p= 0.1 num clusters= 5
linkage completed in  13.584676742553711
silhouette_score of the clusters -0.01594559475407355
sampled assortment [7, 8, 6, 3, 32, 100, 81, 98]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 19: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 6, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 15: 1} [1, 5, 6, 7, 9, 10, 11, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 11: 5, 13: 2, 16: 8, 17: 5, 23: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 11, 17, 23, 16]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 2, 4, 5, 7, 10, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 16: 1, 100: 1} [2, 3, 4, 6, 7, 10, 11, 14, 16, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 7: 1, 9: 1, 10: 1, 14: 1, 26: 2} [1, 3, 7, 9, 10, 14, 26]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 8: 4, 10: 2, 13: 2, 14: 6, 15: 3, 20: 5, 24: 8, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 20, 14, 24]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 100: 1} [2, 1, 3, 6, 10, 11, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1} [1, 3, 5, 7, 9, 10, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 16: 7, 17: 5, 20: 6, 100: 0} [6, 100, 1, 3, 10, 13, 8, 5, 7, 17, 20, 16]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 11: 1, 13: 1, 16: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 11, 13, 16, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 21: 1} [2, 1, 6, 7, 10, 11, 21]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 19: 1} [1, 5, 7, 9, 10, 14, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 11: 1, 13: 1, 100: 1} [8, 1, 2, 3, 7, 11, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 12: 1, 13: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 12, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1} [1, 3, 4, 5, 7, 9, 10, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 11: 5, 13: 2, 15: 3, 17: 7, 20: 5, 21: 7, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 4, 11, 20, 17, 21]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 100: 1} [2, 1, 3, 6, 10, 11, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 18: 1} [1, 3, 5, 7, 9, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 11: 4, 13: 2, 15: 3, 17: 7, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 11, 17]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 12: 1, 20: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 12, 20, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 20: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 20, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 17: 1} [2, 1, 6, 7, 10, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 14: 1} [1, 3, 4, 5, 7, 9, 10, 11, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 5, 10: 2, 13: 2, 16: 8, 19: 5, 23: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 19, 23, 16]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 7: 1, 8: 0, 11: 1, 14: 1, 100: 1} [8, 1, 2, 7, 11, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 10, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1, 15: 1} [1, 3, 4, 7, 9, 10, 13, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 4, 16: 8, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11, 23, 16]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 12: 1, 13: 1, 100: 1} [8, 3, 4, 7, 10, 12, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 19: 0, 100: 0} [3, 4, 5, 6, 9, 11, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 15: 1, 24: 2, 100: 1} [1, 3, 4, 5, 7, 9, 15, 100, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 4, 13: 2, 14: 6, 15: 4, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 7, 11, 15, 5, 17, 20, 14]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 9: 1, 17: 1} [8, 1, 2, 3, 4, 5, 7, 9, 17]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 11: 1, 100: 1} [2, 1, 6, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 14: 1, 15: 1, 100: 1} [1, 3, 4, 5, 7, 9, 14, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 3, 19: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 5, 11, 20, 19]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [3, 4, 5, 6, 7, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 100: 1} [2, 1, 3, 6, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 11, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 15: 3, 16: 7, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 7, 17, 16]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1} [2, 1, 3, 4, 6, 10, 11, 12]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 7: 1, 9: 1, 10: 1, 14: 1, 18: 1} [1, 3, 4, 7, 9, 10, 14, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 2, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 18: 1, 100: 1} [2, 1, 6, 10, 11, 13, 18, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 24: 1, 100: 1} [1, 5, 7, 9, 10, 24, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 4, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 15, 11, 20]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 9: 1, 14: 1, 22: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 9, 14, 22, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 17: 1, 21: 1, 100: 1} [2, 3, 6, 7, 10, 11, 12, 17, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 7: 1, 9: 1, 12: 1, 14: 1, 100: 1} [1, 3, 4, 7, 9, 12, 14, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 8: 4, 10: 1, 11: 5, 13: 2, 14: 5, 15: 3, 100: 0} [6, 100, 10, 1, 3, 13, 15, 8, 7, 11, 14]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 9, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1} [2, 1, 4, 6, 7, 10, 11]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 7: 1, 9: 1, 12: 1, 14: 1, 15: 1, 24: 2} [1, 7, 9, 12, 14, 15, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 8: 4, 10: 2, 13: 2, 14: 5, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 14, 20]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 2, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 21: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 21, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 100: 1} [2, 1, 3, 6, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 13: 1} [1, 3, 4, 5, 7, 9, 10, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 2, 3, 4, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 13: 1, 100: 1} [2, 1, 3, 4, 6, 10, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1} [1, 3, 4, 5, 7, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 3, 6: 0, 7: 4, 10: 2, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 4, 5, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 7: 1, 9: 1, 10: 1, 14: 1, 100: 1} [2, 1, 4, 7, 9, 10, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 12: 1, 13: 1} [1, 4, 5, 7, 9, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 11, 7, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1} [8, 1, 2, 3, 7, 10]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 15: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 12, 15, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 19: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 12, 19, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 9: 1, 10: 1, 11: 1, 22: 2} [1, 3, 5, 6, 9, 10, 11, 22]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 16: 6, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 5, 16, 17]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 12: 1, 17: 1} [8, 1, 2, 3, 5, 7, 12, 17]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 6, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 13: 1, 14: 1} [1, 5, 7, 9, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 3, 10: 2, 11: 5, 13: 2, 15: 4, 17: 7, 100: 0} [6, 100, 1, 3, 10, 13, 8, 7, 15, 5, 11, 17]
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 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 100
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 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 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 81
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 6
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 3
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 3
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 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 7
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 6
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 6
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 6
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 3
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 3
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 100
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 3
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 100
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 100
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 6
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 3
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 6
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 3
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 6
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 3
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 6
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 100
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 6
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 3
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 3
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 3
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 32
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 8
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 6
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 3
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 3
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 6
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 32
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 6
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 3
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 98
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 6
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 98
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 0
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 6
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 3
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 6
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
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 3
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 3
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 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 98
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 3
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 6
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 6
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 100
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 32
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 3
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 3
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 8
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 3
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 3
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 6
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 3
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 100
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 32
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 6
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 6
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 3
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 6
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 6
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 3
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 8
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 81
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 8
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 81
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 7
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
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 100
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 6
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 100
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 3
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 6
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 3
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 6
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 3
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 3
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 98
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 8
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 81
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 6
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 81
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 6
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 0
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 6
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 6
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 7
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 6
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 6
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 100
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 6
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 100
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 3
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 3
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 3
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 7
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 3
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 6
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 100
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 6
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 6
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 7
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 3
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 32
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 3
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 100
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 3
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 81
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 6
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 8
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 7
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 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 3
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 3
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 6
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 7
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 98
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 100
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 3
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 8
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 6
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 98
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 6
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 81
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 3
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 3
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 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 3
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 3
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 32
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 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 6
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 100
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 100
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 7
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 3
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 6
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 32
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 6
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 3
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 3
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 6
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 3
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 3
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 6
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 8
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 6
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 6
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 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 6
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 100
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 8
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 3
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 3
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 3
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 100
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 100
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 6
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 100
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 3
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 3
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 3
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 6
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 6
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 6
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 6
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 3
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 8
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 7
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 6
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 6
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 3
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 100
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 81
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 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 3
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 3
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 3
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 6
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 3
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 8
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 6
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 3
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 81
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 6
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 6
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 7
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 98
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 32
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 6
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 6
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 6
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 3
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 3
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 3
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 3
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 100
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 3
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 6
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 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 3
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 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 100
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 6
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 3
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 6
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 32
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 3
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 6
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 3
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 3
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 3
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 100
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 6
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 100
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 6
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 81
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 6
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 3
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 6
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 32
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 6
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 100
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 98
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 6
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 32
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 81
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 3
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 98
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 3
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 6
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 32
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 32
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 6
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 3
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 100
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 6
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 100
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 6
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 6
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 7
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 100
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 6
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 3
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 6
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 6
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 7
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 6
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 6
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 81
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 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 6
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 3
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 6
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 6
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 7
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 7
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 6
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 3
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 100
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 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 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 6
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 8
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 3
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 6
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 100
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 7
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 81
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 3
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 6
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 6
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 6
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 100
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 6
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 6
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 3
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 3
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 3
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 6
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 6
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 81
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 3
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 3
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 3
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 3
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 98
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 6
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 3
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 8
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 6
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 6
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 6
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 6
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 100
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 3
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 100
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 3
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 81
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 98
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 3
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 81
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 3
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 3
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 8
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 6
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 100
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 32
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 6
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 100
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 100
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 100
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 6
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 6
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 98
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 98
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 6
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 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 7
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 7
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
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 100
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 3
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 6
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 100
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 100
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 6
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 3
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 6
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 100
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 6
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 32
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 7
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 6
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 32
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 6
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 3
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 6
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 3
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 6
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 6
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 6
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 3
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 100
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 6
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 6
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 32
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 3
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 6
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 81
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 3
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 6
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 6
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 0
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 100
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 6
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 3
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 3
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 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 6
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 3
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 8
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 3
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 6
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 100
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 6
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 3
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 8
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 98
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 8
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 98
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 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 3
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 6
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 7
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 6
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 100
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 81
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 3
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 32
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 8
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 6
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 6
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 3
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 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 7
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 6
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 7
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 3
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 100
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 6
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 32
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 7
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 100
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
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 98
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 3
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
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 6
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 6
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 6
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 3
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 3
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 6
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 6
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 0
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 3
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 6
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 3
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 6
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 6
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 3
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 100
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 6
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 7
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 81
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 6
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 32
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 6
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 6
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 6
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 6
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 3
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 6
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 6
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 3
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 32
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 3
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 3
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 3
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 8
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 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 32
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 81
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 8
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 3
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 3
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 3
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 3
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 98
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 3
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 6
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 6
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 6
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 81
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 3
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 6
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 100
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 32
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 6
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 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 81
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 81
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 6
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 3
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 3
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 6
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 7
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 100
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 7
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 6
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 100
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 3
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 7
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 0
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 6
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 7
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 6
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 3
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 3
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 32
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 6
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 7
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 8
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 6
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 6
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 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 6
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 6
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 3
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 3
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 32
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 8
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 3
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 6
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 100
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 3
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 6
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 100
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 6
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 7
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 6
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 3
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 6
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 7
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 7
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 8
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 3
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 100
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 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 6
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 3
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 100
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 100
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 8
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 6
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 3
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 100
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 6
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 6
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 3
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 3
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 3
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 98
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 6
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 8
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 6
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 6
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 6
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 3
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 0
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 100
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 3
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 3
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 100
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 3
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 6
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 6
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 6
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 6
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 6
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 32
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 6
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 8
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 6
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 6
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 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 100
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 3
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 3
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 81
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 6
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 100
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 8
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 6
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 6
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 32
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 6
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 6
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 6
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 3
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 98
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 3
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 6
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 6
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 3
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 32
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 3
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 100
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 3
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 7
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 7
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 3
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 6
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 6
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 6
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 6
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 100
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 100
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 6
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 6
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 100
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 6
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 100
empirical probabilities from test set: {7: 0.12, 8: 0.205, 6: 0.197, 3: 0.168, 32: 0.071, 100: 0.18, 81: 0.024, 98: 0.021, 0: 0.014}
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.08340236150048852), 8: np.float64(0.12089732939847118), 6: np.float64(0.09403802585241235), 3: np.float64(0.07647221339324309), 32: np.float64(0.13770391921738756), 100: np.float64(0.07437439298583375), 81: np.float64(0.13770391921738756), 98: np.float64(0.13770391921738756), 0: np.float64(0.13770391921738756)}
err dic= {7: np.float64(0.036597638499511476), 8: np.float64(0.0841026706015288), 6: np.float64(0.10296197414758766), 3: np.float64(0.09152778660675692), 32: np.float64(0.06670391921738757), 100: np.float64(0.10562560701416625), 81: np.float64(0.11370391921738757), 98: np.float64(0.11670391921738756), 0: np.float64(0.12370391921738756)} 

err list= [np.float64(0.036597638499511476), np.float64(0.0841026706015288), np.float64(0.10296197414758766), np.float64(0.09152778660675692), np.float64(0.06670391921738757), np.float64(0.10562560701416625), np.float64(0.11370391921738757), np.float64(0.11670391921738756), np.float64(0.12370391921738756)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.10394892724262898), 8: np.float64(0.11221993600712507), 6: np.float64(0.11548900452713352), 3: np.float64(0.11843812124771297), 32: np.float64(0.11340632440373927), 100: np.float64(0.09627871336044214), 81: np.float64(0.11340632440373927), 98: np.float64(0.11340632440373927), 0: np.float64(0.11340632440373927)}
err dic= {7: np.float64(0.016051072757371013), 8: np.float64(0.09278006399287492), 6: np.float64(0.08151099547286648), 3: np.float64(0.04956187875228704), 32: np.float64(0.04240632440373927), 100: np.float64(0.08372128663955786), 81: np.float64(0.08940632440373927), 98: np.float64(0.09240632440373926), 0: np.float64(0.09940632440373927)} 

err list= [np.float64(0.016051072757371013), np.float64(0.09278006399287492), np.float64(0.08151099547286648), np.float64(0.04956187875228704), np.float64(0.04240632440373927), np.float64(0.08372128663955786), np.float64(0.08940632440373927), np.float64(0.09240632440373926), np.float64(0.09940632440373927)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.14686968812644516), 8: np.float64(0.09786877765013875), 6: np.float64(0.161372096893523), 3: np.float64(0.1649446478102194), 32: np.float64(0.07504395306092532), 100: np.float64(0.12876897727597278), 81: np.float64(0.07504395306092532), 98: np.float64(0.07504395306092532), 0: np.float64(0.07504395306092532)}
err dic= {7: np.float64(0.026869688126445163), 8: np.float64(0.10713122234986124), 6: np.float64(0.03562790310647701), 3: np.float64(0.003055352189780619), 32: np.float64(0.004043953060925323), 100: np.float64(0.051231022724027214), 81: np.float64(0.051043953060925316), 98: np.float64(0.05404395306092531), 0: np.float64(0.06104395306092532)} 

err list= [np.float64(0.026869688126445163), np.float64(0.10713122234986124), np.float64(0.03562790310647701), np.float64(0.003055352189780619), np.float64(0.004043953060925323), np.float64(0.051231022724027214), np.float64(0.051043953060925316), np.float64(0.05404395306092531), np.float64(0.06104395306092532)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.2 

learned probs for this beta: {7: np.float64(0.2061494397576623), 8: np.float64(0.10947475796818913), 6: np.float64(0.17143452647117366), 3: np.float64(0.35622697519888463), 32: np.float64(0.012227314650822073), 100: np.float64(0.1078050420008027), 81: np.float64(0.012227314650822073), 98: np.float64(0.012227314650822073), 0: np.float64(0.012227314650822073)}
err dic= {7: np.float64(0.08614943975766232), 8: np.float64(0.09552524203181086), 6: np.float64(0.02556547352882635), 3: np.float64(0.18822697519888462), 32: np.float64(0.05877268534917792), 100: np.float64(0.0721949579991973), 81: np.float64(0.011772685349177928), 98: np.float64(0.008772685349177928), 0: np.float64(0.0017726853491779274)} 

err list= [np.float64(0.08614943975766232), np.float64(0.09552524203181086), np.float64(0.02556547352882635), np.float64(0.18822697519888462), np.float64(0.05877268534917792), np.float64(0.0721949579991973), np.float64(0.011772685349177928), np.float64(0.008772685349177928), np.float64(0.0017726853491779274)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.2095080872184565), 8: np.float64(0.1123479353859748), 6: np.float64(0.21999045739797307), 3: np.float64(0.28104827226372103), 32: np.float64(0.01917025053867578), 100: np.float64(0.10042424557917164), 81: np.float64(0.01917025053867578), 98: np.float64(0.01917025053867578), 0: np.float64(0.01917025053867578)}
err dic= {7: np.float64(0.08950808721845652), 8: np.float64(0.09265206461402518), 6: np.float64(0.022990457397973063), 3: np.float64(0.11304827226372102), 32: np.float64(0.05182974946132421), 100: np.float64(0.07957575442082836), 81: np.float64(0.00482974946132422), 98: np.float64(0.0018297494613242204), 0: np.float64(0.0051702505386757806)} 

err list= [np.float64(0.08950808721845652), np.float64(0.09265206461402518), np.float64(0.022990457397973063), np.float64(0.11304827226372102), np.float64(0.05182974946132421), np.float64(0.07957575442082836), np.float64(0.00482974946132422), np.float64(0.0018297494613242204), np.float64(0.0051702505386757806)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.3 

learned probs for this beta: {7: np.float64(0.15564572445147765), 8: np.float64(0.10837934305499647), 6: np.float64(0.177263327174773), 3: np.float64(0.45455935987840856), 32: np.float64(0.0049947134631065536), 100: np.float64(0.08417339158791652), 81: np.float64(0.0049947134631065536), 98: np.float64(0.0049947134631065536), 0: np.float64(0.0049947134631065536)}
err dic= {7: np.float64(0.03564572445147765), 8: np.float64(0.09662065694500352), 6: np.float64(0.01973667282522701), 3: np.float64(0.2865593598784085), 32: np.float64(0.06600528653689344), 100: np.float64(0.09582660841208347), 81: np.float64(0.019005286536893446), 98: np.float64(0.016005286536893447), 0: np.float64(0.009005286536893448)} 

err list= [np.float64(0.03564572445147765), np.float64(0.09662065694500352), np.float64(0.01973667282522701), np.float64(0.2865593598784085), np.float64(0.06600528653689344), np.float64(0.09582660841208347), np.float64(0.019005286536893446), np.float64(0.016005286536893447), np.float64(0.009005286536893448)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.0618069902786203), 8: np.float64(0.12866169799902957), 6: np.float64(0.07835778978709787), 3: np.float64(0.6550500900943811), 32: np.float64(0.0007796059661262064), 100: np.float64(0.07300500797636662), 81: np.float64(0.0007796059661262064), 98: np.float64(0.0007796059661262064), 0: np.float64(0.0007796059661262064)}
err dic= {7: np.float64(0.058193009721379696), 8: np.float64(0.07633830200097041), 6: np.float64(0.11864221021290214), 3: np.float64(0.48705009009438105), 32: np.float64(0.07022039403387378), 100: np.float64(0.10699499202363337), 81: np.float64(0.023220394033873794), 98: np.float64(0.020220394033873795), 0: np.float64(0.013220394033873794)} 

err list= [np.float64(0.058193009721379696), np.float64(0.07633830200097041), np.float64(0.11864221021290214), np.float64(0.48705009009438105), np.float64(0.07022039403387378), np.float64(0.10699499202363337), np.float64(0.023220394033873794), np.float64(0.020220394033873795), np.float64(0.013220394033873794)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.3428661724452044), 8: np.float64(0.18926418698262235), 6: np.float64(0.08959327739944568), 3: np.float64(0.33685097868044267), 32: np.float64(0.00013070720523739203), 100: np.float64(0.04090255567133516), 81: np.float64(0.00013070720523739203), 98: np.float64(0.00013070720523739203), 0: np.float64(0.00013070720523739203)}
err dic= {7: np.float64(0.2228661724452044), 8: np.float64(0.015735813017377642), 6: np.float64(0.10740672260055432), 3: np.float64(0.16885097868044266), 32: np.float64(0.0708692927947626), 100: np.float64(0.13909744432866483), 81: np.float64(0.02386929279476261), 98: np.float64(0.02086929279476261), 0: np.float64(0.013869292794762608)} 

err list= [np.float64(0.2228661724452044), np.float64(0.015735813017377642), np.float64(0.10740672260055432), np.float64(0.16885097868044266), np.float64(0.0708692927947626), np.float64(0.13909744432866483), np.float64(0.02386929279476261), np.float64(0.02086929279476261), np.float64(0.013869292794762608)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  1 

learned probs for this beta: {7: np.float64(0.017414113230560423), 8: np.float64(0.18711691975682593), 6: np.float64(0.12219626501165065), 3: np.float64(0.658953268812586), 32: np.float64(1.7705647980543062e-07), 100: np.float64(0.014318724962458063), 81: np.float64(1.7705647980543062e-07), 98: np.float64(1.7705647980543062e-07), 0: np.float64(1.7705647980543062e-07)}
err dic= {7: np.float64(0.10258588676943957), 8: np.float64(0.01788308024317406), 6: np.float64(0.07480373498834936), 3: np.float64(0.49095326881258594), 32: np.float64(0.07099982294352018), 100: np.float64(0.16568127503754193), 81: np.float64(0.023999822943520197), 98: np.float64(0.020999822943520197), 0: np.float64(0.013999822943520195)} 

err list= [np.float64(0.10258588676943957), np.float64(0.01788308024317406), np.float64(0.07480373498834936), np.float64(0.49095326881258594), np.float64(0.07099982294352018), np.float64(0.16568127503754193), np.float64(0.023999822943520197), np.float64(0.020999822943520197), np.float64(0.013999822943520195)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.1655811965327694), 8: np.float64(0.19934850772421947), 6: np.float64(0.2326423517911252), 3: np.float64(0.38699828676064424), 32: np.float64(1.5527392248383988e-07), 100: np.float64(0.01542903609555182), 81: np.float64(1.5527392248383988e-07), 98: np.float64(1.5527392248383988e-07), 0: np.float64(1.5527392248383988e-07)}
err dic= {7: np.float64(0.0455811965327694), 8: np.float64(0.0056514922757805175), 6: np.float64(0.03564235179112518), 3: np.float64(0.21899828676064423), 32: np.float64(0.07099984472607751), 100: np.float64(0.16457096390444817), 81: np.float64(0.023999844726077517), 98: np.float64(0.020999844726077518), 0: np.float64(0.013999844726077517)} 

err list= [np.float64(0.0455811965327694), np.float64(0.0056514922757805175), np.float64(0.03564235179112518), np.float64(0.21899828676064423), np.float64(0.07099984472607751), np.float64(0.16457096390444817), np.float64(0.023999844726077517), np.float64(0.020999844726077518), np.float64(0.013999844726077517)]
results for assortment [7, 8, 6, 3, 32, 100, 81, 98] :

err MNL dic= {7: np.float64(0.014202057067020574), 8: 0, 6: 0, 3: 0, 32: 0, 100: 0, 81: 0, 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: 0, 3: 0, 32: 0, 100: 0, 81: 0, 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: 0, 32: 0, 100: 0, 81: 0, 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), 0, 0, 0, 0, 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: np.float64(0.060626078301260794), 32: 0, 100: 0, 81: 0, 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), np.float64(0.060626078301260794), 0, 0, 0, 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: np.float64(0.060626078301260794), 32: np.float64(0.020738553417385536), 100: 0, 81: 0, 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), np.float64(0.060626078301260794), np.float64(0.020738553417385536), 0, 0, 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: np.float64(0.060626078301260794), 32: np.float64(0.020738553417385536), 100: np.float64(0.07146483078964831), 81: 0, 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), np.float64(0.060626078301260794), np.float64(0.020738553417385536), np.float64(0.07146483078964831), 0, 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: np.float64(0.060626078301260794), 32: np.float64(0.020738553417385536), 100: np.float64(0.07146483078964831), 81: np.float64(0.059734240212342395), 98: 0, 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), np.float64(0.060626078301260794), np.float64(0.020738553417385536), np.float64(0.07146483078964831), np.float64(0.059734240212342395), 0, 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: np.float64(0.060626078301260794), 32: np.float64(0.020738553417385536), 100: np.float64(0.07146483078964831), 81: np.float64(0.059734240212342395), 98: np.float64(0.06149004644990046), 0: 0} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), np.float64(0.060626078301260794), np.float64(0.020738553417385536), np.float64(0.07146483078964831), np.float64(0.059734240212342395), np.float64(0.06149004644990046), 0]
err MNL dic= {7: np.float64(0.014202057067020574), 8: np.float64(0.09957531519575316), 6: np.float64(0.08946018579960188), 3: np.float64(0.060626078301260794), 32: np.float64(0.020738553417385536), 100: np.float64(0.07146483078964831), 81: np.float64(0.059734240212342395), 98: np.float64(0.06149004644990046), 0: np.float64(0.19336562707365626)} 

err MNL list= [np.float64(0.014202057067020574), np.float64(0.09957531519575316), np.float64(0.08946018579960188), np.float64(0.060626078301260794), np.float64(0.020738553417385536), np.float64(0.07146483078964831), np.float64(0.059734240212342395), np.float64(0.06149004644990046), np.float64(0.19336562707365626)]
sampled assortment [3, 7, 9, 2, 23, 42, 74, 62]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 12: 1} [8, 1, 3, 4, 7, 10, 12]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 16: 0, 18: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 16, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 12: 1, 13: 1} [1, 3, 5, 7, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 15: 3, 17: 6, 20: 4, 26: 7, 100: 0} [6, 100, 1, 3, 10, 15, 7, 8, 11, 20, 17, 26]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 8: 0, 13: 1, 16: 1, 100: 1} [8, 1, 3, 4, 5, 13, 16, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 14: 0, 100: 0} [3, 4, 5, 6, 9, 12, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 4, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1} [1, 5, 7, 9, 10, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 4, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 15, 4, 11, 17]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 5, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 20: 0, 100: 0} [3, 4, 5, 7, 9, 11, 12, 20, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 100: 1} [2, 1, 7, 9, 10, 11, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 9: 1, 100: 1} [1, 4, 5, 9, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 5, 10: 1, 11: 5, 13: 2, 16: 5, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 5, 20, 7, 11, 16, 4]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 17: 1, 100: 1} [8, 1, 3, 4, 7, 17, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 12: 1, 13: 1, 14: 1, 22: 1, 100: 1} [2, 1, 6, 10, 12, 13, 14, 22, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 5, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 3, 10: 2, 11: 5, 13: 2, 15: 3, 17: 5, 20: 5, 21: 7, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 7, 5, 11, 17, 20, 21]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 14: 1} [8, 1, 3, 4, 5, 7, 14]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 21: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 21, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1, 100: 1} [1, 4, 5, 7, 9, 10, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 1, 11: 4, 13: 2, 100: 0} [6, 100, 10, 1, 3, 13, 5, 8, 11, 7]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 5: 1, 7: 1, 8: 0, 12: 1, 13: 1, 100: 1} [8, 3, 5, 7, 12, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 10: 1, 14: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 7, 9, 10, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 14: 1, 15: 1, 18: 1} [1, 3, 4, 5, 6, 7, 10, 11, 13, 14, 15, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 7, 11]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 20: 1} [2, 3, 6, 7, 10, 11, 14, 20]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1} [1, 3, 5, 7, 9, 10, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 11: 1, 12: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 11, 12, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 3, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 14: 1, 100: 1} [1, 3, 5, 7, 9, 14, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 15, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 21: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 19: 1} [1, 3, 5, 9, 10, 11, 12, 14, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 11, 7, 20]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 100: 1} [2, 1, 4, 6, 10, 11, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 12: 1, 15: 1} [1, 3, 4, 5, 6, 7, 9, 12, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 16: 5, 19: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 16, 19]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 6, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [3, 4, 5, 6, 9, 10, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1} [2, 1, 4, 6, 10, 11, 12]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 17: 2, 19: 1} [1, 3, 5, 7, 9, 10, 12, 19, 17]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 3, 20: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 7, 5, 11]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 12: 1} [2, 4, 6, 7, 10, 12]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 13: 3, 15: 3, 19: 5, 20: 4, 25: 8, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 20, 5, 7, 19, 25]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 12: 1, 16: 1, 17: 1} [2, 1, 4, 6, 10, 12, 16, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 15: 1, 26: 2, 100: 1} [1, 3, 5, 6, 7, 9, 15, 100, 26]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 14: 6, 15: 3, 19: 5, 20: 6, 23: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 19, 23, 14, 20]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [3, 4, 5, 6, 7, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 4, 6, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 9: 1, 10: 1, 12: 1, 15: 1, 26: 2} [1, 3, 4, 5, 6, 9, 10, 12, 15, 26]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 10: 2, 11: 5, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 11]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 10: 1, 11: 1, 100: 1} [2, 3, 4, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 6: 1, 9: 1, 10: 1, 11: 1, 17: 1, 100: 1} [1, 3, 4, 6, 9, 10, 11, 17, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 7, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 20, 4]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 7: 1, 10: 1, 11: 1, 19: 1, 100: 1} [2, 1, 3, 7, 10, 11, 19, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 12: 1, 13: 1, 15: 1, 17: 1, 100: 1} [1, 3, 5, 7, 9, 12, 13, 15, 17, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 2, 17: 6, 20: 5, 26: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 20, 4, 17, 26]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 17: 1, 100: 1} [2, 4, 6, 10, 11, 12, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1} [1, 3, 5, 7, 9, 10, 12]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 3, 8: 4, 10: 2, 11: 5, 13: 2, 14: 5, 15: 4, 20: 6, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 15, 11, 14, 20, 23]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 20: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 20, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 7: 1, 10: 1, 12: 1, 17: 1, 18: 1, 100: 1} [2, 1, 3, 7, 10, 12, 17, 18, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 25: 1} [1, 3, 4, 5, 7, 9, 10, 11, 12, 25]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 3, 9: 7, 10: 2, 11: 5, 12: 7, 13: 2, 14: 6, 15: 3, 16: 6, 19: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 7, 15, 20, 5, 11, 19, 14, 16, 9, 12]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 9: 1, 11: 1, 15: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 9, 11, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 5: 1, 6: 1, 10: 1, 11: 1, 14: 1, 20: 2, 100: 1} [2, 1, 5, 6, 10, 11, 14, 100, 20]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 9: 1, 12: 1} [1, 4, 5, 9, 12]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 14: 6, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 20, 11, 14]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 11: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 11, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0, 19: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 14, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 9: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 100: 1} [2, 1, 6, 9, 10, 11, 12, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 13: 1, 25: 2} [1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 25]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 9: 7, 10: 2, 11: 5, 13: 2, 17: 7, 18: 8, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 20, 5, 7, 11, 9, 17, 18]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 62
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 23
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 42
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 7
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 74
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 74
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 9
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 7
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 9
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 9
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 3
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 3
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 7
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 74
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 0
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 2
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 9
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 3
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 7
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 74
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 7
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 23
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 2
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 7
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 7
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 9
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 42
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 3
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 7
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 9
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 42
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 2
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 3
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 9
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 2
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 3
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 3
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 7
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 74
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 2
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 3
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 3
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 7
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 74
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 2
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 3
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 3
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 7
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
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 3
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 3
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 7
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 9
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 9
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 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 62
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 62
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 74
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 3
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 3
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 62
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 3
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 7
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 2
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 42
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 3
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 3
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 23
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 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 42
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 9
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 3
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 7
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 3
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 9
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 3
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 9
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 62
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 3
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 2
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 7
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 3
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 23
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 23
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 7
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 62
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
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 3
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 3
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 9
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 2
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 62
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 62
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 9
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 74
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 42
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 3
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 9
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 9
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 3
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 42
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 9
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 23
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 9
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 62
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 23
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 9
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 3
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 3
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 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 2
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 3
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 7
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 2
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 3
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 3
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 7
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 3
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 3
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 74
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
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 7
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 2
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 2
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 2
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 9
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 3
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 3
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 9
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 42
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 3
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 3
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 2
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 2
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 2
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 0
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 3
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 74
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 7
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 2
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 2
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 74
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 3
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 74
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 74
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 42
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 62
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 9
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 3
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 0
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 3
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 0
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 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 62
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 3
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 2
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 7
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 62
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 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 2
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 3
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 42
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 7
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 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 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 9
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 2
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 7
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 9
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 9
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 9
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 3
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 3
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 2
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 3
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 62
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 3
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 3
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 7
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 3
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 9
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 7
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 42
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 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 3
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 9
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 2
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 7
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 9
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 3
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 9
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 3
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 2
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 7
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 3
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 9
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 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 3
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 2
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 3
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 7
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 3
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 9
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 3
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 3
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 9
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 42
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 3
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 2
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 2
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 2
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 2
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 74
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 7
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 2
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 7
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 7
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 9
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 3
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 62
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 7
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 3
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 7
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 9
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 7
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 23
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 74
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 3
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 3
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 3
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 9
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 23
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 9
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 3
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 3
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 2
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 3
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 7
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 3
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 7
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 42
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 42
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 9
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 3
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 7
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 2
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 42
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 23
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 7
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 7
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 3
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 3
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 9
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 3
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 3
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 23
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 7
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 3
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 0
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 9
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 3
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 23
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 2
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 2
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 3
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 9
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 7
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 3
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 2
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 3
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 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 7
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 23
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 74
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 0
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 23
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 3
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 7
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 3
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 9
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 2
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 3
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 9
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 3
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 3
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 7
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 3
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 9
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 7
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 3
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 9
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 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 9
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 23
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 3
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 9
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 7
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 3
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 62
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 42
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 3
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 62
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 23
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 7
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 3
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 3
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 42
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 23
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 3
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 23
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 9
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 2
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 2
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 62
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 9
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 7
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 2
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 74
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
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 2
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 3
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 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 23
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 62
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 3
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 7
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 62
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 9
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 2
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 7
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 42
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 3
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 42
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 3
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 9
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 3
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 0
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 9
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 62
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 9
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 3
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 74
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 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 23
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 0
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 74
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 23
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 3
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 2
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 3
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 42
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 7
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 3
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 9
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 3
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 3
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 3
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 0
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 3
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 9
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 7
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 3
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 3
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 7
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 3
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 3
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 7
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 3
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 2
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 9
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 2
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 9
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 3
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 42
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 42
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 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 3
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 62
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 9
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 2
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 7
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 3
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 3
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 9
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 3
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 7
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 9
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 42
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 2
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 7
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 7
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 9
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 3
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 9
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 9
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 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 74
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 9
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 9
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 74
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 3
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 3
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 9
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 2
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 3
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 9
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 42
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 3
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 3
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 3
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 3
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 7
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 9
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 7
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 3
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 62
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 3
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 2
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 3
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 9
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 3
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 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 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
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 2
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 2
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 3
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 3
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 23
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 42
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 9
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 42
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 3
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 23
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 0
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 3
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 23
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 9
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 9
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 3
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 9
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 3
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 62
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 3
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 9
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 23
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 3
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 3
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 7
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 3
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 9
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 62
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 7
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 74
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 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 3
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 3
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 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 3
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 7
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 3
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 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 3
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 74
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 7
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 9
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 23
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 74
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 7
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 9
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 3
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 9
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 74
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 9
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 3
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 9
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 42
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 2
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 3
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 9
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 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 9
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 9
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 42
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 9
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 2
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 3
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 42
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 7
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 42
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 62
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 3
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 23
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 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 2
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 3
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 62
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 9
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 42
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 42
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 3
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 3
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 2
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 3
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 9
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 23
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 7
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 62
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 9
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 23
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 3
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 23
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 3
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 3
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 9
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 74
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 2
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 7
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 3
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 9
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 3
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 42
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 3
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 2
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 9
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 3
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 7
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 3
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 62
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 42
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 9
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 74
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 3
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 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 2
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 74
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 7
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 42
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 9
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 3
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 0
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 3
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 7
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 7
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 2
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 74
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 3
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 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 7
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 2
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 7
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 7
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 3
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 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 3
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 0
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 2
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 3
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 9
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 23
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 42
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 3
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 42
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 7
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 62
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 9
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 3
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 3
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 3
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 9
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 23
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 23
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 7
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 3
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 74
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 7
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 74
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 2
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 9
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 3
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 3
empirical probabilities from test set: {3: 0.184, 7: 0.158, 9: 0.196, 2: 0.227, 23: 0.086, 42: 0.051, 74: 0.031, 62: 0.044, 0: 0.023}
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.09505757849039012), 7: np.float64(0.10736066495147346), 9: np.float64(0.09626283574819514), 2: np.float64(0.10827122444116863), 23: np.float64(0.11860953927375445), 42: np.float64(0.11860953927375445), 74: np.float64(0.11860953927375445), 62: np.float64(0.11860953927375445), 0: np.float64(0.11860953927375445)}
err dic= {3: np.float64(0.08894242150960988), 7: np.float64(0.05063933504852654), 9: np.float64(0.09973716425180487), 2: np.float64(0.11872877555883138), 23: np.float64(0.032609539273754456), 42: np.float64(0.06760953927375446), 74: np.float64(0.08760953927375445), 62: np.float64(0.07460953927375445), 0: np.float64(0.09560953927375446)} 

