p= 0.1 num clusters= 2
linkage completed in  10.774961948394775
silhouette_score of the clusters 0.006287393358176328
sampled assortment [56, 82, 63, 84, 41, 23]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 16: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 16]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 14, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 100: 0} [1, 2, 3, 4, 5, 6, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 14, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 14, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 10, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 9]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 10, 11, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 20: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5, 20]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 82
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 41
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 23
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 56
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 41
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 41
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 63
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 82
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 23
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 23
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 82
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 82
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 41
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 84
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 0
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 63
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 23
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 63
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 84
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 63
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 0
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 0
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 41
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 41
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 82
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 0
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 23
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 23
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 84
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 41
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 41
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 84
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 41
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 41
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 0
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 23
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 63
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 84
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 41
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 23
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 84
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 23
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 84
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 56
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 41
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 84
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 0
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 41
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 56
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 82
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 41
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 23
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 23
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 41
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 23
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 23
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 84
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 23
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 82
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 56
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 23
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 23
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 63
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 63
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 41
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 56
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 41
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 82
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 84
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 23
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 84
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 82
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 23
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 84
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 41
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 41
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 41
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 23
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 23
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 23
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 23
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 0
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 23
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 82
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 23
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 56
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 41
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 82
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 56
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 63
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 23
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 84
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 23
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 23
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 82
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 23
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 56
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 41
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 23
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 84
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 84
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 63
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 41
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 63
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 82
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 84
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 84
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 63
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 23
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 56
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 41
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 84
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 56
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 63
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 84
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 82
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 23
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 41
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 23
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 23
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 82
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 41
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 23
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 41
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 23
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 41
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 82
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 82
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 56
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 56
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 41
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 84
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 56
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 63
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 41
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 23
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 41
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 23
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 82
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 82
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 63
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 23
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 63
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 0
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 0
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 82
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 41
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 82
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 0
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 41
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 41
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 23
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 41
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 0
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 82
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 41
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 63
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 23
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 63
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 23
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 23
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 23
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 63
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 23
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 63
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 23
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 82
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 23
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 82
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 82
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 56
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 63
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 82
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 82
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 63
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 23
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 23
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 23
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 41
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 23
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 41
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 23
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 41
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 84
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 82
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 84
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 82
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 63
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 23
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 41
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 56
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 23
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 41
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 23
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 56
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 63
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 63
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 63
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 41
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 82
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 23
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 63
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 41
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 23
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 23
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 56
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 63
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 63
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 84
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 56
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 23
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 56
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 0
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 82
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 23
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 82
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 56
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 63
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 41
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 0
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 82
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 63
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 23
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 84
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 63
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 23
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 0
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 82
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 63
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 56
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 41
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 84
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 41
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 56
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 63
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 41
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 84
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 56
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 0
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 56
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 56
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 84
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 56
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 63
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 23
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 23
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 82
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 84
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 41
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 63
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 84
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 63
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 0
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 63
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 84
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 84
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 41
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 23
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 56
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 63
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 0
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 84
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 82
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 0
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 82
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 63
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 41
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 82
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 56
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 23
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 84
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 63
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 84
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 41
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 63
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 82
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 82
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 23
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 41
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 0
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 41
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 41
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 23
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 84
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 23
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 0
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 23
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 23
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 41
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 84
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 63
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 63
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 82
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 23
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 56
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 82
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 23
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 84
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 84
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 41
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 82
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 56
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 84
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 82
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 63
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 41
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 84
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 23
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 41
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 56
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 82
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 63
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 0
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 41
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 41
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 63
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 82
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 82
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 56
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 84
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 56
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 63
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 63
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 82
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 23
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 23
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 84
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 23
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 23
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 23
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 0
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 23
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 23
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 84
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 84
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 63
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 84
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 41
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 56
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 0
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 63
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 0
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 56
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 41
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 56
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 82
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 23
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 23
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 84
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 41
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 41
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 84
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 23
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 82
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 0
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 23
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 84
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 63
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 41
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 23
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 41
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 56
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 56
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 41
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 63
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 41
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 23
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 82
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 56
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 23
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 56
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 82
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 82
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 23
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 41
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 56
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 84
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 41
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 41
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 41
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 0
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 41
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 41
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 23
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 23
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 41
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 23
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 23
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 84
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 23
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 56
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 82
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 0
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 23
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 82
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 41
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 63
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 23
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 82
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 56
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 23
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 82
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 0
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 41
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 63
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 56
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 63
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 23
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 0
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 23
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 84
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 82
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 56
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 84
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 84
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 0
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 63
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 0
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 84
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 63
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 23
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 0
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 23
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 63
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 82
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 82
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 41
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 23
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 41
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 84
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 0
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 63
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 23
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 63
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 23
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 63
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 0
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 0
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 84
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 82
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 23
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 23
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 41
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 23
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 23
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 0
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 63
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 82
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 23
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 41
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 56
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 82
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 23
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 41
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 23
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 84
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 41
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 63
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 41
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 84
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 56
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 56
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 56
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 23
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 41
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 23
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 23
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 84
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 41
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 41
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 63
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 63
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 82
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 56
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 23
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 23
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 56
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 56
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 84
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 84
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 84
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 23
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 41
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 0
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 41
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 0
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 56
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 56
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 41
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 63
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 56
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 56
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 23
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 41
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 63
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 82
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 63
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 56
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 23
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 63
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 63
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 56
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 23
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 82
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 63
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 56
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 84
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 23
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 82
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 41
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 84
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 23
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 41
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 23
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 41
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 23
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 41
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 23
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 56
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 23
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 82
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 41
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 23
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 23
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 41
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 41
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 41
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 56
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 56
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 41
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 63
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 63
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 63
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 82
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 63
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 23
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 63
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 0
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 84
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 41
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 63
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 84
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 41
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 63
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 56
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 23
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 41
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 41
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 41
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 0
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 41
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 23
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 0
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 63
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 63
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 56
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 41
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 41
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 41
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 56
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 23
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 63
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 0
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 56
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 41
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 23
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 23
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 63
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 41
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 84
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 56
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 63
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 23
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 84
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 0
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 82
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 56
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 23
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 41
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 82
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 84
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 41
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 41
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 23
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 0
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 41
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 82
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 0
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 63
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 56
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 41
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 56
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 84
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 84
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 56
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 84
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 23
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 23
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 23
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 23
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 63
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 84
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 23
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 23
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 23
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 63
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 41
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 63
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 84
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 23
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 41
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 23
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 82
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 84
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 23
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 0
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 56
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 82
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 23
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 41
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 82
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 23
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 41
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 56
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 56
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 23
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 63
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 63
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 23
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 0
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 56
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 82
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 82
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 23
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 0
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 23
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 56
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 41
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 41
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 56
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 56
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 56
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 63
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 41
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 56
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 23
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 63
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 84
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 63
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 84
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 63
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 63
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 23
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 82
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 56
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 23
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 84
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 84
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 0
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 56
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 63
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 41
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 63
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 56
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 63
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 56
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 63
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 63
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 23
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 84
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 23
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 56
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 41
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 23
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 63
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 0
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 56
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 23
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 41
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 23
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 41
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 0
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 56
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 41
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 84
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 23
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 23
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 41
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 0
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 82
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 41
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 23
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 56
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 82
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 56
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 41
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 63
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 23
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 0
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 63
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 63
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 84
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 23
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 56
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 23
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 23
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 23
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 84
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 84
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 0
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 41
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 56
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 23
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 41
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 41
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 63
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 82
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 23
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 23
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 41
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 41
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 0
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 23
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 56
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 82
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 84
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 23
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 23
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 23
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 41
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 23
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 23
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 0
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 23
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 23
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 0
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 63
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 84
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 63
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 23
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 63
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 23
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 41
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 41
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 84
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 82
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 23
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 56
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 82
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 82
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 23
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 63
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 23
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 82
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 0
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 0
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 56
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 84
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 84
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 63
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 84
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 0
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 63
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 41
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 23
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 84
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 23
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 41
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 82
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 82
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 23
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 23
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 56
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 82
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 0
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 84
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 84
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 82
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 82
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 41
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 84
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 23
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 84
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 23
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 0
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 23
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 23
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 63
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 56
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 82
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 23
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 41
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 41
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 23
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 23
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 84
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 56
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 23
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 0
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 84
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 56
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 23
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 23
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 23
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 41
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 23
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 41
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 23
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 23
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 23
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 82
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 63
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 41
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 56
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 0
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 23
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 41
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 63
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 63
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 84
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 56
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 82
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 82
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 84
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 23
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 23
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 0
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 23
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 23
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 23
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 23
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 82
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 0
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 63
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 82
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 23
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 63
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 82
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 0
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 56
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 56
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 56
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 63
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 84
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 82
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 82
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 0
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 63
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 0
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 23
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 63
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 63
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 63
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 23
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 84
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 84
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 23
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 63
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 63
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 82
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 41
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 41
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 23
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 63
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 63
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 56
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 63
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 0
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 23
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 23
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 84
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 82
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 84
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 23
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 63
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 0
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 84
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 23
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 23
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 23
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 23
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 56
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 41
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 23
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 82
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 41
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 23
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 23
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 82
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 23
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 0
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 63
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 82
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 82
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 23
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 82
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 41
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 23
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 41
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 23
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 41
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 63
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 0
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 63
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 84
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 0
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 63
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 41
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 82
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 23
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 23
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 56
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 82
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 41
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 41
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 41
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 0
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 23
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 56
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 82
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 23
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 56
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 63
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 41
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 82
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 23
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 0
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 0
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 41
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 23
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 63
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 41
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 56
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 82
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 63
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 56
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 82
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 84
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 0
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 82
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 84
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 84
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 41
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 84
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 56
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 63
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 84
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 0
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 63
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 56
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 41
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 41
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 41
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 56
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 23
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 56
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 41
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 63
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 41
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 23
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 82
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 23
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 56
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 56
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 41
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 41
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 56
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 84
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 23
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 56
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 41
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 0
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 23
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 23
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 41
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 41
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 41
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 82
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 56
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 23
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 23
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 23
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 23
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 41
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 41
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 56
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 23
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 23
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 84
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 0
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 56
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 56
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 84
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 82
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 84
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 84
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 23
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 0
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 23
empirical probabilities from test set: {56: 0.122, 82: 0.117, 63: 0.137, 84: 0.116, 41: 0.176, 23: 0.249, 0: 0.083}
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  0.025 

learned probs for this beta: {56: np.float64(0.1428571428571422), 82: np.float64(0.1428571428571422), 63: np.float64(0.1428571428571422), 84: np.float64(0.1428571428571422), 41: np.float64(0.1428571428571422), 23: np.float64(0.1428571428571422), 0: np.float64(0.1428571428571422)}
err dic= {56: np.float64(0.020857142857142213), 82: np.float64(0.025857142857142204), 63: np.float64(0.0058571428571422), 84: np.float64(0.026857142857142205), 41: np.float64(0.03314285714285778), 23: np.float64(0.10614285714285779), 0: np.float64(0.059857142857142207)} 

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), np.float64(0.0058571428571422), np.float64(0.026857142857142205), np.float64(0.03314285714285778), np.float64(0.10614285714285779), np.float64(0.059857142857142207)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  0.05 

learned probs for this beta: {56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
err dic= {56: np.float64(0.020857142857142935), 82: np.float64(0.025857142857142926), 63: np.float64(0.005857142857142922), 84: np.float64(0.026857142857142927), 41: np.float64(0.03314285714285706), 23: np.float64(0.10614285714285707), 0: np.float64(0.05985714285714293)} 

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), np.float64(0.005857142857142922), np.float64(0.026857142857142927), np.float64(0.03314285714285706), np.float64(0.10614285714285707), np.float64(0.05985714285714293)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  0.1 

learned probs for this beta: {56: np.float64(0.14285714285714363), 82: np.float64(0.14285714285714363), 63: np.float64(0.14285714285714363), 84: np.float64(0.14285714285714363), 41: np.float64(0.14285714285714363), 23: np.float64(0.14285714285714363), 0: np.float64(0.14285714285714363)}
err dic= {56: np.float64(0.02085714285714363), 82: np.float64(0.02585714285714362), 63: np.float64(0.005857142857143616), 84: np.float64(0.02685714285714362), 41: np.float64(0.03314285714285636), 23: np.float64(0.10614285714285637), 0: np.float64(0.05985714285714362)} 

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), np.float64(0.005857142857143616), np.float64(0.02685714285714362), np.float64(0.03314285714285636), np.float64(0.10614285714285637), np.float64(0.05985714285714362)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  0.25 

learned probs for this beta: {56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
err dic= {56: np.float64(0.020857142857142907), 82: np.float64(0.025857142857142898), 63: np.float64(0.005857142857142894), 84: np.float64(0.0268571428571429), 41: np.float64(0.033142857142857085), 23: np.float64(0.1061428571428571), 0: np.float64(0.0598571428571429)} 

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), np.float64(0.005857142857142894), np.float64(0.0268571428571429), np.float64(0.033142857142857085), np.float64(0.1061428571428571), np.float64(0.0598571428571429)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  0.5 

learned probs for this beta: {56: np.float64(0.14285714285714282), 82: np.float64(0.14285714285714282), 63: np.float64(0.14285714285714282), 84: np.float64(0.14285714285714282), 41: np.float64(0.14285714285714282), 23: np.float64(0.14285714285714282), 0: np.float64(0.14285714285714282)}
err dic= {56: np.float64(0.020857142857142824), 82: np.float64(0.025857142857142815), 63: np.float64(0.005857142857142811), 84: np.float64(0.026857142857142816), 41: np.float64(0.03314285714285717), 23: np.float64(0.10614285714285718), 0: np.float64(0.05985714285714282)} 

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), np.float64(0.005857142857142811), np.float64(0.026857142857142816), np.float64(0.03314285714285717), np.float64(0.10614285714285718), np.float64(0.05985714285714282)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  0.75 

learned probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: np.float64(0.10614285714285715), 0: np.float64(0.059857142857142845)} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), np.float64(0.059857142857142845)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  1 

learned probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: np.float64(0.10614285714285715), 0: np.float64(0.059857142857142845)} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), np.float64(0.059857142857142845)]
results for assortment [56, 82, 63, 84, 41, 23] :

beta is  1.25 

learned probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: np.float64(0.10614285714285715), 0: np.float64(0.059857142857142845)} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), np.float64(0.059857142857142845)]
results for assortment [56, 82, 63, 84, 41, 23] :

err MNL dic= {56: np.float64(0.00524012879173022), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err MNL list= [np.float64(0.00524012879173022), 0, 0, 0, 0, 0, 0]
err MNL dic= {56: np.float64(0.00524012879173022), 82: np.float64(0.0015958312150483184), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err MNL list= [np.float64(0.00524012879173022), np.float64(0.0015958312150483184), 0, 0, 0, 0, 0]
err MNL dic= {56: np.float64(0.00524012879173022), 82: np.float64(0.0015958312150483184), 63: np.float64(0.01927983957521326), 84: 0, 41: 0, 23: 0, 0: 0} 

err MNL list= [np.float64(0.00524012879173022), np.float64(0.0015958312150483184), np.float64(0.01927983957521326), 0, 0, 0, 0]
err MNL dic= {56: np.float64(0.00524012879173022), 82: np.float64(0.0015958312150483184), 63: np.float64(0.01927983957521326), 84: np.float64(0.002346946845167508), 41: 0, 23: 0, 0: 0} 

err MNL list= [np.float64(0.00524012879173022), np.float64(0.0015958312150483184), np.float64(0.01927983957521326), np.float64(0.002346946845167508), 0, 0, 0]
err MNL dic= {56: np.float64(0.00524012879173022), 82: np.float64(0.0015958312150483184), 63: np.float64(0.01927983957521326), 84: np.float64(0.002346946845167508), 41: np.float64(0.05330893068971361), 23: 0, 0: 0} 

err MNL list= [np.float64(0.00524012879173022), np.float64(0.0015958312150483184), np.float64(0.01927983957521326), np.float64(0.002346946845167508), np.float64(0.05330893068971361), 0, 0]
err MNL dic= {56: np.float64(0.00524012879173022), 82: np.float64(0.0015958312150483184), 63: np.float64(0.01927983957521326), 84: np.float64(0.002346946845167508), 41: np.float64(0.05330893068971361), 23: np.float64(0.11766632774106084), 0: 0} 

err MNL list= [np.float64(0.00524012879173022), np.float64(0.0015958312150483184), np.float64(0.01927983957521326), np.float64(0.002346946845167508), np.float64(0.05330893068971361), np.float64(0.11766632774106084), 0]
err MNL dic= {56: np.float64(0.00524012879173022), 82: np.float64(0.0015958312150483184), 63: np.float64(0.01927983957521326), 84: np.float64(0.002346946845167508), 41: np.float64(0.05330893068971361), 23: np.float64(0.11766632774106084), 0: np.float64(0.19943800485793367)} 

err MNL list= [np.float64(0.00524012879173022), np.float64(0.0015958312150483184), np.float64(0.01927983957521326), np.float64(0.002346946845167508), np.float64(0.05330893068971361), np.float64(0.11766632774106084), np.float64(0.19943800485793367)]
sampled assortment [60, 21, 70, 23, 94, 44]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 11: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 11, 100, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 14: 1, 100: 1} [8, 1, 3, 6, 7, 13, 14, 100, 2, 10]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 10: 0, 11: 0, 12: 0, 13: 0, 100: 0} [1, 2, 3, 4, 5, 10, 11, 12, 13, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 11: 1, 14: 2, 100: 1} [8, 1, 2, 3, 6, 7, 11, 100, 4, 5, 10, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 15: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 15, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 10, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 14, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 21
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 44
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 94
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 70
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 60
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 21
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 21
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 44
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 60
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 21
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 21
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 44
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 23
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 60
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 44
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 94
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 44
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 23
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 44
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 21
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 60
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 70
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 21
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 70
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 94
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 44
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 70
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 23
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 0
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 70
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 21
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 0
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 44
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 44
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 23
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 23
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 70
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 21
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 21
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 21
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 21
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 70
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 0
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 70
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 70
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 44
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 44
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 21
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 70
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 0
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 70
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 23
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 23
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 60
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 70
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 44
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 21
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 23
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 60
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 21
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 21
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 23
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 21
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 44
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 70
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 60
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 23
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 21
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 21
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 23
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 21
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 44
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 23
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 0
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 94
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 70
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 23
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 23
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 70
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 21
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 23
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 21
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 23
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 94
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 23
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 60
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 0
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 60
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 44
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 21
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 23
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 21
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 44
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 70
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 70
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 23
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 44
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 0
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 23
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 21
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 60
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 44
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 94
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 44
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 60
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 23
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 0
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 21
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 44
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 21
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 0
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 44
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 60
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 94
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 60
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 23
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 60
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 60
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 0
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 23
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 44
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 21
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 21
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 94
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 94
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 0
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 21
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 44
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 60
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 21
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 21
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 60
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 94
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 44
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 21
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 21
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 70
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 23
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 94
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 21
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 60
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 23
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 70
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 70
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 0
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 94
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 94
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 94
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 0
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 60
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 60
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 23
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 94
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 44
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 23
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 21
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 21
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 0
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 21
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 70
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 70
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 23
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 21
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 23
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 21
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 70
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 21
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 23
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 21
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 21
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 70
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 23
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 0
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 44
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 44
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 70
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 44
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 23
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 21
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 23
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 94
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 23
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 21
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 44
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 21
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 60
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 94
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 0
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 23
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 21
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 94
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 23
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 70
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 23
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 60
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 70
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 21
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 94
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 21
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 94
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 23
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 21
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 21
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 44
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 44
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 60
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 94
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 44
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 60
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 21
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 23
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 23
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 21
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 44
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 44
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 44
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 94
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 23
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 60
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 44
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 60
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 70
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 21
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 94
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 23
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 23
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 94
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 21
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 23
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 70
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 60
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 0
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 21
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 44
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 23
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 70
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 70
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 44
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 21
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 44
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 44
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 60
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 23
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 21
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 21
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 21
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 0
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 44
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 0
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 0
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 70
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 60
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 21
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 0
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 44
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 21
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 21
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 94
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 60
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 23
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 21
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 0
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 94
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 21
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 21
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 21
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 21
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 44
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 23
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 21
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 94
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 21
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 70
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 23
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 21
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 94
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 44
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 23
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 60
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 0
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 94
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 0
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 23
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 44
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 23
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 70
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 23
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 21
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 21
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 0
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 0
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 23
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 23
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 21
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 21
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 60
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 23
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 21
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 70
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 21
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 21
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 94
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 60
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 0
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 60
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 21
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 44
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 0
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 23
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 23
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 23
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 94
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 94
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 0
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 21
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 70
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 23
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 70
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 21
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 44
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 44
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 94
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 23
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 21
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 23
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 21
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 44
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 23
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 21
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 23
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 44
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 23
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 21
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 70
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 44
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 60
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 94
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 21
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 60
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 44
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 21
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 0
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 21
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 0
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 44
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 21
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 21
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 23
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 44
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 94
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 21
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 70
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 21
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 94
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 94
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 60
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 21
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 23
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 70
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 60
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 44
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 70
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 70
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 44
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 21
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 70
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 23
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 21
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 21
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 23
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 23
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 0
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 0
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 23
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 21
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 0
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 60
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 94
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 21
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 21
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 23
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 60
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 44
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 21
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 21
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 21
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 23
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 21
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 44
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 70
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 94
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 94
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 23
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 23
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 44
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 44
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 0
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 23
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 21
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 21
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 70
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 70
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 70
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 21
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 0
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 21
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 0
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 23
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 23
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 23
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 44
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 44
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 21
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 0
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 21
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 44
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 0
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 60
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 44
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 0
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 23
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 21
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 23
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 44
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 44
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 0
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 0
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 23
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 94
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 21
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 94
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 21
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 44
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 21
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 21
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 21
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 21
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 21
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 23
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 70
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 21
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 44
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 60
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 23
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 44
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 94
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 0
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 21
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 23
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 21
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 44
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 23
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 23
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 60
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 23
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 94
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 21
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 44
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 70
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 23
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 21
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 44
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 44
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 21
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 94
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 23
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 21
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 21
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 44
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 70
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 21
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 94
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 21
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 70
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 23
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 21
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 21
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 60
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 21
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 21
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 94
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 23
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 60
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 21
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 44
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 21
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 21
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 70
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 0
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 0
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 70
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 0
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 21
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 23
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 21
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 21
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 0
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 23
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 44
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 0
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 94
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 70
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 94
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 23
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 44
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 70
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 44
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 23
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 44
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 94
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 0
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 23
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 60
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 23
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 44
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 23
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 23
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 21
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 0
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 70
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 94
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 70
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 23
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 23
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 0
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 70
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 70
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 70
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 21
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 70
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 21
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 21
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 60
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 23
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 44
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 44
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 21
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 60
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 94
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 21
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 94
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 21
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 70
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 23
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 60
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 44
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 23
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 94
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 94
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 0
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 70
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 23
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 44
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 21
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 94
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 21
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 21
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 23
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 70
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 70
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 23
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 0
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 23
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 44
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 94
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 21
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 23
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 44
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 21
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 23
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 0
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 21
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 23
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 70
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 60
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 21
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 21
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 60
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 21
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 21
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 21
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 94
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 44
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 21
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 21
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 21
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 44
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 60
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 94
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 0
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 21
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 23
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 21
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 21
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 23
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 60
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 70
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 23
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 21
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 44
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 70
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 0
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 44
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 21
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 23
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 44
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 0
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 0
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 60
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 23
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 70
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 23
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 60
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 21
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 21
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 44
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 60
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 94
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 60
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 23
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 70
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 23
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 21
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 21
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 44
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 23
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 21
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 21
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 23
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 21
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 60
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 0
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 23
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 23
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 60
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 94
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 0
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 23
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 60
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 60
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 21
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 70
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 21
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 23
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 21
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 23
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 21
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 21
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 60
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 21
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 94
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 44
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 44
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 44
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 60
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 23
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 70
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 44
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 70
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 44
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 21
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 94
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 70
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 70
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 44
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 0
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 23
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 94
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 23
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 23
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 44
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 60
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 21
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 23
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 21
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 60
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 44
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 44
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 60
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 23
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 70
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 60
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 44
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 23
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 21
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 21
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 0
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 44
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 70
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 70
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 44
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 44
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 21
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 21
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 0
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 0
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 0
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 21
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 60
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 0
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 94
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 70
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 23
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 0
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 23
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 94
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 23
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 70
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 21
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 94
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 44
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 60
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 94
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 23
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 0
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 60
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 0
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 23
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 44
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 21
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 94
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 60
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 23
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 21
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 44
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 0
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 21
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 44
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 21
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 21
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 23
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 21
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 60
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 21
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 60
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 44
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 23
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 0
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 60
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 23
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 94
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 23
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 70
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 60
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 94
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 70
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 70
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 60
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 60
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 21
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 21
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 70
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 23
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 21
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 44
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 44
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 21
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 60
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 0
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 21
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 94
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 70
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 21
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 70
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 23
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 23
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 23
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 23
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 0
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 60
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 23
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 44
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 94
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 21
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 70
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 21
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 94
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 70
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 44
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 70
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 21
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 70
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 44
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 23
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 21
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 23
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 70
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 21
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 21
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 94
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 0
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 94
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 94
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 23
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 70
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 21
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 21
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 94
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 44
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 60
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 70
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 23
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 23
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 60
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 0
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 23
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 70
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 23
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 23
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 94
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 21
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 44
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 21
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 44
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 21
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 70
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 23
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 44
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 70
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 70
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 70
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 0
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 21
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 21
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 23
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 23
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 21
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 23
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 23
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 23
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 23
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 21
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 70
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 21
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 70
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 23
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 21
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 0
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 94
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 21
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 23
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 60
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 23
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 23
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 44
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 70
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 70
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 21
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 70
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 60
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 94
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 23
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 70
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 23
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 60
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 21
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 23
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 94
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 94
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 70
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 21
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 0
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 44
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 44
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 60
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 21
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 44
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 60
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 23
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 21
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 21
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 94
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 21
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 44
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 21
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 21
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 21
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 23
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 23
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 21
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 21
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 94
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 44
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 60
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 44
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 21
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 23
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 44
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 94
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 23
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 23
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 23
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 23
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 23
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 23
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 94
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 23
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 60
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 94
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 0
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 21
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 0
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 21
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 60
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 60
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 44
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 0
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 21
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 21
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 23
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 23
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 23
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 21
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 21
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 94
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 70
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 94
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 23
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 21
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 60
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 23
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 44
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 60
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 21
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 0
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 21
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 21
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 21
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 94
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 60
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 70
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 70
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 0
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 60
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 70
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 94
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 60
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 21
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 94
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 21
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 21
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 21
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 23
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 44
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 44
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 60
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 21
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 21
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 44
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 70
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 21
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 44
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 0
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 21
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 44
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 60
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 60
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 60
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 60
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 21
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 44
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 23
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 21
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 0
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 70
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 94
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 44
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 21
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 23
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 21
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 23
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 44
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 21
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 23
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 44
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 94
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 60
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 21
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 21
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 23
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 23
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 21
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 21
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 21
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 21
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 23
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 23
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 60
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 60
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 70
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 70
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 94
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 70
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 70
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 23
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 70
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 70
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 21
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 21
empirical probabilities from test set: {60: 0.103, 21: 0.261, 70: 0.117, 23: 0.198, 94: 0.096, 44: 0.139, 0: 0.086}
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  0.025 

learned probs for this beta: {60: np.float64(0.14285714285714218), 21: np.float64(0.14285714285714218), 70: np.float64(0.14285714285714218), 23: np.float64(0.14285714285714218), 94: np.float64(0.14285714285714218), 44: np.float64(0.14285714285714218), 0: np.float64(0.14285714285714218)}
err dic= {60: np.float64(0.03985714285714219), 21: np.float64(0.11814285714285783), 70: np.float64(0.025857142857142176), 23: np.float64(0.055142857142857826), 94: np.float64(0.04685714285714218), 44: np.float64(0.0038571428571421706), 0: np.float64(0.05685714285714219)} 

err list= [np.float64(0.03985714285714219), np.float64(0.11814285714285783), np.float64(0.025857142857142176), np.float64(0.055142857142857826), np.float64(0.04685714285714218), np.float64(0.0038571428571421706), np.float64(0.05685714285714219)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  0.05 

learned probs for this beta: {60: np.float64(0.14285714285714396), 21: np.float64(0.14285714285714396), 70: np.float64(0.14285714285714396), 23: np.float64(0.14285714285714396), 94: np.float64(0.14285714285714396), 44: np.float64(0.14285714285714396), 0: np.float64(0.14285714285714396)}
err dic= {60: np.float64(0.039857142857143965), 21: np.float64(0.11814285714285605), 70: np.float64(0.025857142857143953), 23: np.float64(0.05514285714285605), 94: np.float64(0.04685714285714396), 44: np.float64(0.003857142857143947), 0: np.float64(0.056857142857143966)} 

err list= [np.float64(0.039857142857143965), np.float64(0.11814285714285605), np.float64(0.025857142857143953), np.float64(0.05514285714285605), np.float64(0.04685714285714396), np.float64(0.003857142857143947), np.float64(0.056857142857143966)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  0.1 

learned probs for this beta: {60: np.float64(0.14285714285714285), 21: np.float64(0.14285714285714285), 70: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {60: np.float64(0.039857142857142855), 21: np.float64(0.11814285714285716), 70: np.float64(0.025857142857142842), 23: np.float64(0.05514285714285716), 94: np.float64(0.04685714285714285), 44: np.float64(0.0038571428571428368), 0: np.float64(0.056857142857142856)} 

