p= 0.1 num clusters= 2
linkage completed in  10.707667112350464
silhouette_score of the clusters 0.006287393358176328
samppled assortment [56, 82, 63, 84, 41, 23]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 16: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 16]
learned probs for cluster 2 

{56: np.float64(0.14285714285714327), 82: np.float64(0.14285714285714327), 63: np.float64(0.14285714285714327), 84: np.float64(0.14285714285714327), 41: np.float64(0.14285714285714327), 23: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 16]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285825), 82: np.float64(0.037714285714285825), 63: np.float64(0.037714285714285825), 84: np.float64(0.037714285714285825), 41: np.float64(0.037714285714285825), 23: np.float64(0.037714285714285825), 0: np.float64(0.037714285714285825)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285713966), 82: np.float64(0.14285714285713966), 63: np.float64(0.14285714285713966), 84: np.float64(0.14285714285713966), 41: np.float64(0.14285714285713966), 23: np.float64(0.14285714285713966), 0: np.float64(0.14285714285713966)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714063), 82: np.float64(0.14285714285714063), 63: np.float64(0.14285714285714063), 84: np.float64(0.14285714285714063), 41: np.float64(0.14285714285714063), 23: np.float64(0.14285714285714063), 0: np.float64(0.14285714285714063)}
choice probs for this beta: {56: np.float64(0.14285714285714063), 82: np.float64(0.14285714285714063), 63: np.float64(0.14285714285714063), 84: np.float64(0.14285714285714063), 41: np.float64(0.14285714285714063), 23: np.float64(0.14285714285714063), 0: np.float64(0.14285714285714063)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285735), 82: np.float64(0.037714285714285735), 63: np.float64(0.037714285714285735), 84: np.float64(0.037714285714285735), 41: np.float64(0.037714285714285735), 23: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714435), 82: np.float64(0.14285714285714435), 63: np.float64(0.14285714285714435), 84: np.float64(0.14285714285714435), 41: np.float64(0.14285714285714435), 23: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714396), 82: np.float64(0.14285714285714396), 63: np.float64(0.14285714285714396), 84: np.float64(0.14285714285714396), 41: np.float64(0.14285714285714396), 23: np.float64(0.14285714285714396), 0: np.float64(0.14285714285714396)}
choice probs for this beta: {56: np.float64(0.14285714285714396), 82: np.float64(0.14285714285714396), 63: np.float64(0.14285714285714396), 84: np.float64(0.14285714285714396), 41: np.float64(0.14285714285714396), 23: np.float64(0.14285714285714396), 0: np.float64(0.14285714285714396)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 14, 100, 4]
learned probs for cluster 2 

{56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 13, 14, 100, 4]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428573), 82: np.float64(0.03771428571428573), 63: np.float64(0.03771428571428573), 84: np.float64(0.03771428571428573), 41: np.float64(0.03771428571428573), 23: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714315), 82: np.float64(0.14285714285714315), 63: np.float64(0.14285714285714315), 84: np.float64(0.14285714285714315), 41: np.float64(0.14285714285714315), 23: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714307), 82: np.float64(0.14285714285714307), 63: np.float64(0.14285714285714307), 84: np.float64(0.14285714285714307), 41: np.float64(0.14285714285714307), 23: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
choice probs for this beta: {56: np.float64(0.14285714285714307), 82: np.float64(0.14285714285714307), 63: np.float64(0.14285714285714307), 84: np.float64(0.14285714285714307), 41: np.float64(0.14285714285714307), 23: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5, 12]
learned probs for cluster 2 

{56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4, 5, 12]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428573), 82: np.float64(0.03771428571428573), 63: np.float64(0.03771428571428573), 84: np.float64(0.03771428571428573), 41: np.float64(0.03771428571428573), 23: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 100: 0} [1, 2, 3, 4, 5, 6, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 100]
learned probs (dictionary):

probs= {56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 100]
learned probs for cluster 2 

{56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 4, 6, 7, 10, 100]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428573), 82: np.float64(0.03771428571428573), 63: np.float64(0.03771428571428573), 84: np.float64(0.03771428571428573), 41: np.float64(0.03771428571428573), 23: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714193), 82: np.float64(0.14285714285714193), 63: np.float64(0.14285714285714193), 84: np.float64(0.14285714285714193), 41: np.float64(0.14285714285714193), 23: np.float64(0.14285714285714193), 0: np.float64(0.14285714285714193)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714218), 82: np.float64(0.14285714285714218), 63: np.float64(0.14285714285714218), 84: np.float64(0.14285714285714218), 41: np.float64(0.14285714285714218), 23: np.float64(0.14285714285714218), 0: np.float64(0.14285714285714218)}
choice probs for this beta: {56: np.float64(0.14285714285714218), 82: np.float64(0.14285714285714218), 63: np.float64(0.14285714285714218), 84: np.float64(0.14285714285714218), 41: np.float64(0.14285714285714218), 23: np.float64(0.14285714285714218), 0: np.float64(0.14285714285714218)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428573), 82: np.float64(0.03771428571428573), 63: np.float64(0.03771428571428573), 84: np.float64(0.03771428571428573), 41: np.float64(0.03771428571428573), 23: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714288), 82: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 84: np.float64(0.14285714285714288), 41: np.float64(0.14285714285714288), 23: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714288), 82: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 84: np.float64(0.14285714285714288), 41: np.float64(0.14285714285714288), 23: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {56: np.float64(0.14285714285714288), 82: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 84: np.float64(0.14285714285714288), 41: np.float64(0.14285714285714288), 23: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{56: np.float64(0.14285714285714288), 82: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 84: np.float64(0.14285714285714288), 41: np.float64(0.14285714285714288), 23: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428572), 82: np.float64(0.03771428571428572), 63: np.float64(0.03771428571428572), 84: np.float64(0.03771428571428572), 41: np.float64(0.03771428571428572), 23: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 14, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 12, 14, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100, 4]
learned probs for cluster 2 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100, 4]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285714), 82: np.float64(0.037714285714285714), 63: np.float64(0.037714285714285714), 84: np.float64(0.037714285714285714), 41: np.float64(0.037714285714285714), 23: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2]
learned probs for cluster 2 

{56: np.float64(0.14285714285714288), 82: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 84: np.float64(0.14285714285714288), 41: np.float64(0.14285714285714288), 23: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 2]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428572), 82: np.float64(0.03771428571428572), 63: np.float64(0.03771428571428572), 84: np.float64(0.03771428571428572), 41: np.float64(0.03771428571428572), 23: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714196), 82: np.float64(0.14285714285714196), 63: np.float64(0.14285714285714196), 84: np.float64(0.14285714285714196), 41: np.float64(0.14285714285714196), 23: np.float64(0.14285714285714196), 0: np.float64(0.14285714285714196)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {56: np.float64(0.1428571428571422), 82: np.float64(0.1428571428571422), 63: np.float64(0.1428571428571422), 84: np.float64(0.1428571428571422), 41: np.float64(0.1428571428571422), 23: np.float64(0.1428571428571422), 0: np.float64(0.1428571428571422)}
choice probs for this beta: {56: np.float64(0.1428571428571422), 82: np.float64(0.1428571428571422), 63: np.float64(0.1428571428571422), 84: np.float64(0.1428571428571422), 41: np.float64(0.1428571428571422), 23: np.float64(0.1428571428571422), 0: np.float64(0.1428571428571422)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285735), 82: np.float64(0.037714285714285735), 63: np.float64(0.037714285714285735), 84: np.float64(0.037714285714285735), 41: np.float64(0.037714285714285735), 23: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
choice probs for this beta: {56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs for cluster 2 

{56: np.float64(0.14285714285714315), 82: np.float64(0.14285714285714315), 63: np.float64(0.14285714285714315), 84: np.float64(0.14285714285714315), 41: np.float64(0.14285714285714315), 23: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs (dictionary):

probs= {56: np.float64(0.0377142857142858), 82: np.float64(0.0377142857142858), 63: np.float64(0.0377142857142858), 84: np.float64(0.0377142857142858), 41: np.float64(0.0377142857142858), 23: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 14, 100]
learned probs for cluster 1 

{56: np.float64(0.1428571428571438), 82: np.float64(0.1428571428571438), 63: np.float64(0.1428571428571438), 84: np.float64(0.1428571428571438), 41: np.float64(0.1428571428571438), 23: np.float64(0.1428571428571438), 0: np.float64(0.1428571428571438)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 14, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714363), 82: np.float64(0.14285714285714363), 63: np.float64(0.14285714285714363), 84: np.float64(0.14285714285714363), 41: np.float64(0.14285714285714363), 23: np.float64(0.14285714285714363), 0: np.float64(0.14285714285714363)}
choice probs for this beta: {56: np.float64(0.14285714285714363), 82: np.float64(0.14285714285714363), 63: np.float64(0.14285714285714363), 84: np.float64(0.14285714285714363), 41: np.float64(0.14285714285714363), 23: np.float64(0.14285714285714363), 0: np.float64(0.14285714285714363)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100]
learned probs for cluster 2 

{56: np.float64(0.14285714285714293), 82: np.float64(0.14285714285714293), 63: np.float64(0.14285714285714293), 84: np.float64(0.14285714285714293), 41: np.float64(0.14285714285714293), 23: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285735), 82: np.float64(0.037714285714285735), 63: np.float64(0.037714285714285735), 84: np.float64(0.037714285714285735), 41: np.float64(0.037714285714285735), 23: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {56: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 84: np.float64(0.1428571428571429), 41: np.float64(0.1428571428571429), 23: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 100]
learned probs for cluster 2 