err list= [np.float64(0.08894242150960988), np.float64(0.05063933504852654), np.float64(0.09973716425180487), np.float64(0.11872877555883138), np.float64(0.032609539273754456), np.float64(0.06760953927375446), np.float64(0.08760953927375445), np.float64(0.07460953927375445), np.float64(0.09560953927375446)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.12999599712772722), 7: np.float64(0.10550912706901314), 9: np.float64(0.11397938840354452), 2: np.float64(0.10543604345684296), 23: np.float64(0.1090158887885743), 42: np.float64(0.1090158887885743), 74: np.float64(0.1090158887885743), 62: np.float64(0.1090158887885743), 0: np.float64(0.1090158887885743)}
err dic= {3: np.float64(0.05400400287227278), 7: np.float64(0.052490872930986865), 9: np.float64(0.08202061159645549), 2: np.float64(0.12156395654315705), 23: np.float64(0.0230158887885743), 42: np.float64(0.0580158887885743), 74: np.float64(0.0780158887885743), 62: np.float64(0.0650158887885743), 0: np.float64(0.0860158887885743)} 

err list= [np.float64(0.05400400287227278), np.float64(0.052490872930986865), np.float64(0.08202061159645549), np.float64(0.12156395654315705), np.float64(0.0230158887885743), np.float64(0.0580158887885743), np.float64(0.0780158887885743), np.float64(0.0650158887885743), np.float64(0.0860158887885743)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.19544209741563998), 7: np.float64(0.1485605162960022), 9: np.float64(0.10055721567683608), 2: np.float64(0.13101869707271255), 23: np.float64(0.08965653412638232), 42: np.float64(0.08369123485310584), 74: np.float64(0.08369123485310584), 62: np.float64(0.08369123485310584), 0: np.float64(0.08369123485310584)}
err dic= {3: np.float64(0.011442097415639979), 7: np.float64(0.009439483703997803), 9: np.float64(0.09544278432316393), 2: np.float64(0.09598130292728746), 23: np.float64(0.0036565341263823242), 42: np.float64(0.03269123485310584), 74: np.float64(0.05269123485310584), 62: np.float64(0.03969123485310584), 0: np.float64(0.06069123485310584)} 

err list= [np.float64(0.011442097415639979), np.float64(0.009439483703997803), np.float64(0.09544278432316393), np.float64(0.09598130292728746), np.float64(0.0036565341263823242), np.float64(0.03269123485310584), np.float64(0.05269123485310584), np.float64(0.03969123485310584), np.float64(0.06069123485310584)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.2 

learned probs for this beta: {3: np.float64(0.3201460464564489), 7: np.float64(0.18254680296755285), 9: np.float64(0.09370010380581034), 2: np.float64(0.15239597690391998), 23: np.float64(0.05024221397325361), 42: np.float64(0.05024221397325361), 74: np.float64(0.05024221397325361), 62: np.float64(0.05024221397325361), 0: np.float64(0.05024221397325361)}
err dic= {3: np.float64(0.1361460464564489), 7: np.float64(0.02454680296755285), 9: np.float64(0.10229989619418967), 2: np.float64(0.07460402309608002), 23: np.float64(0.03575778602674638), 42: np.float64(0.0007577860267463862), 74: np.float64(0.01924221397325361), 62: np.float64(0.006242213973253613), 0: np.float64(0.02724221397325361)} 

err list= [np.float64(0.1361460464564489), np.float64(0.02454680296755285), np.float64(0.10229989619418967), np.float64(0.07460402309608002), np.float64(0.03575778602674638), np.float64(0.0007577860267463862), np.float64(0.01924221397325361), np.float64(0.006242213973253613), np.float64(0.02724221397325361)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.48772555772407733), 7: np.float64(0.1829470172587021), 9: np.float64(0.06610781898640632), 2: np.float64(0.1830412367765285), 23: np.float64(0.016035673850857052), 42: np.float64(0.016035673850857052), 74: np.float64(0.016035673850857052), 62: np.float64(0.016035673850857052), 0: np.float64(0.016035673850857052)}
err dic= {3: np.float64(0.30372555772407733), 7: np.float64(0.024947017258702103), 9: np.float64(0.12989218101359368), 2: np.float64(0.0439587632234715), 23: np.float64(0.06996432614914294), 42: np.float64(0.034964326149142945), 74: np.float64(0.014964326149142948), 62: np.float64(0.027964326149142946), 0: np.float64(0.006964326149142948)} 

err list= [np.float64(0.30372555772407733), np.float64(0.024947017258702103), np.float64(0.12989218101359368), np.float64(0.0439587632234715), np.float64(0.06996432614914294), np.float64(0.034964326149142945), np.float64(0.014964326149142948), np.float64(0.027964326149142946), np.float64(0.006964326149142948)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.3 

learned probs for this beta: {3: np.float64(0.5503967202276941), 7: np.float64(0.16489111137716841), 9: np.float64(0.14880005248208855), 2: np.float64(0.09301677289148835), 23: np.float64(0.00857906860431171), 42: np.float64(0.00857906860431171), 74: np.float64(0.00857906860431171), 62: np.float64(0.00857906860431171), 0: np.float64(0.00857906860431171)}
err dic= {3: np.float64(0.36639672022769415), 7: np.float64(0.006891111377168413), 9: np.float64(0.047199947517911456), 2: np.float64(0.13398322710851165), 23: np.float64(0.07742093139568829), 42: np.float64(0.04242093139568828), 74: np.float64(0.02242093139568829), 62: np.float64(0.03542093139568829), 0: np.float64(0.014420931395688289)} 

err list= [np.float64(0.36639672022769415), np.float64(0.006891111377168413), np.float64(0.047199947517911456), np.float64(0.13398322710851165), np.float64(0.07742093139568829), np.float64(0.04242093139568828), np.float64(0.02242093139568829), np.float64(0.03542093139568829), np.float64(0.014420931395688289)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5030292863480914), 7: np.float64(0.1432699206960672), 9: np.float64(0.06265230130604774), 2: np.float64(0.2877309399917647), 23: np.float64(0.0013145905992964719), 42: np.float64(0.0005007402646831704), 74: np.float64(0.0005007402646831704), 62: np.float64(0.0005007402646831704), 0: np.float64(0.0005007402646831704)}
err dic= {3: np.float64(0.3190292863480914), 7: np.float64(0.014730079303932803), 9: np.float64(0.13334769869395227), 2: np.float64(0.06073093999176468), 23: np.float64(0.08468540940070352), 42: np.float64(0.050499259735316826), 74: np.float64(0.03049925973531683), 62: np.float64(0.04349925973531683), 0: np.float64(0.02249925973531683)} 

err list= [np.float64(0.3190292863480914), np.float64(0.014730079303932803), np.float64(0.13334769869395227), np.float64(0.06073093999176468), np.float64(0.08468540940070352), np.float64(0.050499259735316826), np.float64(0.03049925973531683), np.float64(0.04349925973531683), np.float64(0.02249925973531683)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.7370320319976917), 7: np.float64(0.09209843506133308), 9: np.float64(0.045430476839615284), 2: np.float64(0.12533104484103127), 23: np.float64(2.160225206573588e-05), 42: np.float64(2.160225206573588e-05), 74: np.float64(2.160225206573588e-05), 62: np.float64(2.160225206573588e-05), 0: np.float64(2.160225206573588e-05)}
err dic= {3: np.float64(0.5530320319976918), 7: np.float64(0.06590156493866692), 9: np.float64(0.15056952316038472), 2: np.float64(0.10166895515896873), 23: np.float64(0.08597839774793425), 42: np.float64(0.05097839774793426), 74: np.float64(0.030978397747934264), 62: np.float64(0.04397839774793426), 0: np.float64(0.022978397747934264)} 

err list= [np.float64(0.5530320319976918), np.float64(0.06590156493866692), np.float64(0.15056952316038472), np.float64(0.10166895515896873), np.float64(0.08597839774793425), np.float64(0.05097839774793426), np.float64(0.030978397747934264), np.float64(0.04397839774793426), np.float64(0.022978397747934264)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  1 

learned probs for this beta: {3: np.float64(0.48109233332190526), 7: np.float64(0.021030380823197668), 9: np.float64(0.1714754060391178), 2: np.float64(0.3262849599664343), 23: np.float64(2.3383969869021493e-05), 42: np.float64(2.3383969869021493e-05), 74: np.float64(2.3383969869021493e-05), 62: np.float64(2.3383969869021493e-05), 0: np.float64(2.3383969869021493e-05)}
err dic= {3: np.float64(0.29709233332190527), 7: np.float64(0.13696961917680234), 9: np.float64(0.02452459396088222), 2: np.float64(0.0992849599664343), 23: np.float64(0.08597661603013097), 42: np.float64(0.050976616030130976), 74: np.float64(0.03097661603013098), 62: np.float64(0.04397661603013098), 0: np.float64(0.02297661603013098)} 

err list= [np.float64(0.29709233332190527), np.float64(0.13696961917680234), np.float64(0.02452459396088222), np.float64(0.0992849599664343), np.float64(0.08597661603013097), np.float64(0.050976616030130976), np.float64(0.03097661603013098), np.float64(0.04397661603013098), np.float64(0.02297661603013098)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.6420675811696616), 7: np.float64(0.015603797312054463), 9: np.float64(0.011983144756199127), 2: np.float64(0.3303454753214403), 23: np.float64(2.881288573817143e-10), 42: np.float64(2.881288573817143e-10), 74: np.float64(2.881288573817143e-10), 62: np.float64(2.881288573817143e-10), 0: np.float64(2.881288573817143e-10)}
err dic= {3: np.float64(0.45806758116966156), 7: np.float64(0.14239620268794553), 9: np.float64(0.18401685524380088), 2: np.float64(0.10334547532144031), 23: np.float64(0.08599999971187114), 42: np.float64(0.05099999971187114), 74: np.float64(0.030999999711871142), 62: np.float64(0.04399999971187114), 0: np.float64(0.022999999711871142)} 

err list= [np.float64(0.45806758116966156), np.float64(0.14239620268794553), np.float64(0.18401685524380088), np.float64(0.10334547532144031), np.float64(0.08599999971187114), np.float64(0.05099999971187114), np.float64(0.030999999711871142), np.float64(0.04399999971187114), np.float64(0.022999999711871142)]
results for assortment [3, 7, 9, 2, 23, 42, 74, 62] :

err MNL dic= {3: np.float64(0.07524556363021802), 7: 0, 9: 0, 2: 0, 23: 0, 42: 0, 74: 0, 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: 0, 2: 0, 23: 0, 42: 0, 74: 0, 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: 0, 23: 0, 42: 0, 74: 0, 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), 0, 0, 0, 0, 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: np.float64(0.11955534899442284), 23: 0, 42: 0, 74: 0, 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), np.float64(0.11955534899442284), 0, 0, 0, 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: np.float64(0.11955534899442284), 23: np.float64(0.010628358965692072), 42: 0, 74: 0, 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), np.float64(0.11955534899442284), np.float64(0.010628358965692072), 0, 0, 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: np.float64(0.11955534899442284), 23: np.float64(0.010628358965692072), 42: np.float64(0.041572249450735156), 74: 0, 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), np.float64(0.11955534899442284), np.float64(0.010628358965692072), np.float64(0.041572249450735156), 0, 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: np.float64(0.11955534899442284), 23: np.float64(0.010628358965692072), 42: np.float64(0.041572249450735156), 74: np.float64(0.055614838600642216), 62: 0, 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), np.float64(0.11955534899442284), np.float64(0.010628358965692072), np.float64(0.041572249450735156), np.float64(0.055614838600642216), 0, 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: np.float64(0.11955534899442284), 23: np.float64(0.010628358965692072), 42: np.float64(0.041572249450735156), 74: np.float64(0.055614838600642216), 62: np.float64(0.0415585600811222), 0: 0} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), np.float64(0.11955534899442284), np.float64(0.010628358965692072), np.float64(0.041572249450735156), np.float64(0.055614838600642216), np.float64(0.0415585600811222), 0]
err MNL dic= {3: np.float64(0.07524556363021802), 7: np.float64(0.05076660469832685), 9: np.float64(0.09206219367922934), 2: np.float64(0.11955534899442284), 23: np.float64(0.010628358965692072), 42: np.float64(0.041572249450735156), 74: np.float64(0.055614838600642216), 62: np.float64(0.0415585600811222), 0: np.float64(0.18825570390400542)} 

err MNL list= [np.float64(0.07524556363021802), np.float64(0.05076660469832685), np.float64(0.09206219367922934), np.float64(0.11955534899442284), np.float64(0.010628358965692072), np.float64(0.041572249450735156), np.float64(0.055614838600642216), np.float64(0.0415585600811222), np.float64(0.18825570390400542)]
sampled assortment [2, 1, 3, 7, 98, 96, 68, 94]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 16: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 13, 15, 16, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 4, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1} [1, 3, 5, 7, 9, 10, 11, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 1, 13: 2, 14: 6, 15: 3, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 20, 14]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 19: 1, 100: 1} [8, 1, 3, 4, 7, 10, 13, 19, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 23: 1, 100: 0} [3, 4, 5, 6, 9, 12, 100, 23]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1, 19: 1} [1, 3, 4, 5, 7, 9, 10, 13, 14, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 11, 17, 20, 4]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 100: 1} [2, 3, 6, 10, 11, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1, 18: 1} [1, 3, 4, 5, 7, 9, 10, 15, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 8: 4, 10: 2, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 12: 1, 14: 1, 100: 1} [8, 2, 3, 4, 7, 10, 12, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 12: 1, 13: 1} [2, 1, 3, 4, 6, 10, 12, 13]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 14: 1, 15: 1, 24: 1} [1, 3, 4, 5, 7, 9, 10, 11, 14, 15, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 7, 11, 20]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 15: 1, 100: 1} [8, 1, 3, 4, 7, 12, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 15: 1} [1, 3, 5, 6, 7, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 13: 3, 15: 3, 20: 5, 54: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 20, 54]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 6, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 13: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 13, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 11: 4, 13: 2, 15: 3, 16: 7, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 11, 20, 16]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 12: 1, 15: 1, 100: 1} [8, 1, 2, 3, 7, 10, 12, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [3, 4, 5, 6, 7, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 17: 1, 100: 1} [2, 1, 4, 6, 10, 11, 13, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 12: 1, 14: 1, 15: 1, 18: 1} [1, 3, 5, 6, 7, 9, 10, 12, 14, 15, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 19: 5, 24: 9, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11, 5, 19, 24]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 2, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 21: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 21, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1} [2, 1, 6, 10, 11, 13]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 14: 1, 15: 1, 19: 1} [1, 3, 5, 7, 9, 11, 14, 15, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 8: 4, 10: 2, 13: 2, 15: 3, 17: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 20, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 21: 0, 100: 0} [3, 4, 5, 6, 9, 11, 21, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1} [1, 3, 4, 5, 6, 7, 9, 10, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 4, 20: 4, 25: 7, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 15, 20, 5, 11, 25]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 14: 1, 19: 1, 100: 1} [8, 2, 3, 4, 5, 7, 14, 19, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 15: 1, 100: 1} [2, 1, 3, 6, 10, 15, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 11, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 8: 4, 10: 2, 11: 5, 13: 2, 15: 4, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 20, 5, 11]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 6, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 14: 1, 16: 1, 21: 1, 100: 1} [2, 1, 3, 4, 6, 10, 14, 16, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 25: 7, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 11, 25]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 16: 1, 100: 1} [2, 3, 6, 7, 9, 10, 11, 16, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 7: 1, 9: 1, 10: 1} [1, 7, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 14: 5, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 14]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 100: 1} [2, 1, 3, 6, 7, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 12: 1, 13: 1, 14: 1, 17: 1} [1, 5, 6, 7, 9, 10, 12, 13, 14, 17]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 9: 9, 10: 1, 13: 2, 15: 3, 16: 6, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 8, 16, 9]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 14: 1, 100: 1} [2, 1, 3, 6, 7, 10, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 11, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 14: 5, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 15, 5, 7, 20, 14]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 4, 5, 7, 10, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 17: 1, 100: 1} [2, 6, 10, 11, 12, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 15: 1, 100: 1} [1, 3, 5, 7, 9, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 7, 6: 0, 7: 5, 10: 2, 11: 5, 15: 4, 20: 5, 23: 5, 100: 0} [6, 100, 1, 3, 10, 15, 7, 11, 20, 23, 4]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 17: 2, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100, 17]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 9: 1, 10: 1, 11: 1, 13: 1, 17: 1, 100: 1} [2, 1, 3, 6, 9, 10, 11, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 13: 1, 15: 1, 19: 1} [1, 3, 5, 9, 10, 13, 15, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 4, 12: 6, 13: 2, 14: 7, 15: 3, 31: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 11, 5, 7, 12, 14, 31]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 17: 2, 100: 1} [2, 1, 6, 10, 11, 100, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1, 100: 1} [1, 5, 7, 9, 10, 13, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 3, 10: 2, 12: 7, 13: 3, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 7, 13, 15, 20, 5, 12]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 5: 1, 6: 1, 10: 1, 100: 1} [2, 1, 3, 5, 6, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1, 19: 1} [1, 3, 4, 5, 7, 9, 10, 15, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 20: 6, 24: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 5, 20, 24]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 4: 1, 7: 1, 8: 0, 10: 1, 15: 1} [8, 1, 2, 4, 7, 10, 15]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1} [2, 1, 4, 6, 10, 11, 12]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 12: 1, 14: 1, 15: 1, 25: 1} [1, 3, 5, 9, 10, 12, 14, 15, 25]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 3, 10: 2, 11: 5, 13: 2, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11, 20]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1, 22: 1} [1, 5, 7, 9, 10, 15, 22]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 20, 5, 7, 11, 4]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 96
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 7
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 0
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 98
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 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 94
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 7
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 1
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 3
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 3
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 7
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 94
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 94
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 2
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 2
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 3
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 7
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 96
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 98
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 3
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 94
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 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 7
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 7
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 3
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 1
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 7
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 7
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 1
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 3
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 96
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 3
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 3
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 7
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 3
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 1
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 3
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 3
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 1
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 7
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 3
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 7
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 94
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 96
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 3
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 7
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
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 68
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 3
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 1
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 2
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 68
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 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 2
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 96
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 68
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 3
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 68
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 3
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 7
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 1
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 96
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 3
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 68
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 3
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 1
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 3
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 96
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 3
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 7
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 3
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 94
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 7
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 3
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 98
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 68
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 3
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 2
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 0
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 3
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 7
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 7
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 7
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 1
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 7
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
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 3
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 3
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 1
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 2
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 2
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 2
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 7
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 2
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 7
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 3
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 3
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 3
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 7
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 96
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 2
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 98
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 3
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 68
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 7
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 7
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 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 1
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 7
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 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 1
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 1
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 3
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 3
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 1
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 98
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 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 1
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 7
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 1
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 3
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 3
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 96
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 7
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 3
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 7
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
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 7
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 7
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 7
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 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 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 3
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 3
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 2
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 68
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 3
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 1
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 96
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 98
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 1
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 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 3
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 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 7
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 68
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 2
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 3
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 1
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 7
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 0
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 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 1
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 1
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 7
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 96
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 2
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 96
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 3
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 2
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 3
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 96
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 7
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 3
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 3
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 98
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 7
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 1
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 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 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 2
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 96
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 2
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 98
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 1
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 7
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 3
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 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 68
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 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 3
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 3
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 7
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 98
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 7
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 3
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 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 3
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 3
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 68
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 7
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 94
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 3
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 94
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 3
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 2
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 2
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 3
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 0
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 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 3
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 3
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 2
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 3
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 98
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 3
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 68
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 3
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 3
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 3
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 2
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 3
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 3
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 7
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 7
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 3
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 0
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 3
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 3
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 98
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 3
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 1
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 94
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 3
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 2
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 3
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 2
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 1
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 7
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 0
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 2
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 7
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 3
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 3
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 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 0
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 3
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 3
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 3
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 98
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 3
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 7
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 94
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 1
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 3
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 94
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 3
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 3
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 7
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 98
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 96
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 2
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 1
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 7
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 3
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 3
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 3
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 3
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 3
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 3
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 7
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 3
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 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 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 7
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 2
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 1
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 1
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 3
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 96
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 3
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 3
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 3
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 3
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 68
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 94
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 2
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 3
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 7
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 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 3
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 3
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 2
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 3
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 3
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 7
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 3
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 3
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 2
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 3
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 68
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 7
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 1
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 7
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 1
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 3
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 1
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 7
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 3
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 0
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 3
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 3
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 3
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 68
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 3
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 1
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 3
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 3
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 7
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 7
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 3
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 3
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 0
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 94
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 1
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 98
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 2
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 1
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 98
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 7
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 98
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 68
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 3
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 1
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 3
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 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 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 7
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 3
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 3
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 94
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 7
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 7
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 7
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 1
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 2
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 1
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 3
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 3
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 3
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 7
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 3
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 7
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 94
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 3
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 3
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 94
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 96
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 0
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 2
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 2
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 94
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 68
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 2
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 68
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 3
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 3
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 98
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 3
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 3
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 2
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 3
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 98
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 2
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 2
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 3
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 1
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 7
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 98
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 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 1
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 3
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 3
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 98
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 94
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 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 3
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 1
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 7
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 3
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 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 2
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 3
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 96
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 1
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 3
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 3
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 3
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 7
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 7
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 3
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 1
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 2
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 1
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 96
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 0
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 7
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 0
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
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 96
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 94
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 1
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 2
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 1
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 2
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 68
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 68
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 2
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 3
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 3
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 3
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 7
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 3
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 7
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 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 7
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 1
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 7
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 98
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 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 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
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 2
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 94
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 0
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 3
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 2
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 2
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 94
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 94
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 3
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 3
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 68
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 3
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 1
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 1
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 3
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 7
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 3
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 3
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 7
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 3
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 3
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 3
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 0
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 3
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 2
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 68
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 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 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 96
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 3
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 1
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 3
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 7
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 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 3
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 7
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 1
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 7
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 3
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 1
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 2
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 94
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 96
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 7
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 7
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 3
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 3
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 2
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 7
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 3
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 96
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 94
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 3
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 3
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 3
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 3
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 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 3
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 1
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 96
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 2
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 3
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 3
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 68
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 3
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 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 3
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 68
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 94
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 3
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 7
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 1
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 68
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 3
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 2
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 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 1
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 7
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 3
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 68
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 1
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 2
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 3
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 94
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 96
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 3
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 1
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 3
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 3
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 3
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 0
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 68
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 3
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 7
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 3
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 3
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 3
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 7
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 3
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 7
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 3
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 7
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 68
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 94
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 3
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 68
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 94
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 1
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 7
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 7
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 3
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 3
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 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 7
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 2
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 94
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 3
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 96
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 7
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 3
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 7
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 98
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 2
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 3
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 1
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 1
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 3
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 1
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 3
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 2
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 2
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 3
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 7
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 7
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 3
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 96
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 3
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 3
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 3
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 3
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 68
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 3
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 2
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 7
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 3
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 0
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 2
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 98
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 1
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 3
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 3
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 3
empirical probabilities from test set: {2: 0.243, 1: 0.216, 3: 0.209, 7: 0.176, 98: 0.03, 96: 0.036, 68: 0.03, 94: 0.035, 0: 0.025}
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.1063515745481017), 1: np.float64(0.10670308083487193), 3: np.float64(0.09739471461132837), 7: np.float64(0.10396608097118737), 98: np.float64(0.11711690980690213), 96: np.float64(0.11711690980690213), 68: np.float64(0.11711690980690213), 94: np.float64(0.11711690980690213), 0: np.float64(0.11711690980690213)}
err dic= {2: np.float64(0.13664842545189831), 1: np.float64(0.10929691916512807), 3: np.float64(0.11160528538867162), 7: np.float64(0.07203391902881262), 98: np.float64(0.08711690980690213), 96: np.float64(0.08111690980690214), 68: np.float64(0.08711690980690213), 94: np.float64(0.08211690980690213), 0: np.float64(0.09211690980690213)} 

err list= [np.float64(0.13664842545189831), np.float64(0.10929691916512807), np.float64(0.11160528538867162), np.float64(0.07203391902881262), np.float64(0.08711690980690213), np.float64(0.08111690980690214), np.float64(0.08711690980690213), np.float64(0.08211690980690213), np.float64(0.09211690980690213)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.119820581973275), 1: np.float64(0.10871980201374423), 3: np.float64(0.13536800469260024), 7: np.float64(0.10442583070354088), 98: np.float64(0.10633315612336813), 96: np.float64(0.10633315612336813), 68: np.float64(0.10633315612336813), 94: np.float64(0.10633315612336813), 0: np.float64(0.10633315612336813)}
err dic= {2: np.float64(0.123179418026725), 1: np.float64(0.10728019798625577), 3: np.float64(0.07363199530739975), 7: np.float64(0.07157416929645911), 98: np.float64(0.07633315612336813), 96: np.float64(0.07033315612336813), 68: np.float64(0.07633315612336813), 94: np.float64(0.07133315612336813), 0: np.float64(0.08133315612336814)} 

err list= [np.float64(0.123179418026725), np.float64(0.10728019798625577), np.float64(0.07363199530739975), np.float64(0.07157416929645911), np.float64(0.07633315612336813), np.float64(0.07033315612336813), np.float64(0.07633315612336813), np.float64(0.07133315612336813), np.float64(0.08133315612336814)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.09767769647206999), 1: np.float64(0.15489538692110574), 3: np.float64(0.1921707203882155), 7: np.float64(0.17493707343225598), 98: np.float64(0.07606382455727066), 96: np.float64(0.07606382455727066), 68: np.float64(0.07606382455727066), 94: np.float64(0.07606382455727066), 0: np.float64(0.07606382455727066)}
err dic= {2: np.float64(0.14532230352793002), 1: np.float64(0.061104613078894254), 3: np.float64(0.016829279611784487), 7: np.float64(0.0010629265677440103), 98: np.float64(0.04606382455727066), 96: np.float64(0.040063824557270665), 68: np.float64(0.04606382455727066), 94: np.float64(0.04106382455727066), 0: np.float64(0.05106382455727066)} 

err list= [np.float64(0.14532230352793002), np.float64(0.061104613078894254), np.float64(0.016829279611784487), np.float64(0.0010629265677440103), np.float64(0.04606382455727066), np.float64(0.040063824557270665), np.float64(0.04606382455727066), np.float64(0.04106382455727066), np.float64(0.05106382455727066)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.2 