err list= [np.float64(0.039857142857142855), np.float64(0.11814285714285716), np.float64(0.025857142857142842), np.float64(0.05514285714285716), np.float64(0.04685714285714285), np.float64(0.0038571428571428368), np.float64(0.056857142857142856)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  0.25 

learned probs for this beta: {60: np.float64(0.1428571428571423), 21: np.float64(0.1428571428571423), 70: np.float64(0.1428571428571423), 23: np.float64(0.1428571428571423), 94: np.float64(0.1428571428571423), 44: np.float64(0.1428571428571423), 0: np.float64(0.1428571428571423)}
err dic= {60: np.float64(0.0398571428571423), 21: np.float64(0.11814285714285772), 70: np.float64(0.025857142857142287), 23: np.float64(0.055142857142857715), 94: np.float64(0.04685714285714229), 44: np.float64(0.0038571428571422817), 0: np.float64(0.0568571428571423)} 

err list= [np.float64(0.0398571428571423), np.float64(0.11814285714285772), np.float64(0.025857142857142287), np.float64(0.055142857142857715), np.float64(0.04685714285714229), np.float64(0.0038571428571422817), np.float64(0.0568571428571423)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  0.5 

learned probs for this beta: {60: np.float64(0.14285714285714218), 21: np.float64(0.14285714285714218), 70: np.float64(0.14285714285714218), 23: np.float64(0.14285714285714218), 94: np.float64(0.14285714285714218), 44: np.float64(0.14285714285714218), 0: np.float64(0.14285714285714218)}
err dic= {60: np.float64(0.03985714285714219), 21: np.float64(0.11814285714285783), 70: np.float64(0.025857142857142176), 23: np.float64(0.055142857142857826), 94: np.float64(0.04685714285714218), 44: np.float64(0.0038571428571421706), 0: np.float64(0.05685714285714219)} 

err list= [np.float64(0.03985714285714219), np.float64(0.11814285714285783), np.float64(0.025857142857142176), np.float64(0.055142857142857826), np.float64(0.04685714285714218), np.float64(0.0038571428571421706), np.float64(0.05685714285714219)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  0.75 

learned probs for this beta: {60: np.float64(0.14285714285714285), 21: np.float64(0.14285714285714285), 70: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {60: np.float64(0.039857142857142855), 21: np.float64(0.11814285714285716), 70: np.float64(0.025857142857142842), 23: np.float64(0.05514285714285716), 94: np.float64(0.04685714285714285), 44: np.float64(0.0038571428571428368), 0: np.float64(0.056857142857142856)} 

err list= [np.float64(0.039857142857142855), np.float64(0.11814285714285716), np.float64(0.025857142857142842), np.float64(0.05514285714285716), np.float64(0.04685714285714285), np.float64(0.0038571428571428368), np.float64(0.056857142857142856)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  1 

learned probs for this beta: {60: np.float64(0.14285714285714285), 21: np.float64(0.14285714285714285), 70: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {60: np.float64(0.039857142857142855), 21: np.float64(0.11814285714285716), 70: np.float64(0.025857142857142842), 23: np.float64(0.05514285714285716), 94: np.float64(0.04685714285714285), 44: np.float64(0.0038571428571428368), 0: np.float64(0.056857142857142856)} 

err list= [np.float64(0.039857142857142855), np.float64(0.11814285714285716), np.float64(0.025857142857142842), np.float64(0.05514285714285716), np.float64(0.04685714285714285), np.float64(0.0038571428571428368), np.float64(0.056857142857142856)]
results for assortment [60, 21, 70, 23, 94, 44] :

beta is  1.25 

learned probs for this beta: {60: np.float64(0.14285714285714285), 21: np.float64(0.14285714285714285), 70: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {60: np.float64(0.039857142857142855), 21: np.float64(0.11814285714285716), 70: np.float64(0.025857142857142842), 23: np.float64(0.05514285714285716), 94: np.float64(0.04685714285714285), 44: np.float64(0.0038571428571428368), 0: np.float64(0.056857142857142856)} 

err list= [np.float64(0.039857142857142855), np.float64(0.11814285714285716), np.float64(0.025857142857142842), np.float64(0.05514285714285716), np.float64(0.04685714285714285), np.float64(0.0038571428571428368), np.float64(0.056857142857142856)]
results for assortment [60, 21, 70, 23, 94, 44] :

err MNL dic= {60: np.float64(0.011936820614688523), 21: 0, 70: 0, 23: 0, 94: 0, 44: 0, 0: 0} 

err MNL list= [np.float64(0.011936820614688523), 0, 0, 0, 0, 0, 0]
err MNL dic= {60: np.float64(0.011936820614688523), 21: np.float64(0.12818534458974787), 70: 0, 23: 0, 94: 0, 44: 0, 0: 0} 

err MNL list= [np.float64(0.011936820614688523), np.float64(0.12818534458974787), 0, 0, 0, 0, 0]
err MNL dic= {60: np.float64(0.011936820614688523), 21: np.float64(0.12818534458974787), 70: np.float64(0.002394250400044151), 23: 0, 94: 0, 44: 0, 0: 0} 

err MNL list= [np.float64(0.011936820614688523), np.float64(0.12818534458974787), np.float64(0.002394250400044151), 0, 0, 0, 0]
err MNL dic= {60: np.float64(0.011936820614688523), 21: np.float64(0.12818534458974787), 70: np.float64(0.002394250400044151), 23: np.float64(0.06954444628372788), 94: 0, 44: 0, 0: 0} 

err MNL list= [np.float64(0.011936820614688523), np.float64(0.12818534458974787), np.float64(0.002394250400044151), np.float64(0.06954444628372788), 0, 0, 0]
err MNL dic= {60: np.float64(0.011936820614688523), 21: np.float64(0.12818534458974787), 70: np.float64(0.002394250400044151), 23: np.float64(0.06954444628372788), 94: np.float64(0.01617789549191634), 44: 0, 0: 0} 

err MNL list= [np.float64(0.011936820614688523), np.float64(0.12818534458974787), np.float64(0.002394250400044151), np.float64(0.06954444628372788), np.float64(0.01617789549191634), 0, 0]
err MNL dic= {60: np.float64(0.011936820614688523), 21: np.float64(0.12818534458974787), 70: np.float64(0.002394250400044151), 23: np.float64(0.06954444628372788), 94: np.float64(0.01617789549191634), 44: np.float64(0.017883187110301846), 0: 0} 

err MNL list= [np.float64(0.011936820614688523), np.float64(0.12818534458974787), np.float64(0.002394250400044151), np.float64(0.06954444628372788), np.float64(0.01617789549191634), np.float64(0.017883187110301846), 0]
err MNL dic= {60: np.float64(0.011936820614688523), 21: np.float64(0.12818534458974787), 70: np.float64(0.002394250400044151), 23: np.float64(0.06954444628372788), 94: np.float64(0.01617789549191634), 44: np.float64(0.017883187110301846), 0: np.float64(0.1898925122772168)} 

err MNL list= [np.float64(0.011936820614688523), np.float64(0.12818534458974787), np.float64(0.002394250400044151), np.float64(0.06954444628372788), np.float64(0.01617789549191634), np.float64(0.017883187110301846), np.float64(0.1898925122772168)]
sampled assortment [9, 77, 95, 93, 67, 8]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 10, 11, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 9]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 10, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 9]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 9, 11, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 20: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 20]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 2, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 11: 1, 15: 2, 100: 1} [8, 1, 3, 6, 7, 11, 100, 4, 5, 10, 15]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 19: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 19, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 14, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 10, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 11: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 11, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 15, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 67
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 8
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 8
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 67
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 77
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 8
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 95
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 9
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 8
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 8
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 8
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 0
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 9
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 8
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 67
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 8
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 9
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 8
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 8
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 9
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 0
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 8
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 9
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 95
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 8
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 93
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 0
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 8
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 77
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 0
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 8
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 9
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 9
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 9
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 93
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 8
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 95
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 9
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 8
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 95
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 9
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 0
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 9
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 8
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 0
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 8
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 0
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 9
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 77
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 9
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 8
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 8
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 9
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 8
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 9
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 8
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 95
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 93
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 95
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 8
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 0
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 95
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 77
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 67
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 0
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 67
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 9
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 9
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 9
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 93
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 93
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 95
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 67
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 8
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 77
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 9
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 0
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 77
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 8
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 8
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 67
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 9
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 8
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 8
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 77
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 93
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 8
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 8
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 77
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 95
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 9
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 9
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 67
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 8
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 9
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 9
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 9
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 8
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 9
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 0
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 93
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 8
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 9
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 67
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 8
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 9
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 67
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 8
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 77
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 93
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 9
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 9
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 8
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 67
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 8
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 8
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 8
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 67
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 67
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 8
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 8
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 95
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 8
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 77
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 93
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 8
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 95
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 8
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 9
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 9
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 8
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 9
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 77
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 8
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 9
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 95
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 8
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 8
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 9
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 93
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 8
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 8
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 9
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 9
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 95
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 8
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 95
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 8
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 8
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 95
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 8
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 8
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 9
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 8
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 9
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 8
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 95
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 9
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 9
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 67
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 8
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 67
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 0
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 0
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 9
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 77
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 9
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 8
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 95
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 93
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 0
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 9
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 95
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 8
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 8
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 8
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 93
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 9
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 8
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 8
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 8
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 93
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 9
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 8
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 8
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 77
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 9
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 95
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 95
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 8
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 77
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 8
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 67
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 93
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 8
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 8
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 9
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 77
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 8
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 0
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 9
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 9
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 0
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 77
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 8
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 93
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 77
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 77
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 77
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 0
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 77
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 8
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 9
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 9
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 9
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 8
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 9
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 67
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 8
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 9
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 9
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 67
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 93
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 9
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 95
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 95
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 95
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 8
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 0
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 0
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 0
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 9
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 67
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 8
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 95
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 8
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 67
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 9
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 95
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 93
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 8
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 9
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 8
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 9
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 8
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 93
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 77
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 8
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 77
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 8
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 8
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 9
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 8
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 67
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 8
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 8
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 93
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 9
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 8
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 9
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 9
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 67
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 67
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 8
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 8
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 93
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 67
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 67
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 77
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 9
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 8
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 9
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 9
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 67
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 9
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 0
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 67
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 93
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 95
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 8
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 95
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 67
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 9
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 8
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 8
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 8
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 93
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 9
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 8
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 8
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 9
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 8
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 9
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 8
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 95
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 9
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 95
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 9
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 8
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 9
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 8
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 0
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 77
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 95
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 0
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 9
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 0
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 67
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 67
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 9
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 8
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 93
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 9
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 8
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 8
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 77
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 8
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 8
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 8
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 8
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 95
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 67
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 67
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 77
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 77
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 67
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 9
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 9
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 9
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 67
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 8
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 67
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 95
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 77
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 9
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 8
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 67
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 9
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 95
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 8
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 67
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 93
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 95
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 93
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 8
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 8
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 77
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 93
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 77
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 77
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 9
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 9
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 77
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 95
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 9
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 67
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 67
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 95
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 95
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 8
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 8
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 9
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 0
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 95
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 8
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 77
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 95
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 8
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 77
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 9
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 9
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 9
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 9
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 9
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 95
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 9
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 95
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 95
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 9
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 93
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 9
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 8
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 8
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 8
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 0
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 8
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 9
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 0
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 77
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 9
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 8
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 0
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 93
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 67
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 9
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 8
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 8
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 95
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 0
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 67
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 9
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 8
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 77
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 93
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 67
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 9
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 9
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 95
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 95
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 77
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 9
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 9
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 77
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 8
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 9
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 95
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 8
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 0
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 93
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 9
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 93
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 93
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 77
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 77
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 9
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 8
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 8
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 8
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 9
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 9
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 8
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 67
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 77
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 0
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 9
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 9
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 93
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 77
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 93
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 9
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 9
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 95
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 9
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 67
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 0
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 67
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 9
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 95
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 9
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 8
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 77
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 8
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 9
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 9
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 9
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 8
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 8
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 67
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 95
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 8
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 93
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 77
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 8
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 9
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 9
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 93
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 8
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 9
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 9
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 9
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 8
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 95
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 77
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 8
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 8
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 8
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 8
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 9
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 8
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 93
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 9
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 77
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 9
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 9
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 8
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 8
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 8
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 8
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 8
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 95
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 93
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 9
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 9
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 95
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 9
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 77
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 95
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 9
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 9
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 8
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 8
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 9
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 93
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 8
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 9
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 77
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 8
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 9
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 8
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 95
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 95
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 0
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 77
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 9
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 8
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 8
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 9
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 8
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 67
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 67
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 9
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 95
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 67
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 0
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 0
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 9
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 95
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 95
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 9
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 77
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 0
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 8
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 9
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 8
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 67
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 9
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 8
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 9
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 8
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 9
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 0
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 67
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 9
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 93
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 8
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 77
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 0
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 0
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 8
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 8
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 77
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 8
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 93
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 67
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 9
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 9
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 9
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 93
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 93
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 0
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 9
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 95
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 8
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 95
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 67
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 93
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 9
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 9
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 8
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 77
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 8
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 9
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 67
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 0
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 67
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 9
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 9
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 0
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 8
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 8
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 8
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 9
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 9
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 95
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 9
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 9
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 93
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 8
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 77
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 67
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 93
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 67
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 8
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 8
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 8
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 8
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 95
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 8
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 67
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 77
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 8
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 77
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 93
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 8
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 0
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 67
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 8
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 77
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 77
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 9
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 9
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 67
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 0
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 9
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 77
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 8
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 9
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 8
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 8
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 9
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 9
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 0
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 8
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 77
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 8
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 95
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 9
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 0
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 95
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 0
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 93
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 8
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 9
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 9
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 8
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 0
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 9
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 8
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 0
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 9
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 8
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 0
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 8
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 77
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 8
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 8
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 8
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 77
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 67
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 95
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 95
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 0
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 8
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 8
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 8
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 9
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 8
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 0
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 95
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 9
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 77
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 77
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 0
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 77
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 8
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 93
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 9
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 95
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 8
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 8
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 8
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 8
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 8
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 9
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 8
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 9
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 93
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 8
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 95
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 8
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 9
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 9
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 95
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 67
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 9
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 8
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 8
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 93
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 8
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 67
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 9
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 95
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 8
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 9
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 67
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 8
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 8
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 8
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 0
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 8
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 9
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 95
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 93
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 67
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 8
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 95
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 9
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 95
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 8
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 77
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 8
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 8
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 95
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 67
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 77
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 8
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 77
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 8
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 9
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 8
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 9
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 0
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 9
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 9
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 8
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 93
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 67
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 0
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 9
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 9
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 8
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 77
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 67
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 8
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 9
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 67
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 67
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 67
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 8
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 77
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 9
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 0
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 67
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 9
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 93
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 93
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 8
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 8
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 8
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 93
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 8
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 9
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 8
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 9
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 8
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 8
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 67
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 67
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 9
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 8
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 93
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 8
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 9
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 9
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 95
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 8
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 8
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 8
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 0
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 67
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 8
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 8
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 67
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 9
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 8
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 8
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 77
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 93
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 77
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 9
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 67
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 0
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 9
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 9
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 93
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 9
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 77
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 8
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 95
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 0
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 8
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 9
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 9
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 67
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 9
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 77
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 9
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 9
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 9
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 93
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 95
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 8
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 9
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 95
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 9
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 77
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 9
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 8
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 8
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 8
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 0
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 9
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 77
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 9
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 9
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 9
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 95
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 9
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 9
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 8
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 8
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 9
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 9
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 8
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 9
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 8
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 8
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 9
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 9
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 77
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 0
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 9
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 9
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 95
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 8
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 9
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 77
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 8
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 9
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 8
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 8
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 0
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 9
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 95
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 8
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 9
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 8
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 8
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 8
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 8
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 8
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 0
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 67
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 9
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 9
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 95
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 9
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 9
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 8
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 95
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 9
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 8
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 0
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 8
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 0
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 8
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 8
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 9
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 77
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 9
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 8
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 67
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 93
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 9
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 77
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 67
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 67
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 8
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 9
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 8
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 8
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 9
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 8
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 95
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 77
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 93
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 93
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 0
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 8
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 77
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 95
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 93
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 93
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 9
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 9
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 8
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 8
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 8
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 9
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 9
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 95
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 77
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 9
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 9
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 9
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 67
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 8
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 95
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 93
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 8
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 77
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 9
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 77
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 95
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 77
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 8
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 67
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 8
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 77
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 9
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 9
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 8
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 0
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 9
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 8
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 8
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 67
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 9
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 8
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 9
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 67
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 9
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 8
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 8
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 9
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 67
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 77
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 8
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 67
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 9
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 77
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 9
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 8
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 8
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 0
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 95
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 8
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 0
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 0
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 9
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 67
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 8
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 0
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 8
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 93
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 67
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 8
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 8
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 8
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 8
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 9
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 9
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 95
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 93
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 93
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 77
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 0
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 77
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 0
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 9
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 8
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 9
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 9
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 9
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 8
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 9
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 8
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 67
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 93
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 9
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 9
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 77
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 77
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 8
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 9
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 67
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 8
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 9
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 8
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 93
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 77
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 8
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 77
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 9
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 95
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 8
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 8
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 8
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 95
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 0
empirical probabilities from test set: {9: 0.267, 77: 0.095, 95: 0.093, 93: 0.071, 67: 0.092, 8: 0.307, 0: 0.075}
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.11098055679316504), 77: np.float64(0.14914851064819504), 95: np.float64(0.14914851064819504), 93: np.float64(0.14914851064819504), 67: np.float64(0.14914851064819504), 8: np.float64(0.14327688996586121), 0: np.float64(0.14914851064819504)}
err dic= {9: np.float64(0.15601944320683497), 77: np.float64(0.054148510648195036), 95: np.float64(0.05614851064819504), 93: np.float64(0.07814851064819504), 67: np.float64(0.05714851064819504), 8: np.float64(0.16372311003413878), 0: np.float64(0.07414851064819504)} 

err list= [np.float64(0.15601944320683497), np.float64(0.054148510648195036), np.float64(0.05614851064819504), np.float64(0.07814851064819504), np.float64(0.05714851064819504), np.float64(0.16372311003413878), np.float64(0.07414851064819504)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.14691659935639137), 77: np.float64(0.14175289814140532), 95: np.float64(0.14175289814140532), 93: np.float64(0.14175289814140532), 67: np.float64(0.14175289814140532), 8: np.float64(0.14431890993659086), 0: np.float64(0.14175289814140532)}
err dic= {9: np.float64(0.12008340064360865), 77: np.float64(0.04675289814140532), 95: np.float64(0.04875289814140532), 93: np.float64(0.07075289814140533), 67: np.float64(0.04975289814140532), 8: np.float64(0.16268109006340914), 0: np.float64(0.06675289814140532)} 

err list= [np.float64(0.12008340064360865), np.float64(0.04675289814140532), np.float64(0.04875289814140532), np.float64(0.07075289814140533), np.float64(0.04975289814140532), np.float64(0.16268109006340914), np.float64(0.06675289814140532)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.19832594205736662), 77: np.float64(0.12377352505806202), 95: np.float64(0.12377352505806202), 93: np.float64(0.12377352505806202), 67: np.float64(0.12377352505806202), 8: np.float64(0.1828064326523231), 0: np.float64(0.12377352505806202)}
err dic= {9: np.float64(0.0686740579426334), 77: np.float64(0.02877352505806202), 95: np.float64(0.030773525058062023), 93: np.float64(0.05277352505806203), 67: np.float64(0.031773525058062024), 8: np.float64(0.12419356734767689), 0: np.float64(0.048773525058062026)} 

err list= [np.float64(0.0686740579426334), np.float64(0.02877352505806202), np.float64(0.030773525058062023), np.float64(0.05277352505806203), np.float64(0.031773525058062024), np.float64(0.12419356734767689), np.float64(0.048773525058062026)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.42677759883605026), 77: np.float64(0.05946583600012959), 95: np.float64(0.05946583600012959), 93: np.float64(0.05946583600012959), 67: np.float64(0.05946583600012959), 8: np.float64(0.275893221163302), 0: np.float64(0.05946583600012959)}
err dic= {9: np.float64(0.15977759883605025), 77: np.float64(0.03553416399987041), 95: np.float64(0.03353416399987041), 93: np.float64(0.011534163999870402), 67: np.float64(0.03253416399987041), 8: np.float64(0.03110677883669799), 0: np.float64(0.015534163999870405)} 

err list= [np.float64(0.15977759883605025), np.float64(0.03553416399987041), np.float64(0.03353416399987041), np.float64(0.011534163999870402), np.float64(0.03253416399987041), np.float64(0.03110677883669799), np.float64(0.015534163999870405)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.6933429969993028), 77: np.float64(0.007568177735800295), 95: np.float64(0.007568177735800295), 93: np.float64(0.007568177735800295), 67: np.float64(0.007568177735800295), 8: np.float64(0.2688161143216945), 0: np.float64(0.007568177735800295)}
err dic= {9: np.float64(0.4263429969993028), 77: np.float64(0.08743182226419971), 95: np.float64(0.08543182226419971), 93: np.float64(0.0634318222641997), 67: np.float64(0.08443182226419971), 8: np.float64(0.038183885678305496), 0: np.float64(0.0674318222641997)} 

err list= [np.float64(0.4263429969993028), np.float64(0.08743182226419971), np.float64(0.08543182226419971), np.float64(0.0634318222641997), np.float64(0.08443182226419971), np.float64(0.038183885678305496), np.float64(0.0674318222641997)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.7269580451997639), 77: np.float64(0.0015387108261641406), 95: np.float64(0.0015387108261641406), 93: np.float64(0.0015387108261641406), 67: np.float64(0.0015387108261641406), 8: np.float64(0.2653484006694152), 0: np.float64(0.0015387108261641406)}
err dic= {9: np.float64(0.4599580451997639), 77: np.float64(0.09346128917383587), 95: np.float64(0.09146128917383586), 93: np.float64(0.06946128917383586), 67: np.float64(0.09046128917383586), 8: np.float64(0.04165159933058482), 0: np.float64(0.07346128917383586)} 

err list= [np.float64(0.4599580451997639), np.float64(0.09346128917383587), np.float64(0.09146128917383586), np.float64(0.06946128917383586), np.float64(0.09046128917383586), np.float64(0.04165159933058482), np.float64(0.07346128917383586)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  1 

learned probs for this beta: {9: np.float64(0.7357901444390629), 77: np.float64(3.5080985308243825e-05), 95: np.float64(3.5080985308243825e-05), 93: np.float64(3.5080985308243825e-05), 67: np.float64(3.5080985308243825e-05), 8: np.float64(0.26403445063439596), 0: np.float64(3.5080985308243825e-05)}
err dic= {9: np.float64(0.46879014443906286), 77: np.float64(0.09496491901469176), 95: np.float64(0.09296491901469175), 93: np.float64(0.07096491901469175), 67: np.float64(0.09196491901469175), 8: np.float64(0.04296554936560404), 0: np.float64(0.07496491901469175)} 

err list= [np.float64(0.46879014443906286), np.float64(0.09496491901469176), np.float64(0.09296491901469175), np.float64(0.07096491901469175), np.float64(0.09196491901469175), np.float64(0.04296554936560404), np.float64(0.07496491901469175)]
results for assortment [9, 77, 95, 93, 67, 8] :

beta is  1.25 

learned probs for this beta: {9: np.float64(0.735924694872381), 77: np.float64(1.2551252072143815e-05), 95: np.float64(1.2551252072143815e-05), 93: np.float64(1.2551252072143815e-05), 67: np.float64(1.2551252072143815e-05), 8: np.float64(0.26401254886725806), 0: np.float64(1.2551252072143815e-05)}
err dic= {9: np.float64(0.468924694872381), 77: np.float64(0.09498744874792786), 95: np.float64(0.09298744874792786), 93: np.float64(0.07098744874792785), 67: np.float64(0.09198744874792786), 8: np.float64(0.04298745113274194), 0: np.float64(0.07498744874792786)} 

err list= [np.float64(0.468924694872381), np.float64(0.09498744874792786), np.float64(0.09298744874792786), np.float64(0.07098744874792785), np.float64(0.09198744874792786), np.float64(0.04298745113274194), np.float64(0.07498744874792786)]
results for assortment [9, 77, 95, 93, 67, 8] :

err MNL dic= {9: np.float64(0.12905374386139162), 77: 0, 95: 0, 93: 0, 67: 0, 8: 0, 0: 0} 

err MNL list= [np.float64(0.12905374386139162), 0, 0, 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.12905374386139162), 77: np.float64(0.01938503559013409), 95: 0, 93: 0, 67: 0, 8: 0, 0: 0} 

err MNL list= [np.float64(0.12905374386139162), np.float64(0.01938503559013409), 0, 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.12905374386139162), 77: np.float64(0.01938503559013409), 95: np.float64(0.01956414500910446), 93: 0, 67: 0, 8: 0, 0: 0} 

err MNL list= [np.float64(0.12905374386139162), np.float64(0.01938503559013409), np.float64(0.01956414500910446), 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.12905374386139162), 77: np.float64(0.01938503559013409), 95: np.float64(0.01956414500910446), 93: np.float64(0.040129503945262934), 67: 0, 8: 0, 0: 0} 

err MNL list= [np.float64(0.12905374386139162), np.float64(0.01938503559013409), np.float64(0.01956414500910446), np.float64(0.040129503945262934), 0, 0, 0]
err MNL dic= {9: np.float64(0.12905374386139162), 77: np.float64(0.01938503559013409), 95: np.float64(0.01956414500910446), 93: np.float64(0.040129503945262934), 67: np.float64(0.019405396457540164), 8: 0, 0: 0} 

err MNL list= [np.float64(0.12905374386139162), np.float64(0.01938503559013409), np.float64(0.01956414500910446), np.float64(0.040129503945262934), np.float64(0.019405396457540164), 0, 0]
err MNL dic= {9: np.float64(0.12905374386139162), 77: np.float64(0.01938503559013409), 95: np.float64(0.01956414500910446), 93: np.float64(0.040129503945262934), 67: np.float64(0.019405396457540164), 8: np.float64(0.17032284941786677), 0: 0} 

err MNL list= [np.float64(0.12905374386139162), np.float64(0.01938503559013409), np.float64(0.01956414500910446), np.float64(0.040129503945262934), np.float64(0.019405396457540164), np.float64(0.17032284941786677), 0]
err MNL dic= {9: np.float64(0.12905374386139162), 77: np.float64(0.01938503559013409), 95: np.float64(0.01956414500910446), 93: np.float64(0.040129503945262934), 67: np.float64(0.019405396457540164), 8: np.float64(0.17032284941786677), 0: np.float64(0.20089251227721677)} 