{56: np.float64(0.14285714285714277), 82: np.float64(0.14285714285714277), 63: np.float64(0.14285714285714277), 84: np.float64(0.14285714285714277), 41: np.float64(0.14285714285714277), 23: np.float64(0.14285714285714277), 0: np.float64(0.14285714285714277)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 11, 100]
learned probs (dictionary):

probs= {56: np.float64(0.03771428571428569), 82: np.float64(0.03771428571428569), 63: np.float64(0.03771428571428569), 84: np.float64(0.03771428571428569), 41: np.float64(0.03771428571428569), 23: np.float64(0.03771428571428569), 0: np.float64(0.03771428571428569)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714282), 82: np.float64(0.14285714285714282), 63: np.float64(0.14285714285714282), 84: np.float64(0.14285714285714282), 41: np.float64(0.14285714285714282), 23: np.float64(0.14285714285714282), 0: np.float64(0.14285714285714282)}
choice probs for this beta: {56: np.float64(0.14285714285714282), 82: np.float64(0.14285714285714282), 63: np.float64(0.14285714285714282), 84: np.float64(0.14285714285714282), 41: np.float64(0.14285714285714282), 23: np.float64(0.14285714285714282), 0: np.float64(0.14285714285714282)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 11]
learned probs for cluster 2 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 11]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285714), 82: np.float64(0.037714285714285714), 63: np.float64(0.037714285714285714), 84: np.float64(0.037714285714285714), 41: np.float64(0.037714285714285714), 23: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 10, 11, 12, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714288), 82: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 84: np.float64(0.14285714285714288), 41: np.float64(0.14285714285714288), 23: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 10, 11, 12, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 9]
learned probs for cluster 2 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 9]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285714), 82: np.float64(0.037714285714285714), 63: np.float64(0.037714285714285714), 84: np.float64(0.037714285714285714), 41: np.float64(0.037714285714285714), 23: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 10, 11, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 10, 11, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 20: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5, 20]
learned probs for cluster 2 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 100, 5, 20]
learned probs (dictionary):

probs= {56: np.float64(0.037714285714285714), 82: np.float64(0.037714285714285714), 63: np.float64(0.037714285714285714), 84: np.float64(0.037714285714285714), 41: np.float64(0.037714285714285714), 23: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {56: np.float64(0.14285714285714285), 82: np.float64(0.14285714285714285), 63: np.float64(0.14285714285714285), 84: np.float64(0.14285714285714285), 41: np.float64(0.14285714285714285), 23: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 82
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 41
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 23
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 56
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 41
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 41
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 63
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 82
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 23
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 23
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 82
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 82
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 41
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 84
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 0
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 63
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 23
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 63
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 84
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 63
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 0
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 0
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 41
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 41
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 82
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 0
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 23
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 23
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 84
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 41
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 41
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 84
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 41
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 41
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 0
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 23
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 63
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 84
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 41
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 23
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 84
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 23
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 84
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 56
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 41
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 84
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 0
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 41
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 56
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 82
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 41
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 23
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 23
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 41
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 23
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 23
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 84
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 23
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 82
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 56
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 23
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 23
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 63
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 63
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 41
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 56
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 41
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 82
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 84
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 23
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 84
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 82
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 23
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 84
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 41
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 41
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 41
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 23
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 23
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 23
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 23
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 0
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 23
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 82
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 23
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 56
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 41
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 82
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 56
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 63
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 23
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 84
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 23
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 23
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 82
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 23
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 56
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 41
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 23
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 84
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 84
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 63
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 41
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 63
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 82
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 84
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 84
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 63
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 23
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 56
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 41
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 84
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 56
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 63
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 84
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 82
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 23
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 41
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 23
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 23
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 82
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 41
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 23
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 41
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 23
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 41
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 82
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 82
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 56
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 56
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 41
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 84
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 56
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 63
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 41
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 23
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 41
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 23
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 82
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 82
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 63
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 23
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 63
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 0
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 0
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 82
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 41
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 82
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 0
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 41
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 41
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 23
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 41
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 0
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 82
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 41
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 63
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 23
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 63
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 23
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 23
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 23
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 63
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 23
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 63
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 23
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 82
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 23
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 82
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 82
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 56
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 63
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 82
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 82
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 63
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 23
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 23
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 23
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 41
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 23
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 41
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 23
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 41
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 84
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 82
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 84
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 82
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 63
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 23
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 41
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 56
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 23
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 41
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 23
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 56
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 63
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 63
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 63
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 41
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 82
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 23
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 63
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 41
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 23
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 23
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 56
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 63
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 63
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 84
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 56
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 23
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 56
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 0
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 82
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 23
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 82
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 56
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 63
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 41
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 0
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 82
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 63
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 23
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 84
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 63
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 23
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 0
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 82
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 63
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 56
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 41
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 84
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 41
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 56
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 63
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 41
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 84
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 56
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 0
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 56
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 56
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 84
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 56
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 63
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 23
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 23
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 82
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 84
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 41
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 63
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 84
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 63
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 0
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 63
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 84
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 84
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 41
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 23
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 56
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 63
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 0
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 84
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 82
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 0
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 82
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 63
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 41
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 82
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 56
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 23
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 84
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 63
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 84
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 41
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 63
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 82
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 82
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 23
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 41
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 0
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 41
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 41
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 23
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 84
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 23
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 0
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 23
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 23
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 41
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 84
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 63
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 63
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 82
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 23
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 56
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 82
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 23
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 84
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 84
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 41
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 82
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 56
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 84
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 82
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 63
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 41
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 84
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 23
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 41
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 56
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 82
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 63
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 0
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 41
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 41
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 63
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 82
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 82
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 56
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 84
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 56
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 63
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 63
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 82
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 23
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 23
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 84
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 23
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 23
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 23
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 0
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 23
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 23
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 84
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 84
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 63
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 84
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 41
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 56
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 0
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 63
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 0
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 56
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 41
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 56
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 82
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 23
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 23
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 84
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 41
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 41
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 84
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 23
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 82
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 0
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 23
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 84
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 63
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 41
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 23
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 41
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 56
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 56
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 41
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 63
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 41
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 23
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 82
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 56
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 23
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 56
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 82
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 82
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 23
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 41
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 56
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 84
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 41
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 41
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 41
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 0
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 41
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 41
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 23
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 23
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 41
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 23
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 23
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 84
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 23
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 56
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 82
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 0
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 23
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 82
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 41
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 63
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 23
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 82
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 56
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 23
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 82
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 0
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 41
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 63
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 56
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 63
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 23
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 0
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 23
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 84
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 82
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 56
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 84
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 84
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 0
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 63
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 0
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 84
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 63
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 23
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 0
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 23
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 63
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 82
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 82
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 41
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 23
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 41
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 84
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 0
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 63
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 23
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 63
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 23
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 63
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 0
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 0
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 84
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 82
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 23
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 23
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 41
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 23
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 23
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 0
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 63
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 82
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 23
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 41
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 56
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 82
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 23
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 41
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 23
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 84
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 41
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 63
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 41
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 84
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 56
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 56
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 56
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 23
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 41
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 23
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 23
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 84
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 41
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 41
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 63
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 63
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 82
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 56
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 23
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 23
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 56
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 56
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 84
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 84
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 84
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 23
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 41
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 0
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 41
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 0
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 56
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 56
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 41
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 63
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 56
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 56
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 23
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 41
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 63
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 82
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 63
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 56
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 23
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 63
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 63
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 56
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 23
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 82
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 63
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 56
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 84
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 23
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 82
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 41
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 84
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 23
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 41
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 23
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 41
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 23
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 41
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 23
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 56
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 23
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 82
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 41
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 23
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 23
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 41
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 41
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 41
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 56
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 56
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 41
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 63
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 63
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 63
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 82
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 63
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 23
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 63
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 0
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 84
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 41
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 63
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 84
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 41
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 63
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 56
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 23
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 41
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 41
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 41
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 0
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 41
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 23
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 0
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 63
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 63
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 56
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 41
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 41
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 41
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 56
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 23
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 63
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 0
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 56
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 41
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 23
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 23
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 63
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 41
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 84
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 56
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 63
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 23
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 84
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 0
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 82
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 56
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 23
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 41
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 82
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 84
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 41
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 41
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 23
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 0
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 41
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 82
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 0
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 63
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 56
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 41
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 56
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 84
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 84
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 56
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 84
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 23
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 23
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 23
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 23
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 63
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 84
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 23
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 23
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 23
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 63
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 41
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 63
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 84
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 23
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 41
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 23
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 82
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 84
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 23
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 0
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 56
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 82
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 23
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 41
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 82
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 23
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 41
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 56
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 56
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 23
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 63
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 63
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 23
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 0
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 56
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 82
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 82
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 23
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 0
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 23
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 56
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 41
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 41
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 56
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 56
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 56
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 63
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 41
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 56
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 23
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 63
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 84
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 63
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 84
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 63
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 63
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 23
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 82
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 56
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 23
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 84
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 84
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 0
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 56
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 63
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 41
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 63
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 56
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 63
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 56
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 63
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 63
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 23
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 84
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 23
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 56
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 41
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 23
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 63
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 0
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 56
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 23
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 41
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 23
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 41
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 0
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 56
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 41
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 84
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 23
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 23
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 41
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 0
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 82
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 41
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 23
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 56
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 82
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 56
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 41
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 63
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 23
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 0
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 63
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 63
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 84
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 23
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 56
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 23
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 23
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 23
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 84
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 84
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 0
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 41
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 56
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 23
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 41
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 41
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 63
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 82
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 23
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 23
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 41
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 41
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 0
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 23
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 56
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 82
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 84
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 23
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 23
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 23
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 41
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 23
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 23
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 0
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 23
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 23
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 0
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 63
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 84
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 63
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 23
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 63
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 23
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 41
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 41
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 84
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 82
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 23
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 56
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 82
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 82
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 23
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 63
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 23
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 82
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 0
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 0
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 56
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 84
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 84
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 63
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 84
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 0
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 63
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 41
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 23
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 84
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 23
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 41
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 82
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 82
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 23
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 23
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 56
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 82
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 0
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 84
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 84
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 82
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 82
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 41
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 84
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 23
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 84
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 23
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 0
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 23
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 23
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 63
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 56
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 82
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 23
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 41
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 41
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 23
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 23
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 84
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 56
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 23
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 0
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 84
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 56
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 23
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 23
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 23
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 41
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 23
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 41
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 23
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 23
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 23
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 82
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 63
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 41
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 56
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 0
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 23
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 41
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 63
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 63
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 84
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 56
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 82
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 82
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 84
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 23
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 23
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 0
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 23
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 23
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 23
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 23
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 82
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 0
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 63
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 82
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 23
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 63
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 82
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 0
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 56
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 56
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 56
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 63
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 84
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 82
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 82
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 0
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 63
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 0
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 23
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 63
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 63
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 63
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 23
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 84
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 84
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 23
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 63
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 63
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 82
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 41
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 41
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 23
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 63
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 63
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 56
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 63
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 0
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 23
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 23
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 84
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 82
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 84
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 23
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 63
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 0
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 84
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 23
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 23
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 23
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 23
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 56
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 41
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 23
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 82
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 41
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 23
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 23
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 82
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 23
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 0
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 63
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 82
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 82
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 23
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 82
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 41
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 23
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 41
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 23
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 41
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 63
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 0
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 63
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 84
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 0
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 63
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 41
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 82
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 23
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 23
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 56
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 82
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 41
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 41
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 41
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 0
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 23
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 56
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 82
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 23
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 56
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 63
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 41
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 82
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 23
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 0
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 0
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 41
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 23
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 63
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 41
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 56
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 82
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 63
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 56
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 82
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 84
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 0
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 82
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 84
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 84
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 41
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 84
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 56
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 63
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 84
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 0
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 63
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 56
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 41
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 41
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 41
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 56
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 23
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 56
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 41
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 63
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 41
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 23
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 82
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 23
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 56
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 56
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 41
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 41
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 56
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 84
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 23
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 56
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 41
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 0
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 23
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 23
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 41
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 41
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 41
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 82
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 56
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 23
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 23
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 23
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 23
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 41
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 41
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 56
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 23
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 23
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 84
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 0
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 56
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 56
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 84
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 82
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 84
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 84
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 23
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 0
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 23
emperical probablities from test set: {56: 0.122, 82: 0.117, 63: 0.137, 84: 0.116, 41: 0.176, 23: 0.249, 0: 0.083}
beta is  0.025 

