66, 86, 44, 41, 15, 50, 74, 90, 61], [21, 30, 90, 95, 54, 9, 27, 58, 38, 2, 18, 50], [85, 57, 12, 42, 20, 80, 59, 84, 22, 7, 1, 12], [23, 93, 12, 42, 46, 96, 98, 80, 48, 68, 27, 40], [55, 15, 35, 72, 50, 24, 21, 56, 57, 6, 24, 45], [28, 33, 5, 67, 45, 16, 19, 23, 57, 13, 40, 5], [49, 2, 97, 33, 72, 53, 20, 36, 88, 56, 72, 94], [5, 77, 64, 88, 31, 0, 54, 18, 13, 64, 69, 89]], [[5, 61, 76, 34, 51, 84, 4, 19, 50, 54, 12, 51], [9, 71, 69, 58, 42, 90, 72, 30, 9, 37, 23, 26], [30, 19, 59, 36, 63, 20, 8, 98, 94, 27, 28, 49], [58, 85, 6, 22, 42, 25, 45, 1, 35, 82, 89, 63], [60, 44, 1, 65, 72, 70, 47, 5, 40, 15, 43, 93], [74, 80, 11, 48, 45, 65, 2, 11, 41, 72, 59, 6], [94, 34, 26, 34, 64, 48, 35, 58, 76, 41, 44, 69], [45, 40, 42, 37, 50, 80, 1, 1, 66, 72, 73, 8], [20, 44, 78, 92, 34, 20, 79, 77, 83, 73, 18, 81], [62, 91, 97, 46, 95, 34, 5, 62, 19, 10, 84, 31], [65, 58, 57, 22, 78, 69, 85, 80, 48, 67, 58, 93], [84, 24, 52, 12, 65, 37, 98, 83, 28, 4, 53, 8]], [[99, 92, 8, 87, 28, 31, 92, 16, 16, 70, 32, 20], [80, 96, 84, 18, 90, 44, 78, 15, 16, 9, 70, 8], [89, 53, 52, 45, 92, 32, 10, 66, 73, 95, 95, 16], [0, 15, 37, 79, 57, 55, 1, 42, 52, 54, 37, 0], [22, 2, 22, 54, 24, 19, 39, 74, 86, 23, 26, 59], [62, 19, 52, 3, 39, 71, 22, 99, 0, 2, 22, 77], [55, 22, 90, 19, 92, 60, 43, 43, 92, 9, 57, 14], [97, 54, 6, 42, 79, 92, 15, 66, 42, 89, 14, 53], [59, 41, 55, 65, 87, 0, 52, 86, 14, 18, 73, 42], [45, 1, 61, 26, 5, 93, 52, 91, 18, 79, 27, 73], [78, 91, 24, 63, 13, 50, 54, 60, 43, 15, 69, 39], [1, 45, 77, 31, 67, 68, 77, 77, 94, 55, 3, 1]], [[40, 5, 39, 95, 27, 88, 21, 66, 91, 82, 41, 77], [77, 23, 27, 10, 33, 50, 2, 68, 22, 10, 41, 54], [17, 77, 95, 19, 88, 87, 39, 13, 31, 45, 78, 19], [14, 7, 6, 12, 17, 59, 64, 5, 18, 34, 63, 95], [77, 4, 31, 35, 43, 48, 93, 69, 6, 14, 45, 17], [3, 46, 10, 39, 43, 62, 31, 32, 85, 3, 83, 18], [72, 5, 89, 29, 59, 29, 72, 1, 29, 68, 98, 9], [24, 51, 30, 65, 89, 71, 94, 20, 88, 63, 76, 53], [21, 10, 80, 58, 23, 55, 58, 71, 33, 26, 36, 97], [47, 43, 8, 90, 22, 9, 3, 40, 15, 90, 57, 38], [91, 44, 20, 23, 79, 37, 85, 50, 86, 1, 76, 93], [69, 20, 76, 83, 58, 80, 22, 4, 88, 95, 39, 99]], [[65, 53, 9, 46, 37, 92, 66, 71, 43, 76, 80, 93], [47, 8, 54, 25, 72, 3, 65, 49, 31, 14, 19, 50], [91, 53, 29, 5, 35, 26, 58, 81, 24, 2, 65, 92], [32, 3, 13, 7, 83, 12, 8, 61, 85, 71, 75, 18], [23, 52, 2, 93, 76, 28, 41, 90, 44, 10, 25, 29], [48, 23, 39, 95, 91, 54, 56, 11, 40, 91, 61, 16], [74, 52, 38, 38, 7, 38, 95, 13, 69, 48, 80, 95], [41, 6, 36, 89, 37, 21, 4, 35, 37, 92, 29, 7], [38, 0, 19, 91, 22, 62, 80, 77, 21, 70, 5, 95], [97, 70, 51, 9, 73, 16, 81, 94, 44, 85, 92, 0], [15, 94, 65, 99, 66, 95, 35, 44, 21, 18, 74, 94], [39, 72, 57, 29, 72, 60, 23, 30, 93, 97, 48, 78]], [[24, 78, 11, 45, 9, 91, 99, 72, 79, 38, 8, 70], [66, 0, 99, 45, 89, 68, 36, 57, 13, 11, 26, 92], [84, 31, 43, 42, 91, 94, 5, 1, 85, 45, 68, 73], [82, 56, 6, 9, 75, 40, 38, 18, 51, 98, 9, 66], [44, 16, 97, 75, 71, 46, 94, 77, 50, 17, 64, 12], [89, 29, 71, 28, 30, 83, 48, 37, 62, 56, 11, 84], [56, 67, 83, 31, 61, 41, 99, 65, 97, 13, 75, 92], [96, 82, 46, 13, 14, 48, 26, 15, 91, 94, 63, 79], [15, 5, 35, 41, 65, 66, 44, 25, 68, 31, 72, 67], [28, 84, 25, 15, 79, 39, 16, 88, 7, 94, 68, 0], [14, 8, 85, 71, 64, 15, 12, 79, 26, 73, 80, 4], [67, 14, 9, 21, 87, 5, 15, 49, 37, 98, 53, 75]], [[50, 65, 96, 11, 86, 12, 5, 70, 60, 36, 88, 69], [43, 94, 11, 98, 69, 34, 95, 62, 85, 46, 37, 26], [13, 3, 59, 61, 1, 70, 79, 93, 69, 75, 50, 94], [17, 65, 31, 59, 37, 12, 91, 64, 25, 39, 90, 95], [78, 89, 50, 30, 90, 23, 86, 28, 25, 39, 96, 98], [91, 56, 5, 35, 15, 92, 58, 24, 7, 0, 92, 6], [1, 19, 49, 35, 8, 33, 81, 64, 48, 81, 40, 24], [87, 15, 2, 74, 64, 36, 63, 87, 56, 63, 99, 16], [67, 92, 76, 20, 54, 30, 29, 44, 36, 94, 52, 76], [46, 41, 82, 62, 93, 33, 28, 55, 57, 30, 88, 69], [16, 11, 25, 2, 20, 37, 2, 65, 49, 7, 93, 17], [48, 50, 84, 94, 61, 61, 6, 92, 33, 57, 90, 26]], [[25, 33, 68, 16, 68, 50, 9, 74, 88, 61, 29, 16], [42, 47, 65, 84, 14, 83, 64, 6, 83, 27, 81, 81], [62, 18, 57, 71, 67, 14, 60, 74, 60, 12, 62, 26], [52, 44, 67, 31, 40, 23, 16, 12, 80, 72, 52, 88], [20, 85, 56, 63, 62, 2, 77, 60, 8, 6, 55, 1], [20, 40, 81, 28, 67, 15, 88, 54, 2, 69, 92, 7], [19, 98, 29, 91, 8, 52, 84, 98, 8, 32, 76, 13], [11, 21, 46, 96, 3, 50, 8, 42, 25, 21, 71, 15], [77, 95, 37, 8, 3, 13, 85, 48, 85, 15, 76, 86], [22, 61, 29, 43, 11, 22, 48, 88, 87, 29, 41, 16], [26, 98, 52, 16, 10, 13, 97, 8, 71, 14, 26, 78], [44, 22, 26, 15, 75, 4, 97, 0, 8, 87, 96, 32]], [[54, 90, 67, 84, 48, 47, 55, 69, 93, 90, 40, 96], [77, 64, 12, 20, 72, 25, 92, 0, 96, 65, 6, 69], [74, 52, 71, 56, 36, 15, 50, 99, 24, 54, 47, 84], [96, 25, 7, 82, 10, 23, 73, 93, 10, 26, 80, 4], [18, 36, 65, 56, 54, 42, 41, 61, 93, 8, 59, 90], [69, 36, 57, 41, 30, 15, 39, 51, 75, 22, 78, 34], [60, 49, 62, 34, 13, 36, 93, 36, 25, 18, 1, 2], [65, 0, 11, 79, 47, 9, 84, 74, 21, 44, 32, 97], [94, 82, 47, 23, 27, 1, 42, 71, 14, 86, 73, 70], [93, 98, 71, 13, 10, 10, 14, 84, 23, 38, 54, 66], [69, 63, 70, 39, 10, 48, 6, 20, 50, 24, 82, 42], [35, 18, 30, 0, 95, 65, 30, 92, 11, 39, 23, 96]], [[12, 62, 18, 65, 23, 89, 50, 87, 49, 10, 80, 24], [23, 92, 6, 27, 14, 46, 58, 8, 1, 31, 28, 2], [47, 61, 65, 5, 79, 0, 4, 68, 70, 87, 66, 96], [32, 3, 52, 82, 68, 90, 26, 13, 61, 17, 23, 89], [26, 76, 24, 51, 94, 51, 92, 43, 2, 20, 90, 51], [46, 27, 84, 48, 16, 25, 29, 50, 75, 88, 46, 77], [88, 80, 83, 63, 26, 14, 25, 41, 26, 47, 68, 19], [15, 26, 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3, 'k': 8, 'cost': 61}, {'i': 11, 'j': 3, 'k': 9, 'cost': 17}, {'i': 11, 'j': 3, 'k': 10, 'cost': 23}, {'i': 11, 'j': 3, 'k': 11, 'cost': 89}, {'i': 11, 'j': 4, 'k': 0, 'cost': 26}, {'i': 11, 'j': 4, 'k': 1, 'cost': 76}, {'i': 11, 'j': 4, 'k': 2, 'cost': 24}, {'i': 11, 'j': 4, 'k': 3, 'cost': 51}, {'i': 11, 'j': 4, 'k': 4, 'cost': 94}, {'i': 11, 'j': 4, 'k': 5, 'cost': 51}, {'i': 11, 'j': 4, 'k': 6, 'cost': 92}, {'i': 11, 'j': 4, 'k': 7, 'cost': 43}, {'i': 11, 'j': 4, 'k': 8, 'cost': 2}, {'i': 11, 'j': 4, 'k': 9, 'cost': 20}, {'i': 11, 'j': 4, 'k': 10, 'cost': 90}, {'i': 11, 'j': 4, 'k': 11, 'cost': 51}, {'i': 11, 'j': 5, 'k': 0, 'cost': 46}, {'i': 11, 'j': 5, 'k': 1, 'cost': 27}, {'i': 11, 'j': 5, 'k': 2, 'cost': 84}, {'i': 11, 'j': 5, 'k': 3, 'cost': 48}, {'i': 11, 'j': 5, 'k': 4, 'cost': 16}, {'i': 11, 'j': 5, 'k': 5, 'cost': 25}, {'i': 11, 'j': 5, 'k': 6, 'cost': 29}, {'i': 11, 'j': 5, 'k': 7, 'cost': 50}, {'i': 11, 'j': 5, 'k': 8, 'cost': 75}, {'i': 11, 'j': 5, 'k': 9, 'cost': 88}, {'i': 11, 'j': 5, 'k': 10, 'cost': 46}, {'i': 11, 'j': 5, 'k': 11, 'cost': 77}, {'i': 11, 'j': 6, 'k': 0, 'cost': 88}, {'i': 11, 'j': 6, 'k': 1, 'cost': 80}, {'i': 11, 'j': 6, 'k': 2, 'cost': 83}, {'i': 11, 'j': 6, 'k': 3, 'cost': 63}, {'i': 11, 'j': 6, 'k': 4, 'cost': 26}, {'i': 11, 'j': 6, 'k': 5, 'cost': 14}, {'i': 11, 'j': 6, 'k': 6, 'cost': 25}, {'i': 11, 'j': 6, 'k': 7, 'cost': 41}, {'i': 11, 'j': 6, 'k': 8, 'cost': 26}, {'i': 11, 'j': 6, 'k': 9, 'cost': 47}, {'i': 11, 'j': 6, 'k': 10, 'cost': 68}, {'i': 11, 'j': 6, 'k': 11, 'cost': 19}, {'i': 11, 'j': 7, 'k': 0, 'cost': 15}, {'i': 11, 'j': 7, 'k': 1, 'cost': 26}, {'i': 11, 'j': 7, 'k': 2, 'cost': 69}, {'i': 11, 'j': 7, 'k': 3, 'cost': 90}, {'i': 11, 'j': 7, 'k': 4, 'cost': 11}, {'i': 11, 'j': 7, 'k': 5, 'cost': 67}, {'i': 11, 'j': 7, 'k': 6, 'cost': 28}, {'i': 11, 'j': 7, 'k': 7, 'cost': 23}, {'i': 11, 'j': 7, 'k': 8, 'cost': 8}, {'i': 11, 'j': 7, 'k': 9, 'cost': 48}, {'i': 11, 'j': 7, 'k': 10, 'cost': 79}, {'i': 11, 'j': 7, 'k': 11, 'cost': 86}, {'i': 11, 'j': 8, 'k': 0, 'cost': 97}, {'i': 11, 'j': 8, 'k': 1, 'cost': 60}, {'i': 11, 'j': 8, 'k': 2, 'cost': 96}, {'i': 11, 'j': 8, 'k': 3, 'cost': 34}, {'i': 11, 'j': 8, 'k': 4, 'cost': 6}, {'i': 11, 'j': 8, 'k': 5, 'cost': 84}, {'i': 11, 'j': 8, 'k': 6, 'cost': 98}, {'i': 11, 'j': 8, 'k': 7, 'cost': 19}, {'i': 11, 'j': 8, 'k': 8, 'cost': 10}, {'i': 11, 'j': 8, 'k': 9, 'cost': 82}, {'i': 11, 'j': 8, 'k': 10, 'cost': 21}, {'i': 11, 'j': 8, 'k': 11, 'cost': 13}, {'i': 11, 'j': 9, 'k': 0, 'cost': 90}, {'i': 11, 'j': 9, 'k': 1, 'cost': 81}, {'i': 11, 'j': 9, 'k': 2, 'cost': 5}, {'i': 11, 'j': 9, 'k': 3, 'cost': 94}, {'i': 11, 'j': 9, 'k': 4, 'cost': 93}, {'i': 11, 'j': 9, 'k': 5, 'cost': 8}, {'i': 11, 'j': 9, 'k': 6, 'cost': 86}, {'i': 11, 'j': 9, 'k': 7, 'cost': 59}, {'i': 11, 'j': 9, 'k': 8, 'cost': 56}, {'i': 11, 'j': 9, 'k': 9, 'cost': 25}, {'i': 11, 'j': 9, 'k': 10, 'cost': 50}, {'i': 11, 'j': 9, 'k': 11, 'cost': 91}, {'i': 11, 'j': 10, 'k': 0, 'cost': 68}, {'i': 11, 'j': 10, 'k': 1, 'cost': 62}, {'i': 11, 'j': 10, 'k': 2, 'cost': 27}, {'i': 11, 'j': 10, 'k': 3, 'cost': 94}, {'i': 11, 'j': 10, 'k': 4, 'cost': 30}, {'i': 11, 'j': 10, 'k': 5, 'cost': 76}, {'i': 11, 'j': 10, 'k': 6, 'cost': 51}, {'i': 11, 'j': 10, 'k': 7, 'cost': 8}, {'i': 11, 'j': 10, 'k': 8, 'cost': 32}, {'i': 11, 'j': 10, 'k': 9, 'cost': 54}, {'i': 11, 'j': 10, 'k': 10, 'cost': 77}, {'i': 11, 'j': 10, 'k': 11, 'cost': 39}, {'i': 11, 'j': 11, 'k': 0, 'cost': 22}, {'i': 11, 'j': 11, 'k': 1, 'cost': 15}, {'i': 11, 'j': 11, 'k': 2, 'cost': 37}, {'i': 11, 'j': 11, 'k': 3, 'cost': 17}, {'i': 11, 'j': 11, 'k': 4, 'cost': 17}, {'i': 11, 'j': 11, 'k': 5, 'cost': 40}, {'i': 11, 'j': 11, 'k': 6, 'cost': 34}, {'i': 11, 'j': 11, 'k': 7, 'cost': 56}, {'i': 11, 'j': 11, 'k': 8, 'cost': 58}, {'i': 11, 'j': 11, 'k': 9, 'cost': 91}, {'i': 11, 'j': 11, 'k': 10, 'cost': 66}, {'i': 11, 'j': 11, 'k': 11, 'cost': 28}]}","[[0, 3, 8], [1, 1, 10], [2, 5, 9], [3, 0, 6], [4, 11, 0], [5, 6, 7], [6, 4, 2], [7, 9, 11], [8, 10, 3], [9, 8, 4], [10, 7, 1], [11, 2, 5]]",36,nl,0
+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 12 rehearsals, identified as A, B, C, D, E, F, G, H, I, J, K, L.
+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=A
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 55 | 45 | 91 | 78 | 9 | 73 | 51 | 41 | 50 | 18 | 40 | 55 |
+| B | 93 | 27 | 67 | 69 | 22 | 93 | 32 | 96 | 6 | 73 | 53 | 26 |
+| C | 57 | 30 | 40 | 70 | 65 | 28 | 74 | 18 | 3 | 31 | 80 | 39 |
+| D | 76 | 83 | 44 | 27 | 91 | 66 | 97 | 77 | 95 | 60 | 10 | 67 |
+| E | 11 | 27 | 70 | 56 | 19 | 73 | 85 | 49 | 39 | 94 | 32 | 51 |
+| F | 28 | 2 | 20 | 6 | 32 | 20 | 65 | 86 | 10 | 84 | 75 | 81 |
+| G | 5 | 83 | 13 | 1 | 50 | 27 | 63 | 92 | 29 | 18 | 9 | 97 |
+| H | 39 | 2 | 72 | 51 | 91 | 79 | 42 | 59 | 98 | 82 | 25 | 96 |
+| I | 94 | 0 | 61 | 8 | 8 | 17 | 18 | 50 | 69 | 96 | 24 | 58 |
+| J | 86 | 46 | 48 | 77 | 78 | 97 | 2 | 34 | 50 | 91 | 0 | 46 |
+| K | 11 | 74 | 74 | 27 | 89 | 44 | 48 | 7 | 52 | 76 | 8 | 12 |
+| L | 29 | 24 | 58 | 23 | 57 | 72 | 3 | 88 | 70 | 10 | 88 | 70 |
+
+## rehearsal_id=B
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 9 | 60 | 91 | 59 | 25 | 14 | 1 | 68 | 53 | 92 | 62 | 89 |
+| B | 65 | 33 | 54 | 30 | 51 | 7 | 84 | 89 | 94 | 25 | 67 | 36 |
+| C | 10 | 60 | 18 | 21 | 73 | 56 | 66 | 94 | 84 | 87 | 26 | 65 |
+| D | 4 | 4 | 53 | 50 | 49 | 14 | 18 | 38 | 70 | 5 | 51 | 61 |
+| E | 53 | 54 | 96 | 92 | 19 | 92 | 64 | 29 | 1 | 50 | 45 | 88 |
+| F | 71 | 10 | 48 | 94 | 67 | 99 | 33 | 62 | 56 | 41 | 75 | 87 |
+| G | 56 | 93 | 35 | 61 | 5 | 49 | 32 | 74 | 88 | 13 | 15 | 41 |
+| H | 88 | 46 | 64 | 36 | 56 | 11 | 79 | 30 | 82 | 85 | 33 | 34 |
+| I | 43 | 15 | 71 | 50 | 48 | 74 | 29 | 3 | 58 | 73 | 52 | 32 |
+| J | 58 | 8 | 46 | 4 | 65 | 65 | 8 | 58 | 54 | 23 | 36 | 80 |
+| K | 38 | 55 | 41 | 69 | 18 | 82 | 90 | 95 | 35 | 36 | 80 | 65 |
+| L | 4 | 76 | 91 | 91 | 64 | 4 | 3 | 79 | 24 | 35 | 6 | 67 |
+
+## rehearsal_id=C
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 93 | 39 | 51 | 73 | 28 | 35 | 53 | 86 | 74 | 71 | 57 |
+| B | 62 | 72 | 94 | 53 | 85 | 38 | 20 | 26 | 1 | 71 | 7 | 64 |
+| C | 88 | 82 | 85 | 49 | 74 | 86 | 10 | 78 | 74 | 79 | 78 | 49 |
+| D | 2 | 12 | 19 | 12 | 53 | 83 | 29 | 61 | 46 | 16 | 7 | 58 |
+| E | 6 | 37 | 6 | 64 | 84 | 81 | 7 | 58 | 51 | 72 | 46 | 86 |
+| F | 95 | 23 | 11 | 46 | 16 | 10 | 39 | 35 | 87 | 42 | 61 | 26 |
+| G | 20 | 24 | 87 | 31 | 66 | 53 | 46 | 44 | 13 | 74 | 36 | 87 |
+| H | 12 | 30 | 48 | 37 | 54 | 80 | 65 | 25 | 54 | 19 | 9 | 40 |
+| I | 43 | 37 | 32 | 98 | 53 | 5 | 89 | 75 | 4 | 48 | 5 | 68 |
+| J | 64 | 30 | 72 | 88 | 96 | 48 | 9 | 64 | 13 | 43 | 9 | 39 |
+| K | 95 | 83 | 43 | 14 | 45 | 87 | 61 | 50 | 5 | 63 | 73 | 67 |
+| L | 35 | 33 | 44 | 34 | 25 | 15 | 13 | 12 | 63 | 82 | 21 | 0 |
+
+## rehearsal_id=D
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 92 | 53 | 58 | 13 | 4 | 20 | 7 | 30 | 33 | 69 | 45 | 92 |
+| B | 98 | 23 | 47 | 61 | 38 | 12 | 64 | 86 | 52 | 95 | 14 | 31 |
+| C | 43 | 11 | 10 | 35 | 73 | 81 | 70 | 74 | 10 | 77 | 81 | 74 |
+| D | 21 | 75 | 0 | 14 | 34 | 32 | 68 | 92 | 94 | 0 | 63 | 80 |
+| E | 45 | 17 | 11 | 36 | 73 | 87 | 90 | 59 | 56 | 86 | 96 | 65 |
+| F | 19 | 17 | 87 | 16 | 69 | 35 | 13 | 63 | 82 | 6 | 80 | 40 |
+| G | 88 | 34 | 6 | 6 | 46 | 69 | 69 | 99 | 93 | 11 | 17 | 14 |
+| H | 15 | 62 | 82 | 81 | 8 | 23 | 27 | 39 | 77 | 46 | 47 | 29 |
+| I | 52 | 16 | 90 | 83 | 12 | 6 | 56 | 84 | 3 | 90 | 3 | 91 |
+| J | 2 | 93 | 94 | 12 | 95 | 14 | 44 | 96 | 23 | 54 | 7 | 30 |
+| K | 6 | 7 | 18 | 41 | 69 | 70 | 36 | 59 | 52 | 83 | 45 | 54 |
+| L | 4 | 7 | 33 | 71 | 38 | 2 | 3 | 62 | 69 | 48 | 78 | 25 |
+
+## rehearsal_id=E
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 23 | 44 | 50 | 31 | 27 | 80 | 92 | 64 | 0 | 65 | 48 | 83 |
+| B | 99 | 7 | 46 | 49 | 73 | 0 | 92 | 97 | 71 | 68 | 90 | 13 |
+| C | 88 | 2 | 39 | 75 | 84 | 20 | 28 | 35 | 26 | 62 | 90 | 92 |
+| D | 47 | 74 | 23 | 7 | 66 | 28 | 48 | 47 | 32 | 44 | 89 | 78 |
+| E | 75 | 21 | 54 | 69 | 99 | 31 | 32 | 80 | 54 | 52 | 49 | 44 |
+| F | 53 | 34 | 55 | 55 | 47 | 60 | 29 | 1 | 48 | 56 | 5 | 72 |
+| G | 41 | 40 | 8 | 59 | 92 | 74 | 21 | 99 | 42 | 69 | 24 | 46 |
+| H | 89 | 57 | 92 | 34 | 14 | 35 | 96 | 45 | 90 | 44 | 49 | 42 |
+| I | 2 | 79 | 5 | 24 | 77 | 79 | 55 | 80 | 50 | 14 | 44 | 26 |
+| J | 5 | 2 | 33 | 67 | 30 | 72 | 37 | 86 | 94 | 25 | 79 | 7 |
+| K | 21 | 71 | 7 | 21 | 79 | 12 | 96 | 25 | 91 | 92 | 10 | 15 |
+| L | 93 | 20 | 22 | 85 | 3 | 45 | 93 | 14 | 63 | 83 | 24 | 6 |
+
+## rehearsal_id=F
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 4 | 72 | 89 | 34 | 95 | 65 | 43 | 98 | 47 | 92 | 70 | 81 |
+| B | 44 | 73 | 19 | 33 | 87 | 5 | 14 | 65 | 66 | 67 | 92 | 40 |
+| C | 18 | 90 | 0 | 29 | 22 | 47 | 51 | 19 | 78 | 29 | 32 | 82 |
+| D | 2 | 52 | 9 | 60 | 67 | 75 | 47 | 34 | 29 | 13 | 0 | 36 |
+| E | 21 | 1 | 34 | 19 | 7 | 12 | 78 | 15 | 94 | 27 | 49 | 16 |
+| F | 60 | 15 | 87 | 57 | 42 | 75 | 87 | 92 | 24 | 1 | 90 | 75 |
+| G | 7 | 63 | 78 | 9 | 36 | 28 | 66 | 7 | 14 | 58 | 9 | 95 |
+| H | 53 | 54 | 77 | 96 | 76 | 73 | 44 | 89 | 67 | 1 | 54 | 55 |
+| I | 96 | 1 | 6 | 95 | 12 | 49 | 82 | 47 | 36 | 21 | 13 | 98 |
+| J | 96 | 34 | 28 | 81 | 34 | 70 | 17 | 56 | 65 | 14 | 17 | 81 |
+| K | 50 | 12 | 89 | 62 | 39 | 68 | 97 | 44 | 35 | 52 | 80 | 0 |
+| L | 4 | 18 | 70 | 93 | 80 | 51 | 81 | 29 | 99 | 24 | 25 | 90 |
+
+## rehearsal_id=G
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 40 | 49 | 0 | 54 | 71 | 0 | 72 | 55 | 20 | 52 | 19 | 90 |
+| B | 1 | 65 | 6 | 60 | 95 | 36 | 60 | 7 | 23 | 40 | 7 | 40 |
+| C | 45 | 65 | 87 | 1 | 35 | 95 | 36 | 2 | 24 | 24 | 71 | 2 |
+| D | 39 | 91 | 24 | 23 | 98 | 34 | 96 | 55 | 76 | 73 | 58 | 43 |
+| E | 76 | 69 | 48 | 78 | 45 | 11 | 65 | 68 | 6 | 42 | 10 | 75 |
+| F | 20 | 21 | 8 | 25 | 87 | 70 | 37 | 97 | 22 | 22 | 1 | 52 |
+| G | 91 | 54 | 24 | 64 | 10 | 20 | 46 | 66 | 72 | 50 | 60 | 55 |
+| H | 7 | 65 | 88 | 12 | 56 | 64 | 38 | 92 | 9 | 36 | 38 | 47 |
+| I | 5 | 82 | 47 | 82 | 29 | 20 | 26 | 37 | 38 | 90 | 75 | 77 |
+| J | 7 | 7 | 24 | 62 | 73 | 75 | 24 | 79 | 85 | 89 | 38 | 36 |
+| K | 67 | 12 | 73 | 56 | 75 | 25 | 4 | 32 | 68 | 6 | 56 | 83 |
+| L | 76 | 28 | 92 | 50 | 87 | 58 | 56 | 29 | 64 | 62 | 18 | 84 |
+
+## rehearsal_id=H
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 42 | 75 | 47 | 65 | 12 | 78 | 38 | 61 | 65 | 12 | 47 | 65 |
+| B | 12 | 21 | 82 | 19 | 80 | 7 | 85 | 25 | 15 | 42 | 77 | 77 |
+| C | 30 | 87 | 38 | 14 | 6 | 46 | 14 | 27 | 98 | 50 | 68 | 14 |
+| D | 87 | 30 | 23 | 32 | 90 | 85 | 78 | 84 | 70 | 92 | 78 | 67 |
+| E | 7 | 70 | 52 | 8 | 61 | 95 | 69 | 54 | 79 | 39 | 93 | 74 |
+| F | 73 | 37 | 27 | 65 | 53 | 24 | 18 | 60 | 37 | 87 | 77 | 70 |
+| G | 72 | 37 | 1 | 21 | 97 | 55 | 8 | 17 | 8 | 17 | 92 | 23 |
+| H | 42 | 75 | 1 | 48 | 74 | 20 | 45 | 2 | 75 | 60 | 49 | 31 |
+| I | 97 | 73 | 1 | 30 | 71 | 54 | 70 | 22 | 13 | 5 | 58 | 93 |
+| J | 60 | 85 | 81 | 1 | 49 | 62 | 91 | 78 | 57 | 73 | 94 | 24 |
+| K | 12 | 55 | 61 | 97 | 23 | 7 | 39 | 9 | 29 | 65 | 23 | 13 |
+| L | 75 | 39 | 31 | 84 | 73 | 45 | 31 | 59 | 68 | 57 | 41 | 14 |
+
+## rehearsal_id=I
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 66 | 73 | 71 | 16 | 16 | 95 | 69 | 28 | 33 | 23 | 97 | 82 |
+| B | 81 | 1 | 43 | 72 | 89 | 12 | 32 | 62 | 48 | 57 | 78 | 51 |
+| C | 54 | 57 | 63 | 4 | 87 | 34 | 42 | 61 | 16 | 86 | 28 | 92 |
+| D | 16 | 66 | 53 | 58 | 23 | 87 | 96 | 25 | 86 | 39 | 61 | 30 |
+| E | 28 | 52 | 24 | 50 | 53 | 49 | 81 | 44 | 6 | 95 | 33 | 77 |
+| F | 1 | 86 | 68 | 29 | 82 | 72 | 45 | 46 | 61 | 19 | 99 | 73 |
+| G | 66 | 99 | 39 | 78 | 83 | 80 | 54 | 44 | 79 | 38 | 48 | 96 |
+| H | 79 | 66 | 17 | 72 | 83 | 98 | 66 | 86 | 98 | 68 | 59 | 74 |
+| I | 86 | 30 | 37 | 7 | 14 | 78 | 74 | 85 | 97 | 35 | 12 | 78 |
+| J | 58 | 95 | 46 | 85 | 59 | 63 | 59 | 27 | 41 | 17 | 89 | 57 |
+| K | 35 | 58 | 63 | 33 | 74 | 16 | 47 | 53 | 70 | 41 | 59 | 10 |
+| L | 22 | 87 | 39 | 2 | 63 | 97 | 94 | 2 | 5 | 66 | 21 | 53 |
+
+## rehearsal_id=J
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 39 | 92 | 15 | 67 | 98 | 18 | 11 | 24 | 69 | 34 | 35 | 21 |
+| B | 11 | 53 | 86 | 15 | 60 | 63 | 59 | 19 | 62 | 80 | 78 | 24 |
+| C | 87 | 88 | 16 | 58 | 82 | 53 | 19 | 14 | 33 | 15 | 53 | 8 |
+| D | 18 | 9 | 10 | 34 | 56 | 24 | 73 | 97 | 27 | 73 | 23 | 61 |
+| E | 0 | 43 | 70 | 95 | 76 | 6 | 99 | 72 | 82 | 28 | 0 | 21 |
+| F | 77 | 19 | 88 | 65 | 27 | 78 | 3 | 71 | 96 | 83 | 13 | 76 |
+| G | 71 | 35 | 73 | 98 | 32 | 30 | 94 | 18 | 38 | 65 | 28 | 26 |
+| H | 94 | 55 | 89 | 88 | 8 | 46 | 28 | 42 | 7 | 66 | 97 | 13 |
+| I | 22 | 43 | 55 | 94 | 37 | 84 | 89 | 80 | 56 | 58 | 27 | 69 |
+| J | 68 | 79 | 70 | 12 | 5 | 75 | 30 | 97 | 15 | 63 | 0 | 93 |
+| K | 7 | 12 | 89 | 46 | 87 | 19 | 33 | 6 | 40 | 84 | 7 | 82 |
+| L | 32 | 1 | 30 | 42 | 0 | 44 | 7 | 88 | 4 | 53 | 48 | 53 |
+
+## rehearsal_id=K
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 90 | 70 | 12 | 7 | 13 | 2 | 77 | 37 | 55 | 49 | 27 | 53 |
+| B | 74 | 9 | 49 | 30 | 60 | 77 | 27 | 95 | 38 | 50 | 11 | 44 |
+| C | 41 | 38 | 72 | 37 | 4 | 97 | 87 | 13 | 86 | 53 | 6 | 30 |
+| D | 78 | 38 | 81 | 53 | 16 | 64 | 46 | 59 | 57 | 35 | 81 | 52 |
+| E | 58 | 93 | 85 | 81 | 59 | 64 | 59 | 40 | 99 | 78 | 2 | 98 |
+| F | 94 | 28 | 74 | 90 | 8 | 49 | 48 | 42 | 23 | 13 | 74 | 87 |
+| G | 16 | 54 | 92 | 55 | 30 | 61 | 33 | 78 | 60 | 18 | 32 | 46 |
+| H | 60 | 6 | 49 | 73 | 4 | 34 | 33 | 55 | 91 | 59 | 81 | 53 |
+| I | 78 | 36 | 78 | 84 | 56 | 31 | 27 | 84 | 69 | 10 | 78 | 45 |
+| J | 24 | 65 | 11 | 22 | 67 | 54 | 92 | 89 | 25 | 0 | 96 | 62 |
+| K | 81 | 29 | 43 | 83 | 41 | 78 | 12 | 82 | 22 | 12 | 15 | 21 |
+| L | 71 | 77 | 33 | 21 | 57 | 19 | 94 | 9 | 4 | 56 | 29 | 0 |
+
+## rehearsal_id=L
+| room_id\technician_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 94 | 78 | 67 | 33 | 24 | 69 | 92 | 21 | 37 | 35 | 30 | 54 |
+| B | 40 | 70 | 8 | 32 | 99 | 81 | 65 | 70 | 19 | 21 | 98 | 35 |
+| C | 18 | 73 | 92 | 80 | 10 | 52 | 22 | 47 | 67 | 46 | 22 | 42 |
+| D | 26 | 29 | 89 | 18 | 69 | 48 | 18 | 45 | 90 | 63 | 20 | 4 |
+| E | 41 | 66 | 24 | 99 | 20 | 5 | 60 | 55 | 18 | 51 | 39 | 85 |
+| F | 92 | 55 | 22 | 20 | 76 | 59 | 80 | 8 | 84 | 53 | 47 | 12 |
+| G | 64 | 18 | 15 | 5 | 25 | 68 | 11 | 16 | 16 | 4 | 75 | 42 |
+| H | 35 | 80 | 81 | 0 | 66 | 23 | 24 | 66 | 84 | 95 | 36 | 58 |
+| I | 13 | 86 | 55 | 25 | 76 | 65 | 73 | 35 | 56 | 3 | 28 | 75 |
+| J | 12 | 54 | 85 | 20 | 47 | 41 | 55 | 14 | 93 | 61 | 18 | 94 |
+| K | 11 | 53 | 55 | 99 | 13 | 15 | 51 | 45 | 6 | 94 | 24 | 42 |
+| L | 17 | 43 | 97 | 29 | 74 | 39 | 6 | 92 | 80 | 28 | 64 | 56 |
+One triple must be selected for each of the 12 rehearsals (A, B, C, D, E, F, G, H, I, J, K, L) 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': [[[55, 45, 91, 78, 9, 73, 51, 41, 50, 18, 40, 55], [93, 27, 67, 69, 22, 93, 32, 96, 6, 73, 53, 26], [57, 30, 40, 70, 65, 28, 74, 18, 3, 31, 80, 39], [76, 83, 44, 27, 91, 66, 97, 77, 95, 60, 10, 67], [11, 27, 70, 56, 19, 73, 85, 49, 39, 94, 32, 51], [28, 2, 20, 6, 32, 20, 65, 86, 10, 84, 75, 81], [5, 83, 13, 1, 50, 27, 63, 92, 29, 18, 9, 97], [39, 2, 72, 51, 91, 79, 42, 59, 98, 82, 25, 96], [94, 0, 61, 8, 8, 17, 18, 50, 69, 96, 24, 58], [86, 46, 48, 77, 78, 97, 2, 34, 50, 91, 0, 46], [11, 74, 74, 27, 89, 44, 48, 7, 52, 76, 8, 12], [29, 24, 58, 23, 57, 72, 3, 88, 70, 10, 88, 70]], [[9, 60, 91, 59, 25, 14, 1, 68, 53, 92, 62, 89], [65, 33, 54, 30, 51, 7, 84, 89, 94, 25, 67, 36], [10, 60, 18, 21, 73, 56, 66, 94, 84, 87, 26, 65], [4, 4, 53, 50, 49, 14, 18, 38, 70, 5, 51, 61], [53, 54, 96, 92, 19, 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'F', 'k': 'F', 'cost': 59}, {'i': 'L', 'j': 'F', 'k': 'G', 'cost': 80}, {'i': 'L', 'j': 'F', 'k': 'H', 'cost': 8}, {'i': 'L', 'j': 'F', 'k': 'I', 'cost': 84}, {'i': 'L', 'j': 'F', 'k': 'J', 'cost': 53}, {'i': 'L', 'j': 'F', 'k': 'K', 'cost': 47}, {'i': 'L', 'j': 'F', 'k': 'L', 'cost': 12}, {'i': 'L', 'j': 'G', 'k': 'A', 'cost': 64}, {'i': 'L', 'j': 'G', 'k': 'B', 'cost': 18}, {'i': 'L', 'j': 'G', 'k': 'C', 'cost': 15}, {'i': 'L', 'j': 'G', 'k': 'D', 'cost': 5}, {'i': 'L', 'j': 'G', 'k': 'E', 'cost': 25}, {'i': 'L', 'j': 'G', 'k': 'F', 'cost': 68}, {'i': 'L', 'j': 'G', 'k': 'G', 'cost': 11}, {'i': 'L', 'j': 'G', 'k': 'H', 'cost': 16}, {'i': 'L', 'j': 'G', 'k': 'I', 'cost': 16}, {'i': 'L', 'j': 'G', 'k': 'J', 'cost': 4}, {'i': 'L', 'j': 'G', 'k': 'K', 'cost': 75}, {'i': 'L', 'j': 'G', 'k': 'L', 'cost': 42}, {'i': 'L', 'j': 'H', 'k': 'A', 'cost': 35}, {'i': 'L', 'j': 'H', 'k': 'B', 'cost': 80}, {'i': 'L', 'j': 'H', 'k': 'C', 'cost': 81}, {'i': 'L', 'j': 'H', 'k': 'D', 'cost': 0}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 66}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 23}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 24}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 66}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 84}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 95}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 36}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 58}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 13}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 86}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 55}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 25}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 76}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 65}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 73}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 35}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 56}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 3}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 28}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 75}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 12}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 54}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 85}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 20}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 47}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 41}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 55}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 14}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 93}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 61}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 18}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 94}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 11}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 53}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 55}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 99}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 13}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 15}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 51}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 45}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 6}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 94}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 24}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 42}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 17}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 43}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 97}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 29}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 74}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 39}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 6}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 92}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 80}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 28}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 64}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 56}]}","[['A', 'J', 'G'], ['B', 'I', 'H'], ['C', 'B', 'I'], ['D', 'D', 'J'], ['E', 'C', 'B'], ['F', 'K', 'L'], ['G', 'A', 'F'], ['H', 'G', 'C'], ['I', 'F', 'A'], ['J', 'L', 'E'], ['K', 'E', 'K'], ['L', 'H', 'D']]",37,nl,names
+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=11
+# table_identifiers=A, B, C, D, E, F, G, H, I, J, K
+
+# 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=A
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 76 | 66 | 99 | 40 | 47 | 6 | 96 | 42 | 54 | 78 | 18 |
+| B | 10 | 21 | 14 | 43 | 33 | 63 | 74 | 33 | 71 | 7 | 54 |
+| C | 73 | 31 | 49 | 65 | 25 | 86 | 90 | 96 | 30 | 13 | 40 |
+| D | 50 | 17 | 32 | 16 | 11 | 91 | 87 | 98 | 24 | 89 | 90 |
+| E | 94 | 90 | 76 | 32 | 22 | 42 | 18 | 76 | 10 | 70 | 40 |
+| F | 8 | 49 | 47 | 56 | 40 | 6 | 95 | 70 | 85 | 85 | 2 |
+| G | 1 | 68 | 25 | 43 | 88 | 76 | 25 | 24 | 56 | 83 | 32 |
+| H | 91 | 99 | 54 | 74 | 77 | 18 | 84 | 86 | 94 | 31 | 22 |
+| I | 28 | 84 | 28 | 91 | 71 | 38 | 62 | 68 | 29 | 51 | 56 |
+| J | 80 | 18 | 32 | 27 | 63 | 66 | 11 | 36 | 48 | 44 | 51 |
+| K | 83 | 91 | 83 | 44 | 77 | 11 | 82 | 69 | 46 | 25 | 53 |
+
+## table_id=B
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 88 | 52 | 88 | 67 | 85 | 92 | 94 | 51 | 1 | 50 | 40 |
+| B | 16 | 93 | 45 | 34 | 37 | 76 | 25 | 29 | 99 | 32 | 47 |
+| C | 24 | 16 | 37 | 77 | 15 | 36 | 87 | 53 | 23 | 35 | 99 |
+| D | 11 | 13 | 75 | 89 | 82 | 17 | 47 | 50 | 62 | 26 | 0 |
+| E | 97 | 50 | 20 | 11 | 95 | 1 | 54 | 91 | 91 | 45 | 67 |
+| F | 35 | 67 | 69 | 60 | 24 | 46 | 10 | 93 | 51 | 62 | 20 |
+| G | 38 | 79 | 47 | 73 | 76 | 49 | 34 | 61 | 30 | 45 | 73 |
+| H | 33 | 61 | 28 | 21 | 31 | 96 | 67 | 41 | 48 | 64 | 54 |
+| I | 95 | 93 | 33 | 0 | 11 | 3 | 43 | 38 | 25 | 14 | 89 |
+| J | 19 | 25 | 25 | 4 | 15 | 78 | 33 | 76 | 44 | 76 | 29 |
+| K | 63 | 67 | 70 | 17 | 12 | 12 | 34 | 41 | 20 | 82 | 16 |
+
+## table_id=C
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 35 | 39 | 48 | 64 | 63 | 62 | 9 | 4 | 64 | 40 | 66 |
+| B | 79 | 99 | 31 | 54 | 63 | 79 | 64 | 19 | 24 | 43 | 80 |
+| C | 95 | 41 | 80 | 22 | 52 | 86 | 63 | 6 | 78 | 92 | 69 |
+| D | 84 | 5 | 77 | 7 | 0 | 36 | 70 | 46 | 39 | 35 | 53 |
+| E | 9 | 56 | 47 | 41 | 86 | 87 | 23 | 70 | 69 | 25 | 18 |
+| F | 78 | 34 | 34 | 67 | 55 | 64 | 18 | 62 | 64 | 96 | 31 |
+| G | 73 | 54 | 21 | 72 | 23 | 86 | 35 | 54 | 57 | 54 | 25 |
+| H | 98 | 58 | 56 | 72 | 27 | 49 | 91 | 68 | 24 | 38 | 60 |
+| I | 62 | 18 | 44 | 98 | 31 | 68 | 13 | 63 | 38 | 49 | 76 |
+| J | 62 | 87 | 10 | 31 | 67 | 33 | 48 | 19 | 33 | 13 | 67 |
+| K | 72 | 0 | 89 | 35 | 98 | 76 | 69 | 87 | 72 | 90 | 49 |
+
+## table_id=D
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 78 | 84 | 24 | 42 | 14 | 46 | 85 | 26 | 62 | 86 | 6 |
+| B | 98 | 19 | 79 | 18 | 11 | 50 | 98 | 83 | 38 | 45 | 81 |
+| C | 11 | 52 | 36 | 66 | 6 | 16 | 55 | 13 | 76 | 80 | 54 |
+| D | 92 | 59 | 17 | 8 | 66 | 90 | 34 | 14 | 89 | 98 | 35 |
+| E | 74 | 77 | 83 | 22 | 30 | 8 | 50 | 31 | 82 | 21 | 41 |
+| F | 46 | 76 | 2 | 75 | 35 | 81 | 77 | 76 | 37 | 31 | 78 |
+| G | 60 | 25 | 22 | 6 | 25 | 80 | 89 | 67 | 2 | 94 | 50 |
+| H | 20 | 32 | 19 | 64 | 66 | 25 | 5 | 33 | 7 | 35 | 40 |
+| I | 20 | 97 | 89 | 32 | 32 | 31 | 80 | 53 | 41 | 47 | 80 |
+| J | 8 | 21 | 24 | 58 | 51 | 90 | 70 | 91 | 6 | 74 | 9 |
+| K | 72 | 80 | 54 | 43 | 47 | 29 | 21 | 81 | 96 | 22 | 81 |
+
+## table_id=E
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 84 | 29 | 55 | 87 | 76 | 52 | 41 | 68 | 38 | 84 | 65 |
+| B | 76 | 54 | 66 | 72 | 62 | 99 | 97 | 92 | 20 | 28 | 50 |
+| C | 64 | 2 | 56 | 75 | 83 | 23 | 66 | 72 | 81 | 59 | 69 |
+| D | 70 | 7 | 94 | 16 | 83 | 77 | 84 | 40 | 94 | 19 | 17 |
+| E | 62 | 30 | 36 | 7 | 93 | 92 | 55 | 73 | 47 | 4 | 8 |
+| F | 65 | 58 | 62 | 67 | 74 | 72 | 5 | 79 | 87 | 40 | 34 |
+| G | 10 | 28 | 91 | 72 | 76 | 2 | 51 | 41 | 12 | 24 | 90 |
+| H | 8 | 79 | 39 | 98 | 16 | 61 | 38 | 52 | 11 | 38 | 86 |
+| I | 84 | 30 | 14 | 99 | 38 | 79 | 91 | 72 | 72 | 46 | 41 |
+| J | 70 | 42 | 2 | 84 | 97 | 73 | 55 | 3 | 77 | 87 | 40 |
+| K | 3 | 97 | 98 | 36 | 95 | 24 | 78 | 55 | 29 | 5 | 36 |
+
+## table_id=F
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 72 | 44 | 58 | 45 | 59 | 35 | 73 | 17 | 80 | 24 | 41 |
+| B | 73 | 53 | 23 | 54 | 7 | 78 | 22 | 49 | 54 | 40 | 55 |
+| C | 89 | 89 | 89 | 83 | 14 | 20 | 87 | 41 | 40 | 67 | 30 |
+| D | 48 | 66 | 51 | 58 | 56 | 92 | 37 | 37 | 49 | 83 | 66 |
+| E | 37 | 47 | 83 | 36 | 53 | 79 | 83 | 16 | 22 | 84 | 69 |
+| F | 14 | 12 | 70 | 46 | 49 | 64 | 99 | 76 | 1 | 27 | 75 |
+| G | 22 | 35 | 99 | 96 | 50 | 17 | 97 | 68 | 67 | 14 | 80 |
+| H | 21 | 34 | 22 | 52 | 72 | 48 | 63 | 53 | 63 | 15 | 11 |
+| I | 3 | 16 | 87 | 23 | 35 | 0 | 30 | 53 | 37 | 43 | 90 |
+| J | 87 | 66 | 93 | 88 | 86 | 75 | 33 | 40 | 99 | 69 | 66 |
+| K | 42 | 48 | 38 | 26 | 80 | 94 | 19 | 95 | 26 | 99 | 65 |
+
+## table_id=G
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 1 | 84 | 7 | 59 | 34 | 68 | 50 | 31 | 62 | 27 | 50 |
+| B | 70 | 37 | 45 | 11 | 68 | 17 | 71 | 73 | 99 | 69 | 0 |
+| C | 46 | 1 | 53 | 63 | 52 | 24 | 44 | 29 | 64 | 15 | 9 |
+| D | 16 | 28 | 0 | 75 | 39 | 60 | 16 | 81 | 32 | 91 | 71 |
+| E | 7 | 35 | 5 | 51 | 65 | 22 | 44 | 54 | 5 | 0 | 17 |
+| F | 12 | 45 | 34 | 45 | 9 | 98 | 29 | 18 | 67 | 96 | 21 |
+| G | 53 | 47 | 85 | 57 | 56 | 26 | 93 | 92 | 21 | 71 | 75 |
+| H | 10 | 4 | 51 | 37 | 3 | 42 | 42 | 3 | 88 | 56 | 30 |
+| I | 23 | 81 | 30 | 72 | 93 | 77 | 55 | 31 | 85 | 11 | 1 |
+| J | 32 | 81 | 48 | 85 | 52 | 27 | 39 | 35 | 20 | 34 | 56 |
+| K | 95 | 81 | 88 | 11 | 57 | 99 | 57 | 47 | 7 | 28 | 0 |
+
+## table_id=H
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 53 | 98 | 73 | 99 | 12 | 76 | 20 | 13 | 19 | 92 | 36 |
+| B | 10 | 58 | 24 | 9 | 71 | 38 | 76 | 64 | 50 | 55 | 37 |
+| C | 76 | 15 | 47 | 9 | 13 | 25 | 52 | 40 | 82 | 40 | 37 |
+| D | 52 | 13 | 75 | 35 | 21 | 50 | 24 | 33 | 63 | 16 | 12 |
+| E | 0 | 43 | 58 | 55 | 42 | 64 | 21 | 45 | 55 | 45 | 61 |
+| F | 49 | 72 | 78 | 75 | 23 | 65 | 51 | 21 | 55 | 94 | 21 |
+| G | 49 | 24 | 75 | 3 | 77 | 58 | 62 | 12 | 9 | 40 | 29 |
+| H | 76 | 92 | 50 | 80 | 41 | 61 | 81 | 97 | 72 | 4 | 45 |
+| I | 45 | 31 | 80 | 98 | 54 | 13 | 83 | 95 | 50 | 12 | 41 |
+| J | 59 | 68 | 42 | 24 | 79 | 82 | 54 | 16 | 72 | 5 | 17 |
+| K | 4 | 82 | 1 | 66 | 96 | 78 | 56 | 14 | 7 | 28 | 17 |
+
+## table_id=I
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 94 | 48 | 95 | 10 | 97 | 46 | 3 | 94 | 44 | 22 | 84 |
+| B | 7 | 62 | 2 | 27 | 80 | 66 | 58 | 63 | 76 | 99 | 96 |
+| C | 49 | 65 | 85 | 33 | 34 | 32 | 82 | 78 | 16 | 12 | 47 |
+| D | 43 | 54 | 28 | 70 | 17 | 41 | 30 | 53 | 26 | 12 | 73 |
+| E | 34 | 99 | 79 | 6 | 74 | 4 | 21 | 16 | 55 | 52 | 63 |
+| F | 64 | 64 | 68 | 73 | 75 | 87 | 35 | 64 | 31 | 9 | 95 |
+| G | 40 | 63 | 10 | 14 | 51 | 35 | 8 | 98 | 11 | 16 | 99 |
+| H | 12 | 24 | 20 | 22 | 40 | 51 | 86 | 28 | 47 | 87 | 94 |
+| I | 58 | 21 | 94 | 25 | 61 | 15 | 20 | 34 | 51 | 45 | 46 |
+| J | 48 | 17 | 60 | 25 | 60 | 88 | 46 | 84 | 66 | 6 | 57 |
+| K | 51 | 52 | 84 | 93 | 6 | 9 | 63 | 92 | 24 | 9 | 18 |
+
+## table_id=J
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 14 | 0 | 42 | 78 | 34 | 49 | 41 | 36 | 75 | 34 | 3 |
+| B | 81 | 47 | 49 | 36 | 68 | 76 | 33 | 37 | 51 | 23 | 17 |
+| C | 58 | 70 | 96 | 72 | 44 | 68 | 91 | 58 | 1 | 16 | 13 |
+| D | 84 | 20 | 66 | 64 | 96 | 81 | 5 | 21 | 48 | 46 | 55 |
+| E | 48 | 42 | 68 | 49 | 76 | 94 | 73 | 34 | 56 | 53 | 5 |
+| F | 14 | 71 | 4 | 42 | 25 | 61 | 12 | 29 | 71 | 98 | 56 |
+| G | 94 | 22 | 4 | 87 | 24 | 12 | 30 | 66 | 33 | 23 | 77 |
+| H | 42 | 29 | 88 | 20 | 94 | 28 | 70 | 40 | 40 | 66 | 74 |
+| I | 64 | 84 | 33 | 45 | 48 | 17 | 15 | 26 | 80 | 63 | 57 |
+| J | 27 | 51 | 35 | 84 | 78 | 84 | 58 | 8 | 48 | 68 | 47 |
+| K | 17 | 2 | 88 | 74 | 21 | 94 | 4 | 86 | 47 | 66 | 79 |
+
+## table_id=K
+| caterer_id\dessert_id | A | B | C | D | E | F | G | H | I | J | K |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 9 | 52 | 18 | 57 | 99 | 70 | 70 | 28 | 42 | 84 | 3 |
+| B | 71 | 90 | 13 | 96 | 62 | 71 | 17 | 45 | 81 | 38 | 13 |
+| C | 50 | 80 | 94 | 29 | 14 | 63 | 64 | 54 | 69 | 15 | 61 |
+| D | 3 | 20 | 90 | 8 | 0 | 94 | 8 | 86 | 19 | 72 | 83 |
+| E | 53 | 49 | 1 | 45 | 85 | 73 | 83 | 34 | 81 | 6 | 97 |
+| F | 12 | 4 | 3 | 10 | 25 | 79 | 95 | 14 | 49 | 34 | 26 |
+| G | 97 | 72 | 45 | 84 | 9 | 46 | 64 | 24 | 37 | 69 | 25 |
+| H | 84 | 76 | 15 | 73 | 16 | 55 | 81 | 7 | 62 | 58 | 55 |
+| I | 24 | 3 | 42 | 57 | 98 | 81 | 86 | 44 | 41 | 98 | 40 |
+| J | 0 | 51 | 31 | 56 | 89 | 64 | 8 | 97 | 76 | 91 | 42 |
+| K | 67 | 98 | 10 | 20 | 13 | 32 | 72 | 33 | 6 | 61 | 5 |
+
+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': [[[76, 66, 99, 40, 47, 6, 96, 42, 54, 78, 18], [10, 21, 14, 43, 33, 63, 74, 33, 71, 7, 54], [73, 31, 49, 65, 25, 86, 90, 96, 30, 13, 40], [50, 17, 32, 16, 11, 91, 87, 98, 24, 89, 90], [94, 90, 76, 32, 22, 42, 18, 76, 10, 70, 40], [8, 49, 47, 56, 40, 6, 95, 70, 85, 85, 2], [1, 68, 25, 43, 88, 76, 25, 24, 56, 83, 32], [91, 99, 54, 74, 77, 18, 84, 86, 94, 31, 22], [28, 84, 28, 91, 71, 38, 62, 68, 29, 51, 56], [80, 18, 32, 27, 63, 66, 11, 36, 48, 44, 51], [83, 91, 83, 44, 77, 11, 82, 69, 46, 25, 53]], [[88, 52, 88, 67, 85, 92, 94, 51, 1, 50, 40], [16, 93, 45, 34, 37, 76, 25, 29, 99, 32, 47], [24, 16, 37, 77, 15, 36, 87, 53, 23, 35, 99], [11, 13, 75, 89, 82, 17, 47, 50, 62, 26, 0], [97, 50, 20, 11, 95, 1, 54, 91, 91, 45, 67], [35, 67, 69, 60, 24, 46, 10, 93, 51, 62, 20], [38, 79, 47, 73, 76, 49, 34, 61, 30, 45, 73], [33, 61, 28, 21, 31, 96, 67, 41, 48, 64, 54], [95, 93, 33, 0, 11, 3, 43, 38, 25, 14, 89], [19, 25, 25, 4, 15, 78, 33, 76, 44, 76, 29], [63, 67, 70, 17, 12, 12, 34, 41, 20, 82, 16]], [[35, 39, 48, 64, 63, 62, 9, 4, 64, 40, 66], [79, 99, 31, 54, 63, 79, 64, 19, 24, 43, 80], [95, 41, 80, 22, 52, 86, 63, 6, 78, 92, 69], [84, 5, 77, 7, 0, 36, 70, 46, 39, 35, 53], [9, 56, 47, 41, 86, 87, 23, 70, 69, 25, 18], [78, 34, 34, 67, 55, 64, 18, 62, 64, 96, 31], [73, 54, 21, 72, 23, 86, 35, 54, 57, 54, 25], [98, 58, 56, 72, 27, 49, 91, 68, 24, 38, 60], [62, 18, 44, 98, 31, 68, 13, 63, 38, 49, 76], [62, 87, 10, 31, 67, 33, 48, 19, 33, 13, 67], [72, 0, 89, 35, 98, 76, 69, 87, 72, 90, 49]], [[78, 84, 24, 42, 14, 46, 85, 26, 62, 86, 6], [98, 19, 79, 18, 11, 50, 98, 83, 38, 45, 81], [11, 52, 36, 66, 6, 16, 55, 13, 76, 80, 54], [92, 59, 17, 8, 66, 90, 34, 14, 89, 98, 35], [74, 77, 83, 22, 30, 8, 50, 31, 82, 21, 41], [46, 76, 2, 75, 35, 81, 77, 76, 37, 31, 78], [60, 25, 22, 6, 25, 80, 89, 67, 2, 94, 50], [20, 32, 19, 64, 66, 25, 5, 33, 7, 35, 40], [20, 97, 89, 32, 32, 31, 80, 53, 41, 47, 80], [8, 21, 24, 58, 51, 90, 70, 91, 6, 74, 9], [72, 80, 54, 43, 47, 29, 21, 81, 96, 22, 81]], [[84, 29, 55, 87, 76, 52, 41, 68, 38, 84, 65], [76, 54, 66, 72, 62, 99, 97, 92, 20, 28, 50], [64, 2, 56, 75, 83, 23, 66, 72, 81, 59, 69], [70, 7, 94, 16, 83, 77, 84, 40, 94, 19, 17], [62, 30, 36, 7, 93, 92, 55, 73, 47, 4, 8], [65, 58, 62, 67, 74, 72, 5, 79, 87, 40, 34], [10, 28, 91, 72, 76, 2, 51, 41, 12, 24, 90], [8, 79, 39, 98, 16, 61, 38, 52, 11, 38, 86], [84, 30, 14, 99, 38, 79, 91, 72, 72, 46, 41], [70, 42, 2, 84, 97, 73, 55, 3, 77, 87, 40], [3, 97, 98, 36, 95, 24, 78, 55, 29, 5, 36]], [[72, 44, 58, 45, 59, 35, 73, 17, 80, 24, 41], [73, 53, 23, 54, 7, 78, 22, 49, 54, 40, 55], [89, 89, 89, 83, 14, 20, 87, 41, 40, 67, 30], [48, 66, 51, 58, 56, 92, 37, 37, 49, 83, 66], [37, 47, 83, 36, 53, 79, 83, 16, 22, 84, 69], [14, 12, 70, 46, 49, 64, 99, 76, 1, 27, 75], [22, 35, 99, 96, 50, 17, 97, 68, 67, 14, 80], [21, 34, 22, 52, 72, 48, 63, 53, 63, 15, 11], [3, 16, 87, 23, 35, 0, 30, 53, 37, 43, 90], [87, 66, 93, 88, 86, 75, 33, 40, 99, 69, 66], [42, 48, 38, 26, 80, 94, 19, 95, 26, 99, 65]], [[1, 84, 7, 59, 34, 68, 50, 31, 62, 27, 50], [70, 37, 45, 11, 68, 17, 71, 73, 99, 69, 0], [46, 1, 53, 63, 52, 24, 44, 29, 64, 15, 9], [16, 28, 0, 75, 39, 60, 16, 81, 32, 91, 71], [7, 35, 5, 51, 65, 22, 44, 54, 5, 0, 17], [12, 45, 34, 45, 9, 98, 29, 18, 67, 96, 21], [53, 47, 85, 57, 56, 26, 93, 92, 21, 71, 75], [10, 4, 51, 37, 3, 42, 42, 3, 88, 56, 30], [23, 81, 30, 72, 93, 77, 55, 31, 85, 11, 1], [32, 81, 48, 85, 52, 27, 39, 35, 20, 34, 56], [95, 81, 88, 11, 57, 99, 57, 47, 7, 28, 0]], [[53, 98, 73, 99, 12, 76, 20, 13, 19, 92, 36], [10, 58, 24, 9, 71, 38, 76, 64, 50, 55, 37], [76, 15, 47, 9, 13, 25, 52, 40, 82, 40, 37], [52, 13, 75, 35, 21, 50, 24, 33, 63, 16, 12], [0, 43, 58, 55, 42, 64, 21, 45, 55, 45, 61], [49, 72, 78, 75, 23, 65, 51, 21, 55, 94, 21], [49, 24, 75, 3, 77, 58, 62, 12, 9, 40, 29], [76, 92, 50, 80, 41, 61, 81, 97, 72, 4, 45], [45, 31, 80, 98, 54, 13, 83, 95, 50, 12, 41], [59, 68, 42, 24, 79, 82, 54, 16, 72, 5, 17], [4, 82, 1, 66, 96, 78, 56, 14, 7, 28, 17]], [[94, 48, 95, 10, 97, 46, 3, 94, 44, 22, 84], [7, 62, 2, 27, 80, 66, 58, 63, 76, 99, 96], [49, 65, 85, 33, 34, 32, 82, 78, 16, 12, 47], [43, 54, 28, 70, 17, 41, 30, 53, 26, 12, 73], [34, 99, 79, 6, 74, 4, 21, 16, 55, 52, 63], [64, 64, 68, 73, 75, 87, 35, 64, 31, 9, 95], [40, 63, 10, 14, 51, 35, 8, 98, 11, 16, 99], [12, 24, 20, 22, 40, 51, 86, 28, 47, 87, 94], [58, 21, 94, 25, 61, 15, 20, 34, 51, 45, 46], [48, 17, 60, 25, 60, 88, 46, 84, 66, 6, 57], [51, 52, 84, 93, 6, 9, 63, 92, 24, 9, 18]], [[14, 0, 42, 78, 34, 49, 41, 36, 75, 34, 3], [81, 47, 49, 36, 68, 76, 33, 37, 51, 23, 17], [58, 70, 96, 72, 44, 68, 91, 58, 1, 16, 13], [84, 20, 66, 64, 96, 81, 5, 21, 48, 46, 55], [48, 42, 68, 49, 76, 94, 73, 34, 56, 53, 5], [14, 71, 4, 42, 25, 61, 12, 29, 71, 98, 56], [94, 22, 4, 87, 24, 12, 30, 66, 33, 23, 77], [42, 29, 88, 20, 94, 28, 70, 40, 40, 66, 74], [64, 84, 33, 45, 48, 17, 15, 26, 80, 63, 57], [27, 51, 35, 84, 78, 84, 58, 8, 48, 68, 47], [17, 2, 88, 74, 21, 94, 4, 86, 47, 66, 79]], [[9, 52, 18, 57, 99, 70, 70, 28, 42, 84, 3], [71, 90, 13, 96, 62, 71, 17, 45, 81, 38, 13], [50, 80, 94, 29, 14, 63, 64, 54, 69, 15, 61], [3, 20, 90, 8, 0, 94, 8, 86, 19, 72, 83], [53, 49, 1, 45, 85, 73, 83, 34, 81, 6, 97], [12, 4, 3, 10, 25, 79, 95, 14, 49, 34, 26], [97, 72, 45, 84, 9, 46, 64, 24, 37, 69, 25], [84, 76, 15, 73, 16, 55, 81, 7, 62, 58, 55], [24, 3, 42, 57, 98, 81, 86, 44, 41, 98, 40], [0, 51, 31, 56, 89, 64, 8, 97, 76, 91, 42], [67, 98, 10, 20, 13, 32, 72, 33, 6, 61, 5]]], 'objective': 25.0}","[[0, 6, 0], [1, 4, 3], [2, 10, 1], [3, 5, 2], [4, 9, 7], [5, 8, 5], [6, 1, 10], [7, 7, 9], [8, 0, 6], [9, 2, 8], [10, 3, 4]]",25.0,"{'problem_type': 'AP3', 'n': 11, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 76}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 66}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 99}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 40}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 47}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 6}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 96}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 42}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 54}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 78}, {'i': 'A', 'j': 'A', 'k': 'K', 'cost': 18}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 10}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 21}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 14}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 43}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 33}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 63}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 74}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 33}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 71}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 7}, {'i': 'A', 'j': 'B', 'k': 'K', 'cost': 54}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 73}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 31}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 49}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 65}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 25}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 86}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 90}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 96}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 30}, {'i': 'A', 'j': 'C', 'k': 'J', 'cost': 13}, {'i': 'A', 'j': 'C', 'k': 'K', 'cost': 40}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 50}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 17}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 32}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 16}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 11}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 91}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 87}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 98}, {'i': 'A', 'j': 'D', 'k': 'I', 'cost': 24}, {'i': 'A', 'j': 'D', 'k': 'J', 'cost': 89}, {'i': 'A', 'j': 'D', 'k': 'K', 'cost': 90}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 94}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 90}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 76}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 32}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 22}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 42}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 76}, {'i': 'A', 'j': 'E', 'k': 'I', 'cost': 10}, {'i': 'A', 'j': 'E', 'k': 'J', 'cost': 70}, {'i': 'A', 'j': 'E', 'k': 'K', 'cost': 40}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 8}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 49}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 