learned probs for this beta: {2: np.float64(0.12431285477855464), 1: np.float64(0.21342585009646647), 3: np.float64(0.37190865725435324), 7: np.float64(0.20771114620555575), 98: np.float64(0.01652829833301396), 96: np.float64(0.01652829833301396), 68: np.float64(0.01652829833301396), 94: np.float64(0.01652829833301396), 0: np.float64(0.01652829833301396)}
err dic= {2: np.float64(0.11868714522144536), 1: np.float64(0.0025741499035335236), 3: np.float64(0.16290865725435325), 7: np.float64(0.03171114620555576), 98: np.float64(0.013471701666986038), 96: np.float64(0.019471701666986037), 68: np.float64(0.013471701666986038), 94: np.float64(0.018471701666986043), 0: np.float64(0.008471701666986041)} 

err list= [np.float64(0.11868714522144536), np.float64(0.0025741499035335236), np.float64(0.16290865725435325), np.float64(0.03171114620555576), np.float64(0.013471701666986038), np.float64(0.019471701666986037), np.float64(0.013471701666986038), np.float64(0.018471701666986043), np.float64(0.008471701666986041)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.14071135783804087), 1: np.float64(0.19354168820329765), 3: np.float64(0.4017084008880655), 7: np.float64(0.20331691982543204), 98: np.float64(0.012144326649032769), 96: np.float64(0.012144326649032769), 68: np.float64(0.012144326649032769), 94: np.float64(0.012144326649032769), 0: np.float64(0.012144326649032769)}
err dic= {2: np.float64(0.10228864216195913), 1: np.float64(0.02245831179670235), 3: np.float64(0.19270840088806548), 7: np.float64(0.02731691982543205), 98: np.float64(0.01785567335096723), 96: np.float64(0.02385567335096723), 68: np.float64(0.01785567335096723), 94: np.float64(0.022855673350967234), 0: np.float64(0.012855673350967232)} 

err list= [np.float64(0.10228864216195913), np.float64(0.02245831179670235), np.float64(0.19270840088806548), np.float64(0.02731691982543205), np.float64(0.01785567335096723), np.float64(0.02385567335096723), np.float64(0.01785567335096723), np.float64(0.022855673350967234), np.float64(0.012855673350967232)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.3 

learned probs for this beta: {2: np.float64(0.14522431754584716), 1: np.float64(0.26591376945394857), 3: np.float64(0.5121956382067473), 7: np.float64(0.031867654515633816), 98: np.float64(0.00895972405556454), 96: np.float64(0.00895972405556454), 68: np.float64(0.00895972405556454), 94: np.float64(0.00895972405556454), 0: np.float64(0.00895972405556454)}
err dic= {2: np.float64(0.09777568245415283), 1: np.float64(0.04991376945394857), 3: np.float64(0.30319563820674733), 7: np.float64(0.14413234548436618), 98: np.float64(0.021040275944435458), 96: np.float64(0.027040275944435456), 68: np.float64(0.021040275944435458), 94: np.float64(0.026040275944435462), 0: np.float64(0.01604027594443546)} 

err list= [np.float64(0.09777568245415283), np.float64(0.04991376945394857), np.float64(0.30319563820674733), np.float64(0.14413234548436618), np.float64(0.021040275944435458), np.float64(0.027040275944435456), np.float64(0.021040275944435458), np.float64(0.026040275944435462), np.float64(0.01604027594443546)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.16740613591613343), 1: np.float64(0.3057847525185484), 3: np.float64(0.3766959046242983), 7: np.float64(0.1487067839728683), 98: np.float64(0.00028128459363048556), 96: np.float64(0.00028128459363048556), 68: np.float64(0.00028128459363048556), 94: np.float64(0.00028128459363048556), 0: np.float64(0.00028128459363048556)}
err dic= {2: np.float64(0.07559386408386656), 1: np.float64(0.08978475251854842), 3: np.float64(0.16769590462429831), 7: np.float64(0.027293216027131695), 98: np.float64(0.029718715406369514), 96: np.float64(0.03571871540636951), 68: np.float64(0.029718715406369514), 94: np.float64(0.03471871540636952), 0: np.float64(0.024718715406369517)} 

err list= [np.float64(0.07559386408386656), np.float64(0.08978475251854842), np.float64(0.16769590462429831), np.float64(0.027293216027131695), np.float64(0.029718715406369514), np.float64(0.03571871540636951), np.float64(0.029718715406369514), np.float64(0.03471871540636952), np.float64(0.024718715406369517)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.15904707515544925), 1: np.float64(0.30914781598454616), 3: np.float64(0.4765787738530199), 7: np.float64(0.0552023964477469), 98: np.float64(4.7877118475444146e-06), 96: np.float64(4.7877118475444146e-06), 68: np.float64(4.7877118475444146e-06), 94: np.float64(4.7877118475444146e-06), 0: np.float64(4.7877118475444146e-06)}
err dic= {2: np.float64(0.08395292484455075), 1: np.float64(0.09314781598454616), 3: np.float64(0.26757877385301987), 7: np.float64(0.12079760355225308), 98: np.float64(0.029995212288152454), 96: np.float64(0.03599521228815245), 68: np.float64(0.029995212288152454), 94: np.float64(0.03499521228815246), 0: np.float64(0.024995212288152456)} 

err list= [np.float64(0.08395292484455075), np.float64(0.09314781598454616), np.float64(0.26757877385301987), np.float64(0.12079760355225308), np.float64(0.029995212288152454), np.float64(0.03599521228815245), np.float64(0.029995212288152454), np.float64(0.03499521228815246), np.float64(0.024995212288152456)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  1 

learned probs for this beta: {2: np.float64(0.18312651380925116), 1: np.float64(0.3547616545747044), 3: np.float64(0.4376314850781836), 7: np.float64(0.02447980867892738), 98: np.float64(1.0757178669682833e-07), 96: np.float64(1.0757178669682833e-07), 68: np.float64(1.0757178669682833e-07), 94: np.float64(1.0757178669682833e-07), 0: np.float64(1.0757178669682833e-07)}
err dic= {2: np.float64(0.05987348619074884), 1: np.float64(0.13876165457470438), 3: np.float64(0.22863148507818362), 7: np.float64(0.1515201913210726), 98: np.float64(0.029999892428213302), 96: np.float64(0.035999892428213304), 68: np.float64(0.029999892428213302), 94: np.float64(0.03499989242821331), 0: np.float64(0.024999892428213304)} 

err list= [np.float64(0.05987348619074884), np.float64(0.13876165457470438), np.float64(0.22863148507818362), np.float64(0.1515201913210726), np.float64(0.029999892428213302), np.float64(0.035999892428213304), np.float64(0.029999892428213302), np.float64(0.03499989242821331), np.float64(0.024999892428213304)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.17256503925270653), 1: np.float64(0.3792875610624712), 3: np.float64(0.4300021257708687), 7: np.float64(0.018145215531198834), 98: np.float64(1.1676550929569027e-08), 96: np.float64(1.1676550929569027e-08), 68: np.float64(1.1676550929569027e-08), 94: np.float64(1.1676550929569027e-08), 0: np.float64(1.1676550929569027e-08)}
err dic= {2: np.float64(0.07043496074729347), 1: np.float64(0.1632875610624712), 3: np.float64(0.22100212577086872), 7: np.float64(0.15785478446880116), 98: np.float64(0.029999988323449068), 96: np.float64(0.03599998832344907), 68: np.float64(0.029999988323449068), 94: np.float64(0.034999988323449076), 0: np.float64(0.02499998832344907)} 

err list= [np.float64(0.07043496074729347), np.float64(0.1632875610624712), np.float64(0.22100212577086872), np.float64(0.15785478446880116), np.float64(0.029999988323449068), np.float64(0.03599998832344907), np.float64(0.029999988323449068), np.float64(0.034999988323449076), np.float64(0.02499998832344907)]
results for assortment [2, 1, 3, 7, 98, 96, 68, 94] :

err MNL dic= {2: np.float64(0.13515602594742232), 1: 0, 3: 0, 7: 0, 98: 0, 96: 0, 68: 0, 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: 0, 7: 0, 98: 0, 96: 0, 68: 0, 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: 0, 98: 0, 96: 0, 68: 0, 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), 0, 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: np.float64(0.0666623420962786), 98: 0, 96: 0, 68: 0, 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), np.float64(0.0666623420962786), 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: np.float64(0.0666623420962786), 98: np.float64(0.05637760327756913), 96: 0, 68: 0, 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), np.float64(0.0666623420962786), np.float64(0.05637760327756913), 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: np.float64(0.0666623420962786), 98: np.float64(0.05637760327756913), 96: np.float64(0.050377603277569134), 68: 0, 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), np.float64(0.0666623420962786), np.float64(0.05637760327756913), np.float64(0.050377603277569134), 0, 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: np.float64(0.0666623420962786), 98: np.float64(0.05637760327756913), 96: np.float64(0.050377603277569134), 68: np.float64(0.056975076818026646), 94: 0, 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), np.float64(0.0666623420962786), np.float64(0.05637760327756913), np.float64(0.050377603277569134), np.float64(0.056975076818026646), 0, 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: np.float64(0.0666623420962786), 98: np.float64(0.05637760327756913), 96: np.float64(0.050377603277569134), 68: np.float64(0.056975076818026646), 94: np.float64(0.05218846022533288), 0: 0} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), np.float64(0.0666623420962786), np.float64(0.05637760327756913), np.float64(0.050377603277569134), np.float64(0.056975076818026646), np.float64(0.05218846022533288), 0]
err MNL dic= {2: np.float64(0.13515602594742232), 1: np.float64(0.10401638784568111), 3: np.float64(0.09846739501536358), 7: np.float64(0.0666623420962786), 98: np.float64(0.05637760327756913), 96: np.float64(0.050377603277569134), 68: np.float64(0.056975076818026646), 94: np.float64(0.05218846022533288), 0: np.float64(0.18838340730624786)} 

err MNL list= [np.float64(0.13515602594742232), np.float64(0.10401638784568111), np.float64(0.09846739501536358), np.float64(0.0666623420962786), np.float64(0.05637760327756913), np.float64(0.050377603277569134), np.float64(0.056975076818026646), np.float64(0.05218846022533288), np.float64(0.18838340730624786)]
sampled assortment [1, 8, 6, 7, 35, 95, 22, 12]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 3, 4, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 4, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1, 30: 5} [1, 3, 4, 5, 6, 7, 9, 10, 11, 15, 30]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 11, 7, 17, 20, 4]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 11: 1, 100: 1} [8, 1, 2, 3, 4, 7, 11, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 20: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 20, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 14: 1, 16: 2, 17: 1, 100: 1} [2, 1, 3, 6, 10, 11, 14, 17, 100, 16]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 15: 1, 18: 1} [1, 5, 7, 9, 10, 11, 12, 15, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 9: 10, 10: 2, 11: 3, 13: 3, 15: 3, 19: 7, 23: 8, 100: 0} [6, 100, 1, 3, 10, 11, 13, 15, 5, 7, 19, 23, 9]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 6, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 15: 1, 21: 1, 25: 1} [1, 3, 6, 7, 9, 10, 11, 12, 14, 15, 21, 25]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 8: 3, 10: 1, 13: 2, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 8, 15, 5, 20, 17]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 3, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1} [1, 3, 4, 5, 7, 9, 10, 12]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 3, 8: 3, 10: 2, 11: 4, 13: 2, 15: 2, 21: 7, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 11, 5, 21]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 11: 1, 15: 1, 100: 1} [8, 1, 2, 3, 7, 11, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 9: 1, 11: 1, 100: 1} [2, 1, 3, 6, 9, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 15: 1, 100: 1} [1, 4, 5, 7, 9, 10, 12, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 12: 7, 13: 2, 20: 5, 24: 8, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11, 5, 20, 12, 24]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 5, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 19: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 17: 1, 20: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 12, 17, 20, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 9: 1, 10: 1, 15: 1} [1, 3, 4, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 12: 8, 13: 2, 15: 3, 16: 8, 17: 5, 20: 4, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 20, 17, 23, 12, 16]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 12: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 5, 7, 12, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 14: 1} [2, 1, 3, 6, 10, 11, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 4, 5, 6, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 16: 6, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 7, 11, 16, 23]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 4: 1, 7: 1, 8: 0, 9: 1, 13: 1, 14: 1, 100: 1} [8, 1, 2, 4, 7, 9, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 10: 1, 11: 1, 14: 1, 17: 1, 100: 1} [2, 10, 11, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 10: 1, 13: 1, 15: 1} [1, 3, 5, 7, 10, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 20, 11, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 14: 1, 19: 1, 100: 1} [8, 1, 3, 4, 7, 10, 14, 19, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 14: 1, 17: 1, 100: 1} [2, 1, 6, 10, 11, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 19: 1} [1, 3, 5, 7, 9, 10, 11, 12, 14, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 19: 4, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 19, 20]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [4, 5, 6, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 17: 1, 100: 1} [2, 6, 7, 10, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 15: 1} [1, 3, 4, 5, 6, 7, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 8, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 16: 7, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 20, 16, 4]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 11, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 8: 3, 10: 2, 11: 4, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 8, 11, 7]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 3, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 7: 1, 10: 1, 11: 1, 12: 1, 14: 1, 100: 1} [2, 1, 3, 7, 10, 11, 12, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 14: 1, 15: 1} [1, 3, 5, 9, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 3, 10: 2, 11: 5, 13: 2, 15: 3, 17: 7, 18: 7, 25: 7, 100: 0} [6, 100, 1, 3, 10, 13, 7, 15, 5, 11, 17, 18, 25]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 5, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 14: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 3, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1, 19: 1, 100: 1} [1, 3, 4, 5, 7, 9, 10, 11, 15, 19, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 4, 20: 5, 27: 10, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11, 15, 5, 20, 27]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 16: 1, 100: 1} [2, 1, 3, 6, 10, 11, 16, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 10: 1, 12: 1, 15: 1} [1, 3, 4, 6, 7, 9, 10, 12, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 10: 2, 13: 2, 15: 3, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 17, 20]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 17: 1} [2, 1, 3, 6, 10, 11, 13, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 15: 1} [1, 3, 5, 7, 9, 10, 11, 12, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 3, 10: 1, 11: 4, 12: 8, 13: 2, 15: 3, 17: 5, 23: 6, 29: 11, 100: 0} [6, 100, 10, 1, 3, 13, 8, 15, 5, 11, 7, 17, 23, 12, 29]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 17: 1, 100: 1} [2, 3, 6, 7, 10, 11, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1} [1, 3, 5, 7, 9, 10, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 19: 6, 20: 4, 34: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 7, 19, 34]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 2, 3, 4, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 12: 1, 14: 1, 21: 1, 100: 1} [2, 1, 3, 4, 6, 10, 12, 14, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 19: 1, 100: 1} [1, 3, 5, 7, 9, 10, 19, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 11: 4, 13: 2, 14: 6, 15: 3, 21: 8, 23: 8, 25: 6, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11, 14, 25, 21, 23]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 7, 10, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 4, 6, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 12: 2, 15: 1} [1, 3, 4, 5, 6, 7, 9, 10, 15, 12]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 3, 17: 6, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11, 20, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 10: 1, 11: 1, 12: 1, 17: 1, 100: 1} [2, 4, 10, 11, 12, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 4, 15: 3, 16: 8, 17: 5, 19: 5, 100: 0} [6, 100, 1, 3, 10, 15, 7, 8, 11, 13, 17, 19, 16]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 2, 3, 4, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 9: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 9, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 7: 1, 9: 1, 12: 1, 13: 1} [1, 3, 7, 9, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 1, 11: 5, 13: 2, 15: 3, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 15, 7, 8, 20, 5, 11]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 12
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 22
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 7
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 1
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 12
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 7
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 6
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 1
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 1
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 22
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 12
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 12
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 6
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 6
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 22
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 12
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 35
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 95
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 1
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 12
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 6
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 1
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 1
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 6
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 1
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 6
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 6
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 6
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 35
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 6
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 22
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 6
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 35
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 6
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 35
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 6
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 95
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 6
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 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 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 12
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 7
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 8
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 8
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 22
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 6
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
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 35
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 6
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 12
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 12
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 6
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 8
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 22
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 12
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 95
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 6
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 1
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 12
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 7
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 22
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 1
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 6
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 6
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 6
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 35
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 22
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 6
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 6
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 6
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 35
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 35
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 22
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 0
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 7
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 35
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 22
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 6
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 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 7
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 12
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 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 6
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 6
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 1
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 0
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 35
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 22
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 12
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 12
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 6
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 7
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 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 6
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 12
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 6
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 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 8
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 7
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 7
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 7
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 12
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 35
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 1
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 12
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 6
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 12
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 6
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 1
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 6
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 22
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 8
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 7
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 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 6
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 7
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 22
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 95
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 6
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 6
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 95
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 12
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 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 6
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 7
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 22
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 12
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 8
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 22
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 6
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 35
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 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 7
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 8
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 22
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 12
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 35
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 8
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 22
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 6
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 22
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 12
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 7
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 1
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 35
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 6
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 35
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 12
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 22
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 1
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 6
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 22
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 6
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 6
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 7
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 7
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 6
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 6
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 22
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 6
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 7
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 35
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 1
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 35
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 12
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 6
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 8
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 35
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 12
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 22
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 7
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 6
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 6
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 6
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 22
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 6
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 7
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 35
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 6
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 8
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 7
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 35
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 7
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 22
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 7
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 6
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 6
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 12
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 35
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 6
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 12
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 6
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 12
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 6
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 6
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 6
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 12
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 12
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 7
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 12
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 6
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 22
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 6
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 12
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 95
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 12
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 6
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 12
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 7
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 6
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 12
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 12
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 12
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 1
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 6
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 6
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 6
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 8
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 22
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 6
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 6
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 12
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 35
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 6
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 12
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 12
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 12
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 1
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 12
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 35
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 6
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 1
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 6
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 95
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 0
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 6
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 1
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 6
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 1
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 35
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 1
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 0
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 6
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 22
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 12
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 6
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 7
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 6
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 6
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 12
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 8
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 6
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 1
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 12
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 6
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 12
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 12
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 7
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 6
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 12
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 22
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 35
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 6
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 95
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 6
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 12
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 1
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 6
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 22
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 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 12
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 35
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 12
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 6
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 6
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 12
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 6
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 12
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 6
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 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 1
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 1
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 12
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 35
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 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 12
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 8
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 12
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 6
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 12
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 6
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 6
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 95
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 6
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 8
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 12
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 35
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 22
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 8
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 8
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 12
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 12
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 22
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 22
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 12
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 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 6
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 6
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 0
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 6
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 12
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 12
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 12
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 1
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 6
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 6
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 1
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 8
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 12
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 6
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 6
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 12
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 1
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 6
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 6
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 35
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 6
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 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 0
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 6
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 12
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 7
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 6
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 6
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 1
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 22
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 6
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 6
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 7
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 6
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 12
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 6
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 12
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 6
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 6
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 1
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 1
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 8
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 1
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 6
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 6
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 6
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 7
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 6
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 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 1
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 8
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 6
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 1
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 1
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 12
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 6
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 12
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 1
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 22
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 22
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 35
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 8
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 22
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 95
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 22
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 6
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 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 7
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 7
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 1
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 1
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 12
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 35
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 6
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 35
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 22
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 7
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 6
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 7
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 12
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 35
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 1
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 22
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 35
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 1
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 1
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 8
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 1
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 6
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 1
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 6
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 6
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 6
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 1
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 1
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 6
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 6
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 35
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 6
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 22
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 1
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 6
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 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 1
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 0
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 12
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 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 6
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 1
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 22
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 6
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 6
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 6
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 6
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 12
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 6
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 6
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 6
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 12
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 35
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 12
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 7
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 22
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 22
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 12
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 8
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 22
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 7
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 12
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 35
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 6
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 6
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 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 8
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 6
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 22
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 35
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 12
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 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 35
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 12
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 6
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 1
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 1
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 12
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 12
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 12
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 6
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 0
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 12
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 6
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 1
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 8
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 1
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 12
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 6
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 12
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 1
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 12
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 6
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 7
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 8
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 6
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 6
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 6
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 7
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 1
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 35
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 12
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 6
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 12
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 8
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 12
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 6
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 22
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 35
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 22
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 22
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 95
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 6
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 95
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 6
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 7
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 1
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 1
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 1
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 12
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 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 8
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 22
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 1
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 6
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 1
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 35
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 1
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 6
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 12
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 35
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 6
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 22
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 1
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 6
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 1
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 12
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 6
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 6
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 6
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 1
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 12
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 35
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 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 6
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 1
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 6
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 6
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 6
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 12
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 6
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 6
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 6
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 6
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 6
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 6
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 8
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 12
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 8
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 35
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 6
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 1
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 7
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 7
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 6
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 1
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 6
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 8
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 6
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 6
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 1
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 1
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 1
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 1
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 12
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 6
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 6
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 12
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 22
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 1
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 1
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 8
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 7
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 7
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 35
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 1
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 8
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 22
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 6
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 6
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 22
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 6
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 12
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 22
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 7
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 1
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 6
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 6
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 6
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 6
empirical probabilities from test set: {1: 0.178, 8: 0.201, 6: 0.181, 7: 0.145, 35: 0.046, 95: 0.017, 22: 0.117, 12: 0.1, 0: 0.015}
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.10749721174579242), 8: np.float64(0.11322100896394338), 6: np.float64(0.10052193311576905), 7: np.float64(0.08594024286786488), 35: np.float64(0.12215273169357298), 95: np.float64(0.12215273169357298), 22: np.float64(0.12215273169357298), 12: np.float64(0.10420867653234053), 0: np.float64(0.12215273169357298)}
err dic= {1: np.float64(0.07050278825420757), 8: np.float64(0.08777899103605663), 6: np.float64(0.08047806688423094), 7: np.float64(0.05905975713213511), 35: np.float64(0.07615273169357298), 95: np.float64(0.10515273169357298), 22: np.float64(0.0051527316935729706), 12: np.float64(0.004208676532340527), 0: np.float64(0.10715273169357298)} 

err list= [np.float64(0.07050278825420757), np.float64(0.08777899103605663), np.float64(0.08047806688423094), np.float64(0.05905975713213511), np.float64(0.07615273169357298), np.float64(0.10515273169357298), np.float64(0.0051527316935729706), np.float64(0.004208676532340527), np.float64(0.10715273169357298)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.11676957403756864), 8: np.float64(0.09883831357932166), 6: np.float64(0.12866538689829343), 7: np.float64(0.11934989687364768), 35: np.float64(0.10558819179256301), 95: np.float64(0.10558819179256301), 22: np.float64(0.10558819179256301), 12: np.float64(0.11402406144091953), 0: np.float64(0.10558819179256301)}
err dic= {1: np.float64(0.06123042596243135), 8: np.float64(0.10216168642067835), 6: np.float64(0.05233461310170656), 7: np.float64(0.02565010312635231), 35: np.float64(0.059588191792563014), 95: np.float64(0.08858819179256301), 22: np.float64(0.011411808207436994), 12: np.float64(0.014024061440919527), 0: np.float64(0.09058819179256301)} 

err list= [np.float64(0.06123042596243135), np.float64(0.10216168642067835), np.float64(0.05233461310170656), np.float64(0.02565010312635231), np.float64(0.059588191792563014), np.float64(0.08858819179256301), np.float64(0.011411808207436994), np.float64(0.014024061440919527), np.float64(0.09058819179256301)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.16224752404191176), 8: np.float64(0.11723295542971876), 6: np.float64(0.16919783358611706), 7: np.float64(0.20024104340692023), 35: np.float64(0.07021612870706608), 95: np.float64(0.07021612870706608), 22: np.float64(0.07021612870706608), 12: np.float64(0.07021612870706608), 0: np.float64(0.07021612870706608)}
err dic= {1: np.float64(0.015752475958088236), 8: np.float64(0.08376704457028125), 6: np.float64(0.01180216641388293), 7: np.float64(0.05524104340692024), 35: np.float64(0.024216128707066076), 95: np.float64(0.053216128707066074), 22: np.float64(0.04678387129293393), 12: np.float64(0.02978387129293393), 0: np.float64(0.055216128707066076)} 

err list= [np.float64(0.015752475958088236), np.float64(0.08376704457028125), np.float64(0.01180216641388293), np.float64(0.05524104340692024), np.float64(0.024216128707066076), np.float64(0.053216128707066074), np.float64(0.04678387129293393), np.float64(0.02978387129293393), np.float64(0.055216128707066076)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.2 

learned probs for this beta: {1: np.float64(0.24502316584305148), 8: np.float64(0.104199164456028), 6: np.float64(0.27153211569993485), 7: np.float64(0.19488203888464167), 35: np.float64(0.02138991471065757), 95: np.float64(0.02138991471065757), 22: np.float64(0.02138991471065757), 12: np.float64(0.0988038562737131), 0: np.float64(0.02138991471065757)}
err dic= {1: np.float64(0.06702316584305149), 8: np.float64(0.09680083554397201), 6: np.float64(0.09053211569993486), 7: np.float64(0.04988203888464168), 35: np.float64(0.02461008528934243), 95: np.float64(0.004389914710657569), 22: np.float64(0.09561008528934244), 12: np.float64(0.0011961437262869024), 0: np.float64(0.006389914710657571)} 

err list= [np.float64(0.06702316584305149), np.float64(0.09680083554397201), np.float64(0.09053211569993486), np.float64(0.04988203888464168), np.float64(0.02461008528934243), np.float64(0.004389914710657569), np.float64(0.09561008528934244), np.float64(0.0011961437262869024), np.float64(0.006389914710657571)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.27937512300705164), 8: np.float64(0.11509186239018786), 6: np.float64(0.25259442171162205), 7: np.float64(0.20635285793139388), 35: np.float64(0.01018307378288291), 95: np.float64(0.01018307378288291), 22: np.float64(0.01018307378288291), 12: np.float64(0.10585343982821566), 0: np.float64(0.01018307378288291)}
err dic= {1: np.float64(0.10137512300705165), 8: np.float64(0.08590813760981215), 6: np.float64(0.07159442171162206), 7: np.float64(0.06135285793139389), 35: np.float64(0.03581692621711709), 95: np.float64(0.006816926217117091), 22: np.float64(0.1068169262171171), 12: np.float64(0.005853439828215651), 0: np.float64(0.004816926217117089)} 

err list= [np.float64(0.10137512300705165), np.float64(0.08590813760981215), np.float64(0.07159442171162206), np.float64(0.06135285793139389), np.float64(0.03581692621711709), np.float64(0.006816926217117091), np.float64(0.1068169262171171), np.float64(0.005853439828215651), np.float64(0.004816926217117089)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.3 

learned probs for this beta: {1: np.float64(0.2047837959772078), 8: np.float64(0.1117976319358862), 6: np.float64(0.31242114848407254), 7: np.float64(0.281776440348728), 35: np.float64(0.00599404910666326), 95: np.float64(0.00599404910666326), 22: np.float64(0.00599404910666326), 12: np.float64(0.06524478682745088), 0: np.float64(0.00599404910666326)}
err dic= {1: np.float64(0.026783795977207814), 8: np.float64(0.08920236806411382), 6: np.float64(0.13142114848407255), 7: np.float64(0.13677644034872802), 35: np.float64(0.040005950893336736), 95: np.float64(0.011005950893336742), 22: np.float64(0.11100595089333674), 12: np.float64(0.03475521317254912), 0: np.float64(0.00900595089333674)} 

err list= [np.float64(0.026783795977207814), np.float64(0.08920236806411382), np.float64(0.13142114848407255), np.float64(0.13677644034872802), np.float64(0.040005950893336736), np.float64(0.011005950893336742), np.float64(0.11100595089333674), np.float64(0.03475521317254912), np.float64(0.00900595089333674)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.26554845848182274), 8: np.float64(0.17439533366334106), 6: np.float64(0.28578445856548174), 7: np.float64(0.20548245157413822), 35: np.float64(0.0003976891305011542), 95: np.float64(0.0003976891305011542), 22: np.float64(0.0003976891305011542), 12: np.float64(0.0671985411932131), 0: np.float64(0.0003976891305011542)}
err dic= {1: np.float64(0.08754845848182274), 8: np.float64(0.02660466633665895), 6: np.float64(0.10478445856548174), 7: np.float64(0.06048245157413823), 35: np.float64(0.04560231086949885), 95: np.float64(0.016602310869498847), 22: np.float64(0.11660231086949885), 12: np.float64(0.03280145880678691), 0: np.float64(0.014602310869498845)} 

err list= [np.float64(0.08754845848182274), np.float64(0.02660466633665895), np.float64(0.10478445856548174), np.float64(0.06048245157413823), np.float64(0.04560231086949885), np.float64(0.016602310869498847), np.float64(0.11660231086949885), np.float64(0.03280145880678691), np.float64(0.014602310869498845)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.3559009373491563), 8: np.float64(0.1319992945603214), 6: np.float64(0.3422038677865095), 7: np.float64(0.13995434062848736), 35: np.float64(1.6384610431678832e-05), 95: np.float64(1.6384610431678832e-05), 22: np.float64(1.6384610431678832e-05), 12: np.float64(0.029876021233798646), 0: np.float64(1.6384610431678832e-05)}
err dic= {1: np.float64(0.1779009373491563), 8: np.float64(0.06900070543967862), 6: np.float64(0.16120386778650952), 7: np.float64(0.005045659371512634), 35: np.float64(0.04598361538956832), 95: np.float64(0.016983615389568323), 22: np.float64(0.11698361538956832), 12: np.float64(0.07012397876620136), 0: np.float64(0.01498361538956832)} 

err list= [np.float64(0.1779009373491563), np.float64(0.06900070543967862), np.float64(0.16120386778650952), np.float64(0.005045659371512634), np.float64(0.04598361538956832), np.float64(0.016983615389568323), np.float64(0.11698361538956832), np.float64(0.07012397876620136), np.float64(0.01498361538956832)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  1 

learned probs for this beta: {1: np.float64(0.2219153918906236), 8: np.float64(0.1507328607888101), 6: np.float64(0.3296778827288478), 7: np.float64(0.1147626241384026), 35: np.float64(1.1919209781985752e-05), 95: np.float64(1.1919209781985752e-05), 22: np.float64(1.1919209781985752e-05), 12: np.float64(0.18286356361418796), 0: np.float64(1.1919209781985752e-05)}
err dic= {1: np.float64(0.0439153918906236), 8: np.float64(0.050267139211189915), 6: np.float64(0.1486778827288478), 7: np.float64(0.030237375861597388), 35: np.float64(0.04598808079021802), 95: np.float64(0.016988080790218015), 22: np.float64(0.11698808079021802), 12: np.float64(0.08286356361418795), 0: np.float64(0.014988080790218013)} 