err dic= {56: np.float64(0.020857142857142213), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142213), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {56: np.float64(0.020857142857142213), 82: np.float64(0.025857142857142204), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {56: np.float64(0.020857142857142213), 82: np.float64(0.025857142857142204), 63: np.float64(0.0058571428571422), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), np.float64(0.0058571428571422), 0, 0, 0, 0]
beta is  0.025 

err dic= {56: np.float64(0.020857142857142213), 82: np.float64(0.025857142857142204), 63: np.float64(0.0058571428571422), 84: np.float64(0.026857142857142205), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), np.float64(0.0058571428571422), np.float64(0.026857142857142205), 0, 0, 0]
beta is  0.025 

err dic= {56: np.float64(0.020857142857142213), 82: np.float64(0.025857142857142204), 63: np.float64(0.0058571428571422), 84: np.float64(0.026857142857142205), 41: np.float64(0.03314285714285778), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), np.float64(0.0058571428571422), np.float64(0.026857142857142205), np.float64(0.03314285714285778), 0, 0]
beta is  0.025 

err dic= {56: np.float64(0.020857142857142213), 82: np.float64(0.025857142857142204), 63: np.float64(0.0058571428571422), 84: np.float64(0.026857142857142205), 41: np.float64(0.03314285714285778), 23: np.float64(0.10614285714285779), 0: 0} 

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), np.float64(0.0058571428571422), np.float64(0.026857142857142205), np.float64(0.03314285714285778), np.float64(0.10614285714285779), 0]
beta is  0.025 

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

err list= [np.float64(0.020857142857142213), np.float64(0.025857142857142204), np.float64(0.0058571428571422), np.float64(0.026857142857142205), np.float64(0.03314285714285778), np.float64(0.10614285714285779), np.float64(0.059857142857142207)]
beta is  0.05 

err dic= {56: np.float64(0.020857142857142935), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142935), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {56: np.float64(0.020857142857142935), 82: np.float64(0.025857142857142926), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {56: np.float64(0.020857142857142935), 82: np.float64(0.025857142857142926), 63: np.float64(0.005857142857142922), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), np.float64(0.005857142857142922), 0, 0, 0, 0]
beta is  0.05 

err dic= {56: np.float64(0.020857142857142935), 82: np.float64(0.025857142857142926), 63: np.float64(0.005857142857142922), 84: np.float64(0.026857142857142927), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), np.float64(0.005857142857142922), np.float64(0.026857142857142927), 0, 0, 0]
beta is  0.05 

err dic= {56: np.float64(0.020857142857142935), 82: np.float64(0.025857142857142926), 63: np.float64(0.005857142857142922), 84: np.float64(0.026857142857142927), 41: np.float64(0.03314285714285706), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), np.float64(0.005857142857142922), np.float64(0.026857142857142927), np.float64(0.03314285714285706), 0, 0]
beta is  0.05 

err dic= {56: np.float64(0.020857142857142935), 82: np.float64(0.025857142857142926), 63: np.float64(0.005857142857142922), 84: np.float64(0.026857142857142927), 41: np.float64(0.03314285714285706), 23: np.float64(0.10614285714285707), 0: 0} 

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), np.float64(0.005857142857142922), np.float64(0.026857142857142927), np.float64(0.03314285714285706), np.float64(0.10614285714285707), 0]
beta is  0.05 

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

err list= [np.float64(0.020857142857142935), np.float64(0.025857142857142926), np.float64(0.005857142857142922), np.float64(0.026857142857142927), np.float64(0.03314285714285706), np.float64(0.10614285714285707), np.float64(0.05985714285714293)]
beta is  0.1 

err dic= {56: np.float64(0.02085714285714363), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.02085714285714363), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {56: np.float64(0.02085714285714363), 82: np.float64(0.02585714285714362), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {56: np.float64(0.02085714285714363), 82: np.float64(0.02585714285714362), 63: np.float64(0.005857142857143616), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), np.float64(0.005857142857143616), 0, 0, 0, 0]
beta is  0.1 

err dic= {56: np.float64(0.02085714285714363), 82: np.float64(0.02585714285714362), 63: np.float64(0.005857142857143616), 84: np.float64(0.02685714285714362), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), np.float64(0.005857142857143616), np.float64(0.02685714285714362), 0, 0, 0]
beta is  0.1 

err dic= {56: np.float64(0.02085714285714363), 82: np.float64(0.02585714285714362), 63: np.float64(0.005857142857143616), 84: np.float64(0.02685714285714362), 41: np.float64(0.03314285714285636), 23: 0, 0: 0} 

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), np.float64(0.005857142857143616), np.float64(0.02685714285714362), np.float64(0.03314285714285636), 0, 0]
beta is  0.1 

err dic= {56: np.float64(0.02085714285714363), 82: np.float64(0.02585714285714362), 63: np.float64(0.005857142857143616), 84: np.float64(0.02685714285714362), 41: np.float64(0.03314285714285636), 23: np.float64(0.10614285714285637), 0: 0} 

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), np.float64(0.005857142857143616), np.float64(0.02685714285714362), np.float64(0.03314285714285636), np.float64(0.10614285714285637), 0]
beta is  0.1 

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

err list= [np.float64(0.02085714285714363), np.float64(0.02585714285714362), np.float64(0.005857142857143616), np.float64(0.02685714285714362), np.float64(0.03314285714285636), np.float64(0.10614285714285637), np.float64(0.05985714285714362)]
beta is  0.25 

err dic= {56: np.float64(0.020857142857142907), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142907), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {56: np.float64(0.020857142857142907), 82: np.float64(0.025857142857142898), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {56: np.float64(0.020857142857142907), 82: np.float64(0.025857142857142898), 63: np.float64(0.005857142857142894), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), np.float64(0.005857142857142894), 0, 0, 0, 0]
beta is  0.25 

err dic= {56: np.float64(0.020857142857142907), 82: np.float64(0.025857142857142898), 63: np.float64(0.005857142857142894), 84: np.float64(0.0268571428571429), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), np.float64(0.005857142857142894), np.float64(0.0268571428571429), 0, 0, 0]
beta is  0.25 

err dic= {56: np.float64(0.020857142857142907), 82: np.float64(0.025857142857142898), 63: np.float64(0.005857142857142894), 84: np.float64(0.0268571428571429), 41: np.float64(0.033142857142857085), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), np.float64(0.005857142857142894), np.float64(0.0268571428571429), np.float64(0.033142857142857085), 0, 0]
beta is  0.25 

err dic= {56: np.float64(0.020857142857142907), 82: np.float64(0.025857142857142898), 63: np.float64(0.005857142857142894), 84: np.float64(0.0268571428571429), 41: np.float64(0.033142857142857085), 23: np.float64(0.1061428571428571), 0: 0} 