err MNL list= [np.float64(0.12905374386139162), np.float64(0.01938503559013409), np.float64(0.01956414500910446), np.float64(0.040129503945262934), np.float64(0.019405396457540164), np.float64(0.17032284941786677), np.float64(0.20089251227721677)]
sampled assortment [15, 69, 80, 75, 77, 50]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 13, 100, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 10, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 15: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5, 14, 15]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 14, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 15]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 14: 2, 17: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 2, 12, 14, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 16: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 9, 16]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 21: 3, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 21]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 15, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 13, 100, 5, 10]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 10]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 50
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 77
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 80
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 80
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 69
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 80
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 15
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 69
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 69
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 75
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 15
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 69
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 69
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 15
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 0
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 77
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 50
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 15
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 15
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 50
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 15
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 50
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 69
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 50
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 50
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 0
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 75
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 75
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 15
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 50
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 69
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 0
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 80
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 50
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 15
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 15
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 15
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 50
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 77
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 77
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 80
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 15
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 75
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 50
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 69
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 50
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 15
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 50
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 77
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 15
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 69
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 50
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 75
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 0
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 15
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 50
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 15
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 77
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 15
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 0
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 75
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 15
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 80
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 15
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 50
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 15
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 80
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 0
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 77
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 50
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 50
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 15
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 15
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 80
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 0
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 15
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 50
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 75
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 69
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 80
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 80
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 75
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 50
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 69
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 50
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 15
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 69
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 0
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 50
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 80
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 69
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 80
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 15
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 0
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 75
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 15
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 15
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 77
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 69
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 69
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 75
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 15
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 0
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 0
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 80
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 75
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 50
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 80
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 15
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 80
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 69
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 50
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 15
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 15
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 0
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 75
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 15
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 0
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 50
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 80
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 50
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 50
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 15
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 75
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 75
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 75
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 50
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 15
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 80
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 80
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 80
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 77
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 15
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 0
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 69
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 80
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 69
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 80
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 50
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 69
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 75
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 0
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 50
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 15
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 15
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 0
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 77
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 80
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 69
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 69
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 15
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 75
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 75
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 15
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 80
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 15
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 80
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 50
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 15
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 77
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 15
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 80
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 50
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 0
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 15
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 80
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 77
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 80
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 15
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 69
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 80
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 15
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 0
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 50
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 77
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 15
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 50
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 50
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 75
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 0
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 80
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 0
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 15
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 80
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 75
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 77
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 50
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 69
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 15
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 75
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 77
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 15
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 80
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 0
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 50
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 15
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 75
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 77
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 75
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 15
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 75
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 0
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 50
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 75
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 0
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 15
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 77
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 75
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 69
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 15
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 15
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 75
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 50
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 15
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 69
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 77
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 0
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 69
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 15
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 80
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 69
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 80
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 15
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 75
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 69
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 15
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 69
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 77
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 15
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 15
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 0
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 75
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 75
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 50
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 69
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 75
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 15
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 75
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 50
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 75
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 50
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 50
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 77
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 80
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 15
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 15
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 15
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 50
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 15
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 77
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 80
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 15
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 0
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 80
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 15
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 77
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 69
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 80
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 15
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 75
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 75
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 80
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 50
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 0
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 15
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 0
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 80
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 75
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 15
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 15
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 0
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 69
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 80
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 15
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 77
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 15
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 50
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 50
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 0
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 0
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 50
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 69
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 15
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 15
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 0
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 80
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 77
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 50
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 50
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 50
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 80
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 75
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 15
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 50
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 50
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 15
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 0
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 75
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 69
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 15
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 15
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 15
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 69
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 0
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 15
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 50
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 15
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 77
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 50
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 15
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 15
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 0
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 15
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 0
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 75
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 15
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 50
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 77
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 15
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 75
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 0
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 80
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 15
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 50
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 15
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 77
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 69
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 50
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 15
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 15
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 75
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 50
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 75
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 50
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 50
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 77
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 50
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 77
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 50
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 77
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 15
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 50
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 75
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 69
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 50
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 15
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 50
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 15
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 75
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 0
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 15
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 77
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 77
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 15
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 15
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 15
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 15
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 0
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 75
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 69
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 50
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 15
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 80
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 80
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 0
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 75
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 15
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 15
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 0
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 15
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 75
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 15
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 77
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 75
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 80
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 77
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 80
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 50
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 69
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 50
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 15
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 15
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 15
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 77
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 0
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 75
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 0
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 69
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 15
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 15
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 15
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 0
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 0
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 15
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 0
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 15
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 75
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 0
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 15
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 15
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 77
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 80
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 15
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 0
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 15
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 15
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 69
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 15
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 80
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 69
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 50
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 15
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 15
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 77
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 69
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 77
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 77
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 15
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 15
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 15
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 0
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 50
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 15
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 15
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 80
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 69
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 0
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 15
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 77
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 50
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 15
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 75
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 15
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 50
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 69
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 69
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 0
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 77
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 75
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 15
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 15
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 15
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 15
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 80
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 75
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 80
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 69
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 77
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 50
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 15
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 15
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 69
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 77
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 77
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 15
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 77
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 15
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 75
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 0
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 75
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 15
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 15
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 75
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 69
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 50
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 80
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 50
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 75
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 77
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 80
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 50
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 15
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 69
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 15
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 69
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 80
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 50
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 50
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 15
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 69
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 75
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 0
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 0
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 77
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 15
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 0
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 75
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 15
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 50
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 77
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 80
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 75
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 75
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 80
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 80
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 15
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 15
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 77
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 75
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 50
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 80
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 77
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 77
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 69
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 69
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 77
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 69
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 15
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 15
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 15
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 15
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 69
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 15
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 80
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 50
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 50
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 50
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 80
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 75
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 69
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 15
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 50
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 15
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 50
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 50
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 0
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 50
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 80
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 50
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 15
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 69
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 15
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 80
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 15
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 69
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 69
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 69
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 69
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 77
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 75
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 15
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 0
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 15
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 50
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 15
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 77
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 69
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 50
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 15
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 0
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 15
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 15
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 69
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 75
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 15
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 50
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 15
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 77
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 69
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 80
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 77
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 80
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 80
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 15
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 69
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 75
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 15
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 15
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 75
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 77
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 75
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 50
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 0
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 0
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 69
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 15
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 50
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 75
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 77
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 69
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 80
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 15
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 15
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 15
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 77
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 50
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 75
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 80
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 15
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 15
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 69
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 50
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 77
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 15
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 15
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 80
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 15
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 75
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 15
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 50
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 75
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 0
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 50
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 77
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 80
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 0
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 15
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 69
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 77
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 50
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 50
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 15
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 0
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 69
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 50
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 15
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 80
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 80
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 77
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 15
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 50
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 0
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 77
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 77
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 69
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 69
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 77
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 15
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 80
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 0
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 50
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 0
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 0
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 15
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 77
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 77
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 80
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 15
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 15
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 0
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 15
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 15
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 75
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 0
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 0
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 50
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 75
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 0
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 77
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 15
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 15
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 50
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 80
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 50
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 15
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 0
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 50
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 15
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 69
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 15
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 15
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 15
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 15
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 0
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 15
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 75
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 50
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 50
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 80
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 75
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 80
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 77
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 80
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 75
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 15
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 15
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 50
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 15
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 15
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 77
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 69
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 0
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 0
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 15
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 75
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 0
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 15
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 80
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 0
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 50
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 15
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 80
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 15
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 75
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 69
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 0
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 0
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 69
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 15
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 75
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 15
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 77
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 77
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 15
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 80
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 15
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 0
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 75
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 80
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 15
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 50
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 50
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 50
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 15
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 0
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 15
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 77
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 15
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 75
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 15
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 0
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 77
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 15
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 75
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 75
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 77
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 50
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 50
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 50
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 75
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 69
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 69
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 15
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 50
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 15
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 80
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 75
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 69
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 75
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 80
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 0
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 15
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 50
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 80
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 80
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 0
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 15
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 50
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 15
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 15
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 50
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 50
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 80
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 77
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 15
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 50
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 15
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 0
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 15
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 80
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 75
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 50
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 15
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 0
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 77
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 15
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 69
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 80
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 15
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 15
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 77
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 69
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 50
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 0
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 0
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 15
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 15
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 50
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 15
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 15
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 15
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 50
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 80
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 69
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 0
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 50
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 50
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 80
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 15
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 15
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 75
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 50
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 75
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 0
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 15
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 69
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 80
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 50
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 15
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 50
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 50
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 50
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 15
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 69
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 50
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 15
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 15
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 77
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 77
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 50
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 75
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 69
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 77
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 0
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 69
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 50
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 75
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 80
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 15
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 50
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 50
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 75
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 0
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 15
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 15
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 77
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 15
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 77
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 0
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 77
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 50
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 77
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 75
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 75
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 0
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 50
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 50
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 15
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 15
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 15
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 15
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 50
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 0
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 0
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 77
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 15
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 69
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 15
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 50
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 50
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 75
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 77
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 15
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 69
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 69
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 69
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 80
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 0
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 15
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 75
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 0
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 50
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 77
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 75
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 77
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 75
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 80
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 15
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 50
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 15
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 15
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 15
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 69
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 0
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 80
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 75
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 69
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 15
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 0
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 69
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 0
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 77
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 75
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 50
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 75
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 80
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 50
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 69
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 69
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 77
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 69
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 80
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 15
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 75
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 50
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 15
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 50
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 75
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 15
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 77
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 50
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 75
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 15
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 77
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 69
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 69
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 0
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 15
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 77
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 50
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 15
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 69
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 69
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 80
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 50
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 50
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 0
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 69
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 77
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 50
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 80
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 50
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 15
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 69
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 50
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 77
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 77
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 80
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 15
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 77
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 15
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 75
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 15
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 77
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 75
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 75
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 0
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 50
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 15
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 15
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 15
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 15
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 15
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 69
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 15
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 80
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 75
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 15
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 77
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 75
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 50
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 0
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 50
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 15
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 50
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 75
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 69
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 75
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 15
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 69
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 50
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 15
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 80
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 50
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 15
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 15
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 69
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 77
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 77
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 69
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 69
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 15
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 69
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 15
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 15
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 80
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 75
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 80
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 15
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 15
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 77
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 77
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 80
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 15
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 80
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 15
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 77
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 15
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 15
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 15
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 15
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 75
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 69
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 69
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 77
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 75
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 15
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 0
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 75
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 80
empirical probabilities from test set: {15: 0.288, 69: 0.112, 80: 0.108, 75: 0.116, 77: 0.107, 50: 0.163, 0: 0.106}
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  0.025 

learned probs for this beta: {15: np.float64(0.13197090327531058), 69: np.float64(0.14467151612078177), 80: np.float64(0.14467151612078177), 75: np.float64(0.14467151612078177), 77: np.float64(0.14467151612078177), 50: np.float64(0.14467151612078177), 0: np.float64(0.14467151612078177)}
err dic= {15: np.float64(0.1560290967246894), 69: np.float64(0.03267151612078177), 80: np.float64(0.036671516120781775), 75: np.float64(0.028671516120781768), 77: np.float64(0.037671516120781776), 50: np.float64(0.018328483879218233), 0: np.float64(0.038671516120781776)} 

err list= [np.float64(0.1560290967246894), np.float64(0.03267151612078177), np.float64(0.036671516120781775), np.float64(0.028671516120781768), np.float64(0.037671516120781776), np.float64(0.018328483879218233), np.float64(0.038671516120781776)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  0.05 

learned probs for this beta: {15: np.float64(0.14285714285714377), 69: np.float64(0.14285714285714377), 80: np.float64(0.14285714285714377), 75: np.float64(0.14285714285714377), 77: np.float64(0.14285714285714377), 50: np.float64(0.14285714285714377), 0: np.float64(0.14285714285714377)}
err dic= {15: np.float64(0.1451428571428562), 69: np.float64(0.030857142857143763), 80: np.float64(0.034857142857143766), 75: np.float64(0.02685714285714376), 77: np.float64(0.03585714285714377), 50: np.float64(0.02014285714285624), 0: np.float64(0.03685714285714377)} 

err list= [np.float64(0.1451428571428562), np.float64(0.030857142857143763), np.float64(0.034857142857143766), np.float64(0.02685714285714376), np.float64(0.03585714285714377), np.float64(0.02014285714285624), np.float64(0.03685714285714377)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  0.1 

learned probs for this beta: {15: np.float64(0.14285714285714296), 69: np.float64(0.14285714285714296), 80: np.float64(0.14285714285714296), 75: np.float64(0.14285714285714296), 77: np.float64(0.14285714285714296), 50: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
err dic= {15: np.float64(0.14514285714285702), 69: np.float64(0.030857142857142958), 80: np.float64(0.03485714285714296), 75: np.float64(0.026857142857142954), 77: np.float64(0.03585714285714296), 50: np.float64(0.020142857142857046), 0: np.float64(0.03685714285714296)} 

err list= [np.float64(0.14514285714285702), np.float64(0.030857142857142958), np.float64(0.03485714285714296), np.float64(0.026857142857142954), np.float64(0.03585714285714296), np.float64(0.020142857142857046), np.float64(0.03685714285714296)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  0.25 

learned probs for this beta: {15: np.float64(0.14285714285714263), 69: np.float64(0.14285714285714263), 80: np.float64(0.14285714285714263), 75: np.float64(0.14285714285714263), 77: np.float64(0.14285714285714263), 50: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
err dic= {15: np.float64(0.14514285714285735), 69: np.float64(0.030857142857142625), 80: np.float64(0.03485714285714263), 75: np.float64(0.02685714285714262), 77: np.float64(0.03585714285714263), 50: np.float64(0.02014285714285738), 0: np.float64(0.03685714285714263)} 

err list= [np.float64(0.14514285714285735), np.float64(0.030857142857142625), np.float64(0.03485714285714263), np.float64(0.02685714285714262), np.float64(0.03585714285714263), np.float64(0.02014285714285738), np.float64(0.03685714285714263)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  0.5 

learned probs for this beta: {15: np.float64(0.1428571428571428), 69: np.float64(0.1428571428571428), 80: np.float64(0.1428571428571428), 75: np.float64(0.1428571428571428), 77: np.float64(0.1428571428571428), 50: np.float64(0.1428571428571428), 0: np.float64(0.1428571428571428)}
err dic= {15: np.float64(0.14514285714285718), 69: np.float64(0.03085714285714279), 80: np.float64(0.034857142857142795), 75: np.float64(0.026857142857142788), 77: np.float64(0.035857142857142796), 50: np.float64(0.020142857142857212), 0: np.float64(0.0368571428571428)} 

err list= [np.float64(0.14514285714285718), np.float64(0.03085714285714279), np.float64(0.034857142857142795), np.float64(0.026857142857142788), np.float64(0.035857142857142796), np.float64(0.020142857142857212), np.float64(0.0368571428571428)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  0.75 

learned probs for this beta: {15: np.float64(0.7530830451837217), 69: np.float64(0.04115282580271308), 80: np.float64(0.04115282580271308), 75: np.float64(0.04115282580271308), 77: np.float64(0.04115282580271308), 50: np.float64(0.04115282580271308), 0: np.float64(0.04115282580271308)}
err dic= {15: np.float64(0.46508304518372173), 69: np.float64(0.07084717419728692), 80: np.float64(0.06684717419728692), 75: np.float64(0.07484717419728693), 77: np.float64(0.06584717419728692), 50: np.float64(0.12184717419728693), 0: np.float64(0.06484717419728692)} 

err list= [np.float64(0.46508304518372173), np.float64(0.07084717419728692), np.float64(0.06684717419728692), np.float64(0.07484717419728693), np.float64(0.06584717419728692), np.float64(0.12184717419728693), np.float64(0.06484717419728692)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  1 

learned probs for this beta: {15: np.float64(0.14285714285714285), 69: np.float64(0.14285714285714285), 80: np.float64(0.14285714285714285), 75: np.float64(0.14285714285714285), 77: np.float64(0.14285714285714285), 50: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {15: np.float64(0.14514285714285713), 69: np.float64(0.030857142857142847), 80: np.float64(0.03485714285714285), 75: np.float64(0.026857142857142843), 77: np.float64(0.03585714285714285), 50: np.float64(0.020142857142857157), 0: np.float64(0.03685714285714285)} 

err list= [np.float64(0.14514285714285713), np.float64(0.030857142857142847), np.float64(0.03485714285714285), np.float64(0.026857142857142843), np.float64(0.03585714285714285), np.float64(0.020142857142857157), np.float64(0.03685714285714285)]
results for assortment [15, 69, 80, 75, 77, 50] :

beta is  1.25 

learned probs for this beta: {15: np.float64(0.14285714285714285), 69: np.float64(0.14285714285714285), 80: np.float64(0.14285714285714285), 75: np.float64(0.14285714285714285), 77: np.float64(0.14285714285714285), 50: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {15: np.float64(0.14514285714285713), 69: np.float64(0.030857142857142847), 80: np.float64(0.03485714285714285), 75: np.float64(0.026857142857142843), 77: np.float64(0.03585714285714285), 50: np.float64(0.020142857142857157), 0: np.float64(0.03685714285714285)} 

err list= [np.float64(0.14514285714285713), np.float64(0.030857142857142847), np.float64(0.03485714285714285), np.float64(0.026857142857142843), np.float64(0.03585714285714285), np.float64(0.020142857142857157), np.float64(0.03685714285714285)]
results for assortment [15, 69, 80, 75, 77, 50] :

err MNL dic= {15: np.float64(0.15124978879188958), 69: 0, 80: 0, 75: 0, 77: 0, 50: 0, 0: 0} 

err MNL list= [np.float64(0.15124978879188958), 0, 0, 0, 0, 0, 0]
err MNL dic= {15: np.float64(0.15124978879188958), 69: np.float64(0.003854688820050703), 80: 0, 75: 0, 77: 0, 50: 0, 0: 0} 

err MNL list= [np.float64(0.15124978879188958), np.float64(0.003854688820050703), 0, 0, 0, 0, 0]
err MNL dic= {15: np.float64(0.15124978879188958), 69: np.float64(0.003854688820050703), 80: np.float64(0.00926274288932695), 75: 0, 77: 0, 50: 0, 0: 0} 

err MNL list= [np.float64(0.15124978879188958), np.float64(0.003854688820050703), np.float64(0.00926274288932695), 0, 0, 0, 0]
err MNL dic= {15: np.float64(0.15124978879188958), 69: np.float64(0.003854688820050703), 80: np.float64(0.00926274288932695), 75: np.float64(0.0015533652492255579), 77: 0, 50: 0, 0: 0} 

err MNL list= [np.float64(0.15124978879188958), np.float64(0.003854688820050703), np.float64(0.00926274288932695), np.float64(0.0015533652492255579), 0, 0, 0]
err MNL dic= {15: np.float64(0.15124978879188958), 69: np.float64(0.003854688820050703), 80: np.float64(0.00926274288932695), 75: np.float64(0.0015533652492255579), 77: np.float64(0.006996057448606027), 50: 0, 0: 0} 

err MNL list= [np.float64(0.15124978879188958), np.float64(0.003854688820050703), np.float64(0.00926274288932695), np.float64(0.0015533652492255579), np.float64(0.006996057448606027), 0, 0]
err MNL dic= {15: np.float64(0.15124978879188958), 69: np.float64(0.003854688820050703), 80: np.float64(0.00926274288932695), 75: np.float64(0.0015533652492255579), 77: np.float64(0.006996057448606027), 50: np.float64(0.042921148972120515), 0: 0} 

err MNL list= [np.float64(0.15124978879188958), np.float64(0.003854688820050703), np.float64(0.00926274288932695), np.float64(0.0015533652492255579), np.float64(0.006996057448606027), np.float64(0.042921148972120515), 0]
err MNL dic= {15: np.float64(0.15124978879188958), 69: np.float64(0.003854688820050703), 80: np.float64(0.00926274288932695), 75: np.float64(0.0015533652492255579), 77: np.float64(0.006996057448606027), 50: np.float64(0.042921148972120515), 0: np.float64(0.17561081385525207)} 

err MNL list= [np.float64(0.15124978879188958), np.float64(0.003854688820050703), np.float64(0.00926274288932695), np.float64(0.0015533652492255579), np.float64(0.006996057448606027), np.float64(0.042921148972120515), np.float64(0.17561081385525207)]
sampled assortment [18, 89, 79, 92, 61, 20]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 10, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 14, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 20: 2, 100: 1} [8, 1, 3, 5, 6, 7, 100, 20]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 5, 11, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 2, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 3, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 8: 0, 10: 1, 13: 1, 17: 2, 100: 1} [8, 1, 3, 6, 10, 13, 100, 4, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 18
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 0
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 18
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 20
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 61
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 61
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 92
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 20
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 20
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 20
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 18
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 18
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 89
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 92
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 79
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 18
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 89
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 79
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 18
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 18
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 61
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 20
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 79
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 79
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 20
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 20
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 18
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 92
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 18
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 18
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 20
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 89
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 92
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 20
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 92
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 0
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 18
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 18
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 79
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 18
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 18
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 79
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 18
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 18
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 18
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 18
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 18
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 18
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 18
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 0
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 18
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 18
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 92
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 18
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 92
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 89
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 0
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 0
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 18
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 20
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 92
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 18
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 20
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 18
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 89
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 79
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 0
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 20
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 79
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 20
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 20
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 61
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 79
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 92
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 20
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 61
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 20
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 0
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 18
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 20
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 92
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 92
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 20
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 18
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 20
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 18
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 0
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 61
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 61
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 89
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 18
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 20
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 18
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 61
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 0
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 20
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 20
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 89
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 0
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 20
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 18
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 92
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 18
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 89
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 20
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 18
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 18
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 92
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 61
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 20
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 79
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 18
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 20
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 18
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 20
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 18
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 61
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 61
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 18
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 79
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 20
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 92
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 0
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 18
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 0
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 92
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 20
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 18
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 20
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 18
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 20
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 79
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 92
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 18
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 18
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 20
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 92
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 20
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 20
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 89
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 18
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 61
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 61
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 18
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 61
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 92
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 92
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 20
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 20
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 61
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 79
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 18
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 0
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 18
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 18
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 20
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 18
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 18
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 18
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 79
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 20
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 61
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 0
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 18
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 18
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 92
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 20
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 20
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 18
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 79
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 61
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 89
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 89
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 79
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 20
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 79
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 79
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 18
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 61
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 20
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 18
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 18
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 89
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 0
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 79
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 89
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 18
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 20
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 20
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 0
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 79
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 92
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 20
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 18
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 61
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 20
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 20
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 20
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 79
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 89
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 89
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 61
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 20
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 61
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 18
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 20
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 61
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 20
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 0
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 92
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 20
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 18
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 18
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 89
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 0
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 89
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 79
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 18
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 0
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 89
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 0
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 89
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 61
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 61
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 20
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 61
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 89
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 20
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 18
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 89
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 20
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 0
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 92
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 0
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 20
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 20
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 61
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 18
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 20
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 61
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 92
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 92
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 0
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 89
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 89
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 20
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 61
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 89
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 20
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 20
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 20
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 79
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 20
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 89
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 18
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 20
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 61
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 20
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 89
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 18
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 61
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 18
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 18
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 79
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 20
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 89
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 61
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 89
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 18
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 18
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 89
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 61
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 20
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 89
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 18
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 18
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 18
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 18
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 92
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 79
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 61
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 20
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 0
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 61
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 18
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 20
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 18
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 0
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 18
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 18
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 20
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 20
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 18
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 0
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 0
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 18
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 89
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 20
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 18
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 92
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 18
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 20
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 61
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 20
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 92
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 89
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 61
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 61
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 18
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 18
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 18
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 20
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 20
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 79
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 20
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 92
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 89
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 20
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 61
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 79
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 20
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 18
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 79
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 20
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 92
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 18
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 79
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 0
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 20
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 89
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 18
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 20
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 92
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 61
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 18
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 79
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 18
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 20
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 0
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 0
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 61
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 92
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 18
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 20
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 92
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 20
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 0
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 18
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 18
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 61
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 61
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 92
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 89
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 79
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 79
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 18
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 18
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 92
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 0
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 20
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 79
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 79
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 0
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 18
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 18
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 20
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 0
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 20
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 89
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 18
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 92
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 20
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 20
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 61
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 20
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 20
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 61
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 20
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 61
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 18
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 20
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 20
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 79
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 89
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 92
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 20
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 89
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 89
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 20
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 18
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 61
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 0
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 79
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 18
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 61
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 79
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 20
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 89
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 79
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 18
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 18
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 61
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 89
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 20
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 89
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 20
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 18
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 18
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 79
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 20
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 79
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 18
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 79
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 0
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 61
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 18
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 61
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 20
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 20
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 79
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 61
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 89
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 89
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 61
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 20
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 89
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 92
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 20
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 20
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 92
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 92
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 18
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 61
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 20
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 18
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 20
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 89
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 18
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 20
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 61
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 61
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 79
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 18
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 18
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 79
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 61
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 18
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 20
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 79
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 79
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 79
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 20
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 61
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 92
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 18
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 18
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 18
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 20
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 61
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 20
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 61
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 20
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 79
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 0
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 92
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 0
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 18
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 92
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 79
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 18
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 20
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 20
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 18
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 20
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 20
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 18
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 20
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 18
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 61
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 61
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 61
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 0
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 89
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 61
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 18
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 18
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 61
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 79
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 61
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 20
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 20
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 20
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 20
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 61
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 61
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 61
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 61
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 20
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 92
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 18
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 0
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 20
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 61
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 20
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 20
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 61
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 92
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 18
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 0
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 18
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 79
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 79
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 20
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 20
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 18
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 20
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 20
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 89
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 79
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 79
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 92
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 89
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 20
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 61
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 18
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 20
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 20
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 61
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 20
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 79
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 61
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 61
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 79
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 20
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 92
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 20
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 18
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 20
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 20
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 89
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 18
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 79
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 20
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 20
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 18
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 92
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 92
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 20
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 0
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 79
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 0
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 61
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 18
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 79
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 61
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 20
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 18
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 61
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 20
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 18
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 89
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 89
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 0
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 20
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 20
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 89
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 18
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 20
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 18
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 79
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 20
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 18
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 61
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 89
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 20
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 61
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 18
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 18
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 61
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 20
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 20
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 79
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 20
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 92
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 61
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 92
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 89
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 18
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 89
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 92
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 18
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 89
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 79
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 18
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 79
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 18
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 89
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 89
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 20
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 18
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 61
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 61
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 89
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 20
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 18
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 79
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 61
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 20
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 0
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 20
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 18
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 79
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 18
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 92
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 18
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 20
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 89
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 61
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 20
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 89
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 79
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 18
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 79
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 18
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 79
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 20
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 0
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 0
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 89
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 89
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 61
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 79
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 0
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 79
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 92
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 20
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 79
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 20
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 18
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 61
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 92
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 61
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 18
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 61
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 79
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 79
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 79
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 18
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 20
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 89
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 18
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 20
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 0
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 18
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 20
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 20
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 89
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 79
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 18
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 20
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 18
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 79
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 20
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 18
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 18
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 0
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 18
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 18
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 0
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 20
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 89
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 20
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 18
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 0
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 20
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 61
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 18
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 89
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 18
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 20
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 20
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 18
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 79
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 20
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 20
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 61
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 79
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 18
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 18
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 89
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 79
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 61
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 79
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 18
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 20
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 20
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 61
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 0
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 79
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 79
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 0
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 79
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 79
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 0
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 20
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 18
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 18
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 18
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 89
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 0
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 20
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 89
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 18
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 92
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 79
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 0
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 79
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 18
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 18
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 0
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 20
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 61
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 61
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 20
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 61
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 79
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 18
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 61
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 18
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 79
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 18
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 61
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 20
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 18
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 89
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 20
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 18
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 0
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 89
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 20
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 92
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 61
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 0
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 92
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 61
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 20
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 89
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 92
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 18
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 61
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 92
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 20
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 0
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 18
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 20
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 20
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 20
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 61
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 18
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 79
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 20
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 20
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 20
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 0
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 18
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 61
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 92
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 18
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 92
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 18
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 18
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 18
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 18
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 92
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 20
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 92
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 0
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 18
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 79
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 20
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 89
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 61
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 18
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 20
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 61
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 18
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 92
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 92
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 18
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 89
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 61
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 20
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 79
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 79
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 61
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 18
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 20
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 20
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 92
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 61
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 20
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 18
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 0
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 61
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 89
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 0
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 20
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 92
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 20
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 20
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 18
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 18
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 18
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 18
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 18
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 61
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 20
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 20
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 61
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 20
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 20
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 0
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 92
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 20
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 20
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 61
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 18
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 61
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 18
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 20
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 89
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 92
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 18
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 18
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 18
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 20
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 89
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 61
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 18
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 18
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 0
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 61
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 20
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 0
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 89
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 20
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 20
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 61
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 89
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 20
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 61
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 92
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 89
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 18
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 92
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 18
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 18
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 20
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 18
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 20
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 92
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 0
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 18
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 89
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 20
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 20
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 18
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 18
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 79
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 79
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 20
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 61
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 18
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 18
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 18
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 0
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 61
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 20
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 89
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 18
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 79
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 20
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 61
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 92
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 92
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 18
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 18
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 61
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 20
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 18
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 20
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 18
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 18
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 89
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 89
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 18
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 61
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 61
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 92
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 20
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 20
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 0
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 18
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 61
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 89
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 92
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 20
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 20
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 61
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 79
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 20
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 20
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 0
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 20
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 92
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 20
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 20
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 18
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 79
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 89
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 20
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 18
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 61
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 61
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 92
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 61
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 61
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 20
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 18
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 20
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 18
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 0
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 18
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 92
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 79
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 18
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 61
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 20
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 20
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 18
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 20
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 18
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 18
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 18
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 92
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 20
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 89
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 79
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 0
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 79
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 18
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 61
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 61
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 92
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 89
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 20
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 20
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 89
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 18
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 20
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 18
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 20
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 18
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 92
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 0
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 0
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 18
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 20
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 18
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 20
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 18
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 18
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 18
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 61
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 61
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 18
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 92
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 20
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 79
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 18
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 18
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 18
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 20
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 18
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 18
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 20
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 20
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 18
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 20
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 79
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 20
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 20
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 20
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 61
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 92
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 79
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 18
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 0
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 18
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 20
empirical probabilities from test set: {18: 0.255, 89: 0.091, 79: 0.103, 92: 0.085, 61: 0.136, 20: 0.253, 0: 0.077}
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  0.025 

learned probs for this beta: {18: np.float64(0.14285714285714057), 89: np.float64(0.14285714285714057), 79: np.float64(0.14285714285714057), 92: np.float64(0.14285714285714057), 61: np.float64(0.14285714285714057), 20: np.float64(0.14285714285714057), 0: np.float64(0.14285714285714057)}
err dic= {18: np.float64(0.11214285714285943), 89: np.float64(0.051857142857140576), 79: np.float64(0.03985714285714058), 92: np.float64(0.05785714285714057), 61: np.float64(0.0068571428571405635), 20: np.float64(0.11014285714285943), 0: np.float64(0.06585714285714057)} 

err list= [np.float64(0.11214285714285943), np.float64(0.051857142857140576), np.float64(0.03985714285714058), np.float64(0.05785714285714057), np.float64(0.0068571428571405635), np.float64(0.11014285714285943), np.float64(0.06585714285714057)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  0.05 

learned probs for this beta: {18: np.float64(0.14285714285714377), 89: np.float64(0.14285714285714377), 79: np.float64(0.14285714285714377), 92: np.float64(0.14285714285714377), 61: np.float64(0.14285714285714377), 20: np.float64(0.14285714285714377), 0: np.float64(0.14285714285714377)}
err dic= {18: np.float64(0.11214285714285624), 89: np.float64(0.05185714285714377), 79: np.float64(0.03985714285714377), 92: np.float64(0.05785714285714376), 61: np.float64(0.006857142857143755), 20: np.float64(0.11014285714285624), 0: np.float64(0.06585714285714377)} 

err list= [np.float64(0.11214285714285624), np.float64(0.05185714285714377), np.float64(0.03985714285714377), np.float64(0.05785714285714376), np.float64(0.006857142857143755), np.float64(0.11014285714285624), np.float64(0.06585714285714377)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  0.1 

learned probs for this beta: {18: np.float64(0.1428571428571429), 89: np.float64(0.1428571428571429), 79: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 61: np.float64(0.1428571428571429), 20: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
err dic= {18: np.float64(0.1121428571428571), 89: np.float64(0.05185714285714291), 79: np.float64(0.03985714285714291), 92: np.float64(0.0578571428571429), 61: np.float64(0.006857142857142895), 20: np.float64(0.1101428571428571), 0: np.float64(0.0658571428571429)} 