47}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 56}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 40}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 6}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 95}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 70}, {'i': 'A', 'j': 'F', 'k': 'I', 'cost': 85}, {'i': 'A', 'j': 'F', 'k': 'J', 'cost': 85}, {'i': 'A', 'j': 'F', 'k': 'K', 'cost': 2}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 1}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 68}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 25}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 43}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 88}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 76}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 25}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 24}, {'i': 'A', 'j': 'G', 'k': 'I', 'cost': 56}, {'i': 'A', 'j': 'G', 'k': 'J', 'cost': 83}, {'i': 'A', 'j': 'G', 'k': 'K', 'cost': 32}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 91}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 99}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 54}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 74}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 77}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 18}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 84}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 86}, {'i': 'A', 'j': 'H', 'k': 'I', 'cost': 94}, {'i': 'A', 'j': 'H', 'k': 'J', 'cost': 31}, {'i': 'A', 'j': 'H', 'k': 'K', 'cost': 22}, {'i': 'A', 'j': 'I', 'k': 'A', 'cost': 28}, {'i': 'A', 'j': 'I', 'k': 'B', 'cost': 84}, {'i': 'A', 'j': 'I', 'k': 'C', 'cost': 28}, {'i': 'A', 'j': 'I', 'k': 'D', 'cost': 91}, {'i': 'A', 'j': 'I', 'k': 'E', 'cost': 71}, {'i': 'A', 'j': 'I', 'k': 'F', 'cost': 38}, {'i': 'A', 'j': 'I', 'k': 'G', 'cost': 62}, {'i': 'A', 'j': 'I', 'k': 'H', 'cost': 68}, {'i': 'A', 'j': 'I', 'k': 'I', 'cost': 29}, {'i': 'A', 'j': 'I', 'k': 'J', 'cost': 51}, {'i': 'A', 'j': 'I', 'k': 'K', 'cost': 56}, {'i': 'A', 'j': 'J', 'k': 'A', 'cost': 80}, {'i': 'A', 'j': 'J', 'k': 'B', 'cost': 18}, {'i': 'A', 'j': 'J', 'k': 'C', 'cost': 32}, {'i': 'A', 'j': 'J', 'k': 'D', 'cost': 27}, {'i': 'A', 'j': 'J', 'k': 'E', 'cost': 63}, {'i': 'A', 'j': 'J', 'k': 'F', 'cost': 66}, {'i': 'A', 'j': 'J', 'k': 'G', 'cost': 11}, {'i': 'A', 'j': 'J', 'k': 'H', 'cost': 36}, {'i': 'A', 'j': 'J', 'k': 'I', 'cost': 48}, {'i': 'A', 'j': 'J', 'k': 'J', 'cost': 44}, {'i': 'A', 'j': 'J', 'k': 'K', 'cost': 51}, {'i': 'A', 'j': 'K', 'k': 'A', 'cost': 83}, {'i': 'A', 'j': 'K', 'k': 'B', 'cost': 91}, {'i': 'A', 'j': 'K', 'k': 'C', 'cost': 83}, {'i': 'A', 'j': 'K', 'k': 'D', 'cost': 44}, {'i': 'A', 'j': 'K', 'k': 'E', 'cost': 77}, {'i': 'A', 'j': 'K', 'k': 'F', 'cost': 11}, {'i': 'A', 'j': 'K', 'k': 'G', 'cost': 82}, {'i': 'A', 'j': 'K', 'k': 'H', 'cost': 69}, {'i': 'A', 'j': 'K', 'k': 'I', 'cost': 46}, {'i': 'A', 'j': 'K', 'k': 'J', 'cost': 25}, {'i': 'A', 'j': 'K', 'k': 'K', 'cost': 53}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 88}, {'i': 'B', 'j': 'A', 'k': 'B', 'cost': 52}, {'i': 'B', 'j': 'A', 'k': 'C', 'cost': 88}, {'i': 'B', 'j': 'A', 'k': 'D', 'cost': 67}, {'i': 'B', 'j': 'A', 'k': 'E', 'cost': 85}, {'i': 'B', 'j': 'A', 'k': 'F', 'cost': 92}, {'i': 'B', 'j': 'A', 'k': 'G', 'cost': 94}, {'i': 'B', 'j': 'A', 'k': 'H', 'cost': 51}, {'i': 'B', 'j': 'A', 'k': 'I', 'cost': 1}, {'i': 'B', 'j': 'A', 'k': 'J', 'cost': 50}, {'i': 'B', 'j': 'A', 'k': 'K', 'cost': 40}, {'i': 'B', 'j': 'B', 'k': 'A', 'cost': 16}, {'i': 'B', 'j': 'B', 'k': 'B', 'cost': 93}, {'i': 'B', 'j': 'B', 'k': 'C', 'cost': 45}, {'i': 'B', 'j': 'B', 'k': 'D', 'cost': 34}, {'i': 'B', 'j': 'B', 'k': 'E', 'cost': 37}, {'i': 'B', 'j': 'B', 'k': 'F', 'cost': 76}, {'i': 'B', 'j': 'B', 'k': 'G', 'cost': 25}, {'i': 'B', 'j': 'B', 'k': 'H', 'cost': 29}, {'i': 'B', 'j': 'B', 'k': 'I', 'cost': 99}, {'i': 'B', 'j': 'B', 'k': 'J', 'cost': 32}, {'i': 'B', 'j': 'B', 'k': 'K', 'cost': 47}, {'i': 'B', 'j': 'C', 'k': 'A', 'cost': 24}, {'i': 'B', 'j': 'C', 'k': 'B', 'cost': 16}, {'i': 'B', 'j': 'C', 'k': 'C', 'cost': 37}, {'i': 'B', 'j': 'C', 'k': 'D', 'cost': 77}, {'i': 'B', 'j': 'C', 'k': 'E', 'cost': 15}, {'i': 'B', 'j': 'C', 'k': 'F', 'cost': 36}, {'i': 'B', 'j': 'C', 'k': 'G', 'cost': 87}, {'i': 'B', 'j': 'C', 'k': 'H', 'cost': 53}, {'i': 'B', 'j': 'C', 'k': 'I', 'cost': 23}, {'i': 'B', 'j': 'C', 'k': 'J', 'cost': 35}, {'i': 'B', 'j': 'C', 'k': 'K', 'cost': 99}, {'i': 'B', 'j': 'D', 'k': 'A', 'cost': 11}, {'i': 'B', 'j': 'D', 'k': 'B', 'cost': 13}, {'i': 'B', 'j': 'D', 'k': 'C', 'cost': 75}, {'i': 'B', 'j': 'D', 'k': 'D', 'cost': 89}, {'i': 'B', 'j': 'D', 'k': 'E', 'cost': 82}, {'i': 'B', 'j': 'D', 'k': 'F', 'cost': 17}, {'i': 'B', 'j': 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'J', 'j': 'A', 'k': 'E', 'cost': 34}, {'i': 'J', 'j': 'A', 'k': 'F', 'cost': 49}, {'i': 'J', 'j': 'A', 'k': 'G', 'cost': 41}, {'i': 'J', 'j': 'A', 'k': 'H', 'cost': 36}, {'i': 'J', 'j': 'A', 'k': 'I', 'cost': 75}, {'i': 'J', 'j': 'A', 'k': 'J', 'cost': 34}, {'i': 'J', 'j': 'A', 'k': 'K', 'cost': 3}, {'i': 'J', 'j': 'B', 'k': 'A', 'cost': 81}, {'i': 'J', 'j': 'B', 'k': 'B', 'cost': 47}, {'i': 'J', 'j': 'B', 'k': 'C', 'cost': 49}, {'i': 'J', 'j': 'B', 'k': 'D', 'cost': 36}, {'i': 'J', 'j': 'B', 'k': 'E', 'cost': 68}, {'i': 'J', 'j': 'B', 'k': 'F', 'cost': 76}, {'i': 'J', 'j': 'B', 'k': 'G', 'cost': 33}, {'i': 'J', 'j': 'B', 'k': 'H', 'cost': 37}, {'i': 'J', 'j': 'B', 'k': 'I', 'cost': 51}, {'i': 'J', 'j': 'B', 'k': 'J', 'cost': 23}, {'i': 'J', 'j': 'B', 'k': 'K', 'cost': 17}, {'i': 'J', 'j': 'C', 'k': 'A', 'cost': 58}, {'i': 'J', 'j': 'C', 'k': 'B', 'cost': 70}, {'i': 'J', 'j': 'C', 'k': 'C', 'cost': 96}, {'i': 'J', 'j': 'C', 'k': 'D', 'cost': 72}, {'i': 'J', 'j': 'C', 'k': 'E', 'cost': 44}, {'i': 'J', 'j': 'C', 'k': 'F', 'cost': 68}, {'i': 'J', 'j': 'C', 'k': 'G', 'cost': 91}, {'i': 'J', 'j': 'C', 'k': 'H', 'cost': 58}, {'i': 'J', 'j': 'C', 'k': 'I', 'cost': 1}, {'i': 'J', 'j': 'C', 'k': 'J', 'cost': 16}, {'i': 'J', 'j': 'C', 'k': 'K', 'cost': 13}, {'i': 'J', 'j': 'D', 'k': 'A', 'cost': 84}, {'i': 'J', 'j': 'D', 'k': 'B', 'cost': 20}, {'i': 'J', 'j': 'D', 'k': 'C', 'cost': 66}, {'i': 'J', 'j': 'D', 'k': 'D', 'cost': 64}, {'i': 'J', 'j': 'D', 'k': 'E', 'cost': 96}, {'i': 'J', 'j': 'D', 'k': 'F', 'cost': 81}, {'i': 'J', 'j': 'D', 'k': 'G', 'cost': 5}, {'i': 'J', 'j': 'D', 'k': 'H', 'cost': 21}, {'i': 'J', 'j': 'D', 'k': 'I', 'cost': 48}, {'i': 'J', 'j': 'D', 'k': 'J', 'cost': 46}, {'i': 'J', 'j': 'D', 'k': 'K', 'cost': 55}, {'i': 'J', 'j': 'E', 'k': 'A', 'cost': 48}, {'i': 'J', 'j': 'E', 'k': 'B', 'cost': 42}, {'i': 'J', 'j': 'E', 'k': 'C', 'cost': 68}, {'i': 'J', 'j': 'E', 'k': 'D', 'cost': 49}, {'i': 'J', 'j': 'E', 'k': 'E', 'cost': 76}, {'i': 'J', 'j': 'E', 'k': 'F', 'cost': 94}, {'i': 'J', 'j': 'E', 'k': 'G', 'cost': 73}, {'i': 'J', 'j': 'E', 'k': 'H', 'cost': 34}, {'i': 'J', 'j': 'E', 'k': 'I', 'cost': 56}, {'i': 'J', 'j': 'E', 'k': 'J', 'cost': 53}, {'i': 'J', 'j': 'E', 'k': 'K', 'cost': 5}, {'i': 'J', 'j': 'F', 'k': 'A', 'cost': 14}, {'i': 'J', 'j': 'F', 'k': 'B', 'cost': 71}, {'i': 'J', 'j': 'F', 'k': 'C', 'cost': 4}, {'i': 'J', 'j': 'F', 'k': 'D', 'cost': 42}, {'i': 'J', 'j': 'F', 'k': 'E', 'cost': 25}, {'i': 'J', 'j': 'F', 'k': 'F', 'cost': 61}, {'i': 'J', 'j': 'F', 'k': 'G', 'cost': 12}, {'i': 'J', 'j': 'F', 'k': 'H', 'cost': 29}, {'i': 'J', 'j': 'F', 'k': 'I', 'cost': 71}, {'i': 'J', 'j': 'F', 'k': 'J', 'cost': 98}, {'i': 'J', 'j': 'F', 'k': 'K', 'cost': 56}, {'i': 'J', 'j': 'G', 'k': 'A', 'cost': 94}, {'i': 'J', 'j': 'G', 'k': 'B', 'cost': 22}, {'i': 'J', 'j': 'G', 'k': 'C', 'cost': 4}, {'i': 'J', 'j': 'G', 'k': 'D', 'cost': 87}, {'i': 'J', 'j': 'G', 'k': 'E', 'cost': 24}, {'i': 'J', 'j': 'G', 'k': 'F', 'cost': 12}, {'i': 'J', 'j': 'G', 'k': 'G', 'cost': 30}, {'i': 'J', 'j': 'G', 'k': 'H', 'cost': 66}, {'i': 'J', 'j': 'G', 'k': 'I', 'cost': 33}, {'i': 'J', 'j': 'G', 'k': 'J', 'cost': 23}, {'i': 'J', 'j': 'G', 'k': 'K', 'cost': 77}, {'i': 'J', 'j': 'H', 'k': 'A', 'cost': 42}, {'i': 'J', 'j': 'H', 'k': 'B', 'cost': 29}, {'i': 'J', 'j': 'H', 'k': 'C', 'cost': 88}, {'i': 'J', 'j': 'H', 'k': 'D', 'cost': 20}, {'i': 'J', 'j': 'H', 'k': 'E', 'cost': 94}, {'i': 'J', 'j': 'H', 'k': 'F', 'cost': 28}, {'i': 'J', 'j': 'H', 'k': 'G', 'cost': 70}, {'i': 'J', 'j': 'H', 'k': 'H', 'cost': 40}, {'i': 'J', 'j': 'H', 'k': 'I', 'cost': 40}, {'i': 'J', 'j': 'H', 'k': 'J', 'cost': 66}, {'i': 'J', 'j': 'H', 'k': 'K', 'cost': 74}, {'i': 'J', 'j': 'I', 'k': 'A', 'cost': 64}, {'i': 'J', 'j': 'I', 'k': 'B', 'cost': 84}, {'i': 'J', 'j': 'I', 'k': 'C', 'cost': 33}, {'i': 'J', 'j': 'I', 'k': 'D', 'cost': 45}, {'i': 'J', 'j': 'I', 'k': 'E', 'cost': 48}, {'i': 'J', 'j': 'I', 'k': 'F', 'cost': 17}, {'i': 'J', 'j': 'I', 'k': 'G', 'cost': 15}, {'i': 'J', 'j': 'I', 'k': 'H', 'cost': 26}, {'i': 'J', 'j': 'I', 'k': 'I', 'cost': 80}, {'i': 'J', 'j': 'I', 'k': 'J', 'cost': 63}, {'i': 'J', 'j': 'I', 'k': 'K', 'cost': 57}, {'i': 'J', 'j': 'J', 'k': 'A', 'cost': 27}, {'i': 'J', 'j': 'J', 'k': 'B', 'cost': 51}, {'i': 'J', 'j': 'J', 'k': 'C', 'cost': 35}, {'i': 'J', 'j': 'J', 'k': 'D', 'cost': 84}, {'i': 'J', 'j': 'J', 'k': 'E', 'cost': 78}, {'i': 'J', 'j': 'J', 'k': 'F', 'cost': 84}, {'i': 'J', 'j': 'J', 'k': 'G', 'cost': 58}, {'i': 'J', 'j': 'J', 'k': 'H', 'cost': 8}, {'i': 'J', 'j': 'J', 'k': 'I', 'cost': 48}, {'i': 'J', 'j': 'J', 'k': 'J', 'cost': 68}, {'i': 'J', 'j': 'J', 'k': 'K', 'cost': 47}, {'i': 'J', 'j': 'K', 'k': 'A', 'cost': 17}, {'i': 'J', 'j': 'K', 'k': 'B', 'cost': 2}, {'i': 'J', 'j': 'K', 'k': 'C', 'cost': 88}, {'i': 'J', 'j': 'K', 'k': 'D', 'cost': 74}, {'i': 'J', 'j': 'K', 'k': 'E', 'cost': 21}, {'i': 'J', 'j': 'K', 'k': 'F', 'cost': 94}, {'i': 'J', 'j': 'K', 'k': 'G', 'cost': 4}, {'i': 'J', 'j': 'K', 'k': 'H', 'cost': 86}, {'i': 'J', 'j': 'K', 'k': 'I', 'cost': 47}, {'i': 'J', 'j': 'K', 'k': 'J', 'cost': 66}, {'i': 'J', 'j': 'K', 'k': 'K', 'cost': 79}, {'i': 'K', 'j': 'A', 'k': 'A', 'cost': 9}, {'i': 'K', 'j': 'A', 'k': 'B', 'cost': 52}, {'i': 'K', 'j': 'A', 'k': 'C', 'cost': 18}, {'i': 'K', 'j': 'A', 'k': 'D', 'cost': 57}, {'i': 'K', 'j': 'A', 'k': 'E', 'cost': 99}, {'i': 'K', 'j': 'A', 'k': 'F', 'cost': 70}, {'i': 'K', 'j': 'A', 'k': 'G', 'cost': 70}, {'i': 'K', 'j': 'A', 'k': 'H', 'cost': 28}, {'i': 'K', 'j': 'A', 'k': 'I', 'cost': 42}, {'i': 'K', 'j': 'A', 'k': 'J', 'cost': 84}, {'i': 'K', 'j': 'A', 'k': 'K', 'cost': 3}, {'i': 'K', 'j': 'B', 'k': 'A', 'cost': 71}, {'i': 'K', 'j': 'B', 'k': 'B', 'cost': 90}, {'i': 'K', 'j': 'B', 'k': 'C', 'cost': 13}, {'i': 'K', 'j': 'B', 'k': 'D', 'cost': 96}, {'i': 'K', 'j': 'B', 'k': 'E', 'cost': 62}, {'i': 'K', 'j': 'B', 'k': 'F', 'cost': 71}, {'i': 'K', 'j': 'B', 'k': 'G', 'cost': 17}, {'i': 'K', 'j': 'B', 'k': 'H', 'cost': 45}, {'i': 'K', 'j': 'B', 'k': 'I', 'cost': 81}, {'i': 'K', 'j': 'B', 'k': 'J', 'cost': 38}, {'i': 'K', 'j': 'B', 'k': 'K', 'cost': 13}, {'i': 'K', 'j': 'C', 'k': 'A', 'cost': 50}, {'i': 'K', 'j': 'C', 'k': 'B', 'cost': 80}, {'i': 'K', 'j': 'C', 'k': 'C', 'cost': 94}, {'i': 'K', 'j': 'C', 'k': 'D', 'cost': 29}, {'i': 'K', 'j': 'C', 'k': 'E', 'cost': 14}, {'i': 'K', 'j': 'C', 'k': 'F', 'cost': 63}, {'i': 'K', 'j': 'C', 'k': 'G', 'cost': 64}, {'i': 'K', 'j': 'C', 'k': 'H', 'cost': 54}, {'i': 'K', 'j': 'C', 'k': 'I', 'cost': 69}, {'i': 'K', 'j': 'C', 'k': 'J', 'cost': 15}, {'i': 'K', 'j': 'C', 'k': 'K', 'cost': 61}, {'i': 'K', 'j': 'D', 'k': 'A', 'cost': 3}, {'i': 'K', 'j': 'D', 'k': 'B', 'cost': 20}, {'i': 'K', 'j': 'D', 'k': 'C', 'cost': 90}, {'i': 'K', 'j': 'D', 'k': 'D', 'cost': 8}, {'i': 'K', 'j': 'D', 'k': 'E', 'cost': 0}, {'i': 'K', 'j': 'D', 'k': 'F', 'cost': 94}, {'i': 'K', 'j': 'D', 'k': 'G', 'cost': 8}, {'i': 'K', 'j': 'D', 'k': 'H', 'cost': 86}, {'i': 'K', 'j': 'D', 'k': 'I', 'cost': 19}, {'i': 'K', 'j': 'D', 'k': 'J', 'cost': 72}, {'i': 'K', 'j': 'D', 'k': 'K', 'cost': 83}, {'i': 'K', 'j': 'E', 'k': 'A', 'cost': 53}, {'i': 'K', 'j': 'E', 'k': 'B', 'cost': 49}, {'i': 'K', 'j': 'E', 'k': 'C', 'cost': 1}, {'i': 'K', 'j': 'E', 'k': 'D', 'cost': 45}, {'i': 'K', 'j': 'E', 'k': 'E', 'cost': 85}, {'i': 'K', 'j': 'E', 'k': 'F', 'cost': 73}, {'i': 'K', 'j': 'E', 'k': 'G', 'cost': 83}, {'i': 'K', 'j': 'E', 'k': 'H', 'cost': 34}, {'i': 'K', 'j': 'E', 'k': 'I', 'cost': 81}, {'i': 'K', 'j': 'E', 'k': 'J', 'cost': 6}, {'i': 'K', 'j': 'E', 'k': 'K', 'cost': 97}, {'i': 'K', 'j': 'F', 'k': 'A', 'cost': 12}, {'i': 'K', 'j': 'F', 'k': 'B', 'cost': 4}, {'i': 'K', 'j': 'F', 'k': 'C', 'cost': 3}, {'i': 'K', 'j': 'F', 'k': 'D', 'cost': 10}, {'i': 'K', 'j': 'F', 'k': 'E', 'cost': 25}, {'i': 'K', 'j': 'F', 'k': 'F', 'cost': 79}, {'i': 'K', 'j': 'F', 'k': 'G', 'cost': 95}, {'i': 'K', 'j': 'F', 'k': 'H', 'cost': 14}, {'i': 'K', 'j': 'F', 'k': 'I', 'cost': 49}, {'i': 'K', 'j': 'F', 'k': 'J', 'cost': 34}, {'i': 'K', 'j': 'F', 'k': 'K', 'cost': 26}, {'i': 'K', 'j': 'G', 'k': 'A', 'cost': 97}, {'i': 'K', 'j': 'G', 'k': 'B', 'cost': 72}, {'i': 'K', 'j': 'G', 'k': 'C', 'cost': 45}, {'i': 'K', 'j': 'G', 'k': 'D', 'cost': 84}, {'i': 'K', 'j': 'G', 'k': 'E', 'cost': 9}, {'i': 'K', 'j': 'G', 'k': 'F', 'cost': 46}, {'i': 'K', 'j': 'G', 'k': 'G', 'cost': 64}, {'i': 'K', 'j': 'G', 'k': 'H', 'cost': 24}, {'i': 'K', 'j': 'G', 'k': 'I', 'cost': 37}, {'i': 'K', 'j': 'G', 'k': 'J', 'cost': 69}, {'i': 'K', 'j': 'G', 'k': 'K', 'cost': 25}, {'i': 'K', 'j': 'H', 'k': 'A', 'cost': 84}, {'i': 'K', 'j': 'H', 'k': 'B', 'cost': 76}, {'i': 'K', 'j': 'H', 'k': 'C', 'cost': 15}, {'i': 'K', 'j': 'H', 'k': 'D', 'cost': 73}, {'i': 'K', 'j': 'H', 'k': 'E', 'cost': 16}, {'i': 'K', 'j': 'H', 'k': 'F', 'cost': 55}, {'i': 'K', 'j': 'H', 'k': 'G', 'cost': 81}, {'i': 'K', 'j': 'H', 'k': 'H', 'cost': 7}, {'i': 'K', 'j': 'H', 'k': 'I', 'cost': 62}, {'i': 'K', 'j': 'H', 'k': 'J', 'cost': 58}, {'i': 'K', 'j': 'H', 'k': 'K', 'cost': 55}, {'i': 'K', 'j': 'I', 'k': 'A', 'cost': 24}, {'i': 'K', 'j': 'I', 'k': 'B', 'cost': 3}, {'i': 'K', 'j': 'I', 'k': 'C', 'cost': 42}, {'i': 'K', 'j': 'I', 'k': 'D', 'cost': 57}, {'i': 'K', 'j': 'I', 'k': 'E', 'cost': 98}, {'i': 'K', 'j': 'I', 'k': 'F', 'cost': 81}, {'i': 'K', 'j': 'I', 'k': 'G', 'cost': 86}, {'i': 'K', 'j': 'I', 'k': 'H', 'cost': 44}, {'i': 'K', 'j': 'I', 'k': 'I', 'cost': 41}, {'i': 'K', 'j': 'I', 'k': 'J', 'cost': 98}, {'i': 'K', 'j': 'I', 'k': 'K', 'cost': 40}, {'i': 'K', 'j': 'J', 'k': 'A', 'cost': 0}, {'i': 'K', 'j': 'J', 'k': 'B', 'cost': 51}, {'i': 'K', 'j': 'J', 'k': 'C', 'cost': 31}, {'i': 'K', 'j': 'J', 'k': 'D', 'cost': 56}, {'i': 'K', 'j': 'J', 'k': 'E', 'cost': 89}, {'i': 'K', 'j': 'J', 'k': 'F', 'cost': 64}, {'i': 'K', 'j': 'J', 'k': 'G', 'cost': 8}, {'i': 'K', 'j': 'J', 'k': 'H', 'cost': 97}, {'i': 'K', 'j': 'J', 'k': 'I', 'cost': 76}, {'i': 'K', 'j': 'J', 'k': 'J', 'cost': 91}, {'i': 'K', 'j': 'J', 'k': 'K', 'cost': 42}, {'i': 'K', 'j': 'K', 'k': 'A', 'cost': 67}, {'i': 'K', 'j': 'K', 'k': 'B', 'cost': 98}, {'i': 'K', 'j': 'K', 'k': 'C', 'cost': 10}, {'i': 'K', 'j': 'K', 'k': 'D', 'cost': 20}, {'i': 'K', 'j': 'K', 'k': 'E', 'cost': 13}, {'i': 'K', 'j': 'K', 'k': 'F', 'cost': 32}, {'i': 'K', 'j': 'K', 'k': 'G', 'cost': 72}, {'i': 'K', 'j': 'K', 'k': 'H', 'cost': 33}, {'i': 'K', 'j': 'K', 'k': 'I', 'cost': 6}, {'i': 'K', 'j': 'K', 'k': 'J', 'cost': 61}, {'i': 'K', 'j': 'K', 'k': 'K', 'cost': 5}]}","[['A', 'G', 'A'], ['B', 'E', 'D'], ['C', 'K', 'B'], ['D', 'F', 'C'], ['E', 'J', 'H'], ['F', 'I', 'F'], ['G', 'B', 'K'], ['H', 'H', 'J'], ['I', 'A', 'G'], ['J', 'C', 'I'], ['K', 'D', 'E']]",38,csv,names
+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.
+
+{
+  ""num_classes"": 10,
+  ""class_room_ta_ids"": [
+    ""A"",
+    ""B"",
+    ""C"",
+    ""D"",
+    ""E"",
+    ""F"",
+    ""G"",
+    ""H"",
+    ""I"",
+    ""J""
+  ]
+}
+
+# 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=A
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 40 | 74 | 3 | 42 | 30 | 69 | 68 | 12 | 2 | 66 |
+| B | 71 | 59 | 99 | 3 | 31 | 7 | 88 | 25 | 62 | 48 |
+| C | 0 | 42 | 23 | 49 | 63 | 66 | 90 | 59 | 26 | 17 |
+| D | 13 | 96 | 37 | 43 | 81 | 77 | 29 | 91 | 51 | 75 |
+| E | 72 | 68 | 99 | 33 | 6 | 55 | 51 | 67 | 5 | 61 |
+| F | 3 | 78 | 26 | 16 | 88 | 97 | 88 | 55 | 88 | 30 |
+| G | 67 | 89 | 34 | 87 | 14 | 71 | 13 | 75 | 87 | 11 |
+| H | 0 | 39 | 25 | 17 | 95 | 35 | 72 | 86 | 87 | 83 |
+| I | 19 | 82 | 88 | 30 | 38 | 31 | 95 | 45 | 97 | 70 |
+| J | 88 | 78 | 40 | 94 | 66 | 31 | 6 | 6 | 53 | 69 |
+
+## class_id=B
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 92 | 93 | 83 | 68 | 97 | 42 | 8 | 96 | 40 | 38 |
+| B | 0 | 54 | 55 | 5 | 32 | 71 | 59 | 89 | 82 | 93 |
+| C | 33 | 65 | 66 | 40 | 45 | 95 | 83 | 67 | 36 | 28 |
+| D | 85 | 97 | 28 | 52 | 48 | 98 | 25 | 63 | 66 | 93 |
+| E | 37 | 35 | 84 | 65 | 29 | 39 | 33 | 61 | 36 | 94 |
+| F | 27 | 72 | 89 | 35 | 41 | 96 | 51 | 12 | 6 | 56 |
+| G | 25 | 57 | 21 | 63 | 37 | 40 | 90 | 14 | 71 | 75 |
+| H | 75 | 91 | 27 | 10 | 60 | 95 | 64 | 71 | 63 | 84 |
+| I | 10 | 52 | 65 | 23 | 53 | 75 | 10 | 59 | 2 | 82 |
+| J | 18 | 49 | 89 | 36 | 73 | 16 | 88 | 47 | 51 | 17 |
+
+## class_id=C
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 0 | 24 | 67 | 19 | 18 | 49 | 17 | 45 | 27 | 63 |
+| B | 4 | 32 | 36 | 57 | 78 | 51 | 18 | 20 | 0 | 67 |
+| C | 93 | 8 | 28 | 11 | 25 | 53 | 44 | 82 | 52 | 65 |
+| D | 36 | 96 | 98 | 95 | 51 | 30 | 74 | 28 | 86 | 6 |
+| E | 96 | 67 | 37 | 52 | 21 | 45 | 27 | 91 | 2 | 63 |
+| F | 13 | 73 | 13 | 55 | 13 | 96 | 28 | 68 | 67 | 15 |
+| G | 2 | 85 | 34 | 57 | 3 | 51 | 13 | 11 | 17 | 10 |
+| H | 39 | 70 | 48 | 7 | 79 | 80 | 53 | 51 | 37 | 3 |
+| I | 8 | 32 | 21 | 36 | 26 | 90 | 44 | 17 | 60 | 40 |
+| J | 84 | 40 | 12 | 42 | 67 | 29 | 9 | 36 | 1 | 38 |
+
+## class_id=D
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 38 | 80 | 35 | 10 | 59 | 89 | 53 | 81 | 62 | 48 |
+| B | 86 | 79 | 65 | 5 | 3 | 29 | 32 | 2 | 43 | 43 |
+| C | 1 | 17 | 97 | 67 | 13 | 45 | 19 | 66 | 97 | 13 |
+| D | 30 | 48 | 95 | 76 | 57 | 88 | 23 | 58 | 84 | 36 |
+| E | 63 | 79 | 80 | 30 | 69 | 60 | 16 | 39 | 97 | 47 |
+| F | 67 | 70 | 3 | 33 | 27 | 23 | 51 | 65 | 12 | 6 |
+| G | 86 | 16 | 50 | 32 | 78 | 61 | 94 | 68 | 6 | 37 |
+| H | 21 | 50 | 7 | 37 | 83 | 79 | 31 | 95 | 45 | 24 |
+| I | 98 | 21 | 14 | 39 | 1 | 79 | 4 | 23 | 45 | 91 |
+| J | 73 | 98 | 70 | 14 | 6 | 0 | 72 | 30 | 58 | 97 |
+
+## class_id=E
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 70 | 0 | 82 | 30 | 90 | 36 | 94 | 81 | 92 | 73 |
+| B | 85 | 9 | 65 | 73 | 9 | 5 | 62 | 24 | 15 | 5 |
+| C | 26 | 87 | 18 | 70 | 47 | 66 | 82 | 48 | 88 | 39 |
+| D | 43 | 10 | 28 | 93 | 65 | 24 | 59 | 53 | 61 | 40 |
+| E | 5 | 21 | 3 | 17 | 95 | 10 | 74 | 57 | 8 | 27 |
+| F | 82 | 73 | 18 | 17 | 74 | 58 | 96 | 69 | 48 | 41 |
+| G | 19 | 80 | 11 | 1 | 88 | 51 | 20 | 41 | 18 | 83 |
+| H | 59 | 29 | 20 | 85 | 24 | 27 | 88 | 73 | 72 | 71 |
+| I | 83 | 68 | 24 | 39 | 69 | 1 | 87 | 0 | 25 | 43 |
+| J | 82 | 60 | 71 | 61 | 64 | 54 | 15 | 8 | 14 | 64 |
+
+## class_id=F
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 93 | 68 | 57 | 31 | 40 | 29 | 52 | 6 | 66 | 26 |
+| B | 9 | 85 | 24 | 4 | 13 | 98 | 89 | 19 | 38 | 15 |
+| C | 47 | 25 | 22 | 68 | 36 | 84 | 69 | 31 | 97 | 60 |
+| D | 46 | 17 | 59 | 87 | 54 | 69 | 34 | 49 | 76 | 45 |
+| E | 97 | 15 | 54 | 19 | 42 | 66 | 13 | 89 | 54 | 92 |
+| F | 9 | 4 | 75 | 15 | 9 | 46 | 44 | 42 | 86 | 63 |
+| G | 5 | 31 | 6 | 31 | 34 | 63 | 61 | 40 | 42 | 70 |
+| H | 57 | 58 | 86 | 11 | 43 | 86 | 92 | 30 | 82 | 84 |
+| I | 98 | 74 | 35 | 63 | 1 | 98 | 70 | 78 | 54 | 90 |
+| J | 72 | 13 | 83 | 18 | 56 | 91 | 87 | 2 | 82 | 38 |
+
+## class_id=G
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 95 | 92 | 51 | 6 | 35 | 26 | 70 | 81 | 95 | 53 |
+| B | 91 | 51 | 90 | 26 | 75 | 54 | 45 | 74 | 44 | 29 |
+| C | 5 | 67 | 78 | 35 | 71 | 17 | 86 | 79 | 64 | 18 |
+| D | 34 | 37 | 91 | 42 | 61 | 30 | 96 | 64 | 72 | 70 |
+| E | 37 | 56 | 82 | 13 | 33 | 60 | 80 | 60 | 51 | 38 |
+| F | 27 | 94 | 9 | 78 | 16 | 28 | 2 | 16 | 70 | 19 |
+| G | 37 | 44 | 85 | 16 | 6 | 2 | 75 | 88 | 89 | 74 |
+| H | 39 | 18 | 40 | 73 | 89 | 14 | 16 | 11 | 6 | 55 |
+| I | 81 | 80 | 0 | 90 | 14 | 74 | 20 | 69 | 76 | 58 |
+| J | 86 | 99 | 44 | 61 | 90 | 93 | 95 | 5 | 86 | 31 |
+
+## class_id=H
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 19 | 99 | 80 | 34 | 13 | 28 | 2 | 29 | 7 | 70 |
+| B | 8 | 56 | 67 | 30 | 67 | 42 | 16 | 51 | 19 | 11 |
+| C | 95 | 33 | 79 | 14 | 33 | 27 | 23 | 18 | 11 | 69 |
+| D | 17 | 19 | 4 | 22 | 76 | 39 | 5 | 74 | 95 | 21 |
+| E | 54 | 80 | 65 | 86 | 4 | 5 | 11 | 93 | 46 | 1 |
+| F | 92 | 27 | 29 | 22 | 70 | 3 | 83 | 75 | 5 | 46 |
+| G | 18 | 40 | 28 | 95 | 83 | 17 | 72 | 80 | 56 | 26 |
+| H | 16 | 0 | 44 | 18 | 85 | 51 | 74 | 53 | 65 | 65 |
+| I | 9 | 84 | 57 | 93 | 21 | 2 | 68 | 40 | 67 | 38 |
+| J | 80 | 76 | 41 | 90 | 70 | 8 | 65 | 47 | 61 | 89 |
+
+## class_id=I
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 27 | 94 | 37 | 37 | 49 | 97 | 97 | 74 | 56 | 17 |
+| B | 22 | 46 | 13 | 52 | 98 | 20 | 63 | 11 | 80 | 65 |
+| C | 97 | 54 | 62 | 8 | 13 | 12 | 48 | 86 | 86 | 87 |
+| D | 58 | 85 | 15 | 93 | 44 | 2 | 83 | 2 | 3 | 20 |
+| E | 46 | 65 | 30 | 92 | 91 | 35 | 34 | 51 | 46 | 87 |
+| F | 72 | 27 | 52 | 87 | 61 | 91 | 9 | 84 | 37 | 18 |
+| G | 8 | 79 | 3 | 82 | 69 | 25 | 67 | 11 | 17 | 6 |
+| H | 87 | 16 | 51 | 14 | 16 | 49 | 94 | 65 | 22 | 35 |
+| I | 77 | 87 | 96 | 53 | 78 | 26 | 92 | 76 | 27 | 84 |
+| J | 75 | 25 | 36 | 75 | 67 | 34 | 48 | 34 | 83 | 75 |
+
+## class_id=J
+| room_id\ta_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 87 | 32 | 36 | 36 | 68 | 65 | 5 | 50 | 44 | 7 |
+| B | 93 | 48 | 99 | 15 | 83 | 55 | 80 | 53 | 50 | 40 |
+| C | 48 | 47 | 28 | 43 | 69 | 84 | 72 | 90 | 66 | 47 |
+| D | 14 | 66 | 11 | 49 | 91 | 46 | 94 | 60 | 98 | 93 |
+| E | 51 | 68 | 29 | 58 | 45 | 70 | 26 | 38 | 56 | 53 |
+| F | 28 | 10 | 8 | 73 | 92 | 68 | 85 | 37 | 58 | 15 |
+| G | 26 | 43 | 36 | 63 | 58 | 6 | 2 | 67 | 64 | 93 |
+| H | 57 | 70 | 96 | 2 | 43 | 44 | 8 | 48 | 64 | 48 |
+| I | 84 | 21 | 92 | 80 | 49 | 93 | 89 | 35 | 72 | 89 |
+| J | 13 | 53 | 60 | 84 | 12 | 59 | 43 | 25 | 26 | 55 |
+
+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': [[[40, 74, 3, 42, 30, 69, 68, 12, 2, 66], [71, 59, 99, 3, 31, 7, 88, 25, 62, 48], [0, 42, 23, 49, 63, 66, 90, 59, 26, 17], [13, 96, 37, 43, 81, 77, 29, 91, 51, 75], [72, 68, 99, 33, 6, 55, 51, 67, 5, 61], [3, 78, 26, 16, 88, 97, 88, 55, 88, 30], [67, 89, 34, 87, 14, 71, 13, 75, 87, 11], [0, 39, 25, 17, 95, 35, 72, 86, 87, 83], [19, 82, 88, 30, 38, 31, 95, 45, 97, 70], [88, 78, 40, 94, 66, 31, 6, 6, 53, 69]], [[92, 93, 83, 68, 97, 42, 8, 96, 40, 38], [0, 54, 55, 5, 32, 71, 59, 89, 82, 93], [33, 65, 66, 40, 45, 95, 83, 67, 36, 28], [85, 97, 28, 52, 48, 98, 25, 63, 66, 93], [37, 35, 84, 65, 29, 39, 33, 61, 36, 94], [27, 72, 89, 35, 41, 96, 51, 12, 6, 56], [25, 57, 21, 63, 37, 40, 90, 14, 71, 75], [75, 91, 27, 10, 60, 95, 64, 71, 63, 84], [10, 52, 65, 23, 53, 75, 10, 59, 2, 82], [18, 49, 89, 36, 73, 16, 88, 47, 51, 17]], [[0, 24, 67, 19, 18, 49, 17, 45, 27, 63], [4, 32, 36, 57, 78, 51, 18, 20, 0, 67], [93, 8, 28, 11, 25, 53, 44, 82, 52, 65], [36, 96, 98, 95, 51, 30, 74, 28, 86, 6], [96, 67, 37, 52, 21, 45, 27, 91, 2, 63], [13, 73, 13, 55, 13, 96, 28, 68, 67, 15], [2, 85, 34, 57, 3, 51, 13, 11, 17, 10], [39, 70, 48, 7, 79, 80, 53, 51, 37, 3], [8, 32, 21, 36, 26, 90, 44, 17, 60, 40], [84, 40, 12, 42, 67, 29, 9, 36, 1, 38]], [[38, 80, 35, 10, 59, 89, 53, 81, 62, 48], [86, 79, 65, 5, 3, 29, 32, 2, 43, 43], [1, 17, 97, 67, 13, 45, 19, 66, 97, 13], [30, 48, 95, 76, 57, 88, 23, 58, 84, 36], [63, 79, 80, 30, 69, 60, 16, 39, 97, 47], [67, 70, 3, 33, 27, 23, 51, 65, 12, 6], [86, 16, 50, 32, 78, 61, 94, 68, 6, 37], [21, 50, 7, 37, 83, 79, 31, 95, 45, 24], [98, 21, 14, 39, 1, 79, 4, 23, 45, 91], [73, 98, 70, 14, 6, 0, 72, 30, 58, 97]], [[70, 0, 82, 30, 90, 36, 94, 81, 92, 73], [85, 9, 65, 73, 9, 5, 62, 24, 15, 5], [26, 87, 18, 70, 47, 66, 82, 48, 88, 39], [43, 10, 28, 93, 65, 24, 59, 53, 61, 40], [5, 21, 3, 17, 95, 10, 74, 57, 8, 27], [82, 73, 18, 17, 74, 58, 96, 69, 48, 41], [19, 80, 11, 1, 88, 51, 20, 41, 18, 83], [59, 29, 20, 85, 24, 27, 88, 73, 72, 71], [83, 68, 24, 39, 69, 1, 87, 0, 25, 43], [82, 60, 71, 61, 64, 54, 15, 8, 14, 64]], [[93, 68, 57, 31, 40, 29, 52, 6, 66, 26], [9, 85, 24, 4, 13, 98, 89, 19, 38, 15], [47, 25, 22, 68, 36, 84, 69, 31, 97, 60], [46, 17, 59, 87, 54, 69, 34, 49, 76, 45], [97, 15, 54, 19, 42, 66, 13, 89, 54, 92], [9, 4, 75, 15, 9, 46, 44, 42, 86, 63], [5, 31, 6, 31, 34, 63, 61, 40, 42, 70], [57, 58, 86, 11, 43, 86, 92, 30, 82, 84], [98, 74, 35, 63, 1, 98, 70, 78, 54, 90], [72, 13, 83, 18, 56, 91, 87, 2, 82, 38]], [[95, 92, 51, 6, 35, 26, 70, 81, 95, 53], [91, 51, 90, 26, 75, 54, 45, 74, 44, 29], [5, 67, 78, 35, 71, 17, 86, 79, 64, 18], [34, 37, 91, 42, 61, 30, 96, 64, 72, 70], [37, 56, 82, 13, 33, 60, 80, 60, 51, 38], [27, 94, 9, 78, 16, 28, 2, 16, 70, 19], [37, 44, 85, 16, 6, 2, 75, 88, 89, 74], [39, 18, 40, 73, 89, 14, 16, 11, 6, 55], [81, 80, 0, 90, 14, 74, 20, 69, 76, 58], [86, 99, 44, 61, 90, 93, 95, 5, 86, 31]], [[19, 99, 80, 34, 13, 28, 2, 29, 7, 70], [8, 56, 67, 30, 67, 42, 16, 51, 19, 11], [95, 33, 79, 14, 33, 27, 23, 18, 11, 69], [17, 19, 4, 22, 76, 39, 5, 74, 95, 21], [54, 80, 65, 86, 4, 5, 11, 93, 46, 1], [92, 27, 29, 22, 70, 3, 83, 75, 5, 46], [18, 40, 28, 95, 83, 17, 72, 80, 56, 26], [16, 0, 44, 18, 85, 51, 74, 53, 65, 65], [9, 84, 57, 93, 21, 2, 68, 40, 67, 38], [80, 76, 41, 90, 70, 8, 65, 47, 61, 89]], [[27, 94, 37, 37, 49, 97, 97, 74, 56, 17], [22, 46, 13, 52, 98, 20, 63, 11, 80, 65], [97, 54, 62, 8, 13, 12, 48, 86, 86, 87], [58, 85, 15, 93, 44, 2, 83, 2, 3, 20], [46, 65, 30, 92, 91, 35, 34, 51, 46, 87], [72, 27, 52, 87, 61, 91, 9, 84, 37, 18], [8, 79, 3, 82, 69, 25, 67, 11, 17, 6], [87, 16, 51, 14, 16, 49, 94, 65, 22, 35], [77, 87, 96, 53, 78, 26, 92, 76, 27, 84], [75, 25, 36, 75, 67, 34, 48, 34, 83, 75]], [[87, 32, 36, 36, 68, 65, 5, 50, 44, 7], [93, 48, 99, 15, 83, 55, 80, 53, 50, 40], [48, 47, 28, 43, 69, 84, 72, 90, 66, 47], [14, 66, 11, 49, 91, 46, 94, 60, 98, 93], [51, 68, 29, 58, 45, 70, 26, 38, 56, 53], [28, 10, 8, 73, 92, 68, 85, 37, 58, 15], [26, 43, 36, 63, 58, 6, 2, 67, 64, 93], [57, 70, 96, 2, 43, 44, 8, 48, 64, 48], [84, 21, 92, 80, 49, 93, 89, 35, 72, 89], [13, 53, 60, 84, 12, 59, 43, 25, 26, 55]]], 'objective': 21.0}","[[0, 2, 0], [1, 5, 8], [2, 7, 9], [3, 9, 5], [4, 0, 1], [5, 1, 3], [6, 8, 2], [7, 4, 4], [8, 3, 7], [9, 6, 6]]",21.0,"{'problem_type': 'AP3', 'n': 10, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 40}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 74}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 3}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 42}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 30}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 69}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 68}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 12}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 2}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 66}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 71}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 59}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 99}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 3}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 31}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 7}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 88}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 25}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 62}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 48}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 0}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 42}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 23}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 49}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 63}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 66}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 90}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 59}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 26}, {'i': 'A', 'j': 'C', 'k': 'J', 'cost': 17}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 13}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 96}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 37}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 43}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 81}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 77}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 29}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 91}, {'i': 'A', 'j': 'D', 'k': 'I', 'cost': 51}, {'i': 'A', 'j': 'D', 'k': 'J', 'cost': 75}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 72}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 68}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 99}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 33}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 6}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 55}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 51}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 67}, {'i': 'A', 'j': 'E', 'k': 'I', 'cost': 5}, {'i': 'A', 'j': 'E', 'k': 'J', 'cost': 61}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 3}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 78}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 26}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 16}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 88}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 97}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 88}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 55}, {'i': 'A', 'j': 'F', 'k': 'I', 'cost': 88}, {'i': 'A', 'j': 'F', 'k': 'J', 'cost': 30}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 67}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 89}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 34}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 87}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 14}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 71}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 13}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 75}, {'i': 'A', 'j': 'G', 'k': 'I', 'cost': 87}, {'i': 'A', 'j': 'G', 'k': 'J', 'cost': 11}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 0}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 39}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 25}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 17}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 95}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 35}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 72}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 86}, {'i': 'A', 'j': 'H', 'k': 'I', 'cost': 87}, {'i': 'A', 'j': 'H', 'k': 'J', 'cost': 83}, {'i': 'A', 'j': 'I', 'k': 'A', 'cost': 19}, {'i': 'A', 'j': 'I', 'k': 'B', 'cost': 82}, {'i': 'A', 'j': 'I', 'k': 'C', 'cost': 88}, {'i': 'A', 'j': 'I', 'k': 'D', 'cost': 30}, {'i': 'A', 'j': 'I', 'k': 'E', 'cost': 38}, {'i': 'A', 'j': 'I', 'k': 'F', 'cost': 31}, {'i': 'A', 'j': 'I', 'k': 'G', 'cost': 95}, {'i': 'A', 'j': 'I', 'k': 'H', 'cost': 45}, {'i': 'A', 'j': 'I', 'k': 'I', 'cost': 97}, {'i': 'A', 'j': 'I', 'k': 'J', 'cost': 70}, {'i': 'A', 'j': 'J', 'k': 'A', 'cost': 88}, {'i': 'A', 'j': 'J', 'k': 'B', 'cost': 78}, {'i': 'A', 'j': 'J', 'k': 'C', 'cost': 40}, {'i': 'A', 'j': 'J', 'k': 'D', 'cost': 94}, {'i': 'A', 'j': 'J', 'k': 'E', 'cost': 66}, {'i': 'A', 'j': 'J', 'k': 'F', 'cost': 31}, {'i': 'A', 'j': 'J', 'k': 'G', 'cost': 6}, {'i': 'A', 'j': 'J', 'k': 'H', 'cost': 6}, {'i': 'A', 'j': 'J', 'k': 'I', 'cost': 53}, {'i': 'A', 'j': 'J', 'k': 'J', 'cost': 69}, {'i': 'B', 'j': 'A', 'k': 'A', 'cost': 92}, {'i': 'B', 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'H', 'j': 'D', 'k': 'I', 'cost': 95}, {'i': 'H', 'j': 'D', 'k': 'J', 'cost': 21}, {'i': 'H', 'j': 'E', 'k': 'A', 'cost': 54}, {'i': 'H', 'j': 'E', 'k': 'B', 'cost': 80}, {'i': 'H', 'j': 'E', 'k': 'C', 'cost': 65}, {'i': 'H', 'j': 'E', 'k': 'D', 'cost': 86}, {'i': 'H', 'j': 'E', 'k': 'E', 'cost': 4}, {'i': 'H', 'j': 'E', 'k': 'F', 'cost': 5}, {'i': 'H', 'j': 'E', 'k': 'G', 'cost': 11}, {'i': 'H', 'j': 'E', 'k': 'H', 'cost': 93}, {'i': 'H', 'j': 'E', 'k': 'I', 'cost': 46}, {'i': 'H', 'j': 'E', 'k': 'J', 'cost': 1}, {'i': 'H', 'j': 'F', 'k': 'A', 'cost': 92}, {'i': 'H', 'j': 'F', 'k': 'B', 'cost': 27}, {'i': 'H', 'j': 'F', 'k': 'C', 'cost': 29}, {'i': 'H', 'j': 'F', 'k': 'D', 'cost': 22}, {'i': 'H', 'j': 'F', 'k': 'E', 'cost': 70}, {'i': 'H', 'j': 'F', 'k': 'F', 'cost': 3}, {'i': 'H', 'j': 'F', 'k': 'G', 'cost': 83}, {'i': 'H', 'j': 'F', 'k': 'H', 'cost': 75}, {'i': 'H', 'j': 'F', 'k': 'I', 'cost': 5}, {'i': 'H', 'j': 'F', 'k': 'J', 'cost': 46}, {'i': 'H', 'j': 'G', 'k': 'A', 'cost': 18}, {'i': 'H', 'j': 'G', 'k': 'B', 'cost': 40}, {'i': 'H', 'j': 'G', 'k': 'C', 'cost': 28}, {'i': 'H', 'j': 'G', 'k': 'D', 'cost': 95}, {'i': 'H', 'j': 'G', 'k': 'E', 'cost': 83}, {'i': 'H', 'j': 'G', 'k': 'F', 'cost': 17}, {'i': 'H', 'j': 'G', 'k': 'G', 'cost': 72}, {'i': 'H', 'j': 'G', 'k': 'H', 'cost': 80}, {'i': 'H', 'j': 'G', 'k': 'I', 'cost': 56}, {'i': 'H', 'j': 'G', 'k': 'J', 'cost': 26}, {'i': 'H', 'j': 'H', 'k': 'A', 'cost': 16}, {'i': 'H', 'j': 'H', 'k': 'B', 'cost': 0}, {'i': 'H', 'j': 'H', 'k': 'C', 'cost': 44}, {'i': 'H', 'j': 'H', 'k': 'D', 'cost': 18}, {'i': 'H', 'j': 'H', 'k': 'E', 'cost': 85}, {'i': 'H', 'j': 'H', 'k': 'F', 'cost': 51}, {'i': 'H', 'j': 'H', 'k': 'G', 'cost': 74}, {'i': 'H', 'j': 'H', 'k': 'H', 'cost': 53}, {'i': 'H', 'j': 'H', 'k': 'I', 'cost': 65}, {'i': 'H', 'j': 'H', 'k': 'J', 'cost': 65}, {'i': 'H', 'j': 'I', 'k': 'A', 'cost': 9}, {'i': 'H', 'j': 'I', 'k': 'B', 'cost': 84}, {'i': 'H', 'j': 'I', 'k': 'C', 'cost': 57}, {'i': 'H', 'j': 'I', 'k': 'D', 'cost': 93}, {'i': 'H', 'j': 'I', 'k': 'E', 'cost': 21}, {'i': 'H', 'j': 'I', 'k': 'F', 'cost': 2}, {'i': 'H', 'j': 'I', 'k': 'G', 'cost': 68}, {'i': 'H', 'j': 'I', 'k': 'H', 'cost': 40}, {'i': 'H', 'j': 'I', 'k': 'I', 'cost': 67}, {'i': 'H', 'j': 'I', 'k': 'J', 'cost': 38}, {'i': 'H', 'j': 'J', 'k': 'A', 'cost': 80}, {'i': 'H', 'j': 'J', 'k': 'B', 'cost': 76}, {'i': 'H', 'j': 'J', 'k': 'C', 'cost': 41}, {'i': 'H', 'j': 'J', 'k': 'D', 'cost': 90}, {'i': 'H', 'j': 'J', 'k': 'E', 'cost': 70}, {'i': 'H', 'j': 'J', 'k': 'F', 'cost': 8}, {'i': 'H', 'j': 'J', 'k': 'G', 'cost': 65}, {'i': 'H', 'j': 'J', 'k': 'H', 'cost': 47}, {'i': 'H', 'j': 'J', 'k': 'I', 'cost': 61}, {'i': 'H', 'j': 'J', 'k': 'J', 'cost': 89}, {'i': 'I', 'j': 'A', 'k': 'A', 'cost': 27}, {'i': 'I', 'j': 'A', 'k': 'B', 'cost': 94}, {'i': 'I', 'j': 'A', 'k': 'C', 'cost': 37}, {'i': 'I', 'j': 'A', 'k': 'D', 'cost': 37}, {'i': 'I', 'j': 'A', 'k': 'E', 'cost': 49}, {'i': 'I', 'j': 'A', 'k': 'F', 'cost': 97}, {'i': 'I', 'j': 'A', 'k': 'G', 'cost': 97}, {'i': 'I', 'j': 'A', 'k': 'H', 'cost': 74}, {'i': 'I', 'j': 'A', 'k': 'I', 'cost': 56}, {'i': 'I', 'j': 'A', 'k': 'J', 'cost': 17}, {'i': 'I', 'j': 'B', 'k': 'A', 'cost': 22}, {'i': 'I', 'j': 'B', 'k': 'B', 'cost': 46}, {'i': 'I', 'j': 'B', 'k': 'C', 'cost': 13}, {'i': 'I', 'j': 'B', 'k': 'D', 'cost': 52}, {'i': 'I', 'j': 'B', 'k': 'E', 'cost': 98}, {'i': 'I', 'j': 'B', 'k': 'F', 'cost': 20}, {'i': 'I', 'j': 'B', 'k': 'G', 'cost': 63}, {'i': 'I', 'j': 'B', 'k': 'H', 'cost': 11}, {'i': 'I', 'j': 'B', 'k': 'I', 'cost': 80}, {'i': 'I', 'j': 'B', 'k': 'J', 'cost': 65}, {'i': 'I', 'j': 'C', 'k': 'A', 'cost': 97}, {'i': 'I', 'j': 'C', 'k': 'B', 'cost': 54}, {'i': 'I', 'j': 'C', 'k': 'C', 'cost': 62}, {'i': 'I', 'j': 'C', 'k': 'D', 'cost': 8}, {'i': 'I', 'j': 'C', 'k': 'E', 'cost': 13}, {'i': 'I', 'j': 'C', 'k': 'F', 'cost': 12}, {'i': 'I', 'j': 'C', 'k': 'G', 'cost': 48}, {'i': 'I', 'j': 'C', 'k': 'H', 'cost': 86}, {'i': 'I', 'j': 'C', 'k': 'I', 'cost': 86}, {'i': 'I', 'j': 'C', 'k': 'J', 'cost': 87}, {'i': 'I', 'j': 'D', 'k': 'A', 'cost': 58}, {'i': 'I', 'j': 'D', 'k': 'B', 'cost': 85}, {'i': 'I', 'j': 'D', 'k': 'C', 'cost': 15}, {'i': 'I', 'j': 'D', 'k': 'D', 'cost': 93}, {'i': 'I', 'j': 'D', 'k': 'E', 'cost': 44}, {'i': 'I', 'j': 'D', 'k': 'F', 'cost': 2}, {'i': 'I', 'j': 'D', 'k': 'G', 'cost': 83}, {'i': 'I', 'j': 'D', 'k': 'H', 'cost': 2}, {'i': 'I', 'j': 'D', 'k': 'I', 'cost': 3}, {'i': 'I', 'j': 'D', 'k': 'J', 'cost': 20}, {'i': 'I', 'j': 'E', 'k': 'A', 'cost': 46}, {'i': 'I', 'j': 'E', 'k': 'B', 'cost': 65}, {'i': 'I', 'j': 'E', 'k': 'C', 'cost': 30}, {'i': 'I', 'j': 'E', 'k': 'D', 'cost': 92}, {'i': 'I', 'j': 'E', 'k': 'E', 'cost': 91}, {'i': 'I', 'j': 'E', 'k': 'F', 'cost': 35}, {'i': 'I', 'j': 'E', 'k': 'G', 'cost': 34}, {'i': 'I', 'j': 'E', 'k': 'H', 'cost': 51}, {'i': 'I', 'j': 'E', 'k': 'I', 'cost': 46}, {'i': 'I', 'j': 'E', 'k': 'J', 'cost': 87}, {'i': 'I', 'j': 'F', 'k': 'A', 'cost': 72}, {'i': 'I', 'j': 'F', 'k': 'B', 'cost': 27}, {'i': 'I', 'j': 'F', 'k': 'C', 'cost': 52}, {'i': 'I', 'j': 'F', 'k': 'D', 'cost': 87}, {'i': 'I', 'j': 'F', 'k': 'E', 'cost': 61}, {'i': 'I', 'j': 'F', 'k': 'F', 'cost': 91}, {'i': 'I', 'j': 'F', 'k': 'G', 'cost': 9}, {'i': 'I', 'j': 'F', 'k': 'H', 'cost': 84}, {'i': 'I', 'j': 'F', 'k': 'I', 'cost': 37}, {'i': 'I', 'j': 'F', 'k': 'J', 'cost': 18}, {'i': 'I', 'j': 'G', 'k': 'A', 'cost': 8}, {'i': 'I', 'j': 'G', 'k': 'B', 'cost': 79}, {'i': 'I', 'j': 'G', 'k': 'C', 'cost': 3}, {'i': 'I', 'j': 'G', 'k': 'D', 'cost': 82}, {'i': 'I', 'j': 'G', 'k': 'E', 'cost': 69}, {'i': 'I', 'j': 'G', 'k': 'F', 'cost': 25}, {'i': 'I', 'j': 'G', 'k': 'G', 'cost': 67}, {'i': 'I', 'j': 'G', 'k': 'H', 'cost': 11}, {'i': 'I', 'j': 'G', 'k': 'I', 'cost': 17}, {'i': 'I', 'j': 'G', 'k': 'J', 'cost': 6}, {'i': 'I', 'j': 'H', 'k': 'A', 'cost': 87}, {'i': 'I', 'j': 'H', 'k': 'B', 'cost': 16}, {'i': 'I', 'j': 'H', 'k': 'C', 'cost': 51}, {'i': 'I', 'j': 'H', 'k': 'D', 'cost': 14}, {'i': 'I', 'j': 'H', 'k': 'E', 'cost': 16}, {'i': 'I', 'j': 'H', 'k': 'F', 'cost': 49}, {'i': 'I', 'j': 'H', 'k': 'G', 'cost': 94}, {'i': 'I', 'j': 'H', 'k': 'H', 'cost': 65}, {'i': 'I', 'j': 'H', 'k': 'I', 'cost': 22}, {'i': 'I', 'j': 'H', 'k': 'J', 'cost': 35}, {'i': 'I', 'j': 'I', 'k': 'A', 'cost': 77}, {'i': 'I', 'j': 'I', 'k': 'B', 'cost': 87}, {'i': 'I', 'j': 'I', 'k': 'C', 'cost': 96}, {'i': 'I', 'j': 'I', 'k': 'D', 'cost': 53}, {'i': 'I', 'j': 'I', 'k': 'E', 'cost': 78}, {'i': 'I', 'j': 'I', 'k': 'F', 'cost': 26}, {'i': 'I', 'j': 'I', 'k': 'G', 'cost': 92}, {'i': 'I', 'j': 'I', 'k': 'H', 'cost': 76}, {'i': 'I', 'j': 'I', 'k': 'I', 'cost': 27}, {'i': 'I', 'j': 'I', 'k': 'J', 'cost': 84}, {'i': 'I', 'j': 'J', 'k': 'A', 'cost': 75}, {'i': 'I', 'j': 'J', 'k': 'B', 'cost': 25}, {'i': 'I', 'j': 'J', 'k': 'C', 'cost': 36}, {'i': 'I', 'j': 'J', 'k': 'D', 'cost': 75}, {'i': 'I', 'j': 'J', 'k': 'E', 'cost': 67}, {'i': 'I', 'j': 'J', 'k': 'F', 'cost': 34}, {'i': 'I', 'j': 'J', 'k': 'G', 'cost': 48}, {'i': 'I', 'j': 'J', 'k': 'H', 'cost': 34}, {'i': 'I', 'j': 'J', 'k': 'I', 'cost': 83}, {'i': 'I', 'j': 'J', 'k': 'J', 'cost': 75}, {'i': 'J', 'j': 'A', 'k': 'A', 'cost': 87}, {'i': 'J', 'j': 'A', 'k': 'B', 'cost': 32}, {'i': 'J', 'j': 'A', 'k': 'C', 'cost': 36}, {'i': 'J', 'j': 'A', 'k': 'D', 'cost': 36}, {'i': 'J', 'j': 'A', 'k': 'E', 'cost': 68}, {'i': 'J', 'j': 'A', 'k': 'F', 'cost': 65}, {'i': 'J', 'j': 'A', 'k': 'G', 'cost': 5}, {'i': 'J', 'j': 'A', 'k': 'H', 'cost': 50}, {'i': 'J', 'j': 'A', 'k': 'I', 'cost': 44}, {'i': 'J', 'j': 'A', 'k': 'J', 'cost': 7}, {'i': 'J', 'j': 'B', 'k': 'A', 'cost': 93}, {'i': 'J', 'j': 'B', 'k': 'B', 'cost': 48}, {'i': 'J', 'j': 'B', 'k': 'C', 'cost': 99}, {'i': 'J', 'j': 'B', 'k': 'D', 'cost': 15}, {'i': 'J', 'j': 'B', 'k': 'E', 'cost': 83}, {'i': 'J', 'j': 'B', 'k': 'F', 'cost': 55}, {'i': 'J', 'j': 'B', 'k': 'G', 'cost': 80}, {'i': 'J', 'j': 'B', 'k': 'H', 'cost': 53}, {'i': 'J', 'j': 'B', 'k': 'I', 'cost': 50}, {'i': 'J', 'j': 'B', 'k': 'J', 'cost': 40}, {'i': 'J', 'j': 'C', 'k': 'A', 'cost': 48}, {'i': 'J', 'j': 'C', 'k': 'B', 'cost': 47}, {'i': 'J', 'j': 'C', 'k': 'C', 'cost': 28}, {'i': 'J', 'j': 'C', 'k': 'D', 'cost': 43}, {'i': 'J', 'j': 'C', 'k': 'E', 'cost': 69}, {'i': 'J', 'j': 'C', 'k': 'F', 'cost': 84}, {'i': 'J', 'j': 'C', 'k': 'G', 'cost': 72}, {'i': 'J', 'j': 'C', 'k': 'H', 'cost': 90}, {'i': 'J', 'j': 'C', 'k': 'I', 'cost': 66}, {'i': 'J', 'j': 'C', 'k': 'J', 'cost': 47}, {'i': 'J', 'j': 'D', 'k': 'A', 'cost': 14}, {'i': 'J', 'j': 'D', 'k': 'B', 'cost': 66}, {'i': 'J', 'j': 'D', 'k': 'C', 'cost': 11}, {'i': 'J', 'j': 'D', 'k': 'D', 'cost': 49}, {'i': 'J', 'j': 'D', 'k': 'E', 'cost': 91}, {'i': 'J', 'j': 'D', 'k': 'F', 'cost': 46}, {'i': 'J', 'j': 'D', 'k': 'G', 'cost': 94}, {'i': 'J', 'j': 'D', 'k': 'H', 'cost': 60}, {'i': 'J', 'j': 'D', 'k': 'I', 'cost': 98}, {'i': 'J', 'j': 'D', 'k': 'J', 'cost': 93}, {'i': 'J', 'j': 'E', 'k': 'A', 'cost': 51}, {'i': 'J', 'j': 'E', 'k': 'B', 'cost': 68}, {'i': 'J', 'j': 'E', 'k': 'C', 'cost': 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'F', 'cost': 6}, {'i': 'J', 'j': 'G', 'k': 'G', 'cost': 2}, {'i': 'J', 'j': 'G', 'k': 'H', 'cost': 67}, {'i': 'J', 'j': 'G', 'k': 'I', 'cost': 64}, {'i': 'J', 'j': 'G', 'k': 'J', 'cost': 93}, {'i': 'J', 'j': 'H', 'k': 'A', 'cost': 57}, {'i': 'J', 'j': 'H', 'k': 'B', 'cost': 70}, {'i': 'J', 'j': 'H', 'k': 'C', 'cost': 96}, {'i': 'J', 'j': 'H', 'k': 'D', 'cost': 2}, {'i': 'J', 'j': 'H', 'k': 'E', 'cost': 43}, {'i': 'J', 'j': 'H', 'k': 'F', 'cost': 44}, {'i': 'J', 'j': 'H', 'k': 'G', 'cost': 8}, {'i': 'J', 'j': 'H', 'k': 'H', 'cost': 48}, {'i': 'J', 'j': 'H', 'k': 'I', 'cost': 64}, {'i': 'J', 'j': 'H', 'k': 'J', 'cost': 48}, {'i': 'J', 'j': 'I', 'k': 'A', 'cost': 84}, {'i': 'J', 'j': 'I', 'k': 'B', 'cost': 21}, {'i': 'J', 'j': 'I', 'k': 'C', 'cost': 92}, {'i': 'J', 'j': 'I', 'k': 'D', 'cost': 80}, {'i': 'J', 'j': 'I', 'k': 'E', 'cost': 49}, {'i': 'J', 'j': 'I', 'k': 'F', 'cost': 93}, {'i': 'J', 'j': 'I', 'k': 'G', 'cost': 89}, {'i': 'J', 'j': 'I', 'k': 'H', 'cost': 35}, {'i': 'J', 'j': 'I', 'k': 'I', 'cost': 72}, {'i': 'J', 'j': 'I', 'k': 'J', 'cost': 89}, {'i': 'J', 'j': 'J', 'k': 'A', 'cost': 13}, {'i': 'J', 'j': 'J', 'k': 'B', 'cost': 53}, {'i': 'J', 'j': 'J', 'k': 'C', 'cost': 60}, {'i': 'J', 'j': 'J', 'k': 'D', 'cost': 84}, {'i': 'J', 'j': 'J', 'k': 'E', 'cost': 12}, {'i': 'J', 'j': 'J', 'k': 'F', 'cost': 59}, {'i': 'J', 'j': 'J', 'k': 'G', 'cost': 43}, {'i': 'J', 'j': 'J', 'k': 'H', 'cost': 25}, {'i': 'J', 'j': 'J', 'k': 'I', 'cost': 26}, {'i': 'J', 'j': 'J', 'k': 'J', 'cost': 55}]}","[['A', 'C', 'A'], ['B', 'F', 'I'], ['C', 'H', 'J'], ['D', 'J', 'F'], ['E', 'A', 'B'], ['F', 'B', 'D'], ['G', 'I', 'C'], ['H', 'E', 'E'], ['I', 'D', 'H'], ['J', 'G', 'G']]",39,json,names
+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.