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), np.float64(0.005857142857142894), np.float64(0.0268571428571429), np.float64(0.033142857142857085), np.float64(0.1061428571428571), 0]
beta is  0.25 

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

err list= [np.float64(0.020857142857142907), np.float64(0.025857142857142898), np.float64(0.005857142857142894), np.float64(0.0268571428571429), np.float64(0.033142857142857085), np.float64(0.1061428571428571), np.float64(0.0598571428571429)]
beta is  0.5 

err dic= {56: np.float64(0.020857142857142824), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142824), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {56: np.float64(0.020857142857142824), 82: np.float64(0.025857142857142815), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {56: np.float64(0.020857142857142824), 82: np.float64(0.025857142857142815), 63: np.float64(0.005857142857142811), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), np.float64(0.005857142857142811), 0, 0, 0, 0]
beta is  0.5 

err dic= {56: np.float64(0.020857142857142824), 82: np.float64(0.025857142857142815), 63: np.float64(0.005857142857142811), 84: np.float64(0.026857142857142816), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), np.float64(0.005857142857142811), np.float64(0.026857142857142816), 0, 0, 0]
beta is  0.5 

err dic= {56: np.float64(0.020857142857142824), 82: np.float64(0.025857142857142815), 63: np.float64(0.005857142857142811), 84: np.float64(0.026857142857142816), 41: np.float64(0.03314285714285717), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), np.float64(0.005857142857142811), np.float64(0.026857142857142816), np.float64(0.03314285714285717), 0, 0]
beta is  0.5 

err dic= {56: np.float64(0.020857142857142824), 82: np.float64(0.025857142857142815), 63: np.float64(0.005857142857142811), 84: np.float64(0.026857142857142816), 41: np.float64(0.03314285714285717), 23: np.float64(0.10614285714285718), 0: 0} 

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), np.float64(0.005857142857142811), np.float64(0.026857142857142816), np.float64(0.03314285714285717), np.float64(0.10614285714285718), 0]
beta is  0.5 

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

err list= [np.float64(0.020857142857142824), np.float64(0.025857142857142815), np.float64(0.005857142857142811), np.float64(0.026857142857142816), np.float64(0.03314285714285717), np.float64(0.10614285714285718), np.float64(0.05985714285714282)]
beta is  0.75 

err dic= {56: np.float64(0.020857142857142852), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), 0, 0, 0, 0]
beta is  0.75 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), 0, 0, 0]
beta is  0.75 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), 0, 0]
beta is  0.75 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: np.float64(0.10614285714285715), 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), 0]
beta is  0.75 

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

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), np.float64(0.059857142857142845)]
beta is  1 

err dic= {56: np.float64(0.020857142857142852), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), 0, 0, 0, 0, 0]
beta is  1 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), 0, 0, 0, 0]
beta is  1 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), 0, 0, 0]
beta is  1 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), 0, 0]
beta is  1 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: np.float64(0.10614285714285715), 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), 0]
beta is  1 

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

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), np.float64(0.059857142857142845)]
beta is  1.25 

err dic= {56: np.float64(0.020857142857142852), 82: 0, 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: 0, 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: 0, 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), 0, 0, 0, 0]
beta is  1.25 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: 0, 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), 0, 0, 0]
beta is  1.25 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: 0, 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), 0, 0]
beta is  1.25 

err dic= {56: np.float64(0.020857142857142852), 82: np.float64(0.025857142857142842), 63: np.float64(0.0058571428571428386), 84: np.float64(0.026857142857142843), 41: np.float64(0.03314285714285714), 23: np.float64(0.10614285714285715), 0: 0} 

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), 0]
beta is  1.25 

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

err list= [np.float64(0.020857142857142852), np.float64(0.025857142857142842), np.float64(0.0058571428571428386), np.float64(0.026857142857142843), np.float64(0.03314285714285714), np.float64(0.10614285714285715), np.float64(0.059857142857142845)]
samppled assortment [100, 84, 77, 57, 6, 49]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{100: np.float64(0.09416687041995957), 84: np.float64(0.16091991444773354), 77: np.float64(0.16091991444773354), 57: np.float64(0.16091991444773354), 6: np.float64(0.10123355734137468), 49: np.float64(0.16091991444773354), 0: np.float64(0.16091991444773354)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {100: np.float64(0.02486005379086933), 84: np.float64(0.04248285741420166), 77: np.float64(0.04248285741420166), 57: np.float64(0.04248285741420166), 6: np.float64(0.026725659138122918), 49: np.float64(0.04248285741420166), 0: np.float64(0.04248285741420166)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.1114584648271419), 84: np.float64(0.15203341794331604), 77: np.float64(0.15203341794331604), 57: np.float64(0.15203341794331604), 6: np.float64(0.12837444545626148), 49: np.float64(0.15203341794331604), 0: np.float64(0.15203341794331604)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.10689348390364578), 84: np.float64(0.15437945302048228), 77: np.float64(0.15437945302048228), 57: np.float64(0.15437945302048228), 6: np.float64(0.12120925099393136), 49: np.float64(0.15437945302048228), 0: np.float64(0.15437945302048228)}
choice probs for this beta: {100: np.float64(0.10689348390364578), 84: np.float64(0.15437945302048228), 77: np.float64(0.15437945302048228), 57: np.float64(0.15437945302048228), 6: np.float64(0.12120925099393136), 49: np.float64(0.15437945302048228), 0: np.float64(0.15437945302048228)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs for cluster 2 

{100: np.float64(0.13396479015717305), 84: np.float64(0.1408829761874304), 77: np.float64(0.1408829761874304), 57: np.float64(0.1408829761874304), 6: np.float64(0.16162032890568492), 49: np.float64(0.1408829761874304), 0: np.float64(0.1408829761874304)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs (dictionary):

probs= {100: np.float64(0.03536670460149369), 84: np.float64(0.037193105713481625), 77: np.float64(0.037193105713481625), 57: np.float64(0.037193105713481625), 6: np.float64(0.04266776683110082), 49: np.float64(0.037193105713481625), 0: np.float64(0.037193105713481625)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
learned probs for cluster 1 

{100: np.float64(0.12406808148011665), 84: np.float64(0.14522076666470438), 77: np.float64(0.14522076666470438), 57: np.float64(0.14522076666470438), 6: np.float64(0.14982808519637475), 49: np.float64(0.14522076666470438), 0: np.float64(0.14522076666470438)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
learned probs (dictionary):

probs= {100: np.float64(0.12668081257085956), 84: np.float64(0.14407558997870404), 77: np.float64(0.14407558997870404), 57: np.float64(0.14407558997870404), 6: np.float64(0.15294123753563266), 49: np.float64(0.14407558997870404), 0: np.float64(0.14407558997870404)}
choice probs for this beta: {100: np.float64(0.12668081257085956), 84: np.float64(0.14407558997870404), 77: np.float64(0.14407558997870404), 57: np.float64(0.14407558997870404), 6: np.float64(0.15294123753563266), 49: np.float64(0.14407558997870404), 0: np.float64(0.14407558997870404)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 4, 5]
learned probs for cluster 2 

{100: np.float64(0.21062732289012714), 84: np.float64(0.10256922711492629), 77: np.float64(0.10256922711492629), 57: np.float64(0.10256922711492629), 6: np.float64(0.2765265415352434), 49: np.float64(0.10256922711492629), 0: np.float64(0.10256922711492629)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 2, 4, 5]
learned probs (dictionary):

probs= {100: np.float64(0.05560561324299357), 84: np.float64(0.02707827595834054), 77: np.float64(0.02707827595834054), 57: np.float64(0.02707827595834054), 6: np.float64(0.07300300696530426), 49: np.float64(0.02707827595834054), 0: np.float64(0.02707827595834054)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.17191864631650255), 84: np.float64(0.1160787266438613), 77: np.float64(0.1160787266438613), 57: np.float64(0.1160787266438613), 6: np.float64(0.24768772046419238), 49: np.float64(0.1160787266438613), 0: np.float64(0.1160787266438613)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.18213773693193944), 84: np.float64(0.11251221876822247), 77: np.float64(0.11251221876822247), 57: np.float64(0.11251221876822247), 6: np.float64(0.25530116922694984), 49: np.float64(0.11251221876822247), 0: np.float64(0.11251221876822247)}
choice probs for this beta: {100: np.float64(0.18213773693193944), 84: np.float64(0.11251221876822247), 77: np.float64(0.11251221876822247), 57: np.float64(0.11251221876822247), 6: np.float64(0.25530116922694984), 49: np.float64(0.11251221876822247), 0: np.float64(0.11251221876822247)}
#beta= 0.25 

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

{100: np.float64(0.2824343395171807), 84: np.float64(0.019498132148563052), 77: np.float64(0.019498132148563052), 57: np.float64(0.019498132148563052), 6: np.float64(0.6200749997399898), 49: np.float64(0.019498132148563052), 0: np.float64(0.019498132148563052)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 5, 6, 7, 10, 13, 100, 14, 15, 12]
learned probs (dictionary):

probs= {100: np.float64(0.07456266563253572), 84: np.float64(0.005147506887220646), 77: np.float64(0.005147506887220646), 57: np.float64(0.005147506887220646), 6: np.float64(0.1636997999313573), 49: np.float64(0.005147506887220646), 0: np.float64(0.005147506887220646)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.21646505002960506), 84: np.float64(0.03758147767066878), 77: np.float64(0.03758147767066878), 57: np.float64(0.03758147767066878), 6: np.float64(0.5956275616170498), 49: np.float64(0.03758147767066878), 0: np.float64(0.03758147767066878)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.23388094245432503), 84: np.float64(0.032807474452832865), 77: np.float64(0.032807474452832865), 57: np.float64(0.032807474452832865), 6: np.float64(0.6020816852815059), 49: np.float64(0.032807474452832865), 0: np.float64(0.032807474452832865)}
choice probs for this beta: {100: np.float64(0.23388094245432503), 84: np.float64(0.032807474452832865), 77: np.float64(0.032807474452832865), 57: np.float64(0.032807474452832865), 6: np.float64(0.6020816852815059), 49: np.float64(0.032807474452832865), 0: np.float64(0.032807474452832865)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2]
learned probs for cluster 2 