err list= [np.float64(0.0439153918906236), np.float64(0.050267139211189915), np.float64(0.1486778827288478), np.float64(0.030237375861597388), np.float64(0.04598808079021802), np.float64(0.016988080790218015), np.float64(0.11698808079021802), np.float64(0.08286356361418795), np.float64(0.014988080790218013)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.3248306045511872), 8: np.float64(0.2058467247759593), 6: np.float64(0.3569078645779194), 7: np.float64(0.10834057871365936), 35: np.float64(7.647210990038242e-09), 95: np.float64(7.647210990038242e-09), 22: np.float64(7.647210990038242e-09), 12: np.float64(0.004074196792430732), 0: np.float64(7.647210990038242e-09)}
err dic= {1: np.float64(0.14683060455118718), 8: np.float64(0.0048467247759592935), 6: np.float64(0.1759078645779194), 7: np.float64(0.03665942128634063), 35: np.float64(0.04599999235278901), 95: np.float64(0.016999992352789012), 22: np.float64(0.11699999235278902), 12: np.float64(0.09592580320756927), 0: np.float64(0.01499999235278901)} 

err list= [np.float64(0.14683060455118718), np.float64(0.0048467247759592935), np.float64(0.1759078645779194), np.float64(0.03665942128634063), np.float64(0.04599999235278901), np.float64(0.016999992352789012), np.float64(0.11699999235278902), np.float64(0.09592580320756927), np.float64(0.01499999235278901)]
results for assortment [1, 8, 6, 7, 35, 95, 22, 12] :

err MNL dic= {1: np.float64(0.07165969465023943), 8: 0, 6: 0, 7: 0, 35: 0, 95: 0, 22: 0, 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: 0, 7: 0, 35: 0, 95: 0, 22: 0, 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: 0, 35: 0, 95: 0, 22: 0, 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), 0, 0, 0, 0, 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: np.float64(0.03980577954238464), 35: 0, 95: 0, 22: 0, 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), np.float64(0.03980577954238464), 0, 0, 0, 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: np.float64(0.03980577954238464), 35: np.float64(0.04535933854529084), 95: 0, 22: 0, 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), np.float64(0.03980577954238464), np.float64(0.04535933854529084), 0, 0, 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: np.float64(0.03980577954238464), 35: np.float64(0.04535933854529084), 95: np.float64(0.06752376079571039), 22: 0, 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), np.float64(0.03980577954238464), np.float64(0.04535933854529084), np.float64(0.06752376079571039), 0, 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: np.float64(0.03980577954238464), 35: np.float64(0.04535933854529084), 95: np.float64(0.06752376079571039), 22: np.float64(0.01970557897752853), 12: 0, 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), np.float64(0.03980577954238464), np.float64(0.04535933854529084), np.float64(0.06752376079571039), np.float64(0.01970557897752853), 0, 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: np.float64(0.03980577954238464), 35: np.float64(0.04535933854529084), 95: np.float64(0.06752376079571039), 22: np.float64(0.01970557897752853), 12: np.float64(0.0007817936228562), 0: 0} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), np.float64(0.03980577954238464), np.float64(0.04535933854529084), np.float64(0.06752376079571039), np.float64(0.01970557897752853), np.float64(0.0007817936228562), 0]
err MNL dic= {1: np.float64(0.07165969465023943), 8: np.float64(0.09629695878187547), 6: np.float64(0.07429131022062133), 7: np.float64(0.03980577954238464), 35: np.float64(0.04535933854529084), 95: np.float64(0.06752376079571039), 22: np.float64(0.01970557897752853), 12: np.float64(0.0007817936228562), 0: np.float64(0.18965801645450459)} 

err MNL list= [np.float64(0.07165969465023943), np.float64(0.09629695878187547), np.float64(0.07429131022062133), np.float64(0.03980577954238464), np.float64(0.04535933854529084), np.float64(0.06752376079571039), np.float64(0.01970557897752853), np.float64(0.0007817936228562), np.float64(0.18965801645450459)]
sampled assortment [8, 7, 9, 5, 92, 23, 53, 57]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 4: 1, 8: 0} [8, 3, 4]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 11: 1} [2, 1, 3, 6, 11]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 16: 2, 100: 1} [1, 3, 5, 7, 9, 10, 14, 100, 16]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 11: 5, 13: 2, 14: 6, 20: 4, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 20, 7, 11, 14, 23]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 17: 1, 100: 1} [8, 1, 2, 3, 4, 7, 17, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 14: 1, 16: 2, 17: 1, 100: 1} [2, 1, 6, 10, 14, 17, 100, 16]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 10: 1, 12: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 10, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 8, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 12: 7, 13: 2, 15: 3, 17: 6, 20: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 7, 8, 17, 12, 4]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 9: 1, 10: 1, 11: 1, 13: 1, 14: 1, 17: 1, 100: 1} [2, 1, 4, 6, 9, 10, 11, 13, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 11: 3, 13: 2, 14: 6, 16: 6, 18: 9, 19: 5, 100: 0} [6, 100, 1, 3, 10, 13, 11, 5, 7, 19, 14, 16, 18]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 14: 1, 15: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 14, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 15: 1} [1, 3, 5, 7, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 16: 6, 17: 4, 100: 0} [6, 100, 1, 3, 10, 13, 17, 5, 7, 16]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 100: 1} [2, 1, 3, 6, 7, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1} [1, 3, 5, 7, 9, 10, 11, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 3, 15: 3, 17: 5, 20: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 8, 7, 11, 17, 4]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 11: 1, 100: 1} [8, 1, 2, 3, 7, 11, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 7: 1, 10: 1, 11: 1, 17: 1, 100: 1} [2, 1, 4, 7, 10, 11, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 1, 11: 5, 13: 2, 15: 5, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 7, 20, 5, 11, 15]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 14: 1, 16: 1, 100: 1} [2, 1, 3, 6, 10, 11, 14, 16, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 100: 1} [1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 4, 19: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11, 15, 20, 4, 19]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 100: 1} [8, 1, 3, 4, 5, 7, 12, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 16: 1, 18: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 18, 100, 16]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 17: 1, 100: 1} [2, 1, 4, 6, 7, 10, 11, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 19: 1, 100: 1} [1, 5, 7, 9, 10, 12, 19, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 12: 6, 13: 2, 15: 4, 16: 7, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 11, 15, 12, 17, 16]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 7: 1, 8: 0, 11: 1, 100: 1} [8, 1, 4, 7, 11, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 14: 1, 17: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 12, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 14: 1, 25: 1} [1, 3, 5, 9, 14, 25]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 20, 5]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 7: 1, 8: 0, 10: 1, 21: 1, 100: 1} [8, 3, 7, 10, 21, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 5: 1, 6: 1, 7: 1, 10: 1, 11: 1} [2, 1, 5, 6, 7, 10, 11]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 14: 1, 15: 1, 100: 1} [1, 3, 4, 5, 7, 9, 10, 11, 14, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 17: 6, 20: 3, 35: 11, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 8, 7, 11, 17, 35]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1} [8, 1, 4, 7, 13, 14]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 17: 1, 100: 1} [2, 1, 4, 6, 10, 11, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1} [1, 3, 4, 5, 7, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 3, 8: 4, 10: 2, 11: 5, 13: 2, 14: 7, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 7, 15, 8, 11, 20, 14]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 3, 5, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 7: 1, 10: 1, 11: 1, 14: 1, 17: 1} [2, 1, 3, 7, 10, 11, 14, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 15: 1, 24: 2} [1, 3, 4, 5, 6, 7, 9, 10, 15, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 1, 13: 3, 15: 3, 100: 0} [6, 100, 10, 1, 3, 13, 15, 8, 5, 7]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 24: 3} [2, 1, 3, 6, 10, 24]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 100: 1} [1, 5, 7, 9, 10, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 5: 4, 6: 0, 7: 5, 10: 2, 11: 4, 13: 2, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 11, 4, 7, 20]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 25: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 25, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 100: 1} [2, 1, 3, 6, 10, 11, 12, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 13: 2, 15: 3, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 17, 20]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 2, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1} [1, 4, 5, 7, 9, 10, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 3, 13: 2, 14: 7, 15: 3, 17: 6, 25: 5, 34: 9, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 7, 8, 5, 25, 17, 14, 34]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 14: 1, 19: 1, 100: 1} [8, 2, 3, 4, 7, 14, 19, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 6: 1, 10: 1} [2, 3, 4, 6, 10]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 12: 1, 13: 1, 18: 1, 24: 1} [1, 3, 5, 7, 9, 12, 13, 18, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 4, 13: 2, 15: 4, 20: 5, 21: 7, 100: 0} [6, 100, 1, 3, 10, 13, 8, 11, 15, 5, 7, 20, 4, 21]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 4, 6, 7, 10, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 16: 1} [2, 1, 3, 6, 10, 16]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 20: 2} [1, 3, 4, 7, 9, 10, 11, 12, 20]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 3, 10: 2, 13: 2, 15: 4, 18: 7, 19: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 5, 15, 7, 19, 18]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 4: 1, 7: 1, 8: 0, 11: 1, 12: 1, 15: 1, 100: 1} [8, 2, 4, 7, 11, 12, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 5: 2, 6: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 100: 1} [2, 3, 6, 9, 10, 11, 12, 14, 100, 5]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 9: 1, 10: 1} [1, 3, 5, 6, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 14: 5, 15: 4, 17: 5, 20: 4, 22: 7, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 15, 20, 7, 11, 14, 17, 4, 22]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 12: 1, 14: 1} [2, 1, 6, 10, 11, 12, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 24: 2} [1, 5, 6, 7, 9, 10, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 3, 10: 2, 13: 2, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 20, 7]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [3, 4, 5, 6, 7, 9, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 15: 1, 100: 1} [1, 3, 5, 9, 10, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 20: 6, 23: 7, 34: 9, 100: 0} [6, 100, 1, 3, 10, 13, 8, 5, 7, 11, 20, 23, 34]
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 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 5
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 5
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 92
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 5
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 5
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 7
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 23
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 5
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 5
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 9
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 57
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 5
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 5
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 5
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 5
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 5
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 7
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 5
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 5
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 53
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 7
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 23
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 5
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 23
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 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 23
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 5
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 5
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 5
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 57
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 57
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 5
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 5
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 7
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 5
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 5
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 8
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 5
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 5
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 7
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
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 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 23
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 5
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 53
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 23
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 5
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 5
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 8
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 5
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 57
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 7
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 92
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 53
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 5
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 5
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 53
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 9
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 7
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 5
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 5
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 0
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 5
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 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 5
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 23
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 5
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 23
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 7
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 53
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 5
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 5
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 5
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 9
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 8
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 23
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 57
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 5
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 5
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 92
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 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 53
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 5
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 5
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 9
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 5
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 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 7
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 23
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 23
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 9
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 8
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 23
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 57
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 92
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 92
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 23
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 92
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 7
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 5
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 92
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 9
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 7
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 5
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 92
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 8
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 9
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 23
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 92
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 53
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 9
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 7
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 7
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 92
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 92
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 8
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 57
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 5
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 7
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 9
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 57
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 7
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 57
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 7
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 5
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 8
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 57
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 5
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 7
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 5
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 5
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 23
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 5
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 7
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 5
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 5
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 7
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 53
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 5
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 7
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 0
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 5
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 5
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 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 23
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 23
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 5
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 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 8
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 5
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 5
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 5
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 23
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 5
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 92
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 53
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 53
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 5
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 7
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 5
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 7
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 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 7
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 92
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 8
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 5
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 5
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 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 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 5
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 7
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 23
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 92
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 5
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 9
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 53
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 23
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 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 53
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 9
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 23
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 53
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 57
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 92
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 9
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 5
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 5
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 23
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 9
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 53
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 7
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 57
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 5
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 5
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 5
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 7
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 5
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 8
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 5
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 7
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 5
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 5
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 5
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 5
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 8
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 5
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 9
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 53
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 5
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 8
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 92
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 5
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 5
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 5
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 57
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 5
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 5
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 7
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 7
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 57
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 23
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 5
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 7
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 8
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 23
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 23
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 8
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 7
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 5
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 23
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 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 92
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 23
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 5
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 5
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 8
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 53
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 8
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 57
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 23
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 53
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 5
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 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 9
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 5
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 5
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 9
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 53
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 53
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 53
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 5
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 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 7
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 7
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 9
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 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 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 9
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 53
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 5
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 23
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 5
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 5
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 23
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 23
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 5
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 53
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 9
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 9
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 7
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 5
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 57
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 23
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 5
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 23
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 5
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 92
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 5
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 92
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 5
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 5
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 57
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 5
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 5
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 92
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 8
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 23
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 5
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 23
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 53
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 5
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 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 7
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 5
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 5
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 5
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 5
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 57
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 5
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 9
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 5
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 5
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 5
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 9
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 5
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 5
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 5
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 8
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 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 8
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 53
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 9
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 7
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 53
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 57
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 57
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 5
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 5
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 5
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 5
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 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 0
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 7
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 53
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 53
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 7
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 5
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 57
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 5
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 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 8
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 8
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 8
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 9
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 5
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 7
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 7
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 7
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 9
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 5
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 7
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 92
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 8
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 0
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 53
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 5
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 7
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 5
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 23
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 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 9
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 53
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 5
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 5
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 5
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 5
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 5
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 5
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 92
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 23
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 23
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 23
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 5
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 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 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 53
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 5
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 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 5
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 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 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 8
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 5
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 53
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 53
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 5
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 7
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 57
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 5
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 8
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 5
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 5
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 7
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 23
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 9
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 0
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 5
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 57
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 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 5
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 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 92
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 7
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 5
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 9
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 5
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 5
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 5
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 7
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 7
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 8
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 7
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 53
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 5
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 5
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 5
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 23
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 5
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 5
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 57
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 5
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 5
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 9
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 7
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 5
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 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 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 53
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 23
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 5
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 5
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 5
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 5
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 5
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 53
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 5
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 5
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 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 5
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 23
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 5
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 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 5
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 9
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 5
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 7
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 5
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 23
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 23
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 92
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 5
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 23
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 5
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 53
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 5
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 0
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 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 9
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 7
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 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 5
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 9
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 7
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 7
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 5
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 5
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 53
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 7
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 5
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 5
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 5
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 5
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 23
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 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 8
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 23
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 53
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 53
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 5
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 53
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 8
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 8
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 5
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 5
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 8
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 5
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 7
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 53
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 5
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 5
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 53
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 92
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 5
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 8
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 92
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 5
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 7
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 8
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 7
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 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 7
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 7
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 5
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 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 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 5
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 23
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 7
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 7
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 57
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 5
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 9
empirical probabilities from test set: {8: 0.238, 7: 0.163, 9: 0.197, 5: 0.188, 92: 0.031, 23: 0.089, 53: 0.055, 57: 0.025, 0: 0.014}
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.025 

learned probs for this beta: {8: np.float64(0.10952116574655701), 7: np.float64(0.08850330213039903), 9: np.float64(0.09878006579283437), 5: np.float64(0.10209833263709357), 92: np.float64(0.12021942673862329), 23: np.float64(0.12021942673862329), 53: np.float64(0.12021942673862329), 57: np.float64(0.12021942673862329), 0: np.float64(0.12021942673862329)}
err dic= {8: np.float64(0.12847883425344298), 7: np.float64(0.07449669786960098), 9: np.float64(0.09821993420716564), 5: np.float64(0.08590166736290643), 92: np.float64(0.08921942673862329), 23: np.float64(0.031219426738623296), 53: np.float64(0.0652194267386233), 57: np.float64(0.0952194267386233), 0: np.float64(0.1062194267386233)} 

err list= [np.float64(0.12847883425344298), np.float64(0.07449669786960098), np.float64(0.09821993420716564), np.float64(0.08590166736290643), np.float64(0.08921942673862329), np.float64(0.031219426738623296), np.float64(0.0652194267386233), np.float64(0.0952194267386233), np.float64(0.1062194267386233)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.10600008700604495), 7: np.float64(0.12311490505936715), 9: np.float64(0.11997417332565244), 5: np.float64(0.12911008150744854), 92: np.float64(0.10436015062029858), 23: np.float64(0.10436015062029858), 53: np.float64(0.10436015062029858), 57: np.float64(0.10436015062029858), 0: np.float64(0.10436015062029858)}
err dic= {8: np.float64(0.13199991299395503), 7: np.float64(0.03988509494063286), 9: np.float64(0.07702582667434757), 5: np.float64(0.05888991849255146), 92: np.float64(0.07336015062029858), 23: np.float64(0.01536015062029858), 53: np.float64(0.049360150620298575), 57: np.float64(0.07936015062029858), 0: np.float64(0.09036015062029858)} 

err list= [np.float64(0.13199991299395503), np.float64(0.03988509494063286), np.float64(0.07702582667434757), np.float64(0.05888991849255146), np.float64(0.07336015062029858), np.float64(0.01536015062029858), np.float64(0.049360150620298575), np.float64(0.07936015062029858), np.float64(0.09036015062029858)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.11389482321177125), 7: np.float64(0.16317227919680025), 9: np.float64(0.13283465210597492), 5: np.float64(0.1694945849154256), 92: np.float64(0.0841207321140056), 23: np.float64(0.0841207321140056), 53: np.float64(0.0841207321140056), 57: np.float64(0.0841207321140056), 0: np.float64(0.0841207321140056)}
err dic= {8: np.float64(0.12410517678822874), 7: np.float64(0.00017227919680024018), 9: np.float64(0.06416534789402509), 5: np.float64(0.0185054150845744), 92: np.float64(0.0531207321140056), 23: np.float64(0.0048792678859943955), 53: np.float64(0.0291207321140056), 57: np.float64(0.0591207321140056), 0: np.float64(0.0701207321140056)} 

err list= [np.float64(0.12410517678822874), np.float64(0.00017227919680024018), np.float64(0.06416534789402509), np.float64(0.0185054150845744), np.float64(0.0531207321140056), np.float64(0.0048792678859943955), np.float64(0.0291207321140056), np.float64(0.0591207321140056), np.float64(0.0701207321140056)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.2 

learned probs for this beta: {8: np.float64(0.15709257582811315), 7: np.float64(0.22449093591792754), 9: np.float64(0.15036975186429244), 5: np.float64(0.29182047357590496), 92: np.float64(0.03524525256275238), 23: np.float64(0.03524525256275238), 53: np.float64(0.03524525256275238), 57: np.float64(0.03524525256275238), 0: np.float64(0.03524525256275238)}
err dic= {8: np.float64(0.08090742417188684), 7: np.float64(0.061490935917927536), 9: np.float64(0.04663024813570757), 5: np.float64(0.10382047357590496), 92: np.float64(0.004245252562752377), 23: np.float64(0.05375474743724762), 53: np.float64(0.019754747437247623), 57: np.float64(0.010245252562752376), 0: np.float64(0.02124525256275238)} 

err list= [np.float64(0.08090742417188684), np.float64(0.061490935917927536), np.float64(0.04663024813570757), np.float64(0.10382047357590496), np.float64(0.004245252562752377), np.float64(0.05375474743724762), np.float64(0.019754747437247623), np.float64(0.010245252562752376), np.float64(0.02124525256275238)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.14093073523177074), 7: np.float64(0.3291219738346182), 9: np.float64(0.13751763690436453), 5: np.float64(0.308447065408603), 92: np.float64(0.016796517724129465), 23: np.float64(0.016796517724129465), 53: np.float64(0.016796517724129465), 57: np.float64(0.016796517724129465), 0: np.float64(0.016796517724129465)}
err dic= {8: np.float64(0.09706926476822925), 7: np.float64(0.16612197383461821), 9: np.float64(0.05948236309563548), 5: np.float64(0.120447065408603), 92: np.float64(0.014203482275870535), 23: np.float64(0.07220348227587053), 53: np.float64(0.03820348227587053), 57: np.float64(0.008203482275870536), 0: np.float64(0.002796517724129465)} 

err list= [np.float64(0.09706926476822925), np.float64(0.16612197383461821), np.float64(0.05948236309563548), np.float64(0.120447065408603), np.float64(0.014203482275870535), np.float64(0.07220348227587053), np.float64(0.03820348227587053), np.float64(0.008203482275870536), np.float64(0.002796517724129465)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.3 

learned probs for this beta: {8: np.float64(0.19261541397575874), 7: np.float64(0.2499855488816093), 9: np.float64(0.14318647313600644), 5: np.float64(0.2941009420145596), 92: np.float64(0.024022324398413144), 23: np.float64(0.024022324398413144), 53: np.float64(0.024022324398413144), 57: np.float64(0.024022324398413144), 0: np.float64(0.024022324398413144)}
err dic= {8: np.float64(0.04538458602424125), 7: np.float64(0.08698554888160928), 9: np.float64(0.05381352686399357), 5: np.float64(0.10610094201455961), 92: np.float64(0.006977675601586856), 23: np.float64(0.06497767560158685), 53: np.float64(0.030977675601586856), 57: np.float64(0.0009776756015868575), 0: np.float64(0.010022324398413144)} 

err list= [np.float64(0.04538458602424125), np.float64(0.08698554888160928), np.float64(0.05381352686399357), np.float64(0.10610094201455961), np.float64(0.006977675601586856), np.float64(0.06497767560158685), np.float64(0.030977675601586856), np.float64(0.0009776756015868575), np.float64(0.010022324398413144)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.22070509106261757), 7: np.float64(0.2654600216540978), 9: np.float64(0.14186194591618118), 5: np.float64(0.2719475603706662), 92: np.float64(0.020005076199287534), 23: np.float64(0.020005076199287534), 53: np.float64(0.020005076199287534), 57: np.float64(0.020005076199287534), 0: np.float64(0.020005076199287534)}
err dic= {8: np.float64(0.01729490893738242), 7: np.float64(0.10246002165409782), 9: np.float64(0.05513805408381883), 5: np.float64(0.0839475603706662), 92: np.float64(0.010994923800712465), 23: np.float64(0.06899492380071245), 53: np.float64(0.034994923800712466), 57: np.float64(0.004994923800712467), 0: np.float64(0.006005076199287534)} 

err list= [np.float64(0.01729490893738242), np.float64(0.10246002165409782), np.float64(0.05513805408381883), np.float64(0.0839475603706662), np.float64(0.010994923800712465), np.float64(0.06899492380071245), np.float64(0.034994923800712466), np.float64(0.004994923800712467), np.float64(0.006005076199287534)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.19616276662004933), 7: np.float64(0.032358360071816465), 9: np.float64(0.2946822192710299), 5: np.float64(0.47663473208781165), 92: np.float64(3.238438985853843e-05), 23: np.float64(3.238438985853843e-05), 53: np.float64(3.238438985853843e-05), 57: np.float64(3.238438985853843e-05), 0: np.float64(3.238438985853843e-05)}
err dic= {8: np.float64(0.041837233379950656), 7: np.float64(0.13064163992818353), 9: np.float64(0.09768221927102988), 5: np.float64(0.28863473208781165), 92: np.float64(0.030967615610141462), 23: np.float64(0.08896761561014145), 53: np.float64(0.05496761561014146), 57: np.float64(0.024967615610141464), 0: np.float64(0.013967615610141463)} 

err list= [np.float64(0.041837233379950656), np.float64(0.13064163992818353), np.float64(0.09768221927102988), np.float64(0.28863473208781165), np.float64(0.030967615610141462), np.float64(0.08896761561014145), np.float64(0.05496761561014146), np.float64(0.024967615610141464), np.float64(0.013967615610141463)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  1 

learned probs for this beta: {8: np.float64(0.27015212449818987), 7: np.float64(0.10602224971047113), 9: np.float64(0.04948027006355971), 5: np.float64(0.4762875045889641), 92: np.float64(0.019611570227763053), 23: np.float64(0.019611570227763053), 53: np.float64(0.019611570227763053), 57: np.float64(0.019611570227763053), 0: np.float64(0.019611570227763053)}
err dic= {8: np.float64(0.03215212449818988), 7: np.float64(0.05697775028952888), 9: np.float64(0.1475197299364403), 5: np.float64(0.28828750458896407), 92: np.float64(0.011388429772236947), 23: np.float64(0.06938842977223694), 53: np.float64(0.03538842977223695), 57: np.float64(0.005388429772236948), 0: np.float64(0.005611570227763053)} 

err list= [np.float64(0.03215212449818988), np.float64(0.05697775028952888), np.float64(0.1475197299364403), np.float64(0.28828750458896407), np.float64(0.011388429772236947), np.float64(0.06938842977223694), np.float64(0.03538842977223695), np.float64(0.005388429772236948), np.float64(0.005611570227763053)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.26521520794262504), 7: np.float64(0.06681739910393233), 9: np.float64(0.06784243541341531), 5: np.float64(0.5019881789738254), 92: np.float64(0.0196111332218374), 23: np.float64(0.01969224567885236), 53: np.float64(0.0196111332218374), 57: np.float64(0.0196111332218374), 0: np.float64(0.0196111332218374)}
err dic= {8: np.float64(0.027215207942625053), 7: np.float64(0.09618260089606767), 9: np.float64(0.1291575645865847), 5: np.float64(0.3139881789738254), 92: np.float64(0.011388866778162601), 23: np.float64(0.06930775432114764), 53: np.float64(0.0353888667781626), 57: np.float64(0.005388866778162603), 0: np.float64(0.005611133221837398)} 

err list= [np.float64(0.027215207942625053), np.float64(0.09618260089606767), np.float64(0.1291575645865847), np.float64(0.3139881789738254), np.float64(0.011388866778162601), np.float64(0.06930775432114764), np.float64(0.0353888667781626), np.float64(0.005388866778162603), np.float64(0.005611133221837398)]
results for assortment [8, 7, 9, 5, 92, 23, 53, 57] :

err MNL dic= {8: np.float64(0.13228667734052413), 7: 0, 9: 0, 5: 0, 92: 0, 23: 0, 53: 0, 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: 0, 5: 0, 92: 0, 23: 0, 53: 0, 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: 0, 92: 0, 23: 0, 53: 0, 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), 0, 0, 0, 0, 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: np.float64(0.0797165248167186), 92: 0, 23: 0, 53: 0, 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), np.float64(0.0797165248167186), 0, 0, 0, 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: np.float64(0.0797165248167186), 92: np.float64(0.052930226679025874), 23: 0, 53: 0, 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), np.float64(0.0797165248167186), np.float64(0.052930226679025874), 0, 0, 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: np.float64(0.0797165248167186), 92: np.float64(0.052930226679025874), 23: np.float64(0.008160192129434585), 53: 0, 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), np.float64(0.0797165248167186), np.float64(0.052930226679025874), np.float64(0.008160192129434585), 0, 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: np.float64(0.0797165248167186), 92: np.float64(0.052930226679025874), 23: np.float64(0.008160192129434585), 53: np.float64(0.034239066318361856), 57: 0, 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), np.float64(0.0797165248167186), np.float64(0.052930226679025874), np.float64(0.008160192129434585), np.float64(0.034239066318361856), 0, 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: np.float64(0.0797165248167186), 92: np.float64(0.052930226679025874), 23: np.float64(0.008160192129434585), 53: np.float64(0.034239066318361856), 57: np.float64(0.06558734305216146), 0: 0} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), np.float64(0.0797165248167186), np.float64(0.052930226679025874), np.float64(0.008160192129434585), np.float64(0.034239066318361856), np.float64(0.06558734305216146), 0]
err MNL dic= {8: np.float64(0.13228667734052413), 7: np.float64(0.05517999494396224), 9: np.float64(0.09040187073396813), 5: np.float64(0.0797165248167186), 92: np.float64(0.052930226679025874), 23: np.float64(0.008160192129434585), 53: np.float64(0.034239066318361856), 57: np.float64(0.06558734305216146), 0: np.float64(0.19666823965618946)} 