+
+{
+  ""num_visits"": 12,
+  ""visit_ids"": [
+    ""A"",
+    ""B"",
+    ""C"",
+    ""D"",
+    ""E"",
+    ""F"",
+    ""G"",
+    ""H"",
+    ""I"",
+    ""J"",
+    ""K"",
+    ""L""
+  ]
+}
+
+# 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 | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 63 | 73 | 61 | 5 | 23 | 96 | 69 | 79 | 41 | 17 | 45 | 27 |
+| B | 41 | 34 | 83 | 77 | 94 | 75 | 59 | 69 | 39 | 54 | 9 | 41 |
+| C | 6 | 95 | 80 | 74 | 43 | 54 | 26 | 47 | 50 | 77 | 62 | 12 |
+| D | 26 | 48 | 22 | 79 | 81 | 55 | 12 | 60 | 98 | 98 | 26 | 60 |
+| E | 65 | 87 | 62 | 64 | 43 | 73 | 65 | 33 | 77 | 22 | 73 | 78 |
+| F | 47 | 99 | 92 | 92 | 71 | 15 | 36 | 72 | 15 | 90 | 80 | 92 |
+| G | 13 | 76 | 65 | 80 | 2 | 35 | 86 | 0 | 64 | 87 | 27 | 28 |
+| H | 62 | 78 | 7 | 84 | 35 | 98 | 51 | 50 | 45 | 77 | 77 | 35 |
+| I | 60 | 48 | 56 | 8 | 83 | 47 | 33 | 89 | 99 | 63 | 67 | 19 |
+| J | 3 | 74 | 68 | 67 | 81 | 92 | 9 | 96 | 52 | 51 | 8 | 59 |
+| K | 73 | 18 | 33 | 38 | 81 | 36 | 45 | 78 | 86 | 85 | 59 | 96 |
+| L | 36 | 77 | 81 | 22 | 3 | 45 | 71 | 66 | 58 | 80 | 57 | 18 |
+
+## visit_id=B
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 30 | 28 | 1 | 43 | 27 | 55 | 22 | 2 | 58 | 93 | 84 | 17 |
+| B | 54 | 80 | 30 | 55 | 79 | 51 | 7 | 69 | 43 | 27 | 4 | 89 |
+| C | 65 | 19 | 90 | 48 | 13 | 89 | 28 | 9 | 74 | 19 | 16 | 61 |
+| D | 17 | 46 | 1 | 55 | 2 | 68 | 30 | 35 | 48 | 45 | 76 | 77 |
+| E | 46 | 10 | 20 | 42 | 5 | 25 | 93 | 41 | 78 | 37 | 18 | 77 |
+| F | 58 | 69 | 5 | 91 | 7 | 70 | 44 | 54 | 33 | 24 | 21 | 71 |
+| G | 14 | 60 | 49 | 41 | 39 | 24 | 61 | 88 | 59 | 33 | 77 | 23 |
+| H | 99 | 53 | 91 | 74 | 40 | 18 | 5 | 86 | 10 | 89 | 45 | 13 |
+| I | 82 | 80 | 38 | 60 | 6 | 54 | 69 | 29 | 39 | 47 | 31 | 31 |
+| J | 37 | 84 | 11 | 12 | 40 | 50 | 99 | 92 | 41 | 36 | 93 | 48 |
+| K | 93 | 54 | 47 | 61 | 87 | 69 | 36 | 20 | 41 | 42 | 42 | 77 |
+| L | 52 | 27 | 72 | 5 | 21 | 1 | 9 | 91 | 28 | 33 | 79 | 75 |
+
+## visit_id=C
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 8 | 2 | 5 | 69 | 86 | 37 | 42 | 99 | 5 | 36 | 35 | 35 |
+| B | 8 | 61 | 46 | 71 | 22 | 25 | 72 | 24 | 98 | 42 | 33 | 19 |
+| C | 38 | 27 | 17 | 91 | 58 | 94 | 42 | 50 | 27 | 39 | 21 | 19 |
+| D | 6 | 47 | 21 | 35 | 88 | 55 | 24 | 78 | 7 | 5 | 23 | 80 |
+| E | 66 | 46 | 55 | 36 | 85 | 15 | 3 | 65 | 32 | 2 | 10 | 78 |
+| F | 96 | 11 | 32 | 86 | 21 | 66 | 41 | 87 | 64 | 79 | 50 | 18 |
+| G | 64 | 67 | 36 | 94 | 56 | 12 | 43 | 88 | 10 | 49 | 92 | 42 |
+| H | 44 | 1 | 64 | 1 | 82 | 11 | 4 | 95 | 85 | 11 | 5 | 39 |
+| I | 89 | 62 | 36 | 65 | 1 | 33 | 99 | 68 | 76 | 83 | 56 | 43 |
+| J | 97 | 22 | 16 | 38 | 82 | 86 | 65 | 6 | 5 | 83 | 63 | 94 |
+| K | 93 | 19 | 34 | 76 | 98 | 12 | 20 | 97 | 98 | 43 | 10 | 40 |
+| L | 98 | 94 | 67 | 54 | 1 | 14 | 10 | 21 | 34 | 25 | 16 | 16 |
+
+## visit_id=D
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 55 | 25 | 90 | 49 | 3 | 69 | 56 | 4 | 76 | 89 | 37 | 74 |
+| B | 64 | 54 | 81 | 22 | 21 | 10 | 14 | 35 | 75 | 25 | 53 | 84 |
+| C | 40 | 75 | 48 | 47 | 45 | 24 | 9 | 9 | 50 | 54 | 68 | 71 |
+| D | 4 | 14 | 87 | 55 | 97 | 83 | 70 | 53 | 43 | 57 | 88 | 94 |
+| E | 33 | 16 | 20 | 88 | 96 | 4 | 22 | 73 | 10 | 54 | 28 | 30 |
+| F | 20 | 17 | 51 | 83 | 84 | 95 | 75 | 64 | 27 | 19 | 54 | 14 |
+| G | 90 | 33 | 64 | 57 | 69 | 36 | 94 | 13 | 60 | 63 | 42 | 94 |
+| H | 94 | 86 | 23 | 15 | 11 | 40 | 27 | 98 | 63 | 96 | 44 | 17 |
+| I | 96 | 15 | 42 | 65 | 83 | 13 | 81 | 41 | 38 | 50 | 93 | 65 |
+| J | 25 | 13 | 95 | 36 | 41 | 11 | 34 | 57 | 71 | 84 | 1 | 71 |
+| K | 4 | 89 | 3 | 99 | 21 | 19 | 54 | 42 | 19 | 63 | 50 | 65 |
+| L | 6 | 66 | 1 | 74 | 59 | 57 | 20 | 69 | 8 | 7 | 96 | 35 |
+
+## visit_id=E
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 49 | 29 | 36 | 14 | 65 | 56 | 37 | 3 | 80 | 84 | 91 | 77 |
+| B | 26 | 5 | 50 | 72 | 83 | 87 | 29 | 68 | 21 | 46 | 27 | 94 |
+| C | 69 | 26 | 55 | 74 | 36 | 89 | 37 | 31 | 13 | 0 | 49 | 93 |
+| D | 75 | 61 | 23 | 32 | 31 | 53 | 21 | 15 | 92 | 11 | 58 | 30 |
+| E | 61 | 67 | 75 | 89 | 46 | 16 | 20 | 84 | 85 | 11 | 70 | 35 |
+| F | 96 | 73 | 12 | 71 | 82 | 91 | 8 | 8 | 67 | 0 | 10 | 49 |
+| G | 78 | 5 | 74 | 20 | 97 | 34 | 1 | 2 | 33 | 94 | 36 | 61 |
+| H | 90 | 46 | 66 | 60 | 67 | 31 | 60 | 89 | 35 | 43 | 78 | 16 |
+| I | 98 | 45 | 81 | 11 | 63 | 10 | 87 | 28 | 31 | 52 | 37 | 56 |
+| J | 56 | 35 | 51 | 53 | 73 | 60 | 31 | 45 | 26 | 57 | 32 | 52 |
+| K | 13 | 63 | 32 | 94 | 99 | 63 | 45 | 21 | 61 | 72 | 61 | 9 |
+| L | 86 | 92 | 22 | 8 | 18 | 6 | 70 | 64 | 17 | 21 | 59 | 50 |
+
+## visit_id=F
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 51 | 58 | 28 | 95 | 48 | 90 | 29 | 14 | 5 | 45 | 75 | 99 |
+| B | 62 | 8 | 82 | 31 | 61 | 50 | 82 | 24 | 78 | 64 | 18 | 27 |
+| C | 67 | 61 | 24 | 38 | 77 | 75 | 90 | 31 | 63 | 71 | 42 | 7 |
+| D | 74 | 52 | 71 | 36 | 72 | 0 | 73 | 13 | 10 | 32 | 54 | 10 |
+| E | 65 | 43 | 92 | 13 | 3 | 19 | 36 | 99 | 49 | 10 | 30 | 90 |
+| F | 88 | 74 | 12 | 16 | 13 | 75 | 2 | 61 | 78 | 80 | 77 | 30 |
+| G | 31 | 49 | 66 | 55 | 16 | 78 | 89 | 39 | 82 | 66 | 7 | 9 |
+| H | 97 | 95 | 25 | 17 | 58 | 20 | 93 | 41 | 18 | 51 | 66 | 32 |
+| I | 75 | 83 | 14 | 50 | 12 | 69 | 32 | 65 | 22 | 38 | 64 | 54 |
+| J | 43 | 43 | 88 | 31 | 75 | 15 | 7 | 21 | 15 | 47 | 13 | 13 |
+| K | 16 | 20 | 81 | 54 | 72 | 20 | 24 | 20 | 72 | 25 | 21 | 3 |
+| L | 1 | 66 | 90 | 62 | 37 | 6 | 94 | 52 | 81 | 69 | 72 | 12 |
+
+## visit_id=G
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 0 | 31 | 44 | 65 | 32 | 98 | 93 | 26 | 55 | 34 | 45 | 78 |
+| B | 4 | 70 | 45 | 74 | 16 | 75 | 58 | 5 | 26 | 89 | 7 | 19 |
+| C | 62 | 0 | 31 | 15 | 90 | 12 | 5 | 43 | 75 | 0 | 91 | 2 |
+| D | 18 | 92 | 84 | 31 | 67 | 72 | 35 | 61 | 58 | 34 | 24 | 66 |
+| E | 21 | 12 | 86 | 75 | 93 | 66 | 93 | 40 | 70 | 52 | 49 | 26 |
+| F | 70 | 79 | 60 | 85 | 84 | 63 | 41 | 49 | 46 | 76 | 38 | 43 |
+| G | 60 | 51 | 45 | 83 | 75 | 85 | 66 | 86 | 12 | 15 | 14 | 10 |
+| H | 21 | 41 | 77 | 47 | 22 | 28 | 43 | 72 | 42 | 25 | 32 | 6 |
+| I | 22 | 26 | 80 | 76 | 55 | 30 | 89 | 45 | 50 | 23 | 87 | 55 |
+| J | 76 | 97 | 83 | 94 | 83 | 3 | 97 | 54 | 52 | 19 | 73 | 92 |
+| K | 63 | 98 | 9 | 63 | 67 | 49 | 49 | 71 | 53 | 50 | 70 | 20 |
+| L | 71 | 60 | 39 | 10 | 86 | 14 | 78 | 4 | 56 | 10 | 70 | 61 |
+
+## visit_id=H
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 6 | 86 | 25 | 64 | 73 | 72 | 76 | 81 | 71 | 4 | 91 | 17 |
+| B | 2 | 11 | 95 | 42 | 69 | 73 | 88 | 42 | 3 | 58 | 88 | 70 |
+| C | 83 | 68 | 6 | 94 | 13 | 32 | 59 | 23 | 74 | 68 | 4 | 3 |
+| D | 47 | 82 | 98 | 44 | 91 | 75 | 32 | 86 | 51 | 70 | 10 | 69 |
+| E | 50 | 32 | 22 | 10 | 77 | 77 | 19 | 55 | 87 | 68 | 27 | 49 |
+| F | 75 | 52 | 20 | 50 | 16 | 84 | 62 | 83 | 39 | 98 | 97 | 88 |
+| G | 90 | 8 | 98 | 34 | 74 | 65 | 47 | 44 | 8 | 84 | 1 | 72 |
+| H | 10 | 50 | 11 | 21 | 8 | 22 | 52 | 91 | 56 | 24 | 6 | 88 |
+| I | 89 | 28 | 56 | 98 | 45 | 77 | 99 | 99 | 63 | 49 | 41 | 77 |
+| J | 25 | 76 | 69 | 94 | 81 | 74 | 80 | 68 | 1 | 86 | 6 | 44 |
+| K | 17 | 75 | 77 | 46 | 91 | 38 | 48 | 52 | 57 | 2 | 62 | 91 |
+| L | 13 | 15 | 0 | 15 | 99 | 88 | 20 | 26 | 84 | 27 | 94 | 37 |
+
+## visit_id=I
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 90 | 84 | 72 | 56 | 76 | 58 | 53 | 15 | 70 | 88 | 98 | 34 |
+| B | 43 | 90 | 91 | 19 | 68 | 24 | 32 | 48 | 59 | 87 | 48 | 3 |
+| C | 21 | 58 | 74 | 16 | 69 | 76 | 70 | 79 | 90 | 1 | 36 | 72 |
+| D | 11 | 99 | 88 | 54 | 20 | 72 | 45 | 40 | 23 | 27 | 57 | 47 |
+| E | 77 | 93 | 97 | 88 | 87 | 76 | 85 | 74 | 89 | 72 | 66 | 30 |
+| F | 68 | 27 | 34 | 87 | 39 | 88 | 62 | 78 | 67 | 59 | 82 | 9 |
+| G | 3 | 64 | 66 | 0 | 43 | 25 | 50 | 71 | 36 | 15 | 16 | 4 |
+| H | 22 | 72 | 22 | 63 | 71 | 20 | 83 | 3 | 26 | 66 | 48 | 17 |
+| I | 49 | 45 | 64 | 69 | 99 | 17 | 9 | 65 | 55 | 83 | 95 | 19 |
+| J | 42 | 65 | 96 | 1 | 30 | 23 | 80 | 85 | 26 | 81 | 65 | 71 |
+| K | 96 | 48 | 27 | 60 | 83 | 14 | 83 | 30 | 92 | 13 | 9 | 83 |
+| L | 89 | 65 | 10 | 8 | 43 | 76 | 33 | 41 | 97 | 38 | 5 | 9 |
+
+## visit_id=J
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 92 | 82 | 90 | 29 | 45 | 13 | 8 | 68 | 63 | 49 | 70 | 40 |
+| B | 96 | 73 | 96 | 24 | 97 | 32 | 80 | 82 | 13 | 18 | 42 | 20 |
+| C | 90 | 24 | 44 | 75 | 11 | 21 | 83 | 6 | 56 | 95 | 6 | 3 |
+| D | 3 | 72 | 21 | 85 | 13 | 60 | 50 | 6 | 7 | 33 | 37 | 67 |
+| E | 26 | 67 | 16 | 33 | 65 | 33 | 73 | 88 | 36 | 39 | 26 | 91 |
+| F | 53 | 31 | 54 | 84 | 15 | 25 | 12 | 6 | 67 | 28 | 88 | 69 |
+| G | 31 | 91 | 56 | 61 | 1 | 40 | 36 | 70 | 15 | 12 | 8 | 92 |
+| H | 97 | 92 | 83 | 12 | 99 | 77 | 20 | 39 | 41 | 98 | 69 | 88 |
+| I | 76 | 40 | 74 | 51 | 87 | 17 | 56 | 90 | 51 | 39 | 32 | 30 |
+| J | 77 | 98 | 84 | 26 | 81 | 85 | 23 | 87 | 51 | 10 | 75 | 78 |
+| K | 16 | 8 | 96 | 33 | 50 | 80 | 65 | 89 | 11 | 11 | 49 | 1 |
+| L | 49 | 94 | 15 | 75 | 52 | 99 | 74 | 62 | 65 | 38 | 36 | 20 |
+
+## visit_id=K
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 18 | 22 | 64 | 22 | 84 | 8 | 17 | 10 | 61 | 68 | 96 | 78 |
+| B | 42 | 15 | 17 | 35 | 91 | 0 | 81 | 48 | 34 | 79 | 75 | 4 |
+| C | 52 | 87 | 51 | 87 | 27 | 8 | 46 | 50 | 64 | 54 | 93 | 28 |
+| D | 88 | 74 | 33 | 98 | 49 | 43 | 65 | 33 | 21 | 35 | 78 | 61 |
+| E | 7 | 21 | 8 | 53 | 87 | 87 | 63 | 74 | 47 | 61 | 57 | 18 |
+| F | 20 | 7 | 83 | 92 | 83 | 44 | 61 | 68 | 32 | 12 | 3 | 64 |
+| G | 77 | 19 | 6 | 48 | 86 | 10 | 18 | 86 | 63 | 4 | 56 | 86 |
+| H | 59 | 89 | 23 | 71 | 90 | 92 | 25 | 90 | 92 | 24 | 70 | 2 |
+| I | 15 | 95 | 58 | 72 | 29 | 92 | 99 | 98 | 6 | 42 | 73 | 51 |
+| J | 17 | 77 | 3 | 70 | 28 | 5 | 55 | 51 | 49 | 82 | 41 | 56 |
+| K | 41 | 3 | 41 | 34 | 39 | 45 | 88 | 12 | 4 | 2 | 72 | 82 |
+| L | 97 | 81 | 53 | 77 | 90 | 44 | 72 | 97 | 99 | 67 | 4 | 82 |
+
+## visit_id=L
+| nurse_id\kit_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 63 | 87 | 30 | 96 | 57 | 43 | 8 | 42 | 8 | 74 | 23 | 58 |
+| B | 50 | 99 | 78 | 89 | 16 | 6 | 19 | 89 | 20 | 86 | 10 | 63 |
+| C | 35 | 33 | 57 | 9 | 15 | 78 | 49 | 30 | 3 | 40 | 2 | 86 |
+| D | 66 | 60 | 75 | 71 | 77 | 80 | 17 | 31 | 35 | 25 | 44 | 86 |
+| E | 84 | 45 | 20 | 48 | 55 | 23 | 81 | 45 | 32 | 70 | 87 | 70 |
+| F | 42 | 24 | 61 | 57 | 36 | 63 | 38 | 92 | 35 | 40 | 11 | 76 |
+| G | 64 | 45 | 97 | 15 | 39 | 10 | 90 | 61 | 86 | 56 | 30 | 94 |
+| H | 2 | 40 | 34 | 62 | 29 | 76 | 68 | 61 | 67 | 1 | 6 | 42 |
+| I | 72 | 97 | 93 | 13 | 81 | 40 | 1 | 75 | 55 | 86 | 70 | 57 |
+| J | 17 | 18 | 39 | 86 | 39 | 73 | 34 | 96 | 99 | 16 | 55 | 32 |
+| K | 78 | 58 | 7 | 24 | 78 | 90 | 94 | 83 | 52 | 25 | 16 | 70 |
+| L | 16 | 64 | 63 | 10 | 31 | 10 | 24 | 89 | 18 | 22 | 37 | 45 |
+
+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': [[[63, 73, 61, 5, 23, 96, 69, 79, 41, 17, 45, 27], [41, 34, 83, 77, 94, 75, 59, 69, 39, 54, 9, 41], [6, 95, 80, 74, 43, 54, 26, 47, 50, 77, 62, 12], [26, 48, 22, 79, 81, 55, 12, 60, 98, 98, 26, 60], [65, 87, 62, 64, 43, 73, 65, 33, 77, 22, 73, 78], [47, 99, 92, 92, 71, 15, 36, 72, 15, 90, 80, 92], [13, 76, 65, 80, 2, 35, 86, 0, 64, 87, 27, 28], [62, 78, 7, 84, 35, 98, 51, 50, 45, 77, 77, 35], [60, 48, 56, 8, 83, 47, 33, 89, 99, 63, 67, 19], [3, 74, 68, 67, 81, 92, 9, 96, 52, 51, 8, 59], [73, 18, 33, 38, 81, 36, 45, 78, 86, 85, 59, 96], [36, 77, 81, 22, 3, 45, 71, 66, 58, 80, 57, 18]], [[30, 28, 1, 43, 27, 55, 22, 2, 58, 93, 84, 17], [54, 80, 30, 55, 79, 51, 7, 69, 43, 27, 4, 89], [65, 19, 90, 48, 13, 89, 28, 9, 74, 19, 16, 61], [17, 46, 1, 55, 2, 68, 30, 35, 48, 45, 76, 77], [46, 10, 20, 42, 5, 25, 93, 41, 78, 37, 18, 77], [58, 69, 5, 91, 7, 70, 44, 54, 33, 24, 21, 71], [14, 60, 49, 41, 39, 24, 61, 88, 59, 33, 77, 23], [99, 53, 91, 74, 40, 18, 5, 86, 10, 89, 45, 13], [82, 80, 38, 60, 6, 54, 69, 29, 39, 47, 31, 31], [37, 84, 11, 12, 40, 50, 99, 92, 41, 36, 93, 48], [93, 54, 47, 61, 87, 69, 36, 20, 41, 42, 42, 77], [52, 27, 72, 5, 21, 1, 9, 91, 28, 33, 79, 75]], [[8, 2, 5, 69, 86, 37, 42, 99, 5, 36, 35, 35], [8, 61, 46, 71, 22, 25, 72, 24, 98, 42, 33, 19], [38, 27, 17, 91, 58, 94, 42, 50, 27, 39, 21, 19], [6, 47, 21, 35, 88, 55, 24, 78, 7, 5, 23, 80], [66, 46, 55, 36, 85, 15, 3, 65, 32, 2, 10, 78], [96, 11, 32, 86, 21, 66, 41, 87, 64, 79, 50, 18], [64, 67, 36, 94, 56, 12, 43, 88, 10, 49, 92, 42], [44, 1, 64, 1, 82, 11, 4, 95, 85, 11, 5, 39], [89, 62, 36, 65, 1, 33, 99, 68, 76, 83, 56, 43], [97, 22, 16, 38, 82, 86, 65, 6, 5, 83, 63, 94], [93, 19, 34, 76, 98, 12, 20, 97, 98, 43, 10, 40], [98, 94, 67, 54, 1, 14, 10, 21, 34, 25, 16, 16]], [[55, 25, 90, 49, 3, 69, 56, 4, 76, 89, 37, 74], [64, 54, 81, 22, 21, 10, 14, 35, 75, 25, 53, 84], [40, 75, 48, 47, 45, 24, 9, 9, 50, 54, 68, 71], [4, 14, 87, 55, 97, 83, 70, 53, 43, 57, 88, 94], [33, 16, 20, 88, 96, 4, 22, 73, 10, 54, 28, 30], [20, 17, 51, 83, 84, 95, 75, 64, 27, 19, 54, 14], [90, 33, 64, 57, 69, 36, 94, 13, 60, 63, 42, 94], [94, 86, 23, 15, 11, 40, 27, 98, 63, 96, 44, 17], [96, 15, 42, 65, 83, 13, 81, 41, 38, 50, 93, 65], [25, 13, 95, 36, 41, 11, 34, 57, 71, 84, 1, 71], [4, 89, 3, 99, 21, 19, 54, 42, 19, 63, 50, 65], [6, 66, 1, 74, 59, 57, 20, 69, 8, 7, 96, 35]], [[49, 29, 36, 14, 65, 56, 37, 3, 80, 84, 91, 77], [26, 5, 50, 72, 83, 87, 29, 68, 21, 46, 27, 94], [69, 26, 55, 74, 36, 89, 37, 31, 13, 0, 49, 93], [75, 61, 23, 32, 31, 53, 21, 15, 92, 11, 58, 30], [61, 67, 75, 89, 46, 16, 20, 84, 85, 11, 70, 35], [96, 73, 12, 71, 82, 91, 8, 8, 67, 0, 10, 49], [78, 5, 74, 20, 97, 34, 1, 2, 33, 94, 36, 61], [90, 46, 66, 60, 67, 31, 60, 89, 35, 43, 78, 16], [98, 45, 81, 11, 63, 10, 87, 28, 31, 52, 37, 56], [56, 35, 51, 53, 73, 60, 31, 45, 26, 57, 32, 52], [13, 63, 32, 94, 99, 63, 45, 21, 61, 72, 61, 9], [86, 92, 22, 8, 18, 6, 70, 64, 17, 21, 59, 50]], [[51, 58, 28, 95, 48, 90, 29, 14, 5, 45, 75, 99], [62, 8, 82, 31, 61, 50, 82, 24, 78, 64, 18, 27], [67, 61, 24, 38, 77, 75, 90, 31, 63, 71, 42, 7], [74, 52, 71, 36, 72, 0, 73, 13, 10, 32, 54, 10], [65, 43, 92, 13, 3, 19, 36, 99, 49, 10, 30, 90], [88, 74, 12, 16, 13, 75, 2, 61, 78, 80, 77, 30], [31, 49, 66, 55, 16, 78, 89, 39, 82, 66, 7, 9], [97, 95, 25, 17, 58, 20, 93, 41, 18, 51, 66, 32], [75, 83, 14, 50, 12, 69, 32, 65, 22, 38, 64, 54], [43, 43, 88, 31, 75, 15, 7, 21, 15, 47, 13, 13], [16, 20, 81, 54, 72, 20, 24, 20, 72, 25, 21, 3], [1, 66, 90, 62, 37, 6, 94, 52, 81, 69, 72, 12]], [[0, 31, 44, 65, 32, 98, 93, 26, 55, 34, 45, 78], [4, 70, 45, 74, 16, 75, 58, 5, 26, 89, 7, 19], [62, 0, 31, 15, 90, 12, 5, 43, 75, 0, 91, 2], [18, 92, 84, 31, 67, 72, 35, 61, 58, 34, 24, 66], [21, 12, 86, 75, 93, 66, 93, 40, 70, 52, 49, 26], [70, 79, 60, 85, 84, 63, 41, 49, 46, 76, 38, 43], [60, 51, 45, 83, 75, 85, 66, 86, 12, 15, 14, 10], [21, 41, 77, 47, 22, 28, 43, 72, 42, 25, 32, 6], [22, 26, 80, 76, 55, 30, 89, 45, 50, 23, 87, 55], [76, 97, 83, 94, 83, 3, 97, 54, 52, 19, 73, 92], [63, 98, 9, 63, 67, 49, 49, 71, 53, 50, 70, 20], [71, 60, 39, 10, 86, 14, 78, 4, 56, 10, 70, 61]], [[6, 86, 25, 64, 73, 72, 76, 81, 71, 4, 91, 17], [2, 11, 95, 42, 69, 73, 88, 42, 3, 58, 88, 70], [83, 68, 6, 94, 13, 32, 59, 23, 74, 68, 4, 3], [47, 82, 98, 44, 91, 75, 32, 86, 51, 70, 10, 69], [50, 32, 22, 10, 77, 77, 19, 55, 87, 68, 27, 49], [75, 52, 20, 50, 16, 84, 62, 83, 39, 98, 97, 88], [90, 8, 98, 34, 74, 65, 47, 44, 8, 84, 1, 72], [10, 50, 11, 21, 8, 22, 52, 91, 56, 24, 6, 88], [89, 28, 56, 98, 45, 77, 99, 99, 63, 49, 41, 77], [25, 76, 69, 94, 81, 74, 80, 68, 1, 86, 6, 44], [17, 75, 77, 46, 91, 38, 48, 52, 57, 2, 62, 91], [13, 15, 0, 15, 99, 88, 20, 26, 84, 27, 94, 37]], [[90, 84, 72, 56, 76, 58, 53, 15, 70, 88, 98, 34], [43, 90, 91, 19, 68, 24, 32, 48, 59, 87, 48, 3], [21, 58, 74, 16, 69, 76, 70, 79, 90, 1, 36, 72], [11, 99, 88, 54, 20, 72, 45, 40, 23, 27, 57, 47], [77, 93, 97, 88, 87, 76, 85, 74, 89, 72, 66, 30], [68, 27, 34, 87, 39, 88, 62, 78, 67, 59, 82, 9], [3, 64, 66, 0, 43, 25, 50, 71, 36, 15, 16, 4], [22, 72, 22, 63, 71, 20, 83, 3, 26, 66, 48, 17], [49, 45, 64, 69, 99, 17, 9, 65, 55, 83, 95, 19], [42, 65, 96, 1, 30, 23, 80, 85, 26, 81, 65, 71], [96, 48, 27, 60, 83, 14, 83, 30, 92, 13, 9, 83], [89, 65, 10, 8, 43, 76, 33, 41, 97, 38, 5, 9]], [[92, 82, 90, 29, 45, 13, 8, 68, 63, 49, 70, 40], [96, 73, 96, 24, 97, 32, 80, 82, 13, 18, 42, 20], [90, 24, 44, 75, 11, 21, 83, 6, 56, 95, 6, 3], [3, 72, 21, 85, 13, 60, 50, 6, 7, 33, 37, 67], [26, 67, 16, 33, 65, 33, 73, 88, 36, 39, 26, 91], [53, 31, 54, 84, 15, 25, 12, 6, 67, 28, 88, 69], [31, 91, 56, 61, 1, 40, 36, 70, 15, 12, 8, 92], [97, 92, 83, 12, 99, 77, 20, 39, 41, 98, 69, 88], [76, 40, 74, 51, 87, 17, 56, 90, 51, 39, 32, 30], [77, 98, 84, 26, 81, 85, 23, 87, 51, 10, 75, 78], [16, 8, 96, 33, 50, 80, 65, 89, 11, 11, 49, 1], [49, 94, 15, 75, 52, 99, 74, 62, 65, 38, 36, 20]], [[18, 22, 64, 22, 84, 8, 17, 10, 61, 68, 96, 78], [42, 15, 17, 35, 91, 0, 81, 48, 34, 79, 75, 4], [52, 87, 51, 87, 27, 8, 46, 50, 64, 54, 93, 28], [88, 74, 33, 98, 49, 43, 65, 33, 21, 35, 78, 61], [7, 21, 8, 53, 87, 87, 63, 74, 47, 61, 57, 18], [20, 7, 83, 92, 83, 44, 61, 68, 32, 12, 3, 64], [77, 19, 6, 48, 86, 10, 18, 86, 63, 4, 56, 86], [59, 89, 23, 71, 90, 92, 25, 90, 92, 24, 70, 2], [15, 95, 58, 72, 29, 92, 99, 98, 6, 42, 73, 51], [17, 77, 3, 70, 28, 5, 55, 51, 49, 82, 41, 56], [41, 3, 41, 34, 39, 45, 88, 12, 4, 2, 72, 82], [97, 81, 53, 77, 90, 44, 72, 97, 99, 67, 4, 82]], [[63, 87, 30, 96, 57, 43, 8, 42, 8, 74, 23, 58], [50, 99, 78, 89, 16, 6, 19, 89, 20, 86, 10, 63], [35, 33, 57, 9, 15, 78, 49, 30, 3, 40, 2, 86], [66, 60, 75, 71, 77, 80, 17, 31, 35, 25, 44, 86], [84, 45, 20, 48, 55, 23, 81, 45, 32, 70, 87, 70], [42, 24, 61, 57, 36, 63, 38, 92, 35, 40, 11, 76], [64, 45, 97, 15, 39, 10, 90, 61, 86, 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'j': 'C', 'k': 'C', 'cost': 51}, {'i': 'K', 'j': 'C', 'k': 'D', 'cost': 87}, {'i': 'K', 'j': 'C', 'k': 'E', 'cost': 27}, {'i': 'K', 'j': 'C', 'k': 'F', 'cost': 8}, {'i': 'K', 'j': 'C', 'k': 'G', 'cost': 46}, {'i': 'K', 'j': 'C', 'k': 'H', 'cost': 50}, {'i': 'K', 'j': 'C', 'k': 'I', 'cost': 64}, {'i': 'K', 'j': 'C', 'k': 'J', 'cost': 54}, {'i': 'K', 'j': 'C', 'k': 'K', 'cost': 93}, {'i': 'K', 'j': 'C', 'k': 'L', 'cost': 28}, {'i': 'K', 'j': 'D', 'k': 'A', 'cost': 88}, {'i': 'K', 'j': 'D', 'k': 'B', 'cost': 74}, {'i': 'K', 'j': 'D', 'k': 'C', 'cost': 33}, {'i': 'K', 'j': 'D', 'k': 'D', 'cost': 98}, {'i': 'K', 'j': 'D', 'k': 'E', 'cost': 49}, {'i': 'K', 'j': 'D', 'k': 'F', 'cost': 43}, {'i': 'K', 'j': 'D', 'k': 'G', 'cost': 65}, {'i': 'K', 'j': 'D', 'k': 'H', 'cost': 33}, {'i': 'K', 'j': 'D', 'k': 'I', 'cost': 21}, {'i': 'K', 'j': 'D', 'k': 'J', 'cost': 35}, {'i': 'K', 'j': 'D', 'k': 'K', 'cost': 78}, {'i': 'K', 'j': 'D', 'k': 'L', 'cost': 61}, {'i': 'K', 'j': 'E', 'k': 'A', 'cost': 7}, {'i': 'K', 'j': 'E', 'k': 'B', 'cost': 21}, {'i': 'K', 'j': 'E', 'k': 'C', 'cost': 8}, {'i': 'K', 'j': 'E', 'k': 'D', 'cost': 53}, {'i': 'K', 'j': 'E', 'k': 'E', 'cost': 87}, {'i': 'K', 'j': 'E', 'k': 'F', 'cost': 87}, {'i': 'K', 'j': 'E', 'k': 'G', 'cost': 63}, {'i': 'K', 'j': 'E', 'k': 'H', 'cost': 74}, {'i': 'K', 'j': 'E', 'k': 'I', 'cost': 47}, {'i': 'K', 'j': 'E', 'k': 'J', 'cost': 61}, {'i': 'K', 'j': 'E', 'k': 'K', 'cost': 57}, {'i': 'K', 'j': 'E', 'k': 'L', 'cost': 18}, {'i': 'K', 'j': 'F', 'k': 'A', 'cost': 20}, {'i': 'K', 'j': 'F', 'k': 'B', 'cost': 7}, {'i': 'K', 'j': 'F', 'k': 'C', 'cost': 83}, {'i': 'K', 'j': 'F', 'k': 'D', 'cost': 92}, {'i': 'K', 'j': 'F', 'k': 'E', 'cost': 83}, {'i': 'K', 'j': 'F', 'k': 'F', 'cost': 44}, {'i': 'K', 'j': 'F', 'k': 'G', 'cost': 61}, {'i': 'K', 'j': 'F', 'k': 'H', 'cost': 68}, {'i': 'K', 'j': 'F', 'k': 'I', 'cost': 32}, {'i': 'K', 'j': 'F', 'k': 'J', 'cost': 12}, {'i': 'K', 'j': 'F', 'k': 'K', 'cost': 3}, {'i': 'K', 'j': 'F', 'k': 'L', 'cost': 64}, {'i': 'K', 'j': 'G', 'k': 'A', 'cost': 77}, {'i': 'K', 'j': 'G', 'k': 'B', 'cost': 19}, {'i': 'K', 'j': 'G', 'k': 'C', 'cost': 6}, {'i': 'K', 'j': 'G', 'k': 'D', 'cost': 48}, {'i': 'K', 'j': 'G', 'k': 'E', 'cost': 86}, {'i': 'K', 'j': 'G', 'k': 'F', 'cost': 10}, {'i': 'K', 'j': 'G', 'k': 'G', 'cost': 18}, {'i': 'K', 'j': 'G', 'k': 'H', 'cost': 86}, {'i': 'K', 'j': 'G', 'k': 'I', 'cost': 63}, {'i': 'K', 'j': 'G', 'k': 'J', 'cost': 4}, {'i': 'K', 'j': 'G', 'k': 'K', 'cost': 56}, {'i': 'K', 'j': 'G', 'k': 'L', 'cost': 86}, {'i': 'K', 'j': 'H', 'k': 'A', 'cost': 59}, {'i': 'K', 'j': 'H', 'k': 'B', 'cost': 89}, {'i': 'K', 'j': 'H', 'k': 'C', 'cost': 23}, {'i': 'K', 'j': 'H', 'k': 'D', 'cost': 71}, {'i': 'K', 'j': 'H', 'k': 'E', 'cost': 90}, {'i': 'K', 'j': 'H', 'k': 'F', 'cost': 92}, {'i': 'K', 'j': 'H', 'k': 'G', 'cost': 25}, {'i': 'K', 'j': 'H', 'k': 'H', 'cost': 90}, {'i': 'K', 'j': 'H', 'k': 'I', 'cost': 92}, {'i': 'K', 'j': 'H', 'k': 'J', 'cost': 24}, {'i': 'K', 'j': 'H', 'k': 'K', 'cost': 70}, {'i': 'K', 'j': 'H', 'k': 'L', 'cost': 2}, {'i': 'K', 'j': 'I', 'k': 'A', 'cost': 15}, {'i': 'K', 'j': 'I', 'k': 'B', 'cost': 95}, {'i': 'K', 'j': 'I', 'k': 'C', 'cost': 58}, {'i': 'K', 'j': 'I', 'k': 'D', 'cost': 72}, {'i': 'K', 'j': 'I', 'k': 'E', 'cost': 29}, {'i': 'K', 'j': 'I', 'k': 'F', 'cost': 92}, {'i': 'K', 'j': 'I', 'k': 'G', 'cost': 99}, {'i': 'K', 'j': 'I', 'k': 'H', 'cost': 98}, {'i': 'K', 'j': 'I', 'k': 'I', 'cost': 6}, {'i': 'K', 'j': 'I', 'k': 'J', 'cost': 42}, {'i': 'K', 'j': 'I', 'k': 'K', 'cost': 73}, {'i': 'K', 'j': 'I', 'k': 'L', 'cost': 51}, {'i': 'K', 'j': 'J', 'k': 'A', 'cost': 17}, {'i': 'K', 'j': 'J', 'k': 'B', 'cost': 77}, {'i': 'K', 'j': 'J', 'k': 'C', 'cost': 3}, {'i': 'K', 'j': 'J', 'k': 'D', 'cost': 70}, {'i': 'K', 'j': 'J', 'k': 'E', 'cost': 28}, {'i': 'K', 'j': 'J', 'k': 'F', 'cost': 5}, {'i': 'K', 'j': 'J', 'k': 'G', 'cost': 55}, {'i': 'K', 'j': 'J', 'k': 'H', 'cost': 51}, {'i': 'K', 'j': 'J', 'k': 'I', 'cost': 49}, {'i': 'K', 'j': 'J', 'k': 'J', 'cost': 82}, {'i': 'K', 'j': 'J', 'k': 'K', 'cost': 41}, {'i': 'K', 'j': 'J', 'k': 'L', 'cost': 56}, {'i': 'K', 'j': 'K', 'k': 'A', 'cost': 41}, {'i': 'K', 'j': 'K', 'k': 'B', 'cost': 3}, {'i': 'K', 'j': 'K', 'k': 'C', 'cost': 41}, {'i': 'K', 'j': 'K', 'k': 'D', 'cost': 34}, {'i': 'K', 'j': 'K', 'k': 'E', 'cost': 39}, {'i': 'K', 'j': 'K', 'k': 'F', 'cost': 45}, {'i': 'K', 'j': 'K', 'k': 'G', 'cost': 88}, {'i': 'K', 'j': 'K', 'k': 'H', 'cost': 12}, {'i': 'K', 'j': 'K', 'k': 'I', 'cost': 4}, {'i': 'K', 'j': 'K', 'k': 'J', 'cost': 2}, {'i': 'K', 'j': 'K', 'k': 'K', 'cost': 72}, {'i': 'K', 'j': 'K', 'k': 'L', 'cost': 82}, {'i': 'K', 'j': 'L', 'k': 'A', 'cost': 97}, {'i': 'K', 'j': 'L', 'k': 'B', 'cost': 81}, {'i': 'K', 'j': 'L', 'k': 'C', 'cost': 53}, {'i': 'K', 'j': 'L', 'k': 'D', 'cost': 77}, {'i': 'K', 'j': 'L', 'k': 'E', 'cost': 90}, {'i': 'K', 'j': 'L', 'k': 'F', 'cost': 44}, {'i': 'K', 'j': 'L', 'k': 'G', 'cost': 72}, {'i': 'K', 'j': 'L', 'k': 'H', 'cost': 97}, {'i': 'K', 'j': 'L', 'k': 'I', 'cost': 99}, {'i': 'K', 'j': 'L', 'k': 'J', 'cost': 67}, {'i': 'K', 'j': 'L', 'k': 'K', 'cost': 4}, {'i': 'K', 'j': 'L', 'k': 'L', 'cost': 82}, {'i': 'L', 'j': 'A', 'k': 'A', 'cost': 63}, {'i': 'L', 'j': 'A', 'k': 'B', 'cost': 87}, {'i': 'L', 'j': 'A', 'k': 'C', 'cost': 30}, {'i': 'L', 'j': 'A', 'k': 'D', 'cost': 96}, {'i': 'L', 'j': 'A', 'k': 'E', 'cost': 57}, {'i': 'L', 'j': 'A', 'k': 'F', 'cost': 43}, {'i': 'L', 'j': 'A', 'k': 'G', 'cost': 8}, {'i': 'L', 'j': 'A', 'k': 'H', 'cost': 42}, {'i': 'L', 'j': 'A', 'k': 'I', 'cost': 8}, {'i': 'L', 'j': 'A', 'k': 'J', 'cost': 74}, {'i': 'L', 'j': 'A', 'k': 'K', 'cost': 23}, {'i': 'L', 'j': 'A', 'k': 'L', 'cost': 58}, {'i': 'L', 'j': 'B', 'k': 'A', 'cost': 50}, {'i': 'L', 'j': 'B', 'k': 'B', 'cost': 99}, {'i': 'L', 'j': 'B', 'k': 'C', 'cost': 78}, {'i': 'L', 'j': 'B', 'k': 'D', 'cost': 89}, {'i': 'L', 'j': 'B', 'k': 'E', 'cost': 16}, {'i': 'L', 'j': 'B', 'k': 'F', 'cost': 6}, {'i': 'L', 'j': 'B', 'k': 'G', 'cost': 19}, {'i': 'L', 'j': 'B', 'k': 'H', 'cost': 89}, {'i': 'L', 'j': 'B', 'k': 'I', 'cost': 20}, {'i': 'L', 'j': 'B', 'k': 'J', 'cost': 86}, {'i': 'L', 'j': 'B', 'k': 'K', 'cost': 10}, {'i': 'L', 'j': 'B', 'k': 'L', 'cost': 63}, {'i': 'L', 'j': 'C', 'k': 'A', 'cost': 35}, {'i': 'L', 'j': 'C', 'k': 'B', 'cost': 33}, {'i': 'L', 'j': 'C', 'k': 'C', 'cost': 57}, {'i': 'L', 'j': 'C', 'k': 'D', 'cost': 9}, {'i': 'L', 'j': 'C', 'k': 'E', 'cost': 15}, {'i': 'L', 'j': 'C', 'k': 'F', 'cost': 78}, {'i': 'L', 'j': 'C', 'k': 'G', 'cost': 49}, {'i': 'L', 'j': 'C', 'k': 'H', 'cost': 30}, {'i': 'L', 'j': 'C', 'k': 'I', 'cost': 3}, {'i': 'L', 'j': 'C', 'k': 'J', 'cost': 40}, {'i': 'L', 'j': 'C', 'k': 'K', 'cost': 2}, {'i': 'L', 'j': 'C', 'k': 'L', 'cost': 86}, {'i': 'L', 'j': 'D', 'k': 'A', 'cost': 66}, {'i': 'L', 'j': 'D', 'k': 'B', 'cost': 60}, {'i': 'L', 'j': 'D', 'k': 'C', 'cost': 75}, {'i': 'L', 'j': 'D', 'k': 'D', 'cost': 71}, {'i': 'L', 'j': 'D', 'k': 'E', 'cost': 77}, {'i': 'L', 'j': 'D', 'k': 'F', 'cost': 80}, {'i': 'L', 'j': 'D', 'k': 'G', 'cost': 17}, {'i': 'L', 'j': 'D', 'k': 'H', 'cost': 31}, {'i': 'L', 'j': 'D', 'k': 'I', 'cost': 35}, {'i': 'L', 'j': 'D', 'k': 'J', 'cost': 25}, {'i': 'L', 'j': 'D', 'k': 'K', 'cost': 44}, {'i': 'L', 'j': 'D', 'k': 'L', 'cost': 86}, {'i': 'L', 'j': 'E', 'k': 'A', 'cost': 84}, {'i': 'L', 'j': 'E', 'k': 'B', 'cost': 45}, {'i': 'L', 'j': 'E', 'k': 'C', 'cost': 20}, {'i': 'L', 'j': 'E', 'k': 'D', 'cost': 48}, {'i': 'L', 'j': 'E', 'k': 'E', 'cost': 55}, {'i': 'L', 'j': 'E', 'k': 'F', 'cost': 23}, {'i': 'L', 'j': 'E', 'k': 'G', 'cost': 81}, {'i': 'L', 'j': 'E', 'k': 'H', 'cost': 45}, {'i': 'L', 'j': 'E', 'k': 'I', 'cost': 32}, {'i': 'L', 'j': 'E', 'k': 'J', 'cost': 70}, {'i': 'L', 'j': 'E', 'k': 'K', 'cost': 87}, {'i': 'L', 'j': 'E', 'k': 'L', 'cost': 70}, {'i': 'L', 'j': 'F', 'k': 'A', 'cost': 42}, {'i': 'L', 'j': 'F', 'k': 'B', 'cost': 24}, {'i': 'L', 'j': 'F', 'k': 'C', 'cost': 61}, {'i': 'L', 'j': 'F', 'k': 'D', 'cost': 57}, {'i': 'L', 'j': 'F', 'k': 'E', 'cost': 36}, {'i': 'L', 'j': 'F', 'k': 'F', 'cost': 63}, {'i': 'L', 'j': 'F', 'k': 'G', 'cost': 38}, {'i': 'L', 'j': 'F', 'k': 'H', 'cost': 92}, {'i': 'L', 'j': 'F', 'k': 'I', 'cost': 35}, {'i': 'L', 'j': 'F', 'k': 'J', 'cost': 40}, {'i': 'L', 'j': 'F', 'k': 'K', 'cost': 11}, {'i': 'L', 'j': 'F', 'k': 'L', 'cost': 76}, {'i': 'L', 'j': 'G', 'k': 'A', 'cost': 64}, {'i': 'L', 'j': 'G', 'k': 'B', 'cost': 45}, {'i': 'L', 'j': 'G', 'k': 'C', 'cost': 97}, {'i': 'L', 'j': 'G', 'k': 'D', 'cost': 15}, {'i': 'L', 'j': 'G', 'k': 'E', 'cost': 39}, {'i': 'L', 'j': 'G', 'k': 'F', 'cost': 10}, {'i': 'L', 'j': 'G', 'k': 'G', 'cost': 90}, {'i': 'L', 'j': 'G', 'k': 'H', 'cost': 61}, {'i': 'L', 'j': 'G', 'k': 'I', 'cost': 86}, {'i': 'L', 'j': 'G', 'k': 'J', 'cost': 56}, {'i': 'L', 'j': 'G', 'k': 'K', 'cost': 30}, {'i': 'L', 'j': 'G', 'k': 'L', 'cost': 94}, {'i': 'L', 'j': 'H', 'k': 'A', 'cost': 2}, {'i': 'L', 'j': 'H', 'k': 'B', 'cost': 40}, {'i': 'L', 'j': 'H', 'k': 'C', 'cost': 34}, {'i': 'L', 'j': 'H', 'k': 'D', 'cost': 62}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 29}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 76}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 68}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 61}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 67}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 1}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 6}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 42}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 72}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 97}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 93}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 13}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 81}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 40}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 1}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 75}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 55}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 86}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 70}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 57}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 17}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 18}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 39}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 86}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 39}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 73}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 34}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 96}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 99}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 16}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 55}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 32}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 78}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 58}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 7}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 24}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 78}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 90}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 94}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 83}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 52}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 25}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 16}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 70}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 16}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 64}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 63}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 10}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 31}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 10}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 24}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 89}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 18}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 22}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 37}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 45}]}","[['A', 'G', 'H'], ['B', 'E', 'E'], ['C', 'H', 'B'], ['D', 'L', 'C'], ['E', 'C', 'J'], ['F', 'D', 'F'], ['G', 'A', 'A'], ['H', 'B', 'I'], ['I', 'J', 'D'], ['J', 'K', 'L'], ['K', 'F', 'K'], ['L', 'I', 'G']]",40,json,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.
+
+{
+  ""num_spaces"": 9,
+  ""index_identifiers"": [
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8,
+    9
+  ]
+}
+
+# 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=1
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 84 | 61 | 49 | 80 | 51 | 22 | 52 | 41 | 61 |
+| 2 | 14 | 52 | 8 | 51 | 98 | 91 | 80 | 73 | 40 |
+| 3 | 51 | 90 | 9 | 0 | 97 | 68 | 1 | 20 | 8 |
+| 4 | 26 | 32 | 1 | 14 | 13 | 77 | 98 | 27 | 99 |
+| 5 | 36 | 61 | 5 | 8 | 66 | 39 | 96 | 4 | 91 |
+| 6 | 72 | 50 | 52 | 61 | 8 | 57 | 36 | 76 | 85 |
+| 7 | 73 | 38 | 9 | 96 | 78 | 0 | 6 | 62 | 60 |
+| 8 | 21 | 59 | 10 | 42 | 73 | 7 | 87 | 16 | 4 |
+| 9 | 32 | 54 | 62 | 44 | 39 | 74 | 55 | 61 | 29 |
+
+## space_id=2
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 50 | 72 | 19 | 22 | 53 | 73 | 1 | 69 | 6 |
+| 2 | 4 | 79 | 52 | 44 | 26 | 62 | 33 | 87 | 57 |
+| 3 | 51 | 48 | 24 | 8 | 4 | 71 | 63 | 87 | 79 |
+| 4 | 18 | 8 | 44 | 94 | 52 | 85 | 61 | 46 | 68 |
+| 5 | 51 | 10 | 91 | 89 | 73 | 43 | 36 | 4 | 1 |
+| 6 | 46 | 27 | 95 | 65 | 82 | 37 | 67 | 47 | 75 |
+| 7 | 91 | 53 | 40 | 19 | 74 | 2 | 84 | 58 | 44 |
+| 8 | 46 | 7 | 71 | 73 | 85 | 17 | 24 | 46 | 95 |
+| 9 | 82 | 31 | 4 | 74 | 92 | 76 | 34 | 75 | 78 |
+
+## space_id=3
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 37 | 75 | 98 | 67 | 74 | 8 | 43 | 88 | 20 |
+| 2 | 67 | 97 | 14 | 63 | 81 | 75 | 89 | 83 | 93 |
+| 3 | 48 | 13 | 25 | 0 | 81 | 49 | 8 | 87 | 98 |
+| 4 | 15 | 49 | 63 | 88 | 24 | 23 | 34 | 61 | 12 |
+| 5 | 64 | 34 | 83 | 10 | 69 | 94 | 4 | 20 | 23 |
+| 6 | 97 | 75 | 73 | 28 | 42 | 6 | 10 | 31 | 49 |
+| 7 | 95 | 86 | 5 | 58 | 7 | 24 | 13 | 59 | 85 |
+| 8 | 10 | 16 | 70 | 38 | 92 | 87 | 27 | 52 | 53 |
+| 9 | 25 | 73 | 18 | 91 | 69 | 21 | 31 | 43 | 50 |
+
+## space_id=4
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 42 | 97 | 63 | 93 | 28 | 43 | 56 | 6 | 88 |
+| 2 | 87 | 83 | 43 | 62 | 71 | 73 | 47 | 36 | 95 |
+| 3 | 46 | 24 | 15 | 6 | 48 | 43 | 43 | 30 | 15 |
+| 4 | 97 | 82 | 31 | 13 | 93 | 23 | 63 | 50 | 26 |
+| 5 | 80 | 35 | 89 | 26 | 68 | 54 | 45 | 1 | 0 |
+| 6 | 95 | 74 | 40 | 26 | 15 | 72 | 34 | 58 | 85 |
+| 7 | 78 | 63 | 48 | 75 | 56 | 93 | 39 | 59 | 73 |
+| 8 | 95 | 60 | 34 | 27 | 44 | 68 | 27 | 4 | 0 |
+| 9 | 75 | 99 | 77 | 84 | 94 | 86 | 97 | 89 | 39 |
+
+## space_id=5
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 68 | 93 | 73 | 76 | 69 | 98 | 86 | 81 | 13 |
+| 2 | 58 | 77 | 53 | 36 | 86 | 6 | 6 | 99 | 14 |
+| 3 | 13 | 2 | 19 | 84 | 61 | 98 | 48 | 23 | 13 |
+| 4 | 61 | 21 | 48 | 86 | 21 | 20 | 5 | 91 | 90 |
+| 5 | 27 | 48 | 17 | 48 | 52 | 44 | 46 | 70 | 45 |
+| 6 | 91 | 83 | 87 | 88 | 21 | 73 | 49 | 48 | 0 |
+| 7 | 3 | 95 | 40 | 40 | 94 | 44 | 41 | 88 | 84 |
+| 8 | 55 | 91 | 16 | 37 | 12 | 71 | 94 | 13 | 39 |
+| 9 | 60 | 18 | 26 | 19 | 4 | 29 | 52 | 80 | 67 |
+
+## space_id=6
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 17 | 77 | 65 | 94 | 1 | 49 | 67 | 43 | 10 |
+| 2 | 93 | 28 | 69 | 19 | 80 | 89 | 10 | 45 | 72 |
+| 3 | 21 | 43 | 93 | 56 | 95 | 59 | 15 | 15 | 56 |
+| 4 | 31 | 18 | 48 | 25 | 23 | 45 | 94 | 93 | 53 |
+| 5 | 54 | 16 | 23 | 20 | 55 | 12 | 50 | 37 | 30 |
+| 6 | 3 | 5 | 45 | 21 | 83 | 62 | 23 | 31 | 54 |
+| 7 | 61 | 49 | 56 | 6 | 70 | 4 | 58 | 90 | 83 |
+| 8 | 48 | 16 | 22 | 28 | 59 | 66 | 55 | 24 | 75 |
+| 9 | 79 | 63 | 0 | 34 | 60 | 80 | 17 | 31 | 84 |
+
+## space_id=7
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 73 | 44 | 49 | 12 | 37 | 89 | 27 | 0 | 9 |
+| 2 | 54 | 38 | 29 | 14 | 45 | 49 | 2 | 35 | 19 |
+| 3 | 0 | 89 | 88 | 45 | 2 | 79 | 69 | 77 | 46 |
+| 4 | 53 | 2 | 58 | 59 | 96 | 42 | 11 | 31 | 86 |
+| 5 | 59 | 52 | 10 | 71 | 61 | 5 | 99 | 65 | 51 |
+| 6 | 90 | 99 | 85 | 1 | 42 | 98 | 39 | 92 | 71 |
+| 7 | 70 | 43 | 31 | 67 | 78 | 13 | 24 | 62 | 21 |
+| 8 | 45 | 81 | 90 | 84 | 97 | 61 | 87 | 82 | 16 |
+| 9 | 46 | 91 | 88 | 52 | 98 | 31 | 9 | 26 | 20 |
+
+## space_id=8
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 15 | 48 | 36 | 28 | 74 | 61 | 61 | 53 | 9 |
+| 2 | 74 | 59 | 59 | 6 | 39 | 31 | 30 | 63 | 36 |
+| 3 | 1 | 78 | 46 | 24 | 26 | 10 | 97 | 33 | 6 |
+| 4 | 30 | 96 | 97 | 97 | 21 | 76 | 55 | 94 | 21 |
+| 5 | 47 | 66 | 65 | 9 | 12 | 35 | 25 | 94 | 7 |
+| 6 | 84 | 43 | 92 | 15 | 13 | 79 | 37 | 74 | 55 |
+| 7 | 21 | 26 | 88 | 97 | 32 | 11 | 84 | 29 | 31 |
+| 8 | 80 | 12 | 27 | 14 | 86 | 43 | 82 | 43 | 95 |
+| 9 | 78 | 34 | 98 | 37 | 7 | 39 | 37 | 50 | 15 |
+
+## space_id=9
+| artwork_id\lighting_setup_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 60 | 77 | 55 | 38 | 4 | 93 | 63 | 89 | 90 |
+| 2 | 43 | 32 | 15 | 89 | 1 | 16 | 82 | 26 | 89 |
+| 3 | 98 | 23 | 0 | 91 | 38 | 59 | 11 | 20 | 51 |
+| 4 | 94 | 53 | 63 | 2 | 52 | 58 | 5 | 89 | 91 |
+| 5 | 79 | 83 | 60 | 79 | 86 | 4 | 95 | 90 | 46 |
+| 6 | 45 | 14 | 21 | 20 | 8 | 15 | 92 | 74 | 42 |
+| 7 | 84 | 10 | 68 | 45 | 13 | 85 | 4 | 42 | 33 |
+| 8 | 1 | 80 | 84 | 4 | 65 | 43 | 39 | 92 | 11 |
+| 9 | 35 | 19 | 36 | 15 | 93 | 41 | 36 | 93 | 91 |
+