{100: np.float64(0.17655297125169792), 84: np.float64(0.0016309763701103307), 77: np.float64(0.0016309763701103307), 57: np.float64(0.0016309763701103307), 6: np.float64(0.8152921468977525), 49: np.float64(0.0016309763701103307), 0: np.float64(0.0016309763701103307)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 2]
learned probs (dictionary):

probs= {100: np.float64(0.04660998441044825), 84: np.float64(0.0004305777617091273), 77: np.float64(0.0004305777617091273), 57: np.float64(0.0004305777617091273), 6: np.float64(0.21523712678100668), 49: np.float64(0.0004305777617091273), 0: np.float64(0.0004305777617091273)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.1297294832186464), 84: np.float64(0.0021638608598331917), 77: np.float64(0.0021638608598331917), 57: np.float64(0.0021638608598331917), 6: np.float64(0.8594512124821896), 49: np.float64(0.0021638608598331917), 0: np.float64(0.0021638608598331917)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.142090884059372), 84: np.float64(0.0020231793545463566), 77: np.float64(0.0020231793545463566), 57: np.float64(0.0020231793545463566), 6: np.float64(0.8477932191678982), 49: np.float64(0.0020231793545463566), 0: np.float64(0.0020231793545463566)}
choice probs for this beta: {100: np.float64(0.142090884059372), 84: np.float64(0.0020231793545463566), 77: np.float64(0.0020231793545463566), 57: np.float64(0.0020231793545463566), 6: np.float64(0.8477932191678982), 49: np.float64(0.0020231793545463566), 0: np.float64(0.0020231793545463566)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 9: 1, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 9, 10, 100]
learned probs for cluster 2 

{100: np.float64(0.08908276085712948), 84: np.float64(8.73014289909312e-05), 77: np.float64(8.73014289909312e-05), 57: np.float64(8.73014289909312e-05), 6: np.float64(0.910480731997916), 49: np.float64(8.73014289909312e-05), 0: np.float64(8.73014289909312e-05)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {100: np.float64(0.023517848866282182), 84: np.float64(2.3047577253605835e-05), 77: np.float64(2.3047577253605835e-05), 57: np.float64(2.3047577253605835e-05), 6: np.float64(0.24036691324744983), 49: np.float64(2.3047577253605835e-05), 0: np.float64(2.3047577253605835e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11]
learned probs for cluster 1 

{100: np.float64(0.0009580835135853818), 84: np.float64(0.0009580835135853818), 77: np.float64(0.0009580835135853818), 57: np.float64(0.0009580835135853818), 6: np.float64(0.9942514989184877), 49: np.float64(0.0009580835135853818), 0: np.float64(0.0009580835135853818)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11]
learned probs (dictionary):

probs= {100: np.float64(0.024222998332281025), 84: np.float64(0.0007281970432524467), 77: np.float64(0.0007281970432524467), 57: np.float64(0.0007281970432524467), 6: np.float64(0.9721360164514569), 49: np.float64(0.0007281970432524467), 0: np.float64(0.0007281970432524467)}
choice probs for this beta: {100: np.float64(0.024222998332281025), 84: np.float64(0.0007281970432524467), 77: np.float64(0.0007281970432524467), 57: np.float64(0.0007281970432524467), 6: np.float64(0.9721360164514569), 49: np.float64(0.0007281970432524467), 0: np.float64(0.0007281970432524467)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{100: np.float64(0.08255582166364876), 84: np.float64(2.281132425163462e-06), 77: np.float64(2.281132425163462e-06), 57: np.float64(2.281132425163462e-06), 6: np.float64(0.9174327726742257), 49: np.float64(2.281132425163462e-06), 0: np.float64(2.281132425163462e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {100: np.float64(0.021794736919203275), 84: np.float64(6.02218960243154e-07), 77: np.float64(6.02218960243154e-07), 57: np.float64(6.02218960243154e-07), 6: np.float64(0.2422022519859956), 49: np.float64(6.02218960243154e-07), 0: np.float64(6.02218960243154e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 17: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 17, 100]
learned probs for cluster 1 

{100: np.float64(0.019008031861033718), 84: np.float64(1.5917129494357334e-06), 77: np.float64(1.5917129494357334e-06), 57: np.float64(1.5917129494357334e-06), 6: np.float64(0.9809840095742195), 49: np.float64(1.5917129494357334e-06), 0: np.float64(1.5917129494357334e-06)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 17, 100]
learned probs (dictionary):

probs= {100: np.float64(0.03578464836892409), 84: np.float64(1.7737196910278539e-06), 77: np.float64(1.7737196910278539e-06), 57: np.float64(1.7737196910278539e-06), 6: np.float64(0.9642064830326211), 49: np.float64(1.7737196910278539e-06), 0: np.float64(1.7737196910278539e-06)}
choice probs for this beta: {100: np.float64(0.03578464836892409), 84: np.float64(1.7737196910278539e-06), 77: np.float64(1.7737196910278539e-06), 57: np.float64(1.7737196910278539e-06), 6: np.float64(0.9642064830326211), 49: np.float64(1.7737196910278539e-06), 0: np.float64(1.7737196910278539e-06)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 3, 13: 1, 17: 3, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 12, 17]
learned probs for cluster 2 

{100: np.float64(0.01746367799263354), 84: np.float64(3.3907626856564285e-09), 77: np.float64(3.3907626856564285e-09), 57: np.float64(3.3907626856564285e-09), 6: np.float64(0.9825363050535525), 49: np.float64(3.3907626856564285e-09), 0: np.float64(3.3907626856564285e-09)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 12, 17]
learned probs (dictionary):

probs= {100: np.float64(0.004610410990055255), 84: np.float64(8.951613490132971e-10), 77: np.float64(8.951613490132971e-10), 57: np.float64(8.951613490132971e-10), 6: np.float64(0.25938958453413785), 49: np.float64(8.951613490132971e-10), 0: np.float64(8.951613490132971e-10)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.006350583185492757), 84: np.float64(4.130258309908217e-08), 77: np.float64(4.130258309908217e-08), 57: np.float64(4.130258309908217e-08), 6: np.float64(0.9936492103015913), 49: np.float64(4.130258309908217e-08), 0: np.float64(4.130258309908217e-08)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.009284440214577925), 84: np.float64(3.1293862509937774e-08), 77: np.float64(3.1293862509937774e-08), 57: np.float64(3.1293862509937774e-08), 6: np.float64(0.990715403316109), 49: np.float64(3.1293862509937774e-08), 0: np.float64(3.1293862509937774e-08)}
choice probs for this beta: {100: np.float64(0.009284440214577925), 84: np.float64(3.1293862509937774e-08), 77: np.float64(3.1293862509937774e-08), 57: np.float64(3.1293862509937774e-08), 6: np.float64(0.990715403316109), 49: np.float64(3.1293862509937774e-08), 0: np.float64(3.1293862509937774e-08)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{100: np.float64(0.08453159814602026), 84: np.float64(0.16491235934785367), 77: np.float64(0.16491235934785367), 57: np.float64(0.16491235934785367), 6: np.float64(0.09090660511471227), 49: np.float64(0.16491235934785367), 0: np.float64(0.16491235934785367)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {100: np.float64(0.02231634191054935), 84: np.float64(0.04353686286783337), 77: np.float64(0.04353686286783337), 57: np.float64(0.04353686286783337), 6: np.float64(0.02399934375028404), 49: np.float64(0.04353686286783337), 0: np.float64(0.04353686286783337)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.10558347132938194), 84: np.float64(0.1551070025589801), 77: np.float64(0.1551070025589801), 57: np.float64(0.1551070025589801), 6: np.float64(0.1188815158757175), 49: np.float64(0.1551070025589801), 0: np.float64(0.1551070025589801)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.10002577680897445), 84: np.float64(0.15769561675124272), 77: np.float64(0.15769561675124272), 57: np.float64(0.15769561675124272), 6: np.float64(0.11149613943481212), 49: np.float64(0.15769561675124272), 0: np.float64(0.15769561675124272)}
choice probs for this beta: {100: np.float64(0.10002577680897445), 84: np.float64(0.15769561675124272), 77: np.float64(0.15769561675124272), 57: np.float64(0.15769561675124272), 6: np.float64(0.11149613943481212), 49: np.float64(0.15769561675124272), 0: np.float64(0.15769561675124272)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5, 10, 14]
learned probs for cluster 2 