err MNL list= [np.float64(0.13228667734052413), np.float64(0.05517999494396224), np.float64(0.09040187073396813), np.float64(0.0797165248167186), np.float64(0.052930226679025874), np.float64(0.008160192129434585), np.float64(0.034239066318361856), np.float64(0.06558734305216146), np.float64(0.19666823965618946)]
sampled assortment [4, 7, 6, 1, 87, 38, 78, 19]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0} [8, 1, 2, 3, 4, 7]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 14: 1, 17: 1, 100: 1} [2, 1, 3, 6, 10, 11, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 7, 5: 4, 6: 0, 7: 5, 10: 2, 11: 5, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 11, 4]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 14: 1, 100: 1} [8, 1, 3, 4, 5, 7, 12, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1, 17: 1, 100: 1} [2, 3, 4, 6, 7, 9, 10, 13, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1} [1, 3, 5, 7, 9, 10, 11]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 3, 20: 5, 26: 8, 31: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 5, 11, 20, 26, 31]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 9: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 4, 7, 9, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 12: 1, 14: 1, 19: 1} [1, 3, 4, 5, 6, 7, 9, 12, 14, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 1, 13: 2, 15: 3, 17: 5, 20: 5, 100: 0} [6, 100, 10, 1, 3, 13, 15, 8, 5, 7, 17, 20]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 14: 1, 100: 1} [2, 1, 4, 6, 10, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 9: 1, 10: 1} [1, 3, 4, 5, 6, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 3, 17: 6, 25: 7, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 5, 11, 4, 17, 25]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 4, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 13: 1, 14: 1} [1, 3, 5, 7, 9, 11, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 4, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 7, 15, 5, 11, 17]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 4, 6, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 14: 1, 15: 1} [1, 4, 5, 7, 9, 10, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 20, 5, 11]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 16: 0, 100: 0} [3, 4, 5, 6, 9, 11, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 4, 6, 7, 9, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 15: 1, 17: 1} [1, 3, 5, 6, 9, 10, 14, 15, 17]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 67: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 67]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 15: 0, 100: 0} [3, 4, 5, 6, 9, 11, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 15: 1, 17: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 15, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1} [1, 3, 4, 5, 7, 9, 10, 11, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 3, 8: 4, 10: 1, 11: 5, 13: 3, 15: 3, 16: 8, 17: 6, 20: 4, 21: 8, 100: 0} [6, 100, 10, 1, 3, 7, 13, 15, 5, 8, 20, 11, 17, 16, 21]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 10: 1, 16: 1} [2, 6, 10, 16]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 11: 1, 13: 1, 15: 1} [1, 3, 4, 5, 7, 9, 11, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 8, 5: 4, 6: 0, 8: 4, 10: 2, 13: 2, 15: 3, 17: 5, 19: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 20, 17, 19, 4]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 3, 4, 5, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 12: 2, 14: 1, 18: 2} [1, 5, 7, 9, 14, 12, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 12: 8, 13: 2, 15: 3, 21: 8, 25: 7, 36: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 25, 12, 21, 36]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 11: 1, 12: 1, 14: 1} [8, 1, 3, 4, 7, 10, 11, 12, 14]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 18: 2, 100: 1} [2, 1, 3, 6, 10, 11, 100, 18]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 7: 1, 9: 1, 10: 1, 15: 1, 100: 1} [1, 3, 7, 9, 10, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 2: 10, 3: 2, 4: 6, 5: 4, 6: 0, 7: 5, 8: 3, 10: 2, 11: 5, 13: 2, 15: 4, 20: 5, 34: 10, 100: 0} [6, 100, 1, 3, 10, 13, 8, 5, 15, 7, 11, 20, 4, 2, 34]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 13: 1, 14: 1, 100: 1} [8, 2, 3, 4, 7, 12, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 24: 2, 100: 1} [2, 3, 6, 10, 11, 12, 100, 24]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 13: 1, 14: 1} [1, 3, 5, 7, 9, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 11: 4, 13: 2, 14: 6, 17: 5, 20: 6, 31: 9, 100: 0} [6, 100, 1, 3, 10, 13, 11, 7, 17, 14, 20, 31]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 9: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 7, 9, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 14: 0, 27: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 14, 27, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 1, 6, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1, 24: 1} [1, 3, 4, 5, 7, 9, 10, 15, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 13: 3, 14: 5, 16: 6, 23: 6, 25: 7, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 5, 14, 16, 23, 25]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 12: 1, 13: 1} [2, 3, 6, 10, 12, 13]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 15: 1} [1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 6, 13: 2, 14: 6, 15: 3, 18: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 4, 11, 14, 18]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 15: 1, 20: 1, 100: 1} [8, 1, 3, 5, 7, 15, 20, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 18: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 4, 6, 10, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 15: 1} [1, 3, 5, 9, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 3, 6: 0, 7: 5, 8: 4, 10: 2, 11: 6, 13: 2, 15: 3, 16: 7, 17: 5, 24: 9, 34: 8, 100: 0} [6, 100, 1, 3, 10, 13, 5, 15, 8, 7, 17, 11, 16, 34, 24]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 3, 4, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 12: 1, 13: 1, 100: 1} [2, 1, 3, 4, 6, 10, 12, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 12: 1, 15: 1} [1, 3, 5, 7, 9, 12, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 1, 13: 2, 15: 3, 16: 5, 17: 5, 18: 9, 19: 5, 20: 4, 23: 9, 100: 0} [6, 100, 10, 1, 3, 13, 15, 8, 20, 5, 7, 16, 17, 19, 18, 23]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1} [2, 3, 4, 6, 7, 10, 11, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 14: 1} [1, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 17: 5, 20: 5, 25: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 17, 20, 25]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 14: 1, 17: 1} [2, 1, 3, 6, 7, 10, 11, 13, 14, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 12: 1, 13: 1, 15: 1, 26: 1, 100: 1} [1, 3, 5, 9, 10, 12, 13, 15, 26, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 3, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 5, 8, 7]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 18: 0, 100: 0} [3, 4, 5, 6, 9, 11, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 35: 3} [2, 1, 6, 10, 11, 35]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 12: 1, 15: 1} [1, 5, 7, 9, 12, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 17: 7, 21: 7, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 17, 21, 23]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 5: 1, 7: 1, 8: 0} [8, 2, 3, 5, 7]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 7, 9, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 17: 1, 20: 1, 100: 1} [2, 6, 7, 10, 11, 12, 17, 20, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 11: 1, 12: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 11, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 15: 2, 100: 0} [6, 100, 1, 3, 10, 15, 8, 5, 7, 11]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 19
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 6
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 19
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 19
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 4
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 19
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 19
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 7
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 4
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 6
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 19
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 7
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 4
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 19
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 1
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 6
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 6
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 38
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 19
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 7
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 4
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 19
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 4
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 19
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 4
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 6
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 4
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 1
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 19
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 6
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 1
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 6
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 4
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 19
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 7
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 4
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 1
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 6
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 78
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 19
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 4
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 4
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 6
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 7
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 87
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 6
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 4
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 6
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 19
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 4
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 4
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 4
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 6
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 7
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 38
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 4
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 19
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 7
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 6
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 4
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 6
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
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 1
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 6
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 4
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 19
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 1
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 4
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 19
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 19
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 78
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 6
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 19
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 4
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 6
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 19
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 6
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 7
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 1
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 6
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 38
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 6
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 78
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 87
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 78
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 6
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 6
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 19
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 78
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 7
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 19
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 19
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 4
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 4
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 4
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 6
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 19
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 6
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 38
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 38
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 19
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 7
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 78
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 7
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 6
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 19
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 4
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 19
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 4
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 19
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 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 78
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 4
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 19
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 6
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 1
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 38
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 7
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 1
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 78
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 4
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 19
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 6
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 19
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 6
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 7
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 19
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 19
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 4
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 6
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 6
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 7
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 4
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 4
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 7
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 7
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 19
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 6
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 0
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 4
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 6
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 19
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 38
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 6
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 6
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 78
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 6
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 38
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 4
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 7
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 4
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 4
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 19
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 19
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 6
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 19
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 7
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 87
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 4
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 19
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 19
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 6
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 7
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 4
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 4
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 19
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 19
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 1
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 4
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 19
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 6
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 38
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 4
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 4
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 4
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 7
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 7
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 4
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 19
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 7
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 19
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 6
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 4
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 19
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 4
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 6
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 7
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 87
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 1
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 19
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 6
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 1
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 4
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 1
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 6
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 7
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 6
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 4
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 19
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 6
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 78
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 7
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 6
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 4
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 87
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 4
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 19
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 4
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 6
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 1
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 6
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 4
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 4
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 7
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 6
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 38
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 4
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 7
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 19
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 87
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 6
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 6
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 4
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 19
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 19
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 19
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 87
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 19
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 4
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 6
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 6
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 4
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 4
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 4
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 1
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 78
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 4
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 19
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 6
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 19
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 38
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 19
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 6
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 4
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 19
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 6
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 4
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 4
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 7
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 38
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 4
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 6
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 4
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 4
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 78
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 4
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 4
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 6
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 6
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 4
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 6
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 4
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 19
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 38
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 6
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 6
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 7
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 19
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 6
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 19
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 19
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 19
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 19
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 19
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 6
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 1
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 0
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 4
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 6
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 6
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 87
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 38
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 6
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 6
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 4
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 7
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 6
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 4
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 1
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 4
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 1
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 19
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 4
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 4
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 1
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 4
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 6
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 4
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 4
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 6
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 6
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 6
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 6
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 6
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 1
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 4
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 6
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 6
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 1
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 19
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 4
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 7
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 6
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 4
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 78
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 19
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 4
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 6
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 19
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 4
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 4
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 6
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 6
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 4
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 6
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 87
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 19
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 6
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 4
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 38
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 6
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 19
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 4
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 6
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 38
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 19
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 6
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 7
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 19
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 6
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 7
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 78
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 6
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 6
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 6
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 4
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 1
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 6
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 4
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 19
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 6
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 4
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 19
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 1
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 4
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 4
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 19
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 4
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 7
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 1
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 19
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 1
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 6
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 19
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 4
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 4
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 4
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 4
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 6
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 19
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 4
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 4
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 19
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 87
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 19
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 19
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 4
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 38
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 19
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 19
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 19
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 4
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 4
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 19
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 6
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 78
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 19
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 6
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 4
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 6
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 19
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 19
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 78
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 78
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 6
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 4
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 1
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 19
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 4
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 1
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 6
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 6
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 87
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 0
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 7
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 4
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 6
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 19
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 4
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 38
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 4
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 7
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 19
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 7
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 6
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 4
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 6
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 19
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 19
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 38
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 4
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 19
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 19
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 7
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 19
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 6
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 4
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 4
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 6
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 6
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 19
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 19
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 19
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 6
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 4
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 6
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 19
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 6
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 7
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 4
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 4
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 6
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 6
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 4
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 19
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 6
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 6
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 6
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 87
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 4
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 4
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 19
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 4
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 6
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 6
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 4
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 1
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 6
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 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 19
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 19
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 6
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 6
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 19
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 7
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 6
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 7
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 0
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 7
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 38
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 19
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 4
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 19
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 6
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 4
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 78
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 4
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 19
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 4
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 19
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 6
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 6
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 4
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 19
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 4
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 7
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 1
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 19
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 6
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 38
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 19
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 4
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 19
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 6
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 7
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 6
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 6
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 19
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 19
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 4
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 6
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 19
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 0
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 7
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 78
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 1
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 4
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 6
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 7
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 6
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 4
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 4
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 6
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 6
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 4
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 19
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 4
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 1
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 6
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 6
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 4
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 6
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 87
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 19
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 6
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 19
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 1
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 6
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 7
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 19
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 7
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 7
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 6
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 1
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 87
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 6
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 1
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 4
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 78
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 6
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 4
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 6
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 6
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 6
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 78
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 6
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 19
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 7
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 1
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 4
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 19
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 4
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 0
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 19
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 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 87
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 78
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 1
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 19
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 4
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 6
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 6
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 6
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 78
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 4
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 1
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 6
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 78
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 19
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 19
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 19
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 19
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 6
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 4
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 38
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 4
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 6
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 1
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 4
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 78
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 19
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 19
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 6
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 0
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 4
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 6
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 1
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 4
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 4
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 19
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 19
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 6
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 4
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 7
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 19
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 19
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 4
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 4
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 6
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 19
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 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 38
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 6
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 19
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 19
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 4
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 4
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 38
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 6
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 19
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 78
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 4
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 7
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 19
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 19
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 6
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 87
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 6
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 38
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 6
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 6
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 4
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 4
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 4
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 19
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 4
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 4
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 87
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 78
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 1
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 6
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 87
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 19
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 4
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 19
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 6
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 4
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 1
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 6
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 19
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 19
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 4
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 6
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 6
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 1
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 4
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 19
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 4
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 0
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 19
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 6
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 6
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 6
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 19
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 4
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 7
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 4
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 19
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 6
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 6
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 4
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 1
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 6
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 6
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 19
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 19
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 4
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 6
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 6
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 19
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 7
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 7
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 0
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 4
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 19
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 4
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 7
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 1
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 4
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 4
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 19
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 6
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 7
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 19
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 4
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 7
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 6
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 6
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 87
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 19
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 6
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 19
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 19
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 6
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 1
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 4
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 6
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 19
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 1
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 4
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 0
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 4
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 4
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 19
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 38
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 19
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 1
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 19
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 6
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 6
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 4
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 6
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 4
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 7
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 7
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 6
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 6
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 19
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 87
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 4
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 6
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 6
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 6
empirical probabilities from test set: {4: 0.177, 7: 0.155, 6: 0.188, 1: 0.196, 87: 0.02, 38: 0.055, 78: 0.032, 19: 0.164, 0: 0.013}
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.104747275853778), 7: np.float64(0.09520194502327156), 6: np.float64(0.10472849007044886), 1: np.float64(0.10479646896920089), 87: np.float64(0.1181051640166598), 38: np.float64(0.1181051640166598), 78: np.float64(0.1181051640166598), 19: np.float64(0.1181051640166598), 0: np.float64(0.1181051640166598)}
err dic= {4: np.float64(0.072252724146222), 7: np.float64(0.05979805497672844), 6: np.float64(0.08327150992955114), 1: np.float64(0.09120353103079912), 87: np.float64(0.0981051640166598), 38: np.float64(0.0631051640166598), 78: np.float64(0.0861051640166598), 19: np.float64(0.04589483598334021), 0: np.float64(0.1051051640166598)} 

err list= [np.float64(0.072252724146222), np.float64(0.05979805497672844), np.float64(0.08327150992955114), np.float64(0.09120353103079912), np.float64(0.0981051640166598), np.float64(0.0631051640166598), np.float64(0.0861051640166598), np.float64(0.04589483598334021), np.float64(0.1051051640166598)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.13084261553364018), 7: np.float64(0.12290020305013567), 6: np.float64(0.12833101147957895), 1: np.float64(0.10813697285974), 87: np.float64(0.10195783941538192), 38: np.float64(0.10195783941538192), 78: np.float64(0.10195783941538192), 19: np.float64(0.10195783941538192), 0: np.float64(0.10195783941538192)}
err dic= {4: np.float64(0.04615738446635981), 7: np.float64(0.032099796949864326), 6: np.float64(0.059668988520421046), 1: np.float64(0.08786302714026001), 87: np.float64(0.08195783941538191), 38: np.float64(0.04695783941538192), 78: np.float64(0.06995783941538192), 19: np.float64(0.06204216058461809), 0: np.float64(0.08895783941538192)} 

err list= [np.float64(0.04615738446635981), np.float64(0.032099796949864326), np.float64(0.059668988520421046), np.float64(0.08786302714026001), np.float64(0.08195783941538191), np.float64(0.04695783941538192), np.float64(0.06995783941538192), np.float64(0.06204216058461809), np.float64(0.08895783941538192)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.19139828342399787), 7: np.float64(0.16469164011975576), 6: np.float64(0.16339180231075373), 1: np.float64(0.17145693468373255), 87: np.float64(0.061812267892351974), 38: np.float64(0.061812267892351974), 78: np.float64(0.061812267892351974), 19: np.float64(0.061812267892351974), 0: np.float64(0.061812267892351974)}
err dic= {4: np.float64(0.014398283423997876), 7: np.float64(0.009691640119755762), 6: np.float64(0.02460819768924627), 1: np.float64(0.02454306531626746), 87: np.float64(0.04181226789235197), 38: np.float64(0.006812267892351974), 78: np.float64(0.029812267892351973), 19: np.float64(0.10218773210764803), 0: np.float64(0.048812267892351976)} 

err list= [np.float64(0.014398283423997876), np.float64(0.009691640119755762), np.float64(0.02460819768924627), np.float64(0.02454306531626746), np.float64(0.04181226789235197), np.float64(0.006812267892351974), np.float64(0.029812267892351973), np.float64(0.10218773210764803), np.float64(0.048812267892351976)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.2 

learned probs for this beta: {4: np.float64(0.2720169378024494), 7: np.float64(0.17871079683053892), 6: np.float64(0.24134443091946997), 1: np.float64(0.18815759533368048), 87: np.float64(0.02395404782277197), 38: np.float64(0.02395404782277197), 78: np.float64(0.02395404782277197), 19: np.float64(0.02395404782277197), 0: np.float64(0.02395404782277197)}
err dic= {4: np.float64(0.09501693780244941), 7: np.float64(0.02371079683053892), 6: np.float64(0.05334443091946997), 1: np.float64(0.007842404666319525), 87: np.float64(0.003954047822771971), 38: np.float64(0.03104595217722803), 78: np.float64(0.00804595217722803), 19: np.float64(0.14004595217722804), 0: np.float64(0.010954047822771972)} 

err list= [np.float64(0.09501693780244941), np.float64(0.02371079683053892), np.float64(0.05334443091946997), np.float64(0.007842404666319525), np.float64(0.003954047822771971), np.float64(0.03104595217722803), np.float64(0.00804595217722803), np.float64(0.14004595217722804), np.float64(0.010954047822771972)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.23941298305571002), 7: np.float64(0.1669062259529879), 6: np.float64(0.19589075063321432), 1: np.float64(0.3139408452735308), 87: np.float64(0.01676983901691192), 38: np.float64(0.01676983901691192), 78: np.float64(0.01676983901691192), 19: np.float64(0.01676983901691192), 0: np.float64(0.01676983901691192)}
err dic= {4: np.float64(0.062412983055710025), 7: np.float64(0.011906225952987903), 6: np.float64(0.007890750633214316), 1: np.float64(0.11794084527353077), 87: np.float64(0.003230160983088079), 38: np.float64(0.03823016098308808), 78: np.float64(0.01523016098308808), 19: np.float64(0.14723016098308808), 0: np.float64(0.003769839016911922)} 

err list= [np.float64(0.062412983055710025), np.float64(0.011906225952987903), np.float64(0.007890750633214316), np.float64(0.11794084527353077), np.float64(0.003230160983088079), np.float64(0.03823016098308808), np.float64(0.01523016098308808), np.float64(0.14723016098308808), np.float64(0.003769839016911922)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.3 

learned probs for this beta: {4: np.float64(0.3004106818231206), 7: np.float64(0.18052955130737797), 6: np.float64(0.18611676540259858), 1: np.float64(0.30664543601629324), 87: np.float64(0.005044133913447963), 38: np.float64(0.005044133913447963), 78: np.float64(0.005044133913447963), 19: np.float64(0.006121029796817176), 0: np.float64(0.005044133913447963)}
err dic= {4: np.float64(0.1234106818231206), 7: np.float64(0.025529551307377968), 6: np.float64(0.0018832345974014175), 1: np.float64(0.11064543601629323), 87: np.float64(0.014955866086552038), 38: np.float64(0.04995586608655204), 78: np.float64(0.02695586608655204), 19: np.float64(0.15787897020318284), 0: np.float64(0.007955866086552035)} 

err list= [np.float64(0.1234106818231206), np.float64(0.025529551307377968), np.float64(0.0018832345974014175), np.float64(0.11064543601629323), np.float64(0.014955866086552038), np.float64(0.04995586608655204), np.float64(0.02695586608655204), np.float64(0.15787897020318284), np.float64(0.007955866086552035)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.36509043020898174), 7: np.float64(0.14195113705673706), 6: np.float64(0.206970525601317), 1: np.float64(0.28443048489708167), 87: np.float64(0.0003114844471766613), 38: np.float64(0.0003114844471766613), 78: np.float64(0.0003114844471766613), 19: np.float64(0.0003114844471766613), 0: np.float64(0.0003114844471766613)}
err dic= {4: np.float64(0.18809043020898175), 7: np.float64(0.013048862943262934), 6: np.float64(0.018970525601317012), 1: np.float64(0.08843048489708166), 87: np.float64(0.01968851555282334), 38: np.float64(0.054688515552823336), 78: np.float64(0.031688515552823336), 19: np.float64(0.16368851555282335), 0: np.float64(0.012688515552823338)} 

err list= [np.float64(0.18809043020898175), np.float64(0.013048862943262934), np.float64(0.018970525601317012), np.float64(0.08843048489708166), np.float64(0.01968851555282334), np.float64(0.054688515552823336), np.float64(0.031688515552823336), np.float64(0.16368851555282335), np.float64(0.012688515552823338)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.30769861477233323), 7: np.float64(0.06615385684094707), 6: np.float64(0.15494840440345498), 1: np.float64(0.4711734186962969), 87: np.float64(5.141057393561701e-06), 38: np.float64(5.141057393561701e-06), 78: np.float64(5.141057393561701e-06), 19: np.float64(5.141057393561701e-06), 0: np.float64(5.141057393561701e-06)}
err dic= {4: np.float64(0.13069861477233324), 7: np.float64(0.08884614315905293), 6: np.float64(0.033051595596545025), 1: np.float64(0.2751734186962969), 87: np.float64(0.019994858942606438), 38: np.float64(0.05499485894260644), 78: np.float64(0.03199485894260644), 19: np.float64(0.16399485894260646), 0: np.float64(0.012994858942606437)} 

err list= [np.float64(0.13069861477233324), np.float64(0.08884614315905293), np.float64(0.033051595596545025), np.float64(0.2751734186962969), np.float64(0.019994858942606438), np.float64(0.05499485894260644), np.float64(0.03199485894260644), np.float64(0.16399485894260646), np.float64(0.012994858942606437)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  1 

learned probs for this beta: {4: np.float64(0.33322902457476805), 7: np.float64(0.04299806510777349), 6: np.float64(0.15497461635812834), 1: np.float64(0.46879486363921474), 87: np.float64(6.86064023095379e-07), 38: np.float64(6.86064023095379e-07), 78: np.float64(6.86064023095379e-07), 19: np.float64(6.86064023095379e-07), 0: np.float64(6.86064023095379e-07)}
err dic= {4: np.float64(0.15622902457476806), 7: np.float64(0.11200193489222651), 6: np.float64(0.03302538364187166), 1: np.float64(0.27279486363921474), 87: np.float64(0.019999313935976905), 38: np.float64(0.05499931393597691), 78: np.float64(0.03199931393597691), 19: np.float64(0.16399931393597691), 0: np.float64(0.012999313935976904)} 

err list= [np.float64(0.15622902457476806), np.float64(0.11200193489222651), np.float64(0.03302538364187166), np.float64(0.27279486363921474), np.float64(0.019999313935976905), np.float64(0.05499931393597691), np.float64(0.03199931393597691), np.float64(0.16399931393597691), np.float64(0.012999313935976904)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.3699872785922048), 7: np.float64(0.2924088061775755), 6: np.float64(0.18588626120177415), 1: np.float64(0.15168933415846242), 87: np.float64(5.663973996601375e-06), 38: np.float64(5.663973996601375e-06), 78: np.float64(5.663973996601375e-06), 19: np.float64(5.663973996601375e-06), 0: np.float64(5.663973996601375e-06)}
err dic= {4: np.float64(0.19298727859220483), 7: np.float64(0.13740880617757548), 6: np.float64(0.0021137387982258504), 1: np.float64(0.04431066584153759), 87: np.float64(0.0199943360260034), 38: np.float64(0.0549943360260034), 78: np.float64(0.0319943360260034), 19: np.float64(0.1639943360260034), 0: np.float64(0.012994336026003398)} 

err list= [np.float64(0.19298727859220483), np.float64(0.13740880617757548), np.float64(0.0021137387982258504), np.float64(0.04431066584153759), np.float64(0.0199943360260034), np.float64(0.0549943360260034), np.float64(0.0319943360260034), np.float64(0.1639943360260034), np.float64(0.012994336026003398)]
results for assortment [4, 7, 6, 1, 87, 38, 78, 19] :

err MNL dic= {4: np.float64(0.07041157864069589), 7: 0, 6: 0, 1: 0, 87: 0, 38: 0, 78: 0, 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: 0, 1: 0, 87: 0, 38: 0, 78: 0, 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: 0, 87: 0, 38: 0, 78: 0, 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), 0, 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: np.float64(0.08604037124901155), 87: 0, 38: 0, 78: 0, 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), np.float64(0.08604037124901155), 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: np.float64(0.08604037124901155), 87: np.float64(0.06477962292421025), 38: 0, 78: 0, 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), np.float64(0.08604037124901155), np.float64(0.06477962292421025), 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: np.float64(0.08604037124901155), 87: np.float64(0.06477962292421025), 38: np.float64(0.03668851708494609), 78: 0, 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), np.float64(0.08604037124901155), np.float64(0.06477962292421025), np.float64(0.03668851708494609), 0, 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: np.float64(0.08604037124901155), 87: np.float64(0.06477962292421025), 38: np.float64(0.03668851708494609), 78: np.float64(0.05398659841012195), 19: 0, 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), np.float64(0.08604037124901155), np.float64(0.06477962292421025), np.float64(0.03668851708494609), np.float64(0.05398659841012195), 0, 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: np.float64(0.08604037124901155), 87: np.float64(0.06477962292421025), 38: np.float64(0.03668851708494609), 78: np.float64(0.05398659841012195), 19: np.float64(0.06544420859865986), 0: 0} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), np.float64(0.08604037124901155), np.float64(0.06477962292421025), np.float64(0.03668851708494609), np.float64(0.05398659841012195), np.float64(0.06544420859865986), 0]
err MNL dic= {4: np.float64(0.07041157864069589), 7: np.float64(0.04757918175386025), 6: np.float64(0.08107861988596163), 1: np.float64(0.08604037124901155), 87: np.float64(0.06477962292421025), 38: np.float64(0.03668851708494609), 78: np.float64(0.05398659841012195), 19: np.float64(0.06544420859865986), 0: np.float64(0.19509922170891078)} 

err MNL list= [np.float64(0.07041157864069589), np.float64(0.04757918175386025), np.float64(0.08107861988596163), np.float64(0.08604037124901155), np.float64(0.06477962292421025), np.float64(0.03668851708494609), np.float64(0.05398659841012195), np.float64(0.06544420859865986), np.float64(0.19509922170891078)]
sampled assortment [2, 3, 6, 1, 18, 35, 29, 21]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 3, 4, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 15, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 17: 1, 21: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 13, 17, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 10: 1} [1, 3, 4, 5, 6, 7, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 8: 4, 10: 2, 11: 4, 13: 2, 14: 5, 15: 3, 17: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 11, 14, 20, 17]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 13: 1, 15: 1} [1, 3, 5, 7, 9, 11, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 3, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 14: 7, 15: 3, 100: 0} [6, 100, 1, 10, 13, 3, 15, 5, 7, 8, 14]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 4, 6, 7, 9, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 9: 1, 11: 1, 12: 1, 15: 1, 19: 1, 22: 2, 100: 1} [1, 3, 4, 5, 9, 11, 12, 15, 19, 100, 22]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 5: 4, 6: 0, 7: 5, 10: 2, 12: 7, 13: 2, 14: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 4, 7, 14, 20, 12]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 20: 1, 100: 1} [8, 2, 3, 5, 7, 20, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [4, 5, 6, 7, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 100: 1} [2, 1, 3, 7, 9, 10, 11, 12, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1, 15: 1, 17: 2, 24: 2, 100: 1} [1, 5, 6, 7, 9, 10, 13, 14, 15, 100, 17, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 3, 10: 2, 11: 5, 13: 2, 15: 4, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 5, 15, 20, 7, 11]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 4, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 9: 1, 13: 1, 16: 3, 19: 1} [1, 3, 5, 6, 9, 13, 19, 16]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 5: 5, 6: 0, 7: 5, 9: 6, 10: 2, 13: 3, 15: 3, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 4, 5, 7, 9, 17]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1} [8, 1, 2, 3, 5, 6, 7, 10, 13]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 17: 1, 21: 1, 100: 1} [2, 1, 3, 6, 10, 11, 12, 13, 14, 17, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 17: 7, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 5, 11, 20, 17]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 6, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1} [1, 3, 4, 5, 7, 9, 10, 11]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 4, 9: 6, 10: 2, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 7, 5, 4, 9]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 16: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 16, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1} [2, 1, 4, 6, 7, 10, 11, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 8: 4, 10: 1, 12: 6, 13: 2, 14: 7, 15: 3, 32: 9, 100: 0} [6, 100, 10, 1, 3, 13, 15, 8, 5, 12, 14, 32]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 3, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 17: 1, 100: 1} [2, 3, 6, 10, 11, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1, 26: 2} [1, 3, 5, 7, 9, 10, 11, 15, 26]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 11, 5, 7, 17]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 13: 1, 18: 2} [2, 1, 3, 6, 7, 10, 13, 18]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 15: 4, 17: 5, 28: 9, 100: 0} [6, 100, 1, 3, 10, 8, 15, 5, 7, 17, 28]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 10, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 15: 1} [1, 3, 4, 5, 6, 7, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 11: 3, 13: 2, 15: 3, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 7, 17]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 4, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 12, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 14: 1} [1, 3, 4, 5, 7, 9, 10, 11, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 12: 9, 13: 3, 14: 6, 15: 3, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 5, 11, 14, 23, 12]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 7, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 21: 1} [2, 1, 6, 10, 11, 12, 13, 14, 21]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1} [1, 3, 5, 6, 7, 9, 10, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 8: 3, 10: 2, 11: 5, 13: 2, 14: 6, 15: 3, 17: 6, 19: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 11, 20, 4, 14, 17, 19]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 3, 6, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 13: 1, 15: 1, 26: 2} [1, 3, 5, 7, 9, 10, 12, 13, 15, 26]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 11: 5, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 11]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 14: 1, 21: 1, 100: 1} [2, 1, 3, 6, 10, 14, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 3, 6: 0, 7: 5, 10: 2, 11: 5, 13: 2, 15: 3, 20: 5, 21: 6, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 5, 15, 7, 11, 20, 21, 23]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 2, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 10: 1, 11: 1, 12: 1, 13: 1, 17: 1, 100: 1} [2, 1, 3, 10, 11, 12, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 14: 1, 15: 1, 100: 1} [1, 5, 7, 9, 10, 11, 14, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 9: 7, 10: 2, 11: 3, 13: 2, 15: 3, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 5, 8, 7, 17, 9]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 100: 0} [3, 4, 5, 7, 9, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 4, 6, 10, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 15: 1} [1, 3, 5, 6, 7, 9, 10, 11, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 21: 6, 47: 7, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 7, 21, 47]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 4, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 15: 4, 17: 5, 18: 8, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 17, 18]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 11: 1, 14: 1, 15: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 11, 14, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 18: 0, 100: 0} [3, 4, 5, 6, 9, 12, 18, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 9: 1, 10: 1, 15: 1, 100: 1} [2, 1, 3, 6, 7, 9, 10, 15, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1} [1, 3, 5, 7, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 14: 5, 15: 4, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 11, 15, 20, 14, 17]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0} [8, 1, 2, 3, 4, 5, 7]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 9: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 3, 6, 9, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 12: 1, 15: 1, 19: 1} [1, 3, 5, 6, 7, 9, 10, 12, 15, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 16: 7, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 20, 16]
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 1
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 6
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 29
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 18
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 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 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 2
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 6
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 3
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 3
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 6
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 21
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 18
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 6
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 6
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 18
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 35
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 21
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 29
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 21
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 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 35
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 21
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 6
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 3
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 6
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 6
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 18
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 35
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 3
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 3
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 2
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 3
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 35
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 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 6
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 2
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 6
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 6
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 3
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 18
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 2
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 21
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 3
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 6
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 0
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 6
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 3
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 1
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 18
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 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 6
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 6
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 18
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 3
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 3
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 21
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 18
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 35
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 3
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 18
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 1
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 6
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 2
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 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 6
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 6
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 35
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 6
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 3
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 21
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 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 6
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 6
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 21
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 21
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 6
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 3
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 3
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 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 0
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
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 3
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 35
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 1
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 1
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 18
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 2
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 3
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 2
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 3
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 21
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 35
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 1
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 3
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 18
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 21
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 1
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 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 6
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 6
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 1
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 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 1
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 21
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 3
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 3
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 2
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 6
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 6
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 1
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 6
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 6
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 6
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 3
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 3
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 21
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 1
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 3
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 6
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
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 1
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 2
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 2
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 35
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 3
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 6
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 21
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 18
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 2
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 3
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 2
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 6
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 6
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 6
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 35
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 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 3
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 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 29
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 3
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 21
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 0
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 6
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 1
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 6
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 21
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 35
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 2
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 6
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 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 2
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 18
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 3
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 6
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 18
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 6
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 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 1
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 6
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 3
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 6
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 0
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 6
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 21
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 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 35
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 2
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 6
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 35
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 3
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 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 21
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 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 3
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 3
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 21
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 6
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 6
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 2
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 35
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 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 3
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 3
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 6
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 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 35
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 6
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 3
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 6
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 3
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 21
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 29
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 3
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 18
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 21
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 6
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 3
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 3
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 2
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 3
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 18
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 3
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 6
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 6
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 3
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 3
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 18
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 29
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 21
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 2
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 2
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 6
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 21
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 29
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 3
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 6
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 35
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 3
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 18
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 6
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 3
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 18
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 6
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 6
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 18
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 35
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 0
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 6
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 35
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 2
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 35
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 3
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 3
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 35
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 2
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 35
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 6
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 3
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 6
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 2
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 6
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 6
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 18
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 21
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 3
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 6
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 6
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 3
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 6
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 6
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 2
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 21
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 18
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 2
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 1
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 3
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 6
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 6
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 3
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 3
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 6
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 6
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 3
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 3
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 35
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 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 6
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 1
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 6
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 3
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 2
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 6
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 21
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 3
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 6
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 6
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 35
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 18
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 6
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 6
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 3
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 35
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 21
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 2
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 6
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 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 2
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 3
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 3
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 3
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 6
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 3
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 29
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 6
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 3
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 6
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 6
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 1
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 6
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 18
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 18
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 0
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 18
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 35
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 18
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 29
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 35
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 29
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 3
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 3
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 35
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 18
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 35
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 3
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 6
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 29
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 6
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 3
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 18
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 6
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 18
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 6
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 2
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 1
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 6
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 6
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 29
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 29
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 3
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 3
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 6
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 35
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 6
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 3
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 35
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 6
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 35
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 1
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 6
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 21
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 3
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 6
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 3
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 6
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 6
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 6
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 21
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 6
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 3
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 35
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 6
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 6
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 1
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 2
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 2
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 18
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 6
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 21
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 6
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 6
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 18
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 3
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 1
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 3
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 3
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 3
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 3
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 6
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 3
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 6
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 21
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 2
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 3
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 6
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 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 3
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 35
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 18
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 6
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 3
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 3
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 3
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 6
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 21
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 3
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 18
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 18
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 3
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 18
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 2
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 3
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 18
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 6
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 3
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 6
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 3
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 1
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 6
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 6
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 1
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 21
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 35
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 1
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 35
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 29
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
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 18
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 1
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 21
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 6
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 6
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 6
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 18
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 29
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 3
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 3
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 6
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 6
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 18
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 6
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 2
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 6
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 2
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 18
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 6
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 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 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
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 2
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 6
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 6
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 6
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 3
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 6
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 21
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 6
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 21
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 3
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 2
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 29
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 6
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 35
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 21
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 3
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 29
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 3
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 3
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 3
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 6
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 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 3
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 3
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 6
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 3
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 29
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 18
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 35
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 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 18
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 6
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 3
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 21
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 3
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 35
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 3
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 18
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 3
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 1
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 2
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 35
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 1
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 6
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 6
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 3
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 6
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 3
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 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 6
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 1
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 3
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 6
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 6
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 3
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 3
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 3
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 6
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 3
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 21
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 2
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 35
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 1
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 6
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 3
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 3
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 6
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 0
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 35
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 6
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 3
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 2
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 6
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 35
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 6
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 3
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 3
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 2
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 2
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 18
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 6
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 21
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 21
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 6
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 2
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 3
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 29
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 21
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 3
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 6
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 3
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 1
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 3
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 3
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 3
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 18
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 29
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 35
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 6
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 6
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 6
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 3
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 18
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 21
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 35
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 3
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 1
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 6
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 6
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 18
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 6
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 6
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 35
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 6
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 6
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 6
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 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 2
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 3
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 6
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 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 18
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 18
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 6
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 2
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 1
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 6
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 2
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 29
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 6
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 6
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 3
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 6
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 1
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 35
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 6
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 3
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 6
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 6
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 3
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 21
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 0
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 1
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 29
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 2
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 3
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 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 18
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 3
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 6
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 6
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 21
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 18
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 3
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 6
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 6
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 6
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 2
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 6
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 3
empirical probabilities from test set: {2: 0.19, 3: 0.147, 6: 0.169, 1: 0.172, 18: 0.104, 35: 0.046, 29: 0.053, 21: 0.106, 0: 0.013}
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.10935931598196369), 3: np.float64(0.08992420686969743), 6: np.float64(0.09148148063552752), 1: np.float64(0.10135273217469706), 18: np.float64(0.12157645286762314), 35: np.float64(0.12157645286762314), 29: np.float64(0.12157645286762314), 21: np.float64(0.12157645286762314), 0: np.float64(0.12157645286762314)}
err dic= {2: np.float64(0.08064068401803631), 3: np.float64(0.05707579313030256), 6: np.float64(0.07751851936447249), 1: np.float64(0.07064726782530292), 18: np.float64(0.017576452867623146), 35: np.float64(0.07557645286762314), 29: np.float64(0.06857645286762315), 21: np.float64(0.015576452867623145), 0: np.float64(0.10857645286762314)} 