+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': [[[84, 61, 49, 80, 51, 22, 52, 41, 61], [14, 52, 8, 51, 98, 91, 80, 73, 40], [51, 90, 9, 0, 97, 68, 1, 20, 8], [26, 32, 1, 14, 13, 77, 98, 27, 99], [36, 61, 5, 8, 66, 39, 96, 4, 91], [72, 50, 52, 61, 8, 57, 36, 76, 85], [73, 38, 9, 96, 78, 0, 6, 62, 60], [21, 59, 10, 42, 73, 7, 87, 16, 4], [32, 54, 62, 44, 39, 74, 55, 61, 29]], [[50, 72, 19, 22, 53, 73, 1, 69, 6], [4, 79, 52, 44, 26, 62, 33, 87, 57], [51, 48, 24, 8, 4, 71, 63, 87, 79], [18, 8, 44, 94, 52, 85, 61, 46, 68], [51, 10, 91, 89, 73, 43, 36, 4, 1], [46, 27, 95, 65, 82, 37, 67, 47, 75], [91, 53, 40, 19, 74, 2, 84, 58, 44], [46, 7, 71, 73, 85, 17, 24, 46, 95], [82, 31, 4, 74, 92, 76, 34, 75, 78]], [[37, 75, 98, 67, 74, 8, 43, 88, 20], [67, 97, 14, 63, 81, 75, 89, 83, 93], [48, 13, 25, 0, 81, 49, 8, 87, 98], [15, 49, 63, 88, 24, 23, 34, 61, 12], [64, 34, 83, 10, 69, 94, 4, 20, 23], [97, 75, 73, 28, 42, 6, 10, 31, 49], [95, 86, 5, 58, 7, 24, 13, 59, 85], [10, 16, 70, 38, 92, 87, 27, 52, 53], [25, 73, 18, 91, 69, 21, 31, 43, 50]], [[42, 97, 63, 93, 28, 43, 56, 6, 88], [87, 83, 43, 62, 71, 73, 47, 36, 95], [46, 24, 15, 6, 48, 43, 43, 30, 15], [97, 82, 31, 13, 93, 23, 63, 50, 26], [80, 35, 89, 26, 68, 54, 45, 1, 0], [95, 74, 40, 26, 15, 72, 34, 58, 85], [78, 63, 48, 75, 56, 93, 39, 59, 73], [95, 60, 34, 27, 44, 68, 27, 4, 0], [75, 99, 77, 84, 94, 86, 97, 89, 39]], [[68, 93, 73, 76, 69, 98, 86, 81, 13], [58, 77, 53, 36, 86, 6, 6, 99, 14], [13, 2, 19, 84, 61, 98, 48, 23, 13], [61, 21, 48, 86, 21, 20, 5, 91, 90], [27, 48, 17, 48, 52, 44, 46, 70, 45], [91, 83, 87, 88, 21, 73, 49, 48, 0], [3, 95, 40, 40, 94, 44, 41, 88, 84], [55, 91, 16, 37, 12, 71, 94, 13, 39], [60, 18, 26, 19, 4, 29, 52, 80, 67]], [[17, 77, 65, 94, 1, 49, 67, 43, 10], [93, 28, 69, 19, 80, 89, 10, 45, 72], [21, 43, 93, 56, 95, 59, 15, 15, 56], [31, 18, 48, 25, 23, 45, 94, 93, 53], [54, 16, 23, 20, 55, 12, 50, 37, 30], [3, 5, 45, 21, 83, 62, 23, 31, 54], [61, 49, 56, 6, 70, 4, 58, 90, 83], [48, 16, 22, 28, 59, 66, 55, 24, 75], [79, 63, 0, 34, 60, 80, 17, 31, 84]], [[73, 44, 49, 12, 37, 89, 27, 0, 9], [54, 38, 29, 14, 45, 49, 2, 35, 19], [0, 89, 88, 45, 2, 79, 69, 77, 46], [53, 2, 58, 59, 96, 42, 11, 31, 86], [59, 52, 10, 71, 61, 5, 99, 65, 51], [90, 99, 85, 1, 42, 98, 39, 92, 71], [70, 43, 31, 67, 78, 13, 24, 62, 21], [45, 81, 90, 84, 97, 61, 87, 82, 16], [46, 91, 88, 52, 98, 31, 9, 26, 20]], [[15, 48, 36, 28, 74, 61, 61, 53, 9], [74, 59, 59, 6, 39, 31, 30, 63, 36], [1, 78, 46, 24, 26, 10, 97, 33, 6], [30, 96, 97, 97, 21, 76, 55, 94, 21], [47, 66, 65, 9, 12, 35, 25, 94, 7], [84, 43, 92, 15, 13, 79, 37, 74, 55], [21, 26, 88, 97, 32, 11, 84, 29, 31], [80, 12, 27, 14, 86, 43, 82, 43, 95], [78, 34, 98, 37, 7, 39, 37, 50, 15]], [[60, 77, 55, 38, 4, 93, 63, 89, 90], [43, 32, 15, 89, 1, 16, 82, 26, 89], [98, 23, 0, 91, 38, 59, 11, 20, 51], [94, 53, 63, 2, 52, 58, 5, 89, 91], [79, 83, 60, 79, 86, 4, 95, 90, 46], [45, 14, 21, 20, 8, 15, 92, 74, 42], [84, 10, 68, 45, 13, 85, 4, 42, 33], [1, 80, 84, 4, 65, 43, 39, 92, 11], [35, 19, 36, 15, 93, 41, 36, 93, 91]]], 'objective': 19.0}","[[0, 6, 5], [1, 0, 6], [2, 4, 3], [3, 7, 7], [4, 5, 8], [5, 8, 2], [6, 3, 1], [7, 2, 0], [8, 1, 4]]",19.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 84}, {'i': 1, 'j': 1, 'k': 2, 'cost': 61}, {'i': 1, 'j': 1, 'k': 3, 'cost': 49}, {'i': 1, 'j': 1, 'k': 4, 'cost': 80}, {'i': 1, 'j': 1, 'k': 5, 'cost': 51}, {'i': 1, 'j': 1, 'k': 6, 'cost': 22}, {'i': 1, 'j': 1, 'k': 7, 'cost': 52}, {'i': 1, 'j': 1, 'k': 8, 'cost': 41}, {'i': 1, 'j': 1, 'k': 9, 'cost': 61}, {'i': 1, 'j': 2, 'k': 1, 'cost': 14}, {'i': 1, 'j': 2, 'k': 2, 'cost': 52}, {'i': 1, 'j': 2, 'k': 3, 'cost': 8}, {'i': 1, 'j': 2, 'k': 4, 'cost': 51}, {'i': 1, 'j': 2, 'k': 5, 'cost': 98}, {'i': 1, 'j': 2, 'k': 6, 'cost': 91}, {'i': 1, 'j': 2, 'k': 7, 'cost': 80}, {'i': 1, 'j': 2, 'k': 8, 'cost': 73}, {'i': 1, 'j': 2, 'k': 9, 'cost': 40}, {'i': 1, 'j': 3, 'k': 1, 'cost': 51}, {'i': 1, 'j': 3, 'k': 2, 'cost': 90}, {'i': 1, 'j': 3, 'k': 3, 'cost': 9}, {'i': 1, 'j': 3, 'k': 4, 'cost': 0}, {'i': 1, 'j': 3, 'k': 5, 'cost': 97}, {'i': 1, 'j': 3, 'k': 6, 'cost': 68}, {'i': 1, 'j': 3, 'k': 7, 'cost': 1}, {'i': 1, 'j': 3, 'k': 8, 'cost': 20}, {'i': 1, 'j': 3, 'k': 9, 'cost': 8}, {'i': 1, 'j': 4, 'k': 1, 'cost': 26}, {'i': 1, 'j': 4, 'k': 2, 'cost': 32}, {'i': 1, 'j': 4, 'k': 3, 'cost': 1}, {'i': 1, 'j': 4, 'k': 4, 'cost': 14}, {'i': 1, 'j': 4, 'k': 5, 'cost': 13}, {'i': 1, 'j': 4, 'k': 6, 'cost': 77}, {'i': 1, 'j': 4, 'k': 7, 'cost': 98}, {'i': 1, 'j': 4, 'k': 8, 'cost': 27}, {'i': 1, 'j': 4, 'k': 9, 'cost': 99}, {'i': 1, 'j': 5, 'k': 1, 'cost': 36}, {'i': 1, 'j': 5, 'k': 2, 'cost': 61}, {'i': 1, 'j': 5, 'k': 3, 'cost': 5}, {'i': 1, 'j': 5, 'k': 4, 'cost': 8}, {'i': 1, 'j': 5, 'k': 5, 'cost': 66}, {'i': 1, 'j': 5, 'k': 6, 'cost': 39}, {'i': 1, 'j': 5, 'k': 7, 'cost': 96}, {'i': 1, 'j': 5, 'k': 8, 'cost': 4}, {'i': 1, 'j': 5, 'k': 9, 'cost': 91}, {'i': 1, 'j': 6, 'k': 1, 'cost': 72}, {'i': 1, 'j': 6, 'k': 2, 'cost': 50}, {'i': 1, 'j': 6, 'k': 3, 'cost': 52}, {'i': 1, 'j': 6, 'k': 4, 'cost': 61}, {'i': 1, 'j': 6, 'k': 5, 'cost': 8}, {'i': 1, 'j': 6, 'k': 6, 'cost': 57}, {'i': 1, 'j': 6, 'k': 7, 'cost': 36}, {'i': 1, 'j': 6, 'k': 8, 'cost': 76}, {'i': 1, 'j': 6, 'k': 9, 'cost': 85}, {'i': 1, 'j': 7, 'k': 1, 'cost': 73}, {'i': 1, 'j': 7, 'k': 2, 'cost': 38}, {'i': 1, 'j': 7, 'k': 3, 'cost': 9}, {'i': 1, 'j': 7, 'k': 4, 'cost': 96}, {'i': 1, 'j': 7, 'k': 5, 'cost': 78}, {'i': 1, 'j': 7, 'k': 6, 'cost': 0}, {'i': 1, 'j': 7, 'k': 7, 'cost': 6}, {'i': 1, 'j': 7, 'k': 8, 'cost': 62}, {'i': 1, 'j': 7, 'k': 9, 'cost': 60}, {'i': 1, 'j': 8, 'k': 1, 'cost': 21}, {'i': 1, 'j': 8, 'k': 2, 'cost': 59}, {'i': 1, 'j': 8, 'k': 3, 'cost': 10}, {'i': 1, 'j': 8, 'k': 4, 'cost': 42}, {'i': 1, 'j': 8, 'k': 5, 'cost': 73}, {'i': 1, 'j': 8, 'k': 6, 'cost': 7}, {'i': 1, 'j': 8, 'k': 7, 'cost': 87}, {'i': 1, 'j': 8, 'k': 8, 'cost': 16}, {'i': 1, 'j': 8, 'k': 9, 'cost': 4}, {'i': 1, 'j': 9, 'k': 1, 'cost': 32}, {'i': 1, 'j': 9, 'k': 2, 'cost': 54}, {'i': 1, 'j': 9, 'k': 3, 'cost': 62}, {'i': 1, 'j': 9, 'k': 4, 'cost': 44}, {'i': 1, 'j': 9, 'k': 5, 'cost': 39}, {'i': 1, 'j': 9, 'k': 6, 'cost': 74}, {'i': 1, 'j': 9, 'k': 7, 'cost': 55}, {'i': 1, 'j': 9, 'k': 8, 'cost': 61}, {'i': 1, 'j': 9, 'k': 9, 'cost': 29}, {'i': 2, 'j': 1, 'k': 1, 'cost': 50}, {'i': 2, 'j': 1, 'k': 2, 'cost': 72}, {'i': 2, 'j': 1, 'k': 3, 'cost': 19}, {'i': 2, 'j': 1, 'k': 4, 'cost': 22}, {'i': 2, 'j': 1, 'k': 5, 'cost': 53}, {'i': 2, 'j': 1, 'k': 6, 'cost': 73}, {'i': 2, 'j': 1, 'k': 7, 'cost': 1}, {'i': 2, 'j': 1, 'k': 8, 'cost': 69}, {'i': 2, 'j': 1, 'k': 9, 'cost': 6}, {'i': 2, 'j': 2, 'k': 1, 'cost': 4}, {'i': 2, 'j': 2, 'k': 2, 'cost': 79}, {'i': 2, 'j': 2, 'k': 3, 'cost': 52}, {'i': 2, 'j': 2, 'k': 4, 'cost': 44}, {'i': 2, 'j': 2, 'k': 5, 'cost': 26}, {'i': 2, 'j': 2, 'k': 6, 'cost': 62}, {'i': 2, 'j': 2, 'k': 7, 'cost': 33}, {'i': 2, 'j': 2, 'k': 8, 'cost': 87}, {'i': 2, 'j': 2, 'k': 9, 'cost': 57}, {'i': 2, 'j': 3, 'k': 1, 'cost': 51}, {'i': 2, 'j': 3, 'k': 2, 'cost': 48}, {'i': 2, 'j': 3, 'k': 3, 'cost': 24}, {'i': 2, 'j': 3, 'k': 4, 'cost': 8}, {'i': 2, 'j': 3, 'k': 5, 'cost': 4}, {'i': 2, 'j': 3, 'k': 6, 'cost': 71}, {'i': 2, 'j': 3, 'k': 7, 'cost': 63}, {'i': 2, 'j': 3, 'k': 8, 'cost': 87}, {'i': 2, 'j': 3, 'k': 9, 'cost': 79}, {'i': 2, 'j': 4, 'k': 1, 'cost': 18}, {'i': 2, 'j': 4, 'k': 2, 'cost': 8}, {'i': 2, 'j': 4, 'k': 3, 'cost': 44}, {'i': 2, 'j': 4, 'k': 4, 'cost': 94}, {'i': 2, 'j': 4, 'k': 5, 'cost': 52}, {'i': 2, 'j': 4, 'k': 6, 'cost': 85}, {'i': 2, 'j': 4, 'k': 7, 'cost': 61}, {'i': 2, 'j': 4, 'k': 8, 'cost': 46}, {'i': 2, 'j': 4, 'k': 9, 'cost': 68}, {'i': 2, 'j': 5, 'k': 1, 'cost': 51}, {'i': 2, 'j': 5, 'k': 2, 'cost': 10}, {'i': 2, 'j': 5, 'k': 3, 'cost': 91}, {'i': 2, 'j': 5, 'k': 4, 'cost': 89}, {'i': 2, 'j': 5, 'k': 5, 'cost': 73}, {'i': 2, 'j': 5, 'k': 6, 'cost': 43}, {'i': 2, 'j': 5, 'k': 7, 'cost': 36}, {'i': 2, 'j': 5, 'k': 8, 'cost': 4}, {'i': 2, 'j': 5, 'k': 9, 'cost': 1}, {'i': 2, 'j': 6, 'k': 1, 'cost': 46}, {'i': 2, 'j': 6, 'k': 2, 'cost': 27}, {'i': 2, 'j': 6, 'k': 3, 'cost': 95}, {'i': 2, 'j': 6, 'k': 4, 'cost': 65}, {'i': 2, 'j': 6, 'k': 5, 'cost': 82}, {'i': 2, 'j': 6, 'k': 6, 'cost': 37}, {'i': 2, 'j': 6, 'k': 7, 'cost': 67}, {'i': 2, 'j': 6, 'k': 8, 'cost': 47}, {'i': 2, 'j': 6, 'k': 9, 'cost': 75}, {'i': 2, 'j': 7, 'k': 1, 'cost': 91}, {'i': 2, 'j': 7, 'k': 2, 'cost': 53}, {'i': 2, 'j': 7, 'k': 3, 'cost': 40}, {'i': 2, 'j': 7, 'k': 4, 'cost': 19}, {'i': 2, 'j': 7, 'k': 5, 'cost': 74}, {'i': 2, 'j': 7, 'k': 6, 'cost': 2}, {'i': 2, 'j': 7, 'k': 7, 'cost': 84}, {'i': 2, 'j': 7, 'k': 8, 'cost': 58}, {'i': 2, 'j': 7, 'k': 9, 'cost': 44}, {'i': 2, 'j': 8, 'k': 1, 'cost': 46}, {'i': 2, 'j': 8, 'k': 2, 'cost': 7}, {'i': 2, 'j': 8, 'k': 3, 'cost': 71}, {'i': 2, 'j': 8, 'k': 4, 'cost': 73}, {'i': 2, 'j': 8, 'k': 5, 'cost': 85}, {'i': 2, 'j': 8, 'k': 6, 'cost': 17}, {'i': 2, 'j': 8, 'k': 7, 'cost': 24}, {'i': 2, 'j': 8, 'k': 8, 'cost': 46}, {'i': 2, 'j': 8, 'k': 9, 'cost': 95}, {'i': 2, 'j': 9, 'k': 1, 'cost': 82}, {'i': 2, 'j': 9, 'k': 2, 'cost': 31}, {'i': 2, 'j': 9, 'k': 3, 'cost': 4}, {'i': 2, 'j': 9, 'k': 4, 'cost': 74}, {'i': 2, 'j': 9, 'k': 5, 'cost': 92}, {'i': 2, 'j': 9, 'k': 6, 'cost': 76}, {'i': 2, 'j': 9, 'k': 7, 'cost': 34}, {'i': 2, 'j': 9, 'k': 8, 'cost': 75}, {'i': 2, 'j': 9, 'k': 9, 'cost': 78}, {'i': 3, 'j': 1, 'k': 1, 'cost': 37}, {'i': 3, 'j': 1, 'k': 2, 'cost': 75}, {'i': 3, 'j': 1, 'k': 3, 'cost': 98}, {'i': 3, 'j': 1, 'k': 4, 'cost': 67}, {'i': 3, 'j': 1, 'k': 5, 'cost': 74}, {'i': 3, 'j': 1, 'k': 6, 'cost': 8}, {'i': 3, 'j': 1, 'k': 7, 'cost': 43}, {'i': 3, 'j': 1, 'k': 8, 'cost': 88}, {'i': 3, 'j': 1, 'k': 9, 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{'i': 7, 'j': 4, 'k': 1, 'cost': 53}, {'i': 7, 'j': 4, 'k': 2, 'cost': 2}, {'i': 7, 'j': 4, 'k': 3, 'cost': 58}, {'i': 7, 'j': 4, 'k': 4, 'cost': 59}, {'i': 7, 'j': 4, 'k': 5, 'cost': 96}, {'i': 7, 'j': 4, 'k': 6, 'cost': 42}, {'i': 7, 'j': 4, 'k': 7, 'cost': 11}, {'i': 7, 'j': 4, 'k': 8, 'cost': 31}, {'i': 7, 'j': 4, 'k': 9, 'cost': 86}, {'i': 7, 'j': 5, 'k': 1, 'cost': 59}, {'i': 7, 'j': 5, 'k': 2, 'cost': 52}, {'i': 7, 'j': 5, 'k': 3, 'cost': 10}, {'i': 7, 'j': 5, 'k': 4, 'cost': 71}, {'i': 7, 'j': 5, 'k': 5, 'cost': 61}, {'i': 7, 'j': 5, 'k': 6, 'cost': 5}, {'i': 7, 'j': 5, 'k': 7, 'cost': 99}, {'i': 7, 'j': 5, 'k': 8, 'cost': 65}, {'i': 7, 'j': 5, 'k': 9, 'cost': 51}, {'i': 7, 'j': 6, 'k': 1, 'cost': 90}, {'i': 7, 'j': 6, 'k': 2, 'cost': 99}, {'i': 7, 'j': 6, 'k': 3, 'cost': 85}, {'i': 7, 'j': 6, 'k': 4, 'cost': 1}, {'i': 7, 'j': 6, 'k': 5, 'cost': 42}, {'i': 7, 'j': 6, 'k': 6, 'cost': 98}, {'i': 7, 'j': 6, 'k': 7, 'cost': 39}, {'i': 7, 'j': 6, 'k': 8, 'cost': 92}, {'i': 7, 'j': 6, 'k': 9, 'cost': 71}, {'i': 7, 'j': 7, 'k': 1, 'cost': 70}, {'i': 7, 'j': 7, 'k': 2, 'cost': 43}, {'i': 7, 'j': 7, 'k': 3, 'cost': 31}, {'i': 7, 'j': 7, 'k': 4, 'cost': 67}, {'i': 7, 'j': 7, 'k': 5, 'cost': 78}, {'i': 7, 'j': 7, 'k': 6, 'cost': 13}, {'i': 7, 'j': 7, 'k': 7, 'cost': 24}, {'i': 7, 'j': 7, 'k': 8, 'cost': 62}, {'i': 7, 'j': 7, 'k': 9, 'cost': 21}, {'i': 7, 'j': 8, 'k': 1, 'cost': 45}, {'i': 7, 'j': 8, 'k': 2, 'cost': 81}, {'i': 7, 'j': 8, 'k': 3, 'cost': 90}, {'i': 7, 'j': 8, 'k': 4, 'cost': 84}, {'i': 7, 'j': 8, 'k': 5, 'cost': 97}, {'i': 7, 'j': 8, 'k': 6, 'cost': 61}, {'i': 7, 'j': 8, 'k': 7, 'cost': 87}, {'i': 7, 'j': 8, 'k': 8, 'cost': 82}, {'i': 7, 'j': 8, 'k': 9, 'cost': 16}, {'i': 7, 'j': 9, 'k': 1, 'cost': 46}, {'i': 7, 'j': 9, 'k': 2, 'cost': 91}, {'i': 7, 'j': 9, 'k': 3, 'cost': 88}, {'i': 7, 'j': 9, 'k': 4, 'cost': 52}, {'i': 7, 'j': 9, 'k': 5, 'cost': 98}, {'i': 7, 'j': 9, 'k': 6, 'cost': 31}, {'i': 7, 'j': 9, 'k': 7, 'cost': 9}, {'i': 7, 'j': 9, 'k': 8, 'cost': 26}, {'i': 7, 'j': 9, 'k': 9, 'cost': 20}, {'i': 8, 'j': 1, 'k': 1, 'cost': 15}, {'i': 8, 'j': 1, 'k': 2, 'cost': 48}, {'i': 8, 'j': 1, 'k': 3, 'cost': 36}, {'i': 8, 'j': 1, 'k': 4, 'cost': 28}, {'i': 8, 'j': 1, 'k': 5, 'cost': 74}, {'i': 8, 'j': 1, 'k': 6, 'cost': 61}, {'i': 8, 'j': 1, 'k': 7, 'cost': 61}, {'i': 8, 'j': 1, 'k': 8, 'cost': 53}, {'i': 8, 'j': 1, 'k': 9, 'cost': 9}, {'i': 8, 'j': 2, 'k': 1, 'cost': 74}, {'i': 8, 'j': 2, 'k': 2, 'cost': 59}, {'i': 8, 'j': 2, 'k': 3, 'cost': 59}, {'i': 8, 'j': 2, 'k': 4, 'cost': 6}, {'i': 8, 'j': 2, 'k': 5, 'cost': 39}, {'i': 8, 'j': 2, 'k': 6, 'cost': 31}, {'i': 8, 'j': 2, 'k': 7, 'cost': 30}, {'i': 8, 'j': 2, 'k': 8, 'cost': 63}, {'i': 8, 'j': 2, 'k': 9, 'cost': 36}, {'i': 8, 'j': 3, 'k': 1, 'cost': 1}, {'i': 8, 'j': 3, 'k': 2, 'cost': 78}, {'i': 8, 'j': 3, 'k': 3, 'cost': 46}, {'i': 8, 'j': 3, 'k': 4, 'cost': 24}, {'i': 8, 'j': 3, 'k': 5, 'cost': 26}, {'i': 8, 'j': 3, 'k': 6, 'cost': 10}, {'i': 8, 'j': 3, 'k': 7, 'cost': 97}, {'i': 8, 'j': 3, 'k': 8, 'cost': 33}, {'i': 8, 'j': 3, 'k': 9, 'cost': 6}, {'i': 8, 'j': 4, 'k': 1, 'cost': 30}, {'i': 8, 'j': 4, 'k': 2, 'cost': 96}, {'i': 8, 'j': 4, 'k': 3, 'cost': 97}, {'i': 8, 'j': 4, 'k': 4, 'cost': 97}, {'i': 8, 'j': 4, 'k': 5, 'cost': 21}, {'i': 8, 'j': 4, 'k': 6, 'cost': 76}, {'i': 8, 'j': 4, 'k': 7, 'cost': 55}, {'i': 8, 'j': 4, 'k': 8, 'cost': 94}, {'i': 8, 'j': 4, 'k': 9, 'cost': 21}, {'i': 8, 'j': 5, 'k': 1, 'cost': 47}, {'i': 8, 'j': 5, 'k': 2, 'cost': 66}, {'i': 8, 'j': 5, 'k': 3, 'cost': 65}, {'i': 8, 'j': 5, 'k': 4, 'cost': 9}, {'i': 8, 'j': 5, 'k': 5, 'cost': 12}, {'i': 8, 'j': 5, 'k': 6, 'cost': 35}, {'i': 8, 'j': 5, 'k': 7, 'cost': 25}, {'i': 8, 'j': 5, 'k': 8, 'cost': 94}, {'i': 8, 'j': 5, 'k': 9, 'cost': 7}, {'i': 8, 'j': 6, 'k': 1, 'cost': 84}, {'i': 8, 'j': 6, 'k': 2, 'cost': 43}, {'i': 8, 'j': 6, 'k': 3, 'cost': 92}, {'i': 8, 'j': 6, 'k': 4, 'cost': 15}, {'i': 8, 'j': 6, 'k': 5, 'cost': 13}, {'i': 8, 'j': 6, 'k': 6, 'cost': 79}, {'i': 8, 'j': 6, 'k': 7, 'cost': 37}, {'i': 8, 'j': 6, 'k': 8, 'cost': 74}, {'i': 8, 'j': 6, 'k': 9, 'cost': 55}, {'i': 8, 'j': 7, 'k': 1, 'cost': 21}, {'i': 8, 'j': 7, 'k': 2, 'cost': 26}, {'i': 8, 'j': 7, 'k': 3, 'cost': 88}, {'i': 8, 'j': 7, 'k': 4, 'cost': 97}, {'i': 8, 'j': 7, 'k': 5, 'cost': 32}, {'i': 8, 'j': 7, 'k': 6, 'cost': 11}, {'i': 8, 'j': 7, 'k': 7, 'cost': 84}, {'i': 8, 'j': 7, 'k': 8, 'cost': 29}, {'i': 8, 'j': 7, 'k': 9, 'cost': 31}, {'i': 8, 'j': 8, 'k': 1, 'cost': 80}, {'i': 8, 'j': 8, 'k': 2, 'cost': 12}, {'i': 8, 'j': 8, 'k': 3, 'cost': 27}, {'i': 8, 'j': 8, 'k': 4, 'cost': 14}, {'i': 8, 'j': 8, 'k': 5, 'cost': 86}, {'i': 8, 'j': 8, 'k': 6, 'cost': 43}, {'i': 8, 'j': 8, 'k': 7, 'cost': 82}, {'i': 8, 'j': 8, 'k': 8, 'cost': 43}, {'i': 8, 'j': 8, 'k': 9, 'cost': 95}, {'i': 8, 'j': 9, 'k': 1, 'cost': 78}, {'i': 8, 'j': 9, 'k': 2, 'cost': 34}, {'i': 8, 'j': 9, 'k': 3, 'cost': 98}, {'i': 8, 'j': 9, 'k': 4, 'cost': 37}, {'i': 8, 'j': 9, 'k': 5, 'cost': 7}, {'i': 8, 'j': 9, 'k': 6, 'cost': 39}, {'i': 8, 'j': 9, 'k': 7, 'cost': 37}, {'i': 8, 'j': 9, 'k': 8, 'cost': 50}, {'i': 8, 'j': 9, 'k': 9, 'cost': 15}, {'i': 9, 'j': 1, 'k': 1, 'cost': 60}, {'i': 9, 'j': 1, 'k': 2, 'cost': 77}, {'i': 9, 'j': 1, 'k': 3, 'cost': 55}, {'i': 9, 'j': 1, 'k': 4, 'cost': 38}, {'i': 9, 'j': 1, 'k': 5, 'cost': 4}, {'i': 9, 'j': 1, 'k': 6, 'cost': 93}, {'i': 9, 'j': 1, 'k': 7, 'cost': 63}, {'i': 9, 'j': 1, 'k': 8, 'cost': 89}, {'i': 9, 'j': 1, 'k': 9, 'cost': 90}, {'i': 9, 'j': 2, 'k': 1, 'cost': 43}, {'i': 9, 'j': 2, 'k': 2, 'cost': 32}, {'i': 9, 'j': 2, 'k': 3, 'cost': 15}, {'i': 9, 'j': 2, 'k': 4, 'cost': 89}, {'i': 9, 'j': 2, 'k': 5, 'cost': 1}, {'i': 9, 'j': 2, 'k': 6, 'cost': 16}, {'i': 9, 'j': 2, 'k': 7, 'cost': 82}, {'i': 9, 'j': 2, 'k': 8, 'cost': 26}, {'i': 9, 'j': 2, 'k': 9, 'cost': 89}, {'i': 9, 'j': 3, 'k': 1, 'cost': 98}, {'i': 9, 'j': 3, 'k': 2, 'cost': 23}, {'i': 9, 'j': 3, 'k': 3, 'cost': 0}, {'i': 9, 'j': 3, 'k': 4, 'cost': 91}, {'i': 9, 'j': 3, 'k': 5, 'cost': 38}, {'i': 9, 'j': 3, 'k': 6, 'cost': 59}, {'i': 9, 'j': 3, 'k': 7, 'cost': 11}, {'i': 9, 'j': 3, 'k': 8, 'cost': 20}, {'i': 9, 'j': 3, 'k': 9, 'cost': 51}, {'i': 9, 'j': 4, 'k': 1, 'cost': 94}, {'i': 9, 'j': 4, 'k': 2, 'cost': 53}, {'i': 9, 'j': 4, 'k': 3, 'cost': 63}, {'i': 9, 'j': 4, 'k': 4, 'cost': 2}, {'i': 9, 'j': 4, 'k': 5, 'cost': 52}, {'i': 9, 'j': 4, 'k': 6, 'cost': 58}, {'i': 9, 'j': 4, 'k': 7, 'cost': 5}, {'i': 9, 'j': 4, 'k': 8, 'cost': 89}, {'i': 9, 'j': 4, 'k': 9, 'cost': 91}, {'i': 9, 'j': 5, 'k': 1, 'cost': 79}, {'i': 9, 'j': 5, 'k': 2, 'cost': 83}, {'i': 9, 'j': 5, 'k': 3, 'cost': 60}, {'i': 9, 'j': 5, 'k': 4, 'cost': 79}, {'i': 9, 'j': 5, 'k': 5, 'cost': 86}, {'i': 9, 'j': 5, 'k': 6, 'cost': 4}, {'i': 9, 'j': 5, 'k': 7, 'cost': 95}, {'i': 9, 'j': 5, 'k': 8, 'cost': 90}, {'i': 9, 'j': 5, 'k': 9, 'cost': 46}, {'i': 9, 'j': 6, 'k': 1, 'cost': 45}, {'i': 9, 'j': 6, 'k': 2, 'cost': 14}, {'i': 9, 'j': 6, 'k': 3, 'cost': 21}, {'i': 9, 'j': 6, 'k': 4, 'cost': 20}, {'i': 9, 'j': 6, 'k': 5, 'cost': 8}, {'i': 9, 'j': 6, 'k': 6, 'cost': 15}, {'i': 9, 'j': 6, 'k': 7, 'cost': 92}, {'i': 9, 'j': 6, 'k': 8, 'cost': 74}, {'i': 9, 'j': 6, 'k': 9, 'cost': 42}, {'i': 9, 'j': 7, 'k': 1, 'cost': 84}, {'i': 9, 'j': 7, 'k': 2, 'cost': 10}, {'i': 9, 'j': 7, 'k': 3, 'cost': 68}, {'i': 9, 'j': 7, 'k': 4, 'cost': 45}, {'i': 9, 'j': 7, 'k': 5, 'cost': 13}, {'i': 9, 'j': 7, 'k': 6, 'cost': 85}, {'i': 9, 'j': 7, 'k': 7, 'cost': 4}, {'i': 9, 'j': 7, 'k': 8, 'cost': 42}, {'i': 9, 'j': 7, 'k': 9, 'cost': 33}, {'i': 9, 'j': 8, 'k': 1, 'cost': 1}, {'i': 9, 'j': 8, 'k': 2, 'cost': 80}, {'i': 9, 'j': 8, 'k': 3, 'cost': 84}, {'i': 9, 'j': 8, 'k': 4, 'cost': 4}, {'i': 9, 'j': 8, 'k': 5, 'cost': 65}, {'i': 9, 'j': 8, 'k': 6, 'cost': 43}, {'i': 9, 'j': 8, 'k': 7, 'cost': 39}, {'i': 9, 'j': 8, 'k': 8, 'cost': 92}, {'i': 9, 'j': 8, 'k': 9, 'cost': 11}, {'i': 9, 'j': 9, 'k': 1, 'cost': 35}, {'i': 9, 'j': 9, 'k': 2, 'cost': 19}, {'i': 9, 'j': 9, 'k': 3, 'cost': 36}, {'i': 9, 'j': 9, 'k': 4, 'cost': 15}, {'i': 9, 'j': 9, 'k': 5, 'cost': 93}, {'i': 9, 'j': 9, 'k': 6, 'cost': 41}, {'i': 9, 'j': 9, 'k': 7, 'cost': 36}, {'i': 9, 'j': 9, 'k': 8, 'cost': 93}, {'i': 9, 'j': 9, 'k': 9, 'cost': 91}]}","[[1, 7, 6], [2, 1, 7], [3, 5, 4], [4, 8, 8], [5, 6, 9], [6, 9, 3], [7, 4, 2], [8, 3, 1], [9, 2, 5]]",41,json,1
+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 10 production orders identified as A, B, C, D, E, F, G, H, I, J.
+
+*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=A
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 89 | 5 | 80 | 58 | 5 | 68 | 48 | 27 | 86 | 29 |
+| B | 94 | 24 | 41 | 37 | 40 | 58 | 49 | 99 | 86 | 22 |
+| C | 70 | 16 | 59 | 23 | 22 | 74 | 57 | 99 | 97 | 85 |
+| D | 83 | 73 | 65 | 98 | 72 | 0 | 88 | 86 | 76 | 51 |
+| E | 73 | 11 | 57 | 52 | 55 | 32 | 82 | 93 | 99 | 9 |
+| F | 27 | 35 | 19 | 80 | 16 | 16 | 71 | 54 | 80 | 81 |
+| G | 36 | 20 | 99 | 32 | 5 | 81 | 50 | 53 | 31 | 95 |
+| H | 83 | 33 | 4 | 32 | 65 | 63 | 55 | 99 | 14 | 25 |
+| I | 9 | 21 | 55 | 86 | 88 | 43 | 32 | 97 | 3 | 48 |
+| J | 79 | 77 | 3 | 92 | 88 | 48 | 73 | 7 | 16 | 74 |
+
+## order_id=B
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 81 | 34 | 26 | 19 | 89 | 62 | 32 | 6 | 70 | 46 |
+| B | 49 | 39 | 0 | 34 | 26 | 27 | 80 | 42 | 69 | 19 |
+| C | 44 | 57 | 49 | 15 | 58 | 65 | 94 | 84 | 86 | 62 |
+| D | 52 | 52 | 81 | 71 | 39 | 58 | 90 | 4 | 10 | 40 |
+| E | 98 | 99 | 77 | 30 | 97 | 50 | 46 | 75 | 70 | 37 |
+| F | 54 | 29 | 9 | 72 | 51 | 84 | 54 | 19 | 92 | 7 |
+| G | 73 | 17 | 61 | 58 | 64 | 91 | 71 | 94 | 50 | 40 |
+| H | 97 | 45 | 95 | 40 | 69 | 58 | 92 | 33 | 82 | 5 |
+| I | 85 | 40 | 92 | 29 | 99 | 27 | 12 | 82 | 55 | 75 |
+| J | 63 | 96 | 12 | 83 | 77 | 10 | 54 | 39 | 47 | 36 |
+
+## order_id=C
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 27 | 87 | 98 | 58 | 68 | 5 | 69 | 99 | 45 | 74 |
+| B | 97 | 7 | 51 | 76 | 79 | 28 | 59 | 22 | 14 | 16 |
+| C | 87 | 54 | 71 | 91 | 83 | 38 | 82 | 25 | 75 | 19 |
+| D | 43 | 46 | 47 | 49 | 83 | 61 | 46 | 8 | 17 | 0 |
+| E | 56 | 12 | 97 | 11 | 50 | 71 | 16 | 43 | 4 | 15 |
+| F | 55 | 4 | 80 | 28 | 47 | 38 | 61 | 91 | 2 | 6 |
+| G | 8 | 89 | 74 | 27 | 40 | 72 | 26 | 55 | 40 | 73 |
+| H | 72 | 18 | 82 | 58 | 67 | 50 | 2 | 32 | 69 | 66 |
+| I | 55 | 60 | 72 | 28 | 9 | 65 | 60 | 27 | 20 | 89 |
+| J | 75 | 17 | 97 | 43 | 20 | 95 | 79 | 5 | 10 | 15 |
+
+## order_id=D
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 10 | 41 | 4 | 12 | 35 | 32 | 29 | 46 | 30 | 8 |
+| B | 81 | 46 | 1 | 48 | 20 | 70 | 86 | 81 | 19 | 72 |
+| C | 96 | 2 | 48 | 92 | 19 | 39 | 95 | 18 | 37 | 75 |
+| D | 31 | 85 | 48 | 7 | 95 | 54 | 18 | 29 | 85 | 71 |
+| E | 76 | 40 | 86 | 98 | 16 | 82 | 33 | 33 | 46 | 96 |
+| F | 74 | 58 | 66 | 49 | 63 | 62 | 27 | 94 | 99 | 59 |
+| G | 19 | 24 | 93 | 90 | 0 | 85 | 78 | 1 | 21 | 48 |
+| H | 89 | 54 | 84 | 37 | 98 | 34 | 16 | 3 | 23 | 14 |
+| I | 3 | 54 | 8 | 85 | 85 | 4 | 10 | 39 | 60 | 45 |
+| J | 58 | 47 | 96 | 61 | 47 | 52 | 34 | 39 | 94 | 25 |
+
+## order_id=E
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 5 | 96 | 68 | 94 | 38 | 48 | 99 | 92 | 90 | 53 |
+| B | 20 | 90 | 51 | 54 | 1 | 79 | 85 | 1 | 91 | 34 |
+| C | 9 | 46 | 82 | 45 | 0 | 95 | 86 | 43 | 70 | 72 |
+| D | 44 | 66 | 78 | 18 | 57 | 25 | 47 | 55 | 28 | 38 |
+| E | 16 | 19 | 44 | 90 | 65 | 7 | 2 | 7 | 10 | 86 |
+| F | 26 | 16 | 24 | 12 | 38 | 81 | 8 | 80 | 94 | 64 |
+| G | 52 | 85 | 69 | 4 | 3 | 85 | 34 | 57 | 5 | 59 |
+| H | 23 | 73 | 89 | 71 | 36 | 43 | 76 | 3 | 95 | 64 |
+| I | 26 | 72 | 37 | 32 | 49 | 8 | 92 | 2 | 83 | 29 |
+| J | 97 | 85 | 26 | 94 | 85 | 76 | 29 | 70 | 55 | 90 |
+
+## order_id=F
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 2 | 45 | 28 | 51 | 41 | 24 | 31 | 49 | 61 | 60 |
+| B | 61 | 18 | 98 | 61 | 80 | 9 | 51 | 85 | 38 | 91 |
+| C | 91 | 12 | 48 | 49 | 37 | 45 | 41 | 80 | 5 | 93 |
+| D | 20 | 62 | 68 | 29 | 89 | 40 | 59 | 16 | 89 | 49 |
+| E | 37 | 3 | 10 | 74 | 91 | 37 | 0 | 44 | 61 | 42 |
+| F | 31 | 30 | 36 | 71 | 77 | 18 | 9 | 91 | 63 | 84 |
+| G | 62 | 73 | 79 | 79 | 31 | 45 | 39 | 1 | 36 | 29 |
+| H | 0 | 47 | 7 | 11 | 18 | 23 | 14 | 16 | 1 | 28 |
+| I | 90 | 15 | 92 | 84 | 32 | 48 | 44 | 11 | 58 | 31 |
+| J | 50 | 94 | 15 | 86 | 7 | 59 | 30 | 17 | 69 | 88 |
+
+## order_id=G
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 27 | 15 | 12 | 0 | 87 | 59 | 54 | 84 | 24 | 97 |
+| B | 13 | 45 | 62 | 74 | 12 | 81 | 68 | 83 | 81 | 75 |
+| C | 8 | 53 | 41 | 84 | 4 | 49 | 18 | 44 | 15 | 28 |
+| D | 64 | 52 | 62 | 56 | 5 | 24 | 27 | 1 | 83 | 89 |
+| E | 25 | 55 | 24 | 36 | 53 | 36 | 39 | 54 | 70 | 99 |
+| F | 90 | 72 | 26 | 42 | 67 | 92 | 27 | 25 | 39 | 47 |
+| G | 20 | 81 | 8 | 58 | 14 | 47 | 33 | 81 | 3 | 62 |
+| H | 76 | 11 | 99 | 97 | 60 | 93 | 11 | 61 | 2 | 20 |
+| I | 89 | 2 | 47 | 8 | 61 | 61 | 2 | 93 | 86 | 11 |
+| J | 19 | 88 | 3 | 67 | 25 | 50 | 85 | 63 | 68 | 75 |
+
+## order_id=H
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 34 | 13 | 80 | 95 | 24 | 31 | 59 | 0 | 42 | 1 |
+| B | 81 | 68 | 52 | 35 | 81 | 91 | 91 | 55 | 54 | 43 |
+| C | 96 | 36 | 30 | 96 | 84 | 57 | 21 | 10 | 36 | 28 |
+| D | 77 | 18 | 31 | 11 | 86 | 49 | 8 | 56 | 42 | 79 |
+| E | 96 | 49 | 34 | 37 | 23 | 20 | 65 | 72 | 19 | 98 |
+| F | 86 | 32 | 26 | 41 | 21 | 75 | 67 | 79 | 99 | 81 |
+| G | 97 | 25 | 25 | 73 | 85 | 84 | 73 | 55 | 78 | 92 |
+| H | 5 | 47 | 81 | 36 | 24 | 14 | 52 | 42 | 58 | 53 |
+| I | 52 | 17 | 88 | 83 | 91 | 93 | 0 | 22 | 15 | 15 |
+| J | 45 | 56 | 76 | 59 | 31 | 66 | 70 | 14 | 25 | 47 |
+
+## order_id=I
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 89 | 74 | 21 | 90 | 59 | 61 | 73 | 83 | 33 | 91 |
+| B | 59 | 39 | 14 | 76 | 95 | 99 | 18 | 13 | 30 | 85 |
+| C | 67 | 49 | 88 | 36 | 44 | 79 | 38 | 83 | 50 | 81 |
+| D | 98 | 21 | 70 | 47 | 94 | 45 | 50 | 75 | 56 | 48 |
+| E | 50 | 25 | 62 | 13 | 86 | 26 | 38 | 55 | 55 | 52 |
+| F | 38 | 88 | 67 | 92 | 47 | 94 | 48 | 20 | 47 | 64 |
+| G | 99 | 26 | 12 | 83 | 50 | 10 | 67 | 26 | 9 | 65 |
+| H | 23 | 27 | 42 | 84 | 9 | 88 | 94 | 25 | 15 | 99 |
+| I | 74 | 23 | 49 | 71 | 9 | 60 | 63 | 39 | 57 | 47 |
+| J | 75 | 89 | 31 | 41 | 70 | 51 | 38 | 17 | 0 | 45 |
+
+## order_id=J
+| machine_id\operator_id | A | B | C | D | E | F | G | H | I | J |
+|---|---|---|---|---|---|---|---|---|---|---|
+| A | 17 | 38 | 67 | 81 | 55 | 15 | 1 | 53 | 39 | 9 |
+| B | 24 | 61 | 12 | 93 | 15 | 60 | 80 | 84 | 49 | 97 |
+| C | 44 | 96 | 6 | 62 | 57 | 45 | 39 | 34 | 0 | 32 |
+| D | 0 | 25 | 55 | 39 | 35 | 92 | 55 | 40 | 36 | 48 |
+| E | 96 | 19 | 46 | 38 | 25 | 35 | 56 | 7 | 84 | 63 |
+| F | 92 | 39 | 58 | 95 | 84 | 36 | 45 | 76 | 59 | 71 |
+| G | 62 | 13 | 60 | 63 | 30 | 10 | 23 | 85 | 21 | 97 |
+| H | 99 | 85 | 31 | 49 | 69 | 39 | 94 | 20 | 98 | 40 |
+| I | 83 | 13 | 35 | 76 | 1 | 42 | 4 | 13 | 21 | 2 |
+| J | 68 | 65 | 96 | 6 | 60 | 80 | 76 | 83 | 32 | 96 |
+
+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': [[[89, 5, 80, 58, 5, 68, 48, 27, 86, 29], [94, 24, 41, 37, 40, 58, 49, 99, 86, 22], [70, 16, 59, 23, 22, 74, 57, 99, 97, 85], [83, 73, 65, 98, 72, 0, 88, 86, 76, 51], [73, 11, 57, 52, 55, 32, 82, 93, 99, 9], [27, 35, 19, 80, 16, 16, 71, 54, 80, 81], [36, 20, 99, 32, 5, 81, 50, 53, 31, 95], [83, 33, 4, 32, 65, 63, 55, 99, 14, 25], [9, 21, 55, 86, 88, 43, 32, 97, 3, 48], [79, 77, 3, 92, 88, 48, 73, 7, 16, 74]], [[81, 34, 26, 19, 89, 62, 32, 6, 70, 46], [49, 39, 0, 34, 26, 27, 80, 42, 69, 19], [44, 57, 49, 15, 58, 65, 94, 84, 86, 62], [52, 52, 81, 71, 39, 58, 90, 4, 10, 40], [98, 99, 77, 30, 97, 50, 46, 75, 70, 37], [54, 29, 9, 72, 51, 84, 54, 19, 92, 7], [73, 17, 61, 58, 64, 91, 71, 94, 50, 40], [97, 45, 95, 40, 69, 58, 92, 33, 82, 5], [85, 40, 92, 29, 99, 27, 12, 82, 55, 75], [63, 96, 12, 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'I', 'cost': 50}, {'i': 'I', 'j': 'C', 'k': 'J', 'cost': 81}, {'i': 'I', 'j': 'D', 'k': 'A', 'cost': 98}, {'i': 'I', 'j': 'D', 'k': 'B', 'cost': 21}, {'i': 'I', 'j': 'D', 'k': 'C', 'cost': 70}, {'i': 'I', 'j': 'D', 'k': 'D', 'cost': 47}, {'i': 'I', 'j': 'D', 'k': 'E', 'cost': 94}, {'i': 'I', 'j': 'D', 'k': 'F', 'cost': 45}, {'i': 'I', 'j': 'D', 'k': 'G', 'cost': 50}, {'i': 'I', 'j': 'D', 'k': 'H', 'cost': 75}, {'i': 'I', 'j': 'D', 'k': 'I', 'cost': 56}, {'i': 'I', 'j': 'D', 'k': 'J', 'cost': 48}, {'i': 'I', 'j': 'E', 'k': 'A', 'cost': 50}, {'i': 'I', 'j': 'E', 'k': 'B', 'cost': 25}, {'i': 'I', 'j': 'E', 'k': 'C', 'cost': 62}, {'i': 'I', 'j': 'E', 'k': 'D', 'cost': 13}, {'i': 'I', 'j': 'E', 'k': 'E', 'cost': 86}, {'i': 'I', 'j': 'E', 'k': 'F', 'cost': 26}, {'i': 'I', 'j': 'E', 'k': 'G', 'cost': 38}, {'i': 'I', 'j': 'E', 'k': 'H', 'cost': 55}, {'i': 'I', 'j': 'E', 'k': 'I', 'cost': 55}, {'i': 'I', 'j': 'E', 'k': 'J', 'cost': 52}, {'i': 'I', 'j': 'F', 'k': 'A', 'cost': 38}, {'i': 'I', 'j': 'F', 'k': 'B', 'cost': 88}, {'i': 'I', 'j': 'F', 'k': 'C', 'cost': 67}, {'i': 'I', 'j': 'F', 'k': 'D', 'cost': 92}, {'i': 'I', 'j': 'F', 'k': 'E', 'cost': 47}, {'i': 'I', 'j': 'F', 'k': 'F', 'cost': 94}, {'i': 'I', 'j': 'F', 'k': 'G', 'cost': 48}, {'i': 'I', 'j': 'F', 'k': 'H', 'cost': 20}, {'i': 'I', 'j': 'F', 'k': 'I', 'cost': 47}, {'i': 'I', 'j': 'F', 'k': 'J', 'cost': 64}, {'i': 'I', 'j': 'G', 'k': 'A', 'cost': 99}, {'i': 'I', 'j': 'G', 'k': 'B', 'cost': 26}, {'i': 'I', 'j': 'G', 'k': 'C', 'cost': 12}, {'i': 'I', 'j': 'G', 'k': 'D', 'cost': 83}, {'i': 'I', 'j': 'G', 'k': 'E', 'cost': 50}, {'i': 'I', 'j': 'G', 'k': 'F', 'cost': 10}, {'i': 'I', 'j': 'G', 'k': 'G', 'cost': 67}, {'i': 'I', 'j': 'G', 'k': 'H', 'cost': 26}, {'i': 'I', 'j': 'G', 'k': 'I', 'cost': 9}, {'i': 'I', 'j': 'G', 'k': 'J', 'cost': 65}, {'i': 'I', 'j': 'H', 'k': 'A', 'cost': 23}, {'i': 'I', 'j': 'H', 'k': 'B', 'cost': 27}, {'i': 'I', 'j': 'H', 'k': 'C', 'cost': 42}, {'i': 'I', 'j': 'H', 'k': 'D', 'cost': 84}, {'i': 'I', 'j': 'H', 'k': 'E', 'cost': 9}, {'i': 'I', 'j': 'H', 'k': 'F', 'cost': 88}, {'i': 'I', 'j': 'H', 'k': 'G', 'cost': 94}, {'i': 'I', 'j': 'H', 'k': 'H', 'cost': 25}, {'i': 'I', 'j': 'H', 'k': 'I', 'cost': 15}, {'i': 'I', 'j': 'H', 'k': 'J', 'cost': 99}, {'i': 'I', 'j': 'I', 'k': 'A', 'cost': 74}, {'i': 'I', 'j': 'I', 'k': 'B', 'cost': 23}, {'i': 'I', 'j': 'I', 'k': 'C', 'cost': 49}, {'i': 'I', 'j': 'I', 'k': 'D', 'cost': 71}, {'i': 'I', 'j': 'I', 'k': 'E', 'cost': 9}, {'i': 'I', 'j': 'I', 'k': 'F', 'cost': 60}, {'i': 'I', 'j': 'I', 'k': 'G', 'cost': 63}, {'i': 'I', 'j': 'I', 'k': 'H', 'cost': 39}, {'i': 'I', 'j': 'I', 'k': 'I', 'cost': 57}, {'i': 'I', 'j': 'I', 'k': 'J', 'cost': 47}, {'i': 'I', 'j': 'J', 'k': 'A', 'cost': 75}, {'i': 'I', 'j': 'J', 'k': 'B', 'cost': 89}, {'i': 'I', 'j': 'J', 'k': 'C', 'cost': 31}, {'i': 'I', 'j': 'J', 'k': 'D', 'cost': 41}, {'i': 'I', 'j': 'J', 'k': 'E', 'cost': 70}, {'i': 'I', 'j': 'J', 'k': 'F', 'cost': 51}, {'i': 'I', 'j': 'J', 'k': 'G', 'cost': 38}, {'i': 'I', 'j': 'J', 'k': 'H', 'cost': 17}, {'i': 'I', 'j': 'J', 'k': 'I', 'cost': 0}, {'i': 'I', 'j': 'J', 'k': 'J', 'cost': 45}, {'i': 'J', 'j': 'A', 'k': 'A', 'cost': 17}, {'i': 'J', 'j': 'A', 'k': 'B', 'cost': 38}, {'i': 'J', 'j': 'A', 'k': 'C', 'cost': 67}, {'i': 'J', 'j': 'A', 'k': 'D', 'cost': 81}, {'i': 'J', 'j': 'A', 'k': 'E', 'cost': 55}, {'i': 'J', 'j': 'A', 'k': 'F', 'cost': 15}, {'i': 'J', 'j': 'A', 'k': 'G', 'cost': 1}, {'i': 'J', 'j': 'A', 'k': 'H', 'cost': 53}, {'i': 'J', 'j': 'A', 'k': 'I', 'cost': 39}, {'i': 'J', 'j': 'A', 'k': 'J', 'cost': 9}, {'i': 'J', 'j': 'B', 'k': 'A', 'cost': 24}, {'i': 'J', 'j': 'B', 'k': 'B', 'cost': 61}, {'i': 'J', 'j': 'B', 'k': 'C', 'cost': 12}, {'i': 'J', 'j': 'B', 'k': 'D', 'cost': 93}, {'i': 'J', 'j': 'B', 'k': 'E', 'cost': 15}, {'i': 'J', 'j': 'B', 'k': 'F', 'cost': 60}, {'i': 'J', 'j': 'B', 'k': 'G', 'cost': 80}, {'i': 'J', 'j': 'B', 'k': 'H', 'cost': 84}, {'i': 'J', 'j': 'B', 'k': 'I', 'cost': 49}, {'i': 'J', 'j': 'B', 'k': 'J', 'cost': 97}, {'i': 'J', 'j': 'C', 'k': 'A', 'cost': 44}, {'i': 'J', 'j': 'C', 'k': 'B', 'cost': 96}, {'i': 'J', 'j': 'C', 'k': 'C', 'cost': 6}, {'i': 'J', 'j': 'C', 'k': 'D', 'cost': 62}, {'i': 'J', 'j': 'C', 'k': 'E', 'cost': 57}, {'i': 'J', 'j': 'C', 'k': 'F', 'cost': 45}, {'i': 'J', 'j': 'C', 'k': 'G', 'cost': 39}, {'i': 'J', 'j': 'C', 'k': 'H', 'cost': 34}, {'i': 'J', 'j': 'C', 'k': 'I', 'cost': 0}, {'i': 'J', 'j': 'C', 'k': 'J', 'cost': 32}, {'i': 'J', 'j': 'D', 'k': 'A', 'cost': 0}, {'i': 'J', 'j': 'D', 'k': 'B', 'cost': 25}, {'i': 'J', 'j': 'D', 'k': 'C', 'cost': 55}, {'i': 'J', 'j': 'D', 'k': 'D', 'cost': 39}, {'i': 'J', 'j': 'D', 'k': 'E', 'cost': 35}, {'i': 'J', 'j': 'D', 'k': 'F', 'cost': 92}, {'i': 'J', 'j': 'D', 'k': 'G', 'cost': 55}, {'i': 'J', 'j': 'D', 'k': 'H', 'cost': 40}, {'i': 'J', 'j': 'D', 'k': 'I', 'cost': 36}, {'i': 'J', 'j': 'D', 'k': 'J', 'cost': 48}, {'i': 'J', 'j': 'E', 'k': 'A', 'cost': 96}, {'i': 'J', 'j': 'E', 'k': 'B', 'cost': 19}, {'i': 'J', 'j': 'E', 'k': 'C', 'cost': 46}, {'i': 'J', 'j': 'E', 'k': 'D', 'cost': 38}, {'i': 'J', 'j': 'E', 'k': 'E', 'cost': 25}, {'i': 'J', 'j': 'E', 'k': 'F', 'cost': 35}, {'i': 'J', 'j': 'E', 'k': 'G', 'cost': 56}, {'i': 'J', 'j': 'E', 'k': 'H', 'cost': 7}, {'i': 'J', 'j': 'E', 'k': 'I', 'cost': 84}, {'i': 'J', 'j': 'E', 'k': 'J', 'cost': 63}, {'i': 'J', 'j': 'F', 'k': 'A', 'cost': 92}, {'i': 'J', 'j': 'F', 'k': 'B', 'cost': 39}, {'i': 'J', 'j': 'F', 'k': 'C', 'cost': 58}, {'i': 'J', 'j': 'F', 'k': 'D', 'cost': 95}, {'i': 'J', 'j': 'F', 'k': 'E', 'cost': 84}, {'i': 'J', 'j': 'F', 'k': 'F', 'cost': 36}, {'i': 'J', 'j': 'F', 'k': 'G', 'cost': 45}, {'i': 'J', 'j': 'F', 'k': 'H', 'cost': 76}, {'i': 'J', 'j': 'F', 'k': 'I', 'cost': 59}, {'i': 'J', 'j': 'F', 'k': 'J', 'cost': 71}, {'i': 'J', 'j': 'G', 'k': 'A', 'cost': 62}, {'i': 'J', 'j': 'G', 'k': 'B', 'cost': 13}, {'i': 'J', 'j': 'G', 'k': 'C', 'cost': 60}, {'i': 'J', 'j': 'G', 'k': 'D', 'cost': 63}, {'i': 'J', 'j': 'G', 'k': 'E', 'cost': 30}, {'i': 'J', 'j': 'G', 'k': 'F', 'cost': 10}, {'i': 'J', 'j': 'G', 'k': 'G', 'cost': 23}, {'i': 'J', 'j': 'G', 'k': 'H', 'cost': 85}, {'i': 'J', 'j': 'G', 'k': 'I', 'cost': 21}, {'i': 'J', 'j': 'G', 'k': 'J', 'cost': 97}, {'i': 'J', 'j': 'H', 'k': 'A', 'cost': 99}, {'i': 'J', 'j': 'H', 'k': 'B', 'cost': 85}, {'i': 'J', 'j': 'H', 'k': 'C', 'cost': 31}, {'i': 'J', 'j': 'H', 'k': 'D', 'cost': 49}, {'i': 'J', 'j': 'H', 'k': 'E', 'cost': 69}, {'i': 'J', 'j': 'H', 'k': 'F', 'cost': 39}, {'i': 'J', 'j': 'H', 'k': 'G', 'cost': 94}, {'i': 'J', 'j': 'H', 'k': 'H', 'cost': 20}, {'i': 'J', 'j': 'H', 'k': 'I', 'cost': 98}, {'i': 'J', 'j': 'H', 'k': 'J', 'cost': 40}, {'i': 'J', 'j': 'I', 'k': 'A', 'cost': 83}, {'i': 'J', 'j': 'I', 'k': 'B', 'cost': 13}, {'i': 'J', 'j': 'I', 'k': 'C', 'cost': 35}, {'i': 'J', 'j': 'I', 'k': 'D', 'cost': 76}, {'i': 'J', 'j': 'I', 'k': 'E', 'cost': 1}, {'i': 'J', 'j': 'I', 'k': 'F', 'cost': 42}, {'i': 'J', 'j': 'I', 'k': 'G', 'cost': 4}, {'i': 'J', 'j': 'I', 'k': 'H', 'cost': 13}, {'i': 'J', 'j': 'I', 'k': 'I', 'cost': 21}, {'i': 'J', 'j': 'I', 'k': 'J', 'cost': 2}, {'i': 'J', 'j': 'J', 'k': 'A', 'cost': 68}, {'i': 'J', 'j': 'J', 'k': 'B', 'cost': 65}, {'i': 'J', 'j': 'J', 'k': 'C', 'cost': 96}, {'i': 'J', 'j': 'J', 'k': 'D', 'cost': 6}, {'i': 'J', 'j': 'J', 'k': 'E', 'cost': 60}, {'i': 'J', 'j': 'J', 'k': 'F', 'cost': 80}, {'i': 'J', 'j': 'J', 'k': 'G', 'cost': 76}, {'i': 'J', 'j': 'J', 'k': 'H', 'cost': 83}, {'i': 'J', 'j': 'J', 'k': 'I', 'cost': 32}, {'i': 'J', 'j': 'J', 'k': 'J', 'cost': 96}]}","[['A', 'D', 'F'], ['B', 'B', 'C'], ['C', 'F', 'B'], ['D', 'G', 'H'], ['E', 'C', 'E'], ['F', 'E', 'G'], ['G', 'A', 'D'], ['H', 'H', 'A'], ['I', 'J', 'I'], ['J', 'I', 'J']]",42,markdown_table,names
+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.
+
+There are 11 outreach sites (and 11 volunteers and 11 vehicles) labeled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11; the feasible volunteer+vehicle assignments and their travel+coordination costs are listed below.
+
+*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 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 98 | 21 | 40 | 1 | 98 | 69 | 24 | 59 | 51 | 57 | 28 |
+| 2 | 82 | 71 | 95 | 68 | 16 | 19 | 99 | 40 | 74 | 9 | 40 |
+| 3 | 5 | 68 | 64 | 32 | 49 | 4 | 41 | 53 | 3 | 10 | 44 |
+| 4 | 16 | 74 | 27 | 70 | 49 | 56 | 61 | 43 | 38 | 18 | 64 |
+| 5 | 52 | 25 | 42 | 82 | 49 | 4 | 54 | 78 | 13 | 12 | 1 |
+| 6 | 52 | 26 | 60 | 80 | 99 | 94 | 99 | 17 | 55 | 3 | 79 |
+| 7 | 62 | 22 | 78 | 74 | 94 | 15 | 38 | 98 | 83 | 85 | 71 |
+| 8 | 75 | 37 | 9 | 63 | 85 | 28 | 73 | 29 | 70 | 81 | 20 |
+| 9 | 82 | 47 | 6 | 56 | 44 | 6 | 87 | 60 | 98 | 23 | 0 |
+| 10 | 81 | 11 | 45 | 15 | 47 | 64 | 12 | 70 | 27 | 88 | 14 |
+| 11 | 30 | 57 | 26 | 41 | 23 | 29 | 7 | 88 | 44 | 41 | 40 |
+
+## site_id=2
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 12 | 48 | 91 | 98 | 39 | 56 | 76 | 85 | 12 | 14 | 32 |
+| 2 | 47 | 85 | 70 | 94 | 7 | 95 | 58 | 98 | 81 | 65 | 50 |
+| 3 | 11 | 76 | 66 | 14 | 7 | 48 | 65 | 60 | 49 | 39 | 64 |
+| 4 | 10 | 54 | 90 | 80 | 15 | 30 | 2 | 88 | 51 | 41 | 20 |
+| 5 | 6 | 70 | 71 | 53 | 36 | 64 | 78 | 52 | 79 | 75 | 91 |
+| 6 | 96 | 9 | 62 | 79 | 44 | 78 | 82 | 28 | 77 | 6 | 13 |
+| 7 | 81 | 8 | 27 | 62 | 24 | 24 | 22 | 21 | 26 | 38 | 63 |
+| 8 | 39 | 13 | 6 | 97 | 56 | 23 | 67 | 95 | 86 | 46 | 53 |
+| 9 | 35 | 53 | 74 | 41 | 13 | 33 | 86 | 99 | 36 | 44 | 61 |
+| 10 | 46 | 1 | 94 | 0 | 28 | 59 | 43 | 46 | 89 | 63 | 4 |
+| 11 | 25 | 62 | 6 | 56 | 62 | 12 | 76 | 19 | 99 | 0 | 77 |
+
+## site_id=3
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 61 | 70 | 4 | 40 | 74 | 13 | 88 | 24 | 36 | 43 | 42 |
+| 2 | 94 | 18 | 48 | 8 | 3 | 19 | 8 | 68 | 66 | 10 | 53 |
+| 3 | 95 | 77 | 59 | 75 | 33 | 66 | 60 | 28 | 38 | 25 | 13 |
+| 4 | 29 | 51 | 85 | 12 | 59 | 56 | 44 | 93 | 22 | 40 | 90 |
+| 5 | 27 | 32 | 61 | 84 | 75 | 80 | 14 | 36 | 83 | 1 | 21 |
+| 6 | 2 | 82 | 15 | 31 | 3 | 47 | 58 | 97 | 1 | 40 | 23 |
+| 7 | 9 | 8 | 66 | 45 | 80 | 94 | 28 | 2 | 85 | 38 | 17 |
+| 8 | 54 | 1 | 24 | 63 | 24 | 85 | 95 | 66 | 99 | 44 | 72 |
+| 9 | 35 | 47 | 52 | 51 | 42 | 53 | 98 | 94 | 36 | 68 | 44 |
+| 10 | 4 | 3 | 93 | 52 | 82 | 26 | 19 | 77 | 28 | 58 | 3 |
+| 11 | 56 | 77 | 66 | 74 | 48 | 72 | 2 | 53 | 11 | 64 | 47 |
+
+## site_id=4
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 85 | 74 | 16 | 15 | 90 | 78 | 48 | 64 | 60 | 32 | 45 |
+| 2 | 62 | 59 | 65 | 97 | 92 | 28 | 36 | 38 | 66 | 33 | 35 |
+| 3 | 95 | 60 | 82 | 5 | 12 | 98 | 13 | 45 | 8 | 57 | 78 |
+| 4 | 11 | 54 | 48 | 55 | 70 | 72 | 76 | 46 | 87 | 2 | 64 |
+| 5 | 53 | 97 | 50 | 61 | 54 | 92 | 50 | 17 | 62 | 76 | 77 |
+| 6 | 9 | 32 | 57 | 22 | 63 | 37 | 14 | 12 | 65 | 91 | 97 |
+| 7 | 83 | 10 | 34 | 11 | 48 | 64 | 45 | 28 | 0 | 74 | 21 |
+| 8 | 58 | 90 | 0 | 47 | 80 | 51 | 44 | 32 | 46 | 64 | 64 |
+| 9 | 20 | 15 | 78 | 72 | 18 | 5 | 13 | 31 | 34 | 80 | 38 |
+| 10 | 93 | 3 | 80 | 58 | 96 | 1 | 27 | 50 | 80 | 60 | 99 |
+| 11 | 60 | 89 | 43 | 83 | 66 | 45 | 71 | 77 | 16 | 22 | 36 |
+
+## site_id=5
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 4 | 80 | 89 | 9 | 13 | 83 | 60 | 97 | 61 | 40 | 79 |
+| 2 | 7 | 10 | 67 | 49 | 97 | 52 | 76 | 29 | 63 | 63 | 88 |
+| 3 | 94 | 18 | 65 | 18 | 84 | 49 | 44 | 78 | 37 | 9 | 7 |
+| 4 | 10 | 25 | 32 | 25 | 38 | 25 | 55 | 49 | 55 | 68 | 71 |
+| 5 | 66 | 87 | 74 | 7 | 79 | 48 | 72 | 19 | 94 | 25 | 19 |
+| 6 | 75 | 18 | 57 | 75 | 35 | 34 | 17 | 31 | 63 | 95 | 83 |
+| 7 | 22 | 71 | 5 | 41 | 74 | 51 | 62 | 67 | 42 | 3 | 28 |
+| 8 | 83 | 20 | 75 | 21 | 99 | 45 | 59 | 95 | 93 | 18 | 19 |
+| 9 | 94 | 26 | 25 | 0 | 66 | 53 | 0 | 85 | 79 | 25 | 5 |
+| 10 | 13 | 51 | 68 | 86 | 52 | 28 | 92 | 73 | 77 | 37 | 30 |
+| 11 | 37 | 55 | 0 | 22 | 53 | 80 | 89 | 49 | 58 | 67 | 27 |
+
+## site_id=6
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 74 | 57 | 25 | 4 | 96 | 97 | 87 | 65 | 12 | 33 | 86 |
+| 2 | 59 | 95 | 27 | 88 | 88 | 42 | 63 | 24 | 35 | 45 | 33 |
+| 3 | 68 | 68 | 0 | 76 | 51 | 43 | 97 | 68 | 73 | 3 | 46 |
+| 4 | 2 | 68 | 28 | 26 | 71 | 36 | 78 | 74 | 31 | 47 | 79 |
+| 5 | 29 | 88 | 84 | 50 | 0 | 69 | 32 | 16 | 23 | 74 | 80 |
+| 6 | 8 | 27 | 90 | 11 | 24 | 15 | 39 | 10 | 71 | 24 | 71 |
+| 7 | 61 | 4 | 83 | 81 | 5 | 44 | 37 | 55 | 45 | 70 | 7 |
+| 8 | 78 | 35 | 50 | 86 | 37 | 48 | 99 | 67 | 68 | 28 | 56 |
+| 9 | 58 | 43 | 20 | 82 | 12 | 24 | 46 | 77 | 0 | 31 | 54 |
+| 10 | 20 | 74 | 43 | 81 | 69 | 54 | 24 | 99 | 97 | 86 | 41 |
+| 11 | 85 | 85 | 55 | 27 | 95 | 18 | 13 | 70 | 69 | 30 | 2 |
+
+## site_id=7
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 68 | 67 | 10 | 81 | 10 | 69 | 11 | 83 | 15 | 36 | 35 |
+| 2 | 81 | 37 | 76 | 52 | 21 | 68 | 78 | 70 | 73 | 54 | 9 |
+| 3 | 7 | 50 | 14 | 53 | 22 | 0 | 58 | 58 | 39 | 93 | 51 |
+| 4 | 7 | 67 | 43 | 88 | 20 | 87 | 40 | 97 | 53 | 39 | 40 |
+| 5 | 47 | 43 | 43 | 90 | 11 | 34 | 43 | 60 | 76 | 22 | 17 |
+| 6 | 92 | 64 | 61 | 36 | 63 | 69 | 92 | 85 | 69 | 21 | 72 |
+| 7 | 97 | 89 | 40 | 53 | 0 | 86 | 72 | 38 | 53 | 23 | 86 |
+| 8 | 12 | 1 | 34 | 21 | 12 | 5 | 10 | 83 | 28 | 9 | 16 |
+| 9 | 57 | 85 | 13 | 25 | 55 | 76 | 45 | 61 | 70 | 76 | 62 |
+| 10 | 7 | 45 | 57 | 82 | 96 | 39 | 38 | 16 | 80 | 93 | 99 |
+| 11 | 56 | 61 | 77 | 73 | 21 | 20 | 31 | 33 | 24 | 36 | 47 |
+
+## site_id=8
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 78 | 33 | 79 | 32 | 79 | 37 | 2 | 23 | 21 | 21 | 12 |
+| 2 | 86 | 42 | 93 | 4 | 65 | 74 | 41 | 61 | 95 | 5 | 98 |
+| 3 | 34 | 55 | 31 | 9 | 27 | 52 | 57 | 85 | 12 | 10 | 11 |
+| 4 | 3 | 79 | 80 | 45 | 15 | 59 | 30 | 88 | 83 | 15 | 71 |
+| 5 | 95 | 63 | 57 | 10 | 51 | 48 | 63 | 38 | 8 | 68 | 70 |
+| 6 | 61 | 71 | 70 | 8 | 44 | 42 | 37 | 74 | 85 | 66 | 64 |
+| 7 | 7 | 66 | 39 | 46 | 28 | 68 | 74 | 40 | 32 | 36 | 92 |
+| 8 | 46 | 34 | 75 | 45 | 21 | 31 | 98 | 96 | 50 | 35 | 57 |
+| 9 | 10 | 94 | 44 | 46 | 87 | 75 | 48 | 60 | 8 | 36 | 10 |
+| 10 | 75 | 85 | 47 | 47 | 29 | 36 | 64 | 78 | 89 | 29 | 5 |
+| 11 | 18 | 6 | 75 | 38 | 72 | 63 | 98 | 30 | 16 | 29 | 99 |
+
+## site_id=9
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 68 | 65 | 38 | 80 | 10 | 8 | 44 | 19 | 1 | 78 | 15 |
+| 2 | 43 | 79 | 36 | 68 | 51 | 30 | 64 | 82 | 54 | 23 | 87 |
+| 3 | 97 | 54 | 8 | 65 | 36 | 21 | 68 | 98 | 94 | 12 | 40 |
+| 4 | 69 | 68 | 77 | 15 | 37 | 55 | 34 | 31 | 65 | 73 | 16 |
+| 5 | 1 | 3 | 87 | 66 | 55 | 72 | 47 | 47 | 62 | 41 | 61 |
+| 6 | 21 | 17 | 82 | 28 | 61 | 36 | 5 | 63 | 77 | 90 | 30 |
+| 7 | 58 | 32 | 56 | 42 | 36 | 83 | 17 | 34 | 79 | 71 | 95 |
+| 8 | 21 | 76 | 7 | 10 | 30 | 76 | 50 | 68 | 87 | 55 | 12 |
+| 9 | 38 | 35 | 56 | 0 | 49 | 96 | 28 | 49 | 51 | 25 | 24 |
+| 10 | 30 | 28 | 99 | 86 | 10 | 22 | 51 | 97 | 90 | 33 | 28 |
+| 11 | 84 | 50 | 25 | 31 | 72 | 80 | 22 | 39 | 27 | 90 | 80 |
+
+## site_id=10
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 33 | 79 | 97 | 60 | 22 | 86 | 33 | 16 | 81 | 95 | 10 |
+| 2 | 20 | 24 | 18 | 7 | 30 | 72 | 65 | 3 | 29 | 18 | 56 |
+| 3 | 76 | 34 | 15 | 88 | 99 | 4 | 38 | 60 | 57 | 60 | 85 |
+| 4 | 98 | 62 | 43 | 96 | 24 | 42 | 26 | 23 | 43 | 95 | 64 |
+| 5 | 11 | 47 | 16 | 68 | 98 | 91 | 32 | 54 | 90 | 62 | 79 |
+| 6 | 81 | 40 | 83 | 88 | 80 | 53 | 53 | 97 | 10 | 32 | 59 |
+| 7 | 54 | 1 | 2 | 20 | 56 | 97 | 70 | 74 | 80 | 41 | 48 |
+| 8 | 84 | 19 | 98 | 94 | 25 | 24 | 23 | 35 | 59 | 97 | 41 |
+| 9 | 51 | 51 | 16 | 65 | 60 | 49 | 10 | 80 | 92 | 3 | 48 |
+| 10 | 16 | 70 | 39 | 80 | 51 | 18 | 70 | 58 | 4 | 45 | 48 |
+| 11 | 23 | 91 | 92 | 14 | 6 | 10 | 89 | 39 | 31 | 44 | 82 |
+
+## site_id=11
+| volunteer_id\vehicle_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 33 | 5 | 63 | 67 | 37 | 18 | 4 | 63 | 93 | 58 | 30 |
+| 2 | 85 | 82 | 50 | 59 | 14 | 61 | 52 | 95 | 75 | 91 | 82 |
+| 3 | 31 | 87 | 66 | 88 | 38 | 57 | 4 | 82 | 73 | 43 | 75 |
+| 4 | 91 | 16 | 33 | 40 | 47 | 34 | 27 | 2 | 34 | 80 | 19 |
+| 5 | 93 | 95 | 21 | 63 | 53 | 62 | 50 | 8 | 21 | 5 | 44 |
+| 6 | 53 | 71 | 1 | 78 | 70 | 2 | 41 | 55 | 44 | 18 | 56 |
+| 7 | 37 | 94 | 28 | 75 | 86 | 74 | 58 | 39 | 97 | 38 | 54 |
+| 8 | 28 | 56 | 4 | 68 | 23 | 82 | 84 | 99 | 55 | 95 | 68 |
+| 9 | 82 | 56 | 30 | 80 | 74 | 99 | 31 | 23 | 24 | 79 | 76 |
+| 10 | 31 | 0 | 32 | 82 | 61 | 84 | 57 | 58 | 25 | 40 | 28 |
+| 11 | 69 | 15 | 30 | 3 | 21 | 60 | 4 | 62 | 72 | 84 | 95 |
+
+Choose exactly one listed assignment for each of the 11 sites so that the sum of the chosen costs is minimized; no volunteer or vehicle may be used more than once.