{100: np.float64(0.13975516313976216), 84: np.float64(0.13984572548460103), 77: np.float64(0.13984572548460103), 57: np.float64(0.13984572548460103), 6: np.float64(0.16101620943724215), 49: np.float64(0.13984572548460103), 0: np.float64(0.13984572548460103)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 5, 10, 14]
learned probs (dictionary):

probs= {100: np.float64(0.036895363068897215), 84: np.float64(0.03691927152793467), 77: np.float64(0.03691927152793467), 57: np.float64(0.03691927152793467), 6: np.float64(0.04250827929143193), 49: np.float64(0.03691927152793467), 0: np.float64(0.03691927152793467)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.1308989595389958), 84: np.float64(0.14076193293473663), 77: np.float64(0.14076193293473663), 57: np.float64(0.14076193293473663), 6: np.float64(0.16529137578733175), 49: np.float64(0.14076193293473663), 0: np.float64(0.14076193293473663)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.13323699728959812), 84: np.float64(0.1405200541679008), 77: np.float64(0.1405200541679008), 57: np.float64(0.1405200541679008), 6: np.float64(0.16416273187090807), 49: np.float64(0.1405200541679008), 0: np.float64(0.1405200541679008)}
choice probs for this beta: {100: np.float64(0.13323699728959812), 84: np.float64(0.1405200541679008), 77: np.float64(0.1405200541679008), 57: np.float64(0.1405200541679008), 6: np.float64(0.16416273187090807), 49: np.float64(0.1405200541679008), 0: np.float64(0.1405200541679008)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 11]
learned probs for cluster 2 

{100: np.float64(0.21404051212394207), 84: np.float64(0.09615121886512651), 77: np.float64(0.09615121886512651), 57: np.float64(0.09615121886512651), 6: np.float64(0.3052033935504256), 49: np.float64(0.09615121886512651), 0: np.float64(0.09615121886512651)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 11]
learned probs (dictionary):

probs= {100: np.float64(0.05650669520072071), 84: np.float64(0.0253839217803934), 77: np.float64(0.0253839217803934), 57: np.float64(0.0253839217803934), 6: np.float64(0.08057369589731236), 49: np.float64(0.0253839217803934), 0: np.float64(0.0253839217803934)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{100: np.float64(0.17191864631650255), 84: np.float64(0.1160787266438613), 77: np.float64(0.1160787266438613), 57: np.float64(0.1160787266438613), 6: np.float64(0.24768772046419238), 49: np.float64(0.1160787266438613), 0: np.float64(0.1160787266438613)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {100: np.float64(0.18303881888966658), 84: np.float64(0.11081786459027532), 77: np.float64(0.11081786459027532), 57: np.float64(0.11081786459027532), 6: np.float64(0.26287185815895797), 49: np.float64(0.11081786459027532), 0: np.float64(0.11081786459027532)}
choice probs for this beta: {100: np.float64(0.18303881888966658), 84: np.float64(0.11081786459027532), 77: np.float64(0.11081786459027532), 57: np.float64(0.11081786459027532), 6: np.float64(0.26287185815895797), 49: np.float64(0.11081786459027532), 0: np.float64(0.11081786459027532)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 11]
learned probs for cluster 2 

{100: np.float64(0.2700571645405225), 84: np.float64(0.025956307368263782), 77: np.float64(0.025956307368263782), 57: np.float64(0.025956307368263782), 6: np.float64(0.6001612986181588), 49: np.float64(0.025956307368263782), 0: np.float64(0.025956307368263782)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 11]
learned probs (dictionary):

probs= {100: np.float64(0.07129509143869794), 84: np.float64(0.006852465145221639), 77: np.float64(0.006852465145221639), 57: np.float64(0.006852465145221639), 6: np.float64(0.15844258283519394), 49: np.float64(0.006852465145221639), 0: np.float64(0.006852465145221639)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.19598293857170868), 84: np.float64(0.03179387716817668), 77: np.float64(0.03179387716817668), 57: np.float64(0.03179387716817668), 6: np.float64(0.6450476755874114), 49: np.float64(0.03179387716817668), 0: np.float64(0.03179387716817668)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.21553853422747551), 84: np.float64(0.030252758740999676), 77: np.float64(0.030252758740999676), 57: np.float64(0.030252758740999676), 6: np.float64(0.6331976720675287), 49: np.float64(0.030252758740999676), 0: np.float64(0.030252758740999676)}
choice probs for this beta: {100: np.float64(0.21553853422747551), 84: np.float64(0.030252758740999676), 77: np.float64(0.030252758740999676), 57: np.float64(0.030252758740999676), 6: np.float64(0.6331976720675287), 49: np.float64(0.030252758740999676), 0: np.float64(0.030252758740999676)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 14]
learned probs for cluster 2 

{100: np.float64(0.23215287883851504), 84: np.float64(0.002133712971588569), 77: np.float64(0.002133712971588569), 57: np.float64(0.002133712971588569), 6: np.float64(0.7571785563035422), 49: np.float64(0.002133712971588569), 0: np.float64(0.002133712971588569)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 14]
learned probs (dictionary):

probs= {100: np.float64(0.06128836001336797), 84: np.float64(0.0005633002244993823), 77: np.float64(0.0005633002244993823), 57: np.float64(0.0005633002244993823), 6: np.float64(0.19989513886413515), 49: np.float64(0.0005633002244993823), 0: np.float64(0.0005633002244993823)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{100: np.float64(0.17433473002447017), 84: np.float64(0.0030287974500592986), 77: np.float64(0.0030287974500592986), 57: np.float64(0.0030287974500592986), 6: np.float64(0.8105212827252347), 49: np.float64(0.0030287974500592986), 0: np.float64(0.0030287974500592986)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {100: np.float64(0.189598721311378), 84: np.float64(0.002792495147743026), 77: np.float64(0.002792495147743026), 57: np.float64(0.002792495147743026), 6: np.float64(0.7964388029499079), 49: np.float64(0.002792495147743026), 0: np.float64(0.002792495147743026)}
choice probs for this beta: {100: np.float64(0.189598721311378), 84: np.float64(0.002792495147743026), 77: np.float64(0.002792495147743026), 57: np.float64(0.002792495147743026), 6: np.float64(0.7964388029499079), 49: np.float64(0.002792495147743026), 0: np.float64(0.002792495147743026)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
learned probs for cluster 2 

{100: np.float64(0.05300645909899264), 84: np.float64(1.4695103092342828e-05), 77: np.float64(1.4695103092342828e-05), 57: np.float64(1.4695103092342828e-05), 6: np.float64(0.9469200653855457), 49: np.float64(1.4695103092342828e-05), 0: np.float64(1.4695103092342828e-05)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
learned probs (dictionary):

probs= {100: np.float64(0.013993705202134058), 84: np.float64(3.879507216378507e-06), 77: np.float64(3.879507216378507e-06), 57: np.float64(3.879507216378507e-06), 6: np.float64(0.24998689726178408), 49: np.float64(3.879507216378507e-06), 0: np.float64(3.879507216378507e-06)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.9525658747613788), 84: np.float64(0.007905687539770199), 77: np.float64(0.007905687539770199), 57: np.float64(0.007905687539770199), 6: np.float64(0.007905687539770199), 49: np.float64(0.007905687539770199), 0: np.float64(0.007905687539770199)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.7150821890265088), 84: np.float64(0.005822465536487244), 77: np.float64(0.005822465536487244), 57: np.float64(0.005822465536487244), 6: np.float64(0.25580548329105496), 49: np.float64(0.005822465536487244), 0: np.float64(0.005822465536487244)}
choice probs for this beta: {100: np.float64(0.7150821890265088), 84: np.float64(0.005822465536487244), 77: np.float64(0.005822465536487244), 57: np.float64(0.005822465536487244), 6: np.float64(0.25580548329105496), 49: np.float64(0.005822465536487244), 0: np.float64(0.005822465536487244)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 4]
learned probs for cluster 2 

{100: np.float64(0.04071038514208088), 84: np.float64(1.2278148938881137e-06), 77: np.float64(1.2278148938881137e-06), 57: np.float64(1.2278148938881137e-06), 6: np.float64(0.9592834757834497), 49: np.float64(1.2278148938881137e-06), 0: np.float64(1.2278148938881137e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 4]
learned probs (dictionary):

probs= {100: np.float64(0.010747541677509352), 84: np.float64(3.24143131986462e-07), 77: np.float64(3.24143131986462e-07), 57: np.float64(3.24143131986462e-07), 6: np.float64(0.25325083760683076), 49: np.float64(3.24143131986462e-07), 0: np.float64(3.24143131986462e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{100: np.float64(0.008520151475510497), 84: np.float64(7.921847584319055e-07), 77: np.float64(7.921847584319055e-07), 57: np.float64(7.921847584319055e-07), 6: np.float64(0.9914758876006978), 49: np.float64(7.921847584319055e-07), 0: np.float64(7.921847584319055e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {100: np.float64(0.017018373163485076), 84: np.float64(9.071911141923444e-07), 77: np.float64(9.071911141923444e-07), 57: np.float64(9.071911141923444e-07), 6: np.float64(0.9829770908809443), 49: np.float64(9.071911141923444e-07), 0: np.float64(9.071911141923444e-07)}
choice probs for this beta: {100: np.float64(0.017018373163485076), 84: np.float64(9.071911141923444e-07), 77: np.float64(9.071911141923444e-07), 57: np.float64(9.071911141923444e-07), 6: np.float64(0.9829770908809443), 49: np.float64(9.071911141923444e-07), 0: np.float64(9.071911141923444e-07)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs for cluster 2 

{100: np.float64(0.04511781975941347), 84: np.float64(2.122694168879897e-08), 77: np.float64(2.122694168879897e-08), 57: np.float64(2.122694168879897e-08), 6: np.float64(0.9548820741058781), 49: np.float64(2.122694168879897e-08), 0: np.float64(2.122694168879897e-08)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs (dictionary):

probs= {100: np.float64(0.011911104416485158), 84: np.float64(5.603912605842929e-09), 77: np.float64(5.603912605842929e-09), 57: np.float64(5.603912605842929e-09), 6: np.float64(0.2520888675639518), 49: np.float64(5.603912605842929e-09), 0: np.float64(5.603912605842929e-09)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
learned probs for cluster 1 