err list= [np.float64(0.1121428571428571), np.float64(0.05185714285714291), np.float64(0.03985714285714291), np.float64(0.0578571428571429), np.float64(0.006857142857142895), np.float64(0.1101428571428571), np.float64(0.0658571428571429)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  0.25 

learned probs for this beta: {18: np.float64(0.14285714285714263), 89: np.float64(0.14285714285714263), 79: np.float64(0.14285714285714263), 92: np.float64(0.14285714285714263), 61: np.float64(0.14285714285714263), 20: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
err dic= {18: np.float64(0.11214285714285738), 89: np.float64(0.05185714285714263), 79: np.float64(0.03985714285714263), 92: np.float64(0.05785714285714262), 61: np.float64(0.006857142857142617), 20: np.float64(0.11014285714285738), 0: np.float64(0.06585714285714263)} 

err list= [np.float64(0.11214285714285738), np.float64(0.05185714285714263), np.float64(0.03985714285714263), np.float64(0.05785714285714262), np.float64(0.006857142857142617), np.float64(0.11014285714285738), np.float64(0.06585714285714263)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  0.5 

learned probs for this beta: {18: np.float64(0.14285714285714285), 89: np.float64(0.14285714285714285), 79: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 61: np.float64(0.14285714285714285), 20: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {18: np.float64(0.11214285714285716), 89: np.float64(0.05185714285714285), 79: np.float64(0.039857142857142855), 92: np.float64(0.05785714285714284), 61: np.float64(0.0068571428571428394), 20: np.float64(0.11014285714285715), 0: np.float64(0.06585714285714285)} 

err list= [np.float64(0.11214285714285716), np.float64(0.05185714285714285), np.float64(0.039857142857142855), np.float64(0.05785714285714284), np.float64(0.0068571428571428394), np.float64(0.11014285714285715), np.float64(0.06585714285714285)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  0.75 

learned probs for this beta: {18: np.float64(0.14285714285714285), 89: np.float64(0.14285714285714285), 79: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 61: np.float64(0.14285714285714285), 20: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {18: np.float64(0.11214285714285716), 89: np.float64(0.05185714285714285), 79: np.float64(0.039857142857142855), 92: np.float64(0.05785714285714284), 61: np.float64(0.0068571428571428394), 20: np.float64(0.11014285714285715), 0: np.float64(0.06585714285714285)} 

err list= [np.float64(0.11214285714285716), np.float64(0.05185714285714285), np.float64(0.039857142857142855), np.float64(0.05785714285714284), np.float64(0.0068571428571428394), np.float64(0.11014285714285715), np.float64(0.06585714285714285)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  1 

learned probs for this beta: {18: np.float64(0.14285714285714285), 89: np.float64(0.14285714285714285), 79: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 61: np.float64(0.14285714285714285), 20: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {18: np.float64(0.11214285714285716), 89: np.float64(0.05185714285714285), 79: np.float64(0.039857142857142855), 92: np.float64(0.05785714285714284), 61: np.float64(0.0068571428571428394), 20: np.float64(0.11014285714285715), 0: np.float64(0.06585714285714285)} 

err list= [np.float64(0.11214285714285716), np.float64(0.05185714285714285), np.float64(0.039857142857142855), np.float64(0.05785714285714284), np.float64(0.0068571428571428394), np.float64(0.11014285714285715), np.float64(0.06585714285714285)]
results for assortment [18, 89, 79, 92, 61, 20] :

beta is  1.25 

learned probs for this beta: {18: np.float64(0.14285714285714285), 89: np.float64(0.14285714285714285), 79: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 61: np.float64(0.14285714285714285), 20: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {18: np.float64(0.11214285714285716), 89: np.float64(0.05185714285714285), 79: np.float64(0.039857142857142855), 92: np.float64(0.05785714285714284), 61: np.float64(0.0068571428571428394), 20: np.float64(0.11014285714285715), 0: np.float64(0.06585714285714285)} 

err list= [np.float64(0.11214285714285716), np.float64(0.05185714285714285), np.float64(0.039857142857142855), np.float64(0.05785714285714284), np.float64(0.0068571428571428394), np.float64(0.11014285714285715), np.float64(0.06585714285714285)]
results for assortment [18, 89, 79, 92, 61, 20] :

err MNL dic= {18: np.float64(0.11936552716008406), 89: 0, 79: 0, 92: 0, 61: 0, 20: 0, 0: 0} 

err MNL list= [np.float64(0.11936552716008406), 0, 0, 0, 0, 0, 0]
err MNL dic= {18: np.float64(0.11936552716008406), 89: np.float64(0.021678393627613687), 79: 0, 92: 0, 61: 0, 20: 0, 0: 0} 

err MNL list= [np.float64(0.11936552716008406), np.float64(0.021678393627613687), 0, 0, 0, 0, 0]
err MNL dic= {18: np.float64(0.11936552716008406), 89: np.float64(0.021678393627613687), 79: np.float64(0.012886713131983626), 92: 0, 61: 0, 20: 0, 0: 0} 

err MNL list= [np.float64(0.11936552716008406), np.float64(0.021678393627613687), np.float64(0.012886713131983626), 0, 0, 0, 0]
err MNL dic= {18: np.float64(0.11936552716008406), 89: np.float64(0.021678393627613687), 79: np.float64(0.012886713131983626), 92: np.float64(0.028452815576944374), 61: 0, 20: 0, 0: 0} 

err MNL list= [np.float64(0.11936552716008406), np.float64(0.021678393627613687), np.float64(0.012886713131983626), np.float64(0.028452815576944374), 0, 0, 0]
err MNL dic= {18: np.float64(0.11936552716008406), 89: np.float64(0.021678393627613687), 79: np.float64(0.012886713131983626), 92: np.float64(0.028452815576944374), 61: np.float64(0.01917291735811484), 20: 0, 0: 0} 

err MNL list= [np.float64(0.11936552716008406), np.float64(0.021678393627613687), np.float64(0.012886713131983626), np.float64(0.028452815576944374), np.float64(0.01917291735811484), 0, 0]
err MNL dic= {18: np.float64(0.11936552716008406), 89: np.float64(0.021678393627613687), 79: np.float64(0.012886713131983626), 92: np.float64(0.028452815576944374), 61: np.float64(0.01917291735811484), 20: np.float64(0.12405874543644207), 0: 0} 

err MNL list= [np.float64(0.11936552716008406), np.float64(0.021678393627613687), np.float64(0.012886713131983626), np.float64(0.028452815576944374), np.float64(0.01917291735811484), np.float64(0.12405874543644207), 0]
err MNL dic= {18: np.float64(0.11936552716008406), 89: np.float64(0.021678393627613687), 79: np.float64(0.012886713131983626), 92: np.float64(0.028452815576944374), 61: np.float64(0.01917291735811484), 20: np.float64(0.12405874543644207), 0: np.float64(0.19957926761809935)} 

err MNL list= [np.float64(0.11936552716008406), np.float64(0.021678393627613687), np.float64(0.012886713131983626), np.float64(0.028452815576944374), np.float64(0.01917291735811484), np.float64(0.12405874543644207), np.float64(0.19957926761809935)]
sampled assortment [91, 42, 10, 22, 61, 40]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 9, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 17: 4, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 14, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 14: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 14, 15, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 11: 2, 17: 2, 100: 1} [8, 1, 3, 6, 7, 100, 4, 11, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 17: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 15]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 11, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 10, 12, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 61
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 22
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 42
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 10
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 10
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 22
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 91
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 42
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 91
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 91
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 42
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 10
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 10
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 40
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 91
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 22
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 42
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 42
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 22
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 10
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 91
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 10
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 10
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 40
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 40
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 10
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 22
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 10
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 40
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 10
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 10
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 61
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 40
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 10
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 42
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 0
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 42
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 0
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 10
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 42
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 22
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 10
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 40
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 0
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 10
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 40
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 10
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 22
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 40
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 0
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 10
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 22
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 42
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 0
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 61
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 42
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 22
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 0
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 10
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 10
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 40
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 91
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 0
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 61
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 22
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 10
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 22
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 22
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 22
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 10
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 10
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 61
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 22
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 22
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 42
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 40
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 10
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 22
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 61
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 61
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 22
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 10
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 61
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 91
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 10
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 0
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 40
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 61
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 61
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 42
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 40
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 10
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 22
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 22
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 91
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 22
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 61
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 61
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 10
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 10
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 10
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 91
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 40
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 10
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 10
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 42
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 22
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 22
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 22
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 42
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 10
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 10
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 42
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 22
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 42
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 40
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 10
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 61
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 22
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 40
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 10
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 61
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 42
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 40
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 91
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 91
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 91
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 10
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 0
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 10
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 91
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 22
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 42
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 22
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 10
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 10
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 42
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 0
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 61
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 91
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 91
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 42
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 61
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 22
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 22
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 91
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 40
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 0
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 91
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 61
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 10
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 91
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 61
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 91
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 0
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 42
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 42
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 10
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 10
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 10
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 61
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 61
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 42
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 42
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 40
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 40
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 91
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 10
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 91
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 61
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 42
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 10
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 91
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 22
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 40
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 61
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 10
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 22
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 40
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 40
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 91
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 0
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 22
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 91
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 61
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 10
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 10
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 22
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 10
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 10
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 10
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 10
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 0
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 10
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 22
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 10
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 10
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 91
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 10
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 0
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 22
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 42
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 0
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 22
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 10
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 40
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 61
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 42
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 61
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 10
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 42
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 10
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 10
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 22
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 91
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 22
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 10
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 40
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 0
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 22
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 22
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 40
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 10
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 61
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 22
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 61
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 22
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 10
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 10
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 40
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 10
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 10
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 10
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 22
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 10
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 61
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 0
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 42
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 91
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 61
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 10
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 10
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 91
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 10
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 22
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 40
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 10
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 42
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 10
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 22
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 0
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 22
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 22
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 22
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 10
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 40
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 61
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 22
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 91
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 22
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 0
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 61
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 42
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 22
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 22
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 40
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 91
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 22
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 10
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 61
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 42
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 91
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 22
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 0
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 10
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 22
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 10
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 42
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 40
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 10
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 61
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 22
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 91
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 42
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 91
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 40
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 10
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 61
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 91
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 0
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 91
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 22
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 10
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 10
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 0
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 42
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 10
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 22
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 40
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 22
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 10
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 40
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 61
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 40
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 10
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 91
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 61
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 61
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 10
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 10
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 10
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 22
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 40
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 10
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 10
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 42
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 61
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 42
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 22
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 42
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 61
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 10
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 22
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 91
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 10
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 10
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 22
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 40
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 10
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 91
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 10
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 42
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 91
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 10
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 22
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 10
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 91
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 10
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 22
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 10
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 22
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 10
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 22
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 10
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 10
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 40
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 42
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 10
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 40
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 22
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 91
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 0
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 10
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 10
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 0
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 40
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 91
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 10
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 10
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 22
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 91
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 22
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 10
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 10
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 10
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 10
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 42
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 61
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 0
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 10
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 10
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 10
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 40
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 42
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 40
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 40
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 40
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 40
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 22
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 42
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 42
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 10
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 10
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 42
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 10
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 61
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 22
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 10
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 10
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 40
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 10
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 22
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 91
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 91
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 22
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 10
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 91
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 22
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 91
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 61
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 22
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 40
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 10
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 40
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 10
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 22
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 91
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 10
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 40
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 22
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 61
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 10
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 42
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 42
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 10
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 0
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 91
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 61
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 10
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 22
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 22
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 22
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 42
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 22
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 10
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 10
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 10
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 10
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 10
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 22
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 10
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 10
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 61
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 22
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 22
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 61
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 10
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 40
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 0
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 42
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 22
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 42
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 61
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 22
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 10
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 22
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 42
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 40
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 22
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 42
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 91
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 40
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 42
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 22
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 40
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 42
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 40
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 40
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 10
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 40
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 61
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 10
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 42
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 10
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 42
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 10
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 0
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 61
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 22
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 10
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 42
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 22
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 10
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 10
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 42
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 0
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 42
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 22
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 42
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 61
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 0
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 42
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 22
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 22
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 22
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 10
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 22
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 10
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 40
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 61
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 42
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 10
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 61
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 0
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 61
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 22
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 22
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 10
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 10
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 42
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 10
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 40
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 10
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 22
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 40
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 61
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 10
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 10
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 91
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 42
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 91
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 42
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 10
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 61
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 10
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 61
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 22
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 42
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 91
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 22
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 40
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 91
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 22
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 40
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 0
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 91
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 10
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 61
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 10
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 10
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 22
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 42
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 42
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 40
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 22
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 10
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 42
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 10
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 91
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 0
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 0
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 0
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 22
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 40
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 10
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 10
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 10
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 0
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 42
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 10
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 42
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 42
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 10
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 10
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 10
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 22
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 22
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 40
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 10
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 10
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 40
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 10
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 42
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 0
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 91
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 10
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 22
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 0
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 91
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 42
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 0
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 40
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 61
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 22
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 22
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 10
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 91
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 0
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 22
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 42
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 40
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 10
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 22
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 22
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 10
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 91
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 22
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 10
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 22
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 0
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 91
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 22
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 40
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 42
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 10
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 10
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 61
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 61
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 22
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 10
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 22
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 40
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 10
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 61
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 91
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 42
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 61
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 22
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 10
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 22
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 40
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 22
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 40
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 10
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 40
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 40
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 10
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 22
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 10
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 22
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 22
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 22
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 22
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 22
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 10
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 40
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 61
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 61
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 22
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 61
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 91
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 10
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 22
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 40
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 22
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 10
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 22
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 91
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 22
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 61
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 42
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 22
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 91
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 42
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 91
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 10
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 42
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 42
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 10
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 22
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 42
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 22
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 22
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 22
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 61
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 10
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 22
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 22
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 10
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 10
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 0
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 42
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 10
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 40
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 22
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 22
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 42
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 10
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 22
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 10
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 22
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 0
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 10
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 10
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 10
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 22
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 22
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 10
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 40
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 10
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 22
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 22
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 10
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 22
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 0
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 61
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 40
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 40
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 10
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 40
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 10
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 61
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 0
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 10
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 42
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 10
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 61
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 22
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 10
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 10
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 61
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 42
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 22
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 22
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 42
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 0
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 40
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 40
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 0
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 22
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 42
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 42
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 40
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 91
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 10
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 42
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 10
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 22
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 40
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 10
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 10
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 22
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 22
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 91
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 40
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 10
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 42
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 10
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 61
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 91
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 61
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 61
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 61
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 42
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 22
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 10
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 10
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 42
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 10
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 91
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 91
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 10
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 10
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 22
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 61
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 91
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 10
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 22
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 61
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 61
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 0
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 61
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 91
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 22
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 40
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 10
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 10
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 22
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 10
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 42
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 10
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 22
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 10
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 10
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 22
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 22
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 40
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 10
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 0
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 0
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 10
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 61
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 91
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 22
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 22
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 22
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 40
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 22
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 22
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 22
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 22
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 61
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 40
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 40
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 22
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 40
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 10
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 10
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 10
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 22
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 91
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 91
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 10
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 10
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 61
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 10
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 91
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 0
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 42
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 10
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 10
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 22
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 22
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 40
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 22
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 22
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 10
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 61
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 22
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 22
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 40
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 22
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 42
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 10
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 0
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 42
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 42
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 61
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 61
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 40
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 22
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 10
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 22
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 0
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 40
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 42
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 91
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 10
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 22
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 22
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 22
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 22
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 42
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 42
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 10
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 40
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 10
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 22
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 91
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 40
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 10
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 61
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 22
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 42
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 0
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 10
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 22
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 42
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 91
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 22
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 40
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 22
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 22
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 42
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 10
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 91
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 61
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 40
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 10
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 10
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 91
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 22
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 10
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 22
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 22
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 40
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 0
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 22
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 40
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 22
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 0
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 61
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 61
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 22
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 10
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 10
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 10
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 42
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 0
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 91
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 40
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 61
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 22
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 22
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 22
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 0
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 61
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 42
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 40
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 10
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 22
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 42
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 61
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 40
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 10
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 40
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 10
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 61
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 10
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 91
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 10
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 10
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 10
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 10
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 10
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 10
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 61
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 10
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 61
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 42
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 0
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 42
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 10
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 10
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 91
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 42
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 22
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 10
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 22
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 10
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 40
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 40
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 10
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 22
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 10
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 22
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 61
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 0
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 10
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 10
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 10
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 10
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 61
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 0
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 40
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 22
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 40
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 40
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 10
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 40
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 10
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 22
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 10
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 10
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 22
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 42
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 91
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 61
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 42
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 42
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 22
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 22
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 61
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 10
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 10
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 0
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 42
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 10
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 42
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 10
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 42
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 10
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 91
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 10
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 22
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 40
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 10
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 40
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 61
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 10
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 22
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 10
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 22
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 10
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 10
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 22
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 40
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 10
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 10
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 40
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 22
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 10
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 40
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 61
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 10
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 10
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 61
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 10
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 10
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 22
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 61
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 22
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 91
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 40
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 10
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 40
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 40
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 42
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 22
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 10
empirical probabilities from test set: {91: 0.088, 42: 0.117, 10: 0.292, 22: 0.219, 61: 0.103, 40: 0.118, 0: 0.063}
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  0.025 

learned probs for this beta: {91: np.float64(0.144812954157168), 42: np.float64(0.144812954157168), 10: np.float64(0.1311222750569942), 22: np.float64(0.144812954157168), 61: np.float64(0.144812954157168), 40: np.float64(0.144812954157168), 0: np.float64(0.144812954157168)}
err dic= {91: np.float64(0.056812954157168), 42: np.float64(0.027812954157167988), 10: np.float64(0.16087772494300578), 22: np.float64(0.074187045842832), 61: np.float64(0.041812954157168), 40: np.float64(0.026812954157168), 0: np.float64(0.081812954157168)} 

err list= [np.float64(0.056812954157168), np.float64(0.027812954157167988), np.float64(0.16087772494300578), np.float64(0.074187045842832), np.float64(0.041812954157168), np.float64(0.026812954157168), np.float64(0.081812954157168)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  0.05 

learned probs for this beta: {91: np.float64(0.14304617955291934), 42: np.float64(0.14304617955291934), 10: np.float64(0.14172292268249215), 22: np.float64(0.14304617955291934), 61: np.float64(0.14304617955291934), 40: np.float64(0.14304617955291934), 0: np.float64(0.14304617955291934)}
err dic= {91: np.float64(0.05504617955291935), 42: np.float64(0.026046179552919338), 10: np.float64(0.15027707731750783), 22: np.float64(0.07595382044708066), 61: np.float64(0.04004617955291935), 40: np.float64(0.02504617955291935), 0: np.float64(0.08004617955291934)} 

err list= [np.float64(0.05504617955291935), np.float64(0.026046179552919338), np.float64(0.15027707731750783), np.float64(0.07595382044708066), np.float64(0.04004617955291935), np.float64(0.02504617955291935), np.float64(0.08004617955291934)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  0.1 

learned probs for this beta: {91: np.float64(0.13742033871841092), 42: np.float64(0.13742033871841092), 10: np.float64(0.17547796768953497), 22: np.float64(0.13742033871841092), 61: np.float64(0.13742033871841092), 40: np.float64(0.13742033871841092), 0: np.float64(0.13742033871841092)}
err dic= {91: np.float64(0.04942033871841092), 42: np.float64(0.02042033871841091), 10: np.float64(0.11652203231046501), 22: np.float64(0.08157966128158908), 61: np.float64(0.03442033871841092), 40: np.float64(0.019420338718410923), 0: np.float64(0.07442033871841092)} 

err list= [np.float64(0.04942033871841092), np.float64(0.02042033871841091), np.float64(0.11652203231046501), np.float64(0.08157966128158908), np.float64(0.03442033871841092), np.float64(0.019420338718410923), np.float64(0.07442033871841092)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  0.25 

learned probs for this beta: {91: np.float64(0.09369886812761002), 42: np.float64(0.09369886812761002), 10: np.float64(0.43780679123433885), 22: np.float64(0.09369886812761002), 61: np.float64(0.09369886812761002), 40: np.float64(0.09369886812761002), 0: np.float64(0.09369886812761002)}
err dic= {91: np.float64(0.0056988681276100295), 42: np.float64(0.023301131872389982), 10: np.float64(0.14580679123433887), 22: np.float64(0.12530113187238998), 61: np.float64(0.00930113187238997), 40: np.float64(0.02430113187238997), 0: np.float64(0.030698868127610024)} 

err list= [np.float64(0.0056988681276100295), np.float64(0.023301131872389982), np.float64(0.14580679123433887), np.float64(0.12530113187238998), np.float64(0.00930113187238997), np.float64(0.02430113187238997), np.float64(0.030698868127610024)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  0.5 

learned probs for this beta: {91: np.float64(0.11078643827914034), 42: np.float64(0.11078643827914034), 10: np.float64(0.33528137032515887), 22: np.float64(0.11078643827914034), 61: np.float64(0.11078643827914034), 40: np.float64(0.11078643827914034), 0: np.float64(0.11078643827914034)}
err dic= {91: np.float64(0.022786438279140342), 42: np.float64(0.00621356172085967), 10: np.float64(0.043281370325158885), 22: np.float64(0.10821356172085966), 61: np.float64(0.0077864382791403425), 40: np.float64(0.007213561720859657), 0: np.float64(0.047786438279140336)} 

err list= [np.float64(0.022786438279140342), np.float64(0.00621356172085967), np.float64(0.043281370325158885), np.float64(0.10821356172085966), np.float64(0.0077864382791403425), np.float64(0.007213561720859657), np.float64(0.047786438279140336)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  0.75 

learned probs for this beta: {91: np.float64(0.10528484927934292), 42: np.float64(0.10528484927934292), 10: np.float64(0.3682909043239426), 22: np.float64(0.10528484927934292), 61: np.float64(0.10528484927934292), 40: np.float64(0.10528484927934292), 0: np.float64(0.10528484927934292)}
err dic= {91: np.float64(0.01728484927934293), 42: np.float64(0.011715150720657083), 10: np.float64(0.07629090432394264), 22: np.float64(0.11371515072065708), 61: np.float64(0.0022848492793429293), 40: np.float64(0.01271515072065707), 0: np.float64(0.04228484927934292)} 

err list= [np.float64(0.01728484927934293), np.float64(0.011715150720657083), np.float64(0.07629090432394264), np.float64(0.11371515072065708), np.float64(0.0022848492793429293), np.float64(0.01271515072065707), np.float64(0.04228484927934292)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  1 

learned probs for this beta: {91: np.float64(0.1051676051245782), 42: np.float64(0.1051676051245782), 10: np.float64(0.3689943692525307), 22: np.float64(0.1051676051245782), 61: np.float64(0.1051676051245782), 40: np.float64(0.1051676051245782), 0: np.float64(0.1051676051245782)}
err dic= {91: np.float64(0.01716760512457821), 42: np.float64(0.0118323948754218), 10: np.float64(0.07699436925253073), 22: np.float64(0.1138323948754218), 61: np.float64(0.002167605124578212), 40: np.float64(0.012832394875421788), 0: np.float64(0.042167605124578206)} 

err list= [np.float64(0.01716760512457821), np.float64(0.0118323948754218), np.float64(0.07699436925253073), np.float64(0.1138323948754218), np.float64(0.002167605124578212), np.float64(0.012832394875421788), np.float64(0.042167605124578206)]
results for assortment [91, 42, 10, 22, 61, 40] :

beta is  1.25 

learned probs for this beta: {91: np.float64(4.662143319969194e-06), 42: np.float64(4.662143319969194e-06), 10: np.float64(0.9999720271400798), 22: np.float64(4.662143319969194e-06), 61: np.float64(4.662143319969194e-06), 40: np.float64(4.662143319969194e-06), 0: np.float64(4.662143319969194e-06)}
err dic= {91: np.float64(0.08799533785668003), 42: np.float64(0.11699533785668004), 10: np.float64(0.7079720271400798), 22: np.float64(0.21899533785668004), 61: np.float64(0.10299533785668002), 40: np.float64(0.11799533785668002), 0: np.float64(0.06299533785668003)} 

err list= [np.float64(0.08799533785668003), np.float64(0.11699533785668004), np.float64(0.7079720271400798), np.float64(0.21899533785668004), np.float64(0.10299533785668002), np.float64(0.11799533785668002), np.float64(0.06299533785668003)]
results for assortment [91, 42, 10, 22, 61, 40] :

err MNL dic= {91: np.float64(0.024505480052608525), 42: 0, 10: 0, 22: 0, 61: 0, 40: 0, 0: 0} 

err MNL list= [np.float64(0.024505480052608525), 0, 0, 0, 0, 0, 0]
err MNL dic= {91: np.float64(0.024505480052608525), 42: np.float64(0.00016352476983777509), 10: 0, 22: 0, 61: 0, 40: 0, 0: 0} 

err MNL list= [np.float64(0.024505480052608525), np.float64(0.00016352476983777509), 0, 0, 0, 0, 0]
err MNL dic= {91: np.float64(0.024505480052608525), 42: np.float64(0.00016352476983777509), 10: np.float64(0.1557110916264796), 22: 0, 61: 0, 40: 0, 0: 0} 

err MNL list= [np.float64(0.024505480052608525), np.float64(0.00016352476983777509), np.float64(0.1557110916264796), 0, 0, 0, 0]
err MNL dic= {91: np.float64(0.024505480052608525), 42: np.float64(0.00016352476983777509), 10: np.float64(0.1557110916264796), 22: np.float64(0.09356159579131959), 61: 0, 40: 0, 0: 0} 

err MNL list= [np.float64(0.024505480052608525), np.float64(0.00016352476983777509), np.float64(0.1557110916264796), np.float64(0.09356159579131959), 0, 0, 0]
err MNL dic= {91: np.float64(0.024505480052608525), 42: np.float64(0.00016352476983777509), 10: np.float64(0.1557110916264796), 22: np.float64(0.09356159579131959), 61: np.float64(0.011478298991670327), 40: 0, 0: 0} 

err MNL list= [np.float64(0.024505480052608525), np.float64(0.00016352476983777509), np.float64(0.1557110916264796), np.float64(0.09356159579131959), np.float64(0.011478298991670327), 0, 0]
err MNL dic= {91: np.float64(0.024505480052608525), 42: np.float64(0.00016352476983777509), 10: np.float64(0.1557110916264796), 22: np.float64(0.09356159579131959), 61: np.float64(0.011478298991670327), 40: np.float64(0.0021227531784305254), 0: 0} 

err MNL list= [np.float64(0.024505480052608525), np.float64(0.00016352476983777509), np.float64(0.1557110916264796), np.float64(0.09356159579131959), np.float64(0.011478298991670327), np.float64(0.0021227531784305254), 0]
err MNL dic= {91: np.float64(0.024505480052608525), 42: np.float64(0.00016352476983777509), 10: np.float64(0.1557110916264796), 22: np.float64(0.09356159579131959), 61: np.float64(0.011478298991670327), 40: np.float64(0.0021227531784305254), 0: np.float64(0.21100263042525208)} 