+
+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, 21, 40, 1, 98, 69, 24, 59, 51, 57, 28], [82, 71, 95, 68, 16, 19, 99, 40, 74, 9, 40], [5, 68, 64, 32, 49, 4, 41, 53, 3, 10, 44], [16, 74, 27, 70, 49, 56, 61, 43, 38, 18, 64], [52, 25, 42, 82, 49, 4, 54, 78, 13, 12, 1], [52, 26, 60, 80, 99, 94, 99, 17, 55, 3, 79], [62, 22, 78, 74, 94, 15, 38, 98, 83, 85, 71], [75, 37, 9, 63, 85, 28, 73, 29, 70, 81, 20], [82, 47, 6, 56, 44, 6, 87, 60, 98, 23, 0], [81, 11, 45, 15, 47, 64, 12, 70, 27, 88, 14], [30, 57, 26, 41, 23, 29, 7, 88, 44, 41, 40]], [[12, 48, 91, 98, 39, 56, 76, 85, 12, 14, 32], [47, 85, 70, 94, 7, 95, 58, 98, 81, 65, 50], [11, 76, 66, 14, 7, 48, 65, 60, 49, 39, 64], [10, 54, 90, 80, 15, 30, 2, 88, 51, 41, 20], [6, 70, 71, 53, 36, 64, 78, 52, 79, 75, 91], [96, 9, 62, 79, 44, 78, 82, 28, 77, 6, 13], [81, 8, 27, 62, 24, 24, 22, 21, 26, 38, 63], [39, 13, 6, 97, 56, 23, 67, 95, 86, 46, 53], [35, 53, 74, 41, 13, 33, 86, 99, 36, 44, 61], [46, 1, 94, 0, 28, 59, 43, 46, 89, 63, 4], [25, 62, 6, 56, 62, 12, 76, 19, 99, 0, 77]], [[61, 70, 4, 40, 74, 13, 88, 24, 36, 43, 42], [94, 18, 48, 8, 3, 19, 8, 68, 66, 10, 53], [95, 77, 59, 75, 33, 66, 60, 28, 38, 25, 13], [29, 51, 85, 12, 59, 56, 44, 93, 22, 40, 90], [27, 32, 61, 84, 75, 80, 14, 36, 83, 1, 21], [2, 82, 15, 31, 3, 47, 58, 97, 1, 40, 23], [9, 8, 66, 45, 80, 94, 28, 2, 85, 38, 17], [54, 1, 24, 63, 24, 85, 95, 66, 99, 44, 72], [35, 47, 52, 51, 42, 53, 98, 94, 36, 68, 44], [4, 3, 93, 52, 82, 26, 19, 77, 28, 58, 3], [56, 77, 66, 74, 48, 72, 2, 53, 11, 64, 47]], [[85, 74, 16, 15, 90, 78, 48, 64, 60, 32, 45], [62, 59, 65, 97, 92, 28, 36, 38, 66, 33, 35], [95, 60, 82, 5, 12, 98, 13, 45, 8, 57, 78], [11, 54, 48, 55, 70, 72, 76, 46, 87, 2, 64], [53, 97, 50, 61, 54, 92, 50, 17, 62, 76, 77], [9, 32, 57, 22, 63, 37, 14, 12, 65, 91, 97], [83, 10, 34, 11, 48, 64, 45, 28, 0, 74, 21], [58, 90, 0, 47, 80, 51, 44, 32, 46, 64, 64], [20, 15, 78, 72, 18, 5, 13, 31, 34, 80, 38], [93, 3, 80, 58, 96, 1, 27, 50, 80, 60, 99], [60, 89, 43, 83, 66, 45, 71, 77, 16, 22, 36]], [[4, 80, 89, 9, 13, 83, 60, 97, 61, 40, 79], [7, 10, 67, 49, 97, 52, 76, 29, 63, 63, 88], [94, 18, 65, 18, 84, 49, 44, 78, 37, 9, 7], [10, 25, 32, 25, 38, 25, 55, 49, 55, 68, 71], [66, 87, 74, 7, 79, 48, 72, 19, 94, 25, 19], [75, 18, 57, 75, 35, 34, 17, 31, 63, 95, 83], [22, 71, 5, 41, 74, 51, 62, 67, 42, 3, 28], [83, 20, 75, 21, 99, 45, 59, 95, 93, 18, 19], [94, 26, 25, 0, 66, 53, 0, 85, 79, 25, 5], [13, 51, 68, 86, 52, 28, 92, 73, 77, 37, 30], [37, 55, 0, 22, 53, 80, 89, 49, 58, 67, 27]], [[74, 57, 25, 4, 96, 97, 87, 65, 12, 33, 86], [59, 95, 27, 88, 88, 42, 63, 24, 35, 45, 33], [68, 68, 0, 76, 51, 43, 97, 68, 73, 3, 46], [2, 68, 28, 26, 71, 36, 78, 74, 31, 47, 79], [29, 88, 84, 50, 0, 69, 32, 16, 23, 74, 80], [8, 27, 90, 11, 24, 15, 39, 10, 71, 24, 71], [61, 4, 83, 81, 5, 44, 37, 55, 45, 70, 7], [78, 35, 50, 86, 37, 48, 99, 67, 68, 28, 56], [58, 43, 20, 82, 12, 24, 46, 77, 0, 31, 54], [20, 74, 43, 81, 69, 54, 24, 99, 97, 86, 41], [85, 85, 55, 27, 95, 18, 13, 70, 69, 30, 2]], [[68, 67, 10, 81, 10, 69, 11, 83, 15, 36, 35], [81, 37, 76, 52, 21, 68, 78, 70, 73, 54, 9], [7, 50, 14, 53, 22, 0, 58, 58, 39, 93, 51], [7, 67, 43, 88, 20, 87, 40, 97, 53, 39, 40], [47, 43, 43, 90, 11, 34, 43, 60, 76, 22, 17], [92, 64, 61, 36, 63, 69, 92, 85, 69, 21, 72], [97, 89, 40, 53, 0, 86, 72, 38, 53, 23, 86], [12, 1, 34, 21, 12, 5, 10, 83, 28, 9, 16], [57, 85, 13, 25, 55, 76, 45, 61, 70, 76, 62], [7, 45, 57, 82, 96, 39, 38, 16, 80, 93, 99], [56, 61, 77, 73, 21, 20, 31, 33, 24, 36, 47]], [[78, 33, 79, 32, 79, 37, 2, 23, 21, 21, 12], [86, 42, 93, 4, 65, 74, 41, 61, 95, 5, 98], [34, 55, 31, 9, 27, 52, 57, 85, 12, 10, 11], [3, 79, 80, 45, 15, 59, 30, 88, 83, 15, 71], [95, 63, 57, 10, 51, 48, 63, 38, 8, 68, 70], [61, 71, 70, 8, 44, 42, 37, 74, 85, 66, 64], [7, 66, 39, 46, 28, 68, 74, 40, 32, 36, 92], [46, 34, 75, 45, 21, 31, 98, 96, 50, 35, 57], [10, 94, 44, 46, 87, 75, 48, 60, 8, 36, 10], [75, 85, 47, 47, 29, 36, 64, 78, 89, 29, 5], [18, 6, 75, 38, 72, 63, 98, 30, 16, 29, 99]], [[68, 65, 38, 80, 10, 8, 44, 19, 1, 78, 15], [43, 79, 36, 68, 51, 30, 64, 82, 54, 23, 87], [97, 54, 8, 65, 36, 21, 68, 98, 94, 12, 40], [69, 68, 77, 15, 37, 55, 34, 31, 65, 73, 16], [1, 3, 87, 66, 55, 72, 47, 47, 62, 41, 61], [21, 17, 82, 28, 61, 36, 5, 63, 77, 90, 30], [58, 32, 56, 42, 36, 83, 17, 34, 79, 71, 95], [21, 76, 7, 10, 30, 76, 50, 68, 87, 55, 12], [38, 35, 56, 0, 49, 96, 28, 49, 51, 25, 24], [30, 28, 99, 86, 10, 22, 51, 97, 90, 33, 28], [84, 50, 25, 31, 72, 80, 22, 39, 27, 90, 80]], [[33, 79, 97, 60, 22, 86, 33, 16, 81, 95, 10], [20, 24, 18, 7, 30, 72, 65, 3, 29, 18, 56], [76, 34, 15, 88, 99, 4, 38, 60, 57, 60, 85], [98, 62, 43, 96, 24, 42, 26, 23, 43, 95, 64], [11, 47, 16, 68, 98, 91, 32, 54, 90, 62, 79], [81, 40, 83, 88, 80, 53, 53, 97, 10, 32, 59], [54, 1, 2, 20, 56, 97, 70, 74, 80, 41, 48], [84, 19, 98, 94, 25, 24, 23, 35, 59, 97, 41], [51, 51, 16, 65, 60, 49, 10, 80, 92, 3, 48], [16, 70, 39, 80, 51, 18, 70, 58, 4, 45, 48], [23, 91, 92, 14, 6, 10, 89, 39, 31, 44, 82]], [[33, 5, 63, 67, 37, 18, 4, 63, 93, 58, 30], [85, 82, 50, 59, 14, 61, 52, 95, 75, 91, 82], [31, 87, 66, 88, 38, 57, 4, 82, 73, 43, 75], [91, 16, 33, 40, 47, 34, 27, 2, 34, 80, 19], [93, 95, 21, 63, 53, 62, 50, 8, 21, 5, 44], [53, 71, 1, 78, 70, 2, 41, 55, 44, 18, 56], [37, 94, 28, 75, 86, 74, 58, 39, 97, 38, 54], [28, 56, 4, 68, 23, 82, 84, 99, 55, 95, 68], [82, 56, 30, 80, 74, 99, 31, 23, 24, 79, 76], [31, 0, 32, 82, 61, 84, 57, 58, 25, 40, 28], [69, 15, 30, 3, 21, 60, 4, 62, 72, 84, 95]]], 'objective': 16.0}","[[0, 4, 10], [1, 9, 1], [2, 10, 6], [3, 7, 2], [4, 8, 3], [5, 2, 9], [6, 6, 4], [7, 3, 0], [8, 0, 8], [9, 1, 7], [10, 5, 5]]",16.0,"{'problem_type': 'AP3', 'n': 11, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 98}, {'i': 1, 'j': 1, 'k': 2, 'cost': 21}, {'i': 1, 'j': 1, 'k': 3, 'cost': 40}, {'i': 1, 'j': 1, 'k': 4, 'cost': 1}, {'i': 1, 'j': 1, 'k': 5, 'cost': 98}, {'i': 1, 'j': 1, 'k': 6, 'cost': 69}, {'i': 1, 'j': 1, 'k': 7, 'cost': 24}, {'i': 1, 'j': 1, 'k': 8, 'cost': 59}, {'i': 1, 'j': 1, 'k': 9, 'cost': 51}, {'i': 1, 'j': 1, 'k': 10, 'cost': 57}, {'i': 1, 'j': 1, 'k': 11, 'cost': 28}, {'i': 1, 'j': 2, 'k': 1, 'cost': 82}, {'i': 1, 'j': 2, 'k': 2, 'cost': 71}, {'i': 1, 'j': 2, 'k': 3, 'cost': 95}, {'i': 1, 'j': 2, 'k': 4, 'cost': 68}, {'i': 1, 'j': 2, 'k': 5, 'cost': 16}, {'i': 1, 'j': 2, 'k': 6, 'cost': 19}, {'i': 1, 'j': 2, 'k': 7, 'cost': 99}, {'i': 1, 'j': 2, 'k': 8, 'cost': 40}, {'i': 1, 'j': 2, 'k': 9, 'cost': 74}, {'i': 1, 'j': 2, 'k': 10, 'cost': 9}, {'i': 1, 'j': 2, 'k': 11, 'cost': 40}, {'i': 1, 'j': 3, 'k': 1, 'cost': 5}, {'i': 1, 'j': 3, 'k': 2, 'cost': 68}, {'i': 1, 'j': 3, 'k': 3, 'cost': 64}, {'i': 1, 'j': 3, 'k': 4, 'cost': 32}, {'i': 1, 'j': 3, 'k': 5, 'cost': 49}, {'i': 1, 'j': 3, 'k': 6, 'cost': 4}, {'i': 1, 'j': 3, 'k': 7, 'cost': 41}, {'i': 1, 'j': 3, 'k': 8, 'cost': 53}, {'i': 1, 'j': 3, 'k': 9, 'cost': 3}, {'i': 1, 'j': 3, 'k': 10, 'cost': 10}, {'i': 1, 'j': 3, 'k': 11, 'cost': 44}, {'i': 1, 'j': 4, 'k': 1, 'cost': 16}, {'i': 1, 'j': 4, 'k': 2, 'cost': 74}, {'i': 1, 'j': 4, 'k': 3, 'cost': 27}, {'i': 1, 'j': 4, 'k': 4, 'cost': 70}, {'i': 1, 'j': 4, 'k': 5, 'cost': 49}, {'i': 1, 'j': 4, 'k': 6, 'cost': 56}, {'i': 1, 'j': 4, 'k': 7, 'cost': 61}, {'i': 1, 'j': 4, 'k': 8, 'cost': 43}, {'i': 1, 'j': 4, 'k': 9, 'cost': 38}, {'i': 1, 'j': 4, 'k': 10, 'cost': 18}, {'i': 1, 'j': 4, 'k': 11, 'cost': 64}, {'i': 1, 'j': 5, 'k': 1, 'cost': 52}, {'i': 1, 'j': 5, 'k': 2, 'cost': 25}, {'i': 1, 'j': 5, 'k': 3, 'cost': 42}, {'i': 1, 'j': 5, 'k': 4, 'cost': 82}, {'i': 1, 'j': 5, 'k': 5, 'cost': 49}, {'i': 1, 'j': 5, 'k': 6, 'cost': 4}, {'i': 1, 'j': 5, 'k': 7, 'cost': 54}, {'i': 1, 'j': 5, 'k': 8, 'cost': 78}, {'i': 1, 'j': 5, 'k': 9, 'cost': 13}, {'i': 1, 'j': 5, 'k': 10, 'cost': 12}, {'i': 1, 'j': 5, 'k': 11, 'cost': 1}, {'i': 1, 'j': 6, 'k': 1, 'cost': 52}, {'i': 1, 'j': 6, 'k': 2, 'cost': 26}, {'i': 1, 'j': 6, 'k': 3, 'cost': 60}, {'i': 1, 'j': 6, 'k': 4, 'cost': 80}, {'i': 1, 'j': 6, 'k': 5, 'cost': 99}, {'i': 1, 'j': 6, 'k': 6, 'cost': 94}, {'i': 1, 'j': 6, 'k': 7, 'cost': 99}, {'i': 1, 'j': 6, 'k': 8, 'cost': 17}, {'i': 1, 'j': 6, 'k': 9, 'cost': 55}, {'i': 1, 'j': 6, 'k': 10, 'cost': 3}, {'i': 1, 'j': 6, 'k': 11, 'cost': 79}, {'i': 1, 'j': 7, 'k': 1, 'cost': 62}, {'i': 1, 'j': 7, 'k': 2, 'cost': 22}, {'i': 1, 'j': 7, 'k': 3, 'cost': 78}, {'i': 1, 'j': 7, 'k': 4, 'cost': 74}, {'i': 1, 'j': 7, 'k': 5, 'cost': 94}, {'i': 1, 'j': 7, 'k': 6, 'cost': 15}, {'i': 1, 'j': 7, 'k': 7, 'cost': 38}, {'i': 1, 'j': 7, 'k': 8, 'cost': 98}, {'i': 1, 'j': 7, 'k': 9, 'cost': 83}, {'i': 1, 'j': 7, 'k': 10, 'cost': 85}, {'i': 1, 'j': 7, 'k': 11, 'cost': 71}, {'i': 1, 'j': 8, 'k': 1, 'cost': 75}, {'i': 1, 'j': 8, 'k': 2, 'cost': 37}, {'i': 1, 'j': 8, 'k': 3, 'cost': 9}, {'i': 1, 'j': 8, 'k': 4, 'cost': 63}, {'i': 1, 'j': 8, 'k': 5, 'cost': 85}, {'i': 1, 'j': 8, 'k': 6, 'cost': 28}, {'i': 1, 'j': 8, 'k': 7, 'cost': 73}, {'i': 1, 'j': 8, 'k': 8, 'cost': 29}, {'i': 1, 'j': 8, 'k': 9, 'cost': 70}, {'i': 1, 'j': 8, 'k': 10, 'cost': 81}, {'i': 1, 'j': 8, 'k': 11, 'cost': 20}, {'i': 1, 'j': 9, 'k': 1, 'cost': 82}, {'i': 1, 'j': 9, 'k': 2, 'cost': 47}, {'i': 1, 'j': 9, 'k': 3, 'cost': 6}, {'i': 1, 'j': 9, 'k': 4, 'cost': 56}, {'i': 1, 'j': 9, 'k': 5, 'cost': 44}, {'i': 1, 'j': 9, 'k': 6, 'cost': 6}, {'i': 1, 'j': 9, 'k': 7, 'cost': 87}, {'i': 1, 'j': 9, 'k': 8, 'cost': 60}, {'i': 1, 'j': 9, 'k': 9, 'cost': 98}, {'i': 1, 'j': 9, 'k': 10, 'cost': 23}, {'i': 1, 'j': 9, 'k': 11, 'cost': 0}, {'i': 1, 'j': 10, 'k': 1, 'cost': 81}, {'i': 1, 'j': 10, 'k': 2, 'cost': 11}, {'i': 1, 'j': 10, 'k': 3, 'cost': 45}, {'i': 1, 'j': 10, 'k': 4, 'cost': 15}, {'i': 1, 'j': 10, 'k': 5, 'cost': 47}, {'i': 1, 'j': 10, 'k': 6, 'cost': 64}, {'i': 1, 'j': 10, 'k': 7, 'cost': 12}, {'i': 1, 'j': 10, 'k': 8, 'cost': 70}, {'i': 1, 'j': 10, 'k': 9, 'cost': 27}, {'i': 1, 'j': 10, 'k': 10, 'cost': 88}, {'i': 1, 'j': 10, 'k': 11, 'cost': 14}, {'i': 1, 'j': 11, 'k': 1, 'cost': 30}, {'i': 1, 'j': 11, 'k': 2, 'cost': 57}, {'i': 1, 'j': 11, 'k': 3, 'cost': 26}, {'i': 1, 'j': 11, 'k': 4, 'cost': 41}, {'i': 1, 'j': 11, 'k': 5, 'cost': 23}, {'i': 1, 'j': 11, 'k': 6, 'cost': 29}, {'i': 1, 'j': 11, 'k': 7, 'cost': 7}, {'i': 1, 'j': 11, 'k': 8, 'cost': 88}, {'i': 1, 'j': 11, 'k': 9, 'cost': 44}, {'i': 1, 'j': 11, 'k': 10, 'cost': 41}, {'i': 1, 'j': 11, 'k': 11, 'cost': 40}, {'i': 2, 'j': 1, 'k': 1, 'cost': 12}, {'i': 2, 'j': 1, 'k': 2, 'cost': 48}, {'i': 2, 'j': 1, 'k': 3, 'cost': 91}, {'i': 2, 'j': 1, 'k': 4, 'cost': 98}, {'i': 2, 'j': 1, 'k': 5, 'cost': 39}, {'i': 2, 'j': 1, 'k': 6, 'cost': 56}, {'i': 2, 'j': 1, 'k': 7, 'cost': 76}, {'i': 2, 'j': 1, 'k': 8, 'cost': 85}, {'i': 2, 'j': 1, 'k': 9, 'cost': 12}, {'i': 2, 'j': 1, 'k': 10, 'cost': 14}, {'i': 2, 'j': 1, 'k': 11, 'cost': 32}, {'i': 2, 'j': 2, 'k': 1, 'cost': 47}, {'i': 2, 'j': 2, 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'k': 6, 'cost': 53}, {'i': 10, 'j': 6, 'k': 7, 'cost': 53}, {'i': 10, 'j': 6, 'k': 8, 'cost': 97}, {'i': 10, 'j': 6, 'k': 9, 'cost': 10}, {'i': 10, 'j': 6, 'k': 10, 'cost': 32}, {'i': 10, 'j': 6, 'k': 11, 'cost': 59}, {'i': 10, 'j': 7, 'k': 1, 'cost': 54}, {'i': 10, 'j': 7, 'k': 2, 'cost': 1}, {'i': 10, 'j': 7, 'k': 3, 'cost': 2}, {'i': 10, 'j': 7, 'k': 4, 'cost': 20}, {'i': 10, 'j': 7, 'k': 5, 'cost': 56}, {'i': 10, 'j': 7, 'k': 6, 'cost': 97}, {'i': 10, 'j': 7, 'k': 7, 'cost': 70}, {'i': 10, 'j': 7, 'k': 8, 'cost': 74}, {'i': 10, 'j': 7, 'k': 9, 'cost': 80}, {'i': 10, 'j': 7, 'k': 10, 'cost': 41}, {'i': 10, 'j': 7, 'k': 11, 'cost': 48}, {'i': 10, 'j': 8, 'k': 1, 'cost': 84}, {'i': 10, 'j': 8, 'k': 2, 'cost': 19}, {'i': 10, 'j': 8, 'k': 3, 'cost': 98}, {'i': 10, 'j': 8, 'k': 4, 'cost': 94}, {'i': 10, 'j': 8, 'k': 5, 'cost': 25}, {'i': 10, 'j': 8, 'k': 6, 'cost': 24}, {'i': 10, 'j': 8, 'k': 7, 'cost': 23}, {'i': 10, 'j': 8, 'k': 8, 'cost': 35}, {'i': 10, 'j': 8, 'k': 9, 'cost': 59}, {'i': 10, 'j': 8, 'k': 10, 'cost': 97}, {'i': 10, 'j': 8, 'k': 11, 'cost': 41}, {'i': 10, 'j': 9, 'k': 1, 'cost': 51}, {'i': 10, 'j': 9, 'k': 2, 'cost': 51}, {'i': 10, 'j': 9, 'k': 3, 'cost': 16}, {'i': 10, 'j': 9, 'k': 4, 'cost': 65}, {'i': 10, 'j': 9, 'k': 5, 'cost': 60}, {'i': 10, 'j': 9, 'k': 6, 'cost': 49}, {'i': 10, 'j': 9, 'k': 7, 'cost': 10}, {'i': 10, 'j': 9, 'k': 8, 'cost': 80}, {'i': 10, 'j': 9, 'k': 9, 'cost': 92}, {'i': 10, 'j': 9, 'k': 10, 'cost': 3}, {'i': 10, 'j': 9, 'k': 11, 'cost': 48}, {'i': 10, 'j': 10, 'k': 1, 'cost': 16}, {'i': 10, 'j': 10, 'k': 2, 'cost': 70}, {'i': 10, 'j': 10, 'k': 3, 'cost': 39}, {'i': 10, 'j': 10, 'k': 4, 'cost': 80}, {'i': 10, 'j': 10, 'k': 5, 'cost': 51}, {'i': 10, 'j': 10, 'k': 6, 'cost': 18}, {'i': 10, 'j': 10, 'k': 7, 'cost': 70}, {'i': 10, 'j': 10, 'k': 8, 'cost': 58}, {'i': 10, 'j': 10, 'k': 9, 'cost': 4}, {'i': 10, 'j': 10, 'k': 10, 'cost': 45}, {'i': 10, 'j': 10, 'k': 11, 'cost': 48}, {'i': 10, 'j': 11, 'k': 1, 'cost': 23}, {'i': 10, 'j': 11, 'k': 2, 'cost': 91}, {'i': 10, 'j': 11, 'k': 3, 'cost': 92}, {'i': 10, 'j': 11, 'k': 4, 'cost': 14}, {'i': 10, 'j': 11, 'k': 5, 'cost': 6}, {'i': 10, 'j': 11, 'k': 6, 'cost': 10}, {'i': 10, 'j': 11, 'k': 7, 'cost': 89}, {'i': 10, 'j': 11, 'k': 8, 'cost': 39}, {'i': 10, 'j': 11, 'k': 9, 'cost': 31}, {'i': 10, 'j': 11, 'k': 10, 'cost': 44}, {'i': 10, 'j': 11, 'k': 11, 'cost': 82}, {'i': 11, 'j': 1, 'k': 1, 'cost': 33}, {'i': 11, 'j': 1, 'k': 2, 'cost': 5}, {'i': 11, 'j': 1, 'k': 3, 'cost': 63}, {'i': 11, 'j': 1, 'k': 4, 'cost': 67}, {'i': 11, 'j': 1, 'k': 5, 'cost': 37}, {'i': 11, 'j': 1, 'k': 6, 'cost': 18}, {'i': 11, 'j': 1, 'k': 7, 'cost': 4}, {'i': 11, 'j': 1, 'k': 8, 'cost': 63}, {'i': 11, 'j': 1, 'k': 9, 'cost': 93}, {'i': 11, 'j': 1, 'k': 10, 'cost': 58}, {'i': 11, 'j': 1, 'k': 11, 'cost': 30}, {'i': 11, 'j': 2, 'k': 1, 'cost': 85}, {'i': 11, 'j': 2, 'k': 2, 'cost': 82}, {'i': 11, 'j': 2, 'k': 3, 'cost': 50}, {'i': 11, 'j': 2, 'k': 4, 'cost': 59}, {'i': 11, 'j': 2, 'k': 5, 'cost': 14}, {'i': 11, 'j': 2, 'k': 6, 'cost': 61}, {'i': 11, 'j': 2, 'k': 7, 'cost': 52}, {'i': 11, 'j': 2, 'k': 8, 'cost': 95}, {'i': 11, 'j': 2, 'k': 9, 'cost': 75}, {'i': 11, 'j': 2, 'k': 10, 'cost': 91}, {'i': 11, 'j': 2, 'k': 11, 'cost': 82}, {'i': 11, 'j': 3, 'k': 1, 'cost': 31}, {'i': 11, 'j': 3, 'k': 2, 'cost': 87}, {'i': 11, 'j': 3, 'k': 3, 'cost': 66}, {'i': 11, 'j': 3, 'k': 4, 'cost': 88}, {'i': 11, 'j': 3, 'k': 5, 'cost': 38}, {'i': 11, 'j': 3, 'k': 6, 'cost': 57}, {'i': 11, 'j': 3, 'k': 7, 'cost': 4}, {'i': 11, 'j': 3, 'k': 8, 'cost': 82}, {'i': 11, 'j': 3, 'k': 9, 'cost': 73}, {'i': 11, 'j': 3, 'k': 10, 'cost': 43}, {'i': 11, 'j': 3, 'k': 11, 'cost': 75}, {'i': 11, 'j': 4, 'k': 1, 'cost': 91}, {'i': 11, 'j': 4, 'k': 2, 'cost': 16}, {'i': 11, 'j': 4, 'k': 3, 'cost': 33}, {'i': 11, 'j': 4, 'k': 4, 'cost': 40}, {'i': 11, 'j': 4, 'k': 5, 'cost': 47}, {'i': 11, 'j': 4, 'k': 6, 'cost': 34}, {'i': 11, 'j': 4, 'k': 7, 'cost': 27}, {'i': 11, 'j': 4, 'k': 8, 'cost': 2}, {'i': 11, 'j': 4, 'k': 9, 'cost': 34}, {'i': 11, 'j': 4, 'k': 10, 'cost': 80}, {'i': 11, 'j': 4, 'k': 11, 'cost': 19}, {'i': 11, 'j': 5, 'k': 1, 'cost': 93}, {'i': 11, 'j': 5, 'k': 2, 'cost': 95}, {'i': 11, 'j': 5, 'k': 3, 'cost': 21}, {'i': 11, 'j': 5, 'k': 4, 'cost': 63}, {'i': 11, 'j': 5, 'k': 5, 'cost': 53}, {'i': 11, 'j': 5, 'k': 6, 'cost': 62}, {'i': 11, 'j': 5, 'k': 7, 'cost': 50}, {'i': 11, 'j': 5, 'k': 8, 'cost': 8}, {'i': 11, 'j': 5, 'k': 9, 'cost': 21}, {'i': 11, 'j': 5, 'k': 10, 'cost': 5}, {'i': 11, 'j': 5, 'k': 11, 'cost': 44}, {'i': 11, 'j': 6, 'k': 1, 'cost': 53}, {'i': 11, 'j': 6, 'k': 2, 'cost': 71}, {'i': 11, 'j': 6, 'k': 3, 'cost': 1}, {'i': 11, 'j': 6, 'k': 4, 'cost': 78}, {'i': 11, 'j': 6, 'k': 5, 'cost': 70}, {'i': 11, 'j': 6, 'k': 6, 'cost': 2}, {'i': 11, 'j': 6, 'k': 7, 'cost': 41}, {'i': 11, 'j': 6, 'k': 8, 'cost': 55}, {'i': 11, 'j': 6, 'k': 9, 'cost': 44}, {'i': 11, 'j': 6, 'k': 10, 'cost': 18}, {'i': 11, 'j': 6, 'k': 11, 'cost': 56}, {'i': 11, 'j': 7, 'k': 1, 'cost': 37}, {'i': 11, 'j': 7, 'k': 2, 'cost': 94}, {'i': 11, 'j': 7, 'k': 3, 'cost': 28}, {'i': 11, 'j': 7, 'k': 4, 'cost': 75}, {'i': 11, 'j': 7, 'k': 5, 'cost': 86}, {'i': 11, 'j': 7, 'k': 6, 'cost': 74}, {'i': 11, 'j': 7, 'k': 7, 'cost': 58}, {'i': 11, 'j': 7, 'k': 8, 'cost': 39}, {'i': 11, 'j': 7, 'k': 9, 'cost': 97}, {'i': 11, 'j': 7, 'k': 10, 'cost': 38}, {'i': 11, 'j': 7, 'k': 11, 'cost': 54}, {'i': 11, 'j': 8, 'k': 1, 'cost': 28}, {'i': 11, 'j': 8, 'k': 2, 'cost': 56}, {'i': 11, 'j': 8, 'k': 3, 'cost': 4}, {'i': 11, 'j': 8, 'k': 4, 'cost': 68}, {'i': 11, 'j': 8, 'k': 5, 'cost': 23}, {'i': 11, 'j': 8, 'k': 6, 'cost': 82}, {'i': 11, 'j': 8, 'k': 7, 'cost': 84}, {'i': 11, 'j': 8, 'k': 8, 'cost': 99}, {'i': 11, 'j': 8, 'k': 9, 'cost': 55}, {'i': 11, 'j': 8, 'k': 10, 'cost': 95}, {'i': 11, 'j': 8, 'k': 11, 'cost': 68}, {'i': 11, 'j': 9, 'k': 1, 'cost': 82}, {'i': 11, 'j': 9, 'k': 2, 'cost': 56}, {'i': 11, 'j': 9, 'k': 3, 'cost': 30}, {'i': 11, 'j': 9, 'k': 4, 'cost': 80}, {'i': 11, 'j': 9, 'k': 5, 'cost': 74}, {'i': 11, 'j': 9, 'k': 6, 'cost': 99}, {'i': 11, 'j': 9, 'k': 7, 'cost': 31}, {'i': 11, 'j': 9, 'k': 8, 'cost': 23}, {'i': 11, 'j': 9, 'k': 9, 'cost': 24}, {'i': 11, 'j': 9, 'k': 10, 'cost': 79}, {'i': 11, 'j': 9, 'k': 11, 'cost': 76}, {'i': 11, 'j': 10, 'k': 1, 'cost': 31}, {'i': 11, 'j': 10, 'k': 2, 'cost': 0}, {'i': 11, 'j': 10, 'k': 3, 'cost': 32}, {'i': 11, 'j': 10, 'k': 4, 'cost': 82}, {'i': 11, 'j': 10, 'k': 5, 'cost': 61}, {'i': 11, 'j': 10, 'k': 6, 'cost': 84}, {'i': 11, 'j': 10, 'k': 7, 'cost': 57}, {'i': 11, 'j': 10, 'k': 8, 'cost': 58}, {'i': 11, 'j': 10, 'k': 9, 'cost': 25}, {'i': 11, 'j': 10, 'k': 10, 'cost': 40}, {'i': 11, 'j': 10, 'k': 11, 'cost': 28}, {'i': 11, 'j': 11, 'k': 1, 'cost': 69}, {'i': 11, 'j': 11, 'k': 2, 'cost': 15}, {'i': 11, 'j': 11, 'k': 3, 'cost': 30}, {'i': 11, 'j': 11, 'k': 4, 'cost': 3}, {'i': 11, 'j': 11, 'k': 5, 'cost': 21}, {'i': 11, 'j': 11, 'k': 6, 'cost': 60}, {'i': 11, 'j': 11, 'k': 7, 'cost': 4}, {'i': 11, 'j': 11, 'k': 8, 'cost': 62}, {'i': 11, 'j': 11, 'k': 9, 'cost': 72}, {'i': 11, 'j': 11, 'k': 10, 'cost': 84}, {'i': 11, 'j': 11, 'k': 11, 'cost': 95}]}","[[1, 5, 11], [2, 10, 2], [3, 11, 7], [4, 8, 3], [5, 9, 4], [6, 3, 10], [7, 7, 5], [8, 4, 1], [9, 1, 9], [10, 2, 8], [11, 6, 6]]",43,markdown_table,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"": 12,
+  ""index_ids"": [
+    ""A"",
+    ""B"",
+    ""C"",
+    ""D"",
+    ""E"",
+    ""F"",
+    ""G"",
+    ""H"",
+    ""I"",
+    ""J"",
+    ""K"",
+    ""L""
+  ]
+}
+
+# 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 | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 94 | 64 | 14 | 57 | 21 | 26 | 54 | 81 | 10 | 3 | 27 | 58 |
+| B | 65 | 87 | 7 | 89 | 29 | 35 | 49 | 80 | 76 | 44 | 84 | 90 |
+| C | 20 | 95 | 77 | 71 | 81 | 78 | 75 | 90 | 6 | 42 | 11 | 52 |
+| D | 91 | 81 | 4 | 67 | 82 | 59 | 44 | 99 | 95 | 45 | 41 | 86 |
+| E | 24 | 97 | 88 | 46 | 22 | 96 | 81 | 12 | 93 | 44 | 18 | 38 |
+| F | 94 | 24 | 64 | 0 | 92 | 21 | 28 | 95 | 3 | 13 | 48 | 40 |
+| G | 27 | 48 | 43 | 91 | 80 | 76 | 92 | 74 | 15 | 65 | 93 | 90 |
+| H | 18 | 73 | 13 | 7 | 52 | 97 | 23 | 40 | 59 | 10 | 75 | 4 |
+| I | 27 | 45 | 75 | 42 | 91 | 87 | 95 | 39 | 96 | 38 | 2 | 15 |
+| J | 86 | 61 | 13 | 68 | 36 | 8 | 33 | 29 | 11 | 55 | 95 | 44 |
+| K | 11 | 37 | 11 | 25 | 1 | 21 | 99 | 42 | 0 | 11 | 45 | 63 |
+| L | 17 | 69 | 12 | 23 | 62 | 74 | 96 | 74 | 14 | 16 | 99 | 10 |
+
+## customer_id=B
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 23 | 48 | 51 | 59 | 19 | 89 | 92 | 6 | 71 | 66 | 69 | 27 |
+| B | 38 | 74 | 25 | 21 | 40 | 96 | 4 | 92 | 9 | 67 | 44 | 32 |
+| C | 54 | 22 | 37 | 90 | 3 | 91 | 89 | 73 | 84 | 13 | 45 | 53 |
+| D | 33 | 95 | 19 | 70 | 72 | 63 | 14 | 29 | 42 | 96 | 6 | 51 |
+| E | 86 | 65 | 31 | 45 | 86 | 65 | 61 | 87 | 6 | 60 | 71 | 2 |
+| F | 53 | 76 | 3 | 29 | 1 | 13 | 48 | 15 | 61 | 83 | 96 | 16 |
+| G | 51 | 70 | 72 | 1 | 60 | 1 | 31 | 90 | 7 | 28 | 36 | 95 |
+| H | 80 | 97 | 25 | 31 | 91 | 34 | 44 | 60 | 31 | 27 | 79 | 6 |
+| I | 74 | 1 | 92 | 41 | 56 | 97 | 63 | 4 | 53 | 38 | 69 | 28 |
+| J | 85 | 74 | 67 | 2 | 27 | 3 | 15 | 58 | 63 | 75 | 84 | 81 |
+| K | 59 | 34 | 37 | 1 | 49 | 6 | 47 | 46 | 15 | 3 | 84 | 86 |
+| L | 92 | 7 | 92 | 3 | 28 | 81 | 24 | 34 | 60 | 83 | 51 | 5 |
+
+## customer_id=C
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 94 | 39 | 50 | 47 | 24 | 94 | 11 | 18 | 57 | 45 | 34 | 43 |
+| B | 86 | 39 | 26 | 49 | 74 | 94 | 51 | 83 | 70 | 76 | 95 | 78 |
+| C | 73 | 58 | 4 | 4 | 67 | 83 | 70 | 95 | 13 | 10 | 3 | 17 |
+| D | 78 | 86 | 80 | 30 | 55 | 56 | 50 | 69 | 56 | 47 | 94 | 93 |
+| E | 63 | 48 | 22 | 96 | 70 | 81 | 1 | 23 | 31 | 52 | 99 | 4 |
+| F | 60 | 61 | 90 | 52 | 80 | 7 | 44 | 3 | 0 | 82 | 36 | 39 |
+| G | 82 | 62 | 62 | 82 | 34 | 30 | 29 | 28 | 84 | 43 | 61 | 38 |
+| H | 54 | 45 | 54 | 70 | 16 | 38 | 74 | 61 | 63 | 24 | 83 | 45 |
+| I | 19 | 44 | 79 | 66 | 99 | 69 | 95 | 95 | 17 | 4 | 48 | 48 |
+| J | 5 | 27 | 21 | 8 | 94 | 48 | 88 | 92 | 78 | 96 | 46 | 65 |
+| K | 36 | 6 | 67 | 36 | 2 | 19 | 2 | 84 | 78 | 63 | 20 | 58 |
+| L | 83 | 92 | 36 | 62 | 42 | 72 | 67 | 19 | 90 | 60 | 37 | 11 |
+
+## customer_id=D
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 76 | 9 | 42 | 19 | 17 | 24 | 18 | 41 | 8 | 95 | 98 | 66 |
+| B | 35 | 69 | 68 | 62 | 27 | 94 | 72 | 2 | 19 | 72 | 24 | 49 |
+| C | 44 | 75 | 35 | 91 | 6 | 60 | 89 | 62 | 35 | 22 | 33 | 43 |
+| D | 88 | 37 | 71 | 41 | 13 | 40 | 26 | 61 | 45 | 77 | 40 | 42 |
+| E | 65 | 34 | 73 | 51 | 4 | 36 | 98 | 94 | 29 | 42 | 74 | 80 |
+| F | 95 | 73 | 69 | 7 | 76 | 69 | 12 | 28 | 19 | 52 | 53 | 79 |
+| G | 1 | 96 | 43 | 25 | 80 | 99 | 30 | 93 | 94 | 93 | 42 | 17 |
+| H | 25 | 77 | 50 | 5 | 0 | 71 | 12 | 23 | 67 | 97 | 66 | 79 |
+| I | 77 | 27 | 28 | 79 | 32 | 92 | 16 | 30 | 45 | 21 | 14 | 20 |
+| J | 0 | 71 | 82 | 28 | 27 | 17 | 53 | 64 | 29 | 78 | 78 | 56 |
+| K | 32 | 29 | 23 | 74 | 54 | 19 | 95 | 0 | 33 | 85 | 45 | 17 |
+| L | 56 | 11 | 99 | 41 | 42 | 78 | 70 | 44 | 47 | 98 | 3 | 27 |
+
+## customer_id=E
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 21 | 38 | 31 | 25 | 40 | 32 | 33 | 8 | 35 | 57 | 45 | 45 |
+| B | 35 | 61 | 9 | 31 | 84 | 19 | 60 | 70 | 85 | 59 | 97 | 75 |
+| C | 68 | 61 | 0 | 37 | 64 | 66 | 92 | 32 | 23 | 69 | 61 | 69 |
+| D | 78 | 88 | 39 | 44 | 44 | 68 | 80 | 50 | 74 | 68 | 1 | 47 |
+| E | 31 | 38 | 51 | 83 | 85 | 61 | 32 | 52 | 88 | 86 | 20 | 99 |
+| F | 17 | 0 | 62 | 84 | 28 | 83 | 5 | 19 | 80 | 77 | 17 | 58 |
+| G | 21 | 10 | 9 | 45 | 92 | 11 | 87 | 7 | 41 | 15 | 3 | 19 |
+| H | 27 | 95 | 29 | 70 | 1 | 37 | 50 | 31 | 23 | 24 | 23 | 28 |
+| I | 7 | 38 | 23 | 21 | 89 | 47 | 71 | 52 | 39 | 82 | 31 | 42 |
+| J | 60 | 27 | 29 | 0 | 21 | 7 | 18 | 48 | 36 | 98 | 99 | 23 |
+| K | 21 | 77 | 89 | 85 | 71 | 92 | 60 | 87 | 49 | 7 | 2 | 1 |
+| L | 5 | 13 | 98 | 22 | 42 | 56 | 9 | 84 | 68 | 66 | 92 | 39 |
+
+## customer_id=F
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 39 | 56 | 64 | 68 | 48 | 89 | 26 | 48 | 71 | 38 | 23 | 65 |
+| B | 39 | 24 | 78 | 93 | 0 | 7 | 33 | 73 | 7 | 33 | 16 | 36 |
+| C | 43 | 19 | 90 | 81 | 47 | 36 | 30 | 16 | 50 | 38 | 83 | 51 |
+| D | 33 | 22 | 27 | 96 | 67 | 86 | 46 | 9 | 91 | 52 | 43 | 6 |
+| E | 53 | 90 | 35 | 71 | 72 | 30 | 89 | 88 | 86 | 24 | 95 | 35 |
+| F | 71 | 42 | 51 | 69 | 84 | 23 | 45 | 23 | 77 | 33 | 51 | 71 |
+| G | 0 | 39 | 44 | 36 | 65 | 9 | 93 | 10 | 29 | 16 | 45 | 98 |
+| H | 19 | 49 | 55 | 67 | 16 | 7 | 34 | 80 | 50 | 20 | 34 | 96 |
+| I | 5 | 59 | 88 | 21 | 17 | 67 | 33 | 66 | 25 | 31 | 40 | 92 |
+| J | 8 | 23 | 37 | 63 | 75 | 55 | 23 | 11 | 17 | 68 | 71 | 43 |
+| K | 84 | 53 | 72 | 54 | 82 | 93 | 3 | 26 | 92 | 43 | 19 | 67 |
+| L | 70 | 50 | 34 | 3 | 37 | 42 | 44 | 28 | 62 | 10 | 73 | 35 |
+
+## customer_id=G
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 34 | 91 | 52 | 99 | 64 | 2 | 49 | 22 | 88 | 64 | 47 | 1 |
+| B | 11 | 42 | 6 | 75 | 81 | 51 | 86 | 1 | 10 | 64 | 61 | 77 |
+| C | 4 | 69 | 65 | 8 | 6 | 66 | 27 | 4 | 67 | 3 | 53 | 66 |
+| D | 88 | 53 | 94 | 0 | 71 | 78 | 13 | 94 | 53 | 58 | 69 | 28 |
+| E | 15 | 12 | 56 | 24 | 32 | 23 | 75 | 54 | 44 | 71 | 37 | 81 |
+| F | 87 | 28 | 15 | 16 | 52 | 7 | 54 | 29 | 42 | 49 | 51 | 47 |
+| G | 5 | 69 | 74 | 58 | 52 | 86 | 77 | 44 | 81 | 58 | 68 | 23 |
+| H | 99 | 41 | 81 | 68 | 21 | 68 | 13 | 95 | 62 | 0 | 56 | 86 |
+| I | 31 | 3 | 85 | 35 | 57 | 89 | 39 | 13 | 26 | 21 | 49 | 98 |
+| J | 7 | 43 | 26 | 8 | 23 | 33 | 63 | 34 | 39 | 4 | 56 | 41 |
+| K | 71 | 7 | 1 | 6 | 22 | 32 | 11 | 50 | 54 | 78 | 61 | 53 |
+| L | 39 | 5 | 66 | 64 | 93 | 25 | 90 | 37 | 52 | 10 | 29 | 26 |
+
+## customer_id=H
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 47 | 85 | 83 | 39 | 19 | 15 | 50 | 83 | 93 | 18 | 91 | 95 |
+| B | 45 | 71 | 8 | 72 | 13 | 88 | 13 | 71 | 32 | 40 | 33 | 98 |
+| C | 98 | 6 | 82 | 32 | 30 | 42 | 89 | 6 | 53 | 15 | 8 | 79 |
+| D | 44 | 36 | 48 | 59 | 95 | 50 | 14 | 73 | 11 | 13 | 38 | 94 |
+| E | 18 | 65 | 34 | 46 | 55 | 89 | 55 | 69 | 52 | 56 | 31 | 6 |
+| F | 27 | 62 | 85 | 91 | 83 | 26 | 98 | 39 | 37 | 34 | 17 | 3 |
+| G | 8 | 78 | 20 | 73 | 10 | 99 | 88 | 89 | 65 | 90 | 16 | 9 |
+| H | 31 | 58 | 20 | 59 | 58 | 73 | 47 | 88 | 43 | 62 | 20 | 15 |
+| I | 80 | 20 | 58 | 86 | 98 | 69 | 39 | 82 | 67 | 84 | 16 | 15 |
+| J | 58 | 3 | 66 | 83 | 53 | 7 | 52 | 76 | 50 | 16 | 10 | 27 |
+| K | 43 | 85 | 52 | 11 | 35 | 68 | 13 | 80 | 62 | 93 | 98 | 1 |
+| L | 3 | 32 | 64 | 0 | 7 | 52 | 35 | 91 | 19 | 58 | 32 | 77 |
+
+## customer_id=I
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 99 | 29 | 11 | 10 | 69 | 66 | 92 | 64 | 39 | 6 | 91 | 6 |
+| B | 73 | 57 | 83 | 75 | 31 | 38 | 26 | 18 | 99 | 51 | 83 | 28 |
+| C | 32 | 55 | 41 | 26 | 31 | 31 | 11 | 71 | 92 | 24 | 7 | 22 |
+| D | 92 | 71 | 76 | 28 | 63 | 65 | 95 | 47 | 21 | 0 | 99 | 1 |
+| E | 36 | 63 | 6 | 25 | 71 | 8 | 23 | 43 | 18 | 2 | 76 | 26 |
+| F | 83 | 67 | 7 | 75 | 84 | 94 | 89 | 78 | 53 | 98 | 36 | 57 |
+| G | 62 | 26 | 85 | 65 | 78 | 36 | 89 | 87 | 44 | 38 | 95 | 64 |
+| H | 47 | 21 | 36 | 49 | 92 | 32 | 59 | 47 | 83 | 67 | 50 | 60 |
+| I | 29 | 63 | 42 | 73 | 77 | 78 | 15 | 50 | 97 | 60 | 39 | 24 |
+| J | 27 | 53 | 41 | 21 | 23 | 33 | 45 | 0 | 24 | 67 | 88 | 96 |
+| K | 89 | 28 | 29 | 58 | 46 | 16 | 68 | 63 | 13 | 38 | 93 | 46 |
+| L | 19 | 29 | 82 | 33 | 82 | 31 | 10 | 35 | 0 | 11 | 95 | 57 |
+
+## customer_id=J
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 67 | 45 | 76 | 47 | 78 | 33 | 85 | 78 | 64 | 47 | 1 | 66 |
+| B | 70 | 83 | 66 | 75 | 9 | 33 | 61 | 19 | 53 | 79 | 41 | 86 |
+| C | 40 | 20 | 51 | 47 | 53 | 24 | 86 | 52 | 9 | 4 | 16 | 43 |
+| D | 49 | 92 | 81 | 99 | 36 | 75 | 65 | 43 | 13 | 83 | 89 | 6 |
+| E | 62 | 54 | 46 | 10 | 83 | 76 | 37 | 61 | 70 | 3 | 5 | 58 |
+| F | 6 | 79 | 30 | 7 | 96 | 13 | 69 | 35 | 23 | 70 | 92 | 33 |
+| G | 30 | 6 | 67 | 86 | 96 | 90 | 47 | 74 | 7 | 67 | 40 | 56 |
+| H | 80 | 98 | 10 | 16 | 78 | 98 | 71 | 50 | 81 | 52 | 35 | 51 |
+| I | 38 | 93 | 36 | 46 | 85 | 31 | 44 | 61 | 99 | 72 | 62 | 34 |
+| J | 51 | 59 | 69 | 82 | 89 | 45 | 60 | 97 | 44 | 7 | 40 | 45 |
+| K | 7 | 50 | 50 | 34 | 49 | 17 | 46 | 60 | 67 | 99 | 49 | 94 |
+| L | 89 | 48 | 27 | 38 | 7 | 31 | 53 | 26 | 33 | 58 | 31 | 95 |
+
+## customer_id=K
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 39 | 21 | 90 | 14 | 64 | 60 | 12 | 47 | 94 | 99 | 36 | 94 |
+| B | 85 | 26 | 47 | 79 | 89 | 97 | 27 | 42 | 72 | 43 | 68 | 22 |
+| C | 72 | 17 | 30 | 76 | 80 | 48 | 88 | 80 | 57 | 77 | 40 | 50 |
+| D | 2 | 94 | 75 | 35 | 37 | 53 | 32 | 16 | 48 | 57 | 66 | 46 |
+| E | 80 | 30 | 30 | 33 | 81 | 35 | 39 | 18 | 96 | 24 | 50 | 63 |
+| F | 56 | 49 | 84 | 34 | 93 | 45 | 58 | 11 | 18 | 93 | 24 | 37 |
+| G | 0 | 97 | 8 | 51 | 57 | 12 | 86 | 19 | 56 | 60 | 42 | 92 |
+| H | 50 | 69 | 92 | 77 | 16 | 45 | 78 | 67 | 94 | 19 | 73 | 35 |
+| I | 66 | 96 | 36 | 29 | 61 | 93 | 61 | 60 | 33 | 55 | 28 | 37 |
+| J | 24 | 28 | 63 | 8 | 8 | 46 | 72 | 54 | 91 | 61 | 27 | 38 |
+| K | 85 | 44 | 90 | 63 | 96 | 51 | 24 | 76 | 71 | 96 | 14 | 28 |
+| L | 67 | 25 | 13 | 9 | 46 | 23 | 34 | 51 | 76 | 84 | 44 | 35 |
+
+## customer_id=L
+| stylist_id\fitting_room_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 57 | 92 | 24 | 4 | 51 | 43 | 96 | 93 | 98 | 63 | 75 | 21 |
+| B | 52 | 30 | 98 | 18 | 38 | 60 | 71 | 82 | 59 | 82 | 3 | 4 |
+| C | 69 | 72 | 56 | 57 | 63 | 90 | 53 | 16 | 61 | 1 | 87 | 78 |
+| D | 78 | 26 | 60 | 22 | 82 | 54 | 47 | 84 | 48 | 95 | 60 | 9 |
+| E | 5 | 30 | 76 | 37 | 87 | 52 | 72 | 56 | 19 | 29 | 10 | 56 |
+| F | 69 | 49 | 54 | 74 | 7 | 81 | 22 | 6 | 31 | 72 | 76 | 11 |
+| G | 55 | 49 | 49 | 1 | 83 | 98 | 44 | 57 | 18 | 32 | 50 | 9 |
+| H | 90 | 60 | 73 | 82 | 44 | 76 | 58 | 86 | 79 | 65 | 73 | 78 |
+| I | 3 | 53 | 23 | 65 | 79 | 37 | 51 | 68 | 79 | 17 | 88 | 56 |
+| J | 39 | 73 | 52 | 41 | 66 | 99 | 50 | 15 | 80 | 52 | 58 | 57 |
+| K | 56 | 57 | 58 | 5 | 60 | 92 | 21 | 52 | 25 | 86 | 68 | 14 |
+| L | 67 | 82 | 97 | 57 | 7 | 59 | 95 | 54 | 36 | 44 | 4 | 66 |
+
+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': [[[94, 64, 14, 57, 21, 26, 54, 81, 10, 3, 27, 58], [65, 87, 7, 89, 29, 35, 49, 80, 76, 44, 84, 90], [20, 95, 77, 71, 81, 78, 75, 90, 6, 42, 11, 52], [91, 81, 4, 67, 82, 59, 44, 99, 95, 45, 41, 86], [24, 97, 88, 46, 22, 96, 81, 12, 93, 44, 18, 38], [94, 24, 64, 0, 92, 21, 28, 95, 3, 13, 48, 40], [27, 48, 43, 91, 80, 76, 92, 74, 15, 65, 93, 90], [18, 73, 13, 7, 52, 97, 23, 40, 59, 10, 75, 4], [27, 45, 75, 42, 91, 87, 95, 39, 96, 38, 2, 15], [86, 61, 13, 68, 36, 8, 33, 29, 11, 55, 95, 44], [11, 37, 11, 25, 1, 21, 99, 42, 0, 11, 45, 63], [17, 69, 12, 23, 62, 74, 96, 74, 14, 16, 99, 10]], [[23, 48, 51, 59, 19, 89, 92, 6, 71, 66, 69, 27], [38, 74, 25, 21, 40, 96, 4, 92, 9, 67, 44, 32], [54, 22, 37, 90, 3, 91, 89, 73, 84, 13, 45, 53], [33, 95, 19, 70, 72, 63, 14, 29, 42, 96, 6, 51], [86, 65, 31, 45, 86, 65, 61, 87, 6, 60, 71, 2], [53, 76, 3, 29, 1, 13, 48, 15, 61, 83, 96, 16], [51, 70, 72, 1, 60, 1, 31, 90, 7, 28, 36, 95], [80, 97, 25, 31, 91, 34, 44, 60, 31, 27, 79, 6], [74, 1, 92, 41, 56, 97, 63, 4, 53, 38, 69, 28], [85, 74, 67, 2, 27, 3, 15, 58, 63, 75, 84, 81], [59, 34, 37, 1, 49, 6, 47, 46, 15, 3, 84, 86], [92, 7, 92, 3, 28, 81, 24, 34, 60, 83, 51, 5]], [[94, 39, 50, 47, 24, 94, 11, 18, 57, 45, 34, 43], [86, 39, 26, 49, 74, 94, 51, 83, 70, 76, 95, 78], [73, 58, 4, 4, 67, 83, 70, 95, 13, 10, 3, 17], [78, 86, 80, 30, 55, 56, 50, 69, 56, 47, 94, 93], [63, 48, 22, 96, 70, 81, 1, 23, 31, 52, 99, 4], [60, 61, 90, 52, 80, 7, 44, 3, 0, 82, 36, 39], [82, 62, 62, 82, 34, 30, 29, 28, 84, 43, 61, 38], [54, 45, 54, 70, 16, 38, 74, 61, 63, 24, 83, 45], [19, 44, 79, 66, 99, 69, 95, 95, 17, 4, 48, 48], [5, 27, 21, 8, 94, 48, 88, 92, 78, 96, 46, 65], [36, 6, 67, 36, 2, 19, 2, 84, 78, 63, 20, 58], [83, 92, 36, 62, 42, 72, 67, 19, 90, 60, 37, 11]], [[76, 9, 42, 19, 17, 24, 18, 41, 8, 95, 98, 66], [35, 69, 68, 62, 27, 94, 72, 2, 19, 72, 24, 49], [44, 75, 35, 91, 6, 60, 89, 62, 35, 22, 33, 43], [88, 37, 71, 41, 13, 40, 26, 61, 45, 77, 40, 42], [65, 34, 73, 51, 4, 36, 98, 94, 29, 42, 74, 80], [95, 73, 69, 7, 76, 69, 12, 28, 19, 52, 53, 79], [1, 96, 43, 25, 80, 99, 30, 93, 94, 93, 42, 17], [25, 77, 50, 5, 0, 71, 12, 23, 67, 97, 66, 79], [77, 27, 28, 79, 32, 92, 16, 30, 45, 21, 14, 20], [0, 71, 82, 28, 27, 17, 53, 64, 29, 78, 78, 56], [32, 29, 23, 74, 54, 19, 95, 0, 33, 85, 45, 17], [56, 11, 99, 41, 42, 78, 70, 44, 47, 98, 3, 27]], [[21, 38, 31, 25, 40, 32, 33, 8, 35, 57, 45, 45], [35, 61, 9, 31, 84, 19, 60, 70, 85, 59, 97, 75], [68, 61, 0, 37, 64, 66, 92, 32, 23, 69, 61, 69], [78, 88, 39, 44, 44, 68, 80, 50, 74, 68, 1, 47], [31, 38, 51, 83, 85, 61, 32, 52, 88, 86, 20, 99], [17, 0, 62, 84, 28, 83, 5, 19, 80, 77, 17, 58], [21, 10, 9, 45, 92, 11, 87, 7, 41, 15, 3, 19], [27, 95, 29, 70, 1, 37, 50, 31, 23, 24, 23, 28], [7, 38, 23, 21, 89, 47, 71, 52, 39, 82, 31, 42], [60, 27, 29, 0, 21, 7, 18, 48, 36, 98, 99, 23], [21, 77, 89, 85, 71, 92, 60, 87, 49, 7, 2, 1], [5, 13, 98, 22, 42, 56, 9, 84, 68, 66, 92, 39]], [[39, 56, 64, 68, 48, 89, 26, 48, 71, 38, 23, 65], [39, 24, 78, 93, 0, 7, 33, 73, 7, 33, 16, 36], [43, 19, 90, 81, 47, 36, 30, 16, 50, 38, 83, 51], [33, 22, 27, 96, 67, 86, 46, 9, 91, 52, 43, 6], [53, 90, 35, 71, 72, 30, 89, 88, 86, 24, 95, 35], [71, 42, 51, 69, 84, 23, 45, 23, 77, 33, 51, 71], [0, 39, 44, 36, 65, 9, 93, 10, 29, 16, 45, 98], [19, 49, 55, 67, 16, 7, 34, 80, 50, 20, 34, 96], [5, 59, 88, 21, 17, 67, 33, 66, 25, 31, 40, 92], [8, 23, 37, 63, 75, 55, 23, 11, 17, 68, 71, 43], [84, 53, 72, 54, 82, 93, 3, 26, 92, 43, 19, 67], [70, 50, 34, 3, 37, 42, 44, 28, 62, 10, 73, 35]], [[34, 91, 52, 99, 64, 2, 49, 22, 88, 64, 47, 1], [11, 42, 6, 75, 81, 51, 86, 1, 10, 64, 61, 77], [4, 69, 65, 8, 6, 66, 27, 4, 67, 3, 53, 66], [88, 53, 94, 0, 71, 78, 13, 94, 53, 58, 69, 28], [15, 12, 56, 24, 32, 23, 75, 54, 44, 71, 37, 81], [87, 28, 15, 16, 52, 7, 54, 29, 42, 49, 51, 47], [5, 69, 74, 58, 52, 86, 77, 44, 81, 58, 68, 23], [99, 41, 81, 68, 21, 68, 13, 95, 62, 0, 56, 86], [31, 3, 85, 35, 57, 89, 39, 13, 26, 21, 49, 98], [7, 43, 26, 8, 23, 33, 63, 34, 39, 4, 56, 41], [71, 7, 1, 6, 22, 32, 11, 50, 54, 78, 61, 53], [39, 5, 66, 64, 93, 25, 90, 37, 52, 10, 29, 26]], [[47, 85, 83, 39, 19, 15, 50, 83, 93, 18, 91, 95], [45, 71, 8, 72, 13, 88, 13, 71, 32, 40, 33, 98], [98, 6, 82, 32, 30, 42, 89, 6, 53, 15, 8, 79], [44, 36, 48, 59, 95, 50, 14, 73, 11, 13, 38, 94], [18, 65, 34, 46, 55, 89, 55, 69, 52, 56, 31, 6], [27, 62, 85, 91, 83, 26, 98, 39, 37, 34, 17, 3], [8, 78, 20, 73, 10, 99, 88, 89, 65, 90, 16, 9], [31, 58, 20, 59, 58, 73, 47, 88, 43, 62, 20, 15], [80, 20, 58, 86, 98, 69, 39, 82, 67, 84, 16, 15], [58, 3, 66, 83, 53, 7, 52, 76, 50, 16, 10, 27], [43, 85, 52, 11, 35, 68, 13, 80, 62, 93, 98, 1], [3, 32, 64, 0, 7, 52, 35, 91, 19, 58, 32, 77]], [[99, 29, 11, 10, 69, 66, 92, 64, 39, 6, 91, 6], [73, 57, 83, 75, 31, 38, 26, 18, 99, 51, 83, 28], [32, 55, 41, 26, 31, 31, 11, 71, 92, 24, 7, 22], [92, 71, 76, 28, 63, 65, 95, 47, 21, 0, 99, 1], [36, 63, 6, 25, 71, 8, 23, 43, 18, 2, 76, 26], [83, 67, 7, 75, 84, 94, 89, 78, 53, 98, 36, 57], [62, 26, 85, 65, 78, 36, 89, 87, 44, 38, 95, 64], [47, 21, 36, 49, 92, 32, 59, 47, 83, 67, 50, 60], [29, 63, 42, 73, 77, 78, 15, 50, 97, 60, 39, 24], [27, 53, 41, 21, 23, 33, 45, 0, 24, 67, 88, 96], [89, 28, 29, 58, 46, 16, 68, 63, 13, 38, 93, 46], [19, 29, 82, 33, 82, 31, 10, 35, 0, 11, 95, 57]], [[67, 45, 76, 47, 78, 33, 85, 78, 64, 47, 1, 66], [70, 83, 66, 75, 9, 33, 61, 19, 53, 79, 41, 86], [40, 20, 51, 47, 53, 24, 86, 52, 9, 4, 16, 43], [49, 92, 81, 99, 36, 75, 65, 43, 13, 83, 89, 6], [62, 54, 46, 10, 83, 76, 37, 61, 70, 3, 5, 58], [6, 79, 30, 7, 96, 13, 69, 35, 23, 70, 92, 33], [30, 6, 67, 86, 96, 90, 47, 74, 7, 67, 40, 56], [80, 98, 10, 16, 78, 98, 71, 50, 81, 52, 35, 51], [38, 93, 36, 46, 85, 31, 44, 61, 99, 72, 62, 34], [51, 59, 69, 82, 89, 45, 60, 97, 44, 7, 40, 45], [7, 50, 50, 34, 49, 17, 46, 60, 67, 99, 49, 94], [89, 48, 27, 38, 7, 31, 53, 26, 33, 58, 31, 95]], [[39, 21, 90, 14, 64, 60, 12, 47, 94, 99, 36, 94], [85, 26, 47, 79, 89, 97, 27, 42, 72, 43, 68, 22], [72, 17, 30, 76, 80, 48, 88, 80, 57, 77, 40, 50], [2, 94, 75, 35, 37, 53, 32, 16, 48, 57, 66, 46], [80, 30, 30, 33, 81, 35, 39, 18, 96, 24, 50, 63], [56, 49, 84, 34, 93, 45, 58, 11, 18, 93, 24, 37], [0, 97, 8, 51, 57, 12, 86, 19, 56, 60, 42, 92], [50, 69, 92, 77, 16, 45, 78, 67, 94, 19, 73, 35], [66, 96, 36, 29, 61, 93, 61, 60, 33, 55, 28, 37], [24, 28, 63, 8, 8, 46, 72, 54, 91, 61, 27, 38], [85, 44, 90, 63, 96, 51, 24, 76, 71, 96, 14, 28], [67, 25, 13, 9, 46, 23, 34, 51, 76, 84, 44, 35]], [[57, 92, 24, 4, 51, 43, 96, 93, 98, 63, 75, 21], [52, 30, 98, 18, 38, 60, 71, 82, 59, 82, 3, 4], [69, 72, 56, 57, 63, 90, 53, 16, 61, 1, 87, 78], [78, 26, 60, 22, 82, 54, 47, 84, 48, 95, 60, 9], [5, 30, 76, 37, 87, 52, 72, 56, 19, 29, 10, 56], [69, 49, 54, 74, 7, 81, 22, 6, 31, 72, 76, 11], [55, 49, 49, 1, 83, 98, 44, 57, 18, 32, 50, 9], [90, 60, 73, 82, 44, 76, 58, 86, 79, 65, 73, 78], [3, 53, 23, 65, 79, 37, 51, 68, 79, 17, 88, 56], [39, 73, 52, 41, 66, 99, 50, 15, 80, 52, 58, 57], [56, 57, 58, 5, 60, 92, 21, 52, 25, 86, 68, 14], [67, 82, 97, 57, 7, 59, 95, 54, 36, 44, 4, 66]]], 'objective': 17.0}","[[0, 9, 5], [1, 8, 1], [2, 4, 6], [3, 10, 7], [4, 2, 2], [5, 1, 4], [6, 7, 9], [7, 5, 11], [8, 11, 8], [9, 0, 10], [10, 3, 0], [11, 6, 3]]",17.0,"{'problem_type': 'AP3', 'n': 12, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 94}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 64}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 14}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 57}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 21}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 26}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 54}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 81}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 10}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 3}, {'i': 'A', 'j': 'A', 'k': 'K', 'cost': 27}, {'i': 'A', 'j': 'A', 'k': 'L', 'cost': 58}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 65}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 87}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 7}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 89}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 29}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 35}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 49}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 80}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 76}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 44}, {'i': 'A', 'j': 'B', 'k': 'K', 'cost': 84}, {'i': 'A', 'j': 'B', 'k': 'L', 'cost': 90}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 20}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 95}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 77}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 71}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 81}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 78}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 75}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 90}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 6}, {'i': 'A', 'j': 'C', 'k': 'J', 'cost': 42}, {'i': 'A', 'j': 'C', 'k': 'K', 'cost': 11}, {'i': 'A', 'j': 'C', 'k': 'L', 'cost': 52}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 91}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 81}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 4}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 67}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 82}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 59}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 44}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 99}, {'i': 'A', 'j': 'D', 'k': 'I', 'cost': 95}, {'i': 'A', 'j': 'D', 'k': 'J', 'cost': 45}, {'i': 'A', 'j': 'D', 'k': 'K', 'cost': 41}, {'i': 'A', 'j': 'D', 'k': 'L', 'cost': 86}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 24}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 97}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 88}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 46}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 22}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 96}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 81}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 12}, {'i': 'A', 'j': 'E', 'k': 'I', 'cost': 93}, {'i': 'A', 'j': 'E', 'k': 'J', 'cost': 44}, {'i': 'A', 'j': 'E', 'k': 'K', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'L', 'cost': 38}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 94}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 24}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 64}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 0}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 92}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 21}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 28}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 95}, {'i': 'A', 'j': 'F', 'k': 'I', 'cost': 3}, {'i': 'A', 'j': 'F', 'k': 'J', 'cost': 13}, {'i': 'A', 'j': 'F', 'k': 'K', 'cost': 48}, {'i': 'A', 'j': 'F', 'k': 'L', 'cost': 40}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 27}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 48}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 43}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 91}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 80}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 76}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 92}, {'i': 'A', 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'cost': 82}, {'i': 'L', 'j': 'B', 'k': 'I', 'cost': 59}, {'i': 'L', 'j': 'B', 'k': 'J', 'cost': 82}, {'i': 'L', 'j': 'B', 'k': 'K', 'cost': 3}, {'i': 'L', 'j': 'B', 'k': 'L', 'cost': 4}, {'i': 'L', 'j': 'C', 'k': 'A', 'cost': 69}, {'i': 'L', 'j': 'C', 'k': 'B', 'cost': 72}, {'i': 'L', 'j': 'C', 'k': 'C', 'cost': 56}, {'i': 'L', 'j': 'C', 'k': 'D', 'cost': 57}, {'i': 'L', 'j': 'C', 'k': 'E', 'cost': 63}, {'i': 'L', 'j': 'C', 'k': 'F', 'cost': 90}, {'i': 'L', 'j': 'C', 'k': 'G', 'cost': 53}, {'i': 'L', 'j': 'C', 'k': 'H', 'cost': 16}, {'i': 'L', 'j': 'C', 'k': 'I', 'cost': 61}, {'i': 'L', 'j': 'C', 'k': 'J', 'cost': 1}, {'i': 'L', 'j': 'C', 'k': 'K', 'cost': 87}, {'i': 'L', 'j': 'C', 'k': 'L', 'cost': 78}, {'i': 'L', 'j': 'D', 'k': 'A', 'cost': 78}, {'i': 'L', 'j': 'D', 'k': 'B', 'cost': 26}, {'i': 'L', 'j': 'D', 'k': 'C', 'cost': 60}, {'i': 'L', 'j': 'D', 'k': 'D', 'cost': 22}, {'i': 'L', 'j': 'D', 'k': 'E', 'cost': 82}, {'i': 'L', 'j': 'D', 'k': 'F', 'cost': 54}, {'i': 'L', 'j': 'D', 'k': 'G', 'cost': 47}, {'i': 'L', 'j': 'D', 'k': 'H', 'cost': 84}, {'i': 'L', 'j': 'D', 'k': 'I', 'cost': 48}, {'i': 'L', 'j': 'D', 'k': 'J', 'cost': 95}, {'i': 'L', 'j': 'D', 'k': 'K', 'cost': 60}, {'i': 'L', 'j': 'D', 'k': 'L', 'cost': 9}, {'i': 'L', 'j': 'E', 'k': 'A', 'cost': 5}, {'i': 'L', 'j': 'E', 'k': 'B', 'cost': 30}, {'i': 'L', 'j': 'E', 'k': 'C', 'cost': 76}, {'i': 'L', 'j': 'E', 'k': 'D', 'cost': 37}, {'i': 'L', 'j': 'E', 'k': 'E', 'cost': 87}, {'i': 'L', 'j': 'E', 'k': 'F', 'cost': 52}, {'i': 'L', 'j': 'E', 'k': 'G', 'cost': 72}, {'i': 'L', 'j': 'E', 'k': 'H', 'cost': 56}, {'i': 'L', 'j': 'E', 'k': 'I', 'cost': 19}, {'i': 'L', 'j': 'E', 'k': 'J', 'cost': 29}, {'i': 'L', 'j': 'E', 'k': 'K', 'cost': 10}, {'i': 'L', 'j': 'E', 'k': 'L', 'cost': 56}, {'i': 'L', 'j': 'F', 'k': 'A', 'cost': 69}, {'i': 'L', 'j': 'F', 'k': 'B', 'cost': 49}, {'i': 'L', 'j': 'F', 'k': 'C', 'cost': 54}, {'i': 'L', 'j': 'F', 'k': 'D', 'cost': 74}, {'i': 'L', 'j': 'F', 'k': 'E', 'cost': 7}, {'i': 'L', 'j': 'F', 'k': 'F', 'cost': 81}, {'i': 'L', 'j': 'F', 'k': 'G', 'cost': 22}, {'i': 'L', 'j': 'F', 'k': 'H', 'cost': 6}, {'i': 'L', 'j': 'F', 'k': 'I', 'cost': 31}, {'i': 'L', 'j': 'F', 'k': 'J', 'cost': 72}, {'i': 'L', 'j': 'F', 'k': 'K', 'cost': 76}, {'i': 'L', 'j': 'F', 'k': 'L', 'cost': 11}, {'i': 'L', 'j': 'G', 'k': 'A', 'cost': 55}, {'i': 'L', 'j': 'G', 'k': 'B', 'cost': 49}, {'i': 'L', 'j': 'G', 'k': 'C', 'cost': 49}, {'i': 'L', 'j': 'G', 'k': 'D', 'cost': 1}, {'i': 'L', 'j': 'G', 'k': 'E', 'cost': 83}, {'i': 'L', 'j': 'G', 'k': 'F', 'cost': 98}, {'i': 'L', 'j': 'G', 'k': 'G', 'cost': 44}, {'i': 'L', 'j': 'G', 'k': 'H', 'cost': 57}, {'i': 'L', 'j': 'G', 'k': 'I', 'cost': 18}, {'i': 'L', 'j': 'G', 'k': 'J', 'cost': 32}, {'i': 'L', 'j': 'G', 'k': 'K', 'cost': 50}, {'i': 'L', 'j': 'G', 'k': 'L', 'cost': 9}, {'i': 'L', 'j': 'H', 'k': 'A', 'cost': 90}, {'i': 'L', 'j': 'H', 'k': 'B', 'cost': 60}, {'i': 'L', 'j': 'H', 'k': 'C', 'cost': 73}, {'i': 'L', 'j': 'H', 'k': 'D', 'cost': 82}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 44}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 76}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 58}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 86}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 79}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 65}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 73}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 78}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 3}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 53}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 23}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 65}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 79}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 37}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 51}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 68}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 79}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 17}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 88}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 56}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 39}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 73}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 52}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 41}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 66}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 99}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 50}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 15}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 80}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 52}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 58}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 57}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 56}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 57}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 58}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 5}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 60}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 92}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 21}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 52}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 25}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 86}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 68}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 14}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 67}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 82}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 97}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 57}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 7}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 59}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 95}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 54}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 36}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 44}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 4}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 66}]}","[['A', 'J', 'F'], ['B', 'I', 'B'], ['C', 'E', 'G'], ['D', 'K', 'H'], ['E', 'C', 'C'], ['F', 'B', 'E'], ['G', 'H', 'J'], ['H', 'F', 'L'], ['I', 'L', 'I'], ['J', 'A', 'K'], ['K', 'D', 'A'], ['L', 'G', 'D']]",44,json,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"": 9,