{100: np.float64(0.10659816501029025), 84: np.float64(4.654729845739542e-07), 77: np.float64(4.654729845739542e-07), 57: np.float64(4.654729845739542e-07), 6: np.float64(0.8933995076247863), 49: np.float64(4.654729845739542e-07), 0: np.float64(4.654729845739542e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 100]
learned probs (dictionary):

probs= {100: np.float64(0.09036735386405878), 84: np.float64(3.481920292522732e-07), 77: np.float64(3.481920292522732e-07), 57: np.float64(3.481920292522732e-07), 6: np.float64(0.9096309051757945), 49: np.float64(3.481920292522732e-07), 0: np.float64(3.481920292522732e-07)}
choice probs for this beta: {100: np.float64(0.09036735386405878), 84: np.float64(3.481920292522732e-07), 77: np.float64(3.481920292522732e-07), 57: np.float64(3.481920292522732e-07), 6: np.float64(0.9096309051757945), 49: np.float64(3.481920292522732e-07), 0: np.float64(3.481920292522732e-07)}
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 84
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 100
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 100
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 77
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 100
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 77
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 100
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 77
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 57
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 84
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 100
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 57
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 100
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 100
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 100
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 100
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 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 57
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 49
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 84
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 100
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 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 49
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 6
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 77
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 0
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 100
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 84
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 100
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 49
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 77
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 84
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 77
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 57
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 84
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 84
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 84
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 84
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 100
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 6
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 6
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 100
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 0
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 100
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 49
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 49
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 100
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 0
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 0
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 0
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 0
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 49
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 6
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 100
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 100
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 49
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 100
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 100
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 57
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 0
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 49
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 84
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 57
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 100
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 100
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 77
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 6
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 84
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 49
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 6
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 77
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 0
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 100
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 6
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 100
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 0
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 49
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 77
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 6
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 100
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 100
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 49
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 84
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 100
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 6
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 100
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 0
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 0
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 57
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 57
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 57
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 57
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 6
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 100
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 77
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 6
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 100
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 49
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 6
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 100
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 77
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 6
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 100
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 49
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 57
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 77
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 100
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 6
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 6
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 77
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 6
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 84
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 84
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 57
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 6
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 100
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 84
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 0
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 100
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 49
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 84
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 100
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 100
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 77
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 77
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 49
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 100
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 77
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 57
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 6
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 77
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 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 0
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 6
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 100
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 6
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 100
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 77
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 84
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 84
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 84
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 77
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 84
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 84
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 49
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 84
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 57
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 84
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 6
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 84
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 49
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 6
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 77
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 57
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 100
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 100
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 77
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 49
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 49
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 100
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 100
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 77
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 0
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 84
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 84
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 6
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 100
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 0
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 100
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 6
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 49
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 49
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 100
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 100
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 6
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 6
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 57
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 84
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 49
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 6
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 6
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 49
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 57
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 6
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 49
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 84
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 49
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 49
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 77
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 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 77
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 100
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 6
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 6
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 49
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 57
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 84
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 100
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 49
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 6
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 49
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 57
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 49
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 100
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 6
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 6
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 57
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 100
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 100
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 77
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 84
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 100
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 100
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 0
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 100
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 100
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 49
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 100
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 49
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 100
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 84
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 6
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 49
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 77
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 0
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 57
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 49
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 84
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 49
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 57
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 77
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 49
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 100
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 57
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 77
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 6
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 49
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 0
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 84
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 100
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 77
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 49
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 49
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 84
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 6
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 100
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 49
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 6
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 84
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 100
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 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 100
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 6
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 84
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 49
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 57
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 100
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 57
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 57
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 49
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 49
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 57
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 100
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 100
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 84
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 6
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 49
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 49
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 6
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 84
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 77
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 0
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 6
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 6
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 0
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 6
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 6
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 49
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 57
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 6
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 57
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 100
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 77
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 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 57
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 49
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 6
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 77
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 49
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 6
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 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 49
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 6
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 6
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 49
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 77
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 49
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 0
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 57
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 100
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 57
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 0
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 6
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 77
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 6
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 100
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 57
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 6
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 57
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 6
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 49
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 0
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 100
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 57
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 49
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 49
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 49
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 100
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 57
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 100
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 49
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 49
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 100
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 49
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 0
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 49
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 100
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 77
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 6
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 6
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 77
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 100
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 100
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 84
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 0
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 0
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 49
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 0
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 6
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 100
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 77
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 84
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 49
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 6
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 0
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 100
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 77
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 0
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 49
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 84
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 57
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 57
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 100
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 6
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 49
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 6
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 77
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 100
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 84
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 6
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 100
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 77
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 49
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 57
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 0
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 100
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 6
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 57
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 100
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 100
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 100
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 57
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 100
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 100
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 6
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 77
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 100
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 77
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 100
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 100
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 100
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 49
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 77
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 49
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 57
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 100
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 84
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 100
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 84
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 100
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 49
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 49
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 49
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 6
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 49
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 100
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 100
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 6
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 49
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 84
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 100
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 6
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 57
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 84
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 84
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 6
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 100
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 100
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 77
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 6
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 100
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 84
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 84
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 100
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 6
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 84
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 100
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 100
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 57
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 100
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 100
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 100
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 6
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 100
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 49
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 49
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 100
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 100
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 100
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 84
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 84
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 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 6
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 49
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 0
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 84
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 77
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 100
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 49
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 57
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 100
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 84
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 6
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 49
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 57
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 84
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 49
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 77
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 77
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 77
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 57
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 6
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 100
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 77
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 0
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 77
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 100
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 57
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 100
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 100
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 84
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 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 100
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 49
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 100
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 57
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 49
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 100
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 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 6
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 77
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 100
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 100
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 6
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 77
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 100
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 77
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 77
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 84
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 100
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 57
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 6
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 84
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 100
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 0
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 100
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 100
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 49
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 100
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 6
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 49
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 49
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 100
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 49
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 49
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 77
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 6
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 6
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 6
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 100
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 100
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 100
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 100
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 77
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 49
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 57
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 0
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 100
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 84
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 49
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 100
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 100
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 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 49
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 84
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 0
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 77
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 77
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 84
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 57
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 49
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 57
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 84
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 77
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 0
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 84
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 100
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 6
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 77
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 6
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 49
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 100
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 49
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 57
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 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 6
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 77
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 77
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 57
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 0
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 77
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 49
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 77
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 6
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 57
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 100
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 84
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 77
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 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 57
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 77
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 6
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 0
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 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 100
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 49
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 57
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 6
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 49
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 57
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 49
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 57
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 77
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 100
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 100
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 100
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 100
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 77
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 100
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 100
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 57
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 6
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 77
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 77
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 100
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 100
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 57
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 84
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 6
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 100
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 6
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 57
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 0
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 6
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 100
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 57
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 57
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 84
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 49
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 57
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 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 77
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 49
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 100
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 77
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 6
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 49
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 100
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 57
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 100
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 57
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 100
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 100
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 100
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 49
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 100
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 84
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 6
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 84
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 6
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 6
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 77
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 84
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 84
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 49
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 49
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 77
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 57
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 84
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 84
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 100
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 100
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 100
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 77
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 57
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 0
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 100
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 6
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 84
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 49
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 49
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 0
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 77
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 100
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 84
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 100
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 77
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 49
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 6
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 100
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 49
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 49
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 6
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 77
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 100
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 49
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 6
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 49
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 6
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 84
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 6
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 6
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 49
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 100
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 84
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 77
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 77
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 0
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 84
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 100
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 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 100
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 57
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
emperical probablities from test set: {100: 0.302, 84: 0.077, 77: 0.08, 57: 0.081, 6: 0.304, 49: 0.108, 0: 0.048}
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.20197422319102554), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: np.float64(0.08069561675124272), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.20197422319102554), np.float64(0.08069561675124272), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: np.float64(0.08069561675124272), 77: np.float64(0.07769561675124272), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.20197422319102554), np.float64(0.08069561675124272), np.float64(0.07769561675124272), 0, 0, 0, 0]
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: np.float64(0.08069561675124272), 77: np.float64(0.07769561675124272), 57: np.float64(0.07669561675124272), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.20197422319102554), np.float64(0.08069561675124272), np.float64(0.07769561675124272), np.float64(0.07669561675124272), 0, 0, 0]
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: np.float64(0.08069561675124272), 77: np.float64(0.07769561675124272), 57: np.float64(0.07669561675124272), 6: np.float64(0.19250386056518787), 49: 0, 0: 0} 

err list= [np.float64(0.20197422319102554), np.float64(0.08069561675124272), np.float64(0.07769561675124272), np.float64(0.07669561675124272), np.float64(0.19250386056518787), 0, 0]
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: np.float64(0.08069561675124272), 77: np.float64(0.07769561675124272), 57: np.float64(0.07669561675124272), 6: np.float64(0.19250386056518787), 49: np.float64(0.04969561675124272), 0: 0} 

err list= [np.float64(0.20197422319102554), np.float64(0.08069561675124272), np.float64(0.07769561675124272), np.float64(0.07669561675124272), np.float64(0.19250386056518787), np.float64(0.04969561675124272), 0]
beta is  0.025 

err dic= {100: np.float64(0.20197422319102554), 84: np.float64(0.08069561675124272), 77: np.float64(0.07769561675124272), 57: np.float64(0.07669561675124272), 6: np.float64(0.19250386056518787), 49: np.float64(0.04969561675124272), 0: np.float64(0.10969561675124272)} 