err MNL list= [np.float64(0.024505480052608525), np.float64(0.00016352476983777509), np.float64(0.1557110916264796), np.float64(0.09356159579131959), np.float64(0.011478298991670327), np.float64(0.0021227531784305254), np.float64(0.21100263042525208)]
sampled assortment [100, 62, 38, 92, 27, 54]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 15: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 15, 100, 4, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 5, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 10: 0, 11: 0, 12: 0, 13: 0, 100: 0} [1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 10, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 15]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 19: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 19, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 100
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 38
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 100
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 100
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 27
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 92
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 100
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 100
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 100
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 100
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 100
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 0
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 100
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 27
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 27
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 100
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 27
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 100
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 100
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 100
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 100
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 54
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 27
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 100
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 62
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 38
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 27
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 100
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 27
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 100
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 100
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 100
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 27
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 27
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 54
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 100
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 27
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 100
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 54
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 62
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 62
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 27
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 38
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 54
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 54
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 54
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 92
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 54
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 100
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 62
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 92
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 27
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 0
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 62
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 100
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 62
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 100
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 100
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 0
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 100
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 38
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 100
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 27
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 38
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 0
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 0
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 0
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 100
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 62
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 54
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 0
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 100
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 27
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 54
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 62
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 100
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 38
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 54
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 54
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 54
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 100
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 38
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 100
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 0
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 27
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 100
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 100
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 38
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 54
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 62
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 100
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 38
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 0
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 100
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 100
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 27
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 100
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 0
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 100
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 0
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 62
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 92
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 54
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 62
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 54
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 100
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 27
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 27
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 92
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 62
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 38
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 27
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 0
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 62
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 38
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 100
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 62
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 92
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 100
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 27
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 100
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 62
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 27
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 0
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 38
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 92
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 27
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 100
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 100
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 100
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 38
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 92
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 100
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 54
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 100
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 54
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 92
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 100
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 62
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 100
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 62
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 27
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 100
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 54
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 62
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 27
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 100
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 27
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 62
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 54
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 100
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 27
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 38
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 62
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 38
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 54
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 62
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 100
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 27
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 100
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 100
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 62
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 0
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 100
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 38
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 100
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 100
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 38
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 100
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 27
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 0
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 38
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 100
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 27
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 62
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 38
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 100
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 27
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 100
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 38
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 92
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 100
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 100
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 92
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 54
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 92
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 100
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 54
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 100
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 38
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 27
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 38
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 38
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 100
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 100
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 100
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 100
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 100
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 54
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 100
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 38
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 100
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 0
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 27
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 0
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 100
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 92
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 62
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 38
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 38
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 100
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 100
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 92
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 100
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 27
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 100
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 92
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 62
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 38
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 27
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 100
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 54
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 38
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 62
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 62
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 0
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 100
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 62
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 54
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 38
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 100
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 38
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 100
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 38
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 54
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 27
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 27
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 38
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 100
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 27
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 54
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 100
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 54
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 27
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 100
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 38
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 100
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 100
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 62
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 100
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 62
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 27
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 100
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 62
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 100
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 100
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 100
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 62
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 62
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 62
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 100
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 54
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 100
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 92
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 100
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 0
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 38
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 92
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 62
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 27
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 38
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 100
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 38
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 0
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 54
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 100
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 92
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 38
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 0
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 54
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 0
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 100
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 62
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 100
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 92
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 38
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 100
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 38
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 100
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 92
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 38
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 27
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 27
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 38
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 54
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 100
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 0
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 62
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 0
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 62
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 100
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 100
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 27
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 62
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 100
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 27
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 54
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 100
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 54
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 100
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 0
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 100
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 27
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 62
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 27
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 38
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 100
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 100
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 100
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 0
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 100
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 62
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 100
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 38
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 27
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 54
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 27
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 0
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 27
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 100
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 0
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 100
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 100
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 27
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 92
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 100
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 100
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 0
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 100
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 38
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 92
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 27
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 54
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 62
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 92
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 27
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 38
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 27
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 92
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 54
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 54
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 100
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 0
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 38
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 100
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 27
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 92
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 54
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 38
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 27
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 38
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 27
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 100
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 100
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 62
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 27
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 27
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 100
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 27
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 100
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 27
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 27
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 27
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 38
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 0
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 100
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 100
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 54
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 27
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 54
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 100
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 100
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 100
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 38
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 100
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 54
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 27
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 27
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 38
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 62
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 100
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 100
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 100
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 38
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 27
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 54
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 100
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 100
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 100
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 38
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 27
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 38
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 0
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 92
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 100
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 54
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 27
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 0
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 100
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 27
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 62
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 100
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 38
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 100
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 27
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 62
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 38
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 100
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 92
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 27
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 100
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 38
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 100
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 0
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 100
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 100
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 27
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 92
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 0
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 27
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 62
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 0
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 100
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 100
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 38
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 27
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 62
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 0
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 100
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 62
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 38
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 100
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 100
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 38
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 38
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 27
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 27
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 100
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 38
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 100
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 100
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 100
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 27
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 62
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 100
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 0
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 27
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 92
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 27
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 100
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 0
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 62
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 100
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 27
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 38
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 27
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 100
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 92
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 27
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 100
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 92
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 100
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 92
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 62
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 100
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 100
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 54
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 38
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 92
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 27
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 54
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 27
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 38
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 27
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 92
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 100
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 92
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 100
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 54
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 38
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 100
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 0
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 100
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 92
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 27
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 100
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 62
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 92
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 100
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 100
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 92
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 0
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 62
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 27
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 27
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 100
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 100
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 27
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 54
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 27
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 100
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 92
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 38
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 100
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 27
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 0
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 27
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 62
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 62
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 92
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 100
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 92
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 27
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 92
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 62
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 100
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 100
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 38
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 27
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 100
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 38
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 92
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 38
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 38
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 62
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 54
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 100
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 54
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 100
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 27
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 100
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 100
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 54
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 38
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 38
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 27
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 100
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 54
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 27
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 100
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 100
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 38
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 27
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 27
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 27
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 100
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 100
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 0
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 92
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 27
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 100
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 100
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 27
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 100
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 54
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 27
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 38
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 54
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 100
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 100
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 0
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 100
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 100
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 54
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 100
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 27
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 100
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 27
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 92
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 100
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 100
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 0
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 100
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 100
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 27
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 100
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 38
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 27
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 92
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 62
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 100
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 38
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 38
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 100
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 100
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 62
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 92
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 27
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 92
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 100
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 92
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 27
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 38
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 100
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 62
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 62
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 100
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 27
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 62
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 38
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 100
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 100
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 62
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 27
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 100
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 100
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 27
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 0
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 27
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 100
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 62
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 62
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 27
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 100
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 92
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 92
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 100
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 38
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 100
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 27
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 27
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 27
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 100
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 27
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 38
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 100
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 100
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 0
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 62
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 54
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 27
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 54
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 92
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 100
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 92
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 100
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 27
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 100
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 92
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 27
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 100
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 0
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 27
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 0
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 62
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 38
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 38
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 54
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 100
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 38
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 38
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 100
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 38
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 38
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 100
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 92
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 27
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 100
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 38
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 62
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 100
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 62
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 38
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 54
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 92
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 27
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 62
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 27
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 100
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 27
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 100
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 27
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 54
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 0
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 38
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 27
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 100
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 100
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 27
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 100
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 100
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 100
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 27
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 0
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 100
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 54
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 100
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 100
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 27
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 100
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 27
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 27
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 38
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 54
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 27
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 100
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 54
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 54
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 62
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 27
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 38
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 92
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 92
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 27
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 54
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 100
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 27
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 100
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 38
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 92
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 92
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 92
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 27
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 27
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 100
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 100
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 0
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 27
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 0
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 27
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 38
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 27
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 92
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 92
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 27
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 38
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 100
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 100
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 54
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 100
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 54
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 54
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 38
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 100
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 54
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 100
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 27
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 27
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 38
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 38
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 100
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 100
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 100
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 0
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 38
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 27
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 100
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 27
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 38
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 100
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 100
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 27
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 54
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 92
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 62
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 54
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 54
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 62
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 38
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 38
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 54
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 27
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 0
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 27
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 92
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 27
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 100
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 54
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 100
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 100
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 27
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 0
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 62
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 38
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 100
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 27
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 27
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 92
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 27
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 27
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 100
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 27
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 0
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 38
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 100
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 27
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 100
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 100
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 100
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 38
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 62
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 54
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 100
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 38
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 92
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 62
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 38
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 92
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 38
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 100
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 100
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 27
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 100
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 100
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 92
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 38
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 100
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 0
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 54
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 62
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 62
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 100
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 38
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 100
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 38
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 27
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 100
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 0
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 100
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 62
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 100
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 0
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 100
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 27
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 92
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 100
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 54
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 62
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 100
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 100
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 38
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 100
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 100
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 92
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 62
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 92
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 100
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 100
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 54
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 27
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 54
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 100
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 54
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 54
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 92
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 100
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 92
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 62
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 100
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 100
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 54
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 0
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 92
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 100
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 38
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 100
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 38
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 100
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 0
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 0
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 92
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 54
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 100
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 27
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 27
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 38
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 62
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 62
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 27
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 100
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 62
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 100
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 92
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 27
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 27
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 54
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 100
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 100
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 38
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 92
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 27
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 38
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 100
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 100
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 100
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 100
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 38
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 100
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 92
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 54
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 38
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 100
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 100
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 100
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 38
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 100
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 92
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 100
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 92
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 0
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 100
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 62
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 38
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 27
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 27
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 27
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 54
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 27
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 0
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 100
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 38
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 54
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 100
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 54
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 27
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 27
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 100
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 100
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 92
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 62
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 0
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 27
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 100
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 100
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 54
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 62
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 100
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 100
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 0
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 54
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 100
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 0
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 38
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 38
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 100
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 27
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 100
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 38
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 62
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 62
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 54
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 100
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 92
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 54
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 62
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 0
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 38
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 92
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 38
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 38
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 27
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 27
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 100
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 100
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 100
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 54
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 38
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 54
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 27
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 27
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 38
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 62
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 0
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 38
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 100
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 27
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 27
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 27
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 38
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 100
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 100
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 38
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 38
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 100
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 54
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 38
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 62
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 38
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 54
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 100
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 54
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 100
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 27
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 100
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 27
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 27
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 100
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 92
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 100
empirical probabilities from test set: {100: 0.33, 62: 0.094, 38: 0.137, 92: 0.085, 27: 0.186, 54: 0.097, 0: 0.071}
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  0.025 

learned probs for this beta: {100: np.float64(0.10595684062040797), 62: np.float64(0.14900719322993275), 38: np.float64(0.14900719322993275), 92: np.float64(0.14900719322993275), 27: np.float64(0.14900719322993275), 54: np.float64(0.14900719322993275), 0: np.float64(0.14900719322993275)}
err dic= {100: np.float64(0.22404315937959204), 62: np.float64(0.05500719322993275), 38: np.float64(0.012007193229932739), 92: np.float64(0.06400719322993274), 27: np.float64(0.03699280677006725), 54: np.float64(0.05200719322993275), 0: np.float64(0.07800719322993276)} 

err list= [np.float64(0.22404315937959204), np.float64(0.05500719322993275), np.float64(0.012007193229932739), np.float64(0.06400719322993274), np.float64(0.03699280677006725), np.float64(0.05200719322993275), np.float64(0.07800719322993276)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  0.05 

learned probs for this beta: {100: np.float64(0.12591821015910243), 62: np.float64(0.1456802983068182), 38: np.float64(0.1456802983068182), 92: np.float64(0.1456802983068182), 27: np.float64(0.1456802983068182), 54: np.float64(0.1456802983068182), 0: np.float64(0.1456802983068182)}
err dic= {100: np.float64(0.2040817898408976), 62: np.float64(0.051680298306818195), 38: np.float64(0.008680298306818185), 92: np.float64(0.06068029830681819), 27: np.float64(0.0403197016931818), 54: np.float64(0.04868029830681819), 0: np.float64(0.0746802983068182)} 

err list= [np.float64(0.2040817898408976), np.float64(0.051680298306818195), np.float64(0.008680298306818185), np.float64(0.06068029830681819), np.float64(0.0403197016931818), np.float64(0.04868029830681819), np.float64(0.0746802983068182)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  0.1 

learned probs for this beta: {100: np.float64(0.21518499120476067), 62: np.float64(0.13080250146587394), 38: np.float64(0.13080250146587394), 92: np.float64(0.13080250146587394), 27: np.float64(0.13080250146587394), 54: np.float64(0.13080250146587394), 0: np.float64(0.13080250146587394)}
err dic= {100: np.float64(0.11481500879523934), 62: np.float64(0.03680250146587394), 38: np.float64(0.006197498534126072), 92: np.float64(0.04580250146587393), 27: np.float64(0.05519749853412606), 54: np.float64(0.033802501465873935), 0: np.float64(0.059802501465873945)} 

err list= [np.float64(0.11481500879523934), np.float64(0.03680250146587394), np.float64(0.006197498534126072), np.float64(0.04580250146587393), np.float64(0.05519749853412606), np.float64(0.033802501465873935), np.float64(0.059802501465873945)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  0.25 

learned probs for this beta: {100: np.float64(0.39696239250599297), 62: np.float64(0.100506267915668), 38: np.float64(0.100506267915668), 92: np.float64(0.100506267915668), 27: np.float64(0.100506267915668), 54: np.float64(0.100506267915668), 0: np.float64(0.100506267915668)}
err dic= {100: np.float64(0.06696239250599295), 62: np.float64(0.006506267915667996), 38: np.float64(0.036493732084332015), 92: np.float64(0.01550626791566799), 27: np.float64(0.085493732084332), 54: np.float64(0.0035062679156679932), 0: np.float64(0.029506267915668002)} 

err list= [np.float64(0.06696239250599295), np.float64(0.006506267915667996), np.float64(0.036493732084332015), np.float64(0.01550626791566799), np.float64(0.085493732084332), np.float64(0.0035062679156679932), np.float64(0.029506267915668002)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  0.5 

learned probs for this beta: {100: np.float64(0.7516088759472533), 62: np.float64(0.04139852067545796), 38: np.float64(0.04139852067545796), 92: np.float64(0.04139852067545796), 27: np.float64(0.04139852067545796), 54: np.float64(0.04139852067545796), 0: np.float64(0.04139852067545796)}
err dic= {100: np.float64(0.4216088759472533), 62: np.float64(0.05260147932454204), 38: np.float64(0.09560147932454205), 92: np.float64(0.043601479324542045), 27: np.float64(0.14460147932454204), 54: np.float64(0.05560147932454204), 0: np.float64(0.029601479324542032)} 

err list= [np.float64(0.4216088759472533), np.float64(0.05260147932454204), np.float64(0.09560147932454205), np.float64(0.043601479324542045), np.float64(0.14460147932454204), np.float64(0.05560147932454204), np.float64(0.029601479324542032)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  0.75 

learned probs for this beta: {100: np.float64(0.9517825842755503), 62: np.float64(0.008036235954074891), 38: np.float64(0.008036235954074891), 92: np.float64(0.008036235954074891), 27: np.float64(0.008036235954074891), 54: np.float64(0.008036235954074891), 0: np.float64(0.008036235954074891)}
err dic= {100: np.float64(0.6217825842755502), 62: np.float64(0.08596376404592511), 38: np.float64(0.12896376404592513), 92: np.float64(0.07696376404592511), 27: np.float64(0.17796376404592512), 54: np.float64(0.08896376404592511), 0: np.float64(0.0629637640459251)} 

err list= [np.float64(0.6217825842755502), np.float64(0.08596376404592511), np.float64(0.12896376404592513), np.float64(0.07696376404592511), np.float64(0.17796376404592512), np.float64(0.08896376404592511), np.float64(0.0629637640459251)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  1 

learned probs for this beta: {100: np.float64(0.9962431106295282), 62: np.float64(0.0006261482284119744), 38: np.float64(0.0006261482284119744), 92: np.float64(0.0006261482284119744), 27: np.float64(0.0006261482284119744), 54: np.float64(0.0006261482284119744), 0: np.float64(0.0006261482284119744)}
err dic= {100: np.float64(0.6662431106295281), 62: np.float64(0.09337385177158802), 38: np.float64(0.13637385177158803), 92: np.float64(0.08437385177158803), 27: np.float64(0.18537385177158802), 54: np.float64(0.09637385177158803), 0: np.float64(0.07037385177158802)} 

err list= [np.float64(0.6662431106295281), np.float64(0.09337385177158802), np.float64(0.13637385177158803), np.float64(0.08437385177158803), np.float64(0.18537385177158802), np.float64(0.09637385177158803), np.float64(0.07037385177158802)]
results for assortment [100, 62, 38, 92, 27, 54] :

beta is  1.25 

learned probs for this beta: {100: np.float64(0.9996545758848204), 62: np.float64(5.75706858632211e-05), 38: np.float64(5.75706858632211e-05), 92: np.float64(5.75706858632211e-05), 27: np.float64(5.75706858632211e-05), 54: np.float64(5.75706858632211e-05), 0: np.float64(5.75706858632211e-05)}
err dic= {100: np.float64(0.6696545758848205), 62: np.float64(0.09394242931413678), 38: np.float64(0.13694242931413678), 92: np.float64(0.08494242931413679), 27: np.float64(0.18594242931413676), 54: np.float64(0.09694242931413678), 0: np.float64(0.07094242931413677)} 

err list= [np.float64(0.6696545758848205), np.float64(0.09394242931413678), np.float64(0.13694242931413678), np.float64(0.08494242931413679), np.float64(0.18594242931413676), np.float64(0.09694242931413678), np.float64(0.07094242931413677)]
results for assortment [100, 62, 38, 92, 27, 54] :

err MNL dic= {100: np.float64(0.18641053607460328), 62: 0, 38: 0, 92: 0, 27: 0, 54: 0, 0: 0} 

err MNL list= [np.float64(0.18641053607460328), 0, 0, 0, 0, 0, 0]
err MNL dic= {100: np.float64(0.18641053607460328), 62: np.float64(0.02019534274963189), 38: 0, 92: 0, 27: 0, 54: 0, 0: 0} 

err MNL list= [np.float64(0.18641053607460328), np.float64(0.02019534274963189), 0, 0, 0, 0, 0]
err MNL dic= {100: np.float64(0.18641053607460328), 62: np.float64(0.02019534274963189), 38: np.float64(0.014951682390794585), 92: 0, 27: 0, 54: 0, 0: 0} 

err MNL list= [np.float64(0.18641053607460328), np.float64(0.02019534274963189), np.float64(0.014951682390794585), 0, 0, 0, 0]
err MNL dic= {100: np.float64(0.18641053607460328), 62: np.float64(0.02019534274963189), 38: np.float64(0.014951682390794585), 92: np.float64(0.02510525167693735), 27: 0, 54: 0, 0: 0} 

err MNL list= [np.float64(0.18641053607460328), np.float64(0.02019534274963189), np.float64(0.014951682390794585), np.float64(0.02510525167693735), 0, 0, 0]
err MNL dic= {100: np.float64(0.18641053607460328), 62: np.float64(0.02019534274963189), 38: np.float64(0.014951682390794585), 92: np.float64(0.02510525167693735), 27: np.float64(0.059697987675192216), 54: 0, 0: 0} 

err MNL list= [np.float64(0.18641053607460328), np.float64(0.02019534274963189), np.float64(0.014951682390794585), np.float64(0.02510525167693735), np.float64(0.059697987675192216), 0, 0]
err MNL dic= {100: np.float64(0.18641053607460328), 62: np.float64(0.02019534274963189), 38: np.float64(0.014951682390794585), 92: np.float64(0.02510525167693735), 27: np.float64(0.059697987675192216), 54: np.float64(0.014086873534384023), 0: 0} 

err MNL list= [np.float64(0.18641053607460328), np.float64(0.02019534274963189), np.float64(0.014951682390794585), np.float64(0.02510525167693735), np.float64(0.059697987675192216), np.float64(0.014086873534384023), 0]
err MNL dic= {100: np.float64(0.18641053607460328), 62: np.float64(0.02019534274963189), 38: np.float64(0.014951682390794585), 92: np.float64(0.02510525167693735), 27: np.float64(0.059697987675192216), 54: np.float64(0.014086873534384023), 0: np.float64(0.20167273817963682)} 

err MNL list= [np.float64(0.18641053607460328), np.float64(0.02019534274963189), np.float64(0.014951682390794585), np.float64(0.02510525167693735), np.float64(0.059697987675192216), np.float64(0.014086873534384023), np.float64(0.20167273817963682)]
sampled assortment [67, 33, 62, 29, 65, 1]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 20: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 20]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 14, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 14, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 5, 6, 7, 9, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 5, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 15: 1, 17: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 12, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5, 9]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 15, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 5, 6, 9, 11, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 29
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 1
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 29
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 33
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 33
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 1
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 1
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 0
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 67
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 29
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 29
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 62
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 1
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 33
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 67
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 1
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 1
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 1
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 65
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 67
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 65
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 67
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 33
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 33
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 29
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 29
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 33
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 1
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 0
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 29
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 65
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 65
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 1
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 1
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 1
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 65
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 33
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 1
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 62
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 1
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 1
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 65
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 67
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 1
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 33
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 0
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 33
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 33
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 1
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 29
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 29
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 0
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 29
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 62
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 62
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 29
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 1
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 29
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 65
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 29
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 29
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 29
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 33
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 1
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 29
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 1
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 33
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 65
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 1
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 1
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 29
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 1
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 65
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 29
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 1
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 62
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 33
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 29
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 1
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 29
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 65
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 33
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 1
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 1
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 33
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 62
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 1
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 65
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 0
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 1
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 1
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 65
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 1
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 33
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 1
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 29
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 1
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 0
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 29
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 67
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 1
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 29
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 33
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 1
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 0
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 29
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 1
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 1
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 29
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 62
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 1
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 67
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 1
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 29
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 1
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 65
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 65
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 33
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 1
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 0
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 0
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 33
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 0
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 67
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 1
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 65
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 0
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 1
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 33
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 29
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 33
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 1
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 1
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 29
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 62
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 33
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 29
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 29
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 62
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 65
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 33
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 67
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 67
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 33
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 1
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 1
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 0
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 33
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 1
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 1
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 33
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 0
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 33
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 29
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 0
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 67
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 1
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 65
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 62
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 62
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 29
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 67
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 1
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 33
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 33
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 1
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 1
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 1
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 33
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 1
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 1
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 0
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 29
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 1
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 29
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 62
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 1
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 1
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 1
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 67
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 1
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 62
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 1
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 33
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 29
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 65
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 62
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 65
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 1
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 67
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 1
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 1
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 67
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 1
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 65
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 0
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 33
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 1
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 65
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 62
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 67
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 0
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 33
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 1
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 0
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 29
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 33
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 29
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 29
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 65
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 1
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 1
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 62
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 33
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 1
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 1
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 29
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 65
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 62
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 1
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 0
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 29
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 62
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 62
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 29
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 62
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 62
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 29
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 1
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 67
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 33
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 1
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 1
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 65
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 0
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 1
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 1
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 1
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 33
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 1
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 67
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 1
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 67
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 33
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 0
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 33
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 1
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 1
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 33
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 29
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 1
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 0
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 33
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 1
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 1
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 29
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 29
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 1
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 1
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 1
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 62
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 67
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 67
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 29
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 29
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 0
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 65
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 62
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 1
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 62
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 1
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 67
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 1
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 67
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 33
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 0
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 29
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 1
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 1
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 67
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 65
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 67
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 33
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 33
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 29
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 62
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 33
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 67
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 1
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 29
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 29
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 29
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 1
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 1
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 33
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 1
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 33
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 29
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 33
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 1
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 1
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 1
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 29
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 1
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 33
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 1
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 29
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 33
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 1
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 1
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 1
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 29
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 33
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 67
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 62
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 62
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 29
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 1
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 29
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 1
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 1
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 33
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 29
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 33
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 29
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 0
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 29
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 65
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 67
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 33
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 1
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 67
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 62
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 1
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 67
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 0
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 1
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 33
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 29
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 67
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 29
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 67
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 65
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 29
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 62
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 29
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 33
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 0
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 1
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 29
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 1
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 1
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 29
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 65
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 33
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 1
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 65
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 33
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 29
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 0
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 1
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 62
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 1
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 67
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 0
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 29
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 33
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 0
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 0
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 67
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 0
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 1
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 1
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 33
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 1
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 1
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 29
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 29
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 29
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 1
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 33
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 1
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 65
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 65
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 65
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 67
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 29
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 65
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 1
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 62
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 29
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 0
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 29
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 67
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 1
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 62
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 65
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 33
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 1
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 1
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 29
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 0
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 29
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 1
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 33
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 33
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 1
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 33
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 33
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 0
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 62
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 62
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 0
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 1
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 1
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 1
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 0
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 1
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 33
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 29
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 1
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 29
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 29
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 67
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 67
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 1
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 1
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 1
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 1
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 1
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 1
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 29
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 1
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 33
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 67
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 29
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 65
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 1
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 1
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 1
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 33
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 33
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 1
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 0
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 65
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 67
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 1
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 33
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 33
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 67
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 1
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 65
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 65
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 62
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 33
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 65
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 67
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 1
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 65
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 29
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 65
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 1
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 33
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 62
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 0
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 29
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 33
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 33
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 1
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 29
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 29
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 29
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 65
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 1
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 1
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 1
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 62
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 67
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 0
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 1
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 1
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 29
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 0
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 29
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 29
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 29
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 1
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 1
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 62
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 29
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 1
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 67
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 67
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 62
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 29
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 65
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 1
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 29
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 67
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 67
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 29
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 67
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 65
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 1
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 29
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 1
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 29
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 67
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 1
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 1
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 1
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 62
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 29
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 33
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 1
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 1
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 33
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 1
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 62
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 29
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 0
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 0
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 0
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 67
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 65
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 1
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 33
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 1
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 62
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 33
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 65
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 33
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 1
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 1
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 33
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 67
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 33
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 33
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 29
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 1
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 1
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 0
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 65
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 62
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 33
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 1
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 33
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 65
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 33
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 0
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 29
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 1
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 33
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 67
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 67
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 0
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 62
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 1
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 1
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 29
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 33
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 1
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 29
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 33
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 1
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 33
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 29
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 1
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 1
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 65
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 65
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 29
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 33
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 62
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 65
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 33
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 1
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 1
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 29
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 1
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 1
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 33
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 33
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 33
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 65
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 29
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 1
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 1
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 29
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 67
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 33
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 0
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 1
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 0
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 33
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 1
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 65
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 67
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 67
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 1
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 33
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 1
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 62
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 0
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 1
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 33
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 1
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 0
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 33
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 33
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 29
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 33
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 29
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 1
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 29
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 1
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 1
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 1
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 1
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 1
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 1
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 29
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 67
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 1
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 1
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 1
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 33
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 33
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 67
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 33
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 1
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 29
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 1
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 62
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 1
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 65
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 1
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 1
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 29
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 1
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 29
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 65
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 1
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 1
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 65
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 0
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 33
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 0
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 65
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 65
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 33
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 1
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 1
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 29
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 65
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 0
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 33
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 1
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 67
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 65
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 29
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 1
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 1
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 62
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 1
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 62
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 1
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 1
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 0
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 33
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 33
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 67
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 67
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 67
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 62
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 1
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 33
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 67
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 1
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 29
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 67
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 1
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 33
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 33
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 33
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 33
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 1
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 33
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 33
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 1
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 62
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 33
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 29
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 62
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 1
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 1
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 33
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 1
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 1
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 62
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 29
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 67
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 1
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 29
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 33
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 29
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 29
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 65
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 65
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 33
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 29
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 1
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 1
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 1
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 1
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 0
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 1
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 1
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 67
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 62
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 1
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 29
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 1
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 1
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 33
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 33
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 1
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 67
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 29
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 1
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 33
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 1
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 29
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 1
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 33
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 29
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 67
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 67
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 65
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 29
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 67
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 29
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 29
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 29
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 29
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 67
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 1
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 67
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 65
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 65
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 65
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 65
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 67
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 0
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 1
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 33
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 33
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 33
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 1
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 1
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 1
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 1
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 1
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 29
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 33
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 0
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 29
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 1
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 33
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 65
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 29
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 33
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 67
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 29
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 1
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 62
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 67
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 65
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 1
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 1
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 1
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 29
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 33
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 67
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 29
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 1
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 29
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 1
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 65
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 67
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 33
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 0
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 65
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 29
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 1
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 33
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 29
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 33
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 1
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 33
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 1
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 1
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 33
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 65
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 33
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 1
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 65
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 29
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 1
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 1
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 65
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 29
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 1
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 1
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 29
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 1
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 62
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 1
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 1
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 1
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 33
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 29
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 33
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 1
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 29
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 1
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 65
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 1
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 1
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 1
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 1
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 1
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 29
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 65
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 33
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 62
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 62
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 1
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 1
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 33
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 67
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 33
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 65
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 1
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 33
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 1
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 33
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 33
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 1
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 1
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 1
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 0
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 29
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 33
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 33
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 0
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 1
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 65
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 62
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 67
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 29
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 1
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 1
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 1
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 1
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 62
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 65
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 29
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 67
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 1
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 65
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 65
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 33
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 1
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 33
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 33
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 0
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 62
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 33
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 33
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 1
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 1
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 0
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 33
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 1
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 33
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 1
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 29
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 33
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 62
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 67
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 62
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 67
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 62
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 33
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 33
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 0
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 1
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 1
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 29
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 1
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 1
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 1
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 1
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 1
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 1
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 65
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 1
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 33
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 29
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 1
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 1
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 62
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 67
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 1
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 65
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 1
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 1
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 1
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 29
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 29
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 1
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 29
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 29
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 33
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 33
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 1
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 33
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 1
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 29
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 1
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 1
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 62
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 1
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 1
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 67
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 62
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 33
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 1
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 1
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 67
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 67
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 29
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 1
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 29
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 1
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 65
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 62
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 29
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 67
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 1
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 1
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 62
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 1
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 33
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 67
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 29
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 1
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 62
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 1
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 1
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 33
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 62
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 67
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 1
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 65
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 33
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 33
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 29
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 33
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 67
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 1
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 62
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 1
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 33
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 1
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 65
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 0
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 29
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 62
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 65
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 67
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 62
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 62
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 29
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 67
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 1
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 29
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 1
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 67
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 67
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 33
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 1
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 65
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 62
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 0
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 29
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 29
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 67
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 0
empirical probabilities from test set: {67: 0.095, 33: 0.171, 62: 0.076, 29: 0.169, 65: 0.089, 1: 0.333, 0: 0.067}
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  0.025 

learned probs for this beta: {67: np.float64(0.14346839292534025), 33: np.float64(0.14346839292534025), 62: np.float64(0.14346839292534025), 29: np.float64(0.14346839292534025), 65: np.float64(0.14346839292534025), 1: np.float64(0.13918964244794754), 0: np.float64(0.14346839292534025)}
err dic= {67: np.float64(0.04846839292534025), 33: np.float64(0.027531607074659764), 62: np.float64(0.06746839292534025), 29: np.float64(0.025531607074659762), 65: np.float64(0.05446839292534025), 1: np.float64(0.19381035755205248), 0: np.float64(0.07646839292534025)} 

err list= [np.float64(0.04846839292534025), np.float64(0.027531607074659764), np.float64(0.06746839292534025), np.float64(0.025531607074659762), np.float64(0.05446839292534025), np.float64(0.19381035755205248), np.float64(0.07646839292534025)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  0.05 

learned probs for this beta: {67: np.float64(0.14017393105526477), 33: np.float64(0.14017393105526477), 62: np.float64(0.14017393105526477), 29: np.float64(0.14017393105526477), 65: np.float64(0.14017393105526477), 1: np.float64(0.1589564136684124), 0: np.float64(0.14017393105526477)}
err dic= {67: np.float64(0.045173931055264765), 33: np.float64(0.030826068944735247), 62: np.float64(0.06417393105526477), 29: np.float64(0.028826068944735245), 65: np.float64(0.05117393105526477), 1: np.float64(0.17404358633158762), 0: np.float64(0.07317393105526476)} 

err list= [np.float64(0.045173931055264765), np.float64(0.030826068944735247), np.float64(0.06417393105526477), np.float64(0.028826068944735245), np.float64(0.05117393105526477), np.float64(0.17404358633158762), np.float64(0.07317393105526476)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  0.1 