+  ""index_identifiers"": [
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8,
+    9
+  ]
+}
+
+# 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=1
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 34 | 26 | 14 | 99 | 39 | 96 | 47 | 97 | 64 |
+| 2 | 16 | 29 | 74 | 32 | 42 | 26 | 3 | 92 | 53 |
+| 3 | 11 | 93 | 7 | 7 | 89 | 36 | 37 | 54 | 94 |
+| 4 | 34 | 50 | 31 | 75 | 13 | 40 | 63 | 15 | 68 |
+| 5 | 95 | 90 | 55 | 61 | 35 | 21 | 94 | 33 | 54 |
+| 6 | 14 | 25 | 94 | 49 | 39 | 18 | 19 | 12 | 33 |
+| 7 | 80 | 23 | 35 | 48 | 65 | 37 | 23 | 86 | 61 |
+| 8 | 53 | 46 | 52 | 10 | 66 | 67 | 76 | 60 | 52 |
+| 9 | 18 | 94 | 51 | 65 | 91 | 76 | 9 | 45 | 41 |
+
+## screening_id=2
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 59 | 13 | 86 | 97 | 74 | 50 | 5 | 89 | 42 |
+| 2 | 36 | 12 | 40 | 75 | 86 | 84 | 1 | 63 | 62 |
+| 3 | 34 | 81 | 94 | 89 | 65 | 16 | 94 | 77 | 23 |
+| 4 | 89 | 23 | 83 | 44 | 6 | 66 | 66 | 22 | 99 |
+| 5 | 56 | 17 | 45 | 11 | 94 | 71 | 75 | 60 | 11 |
+| 6 | 96 | 61 | 29 | 53 | 55 | 70 | 75 | 42 | 9 |
+| 7 | 18 | 50 | 80 | 53 | 34 | 84 | 53 | 4 | 7 |
+| 8 | 16 | 35 | 87 | 34 | 44 | 4 | 46 | 1 | 96 |
+| 9 | 25 | 32 | 93 | 22 | 34 | 19 | 74 | 53 | 96 |
+
+## screening_id=3
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 79 | 64 | 3 | 94 | 10 | 28 | 13 | 42 | 68 |
+| 2 | 60 | 26 | 54 | 59 | 96 | 10 | 2 | 93 | 36 |
+| 3 | 68 | 54 | 22 | 82 | 2 | 71 | 61 | 29 | 39 |
+| 4 | 35 | 7 | 97 | 88 | 48 | 14 | 69 | 13 | 36 |
+| 5 | 58 | 30 | 60 | 34 | 8 | 37 | 46 | 38 | 32 |
+| 6 | 27 | 93 | 15 | 91 | 56 | 75 | 62 | 35 | 9 |
+| 7 | 39 | 6 | 39 | 54 | 75 | 53 | 72 | 0 | 36 |
+| 8 | 72 | 29 | 2 | 27 | 66 | 85 | 93 | 73 | 17 |
+| 9 | 8 | 33 | 50 | 12 | 63 | 64 | 98 | 63 | 27 |
+
+## screening_id=4
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 90 | 54 | 32 | 31 | 50 | 30 | 48 | 75 | 75 |
+| 2 | 60 | 79 | 12 | 42 | 14 | 95 | 47 | 68 | 27 |
+| 3 | 98 | 24 | 86 | 3 | 34 | 26 | 77 | 96 | 63 |
+| 4 | 77 | 21 | 7 | 93 | 11 | 87 | 39 | 16 | 73 |
+| 5 | 37 | 46 | 21 | 97 | 75 | 70 | 57 | 40 | 84 |
+| 6 | 96 | 29 | 19 | 62 | 53 | 7 | 83 | 29 | 89 |
+| 7 | 83 | 20 | 87 | 58 | 16 | 0 | 0 | 17 | 77 |
+| 8 | 57 | 23 | 47 | 42 | 80 | 19 | 75 | 86 | 57 |
+| 9 | 73 | 82 | 76 | 75 | 63 | 95 | 59 | 84 | 6 |
+
+## screening_id=5
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 72 | 49 | 21 | 71 | 22 | 43 | 31 | 4 | 64 |
+| 2 | 80 | 3 | 60 | 28 | 31 | 63 | 58 | 60 | 32 |
+| 3 | 62 | 63 | 91 | 72 | 92 | 94 | 66 | 0 | 10 |
+| 4 | 45 | 74 | 62 | 77 | 61 | 60 | 66 | 10 | 75 |
+| 5 | 24 | 40 | 91 | 28 | 44 | 76 | 65 | 73 | 0 |
+| 6 | 81 | 25 | 62 | 49 | 1 | 43 | 70 | 65 | 24 |
+| 7 | 92 | 29 | 71 | 26 | 73 | 75 | 3 | 92 | 14 |
+| 8 | 93 | 49 | 52 | 2 | 54 | 28 | 1 | 62 | 74 |
+| 9 | 58 | 43 | 19 | 8 | 0 | 70 | 25 | 83 | 47 |
+
+## screening_id=6
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 96 | 77 | 94 | 42 | 75 | 71 | 1 | 35 | 86 |
+| 2 | 66 | 97 | 4 | 0 | 81 | 78 | 41 | 87 | 91 |
+| 3 | 47 | 85 | 88 | 51 | 15 | 1 | 53 | 25 | 96 |
+| 4 | 77 | 86 | 1 | 31 | 62 | 97 | 97 | 41 | 30 |
+| 5 | 53 | 39 | 73 | 91 | 25 | 25 | 19 | 98 | 67 |
+| 6 | 24 | 17 | 19 | 94 | 41 | 89 | 1 | 52 | 24 |
+| 7 | 93 | 1 | 66 | 46 | 74 | 45 | 29 | 14 | 8 |
+| 8 | 19 | 32 | 94 | 55 | 17 | 7 | 48 | 91 | 53 |
+| 9 | 2 | 1 | 47 | 91 | 55 | 29 | 34 | 60 | 15 |
+
+## screening_id=7
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 94 | 51 | 28 | 54 | 2 | 93 | 17 | 39 | 54 |
+| 2 | 65 | 54 | 20 | 2 | 70 | 30 | 21 | 40 | 57 |
+| 3 | 67 | 75 | 13 | 39 | 33 | 99 | 6 | 40 | 43 |
+| 4 | 73 | 70 | 44 | 88 | 17 | 10 | 93 | 27 | 62 |
+| 5 | 70 | 70 | 70 | 75 | 1 | 42 | 97 | 75 | 68 |
+| 6 | 21 | 24 | 44 | 63 | 33 | 92 | 96 | 68 | 29 |
+| 7 | 88 | 88 | 13 | 46 | 93 | 84 | 41 | 74 | 55 |
+| 8 | 73 | 94 | 17 | 87 | 13 | 42 | 53 | 87 | 23 |
+| 9 | 71 | 72 | 49 | 42 | 6 | 72 | 50 | 71 | 30 |
+
+## screening_id=8
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 17 | 48 | 85 | 52 | 52 | 66 | 92 | 15 | 46 |
+| 2 | 87 | 40 | 83 | 47 | 58 | 71 | 51 | 70 | 8 |
+| 3 | 44 | 63 | 33 | 63 | 5 | 26 | 37 | 90 | 10 |
+| 4 | 75 | 38 | 57 | 60 | 3 | 54 | 72 | 27 | 19 |
+| 5 | 81 | 66 | 84 | 69 | 13 | 17 | 6 | 69 | 16 |
+| 6 | 49 | 93 | 10 | 78 | 11 | 83 | 9 | 69 | 72 |
+| 7 | 11 | 30 | 81 | 89 | 7 | 24 | 29 | 71 | 77 |
+| 8 | 22 | 86 | 55 | 88 | 31 | 19 | 11 | 35 | 65 |
+| 9 | 69 | 85 | 27 | 54 | 14 | 63 | 98 | 42 | 76 |
+
+## screening_id=9
+| technician_id\projector_model_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|
+| 1 | 99 | 56 | 93 | 72 | 45 | 50 | 84 | 89 | 83 |
+| 2 | 72 | 81 | 35 | 6 | 46 | 70 | 37 | 84 | 65 |
+| 3 | 26 | 45 | 82 | 36 | 6 | 65 | 28 | 10 | 47 |
+| 4 | 71 | 47 | 37 | 51 | 29 | 21 | 84 | 28 | 30 |
+| 5 | 44 | 47 | 54 | 72 | 13 | 77 | 5 | 48 | 54 |
+| 6 | 90 | 26 | 8 | 54 | 7 | 96 | 19 | 79 | 5 |
+| 7 | 85 | 25 | 1 | 59 | 18 | 32 | 15 | 95 | 60 |
+| 8 | 13 | 16 | 52 | 24 | 33 | 8 | 55 | 64 | 48 |
+| 9 | 89 | 58 | 60 | 46 | 29 | 48 | 11 | 36 | 31 |
+
+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': [[[34, 26, 14, 99, 39, 96, 47, 97, 64], [16, 29, 74, 32, 42, 26, 3, 92, 53], [11, 93, 7, 7, 89, 36, 37, 54, 94], [34, 50, 31, 75, 13, 40, 63, 15, 68], [95, 90, 55, 61, 35, 21, 94, 33, 54], [14, 25, 94, 49, 39, 18, 19, 12, 33], [80, 23, 35, 48, 65, 37, 23, 86, 61], [53, 46, 52, 10, 66, 67, 76, 60, 52], [18, 94, 51, 65, 91, 76, 9, 45, 41]], [[59, 13, 86, 97, 74, 50, 5, 89, 42], [36, 12, 40, 75, 86, 84, 1, 63, 62], [34, 81, 94, 89, 65, 16, 94, 77, 23], [89, 23, 83, 44, 6, 66, 66, 22, 99], [56, 17, 45, 11, 94, 71, 75, 60, 11], [96, 61, 29, 53, 55, 70, 75, 42, 9], [18, 50, 80, 53, 34, 84, 53, 4, 7], [16, 35, 87, 34, 44, 4, 46, 1, 96], [25, 32, 93, 22, 34, 19, 74, 53, 96]], [[79, 64, 3, 94, 10, 28, 13, 42, 68], [60, 26, 54, 59, 96, 10, 2, 93, 36], [68, 54, 22, 82, 2, 71, 61, 29, 39], [35, 7, 97, 88, 48, 14, 69, 13, 36], [58, 30, 60, 34, 8, 37, 46, 38, 32], [27, 93, 15, 91, 56, 75, 62, 35, 9], [39, 6, 39, 54, 75, 53, 72, 0, 36], [72, 29, 2, 27, 66, 85, 93, 73, 17], [8, 33, 50, 12, 63, 64, 98, 63, 27]], [[90, 54, 32, 31, 50, 30, 48, 75, 75], [60, 79, 12, 42, 14, 95, 47, 68, 27], [98, 24, 86, 3, 34, 26, 77, 96, 63], [77, 21, 7, 93, 11, 87, 39, 16, 73], [37, 46, 21, 97, 75, 70, 57, 40, 84], [96, 29, 19, 62, 53, 7, 83, 29, 89], [83, 20, 87, 58, 16, 0, 0, 17, 77], [57, 23, 47, 42, 80, 19, 75, 86, 57], [73, 82, 76, 75, 63, 95, 59, 84, 6]], [[72, 49, 21, 71, 22, 43, 31, 4, 64], [80, 3, 60, 28, 31, 63, 58, 60, 32], [62, 63, 91, 72, 92, 94, 66, 0, 10], [45, 74, 62, 77, 61, 60, 66, 10, 75], [24, 40, 91, 28, 44, 76, 65, 73, 0], [81, 25, 62, 49, 1, 43, 70, 65, 24], [92, 29, 71, 26, 73, 75, 3, 92, 14], [93, 49, 52, 2, 54, 28, 1, 62, 74], [58, 43, 19, 8, 0, 70, 25, 83, 47]], [[96, 77, 94, 42, 75, 71, 1, 35, 86], [66, 97, 4, 0, 81, 78, 41, 87, 91], [47, 85, 88, 51, 15, 1, 53, 25, 96], [77, 86, 1, 31, 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47, 37, 51, 29, 21, 84, 28, 30], [44, 47, 54, 72, 13, 77, 5, 48, 54], [90, 26, 8, 54, 7, 96, 19, 79, 5], [85, 25, 1, 59, 18, 32, 15, 95, 60], [13, 16, 52, 24, 33, 8, 55, 64, 48], [89, 58, 60, 46, 29, 48, 11, 36, 31]]], 'objective': 33.0}","[[0, 2, 3], [1, 7, 7], [2, 8, 0], [3, 6, 5], [4, 1, 1], [5, 3, 2], [6, 0, 4], [7, 4, 6], [8, 5, 8]]",33.0,"{'problem_type': 'AP3', 'n': 9, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 34}, {'i': 1, 'j': 1, 'k': 2, 'cost': 26}, {'i': 1, 'j': 1, 'k': 3, 'cost': 14}, {'i': 1, 'j': 1, 'k': 4, 'cost': 99}, {'i': 1, 'j': 1, 'k': 5, 'cost': 39}, {'i': 1, 'j': 1, 'k': 6, 'cost': 96}, {'i': 1, 'j': 1, 'k': 7, 'cost': 47}, {'i': 1, 'j': 1, 'k': 8, 'cost': 97}, {'i': 1, 'j': 1, 'k': 9, 'cost': 64}, {'i': 1, 'j': 2, 'k': 1, 'cost': 16}, {'i': 1, 'j': 2, 'k': 2, 'cost': 29}, {'i': 1, 'j': 2, 'k': 3, 'cost': 74}, {'i': 1, 'j': 2, 'k': 4, 'cost': 32}, {'i': 1, 'j': 2, 'k': 5, 'cost': 42}, {'i': 1, 'j': 2, 'k': 6, 'cost': 26}, {'i': 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{'i': 8, 'j': 4, 'k': 2, 'cost': 38}, {'i': 8, 'j': 4, 'k': 3, 'cost': 57}, {'i': 8, 'j': 4, 'k': 4, 'cost': 60}, {'i': 8, 'j': 4, 'k': 5, 'cost': 3}, {'i': 8, 'j': 4, 'k': 6, 'cost': 54}, {'i': 8, 'j': 4, 'k': 7, 'cost': 72}, {'i': 8, 'j': 4, 'k': 8, 'cost': 27}, {'i': 8, 'j': 4, 'k': 9, 'cost': 19}, {'i': 8, 'j': 5, 'k': 1, 'cost': 81}, {'i': 8, 'j': 5, 'k': 2, 'cost': 66}, {'i': 8, 'j': 5, 'k': 3, 'cost': 84}, {'i': 8, 'j': 5, 'k': 4, 'cost': 69}, {'i': 8, 'j': 5, 'k': 5, 'cost': 13}, {'i': 8, 'j': 5, 'k': 6, 'cost': 17}, {'i': 8, 'j': 5, 'k': 7, 'cost': 6}, {'i': 8, 'j': 5, 'k': 8, 'cost': 69}, {'i': 8, 'j': 5, 'k': 9, 'cost': 16}, {'i': 8, 'j': 6, 'k': 1, 'cost': 49}, {'i': 8, 'j': 6, 'k': 2, 'cost': 93}, {'i': 8, 'j': 6, 'k': 3, 'cost': 10}, {'i': 8, 'j': 6, 'k': 4, 'cost': 78}, {'i': 8, 'j': 6, 'k': 5, 'cost': 11}, {'i': 8, 'j': 6, 'k': 6, 'cost': 83}, {'i': 8, 'j': 6, 'k': 7, 'cost': 9}, {'i': 8, 'j': 6, 'k': 8, 'cost': 69}, {'i': 8, 'j': 6, 'k': 9, 'cost': 72}, {'i': 8, 'j': 7, 'k': 1, 'cost': 11}, {'i': 8, 'j': 7, 'k': 2, 'cost': 30}, {'i': 8, 'j': 7, 'k': 3, 'cost': 81}, {'i': 8, 'j': 7, 'k': 4, 'cost': 89}, {'i': 8, 'j': 7, 'k': 5, 'cost': 7}, {'i': 8, 'j': 7, 'k': 6, 'cost': 24}, {'i': 8, 'j': 7, 'k': 7, 'cost': 29}, {'i': 8, 'j': 7, 'k': 8, 'cost': 71}, {'i': 8, 'j': 7, 'k': 9, 'cost': 77}, {'i': 8, 'j': 8, 'k': 1, 'cost': 22}, {'i': 8, 'j': 8, 'k': 2, 'cost': 86}, {'i': 8, 'j': 8, 'k': 3, 'cost': 55}, {'i': 8, 'j': 8, 'k': 4, 'cost': 88}, {'i': 8, 'j': 8, 'k': 5, 'cost': 31}, {'i': 8, 'j': 8, 'k': 6, 'cost': 19}, {'i': 8, 'j': 8, 'k': 7, 'cost': 11}, {'i': 8, 'j': 8, 'k': 8, 'cost': 35}, {'i': 8, 'j': 8, 'k': 9, 'cost': 65}, {'i': 8, 'j': 9, 'k': 1, 'cost': 69}, {'i': 8, 'j': 9, 'k': 2, 'cost': 85}, {'i': 8, 'j': 9, 'k': 3, 'cost': 27}, {'i': 8, 'j': 9, 'k': 4, 'cost': 54}, {'i': 8, 'j': 9, 'k': 5, 'cost': 14}, {'i': 8, 'j': 9, 'k': 6, 'cost': 63}, {'i': 8, 'j': 9, 'k': 7, 'cost': 98}, {'i': 8, 'j': 9, 'k': 8, 'cost': 42}, {'i': 8, 'j': 9, 'k': 9, 'cost': 76}, {'i': 9, 'j': 1, 'k': 1, 'cost': 99}, {'i': 9, 'j': 1, 'k': 2, 'cost': 56}, {'i': 9, 'j': 1, 'k': 3, 'cost': 93}, {'i': 9, 'j': 1, 'k': 4, 'cost': 72}, {'i': 9, 'j': 1, 'k': 5, 'cost': 45}, {'i': 9, 'j': 1, 'k': 6, 'cost': 50}, {'i': 9, 'j': 1, 'k': 7, 'cost': 84}, {'i': 9, 'j': 1, 'k': 8, 'cost': 89}, {'i': 9, 'j': 1, 'k': 9, 'cost': 83}, {'i': 9, 'j': 2, 'k': 1, 'cost': 72}, {'i': 9, 'j': 2, 'k': 2, 'cost': 81}, {'i': 9, 'j': 2, 'k': 3, 'cost': 35}, {'i': 9, 'j': 2, 'k': 4, 'cost': 6}, {'i': 9, 'j': 2, 'k': 5, 'cost': 46}, {'i': 9, 'j': 2, 'k': 6, 'cost': 70}, {'i': 9, 'j': 2, 'k': 7, 'cost': 37}, {'i': 9, 'j': 2, 'k': 8, 'cost': 84}, {'i': 9, 'j': 2, 'k': 9, 'cost': 65}, {'i': 9, 'j': 3, 'k': 1, 'cost': 26}, {'i': 9, 'j': 3, 'k': 2, 'cost': 45}, {'i': 9, 'j': 3, 'k': 3, 'cost': 82}, {'i': 9, 'j': 3, 'k': 4, 'cost': 36}, {'i': 9, 'j': 3, 'k': 5, 'cost': 6}, {'i': 9, 'j': 3, 'k': 6, 'cost': 65}, {'i': 9, 'j': 3, 'k': 7, 'cost': 28}, {'i': 9, 'j': 3, 'k': 8, 'cost': 10}, {'i': 9, 'j': 3, 'k': 9, 'cost': 47}, {'i': 9, 'j': 4, 'k': 1, 'cost': 71}, {'i': 9, 'j': 4, 'k': 2, 'cost': 47}, {'i': 9, 'j': 4, 'k': 3, 'cost': 37}, {'i': 9, 'j': 4, 'k': 4, 'cost': 51}, {'i': 9, 'j': 4, 'k': 5, 'cost': 29}, {'i': 9, 'j': 4, 'k': 6, 'cost': 21}, {'i': 9, 'j': 4, 'k': 7, 'cost': 84}, {'i': 9, 'j': 4, 'k': 8, 'cost': 28}, {'i': 9, 'j': 4, 'k': 9, 'cost': 30}, {'i': 9, 'j': 5, 'k': 1, 'cost': 44}, {'i': 9, 'j': 5, 'k': 2, 'cost': 47}, {'i': 9, 'j': 5, 'k': 3, 'cost': 54}, {'i': 9, 'j': 5, 'k': 4, 'cost': 72}, {'i': 9, 'j': 5, 'k': 5, 'cost': 13}, {'i': 9, 'j': 5, 'k': 6, 'cost': 77}, {'i': 9, 'j': 5, 'k': 7, 'cost': 5}, {'i': 9, 'j': 5, 'k': 8, 'cost': 48}, {'i': 9, 'j': 5, 'k': 9, 'cost': 54}, {'i': 9, 'j': 6, 'k': 1, 'cost': 90}, {'i': 9, 'j': 6, 'k': 2, 'cost': 26}, {'i': 9, 'j': 6, 'k': 3, 'cost': 8}, {'i': 9, 'j': 6, 'k': 4, 'cost': 54}, {'i': 9, 'j': 6, 'k': 5, 'cost': 7}, {'i': 9, 'j': 6, 'k': 6, 'cost': 96}, {'i': 9, 'j': 6, 'k': 7, 'cost': 19}, {'i': 9, 'j': 6, 'k': 8, 'cost': 79}, {'i': 9, 'j': 6, 'k': 9, 'cost': 5}, {'i': 9, 'j': 7, 'k': 1, 'cost': 85}, {'i': 9, 'j': 7, 'k': 2, 'cost': 25}, {'i': 9, 'j': 7, 'k': 3, 'cost': 1}, {'i': 9, 'j': 7, 'k': 4, 'cost': 59}, {'i': 9, 'j': 7, 'k': 5, 'cost': 18}, {'i': 9, 'j': 7, 'k': 6, 'cost': 32}, {'i': 9, 'j': 7, 'k': 7, 'cost': 15}, {'i': 9, 'j': 7, 'k': 8, 'cost': 95}, {'i': 9, 'j': 7, 'k': 9, 'cost': 60}, {'i': 9, 'j': 8, 'k': 1, 'cost': 13}, {'i': 9, 'j': 8, 'k': 2, 'cost': 16}, {'i': 9, 'j': 8, 'k': 3, 'cost': 52}, {'i': 9, 'j': 8, 'k': 4, 'cost': 24}, {'i': 9, 'j': 8, 'k': 5, 'cost': 33}, {'i': 9, 'j': 8, 'k': 6, 'cost': 8}, {'i': 9, 'j': 8, 'k': 7, 'cost': 55}, {'i': 9, 'j': 8, 'k': 8, 'cost': 64}, {'i': 9, 'j': 8, 'k': 9, 'cost': 48}, {'i': 9, 'j': 9, 'k': 1, 'cost': 89}, {'i': 9, 'j': 9, 'k': 2, 'cost': 58}, {'i': 9, 'j': 9, 'k': 3, 'cost': 60}, {'i': 9, 'j': 9, 'k': 4, 'cost': 46}, {'i': 9, 'j': 9, 'k': 5, 'cost': 29}, {'i': 9, 'j': 9, 'k': 6, 'cost': 48}, {'i': 9, 'j': 9, 'k': 7, 'cost': 11}, {'i': 9, 'j': 9, 'k': 8, 'cost': 36}, {'i': 9, 'j': 9, 'k': 9, 'cost': 31}]}","[[1, 3, 4], [2, 8, 8], [3, 9, 1], [4, 7, 6], [5, 2, 2], [6, 4, 3], [7, 1, 5], [8, 5, 7], [9, 6, 9]]",45,json,1
+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.
+
+{
+  ""num_tasks"": 12,
+  ""index_identifiers"": [
+    ""A"",
+    ""B"",
+    ""C"",
+    ""D"",
+    ""E"",
+    ""F"",
+    ""G"",
+    ""H"",
+    ""I"",
+    ""J"",
+    ""K"",
+    ""L""
+  ]
+}
+
+# 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=A
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 19 | 45 | 44 | 90 | 78 | 45 | 50 | 35 | 28 | 34 | 3 | 90 |
+| B | 12 | 63 | 94 | 53 | 60 | 84 | 2 | 80 | 21 | 39 | 11 | 72 |
+| C | 48 | 5 | 75 | 46 | 29 | 39 | 49 | 88 | 2 | 73 | 15 | 22 |
+| D | 67 | 7 | 1 | 50 | 96 | 40 | 1 | 35 | 51 | 16 | 4 | 34 |
+| E | 7 | 68 | 18 | 8 | 89 | 18 | 63 | 79 | 81 | 56 | 64 | 56 |
+| F | 92 | 47 | 8 | 21 | 45 | 63 | 24 | 62 | 66 | 46 | 76 | 72 |
+| G | 62 | 68 | 92 | 23 | 40 | 38 | 83 | 2 | 83 | 69 | 14 | 53 |
+| H | 67 | 27 | 41 | 60 | 35 | 78 | 99 | 4 | 47 | 0 | 45 | 6 |
+| I | 4 | 64 | 35 | 88 | 71 | 63 | 31 | 3 | 17 | 92 | 23 | 33 |
+| J | 27 | 34 | 54 | 84 | 28 | 81 | 94 | 25 | 29 | 13 | 48 | 1 |
+| K | 79 | 27 | 52 | 53 | 63 | 52 | 62 | 21 | 94 | 9 | 50 | 3 |
+| L | 42 | 5 | 35 | 44 | 57 | 42 | 75 | 2 | 27 | 10 | 51 | 73 |
+
+## task_id=B
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 76 | 32 | 49 | 47 | 72 | 40 | 32 | 18 | 2 | 4 | 27 | 63 |
+| B | 68 | 53 | 94 | 94 | 21 | 39 | 89 | 91 | 83 | 81 | 89 | 11 |
+| C | 44 | 42 | 61 | 63 | 59 | 70 | 90 | 6 | 5 | 6 | 5 | 98 |
+| D | 71 | 64 | 0 | 12 | 98 | 55 | 96 | 70 | 6 | 6 | 92 | 17 |
+| E | 96 | 18 | 66 | 90 | 42 | 40 | 72 | 20 | 55 | 77 | 14 | 31 |
+| F | 4 | 22 | 99 | 36 | 54 | 77 | 14 | 41 | 10 | 76 | 70 | 32 |
+| G | 6 | 9 | 50 | 66 | 76 | 68 | 1 | 53 | 82 | 23 | 64 | 61 |
+| H | 28 | 42 | 48 | 78 | 17 | 32 | 54 | 78 | 29 | 66 | 56 | 92 |
+| I | 32 | 60 | 89 | 27 | 40 | 95 | 32 | 78 | 48 | 48 | 65 | 30 |
+| J | 39 | 75 | 3 | 78 | 65 | 20 | 9 | 70 | 48 | 25 | 97 | 7 |
+| K | 64 | 72 | 58 | 3 | 95 | 11 | 72 | 21 | 73 | 57 | 53 | 92 |
+| L | 59 | 53 | 50 | 11 | 35 | 80 | 8 | 54 | 61 | 86 | 50 | 19 |
+
+## task_id=C
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 93 | 74 | 26 | 25 | 40 | 95 | 68 | 96 | 98 | 98 | 61 |
+| B | 28 | 24 | 79 | 66 | 53 | 86 | 66 | 58 | 52 | 40 | 29 | 22 |
+| C | 37 | 4 | 56 | 28 | 26 | 67 | 64 | 75 | 95 | 52 | 44 | 28 |
+| D | 60 | 17 | 71 | 24 | 48 | 36 | 25 | 70 | 33 | 22 | 96 | 6 |
+| E | 87 | 36 | 69 | 56 | 71 | 88 | 86 | 69 | 52 | 56 | 86 | 30 |
+| F | 86 | 16 | 63 | 54 | 93 | 10 | 50 | 57 | 50 | 53 | 37 | 22 |
+| G | 86 | 31 | 36 | 81 | 65 | 40 | 13 | 9 | 86 | 81 | 10 | 8 |
+| H | 85 | 55 | 79 | 96 | 98 | 51 | 84 | 53 | 90 | 10 | 93 | 71 |
+| I | 37 | 10 | 78 | 38 | 14 | 81 | 24 | 67 | 96 | 70 | 82 | 25 |
+| J | 23 | 74 | 60 | 74 | 22 | 46 | 45 | 26 | 24 | 98 | 51 | 77 |
+| K | 33 | 98 | 55 | 42 | 52 | 3 | 84 | 92 | 84 | 19 | 32 | 6 |
+| L | 75 | 24 | 34 | 73 | 70 | 42 | 91 | 19 | 11 | 46 | 67 | 87 |
+
+## task_id=D
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 21 | 51 | 96 | 71 | 88 | 41 | 64 | 94 | 83 | 48 | 54 | 18 |
+| B | 71 | 34 | 44 | 88 | 25 | 8 | 62 | 70 | 4 | 63 | 50 | 36 |
+| C | 36 | 6 | 33 | 58 | 20 | 97 | 55 | 50 | 83 | 70 | 19 | 75 |
+| D | 91 | 79 | 52 | 61 | 51 | 73 | 35 | 47 | 30 | 50 | 75 | 11 |
+| E | 37 | 46 | 68 | 2 | 50 | 1 | 67 | 52 | 82 | 3 | 3 | 48 |
+| F | 72 | 59 | 4 | 15 | 54 | 5 | 14 | 64 | 63 | 37 | 44 | 99 |
+| G | 54 | 61 | 83 | 90 | 43 | 6 | 89 | 35 | 89 | 44 | 77 | 28 |
+| H | 23 | 29 | 80 | 60 | 9 | 34 | 28 | 0 | 62 | 97 | 75 | 11 |
+| I | 19 | 35 | 20 | 3 | 6 | 73 | 71 | 96 | 33 | 52 | 73 | 64 |
+| J | 0 | 91 | 25 | 39 | 19 | 46 | 35 | 88 | 96 | 81 | 80 | 63 |
+| K | 66 | 73 | 45 | 5 | 76 | 50 | 24 | 16 | 51 | 43 | 58 | 63 |
+| L | 40 | 78 | 33 | 12 | 45 | 21 | 37 | 72 | 39 | 97 | 4 | 58 |
+
+## task_id=E
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 71 | 45 | 48 | 10 | 6 | 78 | 59 | 83 | 55 | 19 | 2 | 77 |
+| B | 92 | 22 | 92 | 27 | 53 | 72 | 83 | 68 | 4 | 58 | 89 | 36 |
+| C | 86 | 23 | 15 | 5 | 88 | 30 | 90 | 70 | 59 | 6 | 27 | 94 |
+| D | 65 | 92 | 94 | 82 | 85 | 7 | 23 | 72 | 37 | 29 | 10 | 14 |
+| E | 39 | 61 | 45 | 5 | 73 | 32 | 25 | 40 | 99 | 68 | 48 | 51 |
+| F | 26 | 69 | 38 | 71 | 90 | 73 | 90 | 7 | 19 | 77 | 36 | 55 |
+| G | 39 | 25 | 52 | 85 | 52 | 30 | 23 | 88 | 95 | 85 | 21 | 48 |
+| H | 38 | 28 | 25 | 10 | 8 | 56 | 27 | 98 | 56 | 73 | 91 | 39 |
+| I | 49 | 28 | 79 | 0 | 50 | 97 | 86 | 4 | 97 | 67 | 83 | 70 |
+| J | 41 | 37 | 36 | 82 | 13 | 26 | 47 | 83 | 37 | 79 | 58 | 9 |
+| K | 33 | 14 | 88 | 28 | 85 | 49 | 32 | 27 | 8 | 83 | 33 | 5 |
+| L | 26 | 68 | 44 | 67 | 58 | 57 | 66 | 14 | 22 | 11 | 90 | 31 |
+
+## task_id=F
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 63 | 30 | 62 | 0 | 64 | 26 | 93 | 22 | 91 | 47 | 92 | 1 |
+| B | 70 | 28 | 15 | 28 | 63 | 18 | 96 | 90 | 83 | 46 | 65 | 54 |
+| C | 40 | 58 | 66 | 93 | 64 | 0 | 81 | 90 | 52 | 41 | 89 | 39 |
+| D | 60 | 15 | 39 | 88 | 26 | 7 | 97 | 37 | 67 | 16 | 17 | 25 |
+| E | 48 | 99 | 30 | 47 | 44 | 98 | 65 | 19 | 67 | 38 | 39 | 13 |
+| F | 75 | 58 | 86 | 96 | 23 | 64 | 37 | 82 | 63 | 28 | 33 | 16 |
+| G | 34 | 3 | 70 | 20 | 38 | 40 | 94 | 28 | 91 | 2 | 69 | 51 |
+| H | 68 | 13 | 44 | 73 | 83 | 66 | 99 | 18 | 82 | 32 | 10 | 23 |
+| I | 75 | 74 | 32 | 93 | 3 | 89 | 66 | 35 | 25 | 3 | 8 | 19 |
+| J | 33 | 65 | 12 | 9 | 96 | 88 | 3 | 12 | 24 | 87 | 16 | 57 |
+| K | 58 | 61 | 42 | 51 | 80 | 78 | 13 | 34 | 31 | 69 | 3 | 47 |
+| L | 32 | 55 | 92 | 70 | 93 | 23 | 84 | 20 | 31 | 24 | 58 | 69 |
+
+## task_id=G
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 16 | 90 | 47 | 67 | 86 | 68 | 85 | 45 | 88 | 11 | 23 | 75 |
+| B | 77 | 46 | 84 | 21 | 19 | 84 | 71 | 25 | 5 | 0 | 17 | 82 |
+| C | 42 | 4 | 0 | 19 | 85 | 81 | 41 | 76 | 74 | 93 | 72 | 80 |
+| D | 43 | 74 | 12 | 89 | 88 | 86 | 43 | 32 | 65 | 21 | 35 | 43 |
+| E | 75 | 31 | 71 | 2 | 82 | 69 | 63 | 17 | 71 | 69 | 58 | 94 |
+| F | 65 | 56 | 7 | 50 | 75 | 89 | 24 | 85 | 38 | 35 | 88 | 91 |
+| G | 96 | 97 | 8 | 54 | 15 | 22 | 20 | 98 | 62 | 57 | 56 | 16 |
+| H | 92 | 78 | 95 | 13 | 55 | 34 | 32 | 92 | 16 | 83 | 46 | 13 |
+| I | 49 | 85 | 57 | 8 | 3 | 24 | 89 | 25 | 98 | 52 | 65 | 18 |
+| J | 31 | 77 | 75 | 47 | 63 | 76 | 41 | 3 | 11 | 29 | 70 | 54 |
+| K | 82 | 42 | 25 | 36 | 15 | 18 | 46 | 11 | 69 | 56 | 82 | 73 |
+| L | 57 | 8 | 81 | 91 | 24 | 56 | 24 | 23 | 82 | 44 | 71 | 89 |
+
+## task_id=H
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 8 | 70 | 61 | 32 | 37 | 76 | 30 | 29 | 18 | 87 | 17 | 90 |
+| B | 1 | 44 | 91 | 70 | 66 | 6 | 44 | 52 | 68 | 42 | 22 | 52 |
+| C | 14 | 81 | 60 | 50 | 79 | 7 | 43 | 91 | 65 | 90 | 77 | 4 |
+| D | 14 | 91 | 46 | 23 | 40 | 99 | 57 | 81 | 87 | 53 | 55 | 35 |
+| E | 30 | 61 | 52 | 11 | 39 | 20 | 48 | 38 | 7 | 43 | 8 | 14 |
+| F | 8 | 41 | 38 | 24 | 0 | 4 | 63 | 65 | 27 | 3 | 49 | 94 |
+| G | 44 | 16 | 7 | 39 | 20 | 4 | 2 | 33 | 78 | 28 | 63 | 2 |
+| H | 44 | 58 | 61 | 4 | 46 | 98 | 92 | 58 | 50 | 33 | 66 | 46 |
+| I | 57 | 63 | 80 | 91 | 86 | 51 | 93 | 66 | 22 | 51 | 60 | 27 |
+| J | 0 | 95 | 3 | 20 | 37 | 69 | 3 | 37 | 54 | 69 | 45 | 45 |
+| K | 9 | 24 | 93 | 79 | 19 | 29 | 15 | 80 | 17 | 52 | 46 | 81 |
+| L | 41 | 24 | 75 | 76 | 1 | 46 | 32 | 91 | 12 | 68 | 15 | 1 |
+
+## task_id=I
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 12 | 30 | 1 | 71 | 32 | 66 | 88 | 16 | 29 | 95 | 83 | 67 |
+| B | 53 | 24 | 83 | 70 | 84 | 83 | 73 | 28 | 46 | 30 | 75 | 17 |
+| C | 8 | 28 | 27 | 74 | 49 | 96 | 82 | 28 | 83 | 83 | 84 | 87 |
+| D | 37 | 18 | 29 | 41 | 3 | 27 | 8 | 79 | 12 | 79 | 55 | 67 |
+| E | 29 | 0 | 3 | 55 | 74 | 91 | 30 | 32 | 98 | 72 | 70 | 75 |
+| F | 81 | 47 | 2 | 37 | 35 | 16 | 89 | 93 | 88 | 87 | 40 | 51 |
+| G | 8 | 8 | 41 | 98 | 69 | 11 | 99 | 77 | 31 | 48 | 18 | 60 |
+| H | 31 | 39 | 39 | 68 | 95 | 17 | 73 | 21 | 75 | 97 | 23 | 51 |
+| I | 65 | 45 | 1 | 28 | 7 | 8 | 17 | 75 | 44 | 98 | 1 | 67 |
+| J | 4 | 90 | 63 | 89 | 84 | 14 | 9 | 87 | 76 | 46 | 21 | 21 |
+| K | 20 | 63 | 97 | 18 | 73 | 93 | 50 | 83 | 44 | 61 | 96 | 12 |
+| L | 27 | 17 | 15 | 60 | 9 | 63 | 32 | 43 | 80 | 9 | 66 | 54 |
+
+## task_id=J
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 47 | 72 | 68 | 90 | 51 | 90 | 72 | 95 | 43 | 83 | 25 | 34 |
+| B | 76 | 81 | 8 | 84 | 75 | 77 | 51 | 14 | 90 | 33 | 20 | 46 |
+| C | 48 | 0 | 22 | 85 | 56 | 98 | 81 | 77 | 32 | 32 | 52 | 27 |
+| D | 2 | 21 | 83 | 81 | 22 | 21 | 57 | 90 | 64 | 0 | 28 | 86 |
+| E | 0 | 44 | 44 | 96 | 65 | 41 | 74 | 27 | 25 | 70 | 41 | 99 |
+| F | 59 | 31 | 83 | 61 | 98 | 47 | 7 | 39 | 68 | 66 | 58 | 36 |
+| G | 63 | 27 | 49 | 47 | 11 | 66 | 73 | 10 | 5 | 72 | 58 | 9 |
+| H | 36 | 29 | 83 | 30 | 66 | 94 | 92 | 18 | 97 | 85 | 36 | 71 |
+| I | 34 | 71 | 35 | 22 | 39 | 14 | 66 | 25 | 84 | 61 | 39 | 76 |
+| J | 43 | 82 | 60 | 63 | 93 | 49 | 9 | 88 | 9 | 88 | 95 | 45 |
+| K | 54 | 55 | 62 | 81 | 13 | 6 | 42 | 99 | 12 | 32 | 23 | 34 |
+| L | 46 | 50 | 29 | 42 | 83 | 28 | 16 | 0 | 96 | 30 | 56 | 74 |
+
+## task_id=K
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 14 | 58 | 92 | 7 | 83 | 39 | 14 | 19 | 62 | 66 | 79 | 43 |
+| B | 94 | 47 | 32 | 89 | 48 | 47 | 60 | 15 | 24 | 58 | 45 | 36 |
+| C | 23 | 29 | 63 | 24 | 8 | 98 | 2 | 81 | 23 | 35 | 39 | 73 |
+| D | 4 | 54 | 68 | 55 | 72 | 15 | 37 | 25 | 71 | 49 | 5 | 86 |
+| E | 77 | 73 | 57 | 29 | 89 | 97 | 49 | 17 | 10 | 32 | 76 | 66 |
+| F | 18 | 95 | 62 | 75 | 92 | 24 | 48 | 92 | 19 | 48 | 52 | 27 |
+| G | 41 | 17 | 77 | 68 | 62 | 77 | 58 | 40 | 13 | 59 | 72 | 70 |
+| H | 70 | 94 | 62 | 78 | 31 | 85 | 25 | 32 | 78 | 49 | 66 | 84 |
+| I | 29 | 15 | 96 | 34 | 71 | 23 | 86 | 88 | 10 | 56 | 75 | 47 |
+| J | 49 | 49 | 21 | 18 | 91 | 59 | 87 | 84 | 87 | 9 | 62 | 27 |
+| K | 59 | 47 | 8 | 89 | 39 | 3 | 62 | 87 | 50 | 79 | 78 | 53 |
+| L | 84 | 88 | 26 | 87 | 35 | 22 | 34 | 3 | 36 | 43 | 26 | 78 |
+
+## task_id=L
+| developer_id\test_environment_id | A | B | C | D | E | F | G | H | I | J | K | L |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| A | 73 | 40 | 48 | 84 | 59 | 2 | 98 | 40 | 90 | 64 | 89 | 62 |
+| B | 24 | 88 | 37 | 75 | 20 | 12 | 70 | 99 | 43 | 18 | 16 | 55 |
+| C | 41 | 66 | 67 | 84 | 48 | 75 | 17 | 33 | 71 | 50 | 47 | 22 |
+| D | 33 | 84 | 84 | 17 | 41 | 43 | 40 | 94 | 88 | 72 | 57 | 46 |
+| E | 85 | 81 | 1 | 19 | 48 | 19 | 42 | 87 | 42 | 38 | 45 | 61 |
+| F | 55 | 38 | 58 | 71 | 87 | 78 | 81 | 85 | 70 | 73 | 60 | 12 |
+| G | 7 | 96 | 85 | 90 | 45 | 7 | 75 | 64 | 31 | 76 | 73 | 64 |
+| H | 24 | 47 | 42 | 14 | 44 | 21 | 12 | 73 | 82 | 59 | 24 | 83 |
+| I | 74 | 92 | 45 | 85 | 2 | 66 | 36 | 45 | 0 | 43 | 6 | 66 |
+| J | 86 | 82 | 12 | 6 | 39 | 25 | 46 | 36 | 77 | 66 | 73 | 77 |
+| K | 94 | 99 | 46 | 20 | 21 | 99 | 80 | 88 | 2 | 11 | 37 | 48 |
+| L | 94 | 68 | 32 | 60 | 10 | 32 | 39 | 23 | 21 | 92 | 88 | 11 |
+
+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': [[[19, 45, 44, 90, 78, 45, 50, 35, 28, 34, 3, 90], [12, 63, 94, 53, 60, 84, 2, 80, 21, 39, 11, 72], [48, 5, 75, 46, 29, 39, 49, 88, 2, 73, 15, 22], [67, 7, 1, 50, 96, 40, 1, 35, 51, 16, 4, 34], [7, 68, 18, 8, 89, 18, 63, 79, 81, 56, 64, 56], [92, 47, 8, 21, 45, 63, 24, 62, 66, 46, 76, 72], [62, 68, 92, 23, 40, 38, 83, 2, 83, 69, 14, 53], [67, 27, 41, 60, 35, 78, 99, 4, 47, 0, 45, 6], [4, 64, 35, 88, 71, 63, 31, 3, 17, 92, 23, 33], [27, 34, 54, 84, 28, 81, 94, 25, 29, 13, 48, 1], [79, 27, 52, 53, 63, 52, 62, 21, 94, 9, 50, 3], [42, 5, 35, 44, 57, 42, 75, 2, 27, 10, 51, 73]], [[76, 32, 49, 47, 72, 40, 32, 18, 2, 4, 27, 63], [68, 53, 94, 94, 21, 39, 89, 91, 83, 81, 89, 11], [44, 42, 61, 63, 59, 70, 90, 6, 5, 6, 5, 98], [71, 64, 0, 12, 98, 55, 96, 70, 6, 6, 92, 17], [96, 18, 66, 90, 42, 40, 72, 20, 55, 77, 14, 31], [4, 22, 99, 36, 54, 77, 14, 41, 10, 76, 70, 32], [6, 9, 50, 66, 76, 68, 1, 53, 82, 23, 64, 61], [28, 42, 48, 78, 17, 32, 54, 78, 29, 66, 56, 92], [32, 60, 89, 27, 40, 95, 32, 78, 48, 48, 65, 30], [39, 75, 3, 78, 65, 20, 9, 70, 48, 25, 97, 7], [64, 72, 58, 3, 95, 11, 72, 21, 73, 57, 53, 92], [59, 53, 50, 11, 35, 80, 8, 54, 61, 86, 50, 19]], [[12, 93, 74, 26, 25, 40, 95, 68, 96, 98, 98, 61], [28, 24, 79, 66, 53, 86, 66, 58, 52, 40, 29, 22], [37, 4, 56, 28, 26, 67, 64, 75, 95, 52, 44, 28], [60, 17, 71, 24, 48, 36, 25, 70, 33, 22, 96, 6], [87, 36, 69, 56, 71, 88, 86, 69, 52, 56, 86, 30], [86, 16, 63, 54, 93, 10, 50, 57, 50, 53, 37, 22], [86, 31, 36, 81, 65, 40, 13, 9, 86, 81, 10, 8], [85, 55, 79, 96, 98, 51, 84, 53, 90, 10, 93, 71], [37, 10, 78, 38, 14, 81, 24, 67, 96, 70, 82, 25], [23, 74, 60, 74, 22, 46, 45, 26, 24, 98, 51, 77], [33, 98, 55, 42, 52, 3, 84, 92, 84, 19, 32, 6], [75, 24, 34, 73, 70, 42, 91, 19, 11, 46, 67, 87]], [[21, 51, 96, 71, 88, 41, 64, 94, 83, 48, 54, 18], [71, 34, 44, 88, 25, 8, 62, 70, 4, 63, 50, 36], [36, 6, 33, 58, 20, 97, 55, 50, 83, 70, 19, 75], [91, 79, 52, 61, 51, 73, 35, 47, 30, 50, 75, 11], [37, 46, 68, 2, 50, 1, 67, 52, 82, 3, 3, 48], [72, 59, 4, 15, 54, 5, 14, 64, 63, 37, 44, 99], [54, 61, 83, 90, 43, 6, 89, 35, 89, 44, 77, 28], [23, 29, 80, 60, 9, 34, 28, 0, 62, 97, 75, 11], [19, 35, 20, 3, 6, 73, 71, 96, 33, 52, 73, 64], [0, 91, 25, 39, 19, 46, 35, 88, 96, 81, 80, 63], [66, 73, 45, 5, 76, 50, 24, 16, 51, 43, 58, 63], [40, 78, 33, 12, 45, 21, 37, 72, 39, 97, 4, 58]], [[71, 45, 48, 10, 6, 78, 59, 83, 55, 19, 2, 77], [92, 22, 92, 27, 53, 72, 83, 68, 4, 58, 89, 36], [86, 23, 15, 5, 88, 30, 90, 70, 59, 6, 27, 94], [65, 92, 94, 82, 85, 7, 23, 72, 37, 29, 10, 14], [39, 61, 45, 5, 73, 32, 25, 40, 99, 68, 48, 51], [26, 69, 38, 71, 90, 73, 90, 7, 19, 77, 36, 55], [39, 25, 52, 85, 52, 30, 23, 88, 95, 85, 21, 48], [38, 28, 25, 10, 8, 56, 27, 98, 56, 73, 91, 39], [49, 28, 79, 0, 50, 97, 86, 4, 97, 67, 83, 70], [41, 37, 36, 82, 13, 26, 47, 83, 37, 79, 58, 9], [33, 14, 88, 28, 85, 49, 32, 27, 8, 83, 33, 5], [26, 68, 44, 67, 58, 57, 66, 14, 22, 11, 90, 31]], [[63, 30, 62, 0, 64, 26, 93, 22, 91, 47, 92, 1], [70, 28, 15, 28, 63, 18, 96, 90, 83, 46, 65, 54], [40, 58, 66, 93, 64, 0, 81, 90, 52, 41, 89, 39], [60, 15, 39, 88, 26, 7, 97, 37, 67, 16, 17, 25], [48, 99, 30, 47, 44, 98, 65, 19, 67, 38, 39, 13], [75, 58, 86, 96, 23, 64, 37, 82, 63, 28, 33, 16], [34, 3, 70, 20, 38, 40, 94, 28, 91, 2, 69, 51], [68, 13, 44, 73, 83, 66, 99, 18, 82, 32, 10, 23], [75, 74, 32, 93, 3, 89, 66, 35, 25, 3, 8, 19], [33, 65, 12, 9, 96, 88, 3, 12, 24, 87, 16, 57], [58, 61, 42, 51, 80, 78, 13, 34, 31, 69, 3, 47], [32, 55, 92, 70, 93, 23, 84, 20, 31, 24, 58, 69]], [[16, 90, 47, 67, 86, 68, 85, 45, 88, 11, 23, 75], [77, 46, 84, 21, 19, 84, 71, 25, 5, 0, 17, 82], [42, 4, 0, 19, 85, 81, 41, 76, 74, 93, 72, 80], [43, 74, 12, 89, 88, 86, 43, 32, 65, 21, 35, 43], [75, 31, 71, 2, 82, 69, 63, 17, 71, 69, 58, 94], [65, 56, 7, 50, 75, 89, 24, 85, 38, 35, 88, 91], [96, 97, 8, 54, 15, 22, 20, 98, 62, 57, 56, 16], [92, 78, 95, 13, 55, 34, 32, 92, 16, 83, 46, 13], [49, 85, 57, 8, 3, 24, 89, 25, 98, 52, 65, 18], [31, 77, 75, 47, 63, 76, 41, 3, 11, 29, 70, 54], [82, 42, 25, 36, 15, 18, 46, 11, 69, 56, 82, 73], [57, 8, 81, 91, 24, 56, 24, 23, 82, 44, 71, 89]], [[8, 70, 61, 32, 37, 76, 30, 29, 18, 87, 17, 90], [1, 44, 91, 70, 66, 6, 44, 52, 68, 42, 22, 52], [14, 81, 60, 50, 79, 7, 43, 91, 65, 90, 77, 4], [14, 91, 46, 23, 40, 99, 57, 81, 87, 53, 55, 35], [30, 61, 52, 11, 39, 20, 48, 38, 7, 43, 8, 14], [8, 41, 38, 24, 0, 4, 63, 65, 27, 3, 49, 94], [44, 16, 7, 39, 20, 4, 2, 33, 78, 28, 63, 2], [44, 58, 61, 4, 46, 98, 92, 58, 50, 33, 66, 46], [57, 63, 80, 91, 86, 51, 93, 66, 22, 51, 60, 27], [0, 95, 3, 20, 37, 69, 3, 37, 54, 69, 45, 45], [9, 24, 93, 79, 19, 29, 15, 80, 17, 52, 46, 81], [41, 24, 75, 76, 1, 46, 32, 91, 12, 68, 15, 1]], [[12, 30, 1, 71, 32, 66, 88, 16, 29, 95, 83, 67], [53, 24, 83, 70, 84, 83, 73, 28, 46, 30, 75, 17], [8, 28, 27, 74, 49, 96, 82, 28, 83, 83, 84, 87], [37, 18, 29, 41, 3, 27, 8, 79, 12, 79, 55, 67], [29, 0, 3, 55, 74, 91, 30, 32, 98, 72, 70, 75], [81, 47, 2, 37, 35, 16, 89, 93, 88, 87, 40, 51], [8, 8, 41, 98, 69, 11, 99, 77, 31, 48, 18, 60], [31, 39, 39, 68, 95, 17, 73, 21, 75, 97, 23, 51], [65, 45, 1, 28, 7, 8, 17, 75, 44, 98, 1, 67], [4, 90, 63, 89, 84, 14, 9, 87, 76, 46, 21, 21], [20, 63, 97, 18, 73, 93, 50, 83, 44, 61, 96, 12], [27, 17, 15, 60, 9, 63, 32, 43, 80, 9, 66, 54]], [[47, 72, 68, 90, 51, 90, 72, 95, 43, 83, 25, 34], [76, 81, 8, 84, 75, 77, 51, 14, 90, 33, 20, 46], [48, 0, 22, 85, 56, 98, 81, 77, 32, 32, 52, 27], [2, 21, 83, 81, 22, 21, 57, 90, 64, 0, 28, 86], [0, 44, 44, 96, 65, 41, 74, 27, 25, 70, 41, 99], [59, 31, 83, 61, 98, 47, 7, 39, 68, 66, 58, 36], [63, 27, 49, 47, 11, 66, 73, 10, 5, 72, 58, 9], [36, 29, 83, 30, 66, 94, 92, 18, 97, 85, 36, 71], [34, 71, 35, 22, 39, 14, 66, 25, 84, 61, 39, 76], [43, 82, 60, 63, 93, 49, 9, 88, 9, 88, 95, 45], [54, 55, 62, 81, 13, 6, 42, 99, 12, 32, 23, 34], [46, 50, 29, 42, 83, 28, 16, 0, 96, 30, 56, 74]], [[14, 58, 92, 7, 83, 39, 14, 19, 62, 66, 79, 43], [94, 47, 32, 89, 48, 47, 60, 15, 24, 58, 45, 36], [23, 29, 63, 24, 8, 98, 2, 81, 23, 35, 39, 73], [4, 54, 68, 55, 72, 15, 37, 25, 71, 49, 5, 86], [77, 73, 57, 29, 89, 97, 49, 17, 10, 32, 76, 66], [18, 95, 62, 75, 92, 24, 48, 92, 19, 48, 52, 27], [41, 17, 77, 68, 62, 77, 58, 40, 13, 59, 72, 70], [70, 94, 62, 78, 31, 85, 25, 32, 78, 49, 66, 84], [29, 15, 96, 34, 71, 23, 86, 88, 10, 56, 75, 47], [49, 49, 21, 18, 91, 59, 87, 84, 87, 9, 62, 27], [59, 47, 8, 89, 39, 3, 62, 87, 50, 79, 78, 53], [84, 88, 26, 87, 35, 22, 34, 3, 36, 43, 26, 78]], [[73, 40, 48, 84, 59, 2, 98, 40, 90, 64, 89, 62], [24, 88, 37, 75, 20, 12, 70, 99, 43, 18, 16, 55], [41, 66, 67, 84, 48, 75, 17, 33, 71, 50, 47, 22], [33, 84, 84, 17, 41, 43, 40, 94, 88, 72, 57, 46], [85, 81, 1, 19, 48, 19, 42, 87, 42, 38, 45, 61], [55, 38, 58, 71, 87, 78, 81, 85, 70, 73, 60, 12], [7, 96, 85, 90, 45, 7, 75, 64, 31, 76, 73, 64], [24, 47, 42, 14, 44, 21, 12, 73, 82, 59, 24, 83], [74, 92, 45, 85, 2, 66, 36, 45, 0, 43, 6, 66], [86, 82, 12, 6, 39, 25, 46, 36, 77, 66, 73, 77], [94, 99, 46, 20, 21, 99, 80, 88, 2, 11, 37, 48], [94, 68, 32, 60, 10, 32, 39, 23, 21, 92, 88, 11]]], 'objective': 20.0}","[[0, 7, 9], [1, 3, 2], [2, 6, 11], [3, 9, 0], [4, 8, 3], [5, 10, 10], [6, 1, 8], [7, 5, 4], [8, 4, 1], [9, 11, 7], [10, 2, 6], [11, 0, 5]]",20.0,"{'problem_type': 'AP3', 'n': 12, 'ids': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L'], 'costs': [{'i': 'A', 'j': 'A', 'k': 'A', 'cost': 19}, {'i': 'A', 'j': 'A', 'k': 'B', 'cost': 45}, {'i': 'A', 'j': 'A', 'k': 'C', 'cost': 44}, {'i': 'A', 'j': 'A', 'k': 'D', 'cost': 90}, {'i': 'A', 'j': 'A', 'k': 'E', 'cost': 78}, {'i': 'A', 'j': 'A', 'k': 'F', 'cost': 45}, {'i': 'A', 'j': 'A', 'k': 'G', 'cost': 50}, {'i': 'A', 'j': 'A', 'k': 'H', 'cost': 35}, {'i': 'A', 'j': 'A', 'k': 'I', 'cost': 28}, {'i': 'A', 'j': 'A', 'k': 'J', 'cost': 34}, {'i': 'A', 'j': 'A', 'k': 'K', 'cost': 3}, {'i': 'A', 'j': 'A', 'k': 'L', 'cost': 90}, {'i': 'A', 'j': 'B', 'k': 'A', 'cost': 12}, {'i': 'A', 'j': 'B', 'k': 'B', 'cost': 63}, {'i': 'A', 'j': 'B', 'k': 'C', 'cost': 94}, {'i': 'A', 'j': 'B', 'k': 'D', 'cost': 53}, {'i': 'A', 'j': 'B', 'k': 'E', 'cost': 60}, {'i': 'A', 'j': 'B', 'k': 'F', 'cost': 84}, {'i': 'A', 'j': 'B', 'k': 'G', 'cost': 2}, {'i': 'A', 'j': 'B', 'k': 'H', 'cost': 80}, {'i': 'A', 'j': 'B', 'k': 'I', 'cost': 21}, {'i': 'A', 'j': 'B', 'k': 'J', 'cost': 39}, {'i': 'A', 'j': 'B', 'k': 'K', 'cost': 11}, {'i': 'A', 'j': 'B', 'k': 'L', 'cost': 72}, {'i': 'A', 'j': 'C', 'k': 'A', 'cost': 48}, {'i': 'A', 'j': 'C', 'k': 'B', 'cost': 5}, {'i': 'A', 'j': 'C', 'k': 'C', 'cost': 75}, {'i': 'A', 'j': 'C', 'k': 'D', 'cost': 46}, {'i': 'A', 'j': 'C', 'k': 'E', 'cost': 29}, {'i': 'A', 'j': 'C', 'k': 'F', 'cost': 39}, {'i': 'A', 'j': 'C', 'k': 'G', 'cost': 49}, {'i': 'A', 'j': 'C', 'k': 'H', 'cost': 88}, {'i': 'A', 'j': 'C', 'k': 'I', 'cost': 2}, {'i': 'A', 'j': 'C', 'k': 'J', 'cost': 73}, {'i': 'A', 'j': 'C', 'k': 'K', 'cost': 15}, {'i': 'A', 'j': 'C', 'k': 'L', 'cost': 22}, {'i': 'A', 'j': 'D', 'k': 'A', 'cost': 67}, {'i': 'A', 'j': 'D', 'k': 'B', 'cost': 7}, {'i': 'A', 'j': 'D', 'k': 'C', 'cost': 1}, {'i': 'A', 'j': 'D', 'k': 'D', 'cost': 50}, {'i': 'A', 'j': 'D', 'k': 'E', 'cost': 96}, {'i': 'A', 'j': 'D', 'k': 'F', 'cost': 40}, {'i': 'A', 'j': 'D', 'k': 'G', 'cost': 1}, {'i': 'A', 'j': 'D', 'k': 'H', 'cost': 35}, {'i': 'A', 'j': 'D', 'k': 'I', 'cost': 51}, {'i': 'A', 'j': 'D', 'k': 'J', 'cost': 16}, {'i': 'A', 'j': 'D', 'k': 'K', 'cost': 4}, {'i': 'A', 'j': 'D', 'k': 'L', 'cost': 34}, {'i': 'A', 'j': 'E', 'k': 'A', 'cost': 7}, {'i': 'A', 'j': 'E', 'k': 'B', 'cost': 68}, {'i': 'A', 'j': 'E', 'k': 'C', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'D', 'cost': 8}, {'i': 'A', 'j': 'E', 'k': 'E', 'cost': 89}, {'i': 'A', 'j': 'E', 'k': 'F', 'cost': 18}, {'i': 'A', 'j': 'E', 'k': 'G', 'cost': 63}, {'i': 'A', 'j': 'E', 'k': 'H', 'cost': 79}, {'i': 'A', 'j': 'E', 'k': 'I', 'cost': 81}, {'i': 'A', 'j': 'E', 'k': 'J', 'cost': 56}, {'i': 'A', 'j': 'E', 'k': 'K', 'cost': 64}, {'i': 'A', 'j': 'E', 'k': 'L', 'cost': 56}, {'i': 'A', 'j': 'F', 'k': 'A', 'cost': 92}, {'i': 'A', 'j': 'F', 'k': 'B', 'cost': 47}, {'i': 'A', 'j': 'F', 'k': 'C', 'cost': 8}, {'i': 'A', 'j': 'F', 'k': 'D', 'cost': 21}, {'i': 'A', 'j': 'F', 'k': 'E', 'cost': 45}, {'i': 'A', 'j': 'F', 'k': 'F', 'cost': 63}, {'i': 'A', 'j': 'F', 'k': 'G', 'cost': 24}, {'i': 'A', 'j': 'F', 'k': 'H', 'cost': 62}, {'i': 'A', 'j': 'F', 'k': 'I', 'cost': 66}, {'i': 'A', 'j': 'F', 'k': 'J', 'cost': 46}, {'i': 'A', 'j': 'F', 'k': 'K', 'cost': 76}, {'i': 'A', 'j': 'F', 'k': 'L', 'cost': 72}, {'i': 'A', 'j': 'G', 'k': 'A', 'cost': 62}, {'i': 'A', 'j': 'G', 'k': 'B', 'cost': 68}, {'i': 'A', 'j': 'G', 'k': 'C', 'cost': 92}, {'i': 'A', 'j': 'G', 'k': 'D', 'cost': 23}, {'i': 'A', 'j': 'G', 'k': 'E', 'cost': 40}, {'i': 'A', 'j': 'G', 'k': 'F', 'cost': 38}, {'i': 'A', 'j': 'G', 'k': 'G', 'cost': 83}, {'i': 'A', 'j': 'G', 'k': 'H', 'cost': 2}, {'i': 'A', 'j': 'G', 'k': 'I', 'cost': 83}, {'i': 'A', 'j': 'G', 'k': 'J', 'cost': 69}, {'i': 'A', 'j': 'G', 'k': 'K', 'cost': 14}, {'i': 'A', 'j': 'G', 'k': 'L', 'cost': 53}, {'i': 'A', 'j': 'H', 'k': 'A', 'cost': 67}, {'i': 'A', 'j': 'H', 'k': 'B', 'cost': 27}, {'i': 'A', 'j': 'H', 'k': 'C', 'cost': 41}, {'i': 'A', 'j': 'H', 'k': 'D', 'cost': 60}, {'i': 'A', 'j': 'H', 'k': 'E', 'cost': 35}, {'i': 'A', 'j': 'H', 'k': 'F', 'cost': 78}, {'i': 'A', 'j': 'H', 'k': 'G', 'cost': 99}, {'i': 'A', 'j': 'H', 'k': 'H', 'cost': 4}, {'i': 'A', 'j': 'H', 'k': 'I', 'cost': 47}, {'i': 'A', 'j': 'H', 'k': 'J', 'cost': 0}, {'i': 'A', 'j': 'H', 'k': 'K', 'cost': 45}, {'i': 'A', 'j': 'H', 'k': 'L', 'cost': 6}, {'i': 'A', 'j': 'I', 'k': 'A', 'cost': 4}, {'i': 'A', 'j': 'I', 'k': 'B', 'cost': 64}, {'i': 'A', 'j': 'I', 'k': 'C', 'cost': 35}, {'i': 'A', 'j': 'I', 'k': 'D', 'cost': 88}, {'i': 'A', 'j': 'I', 'k': 'E', 'cost': 71}, {'i': 'A', 'j': 'I', 'k': 'F', 'cost': 63}, {'i': 'A', 'j': 'I', 'k': 'G', 'cost': 31}, {'i': 'A', 'j': 'I', 'k': 'H', 'cost': 3}, {'i': 'A', 'j': 'I', 'k': 'I', 'cost': 17}, {'i': 'A', 'j': 'I', 'k': 'J', 'cost': 92}, {'i': 'A', 'j': 'I', 'k': 'K', 'cost': 23}, {'i': 'A', 'j': 'I', 'k': 'L', 'cost': 33}, {'i': 'A', 'j': 'J', 'k': 'A', 'cost': 27}, {'i': 'A', 'j': 'J', 'k': 'B', 'cost': 34}, {'i': 'A', 'j': 'J', 'k': 'C', 'cost': 54}, {'i': 'A', 'j': 'J', 'k': 'D', 'cost': 84}, {'i': 'A', 'j': 'J', 'k': 'E', 'cost': 28}, {'i': 'A', 'j': 'J', 'k': 'F', 'cost': 81}, {'i': 'A', 'j': 'J', 'k': 'G', 'cost': 94}, {'i': 'A', 'j': 'J', 'k': 'H', 'cost': 25}, {'i': 'A', 'j': 'J', 'k': 'I', 'cost': 29}, {'i': 'A', 'j': 'J', 'k': 'J', 'cost': 13}, {'i': 'A', 'j': 'J', 'k': 'K', 'cost': 48}, {'i': 'A', 'j': 'J', 'k': 'L', 'cost': 1}, {'i': 'A', 'j': 'K', 'k': 'A', 'cost': 79}, {'i': 'A', 'j': 'K', 'k': 'B', 'cost': 27}, {'i': 'A', 'j': 'K', 'k': 'C', 'cost': 52}, {'i': 'A', 'j': 'K', 'k': 'D', 'cost': 53}, {'i': 'A', 'j': 'K', 'k': 'E', 'cost': 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'F', 'k': 'F', 'cost': 78}, {'i': 'L', 'j': 'F', 'k': 'G', 'cost': 81}, {'i': 'L', 'j': 'F', 'k': 'H', 'cost': 85}, {'i': 'L', 'j': 'F', 'k': 'I', 'cost': 70}, {'i': 'L', 'j': 'F', 'k': 'J', 'cost': 73}, {'i': 'L', 'j': 'F', 'k': 'K', 'cost': 60}, {'i': 'L', 'j': 'F', 'k': 'L', 'cost': 12}, {'i': 'L', 'j': 'G', 'k': 'A', 'cost': 7}, {'i': 'L', 'j': 'G', 'k': 'B', 'cost': 96}, {'i': 'L', 'j': 'G', 'k': 'C', 'cost': 85}, {'i': 'L', 'j': 'G', 'k': 'D', 'cost': 90}, {'i': 'L', 'j': 'G', 'k': 'E', 'cost': 45}, {'i': 'L', 'j': 'G', 'k': 'F', 'cost': 7}, {'i': 'L', 'j': 'G', 'k': 'G', 'cost': 75}, {'i': 'L', 'j': 'G', 'k': 'H', 'cost': 64}, {'i': 'L', 'j': 'G', 'k': 'I', 'cost': 31}, {'i': 'L', 'j': 'G', 'k': 'J', 'cost': 76}, {'i': 'L', 'j': 'G', 'k': 'K', 'cost': 73}, {'i': 'L', 'j': 'G', 'k': 'L', 'cost': 64}, {'i': 'L', 'j': 'H', 'k': 'A', 'cost': 24}, {'i': 'L', 'j': 'H', 'k': 'B', 'cost': 47}, {'i': 'L', 'j': 'H', 'k': 'C', 'cost': 42}, {'i': 'L', 'j': 'H', 'k': 'D', 'cost': 14}, {'i': 'L', 'j': 'H', 'k': 'E', 'cost': 44}, {'i': 'L', 'j': 'H', 'k': 'F', 'cost': 21}, {'i': 'L', 'j': 'H', 'k': 'G', 'cost': 12}, {'i': 'L', 'j': 'H', 'k': 'H', 'cost': 73}, {'i': 'L', 'j': 'H', 'k': 'I', 'cost': 82}, {'i': 'L', 'j': 'H', 'k': 'J', 'cost': 59}, {'i': 'L', 'j': 'H', 'k': 'K', 'cost': 24}, {'i': 'L', 'j': 'H', 'k': 'L', 'cost': 83}, {'i': 'L', 'j': 'I', 'k': 'A', 'cost': 74}, {'i': 'L', 'j': 'I', 'k': 'B', 'cost': 92}, {'i': 'L', 'j': 'I', 'k': 'C', 'cost': 45}, {'i': 'L', 'j': 'I', 'k': 'D', 'cost': 85}, {'i': 'L', 'j': 'I', 'k': 'E', 'cost': 2}, {'i': 'L', 'j': 'I', 'k': 'F', 'cost': 66}, {'i': 'L', 'j': 'I', 'k': 'G', 'cost': 36}, {'i': 'L', 'j': 'I', 'k': 'H', 'cost': 45}, {'i': 'L', 'j': 'I', 'k': 'I', 'cost': 0}, {'i': 'L', 'j': 'I', 'k': 'J', 'cost': 43}, {'i': 'L', 'j': 'I', 'k': 'K', 'cost': 6}, {'i': 'L', 'j': 'I', 'k': 'L', 'cost': 66}, {'i': 'L', 'j': 'J', 'k': 'A', 'cost': 86}, {'i': 'L', 'j': 'J', 'k': 'B', 'cost': 82}, {'i': 'L', 'j': 'J', 'k': 'C', 'cost': 12}, {'i': 'L', 'j': 'J', 'k': 'D', 'cost': 6}, {'i': 'L', 'j': 'J', 'k': 'E', 'cost': 39}, {'i': 'L', 'j': 'J', 'k': 'F', 'cost': 25}, {'i': 'L', 'j': 'J', 'k': 'G', 'cost': 46}, {'i': 'L', 'j': 'J', 'k': 'H', 'cost': 36}, {'i': 'L', 'j': 'J', 'k': 'I', 'cost': 77}, {'i': 'L', 'j': 'J', 'k': 'J', 'cost': 66}, {'i': 'L', 'j': 'J', 'k': 'K', 'cost': 73}, {'i': 'L', 'j': 'J', 'k': 'L', 'cost': 77}, {'i': 'L', 'j': 'K', 'k': 'A', 'cost': 94}, {'i': 'L', 'j': 'K', 'k': 'B', 'cost': 99}, {'i': 'L', 'j': 'K', 'k': 'C', 'cost': 46}, {'i': 'L', 'j': 'K', 'k': 'D', 'cost': 20}, {'i': 'L', 'j': 'K', 'k': 'E', 'cost': 21}, {'i': 'L', 'j': 'K', 'k': 'F', 'cost': 99}, {'i': 'L', 'j': 'K', 'k': 'G', 'cost': 80}, {'i': 'L', 'j': 'K', 'k': 'H', 'cost': 88}, {'i': 'L', 'j': 'K', 'k': 'I', 'cost': 2}, {'i': 'L', 'j': 'K', 'k': 'J', 'cost': 11}, {'i': 'L', 'j': 'K', 'k': 'K', 'cost': 37}, {'i': 'L', 'j': 'K', 'k': 'L', 'cost': 48}, {'i': 'L', 'j': 'L', 'k': 'A', 'cost': 94}, {'i': 'L', 'j': 'L', 'k': 'B', 'cost': 68}, {'i': 'L', 'j': 'L', 'k': 'C', 'cost': 32}, {'i': 'L', 'j': 'L', 'k': 'D', 'cost': 60}, {'i': 'L', 'j': 'L', 'k': 'E', 'cost': 10}, {'i': 'L', 'j': 'L', 'k': 'F', 'cost': 32}, {'i': 'L', 'j': 'L', 'k': 'G', 'cost': 39}, {'i': 'L', 'j': 'L', 'k': 'H', 'cost': 23}, {'i': 'L', 'j': 'L', 'k': 'I', 'cost': 21}, {'i': 'L', 'j': 'L', 'k': 'J', 'cost': 92}, {'i': 'L', 'j': 'L', 'k': 'K', 'cost': 88}, {'i': 'L', 'j': 'L', 'k': 'L', 'cost': 11}]}","[['A', 'H', 'J'], ['B', 'D', 'C'], ['C', 'G', 'L'], ['D', 'J', 'A'], ['E', 'I', 'D'], ['F', 'K', 'K'], ['G', 'B', 'I'], ['H', 'F', 'E'], ['I', 'E', 'B'], ['J', 'L', 'H'], ['K', 'C', 'G'], ['L', 'A', 'F']]",46,json,names
+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.