err list= [np.float64(0.08064068401803631), np.float64(0.05707579313030256), np.float64(0.07751851936447249), np.float64(0.07064726782530292), np.float64(0.017576452867623146), np.float64(0.07557645286762314), np.float64(0.06857645286762315), np.float64(0.015576452867623145), np.float64(0.10857645286762314)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.10934797597759235), 3: np.float64(0.1463436968029946), 6: np.float64(0.12966881609284456), 1: np.float64(0.11956943994607774), 18: np.float64(0.0990140142360994), 35: np.float64(0.0990140142360994), 29: np.float64(0.0990140142360994), 21: np.float64(0.0990140142360994), 0: np.float64(0.0990140142360994)}
err dic= {2: np.float64(0.08065202402240765), 3: np.float64(0.0006563031970053812), 6: np.float64(0.039331183907155454), 1: np.float64(0.05243056005392224), 18: np.float64(0.004985985763900594), 35: np.float64(0.0530140142360994), 29: np.float64(0.0460140142360994), 21: np.float64(0.006985985763900596), 0: np.float64(0.0860140142360994)} 

err list= [np.float64(0.08065202402240765), np.float64(0.0006563031970053812), np.float64(0.039331183907155454), np.float64(0.05243056005392224), np.float64(0.004985985763900594), np.float64(0.0530140142360994), np.float64(0.0460140142360994), np.float64(0.006985985763900596), np.float64(0.0860140142360994)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.13423615096661176), 3: np.float64(0.1937337424403142), 6: np.float64(0.12766629373490768), 1: np.float64(0.17987091198993338), 18: np.float64(0.08895801742962844), 35: np.float64(0.06638621657349572), 29: np.float64(0.06638621657349572), 21: np.float64(0.0763762337181136), 0: np.float64(0.06638621657349572)}
err dic= {2: np.float64(0.05576384903338824), 3: np.float64(0.0467337424403142), 6: np.float64(0.041333706265092335), 1: np.float64(0.007870911989933393), 18: np.float64(0.015041982570371551), 35: np.float64(0.020386216573495722), 29: np.float64(0.013386216573495723), 21: np.float64(0.0296237662818864), 0: np.float64(0.05338621657349572)} 

err list= [np.float64(0.05576384903338824), np.float64(0.0467337424403142), np.float64(0.041333706265092335), np.float64(0.007870911989933393), np.float64(0.015041982570371551), np.float64(0.020386216573495722), np.float64(0.013386216573495723), np.float64(0.0296237662818864), np.float64(0.05338621657349572)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.2 

learned probs for this beta: {2: np.float64(0.13895521015682724), 3: np.float64(0.3795450596417545), 6: np.float64(0.1907109907886601), 1: np.float64(0.186402909980015), 18: np.float64(0.020877165886548636), 35: np.float64(0.020877165886548636), 29: np.float64(0.020877165886548636), 21: np.float64(0.020877165886548636), 0: np.float64(0.020877165886548636)}
err dic= {2: np.float64(0.05104478984317276), 3: np.float64(0.2325450596417545), 6: np.float64(0.021710990788660095), 1: np.float64(0.014402909980015005), 18: np.float64(0.08312283411345137), 35: np.float64(0.025122834113451363), 29: np.float64(0.03212283411345136), 21: np.float64(0.08512283411345137), 0: np.float64(0.007877165886548637)} 

err list= [np.float64(0.05104478984317276), np.float64(0.2325450596417545), np.float64(0.021710990788660095), np.float64(0.014402909980015005), np.float64(0.08312283411345137), np.float64(0.025122834113451363), np.float64(0.03212283411345136), np.float64(0.08512283411345137), np.float64(0.007877165886548637)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.12797917740278072), 3: np.float64(0.4012593713061914), 6: np.float64(0.18266862093615407), 1: np.float64(0.23564252626711088), 18: np.float64(0.007591154506488989), 35: np.float64(0.007591154506488989), 29: np.float64(0.007591154506488989), 21: np.float64(0.02208568606180466), 0: np.float64(0.007591154506488989)}
err dic= {2: np.float64(0.06202082259721928), 3: np.float64(0.25425937130619136), 6: np.float64(0.013668620936154063), 1: np.float64(0.0636425262671109), 18: np.float64(0.096408845493511), 35: np.float64(0.03840884549351101), 29: np.float64(0.04540884549351101), 21: np.float64(0.08391431393819535), 0: np.float64(0.0054088454935110105)} 

err list= [np.float64(0.06202082259721928), np.float64(0.25425937130619136), np.float64(0.013668620936154063), np.float64(0.0636425262671109), np.float64(0.096408845493511), np.float64(0.03840884549351101), np.float64(0.04540884549351101), np.float64(0.08391431393819535), np.float64(0.0054088454935110105)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.3 

learned probs for this beta: {2: np.float64(0.19232539104257126), 3: np.float64(0.3940342625915202), 6: np.float64(0.1569538567326888), 1: np.float64(0.22190667546740178), 18: np.float64(0.006955962833163651), 35: np.float64(0.006955962833163651), 29: np.float64(0.006955962833163651), 21: np.float64(0.006955962833163651), 0: np.float64(0.006955962833163651)}
err dic= {2: np.float64(0.002325391042571262), 3: np.float64(0.2470342625915202), 6: np.float64(0.01204614326731121), 1: np.float64(0.049906675467401795), 18: np.float64(0.09704403716683635), 35: np.float64(0.03904403716683635), 29: np.float64(0.046044037166836346), 21: np.float64(0.09904403716683635), 0: np.float64(0.006044037166836348)} 

err list= [np.float64(0.002325391042571262), np.float64(0.2470342625915202), np.float64(0.01204614326731121), np.float64(0.049906675467401795), np.float64(0.09704403716683635), np.float64(0.03904403716683635), np.float64(0.046044037166836346), np.float64(0.09904403716683635), np.float64(0.006044037166836348)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.08509974549577583), 3: np.float64(0.552881553340342), 6: np.float64(0.06772723447366279), 1: np.float64(0.2847403914540903), 18: np.float64(0.0018148344511171222), 35: np.float64(0.0018148344511171222), 29: np.float64(0.0018148344511171222), 21: np.float64(0.00229173743166112), 0: np.float64(0.0018148344511171222)}
err dic= {2: np.float64(0.10490025450422417), 3: np.float64(0.4058815533403419), 6: np.float64(0.10127276552633722), 1: np.float64(0.11274039145409032), 18: np.float64(0.10218516554888288), 35: np.float64(0.044185165548882875), 29: np.float64(0.051185165548882874), 21: np.float64(0.10370826256833887), 0: np.float64(0.011185165548882877)} 

err list= [np.float64(0.10490025450422417), np.float64(0.4058815533403419), np.float64(0.10127276552633722), np.float64(0.11274039145409032), np.float64(0.10218516554888288), np.float64(0.044185165548882875), np.float64(0.051185165548882874), np.float64(0.10370826256833887), np.float64(0.011185165548882877)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.1782399796032676), 3: np.float64(0.4234195361821498), 6: np.float64(0.09547018198562504), 1: np.float64(0.30281045349041474), 18: np.float64(2.3222295632215555e-05), 35: np.float64(9.156610727606908e-06), 29: np.float64(9.156610727606908e-06), 21: np.float64(9.156610727606908e-06), 0: np.float64(9.156610727606908e-06)}
err dic= {2: np.float64(0.011760020396732407), 3: np.float64(0.27641953618214976), 6: np.float64(0.07352981801437497), 1: np.float64(0.13081045349041476), 18: np.float64(0.10397677770436778), 35: np.float64(0.045990843389272396), 29: np.float64(0.052990843389272395), 21: np.float64(0.1059908433892724), 0: np.float64(0.012990843389272392)} 

err list= [np.float64(0.011760020396732407), np.float64(0.27641953618214976), np.float64(0.07352981801437497), np.float64(0.13081045349041476), np.float64(0.10397677770436778), np.float64(0.045990843389272396), np.float64(0.052990843389272395), np.float64(0.1059908433892724), np.float64(0.012990843389272392)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  1 

learned probs for this beta: {2: np.float64(0.1642718693822692), 3: np.float64(0.44184968263276614), 6: np.float64(0.08428363379104864), 1: np.float64(0.30776220912086605), 18: np.float64(0.0018321869761070096), 35: np.float64(1.0452423579189995e-07), 29: np.float64(1.0452423579189995e-07), 21: np.float64(1.0452423579189995e-07), 0: np.float64(1.0452423579189995e-07)}
err dic= {2: np.float64(0.0257281306177308), 3: np.float64(0.2948496826327661), 6: np.float64(0.08471636620895137), 1: np.float64(0.13576220912086606), 18: np.float64(0.10216781302389298), 35: np.float64(0.045999895475764205), 29: np.float64(0.052999895475764204), 21: np.float64(0.1059998954757642), 0: np.float64(0.012999895475764207)} 

err list= [np.float64(0.0257281306177308), np.float64(0.2948496826327661), np.float64(0.08471636620895137), np.float64(0.13576220912086606), np.float64(0.10216781302389298), np.float64(0.045999895475764205), np.float64(0.052999895475764204), np.float64(0.1059998954757642), np.float64(0.012999895475764207)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.1728222386763299), 3: np.float64(0.4639878436511752), 6: np.float64(0.07910712429364944), 1: np.float64(0.28408278618724314), 18: np.float64(1.4383204493381846e-09), 35: np.float64(1.4383204493381846e-09), 29: np.float64(1.4383204493381846e-09), 21: np.float64(1.4383204493381846e-09), 0: np.float64(1.4383204493381846e-09)}
err dic= {2: np.float64(0.017177761323670104), 3: np.float64(0.31698784365117516), 6: np.float64(0.08989287570635057), 1: np.float64(0.11208278618724316), 18: np.float64(0.10399999856167955), 35: np.float64(0.04599999856167955), 29: np.float64(0.05299999856167955), 21: np.float64(0.10599999856167955), 0: np.float64(0.01299999856167955)} 

err list= [np.float64(0.017177761323670104), np.float64(0.31698784365117516), np.float64(0.08989287570635057), np.float64(0.11208278618724316), np.float64(0.10399999856167955), np.float64(0.04599999856167955), np.float64(0.05299999856167955), np.float64(0.10599999856167955), np.float64(0.01299999856167955)]
results for assortment [2, 3, 6, 1, 18, 35, 29, 21] :

err MNL dic= {2: np.float64(0.08733918248534296), 3: 0, 6: 0, 1: 0, 18: 0, 35: 0, 29: 0, 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: 0, 1: 0, 18: 0, 35: 0, 29: 0, 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: 0, 18: 0, 35: 0, 29: 0, 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), 0, 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: np.float64(0.06429633881349678), 18: 0, 35: 0, 29: 0, 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), np.float64(0.06429633881349678), 0, 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: np.float64(0.06429633881349678), 18: np.float64(0.008308966422040917), 35: 0, 29: 0, 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), np.float64(0.06429633881349678), np.float64(0.008308966422040917), 0, 0, 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: np.float64(0.06429633881349678), 18: np.float64(0.008308966422040917), 35: np.float64(0.04350022549300972), 29: 0, 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), np.float64(0.06429633881349678), np.float64(0.008308966422040917), np.float64(0.04350022549300972), 0, 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: np.float64(0.06429633881349678), 18: np.float64(0.008308966422040917), 35: np.float64(0.04350022549300972), 29: np.float64(0.0388371530482555), 21: 0, 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), np.float64(0.06429633881349678), np.float64(0.008308966422040917), np.float64(0.04350022549300972), np.float64(0.0388371530482555), 0, 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: np.float64(0.06429633881349678), 18: np.float64(0.008308966422040917), 35: np.float64(0.04350022549300972), 29: np.float64(0.0388371530482555), 21: np.float64(0.008546021073346732), 0: 0} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), np.float64(0.06429633881349678), np.float64(0.008308966422040917), np.float64(0.04350022549300972), np.float64(0.0388371530482555), np.float64(0.008546021073346732), 0]
err MNL dic= {2: np.float64(0.08733918248534296), 3: np.float64(0.04228924603337296), 6: np.float64(0.0635512689106638), 1: np.float64(0.06429633881349678), 18: np.float64(0.008308966422040917), 35: np.float64(0.04350022549300972), 29: np.float64(0.0388371530482555), 21: np.float64(0.008546021073346732), 0: np.float64(0.19199364519699888)} 

err MNL list= [np.float64(0.08733918248534296), np.float64(0.04228924603337296), np.float64(0.0635512689106638), np.float64(0.06429633881349678), np.float64(0.008308966422040917), np.float64(0.04350022549300972), np.float64(0.0388371530482555), np.float64(0.008546021073346732), np.float64(0.19199364519699888)]
sampled assortment [5, 6, 3, 8, 37, 91, 14, 70]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 15: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 13, 14, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 19: 1, 100: 1} [2, 1, 3, 6, 9, 10, 11, 12, 14, 19, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 7: 1, 9: 1, 10: 1, 20: 2, 24: 1} [1, 3, 7, 9, 10, 24, 20]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 4, 16: 6, 19: 5, 20: 4, 26: 9, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11, 15, 20, 4, 19, 16, 26]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 3, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 11: 1, 100: 1} [2, 1, 3, 4, 6, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1, 24: 1} [1, 3, 5, 7, 9, 10, 11, 15, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 9: 7, 10: 2, 13: 2, 15: 4, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 15, 20, 9]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 13: 1} [8, 1, 2, 3, 5, 6, 7, 13]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 17: 2, 100: 1} [2, 1, 3, 4, 6, 10, 100, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1} [1, 3, 4, 5, 7, 9, 10, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 14: 7, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 20, 14]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1} [8, 2, 3, 4, 5, 7, 13]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 14: 0, 15: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 14, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 22: 1, 100: 1} [2, 4, 6, 7, 10, 11, 12, 22, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1} [1, 3, 5, 7, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 5, 11, 4]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 9: 1, 10: 1, 100: 1} [8, 1, 2, 3, 4, 7, 9, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 9: 1, 10: 1} [2, 1, 6, 7, 9, 10]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 15: 1, 17: 1} [1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 15, 17]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 2: 8, 3: 2, 4: 5, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 12: 8, 13: 3, 15: 5, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 4, 7, 15, 17, 2, 12]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 18: 1, 19: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 19, 100, 18]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1, 26: 1} [1, 3, 5, 7, 9, 10, 14, 15, 26]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 14: 1} [2, 1, 4, 6, 7, 10, 11, 13, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1} [1, 3, 5, 7, 9, 10, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 1, 11: 5, 13: 3, 14: 6, 15: 3, 17: 6, 100: 0} [6, 100, 10, 1, 3, 8, 13, 15, 5, 7, 11, 14, 17]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 17: 1, 100: 1} [2, 1, 3, 6, 10, 11, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 6: 1, 7: 1, 9: 1, 13: 1, 18: 2, 19: 1} [1, 4, 6, 7, 9, 13, 19, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 10: 2, 11: 3, 13: 2, 17: 6, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 11, 7, 17, 23]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 4, 7, 10, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 14: 0, 16: 1, 100: 0} [3, 4, 5, 6, 9, 12, 14, 100, 16]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 12: 1, 14: 1, 100: 1} [2, 1, 3, 6, 7, 10, 12, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1} [1, 3, 5, 6, 7, 9, 10, 11]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11, 20, 17, 4]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 13: 1, 100: 1} [2, 1, 4, 6, 10, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 12: 1, 100: 1} [1, 3, 5, 7, 9, 12, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 13: 2, 15: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 15]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 4: 1, 7: 1, 8: 0, 11: 1, 13: 1, 19: 1, 100: 1} [8, 1, 2, 4, 7, 11, 13, 19, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 19: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 6, 7, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1, 15: 1, 16: 1} [1, 4, 5, 7, 9, 10, 13, 14, 15, 16]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 11]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 14: 1} [2, 1, 6, 10, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 19: 1, 100: 1} [1, 4, 5, 7, 9, 10, 19, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 7, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 11, 17, 23, 4]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 3, 4, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 14: 1, 16: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 12, 14, 16, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1, 100: 1} [1, 4, 5, 7, 9, 10, 13, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 1, 11: 5, 13: 2, 20: 3, 100: 0} [6, 100, 10, 1, 3, 13, 20, 7, 8, 5, 11]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 8: 0, 12: 1, 14: 1, 100: 1} [8, 1, 3, 4, 12, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 14: 1, 100: 1} [2, 1, 6, 10, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 14: 1, 15: 1, 100: 1} [1, 5, 7, 9, 14, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 3, 12: 8, 13: 2, 15: 3, 17: 5, 21: 7, 23: 7, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 7, 8, 17, 21, 23, 12]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 12, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 17: 1, 100: 1} [2, 1, 4, 6, 7, 10, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 11: 1, 13: 1, 24: 2} [1, 3, 4, 5, 7, 9, 11, 13, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 1, 13: 2, 14: 7, 15: 3, 20: 5, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 20, 14]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 15: 1, 100: 1} [8, 1, 3, 4, 5, 7, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 100: 1} [2, 1, 4, 6, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 14: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 11, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 8: 3, 10: 1, 13: 2, 15: 3, 100: 0} [6, 100, 10, 1, 3, 13, 8, 15]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1} [1, 5, 7, 9, 10, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 12: 8, 13: 2, 14: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 7, 20, 14, 12]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 22: 1} [8, 1, 2, 3, 4, 5, 7, 22]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 3, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 9: 1, 14: 1, 19: 1, 100: 1} [1, 3, 5, 6, 9, 14, 19, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 4, 10: 2, 13: 2, 15: 3, 16: 8, 17: 5, 20: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 7, 5, 17, 4, 16]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 11: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 11, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 4, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 15: 1, 19: 1} [1, 3, 5, 7, 9, 10, 11, 12, 15, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 11: 3, 13: 2, 14: 6, 15: 3, 20: 5, 32: 9, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 5, 7, 20, 14, 32]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 11: 0, 14: 0, 100: 0} [3, 4, 5, 7, 9, 10, 11, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 14: 1, 100: 1} [2, 1, 4, 6, 10, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 13: 1} [1, 3, 4, 5, 7, 9, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 19: 5, 47: 11, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 19, 47]
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 5
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 6
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 5
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 14
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 5
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 14
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 5
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 6
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 3
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 3
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 70
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 5
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 5
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 6
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 6
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 3
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 14
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 37
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 91
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 14
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 5
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 3
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 37
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 70
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 91
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 3
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 6
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 5
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 6
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 3
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 6
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 70
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 8
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 3
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 6
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 3
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 3
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 70
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 3
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 6
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 5
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 5
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 14
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 6
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 3
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 3
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 6
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 5
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 6
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 3
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 8
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 5
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 6
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 5
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 5
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 14
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 3
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 5
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 6
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 6
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 14
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 3
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 3
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 5
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 91
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 91
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 6
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 14
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 5
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 3
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 3
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 3
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 5
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 70
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 3
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 5
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 14
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 3
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 3
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 6
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 3
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 3
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 14
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 6
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 6
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 14
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 3
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 6
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 5
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 6
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 5
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 37
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 3
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 5
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 37
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 3
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 14
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 3
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 3
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 5
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 5
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 5
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 3
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 5
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 5
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 14
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 3
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 6
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 14
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 3
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 5
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 3
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 3
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 37
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 5
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 14
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 3
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 14
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 14
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 6
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 6
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 0
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 5
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 14
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 6
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 8
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 6
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 5
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 6
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 37
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 6
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 14
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 14
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 14
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 8
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 3
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 3
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 14
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 3
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 3
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 3
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 5
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 37
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 3
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 6
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 70
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 37
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 5
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 6
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 3
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 6
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 3
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 14
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 37
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 14
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 37
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 5
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 70
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 91
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 37
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 37
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 14
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 6
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 3
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 37
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 5
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 37
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 14
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 3
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 5
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 6
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 5
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 37
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 6
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 14
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 3
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 14
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 5
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 6
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 6
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 6
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 5
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 70
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 3
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 3
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 5
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 70
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 37
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 3
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 5
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 0
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 6
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 6
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 6
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 37
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 5
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 3
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 37
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 14
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 5
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 6
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 5
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 37
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 5
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 91
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 14
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 3
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 6
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 14
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 3
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 6
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 3
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 5
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 5
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 5
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 6
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 37
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 6
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 14
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 37
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 6
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 8
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 3
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 3
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 14
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 6
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 5
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 14
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 5
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 6
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 3
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 3
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 3
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 6
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 6
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 6
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 3
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 5
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 14
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 3
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 6
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 6
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 37
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 6
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 14
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 91
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 3
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 14
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 5
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 5
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 3
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 3
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 6
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 14
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 5
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 14
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 6
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 3
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 5
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 6
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 3
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 5
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 37
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 5
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 37
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 6
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 5
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 6
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 3
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 3
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 14
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 3
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 3
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 37
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 70
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 3
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 6
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 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 3
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 3
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 5
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 5
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 37
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 5
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 14
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 14
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 91
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 3
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 6
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 3
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 3
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 14
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 8
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 37
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 70
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 6
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 6
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 6
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 6
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 3
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 6
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 5
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 6
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 6
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 6
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 5
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 14
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 6
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 5
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 5
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 5
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 91
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 5
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 3
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 8
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 3
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 6
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 14
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 0
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 5
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 14
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 6
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 6
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 37
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 6
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 5
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 5
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 3
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 91
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 37
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 6
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 5
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 3
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 14
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 6
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 70
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 37
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 6
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 6
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 6
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 5
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 8
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 5
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 6
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 37
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 3
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 6
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 6
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 14
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 3
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 3
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 5
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 6
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 14
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 3
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 91
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 8
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 6
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 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 6
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 3
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 6
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 14
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 5
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 70
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 70
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 3
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 5
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 6
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 5
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 6
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 5
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 14
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 6
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 5
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 37
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 14
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 3
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 5
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 14
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 14
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 8
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 6
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 5
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 3
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 3
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 37
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 37
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 5
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 3
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 6
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 3
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 37
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 6
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 6
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 5
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 37
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 6
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 8
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 5
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 3
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 3
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 5
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 3
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 5
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 5
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 3
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 8
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 37
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 5
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 37
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 37
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 3
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 14
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 3
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 37
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 37
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 5
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 37
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 14
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 5
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 14
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 5
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 5
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 6
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 6
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 5
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 14
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 5
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 8
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 5
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 6
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 6
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 5
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 5
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 91
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 6
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 3
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 14
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 6
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 37
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 14
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 3
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 5
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 6
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 3
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 6
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 14
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 6
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 5
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 91
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 14
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 6
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 5
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 6
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 3
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 5
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 6
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 3
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 6
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 5
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 6
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 14
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 5
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 6
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 6
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 3
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 6
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 6
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 5
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 70
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 5
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 14
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 3
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 6
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 37
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 6
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 6
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 0
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 37
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 6
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 3
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 3
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 3
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 3
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 5
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 5
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 6
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 3
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 6
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 37
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 0
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 3
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 37
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 6
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 37
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 6
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 6
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 3
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 3
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 37
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 37
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 5
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 6
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 14
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 6
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 37
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 14
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 37
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 14
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 14
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 14
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 14
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 6
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 37
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 6
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 70
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 14
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 3
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 91
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 14
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 6
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 6
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 3
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 37
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 5
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 6
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 5
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 70
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 37
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 6
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 5
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 6
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 91
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 37
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
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 5
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 5
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 3
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 5
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 6
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 6
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 14
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 3
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 3
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 6
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 6
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 37
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 37
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 14
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 3
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 6
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 5
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 37
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 3
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 6
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 5
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 37
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 3
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 70
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 5
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 70
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 37
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 70
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 14
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 6
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 91
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 6
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 6
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 6
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 6
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 6
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 37
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 14
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 3
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 6
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 14
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 14
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 3
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 14
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 3
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 3
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 91
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 5
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 5
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 91
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 14
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 8
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 5
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 3
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 3
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 3
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 3
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 3
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 70
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 3
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 6
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 6
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 5
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 3
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 6
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 14
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 91
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 70
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 6
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 6
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 14
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 14
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 5
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 14
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 6
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 3
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 37
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 5
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 6
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 3
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 3
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 5
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 5
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 3
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 6
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 5
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 5
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 3
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 5
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 6
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 5
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 5
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 8
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 37
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 91
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 6
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 3
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 70
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 14
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 91
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 6
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 6
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 14
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 5
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 5
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 14
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 6
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 6
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 6
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 6
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 6
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 3
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 3
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 5
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 8
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 14
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 14
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 14
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 70
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 5
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 6
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 3
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 5
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 14
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 6
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 0
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 5
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 6
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 14
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 37
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 6
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 14
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 6
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 3
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 3
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 5
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 3
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 5
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 5
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 5
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 5
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 14
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 3
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 37
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 70
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 5
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 14
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 6
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 14
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 5
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 6
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 5
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 6
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 3
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 37
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 6
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 3
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 3
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 3
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 5
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 6
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 14
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 5
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 14
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 6
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 6
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 6
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 3
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 3
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 70
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 3
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 3
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 5
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 37
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 5
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 3
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 6
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 14
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 14
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 5
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 14
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 6
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 14
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 6
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 37
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 6
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 6
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 3
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 8
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 3
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 3
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 5
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 6
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 6
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 6
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 14
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 14
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 3
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 6
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 5
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 3
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 6
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 37
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 5
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 6
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 8
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 6
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 5
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 3
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 70
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 70
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 3
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 5
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 5
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 6
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 14
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 6
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 3
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 6
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 14
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 5
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 37
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 14
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 14
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 3
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 3
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 6
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 3
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 5
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 8
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 3
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 6
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 6
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 14
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 6
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 0
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 8
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 3
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 14
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 6
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 6
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 14
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 6
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 6
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 3
empirical probabilities from test set: {5: 0.157, 6: 0.197, 3: 0.18, 8: 0.21, 37: 0.071, 91: 0.026, 14: 0.111, 70: 0.035, 0: 0.013}
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.10628813820734048), 6: np.float64(0.10058182993107229), 3: np.float64(0.10778230939685425), 8: np.float64(0.11300526356742568), 37: np.float64(0.11639371545127278), 91: np.float64(0.11639371545127278), 14: np.float64(0.10676759709221655), 70: np.float64(0.11639371545127278), 0: np.float64(0.11639371545127278)}
err dic= {5: np.float64(0.05071186179265952), 6: np.float64(0.09641817006892772), 3: np.float64(0.07221769060314574), 8: np.float64(0.09699473643257431), 37: np.float64(0.045393715451272784), 91: np.float64(0.09039371545127278), 14: np.float64(0.004232402907783456), 70: np.float64(0.08139371545127277), 0: np.float64(0.10339371545127278)} 

err list= [np.float64(0.05071186179265952), np.float64(0.09641817006892772), np.float64(0.07221769060314574), np.float64(0.09699473643257431), np.float64(0.045393715451272784), np.float64(0.09039371545127278), np.float64(0.004232402907783456), np.float64(0.08139371545127277), np.float64(0.10339371545127278)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.1275832168368621), 6: np.float64(0.12002076155303441), 3: np.float64(0.13442324709143239), 8: np.float64(0.10603139505735402), 37: np.float64(0.10411979201910093), 91: np.float64(0.10411979201910093), 14: np.float64(0.09546221138491662), 70: np.float64(0.10411979201910093), 0: np.float64(0.10411979201910093)}
err dic= {5: np.float64(0.029416783163137894), 6: np.float64(0.0769792384469656), 3: np.float64(0.04557675290856761), 8: np.float64(0.10396860494264597), 37: np.float64(0.03311979201910094), 91: np.float64(0.07811979201910094), 14: np.float64(0.015537788615083384), 70: np.float64(0.06911979201910093), 0: np.float64(0.09111979201910093)} 

err list= [np.float64(0.029416783163137894), np.float64(0.0769792384469656), np.float64(0.04557675290856761), np.float64(0.10396860494264597), np.float64(0.03311979201910094), np.float64(0.07811979201910094), np.float64(0.015537788615083384), np.float64(0.06911979201910093), np.float64(0.09111979201910093)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.1582041736953073), 6: np.float64(0.1646592786193197), 3: np.float64(0.21993300676636957), 8: np.float64(0.10374580292386575), 37: np.float64(0.0638557500572703), 91: np.float64(0.0638557500572703), 14: np.float64(0.09803473776605323), 70: np.float64(0.0638557500572703), 0: np.float64(0.0638557500572703)}
err dic= {5: np.float64(0.0012041736953072868), 6: np.float64(0.03234072138068031), 3: np.float64(0.03993300676636957), 8: np.float64(0.10625419707613425), 37: np.float64(0.007144249942729691), 91: np.float64(0.03785575005727031), 14: np.float64(0.01296526223394677), 70: np.float64(0.0288557500572703), 0: np.float64(0.050855750057270305)} 