learned probs for this beta: {67: np.float64(0.09828489280538316), 33: np.float64(0.09828489280538316), 62: np.float64(0.09828489280538316), 29: np.float64(0.09828489280538316), 65: np.float64(0.09828489280538316), 1: np.float64(0.410290643167709), 0: np.float64(0.09828489280538316)}
err dic= {67: np.float64(0.0032848928053831605), 33: np.float64(0.07271510719461685), 62: np.float64(0.022284892805383164), 29: np.float64(0.07071510719461685), 65: np.float64(0.009284892805383166), 1: np.float64(0.077290643167709), 0: np.float64(0.03128489280538316)} 

err list= [np.float64(0.0032848928053831605), np.float64(0.07271510719461685), np.float64(0.022284892805383164), np.float64(0.07071510719461685), np.float64(0.009284892805383166), np.float64(0.077290643167709), np.float64(0.03128489280538316)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  0.25 

learned probs for this beta: {67: np.float64(0.02112562883620058), 33: np.float64(0.02112562883620058), 62: np.float64(0.02112562883620058), 29: np.float64(0.02112562883620058), 65: np.float64(0.02112562883620058), 1: np.float64(0.873246226982798), 0: np.float64(0.02112562883620058)}
err dic= {67: np.float64(0.07387437116379941), 33: np.float64(0.14987437116379942), 62: np.float64(0.05487437116379942), 29: np.float64(0.14787437116379942), 65: np.float64(0.06787437116379941), 1: np.float64(0.5402462269827979), 0: np.float64(0.04587437116379942)} 

err list= [np.float64(0.07387437116379941), np.float64(0.14987437116379942), np.float64(0.05487437116379942), np.float64(0.14787437116379942), np.float64(0.06787437116379941), np.float64(0.5402462269827979), np.float64(0.04587437116379942)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  0.5 

learned probs for this beta: {67: np.float64(0.0008684814919973278), 33: np.float64(0.0008684814919973278), 62: np.float64(0.0008684814919973278), 29: np.float64(0.0008684814919973278), 65: np.float64(0.0008684814919973278), 1: np.float64(0.9947891110480178), 0: np.float64(0.0008684814919973278)}
err dic= {67: np.float64(0.09413151850800268), 33: np.float64(0.17013151850800268), 62: np.float64(0.07513151850800268), 29: np.float64(0.16813151850800268), 65: np.float64(0.08813151850800267), 1: np.float64(0.6617891110480179), 0: np.float64(0.06613151850800268)} 

err list= [np.float64(0.09413151850800268), np.float64(0.17013151850800268), np.float64(0.07513151850800268), np.float64(0.16813151850800268), np.float64(0.08813151850800267), np.float64(0.6617891110480179), np.float64(0.06613151850800268)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  0.75 

learned probs for this beta: {67: np.float64(2.1081149832181632e-05), 33: np.float64(2.1081149832181632e-05), 62: np.float64(2.1081149832181632e-05), 29: np.float64(2.1081149832181632e-05), 65: np.float64(2.1081149832181632e-05), 1: np.float64(0.9998735131010072), 0: np.float64(2.1081149832181632e-05)}
err dic= {67: np.float64(0.09497891885016782), 33: np.float64(0.17097891885016783), 62: np.float64(0.07597891885016782), 29: np.float64(0.16897891885016783), 65: np.float64(0.08897891885016782), 1: np.float64(0.6668735131010073), 0: np.float64(0.06697891885016782)} 

err list= [np.float64(0.09497891885016782), np.float64(0.17097891885016783), np.float64(0.07597891885016782), np.float64(0.16897891885016783), np.float64(0.08897891885016782), np.float64(0.6668735131010073), np.float64(0.06697891885016782)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  1 

learned probs for this beta: {67: np.float64(6.368189495891364e-07), 33: np.float64(6.368189495891364e-07), 62: np.float64(6.368189495891364e-07), 29: np.float64(6.368189495891364e-07), 65: np.float64(6.368189495891364e-07), 1: np.float64(0.9999961790863023), 0: np.float64(6.368189495891364e-07)}
err dic= {67: np.float64(0.09499936318105041), 33: np.float64(0.1709993631810504), 62: np.float64(0.07599936318105041), 29: np.float64(0.1689993631810504), 65: np.float64(0.08899936318105041), 1: np.float64(0.6669961790863024), 0: np.float64(0.06699936318105042)} 

err list= [np.float64(0.09499936318105041), np.float64(0.1709993631810504), np.float64(0.07599936318105041), np.float64(0.1689993631810504), np.float64(0.08899936318105041), np.float64(0.6669961790863024), np.float64(0.06699936318105042)]
results for assortment [67, 33, 62, 29, 65, 1] :

beta is  1.25 

learned probs for this beta: {67: np.float64(3.9625550914192395e-09), 33: np.float64(3.9625550914192395e-09), 62: np.float64(3.9625550914192395e-09), 29: np.float64(3.9625550914192395e-09), 65: np.float64(3.9625550914192395e-09), 1: np.float64(0.9999999762246693), 0: np.float64(3.9625550914192395e-09)}
err dic= {67: np.float64(0.09499999603744491), 33: np.float64(0.17099999603744492), 62: np.float64(0.07599999603744491), 29: np.float64(0.16899999603744492), 65: np.float64(0.0889999960374449), 1: np.float64(0.6669999762246692), 0: np.float64(0.06699999603744491)} 

err list= [np.float64(0.09499999603744491), np.float64(0.17099999603744492), np.float64(0.07599999603744491), np.float64(0.16899999603744492), np.float64(0.0889999960374449), np.float64(0.6669999762246692), np.float64(0.06699999603744491)]
results for assortment [67, 33, 62, 29, 65, 1] :

err MNL dic= {67: np.float64(0.016554002402533588), 33: 0, 62: 0, 29: 0, 65: 0, 1: 0, 0: 0} 

err MNL list= [np.float64(0.016554002402533588), 0, 0, 0, 0, 0, 0]
err MNL dic= {67: np.float64(0.016554002402533588), 33: np.float64(0.04808856612427652), 62: 0, 29: 0, 65: 0, 1: 0, 0: 0} 

err MNL list= [np.float64(0.016554002402533588), np.float64(0.04808856612427652), 0, 0, 0, 0, 0]
err MNL dic= {67: np.float64(0.016554002402533588), 33: np.float64(0.04808856612427652), 62: np.float64(0.03839336027083105), 29: 0, 65: 0, 1: 0, 0: 0} 

err MNL list= [np.float64(0.016554002402533588), np.float64(0.04808856612427652), np.float64(0.03839336027083105), 0, 0, 0, 0]
err MNL dic= {67: np.float64(0.016554002402533588), 33: np.float64(0.04808856612427652), 62: np.float64(0.03839336027083105), 29: np.float64(0.04745364202249648), 65: 0, 1: 0, 0: 0} 

err MNL list= [np.float64(0.016554002402533588), np.float64(0.04808856612427652), np.float64(0.03839336027083105), np.float64(0.04745364202249648), 0, 0, 0]
err MNL dic= {67: np.float64(0.016554002402533588), 33: np.float64(0.04808856612427652), 62: np.float64(0.03839336027083105), 29: np.float64(0.04745364202249648), 65: np.float64(0.02648542098940701), 1: 0, 0: 0} 

err MNL list= [np.float64(0.016554002402533588), np.float64(0.04808856612427652), np.float64(0.03839336027083105), np.float64(0.04745364202249648), np.float64(0.02648542098940701), 0, 0]
err MNL dic= {67: np.float64(0.016554002402533588), 33: np.float64(0.04808856612427652), 62: np.float64(0.03839336027083105), 29: np.float64(0.04745364202249648), 65: np.float64(0.02648542098940701), 1: np.float64(0.19190575515998692), 0: 0} 

err MNL list= [np.float64(0.016554002402533588), np.float64(0.04808856612427652), np.float64(0.03839336027083105), np.float64(0.04745364202249648), np.float64(0.02648542098940701), np.float64(0.19190575515998692), 0]
err MNL dic= {67: np.float64(0.016554002402533588), 33: np.float64(0.04808856612427652), 62: np.float64(0.03839336027083105), 29: np.float64(0.04745364202249648), 65: np.float64(0.02648542098940701), 1: np.float64(0.19190575515998692), 0: np.float64(0.2060151796439882)} 

err MNL list= [np.float64(0.016554002402533588), np.float64(0.04808856612427652), np.float64(0.03839336027083105), np.float64(0.04745364202249648), np.float64(0.02648542098940701), np.float64(0.19190575515998692), np.float64(0.2060151796439882)]
sampled assortment [36, 93, 32, 44, 94, 53]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 4, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 10, 11, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 14: 2, 100: 1} [8, 1, 3, 4, 5, 6, 7, 10, 100, 11, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 17: 3, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 17]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 15: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 15]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 15, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 14, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 11, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 14, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5, 10]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 16: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 16, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 18: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 18, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 4, 5, 6, 7, 10, 15, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 53
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 44
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 53
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 93
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 32
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 36
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 36
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 36
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 32
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 53
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 36
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 44
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 0
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 32
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 44
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 36
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 44
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 32
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 36
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 36
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 44
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 36
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 36
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 93
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 94
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 36
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 93
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 44
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 53
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 0
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 32
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 0
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 44
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 94
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 0
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 32
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 44
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 32
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 0
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 44
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 53
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 36
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 53
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 53
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 32
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 32
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 32
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 32
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 36
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 0
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 32
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 32
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 44
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 53
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 36
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 36
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 94
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 94
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 32
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 94
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 44
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 93
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 53
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 44
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 93
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 36
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 53
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 32
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 94
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 94
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 94
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 53
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 36
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 44
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 36
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 36
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 44
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 94
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 94
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 93
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 44
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 0
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 36
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 32
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 32
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 36
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 93
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 32
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 53
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 93
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 36
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 36
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 53
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 36
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 53
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 36
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 44
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 0
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 36
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 93
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 0
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 44
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 53
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 32
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 53
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 44
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 32
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 93
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 44
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 93
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 94
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 44
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 94
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 53
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 36
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 0
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 32
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 44
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 93
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 93
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 44
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 0
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 93
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 32
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 44
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 53
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 93
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 44
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 36
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 0
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 36
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 32
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 0
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 44
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 53
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 32
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 44
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 36
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 36
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 36
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 32
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 32
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 44
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 93
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 44
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 94
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 32
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 36
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 36
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 93
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 32
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 36
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 53
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 0
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 36
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 94
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 53
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 36
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 53
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 32
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 36
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 32
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 93
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 94
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 53
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 53
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 53
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 32
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 0
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 44
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 36
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 93
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 36
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 36
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 0
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 36
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 32
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 44
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 94
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 32
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 93
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 94
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 53
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 94
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 32
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 53
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 36
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 53
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 0
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 93
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 36
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 53
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 32
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 44
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 44
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 32
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 0
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 36
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 94
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 53
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 93
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 94
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 94
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 94
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 44
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 44
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 93
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 0
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 94
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 94
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 36
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 0
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 44
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 36
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 53
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 44
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 44
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 32
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 0
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 32
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 44
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 32
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 94
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 32
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 94
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 36
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 53
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 94
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 32
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 32
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 44
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 44
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 93
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 0
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 94
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 32
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 0
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 53
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 44
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 32
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 44
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 32
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 93
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 53
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 32
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 36
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 44
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 94
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 44
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 53
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 32
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 44
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 44
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 32
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 36
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 32
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 36
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 93
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 93
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 0
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 53
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 53
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 32
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 53
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 36
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 32
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 0
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 32
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 36
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 32
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 93
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 53
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 32
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 36
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 93
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 32
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 44
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 44
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 94
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 36
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 36
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 0
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 94
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 36
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 36
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 32
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 44
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 32
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 0
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 44
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 32
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 0
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 93
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 36
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 44
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 94
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 36
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 0
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 44
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 53
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 94
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 93
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 93
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 0
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 32
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 93
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 32
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 0
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 44
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 36
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 93
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 94
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 53
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 94
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 36
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 53
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 36
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 0
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 44
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 94
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 44
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 44
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 93
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 53
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 53
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 36
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 32
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 94
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 94
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 32
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 53
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 44
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 44
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 93
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 36
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 44
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 53
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 94
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 93
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 94
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 44
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 44
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 93
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 32
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 36
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 44
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 36
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 53
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 94
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 32
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 94
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 36
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 53
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 53
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 32
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 94
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 44
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 32
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 44
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 36
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 36
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 44
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 0
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 44
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 36
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 36
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 94
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 53
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 32
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 36
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 32
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 32
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 94
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 0
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 32
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 36
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 36
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 93
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 0
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 94
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 32
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 94
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 94
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 32
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 53
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 44
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 53
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 0
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 53
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 44
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 36
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 94
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 32
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 36
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 0
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 44
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 32
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 53
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 36
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 44
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 32
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 32
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 36
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 93
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 32
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 93
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 93
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 32
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 44
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 0
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 93
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 94
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 36
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 32
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 32
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 36
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 44
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 36
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 36
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 94
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 94
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 32
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 36
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 0
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 94
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 94
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 36
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 94
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 32
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 0
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 44
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 44
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 94
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 44
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 36
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 44
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 36
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 32
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 44
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 0
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 44
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 53
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 44
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 53
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 94
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 44
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 36
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 36
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 32
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 36
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 32
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 32
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 44
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 32
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 44
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 93
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 53
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 32
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 44
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 94
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 53
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 44
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 44
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 44
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 0
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 36
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 32
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 94
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 53
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 93
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 93
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 94
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 44
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 36
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 32
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 0
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 44
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 44
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 36
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 53
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 44
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 94
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 36
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 0
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 53
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 44
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 0
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 44
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 32
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 36
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 94
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 93
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 32
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 0
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 53
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 53
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 0
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 93
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 93
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 44
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 93
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 32
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 32
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 36
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 44
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 32
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 53
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 94
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 0
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 44
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 94
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 53
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 94
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 94
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 36
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 93
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 53
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 0
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 44
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 36
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 94
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 36
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 32
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 93
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 36
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 36
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 44
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 44
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 32
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 32
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 32
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 93
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 93
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 53
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 32
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 36
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 53
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 53
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 94
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 93
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 36
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 93
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 36
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 94
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 32
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 93
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 44
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 44
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 0
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 94
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 44
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 53
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 93
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 32
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 32
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 53
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 93
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 44
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 32
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 32
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 93
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 44
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 93
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 53
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 32
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 94
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 36
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 94
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 53
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 0
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 32
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 36
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 93
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 53
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 32
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 36
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 0
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 32
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 94
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 93
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 0
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 36
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 94
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 94
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 0
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 36
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 32
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 44
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 53
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 32
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 94
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 32
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 53
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 32
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 0
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 0
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 93
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 36
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 0
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 32
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 94
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 44
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 36
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 36
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 93
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 44
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 36
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 32
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 53
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 53
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 0
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 94
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 36
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 36
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 93
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 36
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 32
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 0
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 32
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 36
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 36
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 32
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 44
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 93
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 0
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 44
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 32
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 44
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 36
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 36
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 53
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 32
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 94
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 93
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 0
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 32
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 94
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 32
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 53
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 53
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 93
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 53
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 36
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 32
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 94
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 44
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 36
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 32
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 36
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 32
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 94
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 94
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 93
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 44
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 36
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 32
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 36
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 0
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 44
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 36
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 44
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 36
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 94
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 32
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 36
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 44
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 94
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 53
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 53
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 93
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 32
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 0
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 0
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 93
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 32
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 94
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 44
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 44
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 44
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 93
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 32
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 36
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 44
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 53
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 0
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 53
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 93
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 53
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 44
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 44
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 93
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 44
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 36
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 94
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 0
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 36
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 36
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 32
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 32
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 93
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 32
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 44
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 93
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 44
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 36
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 93
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 94
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 0
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 32
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 93
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 94
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 44
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 0
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 0
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 93
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 53
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 94
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 32
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 53
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 0
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 0
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 94
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 53
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 53
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 94
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 93
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 94
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 94
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 36
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 53
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 0
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 32
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 0
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 36
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 53
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 0
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 32
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 32
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 44
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 53
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 93
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 0
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 44
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 93
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 93
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 36
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 32
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 93
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 53
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 32
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 44
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 36
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 44
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 53
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 36
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 32
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 44
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 93
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 32
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 36
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 32
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 93
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 36
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 93
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 32
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 44
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 32
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 32
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 0
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 94
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 93
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 53
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 0
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 32
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 44
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 93
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 36
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 53
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 93
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 93
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 32
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 53
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 94
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 32
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 93
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 32
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 94
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 53
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 36
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 53
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 32
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 94
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 36
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 32
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 93
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 93
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 36
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 36
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 32
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 44
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 93
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 36
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 32
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 32
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 32
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 93
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 32
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 36
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 94
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 0
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 53
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 32
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 44
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 36
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 44
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 44
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 36
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 32
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 36
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 32
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 32
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 32
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 36
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 93
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 0
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 36
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 94
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 53
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 36
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 94
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 32
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 93
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 32
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 36
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 0
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 94
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 94
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 44
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 93
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 36
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 36
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 32
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 36
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 32
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 36
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 36
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 36
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 36
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 53
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 93
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 93
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 94
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 32
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 0
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 36
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 53
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 44
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 93
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 53
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 32
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 53
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 36
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 32
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 44
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 44
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 36
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 32
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 36
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 44
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 36
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 32
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 44
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 32
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 94
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 44
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 0
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 53
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 44
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 93
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 36
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 94
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 0
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 36
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 53
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 32
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 32
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 32
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 0
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 36
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 0
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 32
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 94
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 32
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 36
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 36
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 32
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 32
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 36
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 44
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 36
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 32
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 93
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 53
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 32
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 53
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 36
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 32
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 36
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 94
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 44
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 53
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 36
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 32
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 93
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 0
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 94
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 44
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 93
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 44
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 32
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 53
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 94
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 0
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 32
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 94
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 44
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 36
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 0
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 32
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 32
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 53
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 0
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 0
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 0
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 53
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 53
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 36
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 36
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 32
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 44
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 0
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 0
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 53
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 32
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 44
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 44
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 32
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 53
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 32
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 44
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 53
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 0
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 44
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 36
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 36
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 36
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 44
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 94
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 36
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 93
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 44
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 44
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 94
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 94
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 44
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 32
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 53
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 32
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 32
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 53
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 0
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 44
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 44
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 94
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 36
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 36
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 36
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 36
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 32
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 93
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 32
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 53
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 53
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 32
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 44
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 93
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 32
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 53
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 53
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 44
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 53
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 36
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 93
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 53
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 94
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 53
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 44
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 0
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 32
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 32
empirical probabilities from test set: {36: 0.187, 93: 0.111, 32: 0.2, 44: 0.162, 94: 0.116, 53: 0.128, 0: 0.096}
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  0.025 

learned probs for this beta: {36: np.float64(0.14285714285714723), 93: np.float64(0.14285714285714723), 32: np.float64(0.14285714285714723), 44: np.float64(0.14285714285714723), 94: np.float64(0.14285714285714723), 53: np.float64(0.14285714285714723), 0: np.float64(0.14285714285714723)}
err dic= {36: np.float64(0.044142857142852765), 93: np.float64(0.03185714285714723), 32: np.float64(0.057142857142852777), 44: np.float64(0.01914285714285277), 94: np.float64(0.02685714285714723), 53: np.float64(0.014857142857147232), 0: np.float64(0.04685714285714723)} 

err list= [np.float64(0.044142857142852765), np.float64(0.03185714285714723), np.float64(0.057142857142852777), np.float64(0.01914285714285277), np.float64(0.02685714285714723), np.float64(0.014857142857147232), np.float64(0.04685714285714723)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  0.05 

learned probs for this beta: {36: np.float64(0.14285714285714346), 93: np.float64(0.14285714285714346), 32: np.float64(0.14285714285714346), 44: np.float64(0.14285714285714346), 94: np.float64(0.14285714285714346), 53: np.float64(0.14285714285714346), 0: np.float64(0.14285714285714346)}
err dic= {36: np.float64(0.04414285714285654), 93: np.float64(0.03185714285714346), 32: np.float64(0.05714285714285655), 44: np.float64(0.019142857142856545), 94: np.float64(0.026857142857143454), 53: np.float64(0.014857142857143457), 0: np.float64(0.04685714285714346)} 

err list= [np.float64(0.04414285714285654), np.float64(0.03185714285714346), np.float64(0.05714285714285655), np.float64(0.019142857142856545), np.float64(0.026857142857143454), np.float64(0.014857142857143457), np.float64(0.04685714285714346)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  0.1 

learned probs for this beta: {36: np.float64(0.14285714285714313), 93: np.float64(0.14285714285714313), 32: np.float64(0.14285714285714313), 44: np.float64(0.14285714285714313), 94: np.float64(0.14285714285714313), 53: np.float64(0.14285714285714313), 0: np.float64(0.14285714285714313)}
err dic= {36: np.float64(0.04414285714285687), 93: np.float64(0.031857142857143125), 32: np.float64(0.057142857142856884), 44: np.float64(0.01914285714285688), 94: np.float64(0.02685714285714312), 53: np.float64(0.014857142857143124), 0: np.float64(0.046857142857143125)} 

err list= [np.float64(0.04414285714285687), np.float64(0.031857142857143125), np.float64(0.057142857142856884), np.float64(0.01914285714285688), np.float64(0.02685714285714312), np.float64(0.014857142857143124), np.float64(0.046857142857143125)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  0.25 

learned probs for this beta: {36: np.float64(0.14285714285714285), 93: np.float64(0.14285714285714285), 32: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {36: np.float64(0.04414285714285715), 93: np.float64(0.03185714285714285), 32: np.float64(0.05714285714285716), 44: np.float64(0.019142857142857156), 94: np.float64(0.026857142857142843), 53: np.float64(0.014857142857142847), 0: np.float64(0.04685714285714285)} 

err list= [np.float64(0.04414285714285715), np.float64(0.03185714285714285), np.float64(0.05714285714285716), np.float64(0.019142857142857156), np.float64(0.026857142857142843), np.float64(0.014857142857142847), np.float64(0.04685714285714285)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  0.5 

learned probs for this beta: {36: np.float64(0.1428571428571429), 93: np.float64(0.1428571428571429), 32: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 94: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
err dic= {36: np.float64(0.044142857142857095), 93: np.float64(0.0318571428571429), 32: np.float64(0.057142857142857106), 44: np.float64(0.0191428571428571), 94: np.float64(0.0268571428571429), 53: np.float64(0.014857142857142902), 0: np.float64(0.0468571428571429)} 

err list= [np.float64(0.044142857142857095), np.float64(0.0318571428571429), np.float64(0.057142857142857106), np.float64(0.0191428571428571), np.float64(0.0268571428571429), np.float64(0.014857142857142902), np.float64(0.0468571428571429)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  0.75 

learned probs for this beta: {36: np.float64(0.14285714285714288), 93: np.float64(0.14285714285714288), 32: np.float64(0.14285714285714288), 44: np.float64(0.14285714285714288), 94: np.float64(0.14285714285714288), 53: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
err dic= {36: np.float64(0.04414285714285712), 93: np.float64(0.031857142857142876), 32: np.float64(0.057142857142857134), 44: np.float64(0.019142857142857128), 94: np.float64(0.02685714285714287), 53: np.float64(0.014857142857142874), 0: np.float64(0.046857142857142875)} 

err list= [np.float64(0.04414285714285712), np.float64(0.031857142857142876), np.float64(0.057142857142857134), np.float64(0.019142857142857128), np.float64(0.02685714285714287), np.float64(0.014857142857142874), np.float64(0.046857142857142875)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  1 

learned probs for this beta: {36: np.float64(0.14285714285714285), 93: np.float64(0.14285714285714285), 32: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {36: np.float64(0.04414285714285715), 93: np.float64(0.03185714285714285), 32: np.float64(0.05714285714285716), 44: np.float64(0.019142857142857156), 94: np.float64(0.026857142857142843), 53: np.float64(0.014857142857142847), 0: np.float64(0.04685714285714285)} 

err list= [np.float64(0.04414285714285715), np.float64(0.03185714285714285), np.float64(0.05714285714285716), np.float64(0.019142857142857156), np.float64(0.026857142857142843), np.float64(0.014857142857142847), np.float64(0.04685714285714285)]
results for assortment [36, 93, 32, 44, 94, 53] :

beta is  1.25 

learned probs for this beta: {36: np.float64(0.14285714285714285), 93: np.float64(0.14285714285714285), 32: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 94: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
err dic= {36: np.float64(0.04414285714285715), 93: np.float64(0.03185714285714285), 32: np.float64(0.05714285714285716), 44: np.float64(0.019142857142857156), 94: np.float64(0.026857142857142843), 53: np.float64(0.014857142857142847), 0: np.float64(0.04685714285714285)} 

err list= [np.float64(0.04414285714285715), np.float64(0.03185714285714285), np.float64(0.05714285714285716), np.float64(0.019142857142857156), np.float64(0.026857142857142843), np.float64(0.014857142857142847), np.float64(0.04685714285714285)]
results for assortment [36, 93, 32, 44, 94, 53] :

err MNL dic= {36: np.float64(0.061589700056593144), 93: 0, 32: 0, 44: 0, 94: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.061589700056593144), 0, 0, 0, 0, 0, 0]
err MNL dic= {36: np.float64(0.061589700056593144), 93: np.float64(0.004336728919071858), 32: 0, 44: 0, 94: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.061589700056593144), np.float64(0.004336728919071858), 0, 0, 0, 0, 0]
err MNL dic= {36: np.float64(0.061589700056593144), 93: np.float64(0.004336728919071858), 32: np.float64(0.07481607243916244), 44: 0, 94: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.061589700056593144), np.float64(0.004336728919071858), np.float64(0.07481607243916244), 0, 0, 0, 0]
err MNL dic= {36: np.float64(0.061589700056593144), 93: np.float64(0.004336728919071858), 32: np.float64(0.07481607243916244), 44: np.float64(0.03998528579513301), 94: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.061589700056593144), np.float64(0.004336728919071858), np.float64(0.07481607243916244), np.float64(0.03998528579513301), 0, 0, 0]
err MNL dic= {36: np.float64(0.061589700056593144), 93: np.float64(0.004336728919071858), 32: np.float64(0.07481607243916244), 44: np.float64(0.03998528579513301), 94: np.float64(0.0041720430107527184), 53: 0, 0: 0} 

err MNL list= [np.float64(0.061589700056593144), np.float64(0.004336728919071858), np.float64(0.07481607243916244), np.float64(0.03998528579513301), np.float64(0.0041720430107527184), 0, 0]
err MNL dic= {36: np.float64(0.061589700056593144), 93: np.float64(0.004336728919071858), 32: np.float64(0.07481607243916244), 44: np.float64(0.03998528579513301), 94: np.float64(0.0041720430107527184), 53: np.float64(0.01073910582908888), 0: 0} 

err MNL list= [np.float64(0.061589700056593144), np.float64(0.004336728919071858), np.float64(0.07481607243916244), np.float64(0.03998528579513301), np.float64(0.0041720430107527184), np.float64(0.01073910582908888), 0]
err MNL dic= {36: np.float64(0.061589700056593144), 93: np.float64(0.004336728919071858), 32: np.float64(0.07481607243916244), 44: np.float64(0.03998528579513301), 94: np.float64(0.0041720430107527184), 53: np.float64(0.01073910582908888), 0: np.float64(0.18696547821165813)} 