+
+# num_students=10
+# identifier_sets=1, 2, 3, 4, 5, 6, 7, 8, 9, 10
+
+# 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 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 23 | 91 | 26 | 84 | 52 | 55 | 11 | 70 | 9 | 34 |
+| 2 | 18 | 89 | 15 | 12 | 70 | 80 | 14 | 34 | 85 | 63 |
+| 3 | 58 | 89 | 97 | 63 | 6 | 7 | 10 | 40 | 83 | 4 |
+| 4 | 99 | 51 | 34 | 51 | 18 | 32 | 95 | 13 | 72 | 89 |
+| 5 | 88 | 47 | 72 | 67 | 67 | 25 | 21 | 37 | 26 | 50 |
+| 6 | 82 | 93 | 78 | 88 | 50 | 3 | 4 | 82 | 91 | 85 |
+| 7 | 7 | 92 | 78 | 19 | 99 | 81 | 94 | 10 | 60 | 31 |
+| 8 | 82 | 66 | 52 | 43 | 85 | 90 | 27 | 29 | 76 | 49 |
+| 9 | 61 | 10 | 47 | 13 | 17 | 19 | 52 | 33 | 56 | 43 |
+| 10 | 91 | 71 | 48 | 80 | 38 | 47 | 54 | 82 | 77 | 2 |
+
+## student_id=2
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 29 | 66 | 5 | 62 | 76 | 89 | 26 | 67 | 1 | 66 |
+| 2 | 15 | 66 | 17 | 9 | 7 | 9 | 27 | 80 | 90 | 73 |
+| 3 | 3 | 69 | 78 | 82 | 33 | 61 | 6 | 12 | 9 | 26 |
+| 4 | 10 | 5 | 35 | 32 | 79 | 38 | 59 | 2 | 24 | 22 |
+| 5 | 5 | 57 | 45 | 8 | 92 | 34 | 16 | 24 | 18 | 89 |
+| 6 | 22 | 12 | 57 | 0 | 90 | 35 | 62 | 68 | 48 | 32 |
+| 7 | 92 | 76 | 86 | 62 | 26 | 95 | 84 | 49 | 10 | 54 |
+| 8 | 39 | 69 | 11 | 32 | 22 | 2 | 68 | 38 | 22 | 76 |
+| 9 | 85 | 89 | 4 | 15 | 91 | 10 | 64 | 88 | 78 | 86 |
+| 10 | 6 | 21 | 56 | 19 | 45 | 41 | 3 | 65 | 27 | 52 |
+
+## student_id=3
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 83 | 66 | 87 | 90 | 71 | 35 | 63 | 4 | 81 | 55 |
+| 2 | 55 | 25 | 93 | 95 | 6 | 88 | 16 | 17 | 41 | 21 |
+| 3 | 21 | 97 | 22 | 67 | 80 | 21 | 86 | 5 | 10 | 9 |
+| 4 | 83 | 89 | 54 | 70 | 66 | 19 | 17 | 85 | 79 | 80 |
+| 5 | 51 | 32 | 78 | 49 | 4 | 89 | 47 | 63 | 80 | 0 |
+| 6 | 55 | 68 | 32 | 1 | 7 | 76 | 26 | 24 | 45 | 26 |
+| 7 | 85 | 35 | 60 | 14 | 60 | 50 | 3 | 90 | 81 | 94 |
+| 8 | 10 | 54 | 36 | 33 | 66 | 83 | 92 | 34 | 72 | 65 |
+| 9 | 9 | 1 | 73 | 80 | 68 | 41 | 49 | 3 | 87 | 15 |
+| 10 | 10 | 41 | 12 | 84 | 1 | 71 | 22 | 30 | 15 | 47 |
+
+## student_id=4
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 26 | 19 | 7 | 19 | 53 | 38 | 14 | 99 | 31 | 77 |
+| 2 | 0 | 49 | 85 | 33 | 40 | 73 | 54 | 56 | 67 | 68 |
+| 3 | 61 | 97 | 42 | 42 | 98 | 22 | 23 | 91 | 15 | 98 |
+| 4 | 41 | 96 | 43 | 33 | 18 | 77 | 42 | 24 | 32 | 82 |
+| 5 | 35 | 27 | 91 | 77 | 16 | 88 | 54 | 19 | 5 | 83 |
+| 6 | 9 | 99 | 87 | 47 | 36 | 46 | 69 | 54 | 73 | 48 |
+| 7 | 88 | 78 | 53 | 18 | 15 | 63 | 62 | 57 | 33 | 32 |
+| 8 | 14 | 21 | 10 | 61 | 3 | 70 | 81 | 98 | 1 | 62 |
+| 9 | 82 | 85 | 58 | 92 | 57 | 63 | 82 | 76 | 2 | 16 |
+| 10 | 4 | 38 | 44 | 73 | 25 | 70 | 61 | 52 | 95 | 56 |
+
+## student_id=5
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 25 | 29 | 26 | 28 | 10 | 49 | 5 | 55 | 56 | 94 |
+| 2 | 59 | 55 | 63 | 39 | 78 | 75 | 22 | 1 | 76 | 97 |
+| 3 | 87 | 85 | 90 | 72 | 68 | 20 | 21 | 35 | 28 | 20 |
+| 4 | 26 | 54 | 79 | 2 | 84 | 62 | 58 | 96 | 86 | 42 |
+| 5 | 34 | 80 | 55 | 1 | 10 | 75 | 91 | 3 | 34 | 1 |
+| 6 | 54 | 50 | 46 | 73 | 30 | 53 | 27 | 4 | 47 | 34 |
+| 7 | 96 | 52 | 75 | 19 | 72 | 57 | 9 | 90 | 52 | 91 |
+| 8 | 24 | 68 | 89 | 15 | 72 | 29 | 11 | 86 | 96 | 93 |
+| 9 | 17 | 77 | 50 | 38 | 15 | 83 | 34 | 18 | 34 | 17 |
+| 10 | 66 | 12 | 83 | 14 | 9 | 15 | 94 | 3 | 22 | 73 |
+
+## student_id=6
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 97 | 54 | 0 | 45 | 28 | 63 | 95 | 50 | 65 | 77 |
+| 2 | 46 | 67 | 10 | 99 | 44 | 86 | 18 | 45 | 61 | 88 |
+| 3 | 39 | 58 | 66 | 99 | 13 | 73 | 52 | 49 | 68 | 73 |
+| 4 | 1 | 45 | 33 | 7 | 37 | 2 | 46 | 38 | 1 | 39 |
+| 5 | 52 | 74 | 69 | 18 | 66 | 49 | 43 | 38 | 41 | 79 |
+| 6 | 45 | 6 | 84 | 72 | 13 | 13 | 70 | 86 | 16 | 6 |
+| 7 | 10 | 32 | 9 | 64 | 28 | 48 | 74 | 24 | 4 | 36 |
+| 8 | 80 | 41 | 65 | 66 | 4 | 78 | 26 | 17 | 71 | 74 |
+| 9 | 47 | 19 | 7 | 42 | 99 | 84 | 57 | 74 | 59 | 25 |
+| 10 | 0 | 47 | 95 | 66 | 27 | 62 | 89 | 23 | 32 | 88 |
+
+## student_id=7
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 52 | 28 | 84 | 60 | 53 | 81 | 0 | 15 | 92 | 11 |
+| 2 | 7 | 77 | 58 | 34 | 16 | 21 | 45 | 10 | 90 | 29 |
+| 3 | 37 | 78 | 58 | 71 | 4 | 87 | 41 | 39 | 67 | 58 |
+| 4 | 53 | 37 | 59 | 35 | 73 | 2 | 82 | 42 | 2 | 75 |
+| 5 | 17 | 48 | 66 | 98 | 5 | 75 | 86 | 14 | 62 | 39 |
+| 6 | 5 | 30 | 4 | 68 | 24 | 40 | 8 | 36 | 32 | 8 |
+| 7 | 97 | 47 | 14 | 44 | 16 | 29 | 19 | 27 | 60 | 19 |
+| 8 | 20 | 45 | 90 | 20 | 25 | 85 | 45 | 35 | 76 | 22 |
+| 9 | 51 | 82 | 42 | 40 | 82 | 6 | 10 | 97 | 30 | 12 |
+| 10 | 97 | 49 | 41 | 69 | 58 | 42 | 65 | 30 | 88 | 50 |
+
+## student_id=8
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 71 | 44 | 70 | 66 | 29 | 50 | 86 | 93 | 96 | 46 |
+| 2 | 25 | 64 | 62 | 19 | 48 | 78 | 18 | 62 | 71 | 56 |
+| 3 | 18 | 8 | 34 | 18 | 92 | 52 | 46 | 48 | 9 | 34 |
+| 4 | 35 | 0 | 91 | 26 | 45 | 86 | 62 | 53 | 61 | 95 |
+| 5 | 42 | 39 | 13 | 76 | 73 | 68 | 15 | 17 | 98 | 83 |
+| 6 | 53 | 53 | 61 | 82 | 37 | 58 | 35 | 85 | 28 | 25 |
+| 7 | 54 | 63 | 55 | 98 | 98 | 3 | 72 | 81 | 8 | 65 |
+| 8 | 59 | 63 | 78 | 55 | 44 | 52 | 16 | 61 | 52 | 65 |
+| 9 | 49 | 25 | 24 | 26 | 70 | 68 | 70 | 73 | 87 | 75 |
+| 10 | 29 | 20 | 9 | 96 | 24 | 70 | 73 | 46 | 56 | 21 |
+
+## student_id=9
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 19 | 89 | 44 | 54 | 91 | 70 | 94 | 47 | 85 |
+| 2 | 94 | 12 | 30 | 15 | 81 | 60 | 2 | 30 | 59 | 30 |
+| 3 | 46 | 17 | 17 | 87 | 97 | 50 | 77 | 90 | 39 | 94 |
+| 4 | 47 | 9 | 66 | 43 | 52 | 68 | 21 | 31 | 53 | 77 |
+| 5 | 43 | 12 | 9 | 80 | 75 | 64 | 68 | 47 | 46 | 67 |
+| 6 | 13 | 33 | 18 | 77 | 1 | 28 | 6 | 67 | 33 | 71 |
+| 7 | 84 | 86 | 37 | 62 | 61 | 44 | 9 | 2 | 2 | 11 |
+| 8 | 88 | 85 | 43 | 26 | 59 | 27 | 91 | 44 | 61 | 60 |
+| 9 | 84 | 19 | 13 | 97 | 49 | 93 | 69 | 93 | 68 | 40 |
+| 10 | 19 | 61 | 69 | 14 | 70 | 25 | 96 | 94 | 30 | 70 |
+
+## student_id=10
+| room_id\roommate_option_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 3 | 78 | 10 | 52 | 28 | 64 | 75 | 80 | 58 | 92 |
+| 2 | 26 | 16 | 37 | 1 | 24 | 94 | 98 | 6 | 0 | 31 |
+| 3 | 14 | 23 | 11 | 54 | 15 | 12 | 68 | 79 | 85 | 77 |
+| 4 | 60 | 68 | 19 | 10 | 5 | 55 | 76 | 72 | 16 | 99 |
+| 5 | 88 | 52 | 92 | 75 | 55 | 67 | 36 | 38 | 62 | 41 |
+| 6 | 0 | 44 | 25 | 13 | 18 | 28 | 49 | 97 | 92 | 15 |
+| 7 | 70 | 57 | 95 | 66 | 38 | 76 | 68 | 80 | 45 | 99 |
+| 8 | 78 | 18 | 58 | 91 | 58 | 33 | 50 | 13 | 38 | 88 |
+| 9 | 69 | 64 | 2 | 64 | 48 | 57 | 4 | 11 | 29 | 13 |
+| 10 | 53 | 58 | 10 | 66 | 96 | 44 | 0 | 67 | 75 | 4 |
+
+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': [[[23, 91, 26, 84, 52, 55, 11, 70, 9, 34], [18, 89, 15, 12, 70, 80, 14, 34, 85, 63], [58, 89, 97, 63, 6, 7, 10, 40, 83, 4], [99, 51, 34, 51, 18, 32, 95, 13, 72, 89], [88, 47, 72, 67, 67, 25, 21, 37, 26, 50], [82, 93, 78, 88, 50, 3, 4, 82, 91, 85], [7, 92, 78, 19, 99, 81, 94, 10, 60, 31], [82, 66, 52, 43, 85, 90, 27, 29, 76, 49], [61, 10, 47, 13, 17, 19, 52, 33, 56, 43], [91, 71, 48, 80, 38, 47, 54, 82, 77, 2]], [[29, 66, 5, 62, 76, 89, 26, 67, 1, 66], [15, 66, 17, 9, 7, 9, 27, 80, 90, 73], [3, 69, 78, 82, 33, 61, 6, 12, 9, 26], [10, 5, 35, 32, 79, 38, 59, 2, 24, 22], [5, 57, 45, 8, 92, 34, 16, 24, 18, 89], [22, 12, 57, 0, 90, 35, 62, 68, 48, 32], [92, 76, 86, 62, 26, 95, 84, 49, 10, 54], [39, 69, 11, 32, 22, 2, 68, 38, 22, 76], [85, 89, 4, 15, 91, 10, 64, 88, 78, 86], [6, 21, 56, 19, 45, 41, 3, 65, 27, 52]], [[83, 66, 87, 90, 71, 35, 63, 4, 81, 55], [55, 25, 93, 95, 6, 88, 16, 17, 41, 21], [21, 97, 22, 67, 80, 21, 86, 5, 10, 9], [83, 89, 54, 70, 66, 19, 17, 85, 79, 80], [51, 32, 78, 49, 4, 89, 47, 63, 80, 0], [55, 68, 32, 1, 7, 76, 26, 24, 45, 26], [85, 35, 60, 14, 60, 50, 3, 90, 81, 94], [10, 54, 36, 33, 66, 83, 92, 34, 72, 65], [9, 1, 73, 80, 68, 41, 49, 3, 87, 15], [10, 41, 12, 84, 1, 71, 22, 30, 15, 47]], [[26, 19, 7, 19, 53, 38, 14, 99, 31, 77], [0, 49, 85, 33, 40, 73, 54, 56, 67, 68], [61, 97, 42, 42, 98, 22, 23, 91, 15, 98], [41, 96, 43, 33, 18, 77, 42, 24, 32, 82], [35, 27, 91, 77, 16, 88, 54, 19, 5, 83], [9, 99, 87, 47, 36, 46, 69, 54, 73, 48], [88, 78, 53, 18, 15, 63, 62, 57, 33, 32], [14, 21, 10, 61, 3, 70, 81, 98, 1, 62], [82, 85, 58, 92, 57, 63, 82, 76, 2, 16], [4, 38, 44, 73, 25, 70, 61, 52, 95, 56]], [[25, 29, 26, 28, 10, 49, 5, 55, 56, 94], [59, 55, 63, 39, 78, 75, 22, 1, 76, 97], [87, 85, 90, 72, 68, 20, 21, 35, 28, 20], [26, 54, 79, 2, 84, 62, 58, 96, 86, 42], [34, 80, 55, 1, 10, 75, 91, 3, 34, 1], [54, 50, 46, 73, 30, 53, 27, 4, 47, 34], [96, 52, 75, 19, 72, 57, 9, 90, 52, 91], [24, 68, 89, 15, 72, 29, 11, 86, 96, 93], [17, 77, 50, 38, 15, 83, 34, 18, 34, 17], [66, 12, 83, 14, 9, 15, 94, 3, 22, 73]], [[97, 54, 0, 45, 28, 63, 95, 50, 65, 77], [46, 67, 10, 99, 44, 86, 18, 45, 61, 88], [39, 58, 66, 99, 13, 73, 52, 49, 68, 73], [1, 45, 33, 7, 37, 2, 46, 38, 1, 39], [52, 74, 69, 18, 66, 49, 43, 38, 41, 79], [45, 6, 84, 72, 13, 13, 70, 86, 16, 6], [10, 32, 9, 64, 28, 48, 74, 24, 4, 36], [80, 41, 65, 66, 4, 78, 26, 17, 71, 74], [47, 19, 7, 42, 99, 84, 57, 74, 59, 25], [0, 47, 95, 66, 27, 62, 89, 23, 32, 88]], [[52, 28, 84, 60, 53, 81, 0, 15, 92, 11], [7, 77, 58, 34, 16, 21, 45, 10, 90, 29], [37, 78, 58, 71, 4, 87, 41, 39, 67, 58], [53, 37, 59, 35, 73, 2, 82, 42, 2, 75], [17, 48, 66, 98, 5, 75, 86, 14, 62, 39], [5, 30, 4, 68, 24, 40, 8, 36, 32, 8], [97, 47, 14, 44, 16, 29, 19, 27, 60, 19], [20, 45, 90, 20, 25, 85, 45, 35, 76, 22], [51, 82, 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'j': 3, 'k': 10, 'cost': 77}, {'i': 10, 'j': 4, 'k': 1, 'cost': 60}, {'i': 10, 'j': 4, 'k': 2, 'cost': 68}, {'i': 10, 'j': 4, 'k': 3, 'cost': 19}, {'i': 10, 'j': 4, 'k': 4, 'cost': 10}, {'i': 10, 'j': 4, 'k': 5, 'cost': 5}, {'i': 10, 'j': 4, 'k': 6, 'cost': 55}, {'i': 10, 'j': 4, 'k': 7, 'cost': 76}, {'i': 10, 'j': 4, 'k': 8, 'cost': 72}, {'i': 10, 'j': 4, 'k': 9, 'cost': 16}, {'i': 10, 'j': 4, 'k': 10, 'cost': 99}, {'i': 10, 'j': 5, 'k': 1, 'cost': 88}, {'i': 10, 'j': 5, 'k': 2, 'cost': 52}, {'i': 10, 'j': 5, 'k': 3, 'cost': 92}, {'i': 10, 'j': 5, 'k': 4, 'cost': 75}, {'i': 10, 'j': 5, 'k': 5, 'cost': 55}, {'i': 10, 'j': 5, 'k': 6, 'cost': 67}, {'i': 10, 'j': 5, 'k': 7, 'cost': 36}, {'i': 10, 'j': 5, 'k': 8, 'cost': 38}, {'i': 10, 'j': 5, 'k': 9, 'cost': 62}, {'i': 10, 'j': 5, 'k': 10, 'cost': 41}, {'i': 10, 'j': 6, 'k': 1, 'cost': 0}, {'i': 10, 'j': 6, 'k': 2, 'cost': 44}, {'i': 10, 'j': 6, 'k': 3, 'cost': 25}, {'i': 10, 'j': 6, 'k': 4, 'cost': 13}, {'i': 10, 'j': 6, 'k': 5, 'cost': 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'k': 1, 'cost': 69}, {'i': 10, 'j': 9, 'k': 2, 'cost': 64}, {'i': 10, 'j': 9, 'k': 3, 'cost': 2}, {'i': 10, 'j': 9, 'k': 4, 'cost': 64}, {'i': 10, 'j': 9, 'k': 5, 'cost': 48}, {'i': 10, 'j': 9, 'k': 6, 'cost': 57}, {'i': 10, 'j': 9, 'k': 7, 'cost': 4}, {'i': 10, 'j': 9, 'k': 8, 'cost': 11}, {'i': 10, 'j': 9, 'k': 9, 'cost': 29}, {'i': 10, 'j': 9, 'k': 10, 'cost': 13}, {'i': 10, 'j': 10, 'k': 1, 'cost': 53}, {'i': 10, 'j': 10, 'k': 2, 'cost': 58}, {'i': 10, 'j': 10, 'k': 3, 'cost': 10}, {'i': 10, 'j': 10, 'k': 4, 'cost': 66}, {'i': 10, 'j': 10, 'k': 5, 'cost': 96}, {'i': 10, 'j': 10, 'k': 6, 'cost': 44}, {'i': 10, 'j': 10, 'k': 7, 'cost': 0}, {'i': 10, 'j': 10, 'k': 8, 'cost': 67}, {'i': 10, 'j': 10, 'k': 9, 'cost': 75}, {'i': 10, 'j': 10, 'k': 10, 'cost': 4}]}","[[1, 3, 6], [2, 6, 4], [3, 5, 10], [4, 8, 5], [5, 2, 8], [6, 10, 1], [7, 1, 7], [8, 4, 2], [9, 7, 9], [10, 9, 3]]",47,csv,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.
+
+There are 12 jobs, 12 suppliers, and 12 delivery dates labeled 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
+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=0
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 23 | 26 | 84 | 52 | 11 | 48 | 53 | 58 | 25 | 58 | 34 | 67 |
+| 1 | 58 | 97 | 63 | 6 | 10 | 32 | 66 | 11 | 18 | 22 | 4 | 39 |
+| 2 | 99 | 34 | 51 | 18 | 95 | 47 | 51 | 5 | 44 | 47 | 89 | 46 |
+| 3 | 88 | 72 | 67 | 67 | 21 | 83 | 36 | 70 | 93 | 95 | 50 | 49 |
+| 4 | 7 | 78 | 19 | 99 | 94 | 18 | 85 | 28 | 47 | 23 | 31 | 93 |
+| 5 | 29 | 65 | 65 | 62 | 21 | 82 | 44 | 52 | 32 | 15 | 54 | 33 |
+| 6 | 23 | 30 | 94 | 50 | 78 | 53 | 12 | 78 | 20 | 97 | 30 | 19 |
+| 7 | 79 | 55 | 12 | 92 | 36 | 39 | 95 | 66 | 93 | 19 | 43 | 2 |
+| 8 | 65 | 11 | 3 | 92 | 32 | 95 | 31 | 67 | 83 | 55 | 13 | 63 |
+| 9 | 8 | 61 | 47 | 71 | 97 | 46 | 88 | 71 | 73 | 24 | 86 | 97 |
+| 10 | 91 | 48 | 80 | 38 | 54 | 11 | 42 | 95 | 55 | 32 | 2 | 88 |
+| 11 | 3 | 62 | 65 | 52 | 29 | 39 | 80 | 32 | 12 | 0 | 38 | 69 |
+
+## job_id=1
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 83 | 87 | 90 | 71 | 63 | 71 | 39 | 3 | 63 | 35 | 55 | 53 |
+| 1 | 21 | 22 | 67 | 80 | 86 | 82 | 71 | 46 | 20 | 41 | 9 | 22 |
+| 2 | 83 | 54 | 70 | 66 | 17 | 20 | 94 | 28 | 33 | 81 | 80 | 61 |
+| 3 | 51 | 78 | 49 | 4 | 47 | 53 | 49 | 70 | 33 | 11 | 0 | 63 |
+| 4 | 85 | 60 | 14 | 60 | 3 | 86 | 80 | 61 | 9 | 7 | 94 | 14 |
+| 5 | 69 | 81 | 34 | 29 | 67 | 92 | 52 | 5 | 27 | 23 | 87 | 52 |
+| 6 | 73 | 48 | 81 | 80 | 6 | 11 | 48 | 34 | 11 | 51 | 56 | 34 |
+| 7 | 24 | 13 | 32 | 15 | 98 | 92 | 74 | 4 | 68 | 45 | 44 | 97 |
+| 8 | 19 | 54 | 30 | 36 | 43 | 48 | 80 | 20 | 59 | 36 | 43 | 76 |
+| 9 | 80 | 98 | 9 | 94 | 77 | 20 | 31 | 35 | 30 | 27 | 19 | 38 |
+| 10 | 10 | 12 | 84 | 1 | 22 | 67 | 42 | 44 | 4 | 2 | 47 | 35 |
+| 11 | 86 | 76 | 52 | 59 | 75 | 83 | 26 | 74 | 33 | 43 | 59 | 88 |
+
+## job_id=2
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 26 | 7 | 19 | 53 | 14 | 99 | 52 | 57 | 3 | 96 | 77 | 45 |
+| 1 | 61 | 42 | 42 | 98 | 23 | 82 | 73 | 0 | 17 | 62 | 98 | 92 |
+| 2 | 41 | 43 | 33 | 18 | 42 | 6 | 90 | 27 | 72 | 77 | 82 | 43 |
+| 3 | 35 | 91 | 77 | 16 | 54 | 94 | 38 | 99 | 8 | 20 | 83 | 23 |
+| 4 | 88 | 53 | 18 | 15 | 62 | 6 | 27 | 9 | 54 | 80 | 32 | 68 |
+| 5 | 78 | 31 | 51 | 47 | 33 | 64 | 61 | 41 | 17 | 69 | 69 | 63 |
+| 6 | 69 | 95 | 56 | 25 | 69 | 64 | 28 | 25 | 36 | 21 | 4 | 54 |
+| 7 | 58 | 48 | 26 | 88 | 61 | 69 | 70 | 87 | 35 | 18 | 8 | 10 |
+| 8 | 33 | 38 | 88 | 22 | 11 | 59 | 73 | 81 | 86 | 88 | 30 | 36 |
+| 9 | 48 | 32 | 18 | 29 | 38 | 23 | 79 | 55 | 9 | 47 | 58 | 22 |
+| 10 | 4 | 44 | 73 | 25 | 61 | 52 | 92 | 90 | 24 | 99 | 56 | 29 |
+| 11 | 37 | 34 | 2 | 5 | 21 | 46 | 98 | 73 | 28 | 93 | 61 | 46 |
+
+## job_id=3
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 25 | 26 | 28 | 10 | 5 | 89 | 95 | 91 | 11 | 79 | 94 | 10 |
+| 1 | 87 | 90 | 72 | 68 | 21 | 42 | 48 | 24 | 47 | 6 | 20 | 22 |
+| 2 | 26 | 79 | 2 | 84 | 58 | 72 | 15 | 70 | 44 | 20 | 42 | 40 |
+| 3 | 34 | 55 | 1 | 10 | 91 | 91 | 91 | 12 | 66 | 79 | 1 | 40 |
+| 4 | 96 | 75 | 19 | 72 | 9 | 0 | 11 | 13 | 88 | 36 | 91 | 84 |
+| 5 | 55 | 40 | 64 | 84 | 57 | 60 | 29 | 8 | 98 | 72 | 79 | 16 |
+| 6 | 46 | 52 | 17 | 84 | 22 | 30 | 71 | 55 | 6 | 13 | 68 | 69 |
+| 7 | 92 | 76 | 64 | 72 | 36 | 86 | 26 | 91 | 78 | 31 | 20 | 39 |
+| 8 | 11 | 65 | 96 | 21 | 58 | 70 | 33 | 16 | 1 | 36 | 64 | 37 |
+| 9 | 46 | 38 | 61 | 4 | 29 | 85 | 28 | 25 | 50 | 29 | 59 | 72 |
+| 10 | 66 | 83 | 14 | 9 | 94 | 3 | 73 | 58 | 23 | 90 | 73 | 36 |
+| 11 | 15 | 81 | 63 | 2 | 32 | 91 | 66 | 15 | 99 | 48 | 7 | 6 |
+
+## job_id=4
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 52 | 84 | 60 | 53 | 0 | 77 | 3 | 14 | 54 | 23 | 11 | 76 |
+| 1 | 37 | 58 | 71 | 4 | 41 | 12 | 93 | 47 | 5 | 95 | 58 | 0 |
+| 2 | 53 | 59 | 35 | 73 | 82 | 75 | 66 | 69 | 20 | 94 | 75 | 71 |
+| 3 | 17 | 66 | 98 | 5 | 86 | 81 | 58 | 78 | 60 | 68 | 39 | 22 |
+| 4 | 97 | 14 | 44 | 16 | 19 | 77 | 54 | 43 | 54 | 99 | 19 | 8 |
+| 5 | 50 | 57 | 0 | 59 | 35 | 32 | 24 | 49 | 81 | 62 | 13 | 93 |
+| 6 | 75 | 52 | 20 | 53 | 41 | 84 | 5 | 67 | 13 | 88 | 17 | 37 |
+| 7 | 15 | 86 | 17 | 37 | 29 | 58 | 14 | 58 | 99 | 98 | 33 | 65 |
+| 8 | 83 | 84 | 58 | 18 | 93 | 86 | 18 | 0 | 66 | 22 | 61 | 87 |
+| 9 | 60 | 47 | 14 | 17 | 94 | 11 | 25 | 38 | 37 | 57 | 2 | 72 |
+| 10 | 97 | 41 | 69 | 58 | 65 | 96 | 45 | 6 | 41 | 65 | 50 | 34 |
+| 11 | 22 | 13 | 35 | 5 | 76 | 76 | 2 | 26 | 28 | 10 | 81 | 88 |
+
+## job_id=5
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 27 | 73 | 14 | 29 | 35 | 17 | 3 | 75 | 66 | 99 | 31 | 68 |
+| 1 | 16 | 80 | 22 | 98 | 93 | 82 | 60 | 57 | 93 | 10 | 14 | 39 |
+| 2 | 32 | 36 | 25 | 47 | 74 | 69 | 71 | 90 | 79 | 31 | 17 | 86 |
+| 3 | 13 | 44 | 67 | 32 | 23 | 31 | 70 | 66 | 61 | 86 | 38 | 44 |
+| 4 | 28 | 61 | 72 | 45 | 82 | 11 | 50 | 95 | 2 | 6 | 20 | 81 |
+| 5 | 9 | 45 | 16 | 29 | 64 | 3 | 65 | 20 | 89 | 27 | 67 | 68 |
+| 6 | 20 | 51 | 79 | 14 | 29 | 24 | 39 | 16 | 50 | 25 | 44 | 41 |
+| 7 | 0 | 0 | 33 | 45 | 94 | 30 | 99 | 37 | 25 | 56 | 34 | 78 |
+| 8 | 87 | 90 | 57 | 59 | 8 | 40 | 82 | 63 | 29 | 51 | 39 | 21 |
+| 9 | 47 | 48 | 76 | 71 | 48 | 65 | 74 | 71 | 19 | 51 | 23 | 38 |
+| 10 | 69 | 13 | 35 | 21 | 35 | 58 | 36 | 3 | 86 | 12 | 6 | 98 |
+| 11 | 50 | 46 | 97 | 24 | 11 | 40 | 79 | 31 | 88 | 20 | 74 | 3 |
+
+## job_id=6
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 52 | 51 | 92 | 40 | 67 | 40 | 61 | 43 | 13 | 54 | 67 | 0 |
+| 1 | 64 | 20 | 68 | 85 | 64 | 62 | 92 | 31 | 67 | 90 | 22 | 32 |
+| 2 | 13 | 90 | 2 | 41 | 38 | 89 | 82 | 41 | 26 | 71 | 11 | 89 |
+| 3 | 72 | 20 | 90 | 83 | 69 | 78 | 38 | 44 | 7 | 89 | 60 | 71 |
+| 4 | 53 | 57 | 93 | 46 | 93 | 4 | 75 | 24 | 85 | 32 | 60 | 89 |
+| 5 | 4 | 30 | 43 | 77 | 57 | 28 | 34 | 23 | 31 | 26 | 71 | 72 |
+| 6 | 95 | 15 | 37 | 80 | 63 | 8 | 66 | 12 | 50 | 87 | 47 | 62 |
+| 7 | 24 | 8 | 4 | 19 | 1 | 78 | 48 | 22 | 76 | 76 | 17 | 4 |
+| 8 | 45 | 19 | 75 | 60 | 95 | 98 | 92 | 66 | 41 | 38 | 41 | 41 |
+| 9 | 22 | 99 | 78 | 3 | 81 | 23 | 15 | 94 | 82 | 71 | 70 | 4 |
+| 10 | 21 | 85 | 74 | 70 | 82 | 50 | 22 | 12 | 77 | 26 | 82 | 11 |
+| 11 | 51 | 10 | 43 | 56 | 23 | 78 | 50 | 82 | 27 | 59 | 90 | 10 |
+
+## job_id=7
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 59 | 56 | 44 | 97 | 20 | 92 | 85 | 0 | 36 | 37 | 53 | 23 |
+| 1 | 23 | 31 | 65 | 64 | 60 | 84 | 10 | 8 | 48 | 39 | 90 | 94 |
+| 2 | 69 | 72 | 93 | 99 | 23 | 82 | 29 | 19 | 11 | 49 | 37 | 82 |
+| 3 | 44 | 3 | 72 | 52 | 67 | 97 | 59 | 34 | 68 | 88 | 0 | 64 |
+| 4 | 45 | 52 | 34 | 42 | 13 | 90 | 22 | 56 | 96 | 90 | 32 | 33 |
+| 5 | 22 | 3 | 49 | 0 | 47 | 10 | 62 | 62 | 41 | 34 | 82 | 0 |
+| 6 | 21 | 95 | 68 | 11 | 47 | 49 | 2 | 99 | 92 | 75 | 57 | 91 |
+| 7 | 44 | 74 | 31 | 20 | 88 | 73 | 69 | 97 | 36 | 7 | 25 | 2 |
+| 8 | 38 | 41 | 78 | 64 | 33 | 21 | 3 | 16 | 8 | 20 | 99 | 96 |
+| 9 | 73 | 94 | 22 | 60 | 41 | 1 | 44 | 34 | 16 | 91 | 58 | 19 |
+| 10 | 76 | 66 | 6 | 50 | 76 | 40 | 59 | 82 | 72 | 58 | 10 | 38 |
+| 11 | 78 | 99 | 43 | 6 | 69 | 70 | 1 | 87 | 38 | 48 | 22 | 6 |
+
+## job_id=8
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 40 | 77 | 47 | 50 | 44 | 49 | 26 | 47 | 59 | 46 | 68 | 26 |
+| 1 | 69 | 78 | 73 | 20 | 76 | 56 | 87 | 20 | 53 | 25 | 20 | 1 |
+| 2 | 94 | 95 | 57 | 19 | 78 | 7 | 41 | 19 | 54 | 60 | 31 | 31 |
+| 3 | 97 | 46 | 35 | 41 | 56 | 31 | 35 | 56 | 94 | 4 | 75 | 79 |
+| 4 | 59 | 22 | 82 | 50 | 43 | 76 | 81 | 13 | 79 | 62 | 79 | 76 |
+| 5 | 57 | 66 | 58 | 36 | 12 | 3 | 52 | 73 | 2 | 9 | 10 | 52 |
+| 6 | 81 | 3 | 50 | 27 | 72 | 12 | 94 | 77 | 83 | 70 | 77 | 89 |
+| 7 | 0 | 30 | 3 | 29 | 55 | 50 | 18 | 74 | 55 | 57 | 36 | 30 |
+| 8 | 68 | 52 | 64 | 66 | 35 | 35 | 55 | 94 | 68 | 74 | 90 | 15 |
+| 9 | 36 | 58 | 73 | 69 | 29 | 51 | 22 | 48 | 46 | 12 | 4 | 19 |
+| 10 | 24 | 93 | 40 | 17 | 9 | 71 | 45 | 67 | 27 | 47 | 64 | 32 |
+| 11 | 93 | 3 | 8 | 70 | 27 | 85 | 79 | 59 | 19 | 48 | 85 | 14 |
+
+## job_id=9
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 75 | 26 | 65 | 39 | 54 | 43 | 46 | 50 | 93 | 92 | 62 | 69 |
+| 1 | 71 | 18 | 57 | 54 | 54 | 12 | 72 | 24 | 62 | 22 | 85 | 35 |
+| 2 | 0 | 18 | 24 | 58 | 26 | 51 | 57 | 60 | 16 | 29 | 64 | 50 |
+| 3 | 68 | 54 | 99 | 8 | 45 | 71 | 66 | 66 | 85 | 1 | 41 | 48 |
+| 4 | 57 | 35 | 60 | 36 | 92 | 33 | 94 | 83 | 48 | 43 | 80 | 23 |
+| 5 | 42 | 60 | 71 | 49 | 71 | 83 | 28 | 6 | 21 | 96 | 49 | 68 |
+| 6 | 57 | 82 | 21 | 58 | 29 | 30 | 78 | 92 | 36 | 12 | 79 | 40 |
+| 7 | 42 | 10 | 24 | 46 | 82 | 86 | 81 | 74 | 99 | 28 | 42 | 8 |
+| 8 | 19 | 82 | 87 | 68 | 91 | 97 | 49 | 38 | 12 | 27 | 11 | 74 |
+| 9 | 45 | 53 | 59 | 0 | 83 | 17 | 36 | 8 | 55 | 6 | 87 | 26 |
+| 10 | 95 | 53 | 63 | 66 | 53 | 38 | 13 | 54 | 16 | 41 | 85 | 57 |
+| 11 | 42 | 30 | 12 | 95 | 44 | 21 | 39 | 75 | 9 | 88 | 33 | 73 |
+
+## job_id=10
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 3 | 10 | 52 | 28 | 75 | 46 | 22 | 37 | 27 | 99 | 92 | 89 |
+| 1 | 14 | 11 | 54 | 15 | 68 | 62 | 26 | 62 | 48 | 53 | 77 | 65 |
+| 2 | 60 | 19 | 10 | 5 | 76 | 61 | 41 | 28 | 1 | 62 | 99 | 66 |
+| 3 | 88 | 92 | 75 | 55 | 36 | 99 | 41 | 46 | 61 | 75 | 41 | 82 |
+| 4 | 70 | 95 | 66 | 38 | 68 | 5 | 68 | 98 | 98 | 82 | 99 | 76 |
+| 5 | 58 | 82 | 20 | 83 | 24 | 57 | 89 | 58 | 39 | 18 | 96 | 32 |
+| 6 | 58 | 32 | 41 | 9 | 96 | 42 | 91 | 28 | 12 | 31 | 24 | 92 |
+| 7 | 21 | 32 | 3 | 74 | 74 | 31 | 53 | 75 | 96 | 8 | 86 | 52 |
+| 8 | 1 | 82 | 8 | 80 | 97 | 68 | 77 | 7 | 13 | 94 | 98 | 53 |
+| 9 | 4 | 94 | 58 | 76 | 59 | 98 | 87 | 84 | 6 | 3 | 31 | 83 |
+| 10 | 53 | 10 | 66 | 96 | 0 | 11 | 79 | 61 | 23 | 29 | 4 | 82 |
+| 11 | 92 | 31 | 26 | 8 | 75 | 87 | 76 | 7 | 13 | 27 | 24 | 82 |
+
+## job_id=11
+| supplier_id\delivery_date_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 52 | 80 | 73 | 19 | 86 | 23 | 10 | 47 | 90 | 63 | 95 | 76 |
+| 1 | 34 | 28 | 15 | 66 | 37 | 89 | 43 | 44 | 8 | 87 | 69 | 53 |
+| 2 | 69 | 34 | 31 | 92 | 59 | 18 | 5 | 76 | 9 | 96 | 24 | 15 |
+| 3 | 49 | 79 | 23 | 83 | 96 | 65 | 98 | 43 | 4 | 66 | 19 | 97 |
+| 4 | 94 | 80 | 71 | 76 | 61 | 8 | 13 | 61 | 96 | 70 | 82 | 28 |
+| 5 | 0 | 0 | 24 | 9 | 30 | 47 | 63 | 66 | 65 | 19 | 76 | 55 |
+| 6 | 13 | 85 | 33 | 51 | 24 | 59 | 25 | 93 | 38 | 70 | 33 | 6 |
+| 7 | 10 | 30 | 59 | 32 | 28 | 50 | 1 | 94 | 83 | 13 | 83 | 25 |
+| 8 | 36 | 70 | 49 | 58 | 89 | 13 | 42 | 13 | 40 | 77 | 85 | 43 |
+| 9 | 88 | 49 | 19 | 16 | 33 | 89 | 16 | 76 | 99 | 34 | 52 | 33 |
+| 10 | 93 | 14 | 47 | 73 | 24 | 22 | 51 | 23 | 62 | 1 | 93 | 80 |
+| 11 | 64 | 7 | 41 | 87 | 2 | 26 | 25 | 1 | 0 | 54 | 3 | 6 |
+Minimize the sum of the listed costs to obtain a one-to-one assignment covering all 12 jobs.
+
+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': [[[23, 26, 84, 52, 11, 48, 53, 58, 25, 58, 34, 67], [58, 97, 63, 6, 10, 32, 66, 11, 18, 22, 4, 39], [99, 34, 51, 18, 95, 47, 51, 5, 44, 47, 89, 46], [88, 72, 67, 67, 21, 83, 36, 70, 93, 95, 50, 49], [7, 78, 19, 99, 94, 18, 85, 28, 47, 23, 31, 93], [29, 65, 65, 62, 21, 82, 44, 52, 32, 15, 54, 33], [23, 30, 94, 50, 78, 53, 12, 78, 20, 97, 30, 19], [79, 55, 12, 92, 36, 39, 95, 66, 93, 19, 43, 2], [65, 11, 3, 92, 32, 95, 31, 67, 83, 55, 13, 63], [8, 61, 47, 71, 97, 46, 88, 71, 73, 24, 86, 97], [91, 48, 80, 38, 54, 11, 42, 95, 55, 32, 2, 88], [3, 62, 65, 52, 29, 39, 80, 32, 12, 0, 38, 69]], [[83, 87, 90, 71, 63, 71, 39, 3, 63, 35, 55, 53], [21, 22, 67, 80, 86, 82, 71, 46, 20, 41, 9, 22], [83, 54, 70, 66, 17, 20, 94, 28, 33, 81, 80, 61], [51, 78, 49, 4, 47, 53, 49, 70, 33, 11, 0, 63], [85, 60, 14, 60, 3, 86, 80, 61, 9, 7, 94, 14], [69, 81, 34, 29, 67, 92, 52, 5, 27, 23, 87, 52], [73, 48, 81, 80, 6, 11, 48, 34, 11, 51, 56, 34], [24, 13, 32, 15, 98, 92, 74, 4, 68, 45, 44, 97], [19, 54, 30, 36, 43, 48, 80, 20, 59, 36, 43, 76], [80, 98, 9, 94, 77, 20, 31, 35, 30, 27, 19, 38], [10, 12, 84, 1, 22, 67, 42, 44, 4, 2, 47, 35], [86, 76, 52, 59, 75, 83, 26, 74, 33, 43, 59, 88]], [[26, 7, 19, 53, 14, 99, 52, 57, 3, 96, 77, 45], [61, 42, 42, 98, 23, 82, 73, 0, 17, 62, 98, 92], [41, 43, 33, 18, 42, 6, 90, 27, 72, 77, 82, 43], [35, 91, 77, 16, 54, 94, 38, 99, 8, 20, 83, 23], [88, 53, 18, 15, 62, 6, 27, 9, 54, 80, 32, 68], [78, 31, 51, 47, 33, 64, 61, 41, 17, 69, 69, 63], [69, 95, 56, 25, 69, 64, 28, 25, 36, 21, 4, 54], [58, 48, 26, 88, 61, 69, 70, 87, 35, 18, 8, 10], [33, 38, 88, 22, 11, 59, 73, 81, 86, 88, 30, 36], [48, 32, 18, 29, 38, 23, 79, 55, 9, 47, 58, 22], [4, 44, 73, 25, 61, 52, 92, 90, 24, 99, 56, 29], [37, 34, 2, 5, 21, 46, 98, 73, 28, 93, 61, 46]], [[25, 26, 28, 10, 5, 89, 95, 91, 11, 79, 94, 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94, 11, 25, 38, 37, 57, 2, 72], [97, 41, 69, 58, 65, 96, 45, 6, 41, 65, 50, 34], [22, 13, 35, 5, 76, 76, 2, 26, 28, 10, 81, 88]], [[27, 73, 14, 29, 35, 17, 3, 75, 66, 99, 31, 68], [16, 80, 22, 98, 93, 82, 60, 57, 93, 10, 14, 39], [32, 36, 25, 47, 74, 69, 71, 90, 79, 31, 17, 86], [13, 44, 67, 32, 23, 31, 70, 66, 61, 86, 38, 44], [28, 61, 72, 45, 82, 11, 50, 95, 2, 6, 20, 81], [9, 45, 16, 29, 64, 3, 65, 20, 89, 27, 67, 68], [20, 51, 79, 14, 29, 24, 39, 16, 50, 25, 44, 41], [0, 0, 33, 45, 94, 30, 99, 37, 25, 56, 34, 78], [87, 90, 57, 59, 8, 40, 82, 63, 29, 51, 39, 21], [47, 48, 76, 71, 48, 65, 74, 71, 19, 51, 23, 38], [69, 13, 35, 21, 35, 58, 36, 3, 86, 12, 6, 98], [50, 46, 97, 24, 11, 40, 79, 31, 88, 20, 74, 3]], [[52, 51, 92, 40, 67, 40, 61, 43, 13, 54, 67, 0], [64, 20, 68, 85, 64, 62, 92, 31, 67, 90, 22, 32], [13, 90, 2, 41, 38, 89, 82, 41, 26, 71, 11, 89], [72, 20, 90, 83, 69, 78, 38, 44, 7, 89, 60, 71], [53, 57, 93, 46, 93, 4, 75, 24, 85, 32, 60, 89], [4, 30, 43, 77, 57, 28, 34, 23, 31, 26, 71, 72], [95, 15, 37, 80, 63, 8, 66, 12, 50, 87, 47, 62], [24, 8, 4, 19, 1, 78, 48, 22, 76, 76, 17, 4], [45, 19, 75, 60, 95, 98, 92, 66, 41, 38, 41, 41], [22, 99, 78, 3, 81, 23, 15, 94, 82, 71, 70, 4], [21, 85, 74, 70, 82, 50, 22, 12, 77, 26, 82, 11], [51, 10, 43, 56, 23, 78, 50, 82, 27, 59, 90, 10]], [[59, 56, 44, 97, 20, 92, 85, 0, 36, 37, 53, 23], [23, 31, 65, 64, 60, 84, 10, 8, 48, 39, 90, 94], [69, 72, 93, 99, 23, 82, 29, 19, 11, 49, 37, 82], [44, 3, 72, 52, 67, 97, 59, 34, 68, 88, 0, 64], [45, 52, 34, 42, 13, 90, 22, 56, 96, 90, 32, 33], [22, 3, 49, 0, 47, 10, 62, 62, 41, 34, 82, 0], [21, 95, 68, 11, 47, 49, 2, 99, 92, 75, 57, 91], [44, 74, 31, 20, 88, 73, 69, 97, 36, 7, 25, 2], [38, 41, 78, 64, 33, 21, 3, 16, 8, 20, 99, 96], [73, 94, 22, 60, 41, 1, 44, 34, 16, 91, 58, 19], [76, 66, 6, 50, 76, 40, 59, 82, 72, 58, 10, 38], [78, 99, 43, 6, 69, 70, 1, 87, 38, 48, 22, 6]], [[40, 77, 47, 50, 44, 49, 26, 47, 59, 46, 68, 26], [69, 78, 73, 20, 76, 56, 87, 20, 53, 25, 20, 1], [94, 95, 57, 19, 78, 7, 41, 19, 54, 60, 31, 31], [97, 46, 35, 41, 56, 31, 35, 56, 94, 4, 75, 79], [59, 22, 82, 50, 43, 76, 81, 13, 79, 62, 79, 76], [57, 66, 58, 36, 12, 3, 52, 73, 2, 9, 10, 52], [81, 3, 50, 27, 72, 12, 94, 77, 83, 70, 77, 89], [0, 30, 3, 29, 55, 50, 18, 74, 55, 57, 36, 30], [68, 52, 64, 66, 35, 35, 55, 94, 68, 74, 90, 15], [36, 58, 73, 69, 29, 51, 22, 48, 46, 12, 4, 19], [24, 93, 40, 17, 9, 71, 45, 67, 27, 47, 64, 32], [93, 3, 8, 70, 27, 85, 79, 59, 19, 48, 85, 14]], [[75, 26, 65, 39, 54, 43, 46, 50, 93, 92, 62, 69], [71, 18, 57, 54, 54, 12, 72, 24, 62, 22, 85, 35], [0, 18, 24, 58, 26, 51, 57, 60, 16, 29, 64, 50], [68, 54, 99, 8, 45, 71, 66, 66, 85, 1, 41, 48], [57, 35, 60, 36, 92, 33, 94, 83, 48, 43, 80, 23], [42, 60, 71, 49, 71, 83, 28, 6, 21, 96, 49, 68], [57, 82, 21, 58, 29, 30, 78, 92, 36, 12, 79, 40], [42, 10, 24, 46, 82, 86, 81, 74, 99, 28, 42, 8], [19, 82, 87, 68, 91, 97, 49, 38, 12, 27, 11, 74], [45, 53, 59, 0, 83, 17, 36, 8, 55, 6, 87, 26], [95, 53, 63, 66, 53, 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33, 6], [10, 30, 59, 32, 28, 50, 1, 94, 83, 13, 83, 25], [36, 70, 49, 58, 89, 13, 42, 13, 40, 77, 85, 43], [88, 49, 19, 16, 33, 89, 16, 76, 99, 34, 52, 33], [93, 14, 47, 73, 24, 22, 51, 23, 62, 1, 93, 80], [64, 7, 41, 87, 2, 26, 25, 1, 0, 54, 3, 6]]], 'objective': 8.0}","[[0, 11, 9], [1, 3, 10], [2, 0, 8], [3, 4, 5], [4, 8, 7], [5, 7, 0], [6, 2, 2], [7, 6, 6], [8, 1, 11], [9, 9, 3], [10, 10, 4], [11, 5, 1]]",8.0,"{'problem_type': 'AP3', 'n': 12, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 23}, {'i': 0, 'j': 0, 'k': 1, 'cost': 26}, {'i': 0, 'j': 0, 'k': 2, 'cost': 84}, {'i': 0, 'j': 0, 'k': 3, 'cost': 52}, {'i': 0, 'j': 0, 'k': 4, 'cost': 11}, {'i': 0, 'j': 0, 'k': 5, 'cost': 48}, {'i': 0, 'j': 0, 'k': 6, 'cost': 53}, {'i': 0, 'j': 0, 'k': 7, 'cost': 58}, {'i': 0, 'j': 0, 'k': 8, 'cost': 25}, {'i': 0, 'j': 0, 'k': 9, 'cost': 58}, {'i': 0, 'j': 0, 'k': 10, 'cost': 34}, {'i': 0, 'j': 0, 'k': 11, 'cost': 67}, {'i': 0, 'j': 1, 'k': 0, 'cost': 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{'i': 10, 'j': 5, 'k': 0, 'cost': 58}, {'i': 10, 'j': 5, 'k': 1, 'cost': 82}, {'i': 10, 'j': 5, 'k': 2, 'cost': 20}, {'i': 10, 'j': 5, 'k': 3, 'cost': 83}, {'i': 10, 'j': 5, 'k': 4, 'cost': 24}, {'i': 10, 'j': 5, 'k': 5, 'cost': 57}, {'i': 10, 'j': 5, 'k': 6, 'cost': 89}, {'i': 10, 'j': 5, 'k': 7, 'cost': 58}, {'i': 10, 'j': 5, 'k': 8, 'cost': 39}, {'i': 10, 'j': 5, 'k': 9, 'cost': 18}, {'i': 10, 'j': 5, 'k': 10, 'cost': 96}, {'i': 10, 'j': 5, 'k': 11, 'cost': 32}, {'i': 10, 'j': 6, 'k': 0, 'cost': 58}, {'i': 10, 'j': 6, 'k': 1, 'cost': 32}, {'i': 10, 'j': 6, 'k': 2, 'cost': 41}, {'i': 10, 'j': 6, 'k': 3, 'cost': 9}, {'i': 10, 'j': 6, 'k': 4, 'cost': 96}, {'i': 10, 'j': 6, 'k': 5, 'cost': 42}, {'i': 10, 'j': 6, 'k': 6, 'cost': 91}, {'i': 10, 'j': 6, 'k': 7, 'cost': 28}, {'i': 10, 'j': 6, 'k': 8, 'cost': 12}, {'i': 10, 'j': 6, 'k': 9, 'cost': 31}, {'i': 10, 'j': 6, 'k': 10, 'cost': 24}, {'i': 10, 'j': 6, 'k': 11, 'cost': 92}, {'i': 10, 'j': 7, 'k': 0, 'cost': 21}, {'i': 10, 'j': 7, 'k': 1, 'cost': 32}, {'i': 10, 'j': 7, 'k': 2, 'cost': 3}, {'i': 10, 'j': 7, 'k': 3, 'cost': 74}, {'i': 10, 'j': 7, 'k': 4, 'cost': 74}, {'i': 10, 'j': 7, 'k': 5, 'cost': 31}, {'i': 10, 'j': 7, 'k': 6, 'cost': 53}, {'i': 10, 'j': 7, 'k': 7, 'cost': 75}, {'i': 10, 'j': 7, 'k': 8, 'cost': 96}, {'i': 10, 'j': 7, 'k': 9, 'cost': 8}, {'i': 10, 'j': 7, 'k': 10, 'cost': 86}, {'i': 10, 'j': 7, 'k': 11, 'cost': 52}, {'i': 10, 'j': 8, 'k': 0, 'cost': 1}, {'i': 10, 'j': 8, 'k': 1, 'cost': 82}, {'i': 10, 'j': 8, 'k': 2, 'cost': 8}, {'i': 10, 'j': 8, 'k': 3, 'cost': 80}, {'i': 10, 'j': 8, 'k': 4, 'cost': 97}, {'i': 10, 'j': 8, 'k': 5, 'cost': 68}, {'i': 10, 'j': 8, 'k': 6, 'cost': 77}, {'i': 10, 'j': 8, 'k': 7, 'cost': 7}, {'i': 10, 'j': 8, 'k': 8, 'cost': 13}, {'i': 10, 'j': 8, 'k': 9, 'cost': 94}, {'i': 10, 'j': 8, 'k': 10, 'cost': 98}, {'i': 10, 'j': 8, 'k': 11, 'cost': 53}, {'i': 10, 'j': 9, 'k': 0, 'cost': 4}, {'i': 10, 'j': 9, 'k': 1, 'cost': 94}, {'i': 10, 'j': 9, 'k': 2, 'cost': 58}, {'i': 10, 'j': 9, 'k': 3, 'cost': 76}, {'i': 10, 'j': 9, 'k': 4, 'cost': 59}, {'i': 10, 'j': 9, 'k': 5, 'cost': 98}, {'i': 10, 'j': 9, 'k': 6, 'cost': 87}, {'i': 10, 'j': 9, 'k': 7, 'cost': 84}, {'i': 10, 'j': 9, 'k': 8, 'cost': 6}, {'i': 10, 'j': 9, 'k': 9, 'cost': 3}, {'i': 10, 'j': 9, 'k': 10, 'cost': 31}, {'i': 10, 'j': 9, 'k': 11, 'cost': 83}, {'i': 10, 'j': 10, 'k': 0, 'cost': 53}, {'i': 10, 'j': 10, 'k': 1, 'cost': 10}, {'i': 10, 'j': 10, 'k': 2, 'cost': 66}, {'i': 10, 'j': 10, 'k': 3, 'cost': 96}, {'i': 10, 'j': 10, 'k': 4, 'cost': 0}, {'i': 10, 'j': 10, 'k': 5, 'cost': 11}, {'i': 10, 'j': 10, 'k': 6, 'cost': 79}, {'i': 10, 'j': 10, 'k': 7, 'cost': 61}, {'i': 10, 'j': 10, 'k': 8, 'cost': 23}, {'i': 10, 'j': 10, 'k': 9, 'cost': 29}, {'i': 10, 'j': 10, 'k': 10, 'cost': 4}, {'i': 10, 'j': 10, 'k': 11, 'cost': 82}, {'i': 10, 'j': 11, 'k': 0, 'cost': 92}, {'i': 10, 'j': 11, 'k': 1, 'cost': 31}, {'i': 10, 'j': 11, 'k': 2, 'cost': 26}, {'i': 10, 'j': 11, 'k': 3, 'cost': 8}, {'i': 10, 'j': 11, 'k': 4, 'cost': 75}, {'i': 10, 'j': 11, 'k': 5, 'cost': 87}, {'i': 10, 'j': 11, 'k': 6, 'cost': 76}, {'i': 10, 'j': 11, 'k': 7, 'cost': 7}, {'i': 10, 'j': 11, 'k': 8, 'cost': 13}, {'i': 10, 'j': 11, 'k': 9, 'cost': 27}, {'i': 10, 'j': 11, 'k': 10, 'cost': 24}, {'i': 10, 'j': 11, 'k': 11, 'cost': 82}, {'i': 11, 'j': 0, 'k': 0, 'cost': 52}, {'i': 11, 'j': 0, 'k': 1, 'cost': 80}, {'i': 11, 'j': 0, 'k': 2, 'cost': 73}, {'i': 11, 'j': 0, 'k': 3, 'cost': 19}, {'i': 11, 'j': 0, 'k': 4, 'cost': 86}, {'i': 11, 'j': 0, 'k': 5, 'cost': 23}, {'i': 11, 'j': 0, 'k': 6, 'cost': 10}, {'i': 11, 'j': 0, 'k': 7, 'cost': 47}, {'i': 11, 'j': 0, 'k': 8, 'cost': 90}, {'i': 11, 'j': 0, 'k': 9, 'cost': 63}, {'i': 11, 'j': 0, 'k': 10, 'cost': 95}, {'i': 11, 'j': 0, 'k': 11, 'cost': 76}, {'i': 11, 'j': 1, 'k': 0, 'cost': 34}, {'i': 11, 'j': 1, 'k': 1, 'cost': 28}, {'i': 11, 'j': 1, 'k': 2, 'cost': 15}, {'i': 11, 'j': 1, 'k': 3, 'cost': 66}, {'i': 11, 'j': 1, 'k': 4, 'cost': 37}, {'i': 11, 'j': 1, 'k': 5, 'cost': 89}, {'i': 11, 'j': 1, 'k': 6, 'cost': 43}, {'i': 11, 'j': 1, 'k': 7, 'cost': 44}, {'i': 11, 'j': 1, 'k': 8, 'cost': 8}, {'i': 11, 'j': 1, 'k': 9, 'cost': 87}, {'i': 11, 'j': 1, 'k': 10, 'cost': 69}, {'i': 11, 'j': 1, 'k': 11, 'cost': 53}, {'i': 11, 'j': 2, 'k': 0, 'cost': 69}, {'i': 11, 'j': 2, 'k': 1, 'cost': 34}, {'i': 11, 'j': 2, 'k': 2, 'cost': 31}, {'i': 11, 'j': 2, 'k': 3, 'cost': 92}, {'i': 11, 'j': 2, 'k': 4, 'cost': 59}, {'i': 11, 'j': 2, 'k': 5, 'cost': 18}, {'i': 11, 'j': 2, 'k': 6, 'cost': 5}, {'i': 11, 'j': 2, 'k': 7, 'cost': 76}, {'i': 11, 'j': 2, 'k': 8, 'cost': 9}, {'i': 11, 'j': 2, 'k': 9, 'cost': 96}, {'i': 11, 'j': 2, 'k': 10, 'cost': 24}, {'i': 11, 'j': 2, 'k': 11, 'cost': 15}, {'i': 11, 'j': 3, 'k': 0, 'cost': 49}, {'i': 11, 'j': 3, 'k': 1, 'cost': 79}, {'i': 11, 'j': 3, 'k': 2, 'cost': 23}, {'i': 11, 'j': 3, 'k': 3, 'cost': 83}, {'i': 11, 'j': 3, 'k': 4, 'cost': 96}, {'i': 11, 'j': 3, 'k': 5, 'cost': 65}, {'i': 11, 'j': 3, 'k': 6, 'cost': 98}, {'i': 11, 'j': 3, 'k': 7, 'cost': 43}, {'i': 11, 'j': 3, 'k': 8, 'cost': 4}, {'i': 11, 'j': 3, 'k': 9, 'cost': 66}, {'i': 11, 'j': 3, 'k': 10, 'cost': 19}, {'i': 11, 'j': 3, 'k': 11, 'cost': 97}, {'i': 11, 'j': 4, 'k': 0, 'cost': 94}, {'i': 11, 'j': 4, 'k': 1, 'cost': 80}, {'i': 11, 'j': 4, 'k': 2, 'cost': 71}, {'i': 11, 'j': 4, 'k': 3, 'cost': 76}, {'i': 11, 'j': 4, 'k': 4, 'cost': 61}, {'i': 11, 'j': 4, 'k': 5, 'cost': 8}, {'i': 11, 'j': 4, 'k': 6, 'cost': 13}, {'i': 11, 'j': 4, 'k': 7, 'cost': 61}, {'i': 11, 'j': 4, 'k': 8, 'cost': 96}, {'i': 11, 'j': 4, 'k': 9, 'cost': 70}, {'i': 11, 'j': 4, 'k': 10, 'cost': 82}, {'i': 11, 'j': 4, 'k': 11, 'cost': 28}, {'i': 11, 'j': 5, 'k': 0, 'cost': 0}, {'i': 11, 'j': 5, 'k': 1, 'cost': 0}, {'i': 11, 'j': 5, 'k': 2, 'cost': 24}, {'i': 11, 'j': 5, 'k': 3, 'cost': 9}, {'i': 11, 'j': 5, 'k': 4, 'cost': 30}, {'i': 11, 'j': 5, 'k': 5, 'cost': 47}, {'i': 11, 'j': 5, 'k': 6, 'cost': 63}, {'i': 11, 'j': 5, 'k': 7, 'cost': 66}, {'i': 11, 'j': 5, 'k': 8, 'cost': 65}, {'i': 11, 'j': 5, 'k': 9, 'cost': 19}, {'i': 11, 'j': 5, 'k': 10, 'cost': 76}, {'i': 11, 'j': 5, 'k': 11, 'cost': 55}, {'i': 11, 'j': 6, 'k': 0, 'cost': 13}, {'i': 11, 'j': 6, 'k': 1, 'cost': 85}, {'i': 11, 'j': 6, 'k': 2, 'cost': 33}, {'i': 11, 'j': 6, 'k': 3, 'cost': 51}, {'i': 11, 'j': 6, 'k': 4, 'cost': 24}, {'i': 11, 'j': 6, 'k': 5, 'cost': 59}, {'i': 11, 'j': 6, 'k': 6, 'cost': 25}, {'i': 11, 'j': 6, 'k': 7, 'cost': 93}, {'i': 11, 'j': 6, 'k': 8, 'cost': 38}, {'i': 11, 'j': 6, 'k': 9, 'cost': 70}, {'i': 11, 'j': 6, 'k': 10, 'cost': 33}, {'i': 11, 'j': 6, 'k': 11, 'cost': 6}, {'i': 11, 'j': 7, 'k': 0, 'cost': 10}, {'i': 11, 'j': 7, 'k': 1, 'cost': 30}, {'i': 11, 'j': 7, 'k': 2, 'cost': 59}, {'i': 11, 'j': 7, 'k': 3, 'cost': 32}, {'i': 11, 'j': 7, 'k': 4, 'cost': 28}, {'i': 11, 'j': 7, 'k': 5, 'cost': 50}, {'i': 11, 'j': 7, 'k': 6, 'cost': 1}, {'i': 11, 'j': 7, 'k': 7, 'cost': 94}, {'i': 11, 'j': 7, 'k': 8, 'cost': 83}, {'i': 11, 'j': 7, 'k': 9, 'cost': 13}, {'i': 11, 'j': 7, 'k': 10, 'cost': 83}, {'i': 11, 'j': 7, 'k': 11, 'cost': 25}, {'i': 11, 'j': 8, 'k': 0, 'cost': 36}, {'i': 11, 'j': 8, 'k': 1, 'cost': 70}, {'i': 11, 'j': 8, 'k': 2, 'cost': 49}, {'i': 11, 'j': 8, 'k': 3, 'cost': 58}, {'i': 11, 'j': 8, 'k': 4, 'cost': 89}, {'i': 11, 'j': 8, 'k': 5, 'cost': 13}, {'i': 11, 'j': 8, 'k': 6, 'cost': 42}, {'i': 11, 'j': 8, 'k': 7, 'cost': 13}, {'i': 11, 'j': 8, 'k': 8, 'cost': 40}, {'i': 11, 'j': 8, 'k': 9, 'cost': 77}, {'i': 11, 'j': 8, 'k': 10, 'cost': 85}, {'i': 11, 'j': 8, 'k': 11, 'cost': 43}, {'i': 11, 'j': 9, 'k': 0, 'cost': 88}, {'i': 11, 'j': 9, 'k': 1, 'cost': 49}, {'i': 11, 'j': 9, 'k': 2, 'cost': 19}, {'i': 11, 'j': 9, 'k': 3, 'cost': 16}, {'i': 11, 'j': 9, 'k': 4, 'cost': 33}, {'i': 11, 'j': 9, 'k': 5, 'cost': 89}, {'i': 11, 'j': 9, 'k': 6, 'cost': 16}, {'i': 11, 'j': 9, 'k': 7, 'cost': 76}, {'i': 11, 'j': 9, 'k': 8, 'cost': 99}, {'i': 11, 'j': 9, 'k': 9, 'cost': 34}, {'i': 11, 'j': 9, 'k': 10, 'cost': 52}, {'i': 11, 'j': 9, 'k': 11, 'cost': 33}, {'i': 11, 'j': 10, 'k': 0, 'cost': 93}, {'i': 11, 'j': 10, 'k': 1, 'cost': 14}, {'i': 11, 'j': 10, 'k': 2, 'cost': 47}, {'i': 11, 'j': 10, 'k': 3, 'cost': 73}, {'i': 11, 'j': 10, 'k': 4, 'cost': 24}, {'i': 11, 'j': 10, 'k': 5, 'cost': 22}, {'i': 11, 'j': 10, 'k': 6, 'cost': 51}, {'i': 11, 'j': 10, 'k': 7, 'cost': 23}, {'i': 11, 'j': 10, 'k': 8, 'cost': 62}, {'i': 11, 'j': 10, 'k': 9, 'cost': 1}, {'i': 11, 'j': 10, 'k': 10, 'cost': 93}, {'i': 11, 'j': 10, 'k': 11, 'cost': 80}, {'i': 11, 'j': 11, 'k': 0, 'cost': 64}, {'i': 11, 'j': 11, 'k': 1, 'cost': 7}, {'i': 11, 'j': 11, 'k': 2, 'cost': 41}, {'i': 11, 'j': 11, 'k': 3, 'cost': 87}, {'i': 11, 'j': 11, 'k': 4, 'cost': 2}, {'i': 11, 'j': 11, 'k': 5, 'cost': 26}, {'i': 11, 'j': 11, 'k': 6, 'cost': 25}, {'i': 11, 'j': 11, 'k': 7, 'cost': 1}, {'i': 11, 'j': 11, 'k': 8, 'cost': 0}, {'i': 11, 'j': 11, 'k': 9, 'cost': 54}, {'i': 11, 'j': 11, 'k': 10, 'cost': 3}, {'i': 11, 'j': 11, 'k': 11, 'cost': 6}]}","[[0, 11, 9], [1, 3, 10], [2, 0, 8], [3, 4, 5], [4, 8, 7], [5, 7, 0], [6, 2, 2], [7, 6, 6], [8, 1, 11], [9, 9, 3], [10, 10, 4], [11, 5, 1]]",48,nl,0
+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.