err list= [np.float64(0.0012041736953072868), np.float64(0.03234072138068031), np.float64(0.03993300676636957), np.float64(0.10625419707613425), np.float64(0.007144249942729691), np.float64(0.03785575005727031), np.float64(0.01296526223394677), np.float64(0.0288557500572703), np.float64(0.050855750057270305)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.2 

learned probs for this beta: {5: np.float64(0.1985707393541864), 6: np.float64(0.1936965612237426), 3: np.float64(0.25075971235295946), 8: np.float64(0.1142519467697368), 37: np.float64(0.028538667584573126), 91: np.float64(0.028538667584573126), 14: np.float64(0.12856636996108262), 70: np.float64(0.028538667584573126), 0: np.float64(0.028538667584573126)}
err dic= {5: np.float64(0.0415707393541864), 6: np.float64(0.0033034387762574113), 3: np.float64(0.07075971235295947), 8: np.float64(0.0957480532302632), 37: np.float64(0.042461332415426864), 91: np.float64(0.0025386675845731274), 14: np.float64(0.017566369961082615), 70: np.float64(0.006461332415426877), 0: np.float64(0.015538667584573127)} 

err list= [np.float64(0.0415707393541864), np.float64(0.0033034387762574113), np.float64(0.07075971235295947), np.float64(0.0957480532302632), np.float64(0.042461332415426864), np.float64(0.0025386675845731274), np.float64(0.017566369961082615), np.float64(0.006461332415426877), np.float64(0.015538667584573127)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.22149050431230333), 6: np.float64(0.22670649002495588), 3: np.float64(0.34089231648722834), 8: np.float64(0.11694825880575782), 37: np.float64(0.015500459518317258), 91: np.float64(0.015500459518317258), 14: np.float64(0.031960592296485374), 70: np.float64(0.015500459518317258), 0: np.float64(0.015500459518317258)}
err dic= {5: np.float64(0.06449050431230333), 6: np.float64(0.029706490024955873), 3: np.float64(0.16089231648722835), 8: np.float64(0.09305174119424217), 37: np.float64(0.055499540481682735), 91: np.float64(0.01049954048168274), 14: np.float64(0.07903940770351463), 70: np.float64(0.019499540481682745), 0: np.float64(0.002500459518317259)} 

err list= [np.float64(0.06449050431230333), np.float64(0.029706490024955873), np.float64(0.16089231648722835), np.float64(0.09305174119424217), np.float64(0.055499540481682735), np.float64(0.01049954048168274), np.float64(0.07903940770351463), np.float64(0.019499540481682745), np.float64(0.002500459518317259)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.3 

learned probs for this beta: {5: np.float64(0.21502785567512533), 6: np.float64(0.21889958410831584), 3: np.float64(0.36760797419373187), 8: np.float64(0.12376835255850557), 37: np.float64(0.012021968457811802), 91: np.float64(0.012021968457811802), 14: np.float64(0.026608359633073536), 70: np.float64(0.012021968457811802), 0: np.float64(0.012021968457811802)}
err dic= {5: np.float64(0.058027855675125334), 6: np.float64(0.021899584108315828), 3: np.float64(0.18760797419373187), 8: np.float64(0.08623164744149442), 37: np.float64(0.05897803154218819), 91: np.float64(0.013978031542188197), 14: np.float64(0.08439164036692647), 70: np.float64(0.0229780315421882), 0: np.float64(0.0009780315421881978)} 

err list= [np.float64(0.058027855675125334), np.float64(0.021899584108315828), np.float64(0.18760797419373187), np.float64(0.08623164744149442), np.float64(0.05897803154218819), np.float64(0.013978031542188197), np.float64(0.08439164036692647), np.float64(0.0229780315421882), np.float64(0.0009780315421881978)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.25383634444789627), 6: np.float64(0.15176719138897204), 3: np.float64(0.412195039980736), 8: np.float64(0.14704193622508158), 37: np.float64(0.00037167473928653076), 91: np.float64(0.00037167473928653076), 14: np.float64(0.03367278900016913), 70: np.float64(0.00037167473928653076), 0: np.float64(0.00037167473928653076)}
err dic= {5: np.float64(0.09683634444789627), 6: np.float64(0.045232808611027964), 3: np.float64(0.23219503998073598), 8: np.float64(0.06295806377491842), 37: np.float64(0.07062832526071346), 91: np.float64(0.02562832526071347), 14: np.float64(0.07732721099983086), 70: np.float64(0.03462832526071347), 0: np.float64(0.01262832526071347)} 

err list= [np.float64(0.09683634444789627), np.float64(0.045232808611027964), np.float64(0.23219503998073598), np.float64(0.06295806377491842), np.float64(0.07062832526071346), np.float64(0.02562832526071347), np.float64(0.07732721099983086), np.float64(0.03462832526071347), np.float64(0.01262832526071347)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.12933907472434752), 6: np.float64(0.16094706738207215), 3: np.float64(0.5308086026143735), 8: np.float64(0.17389168168229116), 37: np.float64(6.707331735567355e-06), 91: np.float64(6.707331735567355e-06), 14: np.float64(0.004986744269973329), 70: np.float64(6.707331735567355e-06), 0: np.float64(6.707331735567355e-06)}
err dic= {5: np.float64(0.027660925275652476), 6: np.float64(0.03605293261792786), 3: np.float64(0.35080860261437347), 8: np.float64(0.03610831831770883), 37: np.float64(0.07099329266826443), 91: np.float64(0.02599329266826443), 14: np.float64(0.10601325573002668), 70: np.float64(0.03499329266826444), 0: np.float64(0.012993292668264432)} 

err list= [np.float64(0.027660925275652476), np.float64(0.03605293261792786), np.float64(0.35080860261437347), np.float64(0.03610831831770883), np.float64(0.07099329266826443), np.float64(0.02599329266826443), np.float64(0.10601325573002668), np.float64(0.03499329266826444), np.float64(0.012993292668264432)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  1 

learned probs for this beta: {5: np.float64(0.10163334331269663), 6: np.float64(0.2475063486269147), 3: np.float64(0.4586266568074208), 8: np.float64(0.19220845474062254), 37: np.float64(4.680029268660647e-06), 91: np.float64(4.680029268660647e-06), 14: np.float64(6.476395270661714e-06), 70: np.float64(4.680029268660647e-06), 0: np.float64(4.680029268660647e-06)}
err dic= {5: np.float64(0.05536665668730337), 6: np.float64(0.05050634862691469), 3: np.float64(0.2786266568074208), 8: np.float64(0.017791545259377456), 37: np.float64(0.07099531997073133), 91: np.float64(0.02599531997073134), 14: np.float64(0.11099352360472935), 70: np.float64(0.03499531997073134), 0: np.float64(0.012995319970731339)} 

err list= [np.float64(0.05536665668730337), np.float64(0.05050634862691469), np.float64(0.2786266568074208), np.float64(0.017791545259377456), np.float64(0.07099531997073133), np.float64(0.02599531997073134), np.float64(0.11099352360472935), np.float64(0.03499531997073134), np.float64(0.012995319970731339)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.05964471986355617), 6: np.float64(0.20970855183087056), 3: np.float64(0.5116769965031371), 8: np.float64(0.19998631830202307), 37: np.float64(2.573916664886496e-08), 91: np.float64(2.573916664886496e-08), 14: np.float64(0.01898331054374629), 70: np.float64(2.573916664886496e-08), 0: np.float64(2.573916664886496e-08)}
err dic= {5: np.float64(0.09735528013644383), 6: np.float64(0.012708551830870551), 3: np.float64(0.33167699650313714), 8: np.float64(0.010013681697976923), 37: np.float64(0.07099997426083335), 91: np.float64(0.02599997426083335), 14: np.float64(0.09201668945625371), 70: np.float64(0.03499997426083335), 0: np.float64(0.01299997426083335)} 

err list= [np.float64(0.09735528013644383), np.float64(0.012708551830870551), np.float64(0.33167699650313714), np.float64(0.010013681697976923), np.float64(0.07099997426083335), np.float64(0.02599997426083335), np.float64(0.09201668945625371), np.float64(0.03499997426083335), np.float64(0.01299997426083335)]
results for assortment [5, 6, 3, 8, 37, 91, 14, 70] :

err MNL dic= {5: np.float64(0.049330076907087905), 6: 0, 3: 0, 8: 0, 37: 0, 91: 0, 14: 0, 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: 0, 8: 0, 37: 0, 91: 0, 14: 0, 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: 0, 37: 0, 91: 0, 14: 0, 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), 0, 0, 0, 0, 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: np.float64(0.10457493244647681), 37: 0, 91: 0, 14: 0, 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), np.float64(0.10457493244647681), 0, 0, 0, 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: np.float64(0.10457493244647681), 37: np.float64(0.021205362710455228), 91: 0, 14: 0, 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), np.float64(0.10457493244647681), np.float64(0.021205362710455228), 0, 0, 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: np.float64(0.10457493244647681), 37: np.float64(0.021205362710455228), 91: np.float64(0.05905508210351279), 14: 0, 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), np.float64(0.10457493244647681), np.float64(0.021205362710455228), np.float64(0.05905508210351279), 0, 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: np.float64(0.10457493244647681), 37: np.float64(0.021205362710455228), 91: np.float64(0.05905508210351279), 14: np.float64(0.009690500935356477), 70: 0, 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), np.float64(0.10457493244647681), np.float64(0.021205362710455228), np.float64(0.05905508210351279), np.float64(0.009690500935356477), 0, 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: np.float64(0.10457493244647681), 37: np.float64(0.021205362710455228), 91: np.float64(0.05905508210351279), 14: np.float64(0.009690500935356477), 70: np.float64(0.05072022448555394), 0: 0} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), np.float64(0.10457493244647681), np.float64(0.021205362710455228), np.float64(0.05905508210351279), np.float64(0.009690500935356477), np.float64(0.05072022448555394), 0]
err MNL dic= {5: np.float64(0.049330076907087905), 6: np.float64(0.09036936187902724), 3: np.float64(0.07187279151943461), 8: np.float64(0.10457493244647681), 37: np.float64(0.021205362710455228), 91: np.float64(0.05905508210351279), 14: np.float64(0.009690500935356477), 70: np.float64(0.05072022448555394), 0: np.float64(0.19485699438786117)} 

err MNL list= [np.float64(0.049330076907087905), np.float64(0.09036936187902724), np.float64(0.07187279151943461), np.float64(0.10457493244647681), np.float64(0.021205362710455228), np.float64(0.05905508210351279), np.float64(0.009690500935356477), np.float64(0.05072022448555394), np.float64(0.19485699438786117)]
sampled assortment [9, 2, 8, 7, 53, 13, 30, 34]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 19: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 9: 1, 10: 1, 11: 1, 14: 1, 17: 1} [2, 6, 9, 10, 11, 14, 17]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 14: 1, 15: 1, 100: 1} [1, 3, 5, 7, 9, 11, 14, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 3, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 20, 7, 17]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 19: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 4, 6, 7, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 7: 1, 9: 1, 15: 1, 22: 1} [1, 4, 5, 7, 9, 15, 22]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 5, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 16: 7, 20: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 7, 8, 11, 4, 5, 16]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 3, 6, 7, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 9: 1, 14: 1, 15: 1, 100: 1} [1, 3, 4, 5, 6, 7, 9, 14, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 3, 14: 8, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 7, 11, 14]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1} [8, 1, 2, 3, 4, 5, 7, 12]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 6, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 7: 1, 9: 1, 19: 1} [1, 3, 4, 7, 9, 19]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 12: 7, 13: 2, 15: 3, 16: 7, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 20, 12, 16]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [3, 4, 5, 6, 9, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 13: 1, 22: 1, 100: 1} [2, 1, 3, 6, 10, 13, 22, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 9: 1, 10: 1, 12: 1} [1, 3, 5, 6, 9, 10, 12]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 11: 5, 13: 2, 15: 3, 20: 5, 25: 8, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 11, 20, 25]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 12: 1, 13: 1, 100: 1} [8, 1, 2, 3, 7, 10, 12, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 4, 6, 10, 11, 13, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1} [1, 3, 5, 7, 9, 10, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 14: 6, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 20, 5, 11, 17, 14]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 20: 0, 100: 0} [3, 4, 5, 6, 9, 11, 12, 20, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 17: 1, 18: 1, 21: 1, 100: 1} [2, 6, 7, 10, 11, 17, 18, 21, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1, 15: 1} [1, 3, 4, 6, 7, 9, 10, 13, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 2, 13: 2, 14: 7, 15: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 15, 7, 14]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 3, 4, 7, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 13: 1, 16: 1, 22: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 12, 13, 16, 22, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 13: 1, 14: 1, 17: 1} [1, 3, 5, 6, 7, 9, 13, 14, 17]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 15, 5, 8, 20, 7, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 12: 1, 100: 1} [2, 1, 3, 6, 10, 12, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 9: 1, 11: 1, 13: 1, 14: 1, 15: 1} [1, 3, 4, 5, 9, 11, 13, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 13: 2, 19: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 20, 19]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 1, 6, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 16: 7, 47: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 11, 16, 47]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 5: 2, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 3, 6, 10, 11, 14, 100, 5]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 11: 1, 12: 1, 13: 1, 15: 1, 22: 2, 25: 1} [1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 25, 22]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 14: 6, 15: 3, 20: 5, 24: 8, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 7, 11, 20, 14, 24]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 13: 1, 14: 1} [2, 1, 3, 6, 7, 9, 10, 11, 13, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 9: 1, 10: 1, 15: 1} [1, 3, 5, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 3, 10: 1, 11: 4, 13: 2, 17: 5, 21: 7, 100: 0} [6, 100, 10, 1, 3, 13, 7, 11, 5, 17, 21]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 9: 1, 10: 1, 11: 1, 13: 1, 17: 1, 100: 1} [2, 6, 9, 10, 11, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 13: 1, 14: 1} [1, 3, 5, 7, 9, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 9: 7, 10: 2, 11: 4, 13: 2, 14: 7, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11, 20, 17, 9, 14]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 9: 1, 100: 1} [8, 1, 3, 4, 5, 7, 9, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 3, 4, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 13: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 10, 12, 13, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 3, 10: 2, 11: 5, 13: 3, 14: 6, 15: 3, 20: 6, 100: 0} [6, 100, 1, 3, 10, 8, 13, 15, 7, 5, 11, 14, 20]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 2, 3, 4, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 4, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 13: 1} [1, 3, 5, 7, 9, 10, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 11: 4, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 6, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 15: 1} [1, 3, 4, 5, 7, 9, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 8: 3, 10: 2, 11: 5, 13: 3, 14: 5, 19: 5, 100: 0} [6, 100, 1, 3, 10, 8, 13, 5, 11, 14, 19]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 3, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 6, 7, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 9: 1, 10: 1, 14: 1, 15: 1, 25: 1} [1, 5, 7, 9, 10, 14, 15, 25]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 12: 7, 13: 2, 14: 5, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 11, 14, 12]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 13: 1, 14: 1, 24: 1} [1, 3, 4, 5, 7, 13, 14, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 10: 1, 13: 2, 15: 5, 19: 5, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 5, 20, 15, 19]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 4, 5, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 16: 0, 100: 0} [3, 4, 5, 6, 9, 11, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 4, 6, 10, 11, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1} [1, 3, 4, 5, 7, 9, 10, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 20: 5, 38: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 5, 20, 38]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 9: 1, 10: 1, 11: 1, 17: 1, 100: 1} [2, 1, 3, 6, 9, 10, 11, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 12: 2} [1, 3, 4, 5, 7, 9, 12]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 7, 5: 5, 6: 0, 7: 4, 8: 3, 10: 1, 11: 4, 13: 2, 14: 6, 15: 3, 17: 6, 20: 6, 100: 0} [6, 100, 10, 1, 3, 13, 8, 15, 7, 11, 5, 14, 17, 20, 4]
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 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 34
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 30
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 13
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 34
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 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 2
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 2
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 0
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 7
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 8
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 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 2
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 2
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 8
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 0
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 9
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 53
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 2
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 2
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 13
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 34
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 0
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 7
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 30
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 8
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 13
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 13
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 2
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 13
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 53
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 2
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 53
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 7
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 7
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 7
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 2
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 13
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 34
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 30
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 7
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 7
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 30
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 13
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 30
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 13
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 53
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 13
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 13
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 34
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 13
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 13
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 13
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 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 2
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 13
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 34
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 13
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 13
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 34
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 8
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 2
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 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 34
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 13
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 13
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 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 2
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 2
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 9
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 7
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 7
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 8
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 34
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 9
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 2
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 2
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 2
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 53
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 34
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 53
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 30
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 13
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 13
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 53
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 7
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 34
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 30
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 9
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 8
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 13
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 8
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 13
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 30
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 34
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 30
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 2
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 53
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 2
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 53
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 13
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 30
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 7
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 13
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 7
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 13
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 7
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 13
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 9
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 13
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 2
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 13
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 9
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 13
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 8
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 53
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 8
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 7
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 13
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 34
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 13
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 9
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 13
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 7
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 13
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 2
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 2
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 34
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 8
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 2
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 13
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 13
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 8
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 34
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 13
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 53
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 13
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 2
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 30
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 2
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 2
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 7
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 53
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 13
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 13
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 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 53
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 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 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 30
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 2
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 34
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 2
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 13
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 2
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 13
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 8
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 30
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 7
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 9
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 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 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 13
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 7
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 13
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 8
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 13
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 9
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 34
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 7
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 2
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 34
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 9
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 13
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 2
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 34
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 13
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 53
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 34
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 9
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 30
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 7
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 2
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 13
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 53
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 2
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 13
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 30
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 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 34
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 9
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 9
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 9
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 9
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 30
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 7
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 13
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 13
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 13
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 2
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 13
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 7
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 13
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 34
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 7
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 34
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 34
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 30
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 13
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 7
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 2
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 9
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 13
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 34
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 13
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 2
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 30
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 7
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 34
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 13
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 34
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 7
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 8
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 13
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 8
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 13
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 34
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 2
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 13
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 7
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 7
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 13
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 13
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 34
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 34
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 53
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 13
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 7
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 30
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 9
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 13
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 13
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 34
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 53
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 34
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 2
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 13
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 2
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 30
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 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 9
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 13
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 30
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 2
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 9
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 13
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 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 34
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 7
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 13
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 13
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 2
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 9
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 7
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 13
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 13
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 34
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 2
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 2
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 13
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 9
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 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 13
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 13
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 7
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 2
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 30
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 13
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 34
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 30
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 13
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 7
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 53
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 13
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 53
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 2
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 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 13
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 13
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 13
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 0
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 9
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 30
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 2
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 7
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 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 13
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 53
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 0
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 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 13
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 2
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 34
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 34
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 7
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 9
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 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 34
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 30
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 53
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 2
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 2
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 30
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 13
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 13
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 7
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 30
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 34
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 34
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 53
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 34
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 7
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 2
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 2
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 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 0
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 30
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 13
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 34
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 13
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 13
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 13
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 34
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 2
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 30
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 2
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 8
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 13
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 8
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 8
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 13
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 2
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 13
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 2
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 30
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 2
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 7
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 34
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 9
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 8
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 9
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 8
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 13
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 34
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 2
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 34
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 9
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 30
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 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 34
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 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 13
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 13
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 34
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 9
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 13
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 34
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 34
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 34
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 2
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 13
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 2
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 13
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 13
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 30
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 2
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 13
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 53
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 30
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 13
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 2
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 13
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 30
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 13
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 13
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 34
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 9
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 13
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 53
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 13
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 7
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 2
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 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 30
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 30
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 2
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 13
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 13
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 7
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 34
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 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 34
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 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 30
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 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 13
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 8
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 13
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 13
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 34
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 13
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 2
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 13
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 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 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 7
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 9
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 13
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 30
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 13
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 13
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 7
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 13
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 13
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 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 9
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 13
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 9
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 7
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 9
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 13
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 9
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 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 0
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 9
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 13
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 9
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 30
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 7
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 13
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 34
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 2
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 2
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 2
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 13
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 2
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 13
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 30
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 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 2
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 13
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 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 7
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 30
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 13
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 30
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 13
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 0
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 34
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 2
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 0
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 30
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 2
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 9
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 7
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 0
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 9
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 7
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 53
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 2
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 0
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 53
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 7
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 13
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 8
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 53
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 30
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 2
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 53
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 8
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 34
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 9
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 2
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 53
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 8
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 53
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 34
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 7
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 13
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 34
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 2
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 7
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 30
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 2
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 13
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 30
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 2
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 2
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 53
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 13
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 53
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 13
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 13
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 2
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 30
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 7
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 34
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 8
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 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 13
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 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 7
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 7
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 7
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 13
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 30
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 13
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 13
empirical probabilities from test set: {9: 0.157, 2: 0.189, 8: 0.202, 7: 0.145, 53: 0.037, 13: 0.137, 30: 0.048, 34: 0.061, 0: 0.024}
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.11600854379329748), 2: np.float64(0.10397974018528082), 8: np.float64(0.10687349271522431), 7: np.float64(0.09439920713180341), 53: np.float64(0.11571954176815503), 13: np.float64(0.11586084910177123), 30: np.float64(0.11571954176815503), 34: np.float64(0.11571954176815503), 0: np.float64(0.11571954176815503)}
err dic= {9: np.float64(0.040991456206702526), 2: np.float64(0.08502025981471918), 8: np.float64(0.0951265072847757), 7: np.float64(0.050600792868196576), 53: np.float64(0.07871954176815504), 13: np.float64(0.02113915089822878), 30: np.float64(0.06771954176815503), 34: np.float64(0.054719541768155036), 0: np.float64(0.09171954176815503)} 

err list= [np.float64(0.040991456206702526), np.float64(0.08502025981471918), np.float64(0.0951265072847757), np.float64(0.050600792868196576), np.float64(0.07871954176815504), np.float64(0.02113915089822878), np.float64(0.06771954176815503), np.float64(0.054719541768155036), np.float64(0.09171954176815503)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.10784142537319574), 2: np.float64(0.11978809898267914), 8: np.float64(0.10742986618222286), 7: np.float64(0.11226095433590617), 53: np.float64(0.10969448809235652), 13: np.float64(0.11390170275657216), 30: np.float64(0.10969448809235652), 34: np.float64(0.10969448809235652), 0: np.float64(0.10969448809235652)}
err dic= {9: np.float64(0.04915857462680426), 2: np.float64(0.06921190101732086), 8: np.float64(0.09457013381777715), 7: np.float64(0.032739045664093816), 53: np.float64(0.07269448809235651), 13: np.float64(0.02309829724342785), 30: np.float64(0.06169448809235652), 34: np.float64(0.04869448809235652), 0: np.float64(0.08569448809235652)} 

err list= [np.float64(0.04915857462680426), np.float64(0.06921190101732086), np.float64(0.09457013381777715), np.float64(0.032739045664093816), np.float64(0.07269448809235651), np.float64(0.02309829724342785), np.float64(0.06169448809235652), np.float64(0.04869448809235652), np.float64(0.08569448809235652)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.16022819505562413), 2: np.float64(0.11157657059447434), 8: np.float64(0.11299676784227344), 7: np.float64(0.16188303957530098), 53: np.float64(0.08229281173820903), 13: np.float64(0.1241441799794872), 30: np.float64(0.08229281173820903), 34: np.float64(0.08229281173820903), 0: np.float64(0.08229281173820903)}
err dic= {9: np.float64(0.0032281950556241334), 2: np.float64(0.07742342940552566), 8: np.float64(0.08900323215772657), 7: np.float64(0.01688303957530099), 53: np.float64(0.04529281173820903), 13: np.float64(0.012855820020512818), 30: np.float64(0.03429281173820903), 34: np.float64(0.02129281173820903), 0: np.float64(0.05829281173820903)} 

err list= [np.float64(0.0032281950556241334), np.float64(0.07742342940552566), np.float64(0.08900323215772657), np.float64(0.01688303957530099), np.float64(0.04529281173820903), np.float64(0.012855820020512818), np.float64(0.03429281173820903), np.float64(0.02129281173820903), np.float64(0.05829281173820903)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.2 

learned probs for this beta: {9: np.float64(0.24192041419362623), 2: np.float64(0.13146354312978806), 8: np.float64(0.159734414928539), 7: np.float64(0.19739179573640875), 53: np.float64(0.04511455201300146), 13: np.float64(0.08903162395963131), 30: np.float64(0.04511455201300146), 34: np.float64(0.04511455201300146), 0: np.float64(0.04511455201300146)}
err dic= {9: np.float64(0.08492041419362623), 2: np.float64(0.057536456870211944), 8: np.float64(0.042265585071461026), 7: np.float64(0.05239179573640876), 53: np.float64(0.008114552013001465), 13: np.float64(0.0479683760403687), 30: np.float64(0.0028854479869985378), 34: np.float64(0.015885447986998535), 0: np.float64(0.021114552013001463)} 

err list= [np.float64(0.08492041419362623), np.float64(0.057536456870211944), np.float64(0.042265585071461026), np.float64(0.05239179573640876), np.float64(0.008114552013001465), np.float64(0.0479683760403687), np.float64(0.0028854479869985378), np.float64(0.015885447986998535), np.float64(0.021114552013001463)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.20361016256487566), 2: np.float64(0.20219240670278016), 8: np.float64(0.11885202165572724), 7: np.float64(0.29964329476921236), 53: np.float64(0.020926900190714248), 13: np.float64(0.09199451354454706), 30: np.float64(0.020926900190714248), 34: np.float64(0.020926900190714248), 0: np.float64(0.020926900190714248)}
err dic= {9: np.float64(0.04661016256487566), 2: np.float64(0.013192406702780157), 8: np.float64(0.08314797834427277), 7: np.float64(0.15464329476921237), 53: np.float64(0.01607309980928575), 13: np.float64(0.04500548645545295), 30: np.float64(0.027073099809285753), 34: np.float64(0.04007309980928575), 0: np.float64(0.0030730998092857523)} 

err list= [np.float64(0.04661016256487566), np.float64(0.013192406702780157), np.float64(0.08314797834427277), np.float64(0.15464329476921237), np.float64(0.01607309980928575), np.float64(0.04500548645545295), np.float64(0.027073099809285753), np.float64(0.04007309980928575), np.float64(0.0030730998092857523)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.3 

learned probs for this beta: {9: np.float64(0.2038570105495313), 2: np.float64(0.19467266261689234), 8: np.float64(0.15225490960119714), 7: np.float64(0.30212690336181147), 53: np.float64(0.016521820776035517), 13: np.float64(0.08100123076642578), 30: np.float64(0.016521820776035517), 34: np.float64(0.016521820776035517), 0: np.float64(0.016521820776035517)}
err dic= {9: np.float64(0.046857010549531286), 2: np.float64(0.005672662616892338), 8: np.float64(0.04974509039880287), 7: np.float64(0.15712690336181148), 53: np.float64(0.02047817922396448), 13: np.float64(0.05599876923357423), 30: np.float64(0.03147817922396448), 34: np.float64(0.04447817922396448), 0: np.float64(0.007478179223964484)} 

err list= [np.float64(0.046857010549531286), np.float64(0.005672662616892338), np.float64(0.04974509039880287), np.float64(0.15712690336181148), np.float64(0.02047817922396448), np.float64(0.05599876923357423), np.float64(0.03147817922396448), np.float64(0.04447817922396448), np.float64(0.007478179223964484)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.20985659378811664), 2: np.float64(0.11513321278263741), 8: np.float64(0.16846521961498814), 7: np.float64(0.4574511745490738), 53: np.float64(0.0007950578282157515), 13: np.float64(0.04591356795232144), 30: np.float64(0.0007950578282157515), 34: np.float64(0.0007950578282157515), 0: np.float64(0.0007950578282157515)}
err dic= {9: np.float64(0.052856593788116635), 2: np.float64(0.07386678721736259), 8: np.float64(0.03353478038501187), 7: np.float64(0.3124511745490738), 53: np.float64(0.03620494217178424), 13: np.float64(0.09108643204767858), 30: np.float64(0.047204942171784246), 34: np.float64(0.060204942171784244), 0: np.float64(0.02320494217178425)} 

err list= [np.float64(0.052856593788116635), np.float64(0.07386678721736259), np.float64(0.03353478038501187), np.float64(0.3124511745490738), np.float64(0.03620494217178424), np.float64(0.09108643204767858), np.float64(0.047204942171784246), np.float64(0.060204942171784244), np.float64(0.02320494217178425)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.126625792694531), 2: np.float64(0.1764503503335125), 8: np.float64(0.1942354622964422), 7: np.float64(0.39023996042397774), 53: np.float64(8.311602661618084e-05), 13: np.float64(0.11211597014507169), 30: np.float64(8.311602661618084e-05), 34: np.float64(8.311602661618084e-05), 0: np.float64(8.311602661618084e-05)}
err dic= {9: np.float64(0.030374207305468998), 2: np.float64(0.0125496496664875), 8: np.float64(0.007764537703557811), 7: np.float64(0.24523996042397775), 53: np.float64(0.036916883973383816), 13: np.float64(0.024884029854928325), 30: np.float64(0.04791688397338382), 34: np.float64(0.060916883973383816), 0: np.float64(0.02391688397338382)} 

err list= [np.float64(0.030374207305468998), np.float64(0.0125496496664875), np.float64(0.007764537703557811), np.float64(0.24523996042397775), np.float64(0.036916883973383816), np.float64(0.024884029854928325), np.float64(0.04791688397338382), np.float64(0.060916883973383816), np.float64(0.02391688397338382)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  1 

learned probs for this beta: {9: np.float64(0.43719997655400944), 2: np.float64(0.20876416229458336), 8: np.float64(0.17826856905916316), 7: np.float64(0.12545375438987877), 53: np.float64(1.1591188014601946e-05), 13: np.float64(0.05026717295030695), 30: np.float64(1.1591188014601946e-05), 34: np.float64(1.1591188014601946e-05), 0: np.float64(1.1591188014601946e-05)}
err dic= {9: np.float64(0.2801999765540094), 2: np.float64(0.01976416229458336), 8: np.float64(0.02373143094083685), 7: np.float64(0.01954624561012122), 53: np.float64(0.036988408811985396), 13: np.float64(0.08673282704969307), 30: np.float64(0.0479884088119854), 34: np.float64(0.060988408811985396), 0: np.float64(0.0239884088119854)} 

err list= [np.float64(0.2801999765540094), np.float64(0.01976416229458336), np.float64(0.02373143094083685), np.float64(0.01954624561012122), np.float64(0.036988408811985396), np.float64(0.08673282704969307), np.float64(0.0479884088119854), np.float64(0.060988408811985396), np.float64(0.0239884088119854)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

beta is  1.25 

learned probs for this beta: {9: np.float64(0.12768297311763382), 2: np.float64(0.19565176528249562), 8: np.float64(0.1985510450582485), 7: np.float64(0.4366165474489189), 53: np.float64(6.153268947337117e-08), 13: np.float64(0.04149742296194511), 30: np.float64(6.153268947337117e-08), 34: np.float64(6.153268947337117e-08), 0: np.float64(6.153268947337117e-08)}
err dic= {9: np.float64(0.029317026882366176), 2: np.float64(0.006651765282495614), 8: np.float64(0.003448954941751514), 7: np.float64(0.29161654744891896), 53: np.float64(0.03699993846731053), 13: np.float64(0.0955025770380549), 30: np.float64(0.04799993846731053), 34: np.float64(0.06099993846731053), 0: np.float64(0.023999938467310526)} 