err MNL list= [np.float64(0.061589700056593144), np.float64(0.004336728919071858), np.float64(0.07481607243916244), np.float64(0.03998528579513301), np.float64(0.0041720430107527184), np.float64(0.01073910582908888), np.float64(0.18696547821165813)]
sampled assortment [38, 98, 55, 40, 96, 2]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 19: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 19, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0} [1, 2, 3, 4, 5, 6, 9, 10]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 11, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 14, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 7, 10, 13, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 14, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 55
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 2
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 0
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 40
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 40
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 2
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 38
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 2
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 2
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 2
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 55
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 2
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 40
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 2
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 2
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 96
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 40
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 2
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 55
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 96
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 0
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 38
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 38
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 2
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 98
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 2
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 98
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 55
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 55
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 40
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 0
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 40
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 40
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 2
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 2
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 2
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 38
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 2
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 55
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 38
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 55
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 2
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 2
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 98
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 55
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 2
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 40
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 40
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 40
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 2
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 40
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 40
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 2
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 2
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 2
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 98
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 0
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 55
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 0
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 98
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 38
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 2
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 0
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 2
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 2
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 55
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 2
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 40
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 55
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 40
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 55
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 2
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 55
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 38
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 0
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 2
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 2
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 2
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 2
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 96
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 98
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 55
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 2
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 2
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 2
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 38
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 55
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 2
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 40
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 40
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 40
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 38
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 40
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 2
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 96
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 40
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 38
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 40
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 55
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 2
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 40
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 40
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 40
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 2
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 0
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 96
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 38
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 2
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 2
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 98
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 2
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 2
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 96
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 40
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 38
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 96
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 40
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 96
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 98
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 40
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 96
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 38
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 98
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 40
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 2
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 96
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 55
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 96
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 2
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 55
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 38
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 2
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 0
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 96
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 38
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 55
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 98
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 55
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 96
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 98
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 2
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 38
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 96
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 0
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 96
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 2
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 0
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 2
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 2
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 38
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 55
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 55
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 2
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 98
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 2
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 96
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 55
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 38
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 40
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 98
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 40
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 96
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 38
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 98
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 2
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 2
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 2
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 2
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 38
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 0
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 40
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 96
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 2
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 2
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 2
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 2
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 2
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 2
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 2
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 2
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 55
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 98
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 98
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 98
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 2
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 2
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 2
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 2
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 40
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 96
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 38
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 2
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 2
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 38
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 96
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 40
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 2
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 38
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 55
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 2
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 98
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 38
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 40
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 40
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 40
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 38
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 98
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 96
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 2
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 2
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 55
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 0
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 2
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 40
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 2
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 96
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 55
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 2
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 2
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 40
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 2
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 40
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 2
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 40
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 98
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 0
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 55
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 2
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 2
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 2
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 55
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 2
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 98
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 55
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 55
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 2
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 98
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 96
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 2
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 55
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 2
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 2
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 55
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 2
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 2
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 96
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 2
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 96
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 55
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 2
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 2
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 38
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 2
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 38
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 40
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 38
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 2
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 40
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 55
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 55
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 96
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 98
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 2
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 38
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 2
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 2
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 38
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 2
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 0
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 96
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 55
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 38
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 96
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 2
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 96
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 38
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 55
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 55
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 38
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 40
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 2
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 0
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 40
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 40
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 96
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 2
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 2
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 2
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 38
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 0
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 2
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 2
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 2
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 40
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 2
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 2
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 2
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 40
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 0
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 98
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 55
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 2
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 40
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 40
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 2
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 2
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 0
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 2
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 96
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 96
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 96
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 40
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 2
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 2
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 2
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 2
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 38
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 0
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 98
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 2
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 2
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 2
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 96
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 2
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 38
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 38
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 2
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 40
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 38
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 98
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 2
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 2
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 0
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 96
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 2
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 40
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 2
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 0
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 2
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 40
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 38
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 2
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 2
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 40
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 40
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 38
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 2
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 38
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 40
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 55
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 55
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 38
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 2
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 40
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 98
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 2
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 98
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 38
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 2
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 40
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 0
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 38
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 40
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 2
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 55
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 96
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 96
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 2
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 2
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 96
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 2
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 55
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 2
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 0
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 2
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 40
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 2
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 40
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 40
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 0
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 98
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 98
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 40
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 40
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 2
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 55
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 2
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 2
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 55
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 38
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 98
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 0
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 55
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 2
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 0
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 98
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 98
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 0
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 38
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 98
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 2
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 38
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 2
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 2
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 2
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 2
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 98
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 2
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 38
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 98
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 2
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 2
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 38
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 38
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 2
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 55
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 2
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 38
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 0
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 98
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 40
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 2
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 40
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 55
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 2
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 2
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 0
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 2
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 2
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 0
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 96
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 40
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 2
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 38
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 96
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 2
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 55
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 2
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 55
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 38
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 2
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 38
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 2
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 96
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 0
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 38
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 2
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 55
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 2
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 0
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 38
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 2
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 2
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 0
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 2
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 98
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 40
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 2
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 40
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 98
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 98
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 2
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 2
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 2
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 2
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 38
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 38
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 2
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 2
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 98
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 96
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 55
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 98
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 38
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 2
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 40
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 2
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 40
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 2
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 96
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 0
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 2
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 2
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 38
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 2
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 40
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 98
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 55
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 2
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 2
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 2
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 55
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 2
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 0
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 96
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 2
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 40
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 0
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 98
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 98
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 0
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 38
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 2
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 2
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 2
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 2
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 2
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 2
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 2
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 55
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 55
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 2
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 2
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 38
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 98
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 0
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 98
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 55
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 98
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 98
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 40
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 2
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 40
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 2
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 40
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 40
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 2
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 98
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 38
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 2
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 2
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 38
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 96
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 38
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 2
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 38
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 98
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 2
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 98
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 38
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 38
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 2
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 38
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 2
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 2
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 2
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 2
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 2
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 38
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 2
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 38
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 2
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 38
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 96
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 40
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 40
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 2
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 40
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 2
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 40
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 2
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 2
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 2
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 0
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 98
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 38
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 98
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 38
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 55
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 55
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 2
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 55
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 2
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 2
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 2
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 2
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 2
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 0
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 2
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 96
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 98
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 38
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 2
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 40
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 2
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 96
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 0
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 2
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 40
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 55
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 2
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 55
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 98
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 2
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 98
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 40
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 2
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 2
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 38
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 38
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 2
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 98
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 2
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 38
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 38
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 55
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 40
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 38
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 0
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 40
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 0
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 98
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 40
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 38
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 40
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 96
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 98
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 40
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 98
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 98
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 96
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 55
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 40
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 38
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 96
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 40
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 2
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 96
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 38
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 55
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 98
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 2
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 2
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 40
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 55
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 38
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 40
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 2
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 38
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 40
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 96
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 2
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 38
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 40
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 96
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 2
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 55
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 98
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 0
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 40
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 55
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 55
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 2
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 96
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 2
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 2
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 38
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 40
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 2
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 96
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 2
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 2
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 2
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 2
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 55
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 2
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 0
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 55
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 40
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 38
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 55
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 98
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 55
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 0
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 2
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 38
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 98
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 38
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 40
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 38
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 98
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 38
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 0
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 98
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 2
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 38
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 40
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 96
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 2
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 40
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 40
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 38
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 98
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 38
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 40
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 98
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 0
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 55
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 96
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 55
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 0
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 2
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 55
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 2
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 2
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 2
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 0
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 2
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 0
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 2
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 2
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 40
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 0
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 2
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 96
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 2
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 0
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 98
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 40
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 38
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 98
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 2
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 98
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 2
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 2
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 96
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 98
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 2
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 38
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 2
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 2
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 96
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 40
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 55
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 40
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 96
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 2
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 55
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 40
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 2
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 2
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 38
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 38
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 55
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 40
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 2
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 96
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 0
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 0
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 38
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 2
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 98
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 2
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 2
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 2
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 55
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 0
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 38
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 55
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 38
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 2
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 2
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 96
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 55
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 2
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 2
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 40
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 38
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 0
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 38
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 96
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 0
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 2
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 40
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 2
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 55
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 55
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 96
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 55
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 55
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 2
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 96
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 40
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 96
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 38
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 40
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 0
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 2
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 2
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 2
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 38
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 0
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 2
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 96
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 38
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 2
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 2
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 40
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 2
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 40
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 38
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 98
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 2
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 40
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 0
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 40
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 55
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 38
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 38
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 38
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 96
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 98
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 55
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 98
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 55
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 55
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 38
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 2
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 2
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 96
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 2
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 38
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 38
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 38
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 40
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 38
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 0
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 40
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 55
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 38
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 38
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 2
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 2
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 2
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 2
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 40
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 38
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 98
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 0
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 0
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 38
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 98
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 40
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 0
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 2
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 38
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 96
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 2
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 96
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 2
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 98
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 0
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 38
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 38
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 96
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 2
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 38
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 40
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 0
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 2
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 96
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 2
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 2
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 0
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 2
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 2
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 98
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 38
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 55
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 40
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 2
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 98
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 98
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 0
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 98
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 2
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 2
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 40
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 38
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 0
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 55
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 0
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 40
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 2
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 2
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 2
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 55
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 96
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 2
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 2
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 40
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 2
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 38
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 40
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 40
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 2
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 40
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 98
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 55
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 0
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 40
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 55
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 98
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 98
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 96
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 2
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 40
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 2
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 98
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 55
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 2
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 2
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 2
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 40
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 2
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 98
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 96
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 96
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 96
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 0
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 96
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 2
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 96
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 2
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 55
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 98
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 2
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 0
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 96
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 0
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 0
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 96
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 38
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 0
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 55
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 2
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 40
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 55
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 38
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 40
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 2
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 2
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 38
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 96
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 38
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 40
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 0
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 55
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 38
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 2
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 2
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 2
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 55
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 2
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 2
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 38
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 2
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 96
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 2
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 2
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 2
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 2
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 55
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 0
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 40
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 2
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 40
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 2
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 0
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 55
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 98
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 55
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 55
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 0
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 55
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 55
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 40
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 2
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 2
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 38
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 2
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 2
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 2
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 2
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 40
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 2
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 2
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 96
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 38
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 38
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 96
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 40
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 98
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 55
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 38
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 98
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 40
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 40
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 55
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 0
empirical probabilities from test set: {38: 0.137, 98: 0.094, 55: 0.111, 40: 0.141, 96: 0.088, 2: 0.346, 0: 0.083}
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  0.025 

learned probs for this beta: {38: np.float64(0.14418444407635472), 98: np.float64(0.14418444407635472), 55: np.float64(0.14418444407635472), 40: np.float64(0.14418444407635472), 96: np.float64(0.14418444407635472), 2: np.float64(0.13489333554187305), 0: np.float64(0.14418444407635472)}
err dic= {38: np.float64(0.007184444076354712), 98: np.float64(0.05018444407635472), 55: np.float64(0.03318444407635472), 40: np.float64(0.0031844440763547366), 96: np.float64(0.05618444407635473), 2: np.float64(0.21110666445812692), 0: np.float64(0.06118444407635472)} 

err list= [np.float64(0.007184444076354712), np.float64(0.05018444407635472), np.float64(0.03318444407635472), np.float64(0.0031844440763547366), np.float64(0.05618444407635473), np.float64(0.21110666445812692), np.float64(0.06118444407635472)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  0.05 

learned probs for this beta: {38: np.float64(0.13340509639866652), 98: np.float64(0.13340509639866652), 55: np.float64(0.13340509639866652), 40: np.float64(0.13340509639866652), 96: np.float64(0.13340509639866652), 2: np.float64(0.19956942160800215), 0: np.float64(0.13340509639866652)}
err dic= {38: np.float64(0.0035949036013334934), 98: np.float64(0.03940509639866652), 55: np.float64(0.022405096398666516), 40: np.float64(0.007594903601333469), 96: np.float64(0.04540509639866652), 2: np.float64(0.14643057839199783), 0: np.float64(0.05040509639866651)} 

err list= [np.float64(0.0035949036013334934), np.float64(0.03940509639866652), np.float64(0.022405096398666516), np.float64(0.007594903601333469), np.float64(0.04540509639866652), np.float64(0.14643057839199783), np.float64(0.05040509639866651)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  0.1 

learned probs for this beta: {38: np.float64(0.10906644158529089), 98: np.float64(0.10906644158529089), 55: np.float64(0.10906644158529089), 40: np.float64(0.10906644158529089), 96: np.float64(0.10906644158529089), 2: np.float64(0.3456013504882701), 0: np.float64(0.10906644158529089)}
err dic= {38: np.float64(0.027933558414709125), 98: np.float64(0.015066441585290885), 55: np.float64(0.0019335584147091162), 40: np.float64(0.0319335584147091), 96: np.float64(0.02106644158529089), 2: np.float64(0.00039864951172985386), 0: np.float64(0.02606644158529088)} 

err list= [np.float64(0.027933558414709125), np.float64(0.015066441585290885), np.float64(0.0019335584147091162), np.float64(0.0319335584147091), np.float64(0.02106644158529089), np.float64(0.00039864951172985386), np.float64(0.02606644158529088)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  0.25 

learned probs for this beta: {38: np.float64(0.05659863128117666), 98: np.float64(0.05659863128117666), 55: np.float64(0.05659863128117666), 40: np.float64(0.05659863128117666), 96: np.float64(0.05659863128117666), 2: np.float64(0.6604082123129397), 0: np.float64(0.05659863128117666)}
err dic= {38: np.float64(0.08040136871882335), 98: np.float64(0.03740136871882334), 55: np.float64(0.05440136871882334), 40: np.float64(0.08440136871882332), 96: np.float64(0.03140136871882333), 2: np.float64(0.3144082123129397), 0: np.float64(0.026401368718823343)} 

err list= [np.float64(0.08040136871882335), np.float64(0.03740136871882334), np.float64(0.05440136871882334), np.float64(0.08440136871882332), np.float64(0.03140136871882333), np.float64(0.3144082123129397), np.float64(0.026401368718823343)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  0.5 

learned probs for this beta: {38: np.float64(0.038840147690404794), 98: np.float64(0.038840147690404794), 55: np.float64(0.038840147690404794), 40: np.float64(0.038840147690404794), 96: np.float64(0.038840147690404794), 2: np.float64(0.766959113857573), 0: np.float64(0.038840147690404794)}
err dic= {38: np.float64(0.09815985230959522), 98: np.float64(0.055159852309595206), 55: np.float64(0.07215985230959521), 40: np.float64(0.10215985230959519), 96: np.float64(0.0491598523095952), 2: np.float64(0.420959113857573), 0: np.float64(0.04415985230959521)} 

err list= [np.float64(0.09815985230959522), np.float64(0.055159852309595206), np.float64(0.07215985230959521), np.float64(0.10215985230959519), np.float64(0.0491598523095952), np.float64(0.420959113857573), np.float64(0.04415985230959521)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  0.75 

learned probs for this beta: {38: np.float64(0.03773670429398981), 98: np.float64(0.03773670429398981), 55: np.float64(0.03773670429398981), 40: np.float64(0.03773670429398981), 96: np.float64(0.03773670429398981), 2: np.float64(0.7735797742360611), 0: np.float64(0.03773670429398981)}
err dic= {38: np.float64(0.0992632957060102), 98: np.float64(0.05626329570601019), 55: np.float64(0.0732632957060102), 40: np.float64(0.10326329570601017), 96: np.float64(0.05026329570601019), 2: np.float64(0.4275797742360611), 0: np.float64(0.0452632957060102)} 

err list= [np.float64(0.0992632957060102), np.float64(0.05626329570601019), np.float64(0.0732632957060102), np.float64(0.10326329570601017), np.float64(0.05026329570601019), np.float64(0.4275797742360611), np.float64(0.0452632957060102)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  1 

learned probs for this beta: {38: np.float64(0.03771456097972685), 98: np.float64(0.03771456097972685), 55: np.float64(0.03771456097972685), 40: np.float64(0.03771456097972685), 96: np.float64(0.03771456097972685), 2: np.float64(0.773712634121639), 0: np.float64(0.03771456097972685)}
err dic= {38: np.float64(0.09928543902027316), 98: np.float64(0.05628543902027315), 55: np.float64(0.07328543902027315), 40: np.float64(0.10328543902027314), 96: np.float64(0.050285439020273145), 2: np.float64(0.42771263412163907), 0: np.float64(0.045285439020273155)} 

err list= [np.float64(0.09928543902027316), np.float64(0.05628543902027315), np.float64(0.07328543902027315), np.float64(0.10328543902027314), np.float64(0.050285439020273145), np.float64(0.42771263412163907), np.float64(0.045285439020273155)]
results for assortment [38, 98, 55, 40, 96, 2] :

beta is  1.25 

learned probs for this beta: {38: np.float64(0.03771428607336948), 98: np.float64(0.03771428607336948), 55: np.float64(0.03771428607336948), 40: np.float64(0.03771428607336948), 96: np.float64(0.03771428607336948), 2: np.float64(0.7737142835597829), 0: np.float64(0.03771428607336948)}
err dic= {38: np.float64(0.09928571392663053), 98: np.float64(0.05628571392663052), 55: np.float64(0.07328571392663052), 40: np.float64(0.10328571392663051), 96: np.float64(0.05028571392663052), 2: np.float64(0.4277142835597829), 0: np.float64(0.04528571392663053)} 

err list= [np.float64(0.09928571392663053), np.float64(0.05628571392663052), np.float64(0.07328571392663052), np.float64(0.10328571392663051), np.float64(0.05028571392663052), np.float64(0.4277142835597829), np.float64(0.04528571392663053)]
results for assortment [38, 98, 55, 40, 96, 2] :

err MNL dic= {38: np.float64(0.014735019241341407), 98: 0, 55: 0, 40: 0, 96: 0, 2: 0, 0: 0} 

err MNL list= [np.float64(0.014735019241341407), 0, 0, 0, 0, 0, 0]
err MNL dic= {38: np.float64(0.014735019241341407), 98: np.float64(0.01891918636613525), 55: 0, 40: 0, 96: 0, 2: 0, 0: 0} 

err MNL list= [np.float64(0.014735019241341407), np.float64(0.01891918636613525), 0, 0, 0, 0, 0]
err MNL dic= {38: np.float64(0.014735019241341407), 98: np.float64(0.01891918636613525), 55: np.float64(0.003403518416712492), 40: 0, 96: 0, 2: 0, 0: 0} 

err MNL list= [np.float64(0.014735019241341407), np.float64(0.01891918636613525), np.float64(0.003403518416712492), 0, 0, 0, 0]
err MNL dic= {38: np.float64(0.014735019241341407), 98: np.float64(0.01891918636613525), 55: np.float64(0.003403518416712492), 40: np.float64(0.020934029686641), 96: 0, 2: 0, 0: 0} 

err MNL list= [np.float64(0.014735019241341407), np.float64(0.01891918636613525), np.float64(0.003403518416712492), np.float64(0.020934029686641), 0, 0, 0]
err MNL dic= {38: np.float64(0.014735019241341407), 98: np.float64(0.01891918636613525), 55: np.float64(0.003403518416712492), 40: np.float64(0.020934029686641), 96: np.float64(0.024974161627267732), 2: 0, 0: 0} 

err MNL list= [np.float64(0.014735019241341407), np.float64(0.01891918636613525), np.float64(0.003403518416712492), np.float64(0.020934029686641), np.float64(0.024974161627267732), 0, 0]
err MNL dic= {38: np.float64(0.014735019241341407), 98: np.float64(0.01891918636613525), 55: np.float64(0.003403518416712492), 40: np.float64(0.020934029686641), 96: np.float64(0.024974161627267732), 2: np.float64(0.20350412314458494), 0: 0} 

err MNL list= [np.float64(0.014735019241341407), np.float64(0.01891918636613525), np.float64(0.003403518416712492), np.float64(0.020934029686641), np.float64(0.024974161627267732), np.float64(0.20350412314458494), 0]
err MNL dic= {38: np.float64(0.014735019241341407), 98: np.float64(0.01891918636613525), 55: np.float64(0.003403518416712492), 40: np.float64(0.020934029686641), 96: np.float64(0.024974161627267732), 2: np.float64(0.20350412314458494), 0: np.float64(0.19187630566245184)} 

err MNL list= [np.float64(0.014735019241341407), np.float64(0.01891918636613525), np.float64(0.003403518416712492), np.float64(0.020934029686641), np.float64(0.024974161627267732), np.float64(0.20350412314458494), np.float64(0.19187630566245184)]
sampled assortment [64, 96, 52, 98, 83, 10]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5, 11]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 14, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 13, 100, 4, 5, 10]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 11: 0, 12: 0, 13: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 7, 10, 13, 100]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 13: 1, 25: 5, 100: 1} [8, 1, 3, 6, 7, 13, 100, 25]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 52
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 10
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 0
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 10
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 10
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 10
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 0
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 98
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 10
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 83
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 10
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 10
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 10
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 52
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 0
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 83
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 83
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 64
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 10
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 10
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 52
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 52
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 10
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 64
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 98
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 10
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 98
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 10
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 98
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 10
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 10
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 10
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 0
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 10
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 0
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 96
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 83
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 0
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 10
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 0
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 52
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 10
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 10
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 98
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 10
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 96
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 10
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 64
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 0
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 96
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 10
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 0
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 96
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 96
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 98
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 10
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 10
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 64
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 10
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 10
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 52
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 52
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 52
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 96
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 64
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 96
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 52
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 98
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 98
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 10
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 10
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 96
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 10
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 0
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 96
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 83
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 10
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 96
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 64
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 96
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 98
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 10
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 10
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 52
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 98
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 10
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 10
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 96
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 10
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 10
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 10
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 10
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 10
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 98
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 83
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 83
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 0
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 64
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 52
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 10
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 10
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 0
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 52
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 10
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 10
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 64
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 96
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 96
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 98
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 52
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 10
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 10
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 98
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 96
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 52
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 96
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 96
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 52
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 10
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 10
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 10
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 83
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 10
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 96
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 98
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 52
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 0
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 98
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 0
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 0
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 64
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 52
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 52
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 10
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 10
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 10
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 96
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 96
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 10
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 83
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 64
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 0
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 52
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 96
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 0
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 10
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 98
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 96
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 83
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 64
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 96
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 96
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 10
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 52
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 0
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 0
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 83
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 10
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 10
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 10
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 96
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 0
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 64
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 96
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 64
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 52
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 96
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 10
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 98
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 52
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 96
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 10
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 64
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 64
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 96
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 98
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 10
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 52
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 52
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 64
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 96
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 96
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 98
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 96
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 10
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 10
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 10
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 98
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 52
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 96
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 10
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 10
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 98
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 98
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 10
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 10
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 10
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 83
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 10
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 64
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 96
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 64
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 52
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 52
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 10
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 98
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 52
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 0
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 98
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 10
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 96
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 83
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 10
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 0
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 52
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 98
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 10
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 98
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 10
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 10
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 64
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 0
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 10
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 96
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 10
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 52
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 0
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 10
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 10
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 64
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 10
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 10
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 98
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 98
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 52
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 10
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 98
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 96
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 83
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 98
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 10
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 10
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 83
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 10
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 10
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 83
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 10
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 98
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 10
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 0
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 98
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 10
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 83
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 64
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 10
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 96
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 98
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 10
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 83
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 83
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 52
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 52
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 64
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 98
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 83
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 96
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 96
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 0
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 64
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 64
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 96
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 83
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 0
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 64
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 10
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 10
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 10
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 64
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 0
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 10
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 83
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 83
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 10
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 64
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 52
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 96
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 10
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 83
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 52
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 98
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 64
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 0
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 52
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 10
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 52
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 10
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 10
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 64
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 10
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 0
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 10
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 83
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 64
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 52
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 10
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 64
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 52
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 98
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 96
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 10
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 10
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 10
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 64
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 10
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 10
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 52
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 52
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 98
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 98
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 0
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 52
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 52
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 10
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 83
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 10
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 10
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 98
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 0
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 10
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 83
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 96
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 10
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 83
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 10
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 52
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 10
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 98
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 10
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 52
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 10
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 64
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 10
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 83
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 10
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 0
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 64
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 96
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 10
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 98
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 83
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 0
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 10
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 10
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 64
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 52
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 98
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 98
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 83
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 64
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 10
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 52
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 98
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 10
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 10
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 10
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 64
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 96
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 96
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 98
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 0
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 10
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 10
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 96
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 98
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 52
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 0
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 83
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 83
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 64
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 64
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 10
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 98
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 10
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 83
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 10
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 98
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 83
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 96
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 0
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 52
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 52
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 98
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 64
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 83
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 0
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 10
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 0
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 96
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 64
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 98
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 83
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 0
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 10
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 0
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 10
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 52
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 98
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 10
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 0
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 10
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 10
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 52
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 10
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 0
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 10
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 64
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 96
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 98
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 64
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 52
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 10
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 64
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 10
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 64
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 96
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 10
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 10
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 10
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 10
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 52
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 96
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 10
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 96
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 64
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 52
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 0
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 10
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 10
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 52
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 98
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 10
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 96
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 98
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 10
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 10
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 10
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 83
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 52
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 0
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 10
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 83
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 0
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 64
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 10
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 83
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 83
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 83
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 10
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 98
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 83
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 83
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 52
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 83
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 10
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 98
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 10
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 0
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 64
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 64
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 10
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 52
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 52
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 10
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 52
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 52
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 0
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 10
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 64
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 83
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 98
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 52
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 98
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 98
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 0
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 10
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 10
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 10
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 83
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 98
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 96
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 98
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 64
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 0
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 64
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 52
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 98
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 98
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 10
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 10
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 0
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 10
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 0
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 10
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 10
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 83
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 83
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 10
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 98
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 98
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 98
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 52
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 52
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 83
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 52
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 10
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 96
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 98
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 98
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 96
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 98
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 83
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 52
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 64
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 10
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 52
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 64
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 10
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 10
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 10
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 10
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 64
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 96
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 96
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 83
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 96
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 10
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 52
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 10
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 98
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 0
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 64
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 96
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 52
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 64
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 10
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 10
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 10
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 52
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 52
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 64
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 52
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 98
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 10
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 10
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 10
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 52
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 52
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 98
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 10
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 10
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 0
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 10
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 83
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 10
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 52
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 10
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 52
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 83
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 64
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 52
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 0
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 10
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 52
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 52
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 96
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 96
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 96
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 52
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 83
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 10
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 64
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 10
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 83
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 52
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 10
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 0
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 52
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 10
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 64
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 64
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 96
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 0
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 98
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 0
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 10
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 10
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 83
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 98
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 10
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 10
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 64
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 83
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 10
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 0
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 64
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 98
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 10
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 98
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 10
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 10
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 64
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 83
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 64
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 10
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 64
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 64
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 10
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 96
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 98
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 98
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 98
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 10
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 10
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 10
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 83
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 52
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 83
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 10
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 83
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 52
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 0
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 0
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 96
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 10
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 98
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 10
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 83
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 96
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 52
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 52
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 98
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 0
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 52
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 10
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 52
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 10
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 52
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 83
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 10
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 10
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 98
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 10
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 64
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 10
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 0
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 10
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 10
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 0
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 52
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 10
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 96
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 10
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 10
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 52
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 10
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 0
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 98
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 10
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 52
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 10
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 52
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 64
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 10
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 10
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 52
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 52
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 96
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 0
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 10
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 10
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 52
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 52
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 10
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 52
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 96
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 98
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 83
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 10
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 10
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 96
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 10
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 10
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 98
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 10
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 10
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 98
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 52
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 0
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 10
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 64
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 0
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 83
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 96
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 83
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 64
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 83
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 0
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 64
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 0
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 96
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 98
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 96
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 96
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 52
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 10
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 64
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 10
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 52
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 0
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 10
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 83
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 64
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 52
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 83
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 52
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 10
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 0
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 10
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 98
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 52
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 98
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 10
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 64
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 83
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 10
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 96
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 10
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 0
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 96
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 96
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 64
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 10
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 10
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 10
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 10
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 83
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 96
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 96
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 0
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 10
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 0
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 98
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 64
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 64
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 52
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 10
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 10
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 52
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 10
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 52
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 10
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 10
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 10
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 10
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 83
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 52
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 52
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 10
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 52
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 83
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 10
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 52
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 98
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 52
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 96
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 96
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 10
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 10
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 10
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 83
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 10
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 52
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 98
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 96
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 98
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 98
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 10
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 10
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 10
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 52
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 10
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 64
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 10
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 10
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 52
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 10
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 0
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 98
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 0
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 10
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 10
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 83
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 52
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 98
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 64
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 10
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 83
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 98
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 64
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 10
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 10
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 64
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 64
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 0
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 0
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 83
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 52
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 10
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 0
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 0
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 0
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 0
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 98
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 10
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 10
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 52
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 96
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 96
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 96
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 10
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 52
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 10
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 10
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 96
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 10
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 10
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 10
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 98
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 64
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 98
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 10
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 10
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 98
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 64
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 96
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 10
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 10
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 0
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 96
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 64
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 52
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 64
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 0
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 96
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 10
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 52
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 52
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 10
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 10
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 83
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 10
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 0
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 10
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 52
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 52
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 10
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 98
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 98
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 52
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 98
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 52
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 98
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 10
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 98
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 10
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 10
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 10
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 83
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 96
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 83
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 0
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 96
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 64
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 83
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 64
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 10
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 83
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 98
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 0
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 10
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 52
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 98
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 83
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 98
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 10
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 0
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 10
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 96
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 64
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 64
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 64
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 10
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 10
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 10
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 10
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 10
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 64
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 10
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 98
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 96
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 52
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 96
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 96
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 10
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 10
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 96
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 52
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 10
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 52
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 10
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 96
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 64
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 10
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 0
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 10
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 10
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 52
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 64
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 10
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 10
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 83
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 10
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 96
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 10
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 0
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 10
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 52
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 64
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 10
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 10
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 10
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 52
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 10
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 10
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 52
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 96
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 83
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 52
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 0
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 64
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 52
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 98
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 52
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 10
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 10
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 64
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 96
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 10
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 10
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 98
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 52
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 10
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 10
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 10
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 10
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 98
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 10
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 64
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 98
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 52
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 10
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 10
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 83
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 52
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 52
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 98
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 0
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 10
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 10
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 83
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 64
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 10
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 52
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 10
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 10
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 10
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 52
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 52
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 10
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 52
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 83
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 10
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 98
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 0
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 10
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 98
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 10
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 64
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 52
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 10
empirical probabilities from test set: {64: 0.102, 96: 0.103, 52: 0.148, 98: 0.117, 83: 0.089, 10: 0.347, 0: 0.094}
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  0.025 

learned probs for this beta: {64: np.float64(0.1462515060756193), 96: np.float64(0.1462515060756193), 52: np.float64(0.1462515060756193), 98: np.float64(0.1462515060756193), 83: np.float64(0.1462515060756193), 10: np.float64(0.12249096354627972), 0: np.float64(0.1462515060756193)}
err dic= {64: np.float64(0.0442515060756193), 96: np.float64(0.0432515060756193), 52: np.float64(0.0017484939243807007), 98: np.float64(0.029251506075619285), 83: np.float64(0.057251506075619296), 10: np.float64(0.22450903645372025), 0: np.float64(0.05225150607561929)} 

err list= [np.float64(0.0442515060756193), np.float64(0.0432515060756193), np.float64(0.0017484939243807007), np.float64(0.029251506075619285), np.float64(0.057251506075619296), np.float64(0.22450903645372025), np.float64(0.05225150607561929)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  0.05 

learned probs for this beta: {64: np.float64(0.143062975153689), 96: np.float64(0.143062975153689), 52: np.float64(0.143062975153689), 98: np.float64(0.143062975153689), 83: np.float64(0.143062975153689), 10: np.float64(0.14162214907787526), 0: np.float64(0.143062975153689)}
err dic= {64: np.float64(0.041062975153688994), 96: np.float64(0.04006297515368899), 52: np.float64(0.004937024846311006), 98: np.float64(0.02606297515368898), 83: np.float64(0.05406297515368899), 10: np.float64(0.2053778509221247), 0: np.float64(0.04906297515368899)} 