+
+We have 10 models (and 10 outfits and 10 assistants), identified as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
+
+*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 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 94 | 21 | 26 | 40 | 81 | 10 | 2 | 3 | 27 | 60 |
+| 2 | 24 | 22 | 96 | 81 | 12 | 93 | 59 | 44 | 20 | 49 |
+| 3 | 94 | 92 | 21 | 3 | 95 | 3 | 95 | 13 | 3 | 37 |
+| 4 | 3 | 46 | 42 | 42 | 60 | 76 | 96 | 74 | 67 | 94 |
+| 5 | 18 | 52 | 97 | 71 | 40 | 59 | 63 | 10 | 20 | 16 |
+| 6 | 27 | 91 | 87 | 95 | 39 | 96 | 21 | 38 | 27 | 7 |
+| 7 | 83 | 5 | 23 | 10 | 85 | 98 | 57 | 46 | 8 | 98 |
+| 8 | 86 | 36 | 8 | 20 | 29 | 11 | 96 | 55 | 23 | 51 |
+| 9 | 41 | 80 | 8 | 39 | 88 | 86 | 17 | 91 | 76 | 10 |
+| 10 | 73 | 23 | 89 | 1 | 54 | 26 | 91 | 47 | 23 | 82 |
+
+## model_id=2
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 21 | 40 | 32 | 57 | 8 | 35 | 52 | 57 | 55 | 82 |
+| 2 | 31 | 85 | 61 | 69 | 52 | 88 | 36 | 86 | 93 | 34 |
+| 3 | 17 | 28 | 83 | 6 | 19 | 80 | 61 | 77 | 60 | 98 |
+| 4 | 30 | 84 | 70 | 20 | 91 | 67 | 72 | 30 | 26 | 93 |
+| 5 | 27 | 1 | 37 | 93 | 31 | 23 | 43 | 24 | 66 | 33 |
+| 6 | 7 | 89 | 47 | 28 | 52 | 39 | 19 | 82 | 66 | 45 |
+| 7 | 98 | 94 | 94 | 37 | 86 | 11 | 23 | 59 | 29 | 65 |
+| 8 | 60 | 21 | 7 | 20 | 48 | 36 | 0 | 98 | 29 | 74 |
+| 9 | 71 | 56 | 56 | 16 | 7 | 29 | 81 | 18 | 74 | 80 |
+| 10 | 32 | 54 | 44 | 73 | 29 | 24 | 31 | 18 | 87 | 0 |
+
+## model_id=3
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 39 | 48 | 89 | 49 | 48 | 71 | 47 | 38 | 97 | 86 |
+| 2 | 53 | 72 | 30 | 96 | 88 | 86 | 29 | 24 | 10 | 27 |
+| 3 | 71 | 84 | 23 | 10 | 23 | 77 | 14 | 33 | 26 | 3 |
+| 4 | 14 | 90 | 1 | 41 | 37 | 47 | 5 | 76 | 45 | 66 |
+| 5 | 19 | 16 | 7 | 71 | 80 | 50 | 23 | 20 | 24 | 13 |
+| 6 | 5 | 17 | 67 | 48 | 66 | 25 | 98 | 31 | 10 | 69 |
+| 7 | 79 | 12 | 16 | 98 | 88 | 50 | 77 | 66 | 98 | 87 |
+| 8 | 8 | 75 | 55 | 11 | 11 | 17 | 70 | 68 | 50 | 64 |
+| 9 | 70 | 71 | 82 | 60 | 38 | 10 | 5 | 28 | 61 | 96 |
+| 10 | 47 | 73 | 26 | 95 | 49 | 52 | 78 | 62 | 69 | 5 |
+
+## model_id=4
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 36 | 39 | 94 | 95 | 34 | 26 | 56 | 62 | 18 | 38 |
+| 2 | 74 | 0 | 16 | 47 | 69 | 74 | 87 | 16 | 21 | 66 |
+| 3 | 14 | 28 | 47 | 92 | 50 | 34 | 81 | 40 | 70 | 17 |
+| 4 | 68 | 57 | 16 | 37 | 82 | 97 | 21 | 0 | 93 | 93 |
+| 5 | 29 | 51 | 6 | 84 | 44 | 91 | 43 | 13 | 67 | 2 |
+| 6 | 42 | 14 | 62 | 80 | 77 | 29 | 4 | 17 | 66 | 86 |
+| 7 | 38 | 79 | 21 | 73 | 69 | 32 | 30 | 26 | 96 | 2 |
+| 8 | 6 | 0 | 73 | 83 | 67 | 2 | 73 | 41 | 19 | 80 |
+| 9 | 73 | 76 | 65 | 73 | 20 | 39 | 70 | 74 | 12 | 53 |
+| 10 | 65 | 80 | 66 | 80 | 32 | 30 | 52 | 70 | 23 | 45 |
+
+## model_id=5
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 47 | 19 | 15 | 69 | 83 | 93 | 13 | 18 | 84 | 71 |
+| 2 | 18 | 55 | 89 | 82 | 69 | 52 | 36 | 56 | 73 | 26 |
+| 3 | 27 | 83 | 26 | 41 | 39 | 37 | 47 | 34 | 12 | 33 |
+| 4 | 18 | 85 | 18 | 18 | 65 | 56 | 6 | 12 | 98 | 61 |
+| 5 | 31 | 58 | 73 | 25 | 88 | 43 | 27 | 62 | 84 | 56 |
+| 6 | 80 | 98 | 69 | 47 | 82 | 67 | 93 | 84 | 25 | 16 |
+| 7 | 17 | 23 | 32 | 92 | 93 | 61 | 93 | 60 | 53 | 13 |
+| 8 | 58 | 53 | 7 | 8 | 76 | 50 | 33 | 16 | 95 | 24 |
+| 9 | 17 | 95 | 37 | 2 | 2 | 3 | 35 | 38 | 39 | 59 |
+| 10 | 11 | 86 | 99 | 15 | 55 | 79 | 17 | 86 | 32 | 33 |
+
+## model_id=6
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 99 | 69 | 66 | 0 | 64 | 39 | 89 | 6 | 75 | 97 |
+| 2 | 36 | 71 | 8 | 78 | 43 | 18 | 27 | 2 | 49 | 58 |
+| 3 | 83 | 84 | 94 | 15 | 78 | 53 | 58 | 98 | 78 | 4 |
+| 4 | 67 | 83 | 1 | 97 | 76 | 27 | 30 | 52 | 50 | 84 |
+| 5 | 47 | 92 | 32 | 47 | 47 | 83 | 11 | 67 | 2 | 59 |
+| 6 | 29 | 77 | 78 | 26 | 50 | 97 | 23 | 60 | 4 | 91 |
+| 7 | 8 | 78 | 85 | 76 | 0 | 74 | 77 | 60 | 25 | 40 |
+| 8 | 27 | 23 | 33 | 65 | 0 | 24 | 33 | 67 | 68 | 75 |
+| 9 | 81 | 97 | 93 | 46 | 77 | 46 | 34 | 73 | 9 | 5 |
+| 10 | 93 | 20 | 96 | 76 | 16 | 40 | 93 | 40 | 54 | 17 |
+
+## model_id=7
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 82 | 26 | 71 | 62 | 91 | 91 | 81 | 38 | 55 | 47 |
+| 2 | 92 | 61 | 20 | 5 | 47 | 6 | 46 | 63 | 18 | 71 |
+| 3 | 45 | 72 | 79 | 66 | 4 | 71 | 33 | 9 | 14 | 16 |
+| 4 | 96 | 69 | 92 | 10 | 27 | 75 | 58 | 69 | 62 | 80 |
+| 5 | 31 | 98 | 90 | 74 | 55 | 91 | 17 | 70 | 6 | 11 |
+| 6 | 49 | 37 | 53 | 39 | 97 | 90 | 80 | 4 | 73 | 30 |
+| 7 | 7 | 53 | 51 | 91 | 95 | 62 | 5 | 53 | 62 | 59 |
+| 8 | 96 | 94 | 81 | 41 | 26 | 58 | 83 | 7 | 38 | 95 |
+| 9 | 1 | 42 | 5 | 58 | 84 | 79 | 37 | 37 | 44 | 13 |
+| 10 | 8 | 9 | 64 | 11 | 30 | 28 | 39 | 7 | 39 | 38 |
+
+## model_id=8
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 67 | 78 | 33 | 56 | 78 | 64 | 37 | 47 | 91 | 32 |
+| 2 | 62 | 83 | 76 | 86 | 61 | 70 | 52 | 3 | 47 | 69 |
+| 3 | 6 | 96 | 13 | 23 | 35 | 23 | 86 | 70 | 27 | 30 |
+| 4 | 6 | 53 | 46 | 34 | 62 | 66 | 37 | 45 | 77 | 21 |
+| 5 | 80 | 78 | 98 | 85 | 50 | 81 | 62 | 52 | 66 | 7 |
+| 6 | 38 | 85 | 31 | 44 | 61 | 99 | 31 | 72 | 12 | 73 |
+| 7 | 46 | 73 | 51 | 40 | 47 | 3 | 58 | 31 | 8 | 82 |
+| 8 | 51 | 89 | 45 | 82 | 97 | 44 | 67 | 7 | 71 | 72 |
+| 9 | 68 | 84 | 81 | 76 | 99 | 48 | 94 | 95 | 8 | 0 |
+| 10 | 6 | 29 | 41 | 50 | 34 | 90 | 4 | 60 | 97 | 57 |
+
+## model_id=9
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 94 | 32 | 96 | 46 | 38 | 10 | 44 | 56 | 18 | 23 |
+| 2 | 58 | 83 | 15 | 33 | 91 | 85 | 37 | 5 | 63 | 62 |
+| 3 | 13 | 97 | 33 | 90 | 56 | 63 | 23 | 32 | 81 | 75 |
+| 4 | 76 | 79 | 17 | 27 | 94 | 2 | 38 | 73 | 68 | 91 |
+| 5 | 87 | 19 | 5 | 45 | 96 | 23 | 41 | 84 | 77 | 77 |
+| 6 | 28 | 49 | 30 | 62 | 17 | 19 | 46 | 11 | 86 | 80 |
+| 7 | 95 | 52 | 49 | 85 | 23 | 66 | 67 | 97 | 90 | 10 |
+| 8 | 80 | 99 | 61 | 27 | 51 | 33 | 2 | 80 | 95 | 99 |
+| 9 | 55 | 13 | 34 | 39 | 23 | 2 | 60 | 84 | 43 | 61 |
+| 10 | 78 | 31 | 74 | 83 | 49 | 1 | 74 | 87 | 79 | 94 |
+
+## model_id=10
+| outfit_id\assistant_id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 1 | 66 | 90 | 66 | 31 | 45 | 8 | 28 | 38 | 46 | 30 |
+| 2 | 60 | 33 | 85 | 46 | 55 | 99 | 57 | 5 | 74 | 57 |
+| 3 | 1 | 16 | 76 | 19 | 74 | 95 | 2 | 3 | 49 | 76 |
+| 4 | 89 | 62 | 22 | 7 | 54 | 81 | 79 | 62 | 84 | 34 |
+| 5 | 34 | 89 | 90 | 67 | 50 | 14 | 65 | 10 | 50 | 63 |
+| 6 | 37 | 62 | 95 | 20 | 11 | 31 | 41 | 38 | 97 | 9 |
+| 7 | 3 | 42 | 31 | 11 | 25 | 74 | 52 | 44 | 76 | 45 |
+| 8 | 53 | 99 | 36 | 84 | 86 | 18 | 17 | 83 | 21 | 69 |
+| 9 | 78 | 79 | 15 | 30 | 24 | 4 | 6 | 70 | 78 | 24 |
+| 10 | 84 | 18 | 5 | 6 | 84 | 53 | 98 | 51 | 99 | 98 |
+
+We'll use these lines to choose the pairings that minimize the total cost.
+
+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': [[[94, 21, 26, 40, 81, 10, 2, 3, 27, 60], [24, 22, 96, 81, 12, 93, 59, 44, 20, 49], [94, 92, 21, 3, 95, 3, 95, 13, 3, 37], [3, 46, 42, 42, 60, 76, 96, 74, 67, 94], [18, 52, 97, 71, 40, 59, 63, 10, 20, 16], [27, 91, 87, 95, 39, 96, 21, 38, 27, 7], [83, 5, 23, 10, 85, 98, 57, 46, 8, 98], [86, 36, 8, 20, 29, 11, 96, 55, 23, 51], [41, 80, 8, 39, 88, 86, 17, 91, 76, 10], [73, 23, 89, 1, 54, 26, 91, 47, 23, 82]], [[21, 40, 32, 57, 8, 35, 52, 57, 55, 82], [31, 85, 61, 69, 52, 88, 36, 86, 93, 34], [17, 28, 83, 6, 19, 80, 61, 77, 60, 98], [30, 84, 70, 20, 91, 67, 72, 30, 26, 93], [27, 1, 37, 93, 31, 23, 43, 24, 66, 33], [7, 89, 47, 28, 52, 39, 19, 82, 66, 45], [98, 94, 94, 37, 86, 11, 23, 59, 29, 65], [60, 21, 7, 20, 48, 36, 0, 98, 29, 74], [71, 56, 56, 16, 7, 29, 81, 18, 74, 80], [32, 54, 44, 73, 29, 24, 31, 18, 87, 0]], [[39, 48, 89, 49, 48, 71, 47, 38, 97, 86], [53, 72, 30, 96, 88, 86, 29, 24, 10, 27], [71, 84, 23, 10, 23, 77, 14, 33, 26, 3], [14, 90, 1, 41, 37, 47, 5, 76, 45, 66], [19, 16, 7, 71, 80, 50, 23, 20, 24, 13], [5, 17, 67, 48, 66, 25, 98, 31, 10, 69], [79, 12, 16, 98, 88, 50, 77, 66, 98, 87], [8, 75, 55, 11, 11, 17, 70, 68, 50, 64], [70, 71, 82, 60, 38, 10, 5, 28, 61, 96], [47, 73, 26, 95, 49, 52, 78, 62, 69, 5]], [[36, 39, 94, 95, 34, 26, 56, 62, 18, 38], [74, 0, 16, 47, 69, 74, 87, 16, 21, 66], [14, 28, 47, 92, 50, 34, 81, 40, 70, 17], [68, 57, 16, 37, 82, 97, 21, 0, 93, 93], [29, 51, 6, 84, 44, 91, 43, 13, 67, 2], [42, 14, 62, 80, 77, 29, 4, 17, 66, 86], [38, 79, 21, 73, 69, 32, 30, 26, 96, 2], [6, 0, 73, 83, 67, 2, 73, 41, 19, 80], [73, 76, 65, 73, 20, 39, 70, 74, 12, 53], [65, 80, 66, 80, 32, 30, 52, 70, 23, 45]], [[47, 19, 15, 69, 83, 93, 13, 18, 84, 71], [18, 55, 89, 82, 69, 52, 36, 56, 73, 26], [27, 83, 26, 41, 39, 37, 47, 34, 12, 33], [18, 85, 18, 18, 65, 56, 6, 12, 98, 61], [31, 58, 73, 25, 88, 43, 27, 62, 84, 56], [80, 98, 69, 47, 82, 67, 93, 84, 25, 16], [17, 23, 32, 92, 93, 61, 93, 60, 53, 13], [58, 53, 7, 8, 76, 50, 33, 16, 95, 24], [17, 95, 37, 2, 2, 3, 35, 38, 39, 59], [11, 86, 99, 15, 55, 79, 17, 86, 32, 33]], [[99, 69, 66, 0, 64, 39, 89, 6, 75, 97], [36, 71, 8, 78, 43, 18, 27, 2, 49, 58], [83, 84, 94, 15, 78, 53, 58, 98, 78, 4], [67, 83, 1, 97, 76, 27, 30, 52, 50, 84], [47, 92, 32, 47, 47, 83, 11, 67, 2, 59], [29, 77, 78, 26, 50, 97, 23, 60, 4, 91], [8, 78, 85, 76, 0, 74, 77, 60, 25, 40], [27, 23, 33, 65, 0, 24, 33, 67, 68, 75], [81, 97, 93, 46, 77, 46, 34, 73, 9, 5], [93, 20, 96, 76, 16, 40, 93, 40, 54, 17]], [[82, 26, 71, 62, 91, 91, 81, 38, 55, 47], [92, 61, 20, 5, 47, 6, 46, 63, 18, 71], [45, 72, 79, 66, 4, 71, 33, 9, 14, 16], [96, 69, 92, 10, 27, 75, 58, 69, 62, 80], [31, 98, 90, 74, 55, 91, 17, 70, 6, 11], [49, 37, 53, 39, 97, 90, 80, 4, 73, 30], [7, 53, 51, 91, 95, 62, 5, 53, 62, 59], [96, 94, 81, 41, 26, 58, 83, 7, 38, 95], [1, 42, 5, 58, 84, 79, 37, 37, 44, 13], [8, 9, 64, 11, 30, 28, 39, 7, 39, 38]], [[67, 78, 33, 56, 78, 64, 37, 47, 91, 32], [62, 83, 76, 86, 61, 70, 52, 3, 47, 69], [6, 96, 13, 23, 35, 23, 86, 70, 27, 30], [6, 53, 46, 34, 62, 66, 37, 45, 77, 21], [80, 78, 98, 85, 50, 81, 62, 52, 66, 7], [38, 85, 31, 44, 61, 99, 31, 72, 12, 73], [46, 73, 51, 40, 47, 3, 58, 31, 8, 82], [51, 89, 45, 82, 97, 44, 67, 7, 71, 72], [68, 84, 81, 76, 99, 48, 94, 95, 8, 0], [6, 29, 41, 50, 34, 90, 4, 60, 97, 57]], [[94, 32, 96, 46, 38, 10, 44, 56, 18, 23], [58, 83, 15, 33, 91, 85, 37, 5, 63, 62], [13, 97, 33, 90, 56, 63, 23, 32, 81, 75], [76, 79, 17, 27, 94, 2, 38, 73, 68, 91], [87, 19, 5, 45, 96, 23, 41, 84, 77, 77], [28, 49, 30, 62, 17, 19, 46, 11, 86, 80], [95, 52, 49, 85, 23, 66, 67, 97, 90, 10], [80, 99, 61, 27, 51, 33, 2, 80, 95, 99], [55, 13, 34, 39, 23, 2, 60, 84, 43, 61], [78, 31, 74, 83, 49, 1, 74, 87, 79, 94]], [[66, 90, 66, 31, 45, 8, 28, 38, 46, 30], [60, 33, 85, 46, 55, 99, 57, 5, 74, 57], [1, 16, 76, 19, 74, 95, 2, 3, 49, 76], [89, 62, 22, 7, 54, 81, 79, 62, 84, 34], [34, 89, 90, 67, 50, 14, 65, 10, 50, 63], [37, 62, 95, 20, 11, 31, 41, 38, 97, 9], [3, 42, 31, 11, 25, 74, 52, 44, 76, 45], [53, 99, 36, 84, 86, 18, 17, 83, 21, 69], [78, 79, 15, 30, 24, 4, 6, 70, 78, 24], [84, 18, 5, 6, 84, 53, 98, 51, 99, 98]]], 'objective': 21.0}","[[0, 2, 8], [1, 7, 6], [2, 3, 2], [3, 1, 1], [4, 8, 4], [5, 0, 3], [6, 5, 7], [7, 4, 9], [8, 9, 5], [9, 6, 0]]",21.0,"{'problem_type': 'AP3', 'n': 10, 'ids': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'costs': [{'i': 1, 'j': 1, 'k': 1, 'cost': 94}, {'i': 1, 'j': 1, 'k': 2, 'cost': 21}, {'i': 1, 'j': 1, 'k': 3, 'cost': 26}, {'i': 1, 'j': 1, 'k': 4, 'cost': 40}, {'i': 1, 'j': 1, 'k': 5, 'cost': 81}, {'i': 1, 'j': 1, 'k': 6, 'cost': 10}, {'i': 1, 'j': 1, 'k': 7, 'cost': 2}, {'i': 1, 'j': 1, 'k': 8, 'cost': 3}, {'i': 1, 'j': 1, 'k': 9, 'cost': 27}, {'i': 1, 'j': 1, 'k': 10, 'cost': 60}, {'i': 1, 'j': 2, 'k': 1, 'cost': 24}, {'i': 1, 'j': 2, 'k': 2, 'cost': 22}, {'i': 1, 'j': 2, 'k': 3, 'cost': 96}, {'i': 1, 'j': 2, 'k': 4, 'cost': 81}, {'i': 1, 'j': 2, 'k': 5, 'cost': 12}, {'i': 1, 'j': 2, 'k': 6, 'cost': 93}, {'i': 1, 'j': 2, 'k': 7, 'cost': 59}, {'i': 1, 'j': 2, 'k': 8, 'cost': 44}, {'i': 1, 'j': 2, 'k': 9, 'cost': 20}, {'i': 1, 'j': 2, 'k': 10, 'cost': 49}, {'i': 1, 'j': 3, 'k': 1, 'cost': 94}, {'i': 1, 'j': 3, 'k': 2, 'cost': 92}, {'i': 1, 'j': 3, 'k': 3, 'cost': 21}, {'i': 1, 'j': 3, 'k': 4, 'cost': 3}, {'i': 1, 'j': 3, 'k': 5, 'cost': 95}, {'i': 1, 'j': 3, 'k': 6, 'cost': 3}, {'i': 1, 'j': 3, 'k': 7, 'cost': 95}, {'i': 1, 'j': 3, 'k': 8, 'cost': 13}, {'i': 1, 'j': 3, 'k': 9, 'cost': 3}, {'i': 1, 'j': 3, 'k': 10, 'cost': 37}, {'i': 1, 'j': 4, 'k': 1, 'cost': 3}, {'i': 1, 'j': 4, 'k': 2, 'cost': 46}, {'i': 1, 'j': 4, 'k': 3, 'cost': 42}, {'i': 1, 'j': 4, 'k': 4, 'cost': 42}, {'i': 1, 'j': 4, 'k': 5, 'cost': 60}, {'i': 1, 'j': 4, 'k': 6, 'cost': 76}, {'i': 1, 'j': 4, 'k': 7, 'cost': 96}, {'i': 1, 'j': 4, 'k': 8, 'cost': 74}, {'i': 1, 'j': 4, 'k': 9, 'cost': 67}, {'i': 1, 'j': 4, 'k': 10, 'cost': 94}, {'i': 1, 'j': 5, 'k': 1, 'cost': 18}, {'i': 1, 'j': 5, 'k': 2, 'cost': 52}, {'i': 1, 'j': 5, 'k': 3, 'cost': 97}, {'i': 1, 'j': 5, 'k': 4, 'cost': 71}, {'i': 1, 'j': 5, 'k': 5, 'cost': 40}, {'i': 1, 'j': 5, 'k': 6, 'cost': 59}, {'i': 1, 'j': 5, 'k': 7, 'cost': 63}, {'i': 1, 'j': 5, 'k': 8, 'cost': 10}, {'i': 1, 'j': 5, 'k': 9, 'cost': 20}, {'i': 1, 'j': 5, 'k': 10, 'cost': 16}, {'i': 1, 'j': 6, 'k': 1, 'cost': 27}, {'i': 1, 'j': 6, 'k': 2, 'cost': 91}, {'i': 1, 'j': 6, 'k': 3, 'cost': 87}, {'i': 1, 'j': 6, 'k': 4, 'cost': 95}, {'i': 1, 'j': 6, 'k': 5, 'cost': 39}, {'i': 1, 'j': 6, 'k': 6, 'cost': 96}, {'i': 1, 'j': 6, 'k': 7, 'cost': 21}, {'i': 1, 'j': 6, 'k': 8, 'cost': 38}, {'i': 1, 'j': 6, 'k': 9, 'cost': 27}, {'i': 1, 'j': 6, 'k': 10, 'cost': 7}, {'i': 1, 'j': 7, 'k': 1, 'cost': 83}, {'i': 1, 'j': 7, 'k': 2, 'cost': 5}, {'i': 1, 'j': 7, 'k': 3, 'cost': 23}, {'i': 1, 'j': 7, 'k': 4, 'cost': 10}, {'i': 1, 'j': 7, 'k': 5, 'cost': 85}, {'i': 1, 'j': 7, 'k': 6, 'cost': 98}, {'i': 1, 'j': 7, 'k': 7, 'cost': 57}, {'i': 1, 'j': 7, 'k': 8, 'cost': 46}, {'i': 1, 'j': 7, 'k': 9, 'cost': 8}, {'i': 1, 'j': 7, 'k': 10, 'cost': 98}, {'i': 1, 'j': 8, 'k': 1, 'cost': 86}, {'i': 1, 'j': 8, 'k': 2, 'cost': 36}, {'i': 1, 'j': 8, 'k': 3, 'cost': 8}, {'i': 1, 'j': 8, 'k': 4, 'cost': 20}, {'i': 1, 'j': 8, 'k': 5, 'cost': 29}, {'i': 1, 'j': 8, 'k': 6, 'cost': 11}, {'i': 1, 'j': 8, 'k': 7, 'cost': 96}, {'i': 1, 'j': 8, 'k': 8, 'cost': 55}, {'i': 1, 'j': 8, 'k': 9, 'cost': 23}, {'i': 1, 'j': 8, 'k': 10, 'cost': 51}, {'i': 1, 'j': 9, 'k': 1, 'cost': 41}, {'i': 1, 'j': 9, 'k': 2, 'cost': 80}, {'i': 1, 'j': 9, 'k': 3, 'cost': 8}, {'i': 1, 'j': 9, 'k': 4, 'cost': 39}, {'i': 1, 'j': 9, 'k': 5, 'cost': 88}, {'i': 1, 'j': 9, 'k': 6, 'cost': 86}, {'i': 1, 'j': 9, 'k': 7, 'cost': 17}, {'i': 1, 'j': 9, 'k': 8, 'cost': 91}, {'i': 1, 'j': 9, 'k': 9, 'cost': 76}, {'i': 1, 'j': 9, 'k': 10, 'cost': 10}, {'i': 1, 'j': 10, 'k': 1, 'cost': 73}, {'i': 1, 'j': 10, 'k': 2, 'cost': 23}, {'i': 1, 'j': 10, 'k': 3, 'cost': 89}, {'i': 1, 'j': 10, 'k': 4, 'cost': 1}, {'i': 1, 'j': 10, 'k': 5, 'cost': 54}, {'i': 1, 'j': 10, 'k': 6, 'cost': 26}, {'i': 1, 'j': 10, 'k': 7, 'cost': 91}, {'i': 1, 'j': 10, 'k': 8, 'cost': 47}, {'i': 1, 'j': 10, 'k': 9, 'cost': 23}, {'i': 1, 'j': 10, 'k': 10, 'cost': 82}, {'i': 2, 'j': 1, 'k': 1, 'cost': 21}, {'i': 2, 'j': 1, 'k': 2, 'cost': 40}, {'i': 2, 'j': 1, 'k': 3, 'cost': 32}, {'i': 2, 'j': 1, 'k': 4, 'cost': 57}, {'i': 2, 'j': 1, 'k': 5, 'cost': 8}, {'i': 2, 'j': 1, 'k': 6, 'cost': 35}, {'i': 2, 'j': 1, 'k': 7, 'cost': 52}, {'i': 2, 'j': 1, 'k': 8, 'cost': 57}, {'i': 2, 'j': 1, 'k': 9, 'cost': 55}, {'i': 2, 'j': 1, 'k': 10, 'cost': 82}, {'i': 2, 'j': 2, 'k': 1, 'cost': 31}, {'i': 2, 'j': 2, 'k': 2, 'cost': 85}, {'i': 2, 'j': 2, 'k': 3, 'cost': 61}, {'i': 2, 'j': 2, 'k': 4, 'cost': 69}, {'i': 2, 'j': 2, 'k': 5, 'cost': 52}, {'i': 2, 'j': 2, 'k': 6, 'cost': 88}, {'i': 2, 'j': 2, 'k': 7, 'cost': 36}, {'i': 2, 'j': 2, 'k': 8, 'cost': 86}, {'i': 2, 'j': 2, 'k': 9, 'cost': 93}, {'i': 2, 'j': 2, 'k': 10, 'cost': 34}, {'i': 2, 'j': 3, 'k': 1, 'cost': 17}, {'i': 2, 'j': 3, 'k': 2, 'cost': 28}, {'i': 2, 'j': 3, 'k': 3, 'cost': 83}, {'i': 2, 'j': 3, 'k': 4, 'cost': 6}, {'i': 2, 'j': 3, 'k': 5, 'cost': 19}, {'i': 2, 'j': 3, 'k': 6, 'cost': 80}, {'i': 2, 'j': 3, 'k': 7, 'cost': 61}, {'i': 2, 'j': 3, 'k': 8, 'cost': 77}, {'i': 2, 'j': 3, 'k': 9, 'cost': 60}, {'i': 2, 'j': 3, 'k': 10, 'cost': 98}, {'i': 2, 'j': 4, 'k': 1, 'cost': 30}, {'i': 2, 'j': 4, 'k': 2, 'cost': 84}, {'i': 2, 'j': 4, 'k': 3, 'cost': 70}, {'i': 2, 'j': 4, 'k': 4, 'cost': 20}, {'i': 2, 'j': 4, 'k': 5, 'cost': 91}, {'i': 2, 'j': 4, 'k': 6, 'cost': 67}, {'i': 2, 'j': 4, 'k': 7, 'cost': 72}, {'i': 2, 'j': 4, 'k': 8, 'cost': 30}, {'i': 2, 'j': 4, 'k': 9, 'cost': 26}, {'i': 2, 'j': 4, 'k': 10, 'cost': 93}, {'i': 2, 'j': 5, 'k': 1, 'cost': 27}, {'i': 2, 'j': 5, 'k': 2, 'cost': 1}, {'i': 2, 'j': 5, 'k': 3, 'cost': 37}, {'i': 2, 'j': 5, 'k': 4, 'cost': 93}, {'i': 2, 'j': 5, 'k': 5, 'cost': 31}, {'i': 2, 'j': 5, 'k': 6, 'cost': 23}, {'i': 2, 'j': 5, 'k': 7, 'cost': 43}, {'i': 2, 'j': 5, 'k': 8, 'cost': 24}, {'i': 2, 'j': 5, 'k': 9, 'cost': 66}, {'i': 2, 'j': 5, 'k': 10, 'cost': 33}, {'i': 2, 'j': 6, 'k': 1, 'cost': 7}, {'i': 2, 'j': 6, 'k': 2, 'cost': 89}, {'i': 2, 'j': 6, 'k': 3, 'cost': 47}, {'i': 2, 'j': 6, 'k': 4, 'cost': 28}, {'i': 2, 'j': 6, 'k': 5, 'cost': 52}, {'i': 2, 'j': 6, 'k': 6, 'cost': 39}, {'i': 2, 'j': 6, 'k': 7, 'cost': 19}, {'i': 2, 'j': 6, 'k': 8, 'cost': 82}, {'i': 2, 'j': 6, 'k': 9, 'cost': 66}, {'i': 2, 'j': 6, 'k': 10, 'cost': 45}, {'i': 2, 'j': 7, 'k': 1, 'cost': 98}, {'i': 2, 'j': 7, 'k': 2, 'cost': 94}, {'i': 2, 'j': 7, 'k': 3, 'cost': 94}, {'i': 2, 'j': 7, 'k': 4, 'cost': 37}, {'i': 2, 'j': 7, 'k': 5, 'cost': 86}, {'i': 2, 'j': 7, 'k': 6, 'cost': 11}, {'i': 2, 'j': 7, 'k': 7, 'cost': 23}, {'i': 2, 'j': 7, 'k': 8, 'cost': 59}, {'i': 2, 'j': 7, 'k': 9, 'cost': 29}, {'i': 2, 'j': 7, 'k': 10, 'cost': 65}, {'i': 2, 'j': 8, 'k': 1, 'cost': 60}, {'i': 2, 'j': 8, 'k': 2, 'cost': 21}, {'i': 2, 'j': 8, 'k': 3, 'cost': 7}, {'i': 2, 'j': 8, 'k': 4, 'cost': 20}, {'i': 2, 'j': 8, 'k': 5, 'cost': 48}, {'i': 2, 'j': 8, 'k': 6, 'cost': 36}, {'i': 2, 'j': 8, 'k': 7, 'cost': 0}, {'i': 2, 'j': 8, 'k': 8, 'cost': 98}, {'i': 2, 'j': 8, 'k': 9, 'cost': 29}, {'i': 2, 'j': 8, 'k': 10, 'cost': 74}, {'i': 2, 'j': 9, 'k': 1, 'cost': 71}, {'i': 2, 'j': 9, 'k': 2, 'cost': 56}, {'i': 2, 'j': 9, 'k': 3, 'cost': 56}, {'i': 2, 'j': 9, 'k': 4, 'cost': 16}, {'i': 2, 'j': 9, 'k': 5, 'cost': 7}, {'i': 2, 'j': 9, 'k': 6, 'cost': 29}, {'i': 2, 'j': 9, 'k': 7, 'cost': 81}, {'i': 2, 'j': 9, 'k': 8, 'cost': 18}, {'i': 2, 'j': 9, 'k': 9, 'cost': 74}, {'i': 2, 'j': 9, 'k': 10, 'cost': 80}, {'i': 2, 'j': 10, 'k': 1, 'cost': 32}, {'i': 2, 'j': 10, 'k': 2, 'cost': 54}, {'i': 2, 'j': 10, 'k': 3, 'cost': 44}, {'i': 2, 'j': 10, 'k': 4, 'cost': 73}, {'i': 2, 'j': 10, 'k': 5, 'cost': 29}, {'i': 2, 'j': 10, 'k': 6, 'cost': 24}, {'i': 2, 'j': 10, 'k': 7, 'cost': 31}, {'i': 2, 'j': 10, 'k': 8, 'cost': 18}, {'i': 2, 'j': 10, 'k': 9, 'cost': 87}, {'i': 2, 'j': 10, 'k': 10, 'cost': 0}, {'i': 3, 'j': 1, 'k': 1, 'cost': 39}, {'i': 3, 'j': 1, 'k': 2, 'cost': 48}, {'i': 3, 'j': 1, 'k': 3, 'cost': 89}, {'i': 3, 'j': 1, 'k': 4, 'cost': 49}, {'i': 3, 'j': 1, 'k': 5, 'cost': 48}, {'i': 3, 'j': 1, 'k': 6, 'cost': 71}, {'i': 3, 'j': 1, 'k': 7, 'cost': 47}, {'i': 3, 'j': 1, 'k': 8, 'cost': 38}, {'i': 3, 'j': 1, 'k': 9, 'cost': 97}, {'i': 3, 'j': 1, 'k': 10, 'cost': 86}, {'i': 3, 'j': 2, 'k': 1, 'cost': 53}, {'i': 3, 'j': 2, 'k': 2, 'cost': 72}, {'i': 3, 'j': 2, 'k': 3, 'cost': 30}, {'i': 3, 'j': 2, 'k': 4, 'cost': 96}, {'i': 3, 'j': 2, 'k': 5, 'cost': 88}, {'i': 3, 'j': 2, 'k': 6, 'cost': 86}, {'i': 3, 'j': 2, 'k': 7, 'cost': 29}, {'i': 3, 'j': 2, 'k': 8, 'cost': 24}, {'i': 3, 'j': 2, 'k': 9, 'cost': 10}, {'i': 3, 'j': 2, 'k': 10, 'cost': 27}, {'i': 3, 'j': 3, 'k': 1, 'cost': 71}, {'i': 3, 'j': 3, 'k': 2, 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{'i': 10, 'j': 1, 'k': 4, 'cost': 31}, {'i': 10, 'j': 1, 'k': 5, 'cost': 45}, {'i': 10, 'j': 1, 'k': 6, 'cost': 8}, {'i': 10, 'j': 1, 'k': 7, 'cost': 28}, {'i': 10, 'j': 1, 'k': 8, 'cost': 38}, {'i': 10, 'j': 1, 'k': 9, 'cost': 46}, {'i': 10, 'j': 1, 'k': 10, 'cost': 30}, {'i': 10, 'j': 2, 'k': 1, 'cost': 60}, {'i': 10, 'j': 2, 'k': 2, 'cost': 33}, {'i': 10, 'j': 2, 'k': 3, 'cost': 85}, {'i': 10, 'j': 2, 'k': 4, 'cost': 46}, {'i': 10, 'j': 2, 'k': 5, 'cost': 55}, {'i': 10, 'j': 2, 'k': 6, 'cost': 99}, {'i': 10, 'j': 2, 'k': 7, 'cost': 57}, {'i': 10, 'j': 2, 'k': 8, 'cost': 5}, {'i': 10, 'j': 2, 'k': 9, 'cost': 74}, {'i': 10, 'j': 2, 'k': 10, 'cost': 57}, {'i': 10, 'j': 3, 'k': 1, 'cost': 1}, {'i': 10, 'j': 3, 'k': 2, 'cost': 16}, {'i': 10, 'j': 3, 'k': 3, 'cost': 76}, {'i': 10, 'j': 3, 'k': 4, 'cost': 19}, {'i': 10, 'j': 3, 'k': 5, 'cost': 74}, {'i': 10, 'j': 3, 'k': 6, 'cost': 95}, {'i': 10, 'j': 3, 'k': 7, 'cost': 2}, {'i': 10, 'j': 3, 'k': 8, 'cost': 3}, {'i': 10, 'j': 3, 'k': 9, 'cost': 49}, {'i': 10, 'j': 3, 'k': 10, 'cost': 76}, {'i': 10, 'j': 4, 'k': 1, 'cost': 89}, {'i': 10, 'j': 4, 'k': 2, 'cost': 62}, {'i': 10, 'j': 4, 'k': 3, 'cost': 22}, {'i': 10, 'j': 4, 'k': 4, 'cost': 7}, {'i': 10, 'j': 4, 'k': 5, 'cost': 54}, {'i': 10, 'j': 4, 'k': 6, 'cost': 81}, {'i': 10, 'j': 4, 'k': 7, 'cost': 79}, {'i': 10, 'j': 4, 'k': 8, 'cost': 62}, {'i': 10, 'j': 4, 'k': 9, 'cost': 84}, {'i': 10, 'j': 4, 'k': 10, 'cost': 34}, {'i': 10, 'j': 5, 'k': 1, 'cost': 34}, {'i': 10, 'j': 5, 'k': 2, 'cost': 89}, {'i': 10, 'j': 5, 'k': 3, 'cost': 90}, {'i': 10, 'j': 5, 'k': 4, 'cost': 67}, {'i': 10, 'j': 5, 'k': 5, 'cost': 50}, {'i': 10, 'j': 5, 'k': 6, 'cost': 14}, {'i': 10, 'j': 5, 'k': 7, 'cost': 65}, {'i': 10, 'j': 5, 'k': 8, 'cost': 10}, {'i': 10, 'j': 5, 'k': 9, 'cost': 50}, {'i': 10, 'j': 5, 'k': 10, 'cost': 63}, {'i': 10, 'j': 6, 'k': 1, 'cost': 37}, {'i': 10, 'j': 6, 'k': 2, 'cost': 62}, {'i': 10, 'j': 6, 'k': 3, 'cost': 95}, {'i': 10, 'j': 6, 'k': 4, 'cost': 20}, {'i': 10, 'j': 6, 'k': 5, 'cost': 11}, {'i': 10, 'j': 6, 'k': 6, 'cost': 31}, {'i': 10, 'j': 6, 'k': 7, 'cost': 41}, {'i': 10, 'j': 6, 'k': 8, 'cost': 38}, {'i': 10, 'j': 6, 'k': 9, 'cost': 97}, {'i': 10, 'j': 6, 'k': 10, 'cost': 9}, {'i': 10, 'j': 7, 'k': 1, 'cost': 3}, {'i': 10, 'j': 7, 'k': 2, 'cost': 42}, {'i': 10, 'j': 7, 'k': 3, 'cost': 31}, {'i': 10, 'j': 7, 'k': 4, 'cost': 11}, {'i': 10, 'j': 7, 'k': 5, 'cost': 25}, {'i': 10, 'j': 7, 'k': 6, 'cost': 74}, {'i': 10, 'j': 7, 'k': 7, 'cost': 52}, {'i': 10, 'j': 7, 'k': 8, 'cost': 44}, {'i': 10, 'j': 7, 'k': 9, 'cost': 76}, {'i': 10, 'j': 7, 'k': 10, 'cost': 45}, {'i': 10, 'j': 8, 'k': 1, 'cost': 53}, {'i': 10, 'j': 8, 'k': 2, 'cost': 99}, {'i': 10, 'j': 8, 'k': 3, 'cost': 36}, {'i': 10, 'j': 8, 'k': 4, 'cost': 84}, {'i': 10, 'j': 8, 'k': 5, 'cost': 86}, {'i': 10, 'j': 8, 'k': 6, 'cost': 18}, {'i': 10, 'j': 8, 'k': 7, 'cost': 17}, {'i': 10, 'j': 8, 'k': 8, 'cost': 83}, {'i': 10, 'j': 8, 'k': 9, 'cost': 21}, {'i': 10, 'j': 8, 'k': 10, 'cost': 69}, {'i': 10, 'j': 9, 'k': 1, 'cost': 78}, {'i': 10, 'j': 9, 'k': 2, 'cost': 79}, {'i': 10, 'j': 9, 'k': 3, 'cost': 15}, {'i': 10, 'j': 9, 'k': 4, 'cost': 30}, {'i': 10, 'j': 9, 'k': 5, 'cost': 24}, {'i': 10, 'j': 9, 'k': 6, 'cost': 4}, {'i': 10, 'j': 9, 'k': 7, 'cost': 6}, {'i': 10, 'j': 9, 'k': 8, 'cost': 70}, {'i': 10, 'j': 9, 'k': 9, 'cost': 78}, {'i': 10, 'j': 9, 'k': 10, 'cost': 24}, {'i': 10, 'j': 10, 'k': 1, 'cost': 84}, {'i': 10, 'j': 10, 'k': 2, 'cost': 18}, {'i': 10, 'j': 10, 'k': 3, 'cost': 5}, {'i': 10, 'j': 10, 'k': 4, 'cost': 6}, {'i': 10, 'j': 10, 'k': 5, 'cost': 84}, {'i': 10, 'j': 10, 'k': 6, 'cost': 53}, {'i': 10, 'j': 10, 'k': 7, 'cost': 98}, {'i': 10, 'j': 10, 'k': 8, 'cost': 51}, {'i': 10, 'j': 10, 'k': 9, 'cost': 99}, {'i': 10, 'j': 10, 'k': 10, 'cost': 98}]}","[[1, 3, 9], [2, 8, 7], [3, 4, 3], [4, 2, 2], [5, 9, 5], [6, 1, 4], [7, 6, 8], [8, 5, 10], [9, 10, 6], [10, 7, 1]]",49,markdown_table,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.
+
+There are 10 reading sessions, storytellers, and seating layouts labeled 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
+
+*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=0
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 24 | 78 | 37 | 41 | 95 | 55 | 49 | 1 | 19 | 72 |
+| 1 | 91 | 72 | 53 | 77 | 40 | 21 | 32 | 22 | 37 | 42 |
+| 2 | 74 | 24 | 56 | 8 | 28 | 12 | 49 | 51 | 90 | 78 |
+| 3 | 87 | 77 | 23 | 8 | 81 | 55 | 81 | 24 | 7 | 80 |
+| 4 | 80 | 76 | 22 | 89 | 86 | 85 | 79 | 94 | 34 | 33 |
+| 5 | 25 | 90 | 43 | 95 | 35 | 4 | 24 | 69 | 30 | 5 |
+| 6 | 28 | 73 | 83 | 81 | 62 | 73 | 2 | 94 | 75 | 35 |
+| 7 | 65 | 85 | 42 | 72 | 75 | 80 | 77 | 75 | 47 | 70 |
+| 8 | 8 | 96 | 34 | 91 | 62 | 64 | 61 | 23 | 55 | 20 |
+| 9 | 84 | 82 | 89 | 35 | 33 | 60 | 91 | 16 | 29 | 6 |
+
+## session_id=1
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 18 | 70 | 23 | 89 | 30 | 6 | 5 | 74 | 15 | 9 |
+| 1 | 28 | 75 | 96 | 73 | 82 | 79 | 25 | 67 | 61 | 0 |
+| 2 | 1 | 51 | 22 | 5 | 1 | 29 | 42 | 60 | 70 | 68 |
+| 3 | 51 | 13 | 47 | 3 | 68 | 8 | 96 | 35 | 10 | 42 |
+| 4 | 62 | 17 | 82 | 80 | 72 | 7 | 33 | 30 | 37 | 85 |
+| 5 | 74 | 7 | 30 | 40 | 52 | 52 | 5 | 56 | 18 | 21 |
+| 6 | 5 | 60 | 45 | 89 | 23 | 38 | 63 | 50 | 66 | 46 |
+| 7 | 80 | 88 | 56 | 61 | 75 | 76 | 33 | 50 | 57 | 67 |
+| 8 | 22 | 8 | 46 | 73 | 93 | 96 | 2 | 47 | 64 | 26 |
+| 9 | 96 | 0 | 82 | 84 | 19 | 83 | 39 | 90 | 40 | 75 |
+
+## session_id=2
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 16 | 82 | 68 | 10 | 26 | 93 | 22 | 16 | 2 | 46 |
+| 1 | 98 | 84 | 28 | 31 | 30 | 94 | 24 | 3 | 77 | 73 |
+| 2 | 15 | 66 | 32 | 12 | 24 | 94 | 57 | 28 | 10 | 57 |
+| 3 | 41 | 14 | 40 | 96 | 4 | 45 | 95 | 76 | 17 | 19 |
+| 4 | 29 | 78 | 72 | 62 | 42 | 97 | 18 | 98 | 43 | 56 |
+| 5 | 15 | 72 | 22 | 75 | 55 | 61 | 6 | 22 | 65 | 7 |
+| 6 | 82 | 31 | 75 | 29 | 11 | 28 | 36 | 61 | 16 | 47 |
+| 7 | 69 | 34 | 72 | 10 | 6 | 59 | 0 | 44 | 26 | 68 |
+| 8 | 95 | 15 | 66 | 58 | 68 | 35 | 80 | 55 | 51 | 20 |
+| 9 | 61 | 99 | 45 | 39 | 65 | 41 | 97 | 4 | 45 | 66 |
+
+## session_id=3
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 99 | 29 | 29 | 14 | 99 | 8 | 50 | 50 | 64 | 70 |
+| 1 | 44 | 50 | 61 | 19 | 16 | 71 | 91 | 9 | 46 | 72 |
+| 2 | 64 | 67 | 28 | 94 | 14 | 90 | 77 | 80 | 25 | 1 |
+| 3 | 45 | 50 | 22 | 46 | 30 | 60 | 23 | 63 | 87 | 24 |
+| 4 | 33 | 93 | 51 | 65 | 24 | 56 | 12 | 93 | 25 | 21 |
+| 5 | 74 | 4 | 4 | 3 | 3 | 28 | 41 | 27 | 14 | 35 |
+| 6 | 92 | 64 | 21 | 19 | 8 | 19 | 83 | 22 | 56 | 69 |
+| 7 | 53 | 25 | 77 | 21 | 78 | 70 | 16 | 23 | 73 | 29 |
+| 8 | 69 | 53 | 60 | 73 | 41 | 8 | 96 | 34 | 44 | 74 |
+| 9 | 77 | 58 | 78 | 3 | 77 | 79 | 31 | 19 | 90 | 59 |
+
+## session_id=4
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 34 | 95 | 52 | 33 | 41 | 57 | 95 | 28 | 56 | 4 |
+| 1 | 88 | 23 | 90 | 43 | 48 | 70 | 96 | 28 | 80 | 95 |
+| 2 | 77 | 93 | 14 | 56 | 87 | 90 | 83 | 36 | 95 | 25 |
+| 3 | 48 | 1 | 8 | 29 | 49 | 47 | 15 | 85 | 83 | 61 |
+| 4 | 19 | 87 | 24 | 42 | 88 | 24 | 78 | 55 | 77 | 55 |
+| 5 | 65 | 79 | 23 | 22 | 86 | 21 | 84 | 37 | 95 | 66 |
+| 6 | 21 | 49 | 34 | 79 | 49 | 8 | 78 | 85 | 84 | 9 |
+| 7 | 2 | 59 | 5 | 54 | 95 | 70 | 35 | 44 | 19 | 79 |
+| 8 | 11 | 44 | 70 | 35 | 88 | 32 | 40 | 65 | 10 | 51 |
+| 9 | 48 | 65 | 69 | 45 | 19 | 14 | 12 | 28 | 19 | 43 |
+
+## session_id=5
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 93 | 85 | 3 | 51 | 70 | 13 | 43 | 45 | 72 | 38 |
+| 1 | 31 | 8 | 74 | 78 | 83 | 58 | 59 | 89 | 27 | 61 |
+| 2 | 43 | 0 | 70 | 1 | 50 | 82 | 85 | 58 | 40 | 6 |
+| 3 | 39 | 1 | 17 | 58 | 43 | 10 | 49 | 40 | 70 | 89 |
+| 4 | 50 | 30 | 94 | 19 | 70 | 62 | 86 | 49 | 7 | 92 |
+| 5 | 39 | 33 | 43 | 14 | 85 | 10 | 16 | 93 | 24 | 76 |
+| 6 | 23 | 5 | 65 | 65 | 68 | 9 | 97 | 10 | 75 | 61 |
+| 7 | 27 | 14 | 74 | 87 | 39 | 92 | 11 | 19 | 68 | 95 |
+| 8 | 76 | 30 | 41 | 43 | 36 | 42 | 27 | 76 | 86 | 58 |
+| 9 | 24 | 67 | 74 | 61 | 64 | 50 | 16 | 19 | 74 | 58 |
+
+## session_id=6
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 21 | 69 | 45 | 83 | 50 | 56 | 9 | 24 | 77 | 67 |
+| 1 | 98 | 99 | 47 | 27 | 89 | 86 | 36 | 96 | 58 | 15 |
+| 2 | 11 | 20 | 24 | 18 | 99 | 36 | 73 | 34 | 52 | 41 |
+| 3 | 17 | 35 | 17 | 27 | 70 | 13 | 42 | 32 | 6 | 42 |
+| 4 | 48 | 73 | 66 | 85 | 30 | 59 | 31 | 98 | 85 | 56 |
+| 5 | 68 | 44 | 25 | 22 | 81 | 34 | 65 | 41 | 25 | 53 |
+| 6 | 12 | 41 | 19 | 80 | 69 | 81 | 23 | 70 | 25 | 1 |
+| 7 | 69 | 54 | 52 | 24 | 80 | 86 | 22 | 11 | 81 | 99 |
+| 8 | 22 | 57 | 71 | 15 | 70 | 43 | 92 | 69 | 58 | 41 |
+| 9 | 10 | 91 | 53 | 97 | 3 | 48 | 27 | 88 | 57 | 88 |
+
+## session_id=7
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 49 | 97 | 6 | 82 | 3 | 84 | 33 | 14 | 86 | 2 |
+| 1 | 50 | 96 | 26 | 73 | 74 | 75 | 8 | 19 | 75 | 89 |
+| 2 | 84 | 44 | 12 | 52 | 13 | 23 | 67 | 83 | 78 | 60 |
+| 3 | 39 | 60 | 18 | 43 | 64 | 5 | 85 | 93 | 5 | 59 |
+| 4 | 60 | 37 | 12 | 14 | 28 | 13 | 18 | 1 | 58 | 52 |
+| 5 | 29 | 74 | 55 | 77 | 7 | 20 | 11 | 14 | 36 | 49 |
+| 6 | 83 | 38 | 1 | 65 | 28 | 30 | 32 | 75 | 40 | 89 |
+| 7 | 31 | 52 | 69 | 12 | 3 | 49 | 72 | 39 | 73 | 57 |
+| 8 | 59 | 81 | 9 | 67 | 15 | 34 | 30 | 23 | 34 | 86 |
+| 9 | 68 | 40 | 28 | 20 | 79 | 76 | 85 | 37 | 81 | 82 |
+
+## session_id=8
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 98 | 92 | 9 | 60 | 44 | 72 | 25 | 31 | 48 | 25 |
+| 1 | 30 | 81 | 54 | 11 | 99 | 92 | 96 | 20 | 60 | 50 |
+| 2 | 72 | 42 | 15 | 93 | 75 | 90 | 63 | 63 | 83 | 16 |
+| 3 | 28 | 8 | 38 | 79 | 78 | 21 | 48 | 12 | 75 | 41 |
+| 4 | 27 | 34 | 73 | 87 | 66 | 58 | 40 | 50 | 97 | 62 |
+| 5 | 43 | 7 | 89 | 4 | 78 | 66 | 6 | 49 | 97 | 80 |
+| 6 | 10 | 87 | 72 | 19 | 25 | 6 | 94 | 46 | 23 | 28 |
+| 7 | 82 | 32 | 62 | 43 | 43 | 71 | 85 | 41 | 34 | 31 |
+| 8 | 95 | 15 | 54 | 0 | 39 | 69 | 37 | 97 | 85 | 53 |
+| 9 | 5 | 66 | 56 | 39 | 27 | 11 | 1 | 4 | 97 | 7 |
+
+## session_id=9
+| storyteller_id\seating_layout_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+|---|---|---|---|---|---|---|---|---|---|---|
+| 0 | 47 | 52 | 52 | 36 | 36 | 81 | 36 | 14 | 28 | 18 |
+| 1 | 71 | 49 | 38 | 41 | 45 | 39 | 94 | 6 | 90 | 29 |
+| 2 | 86 | 51 | 41 | 60 | 9 | 49 | 40 | 52 | 49 | 95 |
+| 3 | 75 | 94 | 34 | 80 | 21 | 82 | 62 | 14 | 22 | 80 |
+| 4 | 18 | 52 | 71 | 84 | 98 | 56 | 74 | 72 | 5 | 47 |
+| 5 | 85 | 33 | 5 | 44 | 74 | 52 | 43 | 89 | 30 | 36 |
+| 6 | 44 | 84 | 66 | 34 | 19 | 11 | 0 | 61 | 83 | 57 |
+| 7 | 37 | 70 | 59 | 24 | 66 | 40 | 63 | 18 | 43 | 16 |
+| 8 | 11 | 48 | 56 | 87 | 47 | 92 | 53 | 37 | 48 | 17 |
+| 9 | 83 | 2 | 23 | 31 | 44 | 67 | 15 | 15 | 88 | 16 |
+
+I will pick one triple per session to minimize the total cost.
+
+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': [[[24, 78, 37, 41, 95, 55, 49, 1, 19, 72], [91, 72, 53, 77, 40, 21, 32, 22, 37, 42], [74, 24, 56, 8, 28, 12, 49, 51, 90, 78], [87, 77, 23, 8, 81, 55, 81, 24, 7, 80], [80, 76, 22, 89, 86, 85, 79, 94, 34, 33], [25, 90, 43, 95, 35, 4, 24, 69, 30, 5], [28, 73, 83, 81, 62, 73, 2, 94, 75, 35], [65, 85, 42, 72, 75, 80, 77, 75, 47, 70], [8, 96, 34, 91, 62, 64, 61, 23, 55, 20], [84, 82, 89, 35, 33, 60, 91, 16, 29, 6]], [[18, 70, 23, 89, 30, 6, 5, 74, 15, 9], [28, 75, 96, 73, 82, 79, 25, 67, 61, 0], [1, 51, 22, 5, 1, 29, 42, 60, 70, 68], [51, 13, 47, 3, 68, 8, 96, 35, 10, 42], [62, 17, 82, 80, 72, 7, 33, 30, 37, 85], [74, 7, 30, 40, 52, 52, 5, 56, 18, 21], [5, 60, 45, 89, 23, 38, 63, 50, 66, 46], [80, 88, 56, 61, 75, 76, 33, 50, 57, 67], [22, 8, 46, 73, 93, 96, 2, 47, 64, 26], [96, 0, 82, 84, 19, 83, 39, 90, 40, 75]], [[16, 82, 68, 10, 26, 93, 22, 16, 2, 46], [98, 84, 28, 31, 30, 94, 24, 3, 77, 73], [15, 66, 32, 12, 24, 94, 57, 28, 10, 57], [41, 14, 40, 96, 4, 45, 95, 76, 17, 19], [29, 78, 72, 62, 42, 97, 18, 98, 43, 56], [15, 72, 22, 75, 55, 61, 6, 22, 65, 7], [82, 31, 75, 29, 11, 28, 36, 61, 16, 47], [69, 34, 72, 10, 6, 59, 0, 44, 26, 68], [95, 15, 66, 58, 68, 35, 80, 55, 51, 20], [61, 99, 45, 39, 65, 41, 97, 4, 45, 66]], [[99, 29, 29, 14, 99, 8, 50, 50, 64, 70], [44, 50, 61, 19, 16, 71, 91, 9, 46, 72], [64, 67, 28, 94, 14, 90, 77, 80, 25, 1], [45, 50, 22, 46, 30, 60, 23, 63, 87, 24], [33, 93, 51, 65, 24, 56, 12, 93, 25, 21], [74, 4, 4, 3, 3, 28, 41, 27, 14, 35], [92, 64, 21, 19, 8, 19, 83, 22, 56, 69], [53, 25, 77, 21, 78, 70, 16, 23, 73, 29], [69, 53, 60, 73, 41, 8, 96, 34, 44, 74], [77, 58, 78, 3, 77, 79, 31, 19, 90, 59]], [[34, 95, 52, 33, 41, 57, 95, 28, 56, 4], [88, 23, 90, 43, 48, 70, 96, 28, 80, 95], [77, 93, 14, 56, 87, 90, 83, 36, 95, 25], [48, 1, 8, 29, 49, 47, 15, 85, 83, 61], [19, 87, 24, 42, 88, 24, 78, 55, 77, 55], [65, 79, 23, 22, 86, 21, 84, 37, 95, 66], [21, 49, 34, 79, 49, 8, 78, 85, 84, 9], [2, 59, 5, 54, 95, 70, 35, 44, 19, 79], [11, 44, 70, 35, 88, 32, 40, 65, 10, 51], [48, 65, 69, 45, 19, 14, 12, 28, 19, 43]], [[93, 85, 3, 51, 70, 13, 43, 45, 72, 38], [31, 8, 74, 78, 83, 58, 59, 89, 27, 61], [43, 0, 70, 1, 50, 82, 85, 58, 40, 6], [39, 1, 17, 58, 43, 10, 49, 40, 70, 89], [50, 30, 94, 19, 70, 62, 86, 49, 7, 92], [39, 33, 43, 14, 85, 10, 16, 93, 24, 76], [23, 5, 65, 65, 68, 9, 97, 10, 75, 61], [27, 14, 74, 87, 39, 92, 11, 19, 68, 95], [76, 30, 41, 43, 36, 42, 27, 76, 86, 58], [24, 67, 74, 61, 64, 50, 16, 19, 74, 58]], [[21, 69, 45, 83, 50, 56, 9, 24, 77, 67], [98, 99, 47, 27, 89, 86, 36, 96, 58, 15], [11, 20, 24, 18, 99, 36, 73, 34, 52, 41], [17, 35, 17, 27, 70, 13, 42, 32, 6, 42], [48, 73, 66, 85, 30, 59, 31, 98, 85, 56], [68, 44, 25, 22, 81, 34, 65, 41, 25, 53], [12, 41, 19, 80, 69, 81, 23, 70, 25, 1], [69, 54, 52, 24, 80, 86, 22, 11, 81, 99], [22, 57, 71, 15, 70, 43, 92, 69, 58, 41], [10, 91, 53, 97, 3, 48, 27, 88, 57, 88]], [[49, 97, 6, 82, 3, 84, 33, 14, 86, 2], [50, 96, 26, 73, 74, 75, 8, 19, 75, 89], [84, 44, 12, 52, 13, 23, 67, 83, 78, 60], [39, 60, 18, 43, 64, 5, 85, 93, 5, 59], [60, 37, 12, 14, 28, 13, 18, 1, 58, 52], [29, 74, 55, 77, 7, 20, 11, 14, 36, 49], [83, 38, 1, 65, 28, 30, 32, 75, 40, 89], [31, 52, 69, 12, 3, 49, 72, 39, 73, 57], [59, 81, 9, 67, 15, 34, 30, 23, 34, 86], [68, 40, 28, 20, 79, 76, 85, 37, 81, 82]], [[98, 92, 9, 60, 44, 72, 25, 31, 48, 25], [30, 81, 54, 11, 99, 92, 96, 20, 60, 50], [72, 42, 15, 93, 75, 90, 63, 63, 83, 16], [28, 8, 38, 79, 78, 21, 48, 12, 75, 41], [27, 34, 73, 87, 66, 58, 40, 50, 97, 62], [43, 7, 89, 4, 78, 66, 6, 49, 97, 80], [10, 87, 72, 19, 25, 6, 94, 46, 23, 28], [82, 32, 62, 43, 43, 71, 85, 41, 34, 31], [95, 15, 54, 0, 39, 69, 37, 97, 85, 53], [5, 66, 56, 39, 27, 11, 1, 4, 97, 7]], [[47, 52, 52, 36, 36, 81, 36, 14, 28, 18], [71, 49, 38, 41, 45, 39, 94, 6, 90, 29], [86, 51, 41, 60, 9, 49, 40, 52, 49, 95], [75, 94, 34, 80, 21, 82, 62, 14, 22, 80], [18, 52, 71, 84, 98, 56, 74, 72, 5, 47], [85, 33, 5, 44, 74, 52, 43, 89, 30, 36], [44, 84, 66, 34, 19, 11, 0, 61, 83, 57], [37, 70, 59, 24, 66, 40, 63, 18, 43, 16], [11, 48, 56, 87, 47, 92, 53, 37, 48, 17], [83, 2, 23, 31, 44, 67, 15, 15, 88, 16]]], 'objective': 25.0}","[[0, 5, 5], [1, 0, 6], [2, 1, 7], [3, 2, 9], [4, 7, 0], [5, 3, 1], [6, 9, 4], [7, 6, 2], [8, 8, 3], [9, 4, 8]]",25.0,"{'problem_type': 'AP3', 'n': 10, 'ids': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'costs': [{'i': 0, 'j': 0, 'k': 0, 'cost': 24}, {'i': 0, 'j': 0, 'k': 1, 'cost': 78}, {'i': 0, 'j': 0, 'k': 2, 'cost': 37}, {'i': 0, 'j': 0, 'k': 3, 'cost': 41}, {'i': 0, 'j': 0, 'k': 4, 'cost': 95}, {'i': 0, 'j': 0, 'k': 5, 'cost': 55}, {'i': 0, 'j': 0, 'k': 6, 'cost': 49}, {'i': 0, 'j': 0, 'k': 7, 'cost': 1}, {'i': 0, 'j': 0, 'k': 8, 'cost': 19}, {'i': 0, 'j': 0, 'k': 9, 'cost': 72}, {'i': 0, 'j': 1, 'k': 0, 'cost': 91}, {'i': 0, 'j': 1, 'k': 1, 'cost': 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