err list= [np.float64(0.029317026882366176), np.float64(0.006651765282495614), np.float64(0.003448954941751514), np.float64(0.29161654744891896), np.float64(0.03699993846731053), np.float64(0.0955025770380549), np.float64(0.04799993846731053), np.float64(0.06099993846731053), np.float64(0.023999938467310526)]
results for assortment [9, 2, 8, 7, 53, 13, 30, 34] :

err MNL dic= {9: np.float64(0.05422233619168752), 2: 0, 8: 0, 7: 0, 53: 0, 13: 0, 30: 0, 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: 0, 7: 0, 53: 0, 13: 0, 30: 0, 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: 0, 53: 0, 13: 0, 30: 0, 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), 0, 0, 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: np.float64(0.039555450703647466), 53: 0, 13: 0, 30: 0, 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), np.float64(0.039555450703647466), 0, 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: np.float64(0.039555450703647466), 53: np.float64(0.050309727977680206), 13: 0, 30: 0, 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), np.float64(0.039555450703647466), np.float64(0.050309727977680206), 0, 0, 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: np.float64(0.039555450703647466), 53: np.float64(0.050309727977680206), 13: np.float64(0.03430439420670414), 30: 0, 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), np.float64(0.039555450703647466), np.float64(0.050309727977680206), np.float64(0.03430439420670414), 0, 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: np.float64(0.039555450703647466), 53: np.float64(0.050309727977680206), 13: np.float64(0.03430439420670414), 30: np.float64(0.04616157223156772), 34: 0, 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), np.float64(0.039555450703647466), np.float64(0.050309727977680206), np.float64(0.03430439420670414), np.float64(0.04616157223156772), 0, 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: np.float64(0.039555450703647466), 53: np.float64(0.050309727977680206), 13: np.float64(0.03430439420670414), 30: np.float64(0.04616157223156772), 34: np.float64(0.03152041193123539), 0: 0} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), np.float64(0.039555450703647466), np.float64(0.050309727977680206), np.float64(0.03430439420670414), np.float64(0.04616157223156772), np.float64(0.03152041193123539), 0]
err MNL dic= {9: np.float64(0.05422233619168752), 2: np.float64(0.0830631026135478), 8: np.float64(0.09799146596643828), 7: np.float64(0.039555450703647466), 53: np.float64(0.050309727977680206), 13: np.float64(0.03430439420670414), 30: np.float64(0.04616157223156772), 34: np.float64(0.03152041193123539), 0: np.float64(0.1811450375415419)} 

err MNL list= [np.float64(0.05422233619168752), np.float64(0.0830631026135478), np.float64(0.09799146596643828), np.float64(0.039555450703647466), np.float64(0.050309727977680206), np.float64(0.03430439420670414), np.float64(0.04616157223156772), np.float64(0.03152041193123539), np.float64(0.1811450375415419)]
sampled assortment [4, 8, 3, 5, 57, 59, 24, 53]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 22: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 12, 22, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 14: 0, 15: 0, 100: 0} [3, 4, 5, 6, 9, 12, 14, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 14: 1, 23: 2} [2, 1, 6, 10, 11, 14, 23]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 12: 1, 14: 1, 15: 1} [1, 3, 5, 7, 9, 11, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 14: 6, 15: 3, 25: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 14, 25]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 7: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 7, 10, 11, 12, 13, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1} [1, 3, 4, 5, 7, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 11: 5, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 8, 5, 7, 11, 17, 20]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1, 100: 1} [1, 3, 4, 5, 7, 9, 10, 13, 15, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 20: 4, 23: 8, 100: 0} [6, 100, 1, 3, 10, 13, 20, 5, 7, 23]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 13: 1, 15: 1, 100: 1} [8, 1, 2, 3, 7, 13, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 12: 0, 21: 0, 100: 0} [3, 4, 5, 7, 9, 12, 21, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1} [2, 1, 6, 10, 11, 12, 13]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 9: 1, 10: 1, 11: 1, 12: 1, 13: 1} [1, 3, 4, 5, 9, 10, 11, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 13: 3, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 20]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 5, 7, 10, 15, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 14: 1, 100: 1} [2, 1, 6, 7, 10, 11, 12, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1} [1, 3, 4, 5, 7, 9, 10]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 3, 18: 9, 20: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 20, 18]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 11: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 11, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 16: 1, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100, 16]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 12: 1, 14: 1, 15: 1} [1, 3, 5, 6, 7, 9, 12, 14, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 1, 11: 4, 12: 7, 13: 2, 15: 3, 19: 5, 20: 4, 37: 10, 100: 0} [6, 100, 10, 1, 3, 13, 15, 7, 11, 20, 5, 19, 12, 37]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 14: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 12, 14, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 14: 1} [1, 3, 5, 7, 9, 10, 13, 14]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 12: 8, 13: 2, 15: 3, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 11, 20, 12]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1} [8, 1, 2, 3, 7, 10]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 17: 1, 100: 1} [2, 1, 6, 10, 11, 12, 13, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 15: 1, 21: 1} [1, 3, 5, 7, 9, 10, 12, 15, 21]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 9: 7, 10: 2, 11: 3, 13: 2, 15: 4, 17: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 11, 7, 8, 15, 17, 20, 9]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 21: 1} [2, 1, 3, 4, 6, 10, 11, 14, 21]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 13: 1} [1, 3, 5, 7, 9, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 16: 7, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 7, 16]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 3, 4, 7, 10, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 17: 1, 100: 1} [2, 3, 4, 6, 10, 11, 12, 13, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 100: 1} [1, 3, 4, 5, 7, 9, 10, 12, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 7]
#beta= 0.025 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 8: 0, 20: 1, 100: 1} [8, 1, 2, 3, 4, 20, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 17: 1, 100: 1} [2, 3, 6, 10, 11, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 12: 1, 15: 1} [1, 3, 5, 7, 9, 10, 12, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 6: 0, 7: 5, 8: 4, 10: 2, 11: 4, 13: 2, 14: 6, 15: 4, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 8, 11, 15, 7, 14, 23]
#beta= 0.05 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 18: 0, 19: 0, 100: 0} [3, 4, 5, 6, 9, 10, 11, 12, 18, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 14: 1, 17: 1, 100: 1} [2, 1, 6, 7, 10, 11, 12, 14, 17, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1, 19: 1, 100: 1} [1, 3, 4, 5, 7, 9, 10, 11, 15, 19, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 2: 11, 3: 2, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 19: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 11, 17, 19, 2]
#beta= 0.1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 7, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 18: 0, 19: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 18, 19, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1, 17: 1, 25: 2, 100: 1} [2, 1, 3, 6, 7, 9, 10, 11, 12, 14, 17, 100, 25]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 13: 1, 24: 1} [1, 3, 5, 7, 9, 11, 13, 24]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 7, 11, 17]
#beta= 0.2 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1} [2, 1, 6, 10]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 7: 1, 9: 1, 10: 1, 11: 1, 15: 1} [1, 3, 7, 9, 10, 11, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 10: 2, 13: 2, 14: 6, 15: 4, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 20, 14]
#beta= 0.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {3: 1, 4: 1, 7: 1, 8: 0, 9: 1, 100: 1} [8, 3, 4, 7, 9, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 13: 1, 15: 1} [1, 3, 5, 7, 9, 10, 13, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 4: 8, 5: 4, 6: 0, 7: 4, 8: 3, 10: 2, 13: 2, 15: 3, 16: 9, 17: 5, 20: 4, 21: 8, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 7, 20, 17, 4, 21, 16]
#beta= 0.3 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 13: 1} [8, 1, 3, 4, 5, 6, 7, 13]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 4, 6, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 10: 1, 15: 1} [1, 3, 5, 7, 9, 10, 15]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 1, 11: 5, 13: 2, 14: 6, 15: 3, 23: 8, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 11, 14, 23]
#beta= 0.5 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 7, 10, 14, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 10: 1, 15: 1, 100: 1} [2, 1, 4, 6, 10, 15, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 6: 1, 7: 1, 9: 1, 12: 1, 13: 1} [1, 3, 5, 6, 7, 9, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 10: 2, 11: 4, 13: 2, 15: 4, 100: 0} [6, 100, 1, 3, 10, 13, 7, 11, 15, 5]
#beta= 0.75 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 17: 1} [8, 1, 2, 3, 4, 5, 7, 13, 17]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [3, 4, 5, 6, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 9: 1, 10: 1, 11: 1, 12: 1, 14: 1} [2, 1, 9, 10, 11, 12, 14]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 5: 1, 7: 1, 9: 1, 11: 1, 19: 1, 22: 1, 100: 1} [1, 3, 5, 7, 9, 11, 19, 22, 100]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 8, 20, 5, 7, 17]
#beta= 1 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 12: 1, 100: 1} [8, 1, 2, 3, 5, 7, 12, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 12: 0, 16: 0, 100: 0} [3, 4, 5, 6, 12, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 7: 1, 9: 1, 12: 1, 13: 1, 14: 1, 15: 1, 18: 1} [1, 3, 4, 5, 7, 9, 12, 13, 14, 15, 18]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 14: 5, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 14]
#beta= 1.25 

#cluster  4 with weight 0.2095
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 13, 100]
#cluster  3 with weight 0.39475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [3, 4, 5, 6, 9, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 9: 1, 11: 1, 13: 1} [2, 1, 3, 4, 6, 7, 9, 11, 13]
#cluster  2 with weight 0.16475
Learned cluster center of cluster 2:  {1: 0, 3: 1, 4: 1, 5: 1, 9: 1, 10: 1, 12: 1, 13: 1} [1, 3, 4, 5, 9, 10, 12, 13]
#cluster  5 with weight 0.0545
Learned cluster center of cluster 5:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 17: 6, 19: 5, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 19, 17, 23]
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 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 5
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 5
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 24
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 5
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 5
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 4
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 3
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 3
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 59
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 4
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 5
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 5
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 59
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 3
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 3
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 3
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 5
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 53
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 4
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 5
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 3
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 4
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 5
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 4
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 53
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 3
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 59
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 5
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 5
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 4
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 24
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 4
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 24
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 8
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 5
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 3
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 3
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 3
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 3
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 3
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 5
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 5
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 5
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 59
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 4
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 3
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 24
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 5
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 4
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 4
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 24
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 4
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 3
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 5
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 5
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 4
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 24
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 3
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 5
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 4
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 24
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 4
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 3
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 3
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 5
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 4
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 24
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 4
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 4
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 8
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 5
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 4
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 59
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 3
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 5
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 4
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 3
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 5
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 5
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 3
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 3
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 5
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 3
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 3
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 57
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 24
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 4
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 24
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 59
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 3
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 3
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 5
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 24
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 4
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 4
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 4
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 5
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 24
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 57
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 5
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 3
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 3
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 5
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 5
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 5
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 24
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 3
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 4
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 24
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 59
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 3
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 3
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 3
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 57
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 3
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 3
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 24
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 5
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 5
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 3
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 24
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 24
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 0
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 4
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 57
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 5
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 5
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 57
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 4
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 4
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 4
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 4
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 4
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 4
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 4
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 59
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 3
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 24
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 3
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 3
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 4
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 3
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 57
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 3
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 57
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 53
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 57
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 3
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 5
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 3
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 59
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 3
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 57
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 4
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 5
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 57
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 4
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 3
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 24
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 3
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 53
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 3
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 59
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 4
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 57
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 4
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 3
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 5
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 4
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 5
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 4
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 4
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 4
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 4
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 4
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 5
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 24
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 24
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 8
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 24
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 57
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 3
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 4
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 4
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 5
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 4
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 3
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 5
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 24
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 4
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 3
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 53
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 3
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 5
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 3
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 59
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 5
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 24
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 5
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 4
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 5
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 57
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 24
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 3
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 57
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 4
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 3
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 3
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 53
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 5
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 4
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 5
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 4
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 24
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 4
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 5
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 57
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 24
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 3
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 4
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 5
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 3
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 5
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 4
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 4
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 4
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 3
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 4
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 3
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 5
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 4
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 4
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 3
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 59
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 24
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 3
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 0
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 0
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 4
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 4
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 3
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 4
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 4
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 5
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 5
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 3
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 3
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 4
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 3
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 24
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 24
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 5
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 4
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 3
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 0
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 5
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 24
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 3
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 5
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 4
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 5
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 8
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 4
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 8
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 4
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 3
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 4
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 4
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 3
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 4
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 3
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 4
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 4
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 3
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 24
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 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 59
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 57
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 4
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 5
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 5
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 24
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 5
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 24
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 53
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 3
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 59
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 3
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 3
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 59
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 59
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 3
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 24
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 4
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 4
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 57
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 4
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 3
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 5
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 5
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 5
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 24
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 5
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 5
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 4
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 5
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 5
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 24
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 5
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 3
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 4
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 3
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 4
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 4
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 59
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 4
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 5
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 3
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 4
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 3
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 5
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 5
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 5
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 4
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 5
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 4
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 24
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 5
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 3
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 3
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 4
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 3
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 4
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 4
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 57
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 5
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 59
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 5
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 4
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 4
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 4
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 4
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 24
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 3
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 4
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 3
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 5
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 5
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 4
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 4
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 59
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 4
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 24
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 5
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 3
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 4
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 53
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 57
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 24
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 3
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 5
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 3
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 5
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 4
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 4
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 5
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 53
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 4
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 5
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 3
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 5
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 3
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 3
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 4
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 8
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 4
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 4
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 3
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 4
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 3
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 3
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 3
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 5
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 3
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 3
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 3
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 4
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 4
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 4
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 5
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 3
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 4
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 4
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 57
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 24
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 3
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 3
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 4
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 24
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 5
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 5
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 3
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 4
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 24
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 24
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 5
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 24
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 3
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 3
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 8
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 8
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 3
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 3
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 57
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 59
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 5
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 4
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 59
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 5
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 24
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 5
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 53
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 24
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 5
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 4
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 5
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 5
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 4
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 4
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 4
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 5
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 4
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
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 8
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 3
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 4
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 5
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 24
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 8
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 53
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 5
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 4
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 3
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 4
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 59
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 5
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 4
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 24
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 4
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 4
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 5
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 5
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 3
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 57
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 24
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 3
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 5
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 53
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 3
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 24
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 4
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 5
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 4
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 3
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 3
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 5
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 53
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 5
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 4
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 4
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 3
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 4
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 4
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 53
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 4
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 4
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 57
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 3
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 4
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 3
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 57
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 3
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 3
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 24
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 5
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 3
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 5
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 24
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 57
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 3
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 4
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 3
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 24
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 3
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 3
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 3
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 5
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 57
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 5
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 4
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 8
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 4
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 4
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 4
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 53
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 3
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 3
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 4
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 4
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 8
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 3
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 4
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 59
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 8
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 3
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 59
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 24
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 4
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 4
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 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 5
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 59
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 4
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 5
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 4
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 0
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 5
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 3
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 59
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
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 4
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 5
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 4
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 4
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 4
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 24
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 5
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 4
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 24
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 3
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 24
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 3
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 4
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 3
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 8
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 5
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 4
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 3
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 3
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 5
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 8
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 3
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 53
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 5
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 4
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 4
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 5
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 24
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 4
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 4
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 57
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 3
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 24
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 3
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 24
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 5
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 3
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 4
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 5
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 3
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 5
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 3
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 3
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 57
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 5
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 5
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 0
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 24
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 8
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 5
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 3
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 3
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 3
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 3
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 3
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 24
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 3
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 4
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 5
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 24
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 5
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 4
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 3
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 53
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 24
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 4
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 0
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 5
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 5
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 4
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 5
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 5
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 4
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 5
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 3
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 3
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 4
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 53
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 3
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 5
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 5
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 24
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 24
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 5
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 5
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 3
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 57
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 5
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 4
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 5
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 24
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 24
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 4
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 4
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 3
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 3
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 3
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 4
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 5
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 4
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 4
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 5
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 5
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 5
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 4
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 4
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 4
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 3
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 59
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 3
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 3
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 5
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 53
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 53
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 24
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 53
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 24
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 5
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 3
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 5
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 24
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 4
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 53
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 5
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 24
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 4
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 4
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 4
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 5
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 4
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 3
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 5
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 57
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 5
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 57
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 5
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 5
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 5
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 3
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 24
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 4
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 4
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 24
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 5
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 3
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 5
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 59
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 5
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 5
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 24
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 4
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 4
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 3
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 3
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 3
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 5
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 24
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 4
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 5
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 3
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 5
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 3
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 3
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 4
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 3
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 3
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 4
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 4
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 5
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 3
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 59
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 4
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 5
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 4
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 5
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 5
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 3
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 24
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 53
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 5
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 4
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 3
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 24
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 3
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 3
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 5
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 4
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 24
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 4
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 4
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 59
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 5
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 57
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 5
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 4
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 5
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 5
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 8
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 3
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 5
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 3
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 53
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 57
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 3
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 5
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 5
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 4
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 53
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 5
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 57
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 4
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 24
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 4
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 24
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 4
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 3
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 3
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 57
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 3
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 5
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 8
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 3
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 4
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 59
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 24
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 4
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 5
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 3
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 24
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 59
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 3
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 3
empirical probabilities from test set: {4: 0.197, 8: 0.215, 3: 0.197, 5: 0.175, 57: 0.035, 59: 0.032, 24: 0.085, 53: 0.041, 0: 0.023}
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.09612841419733281), 8: np.float64(0.11113473638657147), 3: np.float64(0.08796248725911271), 5: np.float64(0.10179675969350095), 57: np.float64(0.12059552049269634), 59: np.float64(0.12059552049269634), 24: np.float64(0.12059552049269634), 53: np.float64(0.12059552049269634), 0: np.float64(0.12059552049269634)}
err dic= {4: np.float64(0.1008715858026672), 8: np.float64(0.10386526361342853), 3: np.float64(0.1090375127408873), 5: np.float64(0.07320324030649904), 57: np.float64(0.08559552049269634), 59: np.float64(0.08859552049269634), 24: np.float64(0.035595520492696334), 53: np.float64(0.07959552049269633), 0: np.float64(0.09759552049269635)} 

err list= [np.float64(0.1008715858026672), np.float64(0.10386526361342853), np.float64(0.1090375127408873), np.float64(0.07320324030649904), np.float64(0.08559552049269634), np.float64(0.08859552049269634), np.float64(0.035595520492696334), np.float64(0.07959552049269633), np.float64(0.09759552049269635)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.13824959508772075), 8: np.float64(0.10802429579718265), 3: np.float64(0.14984336708908885), 5: np.float64(0.13337464164104496), 57: np.float64(0.09410162007699319), 59: np.float64(0.09410162007699319), 24: np.float64(0.09410162007699319), 53: np.float64(0.09410162007699319), 0: np.float64(0.09410162007699319)}
err dic= {4: np.float64(0.05875040491227926), 8: np.float64(0.10697570420281735), 3: np.float64(0.047156632910911156), 5: np.float64(0.041625358358955034), 57: np.float64(0.05910162007699318), 59: np.float64(0.062101620076993186), 24: np.float64(0.00910162007699318), 53: np.float64(0.053101620076993185), 0: np.float64(0.0711016200769932)} 

err list= [np.float64(0.05875040491227926), np.float64(0.10697570420281735), np.float64(0.047156632910911156), np.float64(0.041625358358955034), np.float64(0.05910162007699318), np.float64(0.062101620076993186), np.float64(0.00910162007699318), np.float64(0.053101620076993185), np.float64(0.0711016200769932)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.15025934889422346), 8: np.float64(0.09276834920118074), 3: np.float64(0.2578774810685135), 5: np.float64(0.15968816558264481), 57: np.float64(0.06614409058211788), 59: np.float64(0.06614409058211788), 24: np.float64(0.07483029292496347), 53: np.float64(0.06614409058211788), 0: np.float64(0.06614409058211788)}
err dic= {4: np.float64(0.04674065110577655), 8: np.float64(0.12223165079881926), 3: np.float64(0.060877481068513484), 5: np.float64(0.015311834417355175), 57: np.float64(0.03114409058211788), 59: np.float64(0.034144090582117884), 24: np.float64(0.010169707075036533), 53: np.float64(0.025144090582117883), 0: np.float64(0.043144090582117885)} 

err list= [np.float64(0.04674065110577655), np.float64(0.12223165079881926), np.float64(0.060877481068513484), np.float64(0.015311834417355175), np.float64(0.03114409058211788), np.float64(0.034144090582117884), np.float64(0.010169707075036533), np.float64(0.025144090582117883), np.float64(0.043144090582117885)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.2 

learned probs for this beta: {4: np.float64(0.1939646768056765), 8: np.float64(0.11440579255342744), 3: np.float64(0.33142474656529824), 5: np.float64(0.1766660171011111), 57: np.float64(0.03670775339489758), 59: np.float64(0.03670775339489758), 24: np.float64(0.03670775339489758), 53: np.float64(0.03670775339489758), 0: np.float64(0.03670775339489758)}
err dic= {4: np.float64(0.003035323194323508), 8: np.float64(0.10059420744657256), 3: np.float64(0.13442474656529824), 5: np.float64(0.0016660171011111113), 57: np.float64(0.0017077533948975793), 59: np.float64(0.004707753394897582), 24: np.float64(0.048292246605102424), 53: np.float64(0.004292246605102419), 0: np.float64(0.013707753394897583)} 

err list= [np.float64(0.003035323194323508), np.float64(0.10059420744657256), np.float64(0.13442474656529824), np.float64(0.0016660171011111113), np.float64(0.0017077533948975793), np.float64(0.004707753394897582), np.float64(0.048292246605102424), np.float64(0.004292246605102419), np.float64(0.013707753394897583)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.20077533285713833), 8: np.float64(0.11995269062435496), 3: np.float64(0.3542368192135215), 5: np.float64(0.19355875789064658), 57: np.float64(0.02629527988286829), 59: np.float64(0.02629527988286829), 24: np.float64(0.02629527988286829), 53: np.float64(0.02629527988286829), 0: np.float64(0.02629527988286829)}
err dic= {4: np.float64(0.003775332857138325), 8: np.float64(0.09504730937564504), 3: np.float64(0.1572368192135215), 5: np.float64(0.018558757890646593), 57: np.float64(0.008704720117131713), 59: np.float64(0.0057047201171317105), 24: np.float64(0.058704720117131716), 53: np.float64(0.014704720117131712), 0: np.float64(0.0032952798828682905)} 

err list= [np.float64(0.003775332857138325), np.float64(0.09504730937564504), np.float64(0.1572368192135215), np.float64(0.018558757890646593), np.float64(0.008704720117131713), np.float64(0.0057047201171317105), np.float64(0.058704720117131716), np.float64(0.014704720117131712), np.float64(0.0032952798828682905)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.3 

learned probs for this beta: {4: np.float64(0.290966399244464), 8: np.float64(0.09797450995701876), 3: np.float64(0.34946436053756313), 5: np.float64(0.20946285539928672), 57: np.float64(0.010426374972333417), 59: np.float64(0.010426374972333417), 24: np.float64(0.010426374972333417), 53: np.float64(0.010426374972333417), 0: np.float64(0.010426374972333417)}
err dic= {4: np.float64(0.09396639924446398), 8: np.float64(0.11702549004298124), 3: np.float64(0.15246436053756313), 5: np.float64(0.03446285539928673), 57: np.float64(0.024573625027666586), 59: np.float64(0.021573625027666583), 24: np.float64(0.0745736250276666), 53: np.float64(0.030573625027666584), 0: np.float64(0.012573625027666582)} 

err list= [np.float64(0.09396639924446398), np.float64(0.11702549004298124), np.float64(0.15246436053756313), np.float64(0.03446285539928673), np.float64(0.024573625027666586), np.float64(0.021573625027666583), np.float64(0.0745736250276666), np.float64(0.030573625027666584), np.float64(0.012573625027666582)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.28911172710596833), 8: np.float64(0.20369338925683958), 3: np.float64(0.3530334478801238), 5: np.float64(0.14275812292534926), 57: np.float64(0.002280662566343921), 59: np.float64(0.002280662566343921), 24: np.float64(0.002280662566343921), 53: np.float64(0.002280662566343921), 0: np.float64(0.002280662566343921)}
err dic= {4: np.float64(0.09211172710596832), 8: np.float64(0.011306610743160417), 3: np.float64(0.1560334478801238), 5: np.float64(0.03224187707465073), 57: np.float64(0.032719337433656084), 59: np.float64(0.029719337433656078), 24: np.float64(0.08271933743365609), 53: np.float64(0.03871933743365608), 0: np.float64(0.020719337433656077)} 

err list= [np.float64(0.09211172710596832), np.float64(0.011306610743160417), np.float64(0.1560334478801238), np.float64(0.03224187707465073), np.float64(0.032719337433656084), np.float64(0.029719337433656078), np.float64(0.08271933743365609), np.float64(0.03871933743365608), np.float64(0.020719337433656077)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.14203703347420862), 8: np.float64(0.19187096841801296), 3: np.float64(0.43590979897998305), 5: np.float64(0.13210468159429292), 57: np.float64(0.01961550350670047), 59: np.float64(0.01961550350670047), 24: np.float64(0.01961550350670047), 53: np.float64(0.01961550350670047), 0: np.float64(0.01961550350670047)}
err dic= {4: np.float64(0.054962966525791385), 8: np.float64(0.023129031581987036), 3: np.float64(0.23890979897998305), 5: np.float64(0.04289531840570707), 57: np.float64(0.015384496493299534), 59: np.float64(0.012384496493299531), 24: np.float64(0.06538449649329954), 53: np.float64(0.021384496493299533), 0: np.float64(0.0033844964932995304)} 

err list= [np.float64(0.054962966525791385), np.float64(0.023129031581987036), np.float64(0.23890979897998305), np.float64(0.04289531840570707), np.float64(0.015384496493299534), np.float64(0.012384496493299531), np.float64(0.06538449649329954), np.float64(0.021384496493299533), np.float64(0.0033844964932995304)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  1 

learned probs for this beta: {4: np.float64(0.15653666709958725), 8: np.float64(0.20735835668889718), 3: np.float64(0.4576458629255529), 5: np.float64(0.08040315003152877), 57: np.float64(0.01961119265088679), 59: np.float64(0.01961119265088679), 24: np.float64(0.01961119265088679), 53: np.float64(0.01961119265088679), 0: np.float64(0.01961119265088679)}
err dic= {4: np.float64(0.04046333290041276), 8: np.float64(0.007641643311102814), 3: np.float64(0.2606458629255529), 5: np.float64(0.09459684996847122), 57: np.float64(0.015388807349113215), 59: np.float64(0.012388807349113212), 24: np.float64(0.06538880734911322), 53: np.float64(0.021388807349113213), 0: np.float64(0.003388807349113211)} 

err list= [np.float64(0.04046333290041276), np.float64(0.007641643311102814), np.float64(0.2606458629255529), np.float64(0.09459684996847122), np.float64(0.015388807349113215), np.float64(0.012388807349113212), np.float64(0.06538880734911322), np.float64(0.021388807349113213), np.float64(0.003388807349113211)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.15905711517878157), 8: np.float64(0.1977214120226224), 3: np.float64(0.6087121107361345), 5: np.float64(0.034509346708531466), 57: np.float64(3.0707860162461145e-09), 59: np.float64(3.0707860162461145e-09), 24: np.float64(3.0707860162461145e-09), 53: np.float64(3.0707860162461145e-09), 0: np.float64(3.0707860162461145e-09)}
err dic= {4: np.float64(0.03794288482121844), 8: np.float64(0.017278587977377607), 3: np.float64(0.4117121107361345), 5: np.float64(0.14049065329146854), 57: np.float64(0.03499999692921399), 59: np.float64(0.031999996929213986), 24: np.float64(0.08499999692921399), 53: np.float64(0.04099999692921399), 0: np.float64(0.022999996929213982)} 

err list= [np.float64(0.03794288482121844), np.float64(0.017278587977377607), np.float64(0.4117121107361345), np.float64(0.14049065329146854), np.float64(0.03499999692921399), np.float64(0.031999996929213986), np.float64(0.08499999692921399), np.float64(0.04099999692921399), np.float64(0.022999996929213982)]
results for assortment [4, 8, 3, 5, 57, 59, 24, 53] :

err MNL dic= {4: np.float64(0.09087944098333055), 8: 0, 3: 0, 5: 0, 57: 0, 59: 0, 24: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), 0, 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: 0, 5: 0, 57: 0, 59: 0, 24: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), 0, 0, 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: 0, 57: 0, 59: 0, 24: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), 0, 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: np.float64(0.06887944098333053), 57: 0, 59: 0, 24: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), np.float64(0.06887944098333053), 0, 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: np.float64(0.06887944098333053), 57: np.float64(0.05062047482741201), 59: 0, 24: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), np.float64(0.06887944098333053), np.float64(0.05062047482741201), 0, 0, 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: np.float64(0.06887944098333053), 57: np.float64(0.05062047482741201), 59: np.float64(0.05576730089240613), 24: 0, 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), np.float64(0.06887944098333053), np.float64(0.05062047482741201), np.float64(0.05576730089240613), 0, 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: np.float64(0.06887944098333053), 57: np.float64(0.05062047482741201), 59: np.float64(0.05576730089240613), 24: np.float64(0.014637986192961763), 53: 0, 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), np.float64(0.06887944098333053), np.float64(0.05062047482741201), np.float64(0.05576730089240613), np.float64(0.014637986192961763), 0, 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: np.float64(0.06887944098333053), 57: np.float64(0.05062047482741201), 59: np.float64(0.05576730089240613), 24: np.float64(0.014637986192961763), 53: np.float64(0.04874574844249873), 0: 0} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), np.float64(0.06887944098333053), np.float64(0.05062047482741201), np.float64(0.05576730089240613), np.float64(0.014637986192961763), np.float64(0.04874574844249873), 0]
err MNL dic= {4: np.float64(0.09087944098333055), 8: np.float64(0.10951086041421115), 3: np.float64(0.0879749116012797), 5: np.float64(0.06887944098333053), 57: np.float64(0.05062047482741201), 59: np.float64(0.05576730089240613), 24: np.float64(0.014637986192961763), 53: np.float64(0.04874574844249873), 0: np.float64(0.18747314362687323)} 

err MNL list= [np.float64(0.09087944098333055), np.float64(0.10951086041421115), np.float64(0.0879749116012797), np.float64(0.06887944098333053), np.float64(0.05062047482741201), np.float64(0.05576730089240613), np.float64(0.014637986192961763), np.float64(0.04874574844249873), np.float64(0.18747314362687323)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.2, 0.25, 0.3, 0.5, 0.75, 1, 1.25]
 mean error for all betas:

mean_err= [0.08599502 0.07127619 0.06192145 0.05511964 0.0522231  0.05392272
 0.0540971  0.05397134 0.05441023 0.05811836]
mean_std= [0.         0.01471883 0.01787321 0.01945206 0.01833755 0.01716581
 0.01589819 0.01487512 0.01407923 0.01738259]
MNL: [0.07451744 0.07502882 0.08984492 0.06723136 0.07946335 0.07790088
 0.06096245 0.07240837 0.06869706 0.0793877 ]
 mean error for MNL:

mean_err_MNL= 0.07454423475353154
mean_std_MNL= 0.0075496023729700506