err list= [np.float64(0.041062975153688994), np.float64(0.04006297515368899), np.float64(0.004937024846311006), np.float64(0.02606297515368898), np.float64(0.05406297515368899), np.float64(0.2053778509221247), np.float64(0.04906297515368899)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  0.1 

learned probs for this beta: {64: np.float64(0.14007110459367772), 96: np.float64(0.14007110459367772), 52: np.float64(0.14007110459367772), 98: np.float64(0.14007110459367772), 83: np.float64(0.14007110459367772), 10: np.float64(0.15957337243793587), 0: np.float64(0.14007110459367772)}
err dic= {64: np.float64(0.038071104593677726), 96: np.float64(0.037071104593677726), 52: np.float64(0.007928895406322273), 98: np.float64(0.023071104593677713), 83: np.float64(0.051071104593677724), 10: np.float64(0.1874266275620641), 0: np.float64(0.04607110459367772)} 

err list= [np.float64(0.038071104593677726), np.float64(0.037071104593677726), np.float64(0.007928895406322273), np.float64(0.023071104593677713), np.float64(0.051071104593677724), np.float64(0.1874266275620641), np.float64(0.04607110459367772)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  0.25 

learned probs for this beta: {64: np.float64(0.0716722616230854), 96: np.float64(0.0716722616230854), 52: np.float64(0.0716722616230854), 98: np.float64(0.0716722616230854), 83: np.float64(0.0716722616230854), 10: np.float64(0.5699664302614889), 0: np.float64(0.0716722616230854)}
err dic= {64: np.float64(0.03032773837691459), 96: np.float64(0.03132773837691459), 52: np.float64(0.07632773837691459), 98: np.float64(0.0453277383769146), 83: np.float64(0.017327738376914592), 10: np.float64(0.22296643026148888), 0: np.float64(0.022327738376914597)} 

err list= [np.float64(0.03032773837691459), np.float64(0.03132773837691459), np.float64(0.07632773837691459), np.float64(0.0453277383769146), np.float64(0.017327738376914592), np.float64(0.22296643026148888), np.float64(0.022327738376914597)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  0.5 

learned probs for this beta: {64: np.float64(0.11067118138354422), 96: np.float64(0.11067118138354422), 52: np.float64(0.11067118138354422), 98: np.float64(0.11067118138354422), 83: np.float64(0.11067118138354422), 10: np.float64(0.3359729116987358), 0: np.float64(0.11067118138354422)}
err dic= {64: np.float64(0.008671181383544224), 96: np.float64(0.007671181383544223), 52: np.float64(0.037328818616455775), 98: np.float64(0.006328818616455789), 83: np.float64(0.021671181383544222), 10: np.float64(0.011027088301264198), 0: np.float64(0.016671181383544217)} 

err list= [np.float64(0.008671181383544224), np.float64(0.007671181383544223), np.float64(0.037328818616455775), np.float64(0.006328818616455789), np.float64(0.021671181383544222), np.float64(0.011027088301264198), np.float64(0.016671181383544217)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  0.75 

learned probs for this beta: {64: np.float64(0.14285714285714288), 96: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 98: np.float64(0.14285714285714288), 83: np.float64(0.14285714285714288), 10: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
err dic= {64: np.float64(0.040857142857142884), 96: np.float64(0.03985714285714288), 52: np.float64(0.005142857142857116), 98: np.float64(0.02585714285714287), 83: np.float64(0.05385714285714288), 10: np.float64(0.2041428571428571), 0: np.float64(0.04885714285714288)} 

err list= [np.float64(0.040857142857142884), np.float64(0.03985714285714288), np.float64(0.005142857142857116), np.float64(0.02585714285714287), np.float64(0.05385714285714288), np.float64(0.2041428571428571), np.float64(0.04885714285714288)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  1 

learned probs for this beta: {64: np.float64(0.1051699272669473), 96: np.float64(0.1051699272669473), 52: np.float64(0.1051699272669473), 98: np.float64(0.1051699272669473), 83: np.float64(0.1051699272669473), 10: np.float64(0.3689804363983163), 0: np.float64(0.1051699272669473)}
err dic= {64: np.float64(0.0031699272669473005), 96: np.float64(0.0021699272669472996), 52: np.float64(0.0428300727330527), 98: np.float64(0.011830072733052713), 83: np.float64(0.016169927266947298), 10: np.float64(0.021980436398316316), 0: np.float64(0.011169927266947294)} 

err list= [np.float64(0.0031699272669473005), np.float64(0.0021699272669472996), np.float64(0.0428300727330527), np.float64(0.011830072733052713), np.float64(0.016169927266947298), np.float64(0.021980436398316316), np.float64(0.011169927266947294)]
results for assortment [64, 96, 52, 98, 83, 10] :

beta is  1.25 

learned probs for this beta: {64: np.float64(0.10514299658356532), 96: np.float64(0.10514299658356532), 52: np.float64(0.10514299658356532), 98: np.float64(0.10514299658356532), 83: np.float64(0.10514299658356532), 10: np.float64(0.3691420204986079), 0: np.float64(0.10514299658356532)}
err dic= {64: np.float64(0.00314299658356533), 96: np.float64(0.002142996583565329), 52: np.float64(0.04285700341643467), 98: np.float64(0.011857003416434683), 83: np.float64(0.016142996583565328), 10: np.float64(0.022142020498607917), 0: np.float64(0.011142996583565323)} 

err list= [np.float64(0.00314299658356533), np.float64(0.002142996583565329), np.float64(0.04285700341643467), np.float64(0.011857003416434683), np.float64(0.016142996583565328), np.float64(0.022142020498607917), np.float64(0.011142996583565323)]
results for assortment [64, 96, 52, 98, 83, 10] :

err MNL dic= {64: np.float64(0.015647058823529403), 96: 0, 52: 0, 98: 0, 83: 0, 10: 0, 0: 0} 

err MNL list= [np.float64(0.015647058823529403), 0, 0, 0, 0, 0, 0]
err MNL dic= {64: np.float64(0.015647058823529403), 96: np.float64(0.011539187432898237), 52: 0, 98: 0, 83: 0, 10: 0, 0: 0} 

err MNL list= [np.float64(0.015647058823529403), np.float64(0.011539187432898237), 0, 0, 0, 0, 0]
err MNL dic= {64: np.float64(0.015647058823529403), 96: np.float64(0.011539187432898237), 52: np.float64(0.02792315081652258), 98: 0, 83: 0, 10: 0, 0: 0} 

err MNL list= [np.float64(0.015647058823529403), np.float64(0.011539187432898237), np.float64(0.02792315081652258), 0, 0, 0, 0]
err MNL dic= {64: np.float64(0.015647058823529403), 96: np.float64(0.011539187432898237), 52: np.float64(0.02792315081652258), 98: np.float64(0.004269028648923562), 83: 0, 10: 0, 0: 0} 

err MNL list= [np.float64(0.015647058823529403), np.float64(0.011539187432898237), np.float64(0.02792315081652258), np.float64(0.004269028648923562), 0, 0, 0]
err MNL dic= {64: np.float64(0.015647058823529403), 96: np.float64(0.011539187432898237), 52: np.float64(0.02792315081652258), 98: np.float64(0.004269028648923562), 83: np.float64(0.024522065886873473), 10: 0, 0: 0} 

err MNL list= [np.float64(0.015647058823529403), np.float64(0.011539187432898237), np.float64(0.02792315081652258), np.float64(0.004269028648923562), np.float64(0.024522065886873473), 0, 0]
err MNL dic= {64: np.float64(0.015647058823529403), 96: np.float64(0.011539187432898237), 52: np.float64(0.02792315081652258), 98: np.float64(0.004269028648923562), 83: np.float64(0.024522065886873473), 10: np.float64(0.20804989546250774), 0: 0} 

err MNL list= [np.float64(0.015647058823529403), np.float64(0.011539187432898237), np.float64(0.02792315081652258), np.float64(0.004269028648923562), np.float64(0.024522065886873473), np.float64(0.20804989546250774), 0]
err MNL dic= {64: np.float64(0.015647058823529403), 96: np.float64(0.011539187432898237), 52: np.float64(0.02792315081652258), 98: np.float64(0.004269028648923562), 83: np.float64(0.024522065886873473), 10: np.float64(0.20804989546250774), 0: np.float64(0.18853376278465275)} 

err MNL list= [np.float64(0.015647058823529403), np.float64(0.011539187432898237), np.float64(0.02792315081652258), np.float64(0.004269028648923562), np.float64(0.024522065886873473), np.float64(0.20804989546250774), np.float64(0.18853376278465275)]
sampled assortment [97, 8, 78, 7, 20, 32]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 100, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 15, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 14, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 3, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 1, 19: 1, 100: 1} [8, 1, 3, 6, 7, 10, 14, 19, 100, 4]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0} [1, 2, 3, 4, 5, 7, 9, 11, 12, 14]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 20: 2, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 13, 100, 5, 20]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 10, 11, 12, 100]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 9]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 12: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 11, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 14: 1, 16: 2, 100: 1} [8, 1, 3, 4, 5, 6, 7, 10, 13, 14, 100, 2, 12, 16]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 2]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 19: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 11, 19]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 100]
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 14]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 12: 3, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 2, 5, 12]
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 100]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 8
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 8
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 8
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 20
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 32
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 8
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 78
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 20
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 20
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 8
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 8
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 7
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 78
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 8
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 0
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 8
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 32
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 8
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 7
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 0
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 7
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 20
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 7
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 20
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 8
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 20
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 20
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 8
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 8
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 20
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 20
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 78
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 8
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 97
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 7
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 8
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 7
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 32
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 8
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 8
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 97
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 78
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 7
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 8
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 20
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 8
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 32
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 7
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 0
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 7
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 8
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 8
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 8
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 8
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 7
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 8
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 20
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 97
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 78
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 8
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 97
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 0
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 97
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 20
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 0
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 0
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 8
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 20
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 7
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 20
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 7
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 20
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 0
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 8
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 20
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 8
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 20
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 8
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 7
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 20
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 7
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 32
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 20
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 8
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 97
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 7
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 8
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 8
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 78
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 97
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 32
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 20
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 0
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 8
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 0
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 20
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 0
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 8
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 7
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 20
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 8
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 8
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 7
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 32
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 20
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 20
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 0
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 7
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 0
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 20
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 97
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 8
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 8
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 78
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 8
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 8
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 32
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 7
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 7
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 8
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 8
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 8
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 7
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 32
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 7
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 8
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 7
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 7
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 20
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 7
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 8
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 32
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 20
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 8
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 7
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 78
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 8
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 20
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 20
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 78
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 8
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 8
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 0
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 97
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 97
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 8
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 8
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 7
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 20
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 20
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 8
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 8
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 7
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 0
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 7
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 8
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 0
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 78
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 97
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 32
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 8
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 32
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 78
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 8
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 8
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 7
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 20
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 7
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 32
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 7
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 7
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 7
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 97
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 32
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 20
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 8
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 32
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 8
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 0
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 8
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 20
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 7
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 20
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 7
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 32
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 0
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 20
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 78
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 20
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 97
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 0
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 7
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 7
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 8
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 8
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 7
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 20
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 20
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 7
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 7
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 7
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 97
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 20
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 97
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 8
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 7
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 32
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 20
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 0
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 8
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 7
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 78
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 20
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 8
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 78
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 7
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 7
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 32
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 8
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 32
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 20
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 20
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 20
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 32
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 20
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 20
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 0
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 8
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 97
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 32
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 20
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 7
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 7
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 7
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 20
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 8
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 20
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 7
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 20
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 0
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 8
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 32
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 8
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 7
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 7
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 20
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 7
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 8
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 20
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 8
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 8
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 78
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 8
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 32
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 8
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 8
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 0
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 20
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 8
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 0
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 7
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 20
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 32
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 8
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 7
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 32
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 7
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 32
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 8
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 8
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 8
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 7
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 78
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 97
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 97
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 7
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 32
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 7
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 7
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 7
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 8
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 7
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 8
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 8
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 8
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 32
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 20
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 32
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 7
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 7
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 32
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 20
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 0
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 7
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 20
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 7
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 32
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 97
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 8
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 78
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 8
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 78
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 32
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 20
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 8
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 7
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 8
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 7
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 8
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 32
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 7
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 20
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 20
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 8
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 20
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 7
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 8
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 8
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 8
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 0
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 7
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 0
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 78
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 20
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 78
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 78
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 8
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 8
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 7
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 20
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 8
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 7
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 7
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 8
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 7
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 8
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 78
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 20
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 97
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 8
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 7
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 7
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 7
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 20
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 8
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 20
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 32
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 8
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 20
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 7
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 7
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 0
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 97
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 7
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 32
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 8
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 7
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 7
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 97
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 8
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 8
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 78
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 97
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 78
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 8
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 7
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 7
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 20
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 7
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 0
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 32
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 32
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 32
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 7
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 20
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 97
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 78
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 20
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 97
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 7
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 20
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 8
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 8
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 8
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 7
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 20
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 78
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 78
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 20
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 78
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 7
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 97
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 32
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 20
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 32
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 8
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 7
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 97
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 97
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 32
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 32
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 97
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 7
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 20
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 8
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 7
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 78
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 32
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 78
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 20
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 78
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 20
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 0
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 8
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 0
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 7
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 8
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 20
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 20
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 7
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 7
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 32
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 32
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 20
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 20
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 78
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 8
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 20
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 20
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 8
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 8
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 7
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 7
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 20
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 20
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 20
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 7
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 7
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 8
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 0
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 32
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 0
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 32
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 20
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 7
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 32
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 32
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 7
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 8
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 8
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 32
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 97
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 0
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 7
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 0
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 8
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 8
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 20
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 8
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 8
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 20
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 20
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 8
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 7
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 97
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 78
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 32
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 78
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 97
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 7
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 8
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 7
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 8
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 20
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 8
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 8
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 8
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 7
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 8
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 7
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 20
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 97
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 32
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 7
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 8
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 20
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 0
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 8
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 8
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 97
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 20
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 20
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 8
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 7
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 0
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 97
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 7
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 32
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 8
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 8
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 8
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 20
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 7
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 8
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 20
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 32
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 8
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 97
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 8
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 97
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 7
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 7
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 7
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 7
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 7
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 8
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 97
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 8
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 32
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 78
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 7
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 7
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 20
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 97
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 7
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 20
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 20
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 32
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 20
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 32
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 78
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 8
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 8
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 20
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 32
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 20
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 8
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 20
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 8
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 97
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 7
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 7
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 7
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 20
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 8
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 78
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 20
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 20
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 8
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 8
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 8
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 8
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 20
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 78
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 32
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 20
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 20
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 0
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 7
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 7
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 7
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 7
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 8
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 20
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 32
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 7
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 8
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 20
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 8
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 78
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 8
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 7
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 78
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 7
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 20
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 78
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 97
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 32
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 8
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 8
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 8
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 78
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 20
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 78
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 78
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 7
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 32
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 8
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 7
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 32
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 32
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 32
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 8
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 8
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 8
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 8
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 20
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 8
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 20
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 20
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 8
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 7
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 20
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 20
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 20
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 0
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 8
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 32
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 78
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 32
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 7
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 32
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 20
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 97
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 7
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 7
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 32
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 8
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 32
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 8
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 20
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 32
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 0
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 7
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 8
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 78
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 7
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 7
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 8
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 7
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 7
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 8
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 78
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 7
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 8
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 20
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 7
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 20
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 7
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 7
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 8
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 20
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 8
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 32
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 8
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 7
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 8
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 7
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 7
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 7
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 97
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 97
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 8
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 8
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 20
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 32
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 8
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 97
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 7
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 7
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 97
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 0
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 20
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 97
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 8
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 20
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 8
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 78
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 8
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 20
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 8
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 20
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 7
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 0
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 20
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 78
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 7
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 8
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 8
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 8
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 20
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 7
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 7
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 20
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 20
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 8
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 8
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 20
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 8
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 7
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 7
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 0
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 0
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 32
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 8
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 8
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 8
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 8
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 7
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 8
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 32
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 7
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 7
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 78
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 8
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 78
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 7
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 78
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 8
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 7
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 7
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 8
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 32
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 78
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 7
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 8
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 7
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 7
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 20
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 8
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 7
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 7
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 78
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 20
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 8
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 7
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 7
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 7
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 20
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 8
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 8
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 78
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 7
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 8
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 32
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 20
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 7
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 7
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 7
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 20
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 78
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 0
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 8
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 7
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 20
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 20
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 8
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 8
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 7
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 97
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 97
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 20
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 8
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 7
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 20
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 8
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 7
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 78
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 7
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 97
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 32
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 8
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 32
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 20
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 7
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 97
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 8
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 8
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 20
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 7
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 8
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 8
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 7
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 7
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 8
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 20
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 97
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 7
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 7
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 20
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 78
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 0
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 8
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 20
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 20
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 0
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 7
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 8
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 32
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 20
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 32
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 20
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 7
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 32
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 78
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 8
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 0
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 20
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 97
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 32
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 20
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 8
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 8
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 32
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 32
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 20
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 20
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 8
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 20
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 8
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 20
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 32
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 78
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 97
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 7
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 7
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 7
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 20
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 32
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 20
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 32
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 32
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 8
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 8
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 8
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 8
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 8
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 7
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 97
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 20
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 7
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 78
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 32
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 7
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 8
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 20
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 8
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 78
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 7
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 8
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 8
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 7
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 20
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 0
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 8
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 20
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 8
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 8
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 8
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 8
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 8
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 78
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 32
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 32
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 8
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 0
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 97
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 7
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 78
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 7
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 8
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 8
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 7
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 8
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 20
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 8
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 8
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 8
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 7
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 32
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 8
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 7
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 32
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 7
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 8
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 78
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 7
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 78
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 20
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 8
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 8
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 20
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 32
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 8
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 78
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 32
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 32
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 8
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 8
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 8
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 20
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 32
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 7
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 97
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 97
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 8
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 8
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 32
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 7
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 20
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 32
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 32
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 8
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 32
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 0
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 20
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 8
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 7
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 32
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 8
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 20
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 20
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 7
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 20
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 0
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 8
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 20
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 97
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 0
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 32
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 20
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 8
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 32
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 32
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 8
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 8
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 7
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 78
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 32
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 20
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 8
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 78
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 8
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 8
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 7
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 32
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 7
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 20
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 32
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 78
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 7
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 7
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 8
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 8
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 97
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 20
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 32
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 7
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 32
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 7
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 8
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 32
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 8
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 8
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 0
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 8
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 7
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 7
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 8
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 8
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 7
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 8
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 7
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 0
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 20
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 32
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 20
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 7
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 32
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 7
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 8
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 20
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 32
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 8
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 8
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 78
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 7
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 20
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 32
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 32
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 32
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 0
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 7
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 8
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 20
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 7
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 32
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 7
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 8
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 7
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 20
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 8
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 20
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 97
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 32
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 8
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 8
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 8
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 0
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 20
empirical probabilities from test set: {97: 0.061, 8: 0.28, 78: 0.071, 7: 0.225, 20: 0.187, 32: 0.12, 0: 0.056}
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  0.025 

learned probs for this beta: {97: np.float64(0.14770342149585), 8: np.float64(0.14272693075614004), 78: np.float64(0.14770342149585), 7: np.float64(0.11875596176461242), 20: np.float64(0.14770342149585), 32: np.float64(0.14770342149585), 0: np.float64(0.14770342149585)}
err dic= {97: np.float64(0.08670342149585), 8: np.float64(0.13727306924385999), 78: np.float64(0.07670342149585001), 7: np.float64(0.10624403823538758), 20: np.float64(0.03929657850415), 32: np.float64(0.027703421495850006), 0: np.float64(0.09170342149585001)} 

err list= [np.float64(0.08670342149585), np.float64(0.13727306924385999), np.float64(0.07670342149585001), np.float64(0.10624403823538758), np.float64(0.03929657850415), np.float64(0.027703421495850006), np.float64(0.09170342149585001)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  0.05 

learned probs for this beta: {97: np.float64(0.13892207697133033), 8: np.float64(0.1570672614639566), 78: np.float64(0.13892207697133033), 7: np.float64(0.14832235367940103), 20: np.float64(0.13892207697133033), 32: np.float64(0.13892207697133033), 0: np.float64(0.13892207697133033)}
err dic= {97: np.float64(0.07792207697133033), 8: np.float64(0.12293273853604342), 78: np.float64(0.06792207697133033), 7: np.float64(0.07667764632059898), 20: np.float64(0.04807792302866967), 32: np.float64(0.01892207697133033), 0: np.float64(0.08292207697133033)} 

err list= [np.float64(0.07792207697133033), np.float64(0.12293273853604342), np.float64(0.06792207697133033), np.float64(0.07667764632059898), np.float64(0.04807792302866967), np.float64(0.01892207697133033), np.float64(0.08292207697133033)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  0.1 

learned probs for this beta: {97: np.float64(0.1216074297361495), 8: np.float64(0.21794622886821127), 78: np.float64(0.1216074297361495), 7: np.float64(0.1740166224510522), 20: np.float64(0.1216074297361495), 32: np.float64(0.1216074297361495), 0: np.float64(0.1216074297361495)}
err dic= {97: np.float64(0.06060742973614951), 8: np.float64(0.062053771131788754), 78: np.float64(0.05060742973614951), 7: np.float64(0.0509833775489478), 20: np.float64(0.0653925702638505), 32: np.float64(0.00160742973614951), 0: np.float64(0.0656074297361495)} 

err list= [np.float64(0.06060742973614951), np.float64(0.062053771131788754), np.float64(0.05060742973614951), np.float64(0.0509833775489478), np.float64(0.0653925702638505), np.float64(0.00160742973614951), np.float64(0.0656074297361495)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  0.25 

learned probs for this beta: {97: np.float64(0.04983412331934364), 8: np.float64(0.22060827542272995), 78: np.float64(0.04983412331934364), 7: np.float64(0.5302211079805517), 20: np.float64(0.04983412331934364), 32: np.float64(0.04983412331934364), 0: np.float64(0.04983412331934364)}
err dic= {97: np.float64(0.011165876680656356), 8: np.float64(0.05939172457727007), 78: np.float64(0.02116587668065635), 7: np.float64(0.3052211079805517), 20: np.float64(0.13716587668065636), 32: np.float64(0.07016587668065635), 0: np.float64(0.006165876680656358)} 

err list= [np.float64(0.011165876680656356), np.float64(0.05939172457727007), np.float64(0.02116587668065635), np.float64(0.3052211079805517), np.float64(0.13716587668065636), np.float64(0.07016587668065635), np.float64(0.006165876680656358)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  0.5 

learned probs for this beta: {97: np.float64(0.10519428021497039), 8: np.float64(0.32171501542833403), 78: np.float64(0.10519428021497039), 7: np.float64(0.1523135834968146), 20: np.float64(0.10519428021497039), 32: np.float64(0.10519428021497039), 0: np.float64(0.10519428021497039)}
err dic= {97: np.float64(0.04419428021497039), 8: np.float64(0.041715015428334), 78: np.float64(0.034194280214970396), 7: np.float64(0.07268641650318541), 20: np.float64(0.08180571978502961), 32: np.float64(0.014805719785029606), 0: np.float64(0.04919428021497039)} 

err list= [np.float64(0.04419428021497039), np.float64(0.041715015428334), np.float64(0.034194280214970396), np.float64(0.07268641650318541), np.float64(0.08180571978502961), np.float64(0.014805719785029606), np.float64(0.04919428021497039)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  0.75 

learned probs for this beta: {97: np.float64(0.10514356105726134), 8: np.float64(0.3456012357210425), 78: np.float64(0.10514356105726134), 7: np.float64(0.12868095899265103), 20: np.float64(0.10514356105726134), 32: np.float64(0.10514356105726134), 0: np.float64(0.10514356105726134)}
err dic= {97: np.float64(0.044143561057261346), 8: np.float64(0.06560123572104248), 78: np.float64(0.03414356105726135), 7: np.float64(0.09631904100734898), 20: np.float64(0.08185643894273865), 32: np.float64(0.01485643894273865), 0: np.float64(0.049143561057261344)} 

err list= [np.float64(0.044143561057261346), np.float64(0.06560123572104248), np.float64(0.03414356105726135), np.float64(0.09631904100734898), np.float64(0.08185643894273865), np.float64(0.01485643894273865), np.float64(0.049143561057261344)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  1 

learned probs for this beta: {97: np.float64(1.3607455372106143e-05), 8: np.float64(0.25326565291617353), 78: np.float64(1.3607455372106143e-05), 7: np.float64(0.7466663098069661), 20: np.float64(1.3607455372106143e-05), 32: np.float64(1.3607455372106143e-05), 0: np.float64(1.3607455372106143e-05)}
err dic= {97: np.float64(0.06098639254462789), 8: np.float64(0.026734347083826493), 78: np.float64(0.0709863925446279), 7: np.float64(0.5216663098069662), 20: np.float64(0.1869863925446279), 32: np.float64(0.1199863925446279), 0: np.float64(0.055986392544627894)} 

err list= [np.float64(0.06098639254462789), np.float64(0.026734347083826493), np.float64(0.0709863925446279), np.float64(0.5216663098069662), np.float64(0.1869863925446279), np.float64(0.1199863925446279), np.float64(0.055986392544627894)]
results for assortment [97, 8, 78, 7, 20, 32] :

beta is  1.25 

learned probs for this beta: {97: np.float64(1.480321889374064e-07), 8: np.float64(0.2593897362899494), 78: np.float64(1.480321889374064e-07), 7: np.float64(0.7406095235491056), 20: np.float64(1.480321889374064e-07), 32: np.float64(1.480321889374064e-07), 0: np.float64(1.480321889374064e-07)}
err dic= {97: np.float64(0.06099985196781106), 8: np.float64(0.020610263710050647), 78: np.float64(0.07099985196781106), 7: np.float64(0.5156095235491056), 20: np.float64(0.18699985196781108), 32: np.float64(0.11999985196781106), 0: np.float64(0.055999851967811064)} 

err list= [np.float64(0.06099985196781106), np.float64(0.020610263710050647), np.float64(0.07099985196781106), np.float64(0.5156095235491056), np.float64(0.18699985196781108), np.float64(0.11999985196781106), np.float64(0.055999851967811064)]
results for assortment [97, 8, 78, 7, 20, 32] :

err MNL dic= {97: np.float64(0.049190776465558694), 8: 0, 78: 0, 7: 0, 20: 0, 32: 0, 0: 0} 

err MNL list= [np.float64(0.049190776465558694), 0, 0, 0, 0, 0, 0]
err MNL dic= {97: np.float64(0.049190776465558694), 8: np.float64(0.1434639021001443), 78: 0, 7: 0, 20: 0, 32: 0, 0: 0} 

err MNL list= [np.float64(0.049190776465558694), np.float64(0.1434639021001443), 0, 0, 0, 0, 0]
err MNL dic= {97: np.float64(0.049190776465558694), 8: np.float64(0.1434639021001443), 78: np.float64(0.03865638860685085), 7: 0, 20: 0, 32: 0, 0: 0} 

err MNL list= [np.float64(0.049190776465558694), np.float64(0.1434639021001443), np.float64(0.03865638860685085), 0, 0, 0, 0]
err MNL dic= {97: np.float64(0.049190776465558694), 8: np.float64(0.1434639021001443), 78: np.float64(0.03865638860685085), 7: np.float64(0.09049457596323413), 20: 0, 32: 0, 0: 0} 

err MNL list= [np.float64(0.049190776465558694), np.float64(0.1434639021001443), np.float64(0.03865638860685085), np.float64(0.09049457596323413), 0, 0, 0]
err MNL dic= {97: np.float64(0.049190776465558694), 8: np.float64(0.1434639021001443), 78: np.float64(0.03865638860685085), 7: np.float64(0.09049457596323413), 20: np.float64(0.06093790413081815), 32: 0, 0: 0} 

err MNL list= [np.float64(0.049190776465558694), np.float64(0.1434639021001443), np.float64(0.03865638860685085), np.float64(0.09049457596323413), np.float64(0.06093790413081815), 0, 0]
err MNL dic= {97: np.float64(0.049190776465558694), 8: np.float64(0.1434639021001443), 78: np.float64(0.03865638860685085), 7: np.float64(0.09049457596323413), 20: np.float64(0.06093790413081815), 32: np.float64(0.004144712232138095), 0: 0} 

err MNL list= [np.float64(0.049190776465558694), np.float64(0.1434639021001443), np.float64(0.03865638860685085), np.float64(0.09049457596323413), np.float64(0.06093790413081815), np.float64(0.004144712232138095), 0]
err MNL dic= {97: np.float64(0.049190776465558694), 8: np.float64(0.1434639021001443), 78: np.float64(0.03865638860685085), 7: np.float64(0.09049457596323413), 20: np.float64(0.06093790413081815), 32: np.float64(0.004144712232138095), 0: np.float64(0.21119392935392506)} 

err MNL list= [np.float64(0.049190776465558694), np.float64(0.1434639021001443), np.float64(0.03865638860685085), np.float64(0.09049457596323413), np.float64(0.06093790413081815), np.float64(0.004144712232138095), np.float64(0.21119392935392506)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25]
 mean error for all betas:

mean_err= [0.08080391 0.075786   0.06751731 0.07243949 0.06762575 0.06554679
 0.07747547 0.08620566]
mean_std= [0.         0.00501791 0.01239068 0.01370512 0.01558693 0.01496899
 0.03233915 0.03806057]
MNL: [0.05698229 0.06228778 0.08553617 0.05592123 0.07502777 0.07122077
 0.07458863 0.08212799 0.05465777 0.06833519 0.06864059 0.08544031]
 mean error for MNL:

mean_err_MNL= 0.07006387440265775
mean_std_MNL= 0.010574315230949531