err list= [np.float64(0.20197422319102554), np.float64(0.08069561675124272), np.float64(0.07769561675124272), np.float64(0.07669561675124272), np.float64(0.19250386056518787), np.float64(0.04969561675124272), np.float64(0.10969561675124272)]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.16876300271040187), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: np.float64(0.06352005416790081), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.16876300271040187), np.float64(0.06352005416790081), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: np.float64(0.06352005416790081), 77: np.float64(0.06052005416790081), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.16876300271040187), np.float64(0.06352005416790081), np.float64(0.06052005416790081), 0, 0, 0, 0]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: np.float64(0.06352005416790081), 77: np.float64(0.06052005416790081), 57: np.float64(0.05952005416790081), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.16876300271040187), np.float64(0.06352005416790081), np.float64(0.06052005416790081), np.float64(0.05952005416790081), 0, 0, 0]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: np.float64(0.06352005416790081), 77: np.float64(0.06052005416790081), 57: np.float64(0.05952005416790081), 6: np.float64(0.13983726812909192), 49: 0, 0: 0} 

err list= [np.float64(0.16876300271040187), np.float64(0.06352005416790081), np.float64(0.06052005416790081), np.float64(0.05952005416790081), np.float64(0.13983726812909192), 0, 0]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: np.float64(0.06352005416790081), 77: np.float64(0.06052005416790081), 57: np.float64(0.05952005416790081), 6: np.float64(0.13983726812909192), 49: np.float64(0.03252005416790081), 0: 0} 

err list= [np.float64(0.16876300271040187), np.float64(0.06352005416790081), np.float64(0.06052005416790081), np.float64(0.05952005416790081), np.float64(0.13983726812909192), np.float64(0.03252005416790081), 0]
beta is  0.05 

err dic= {100: np.float64(0.16876300271040187), 84: np.float64(0.06352005416790081), 77: np.float64(0.06052005416790081), 57: np.float64(0.05952005416790081), 6: np.float64(0.13983726812909192), 49: np.float64(0.03252005416790081), 0: np.float64(0.09252005416790081)} 

err list= [np.float64(0.16876300271040187), np.float64(0.06352005416790081), np.float64(0.06052005416790081), np.float64(0.05952005416790081), np.float64(0.13983726812909192), np.float64(0.03252005416790081), np.float64(0.09252005416790081)]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11896118111033341), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: np.float64(0.03381786459027532), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11896118111033341), np.float64(0.03381786459027532), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: np.float64(0.03381786459027532), 77: np.float64(0.030817864590275315), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11896118111033341), np.float64(0.03381786459027532), np.float64(0.030817864590275315), 0, 0, 0, 0]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: np.float64(0.03381786459027532), 77: np.float64(0.030817864590275315), 57: np.float64(0.029817864590275314), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11896118111033341), np.float64(0.03381786459027532), np.float64(0.030817864590275315), np.float64(0.029817864590275314), 0, 0, 0]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: np.float64(0.03381786459027532), 77: np.float64(0.030817864590275315), 57: np.float64(0.029817864590275314), 6: np.float64(0.04112814184104202), 49: 0, 0: 0} 

err list= [np.float64(0.11896118111033341), np.float64(0.03381786459027532), np.float64(0.030817864590275315), np.float64(0.029817864590275314), np.float64(0.04112814184104202), 0, 0]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: np.float64(0.03381786459027532), 77: np.float64(0.030817864590275315), 57: np.float64(0.029817864590275314), 6: np.float64(0.04112814184104202), 49: np.float64(0.002817864590275318), 0: 0} 

err list= [np.float64(0.11896118111033341), np.float64(0.03381786459027532), np.float64(0.030817864590275315), np.float64(0.029817864590275314), np.float64(0.04112814184104202), np.float64(0.002817864590275318), 0]
beta is  0.1 

err dic= {100: np.float64(0.11896118111033341), 84: np.float64(0.03381786459027532), 77: np.float64(0.030817864590275315), 57: np.float64(0.029817864590275314), 6: np.float64(0.04112814184104202), 49: np.float64(0.002817864590275318), 0: np.float64(0.06281786459027532)} 

err list= [np.float64(0.11896118111033341), np.float64(0.03381786459027532), np.float64(0.030817864590275315), np.float64(0.029817864590275314), np.float64(0.04112814184104202), np.float64(0.002817864590275318), np.float64(0.06281786459027532)]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.08646146577252448), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: np.float64(0.04674724125900032), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.08646146577252448), np.float64(0.04674724125900032), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: np.float64(0.04674724125900032), 77: np.float64(0.049747241259000326), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.08646146577252448), np.float64(0.04674724125900032), np.float64(0.049747241259000326), 0, 0, 0, 0]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: np.float64(0.04674724125900032), 77: np.float64(0.049747241259000326), 57: np.float64(0.05074724125900033), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.08646146577252448), np.float64(0.04674724125900032), np.float64(0.049747241259000326), np.float64(0.05074724125900033), 0, 0, 0]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: np.float64(0.04674724125900032), 77: np.float64(0.049747241259000326), 57: np.float64(0.05074724125900033), 6: np.float64(0.32919767206752876), 49: 0, 0: 0} 

err list= [np.float64(0.08646146577252448), np.float64(0.04674724125900032), np.float64(0.049747241259000326), np.float64(0.05074724125900033), np.float64(0.32919767206752876), 0, 0]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: np.float64(0.04674724125900032), 77: np.float64(0.049747241259000326), 57: np.float64(0.05074724125900033), 6: np.float64(0.32919767206752876), 49: np.float64(0.07774724125900032), 0: 0} 

err list= [np.float64(0.08646146577252448), np.float64(0.04674724125900032), np.float64(0.049747241259000326), np.float64(0.05074724125900033), np.float64(0.32919767206752876), np.float64(0.07774724125900032), 0]
beta is  0.25 

err dic= {100: np.float64(0.08646146577252448), 84: np.float64(0.04674724125900032), 77: np.float64(0.049747241259000326), 57: np.float64(0.05074724125900033), 6: np.float64(0.32919767206752876), 49: np.float64(0.07774724125900032), 0: np.float64(0.017747241259000325)} 

err list= [np.float64(0.08646146577252448), np.float64(0.04674724125900032), np.float64(0.049747241259000326), np.float64(0.05074724125900033), np.float64(0.32919767206752876), np.float64(0.07774724125900032), np.float64(0.017747241259000325)]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11240127868862199), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: np.float64(0.07420750485225697), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11240127868862199), np.float64(0.07420750485225697), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: np.float64(0.07420750485225697), 77: np.float64(0.07720750485225697), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11240127868862199), np.float64(0.07420750485225697), np.float64(0.07720750485225697), 0, 0, 0, 0]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: np.float64(0.07420750485225697), 77: np.float64(0.07720750485225697), 57: np.float64(0.07820750485225697), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.11240127868862199), np.float64(0.07420750485225697), np.float64(0.07720750485225697), np.float64(0.07820750485225697), 0, 0, 0]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: np.float64(0.07420750485225697), 77: np.float64(0.07720750485225697), 57: np.float64(0.07820750485225697), 6: np.float64(0.4924388029499079), 49: 0, 0: 0} 

err list= [np.float64(0.11240127868862199), np.float64(0.07420750485225697), np.float64(0.07720750485225697), np.float64(0.07820750485225697), np.float64(0.4924388029499079), 0, 0]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: np.float64(0.07420750485225697), 77: np.float64(0.07720750485225697), 57: np.float64(0.07820750485225697), 6: np.float64(0.4924388029499079), 49: np.float64(0.10520750485225697), 0: 0} 

err list= [np.float64(0.11240127868862199), np.float64(0.07420750485225697), np.float64(0.07720750485225697), np.float64(0.07820750485225697), np.float64(0.4924388029499079), np.float64(0.10520750485225697), 0]
beta is  0.5 

err dic= {100: np.float64(0.11240127868862199), 84: np.float64(0.07420750485225697), 77: np.float64(0.07720750485225697), 57: np.float64(0.07820750485225697), 6: np.float64(0.4924388029499079), 49: np.float64(0.10520750485225697), 0: np.float64(0.045207504852256976)} 

err list= [np.float64(0.11240127868862199), np.float64(0.07420750485225697), np.float64(0.07720750485225697), np.float64(0.07820750485225697), np.float64(0.4924388029499079), np.float64(0.10520750485225697), np.float64(0.045207504852256976)]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.4130821890265088), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: np.float64(0.07117753446351276), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.4130821890265088), np.float64(0.07117753446351276), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: np.float64(0.07117753446351276), 77: np.float64(0.07417753446351276), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.4130821890265088), np.float64(0.07117753446351276), np.float64(0.07417753446351276), 0, 0, 0, 0]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: np.float64(0.07117753446351276), 77: np.float64(0.07417753446351276), 57: np.float64(0.07517753446351276), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.4130821890265088), np.float64(0.07117753446351276), np.float64(0.07417753446351276), np.float64(0.07517753446351276), 0, 0, 0]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: np.float64(0.07117753446351276), 77: np.float64(0.07417753446351276), 57: np.float64(0.07517753446351276), 6: np.float64(0.048194516708945034), 49: 0, 0: 0} 

err list= [np.float64(0.4130821890265088), np.float64(0.07117753446351276), np.float64(0.07417753446351276), np.float64(0.07517753446351276), np.float64(0.048194516708945034), 0, 0]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: np.float64(0.07117753446351276), 77: np.float64(0.07417753446351276), 57: np.float64(0.07517753446351276), 6: np.float64(0.048194516708945034), 49: np.float64(0.10217753446351276), 0: 0} 

err list= [np.float64(0.4130821890265088), np.float64(0.07117753446351276), np.float64(0.07417753446351276), np.float64(0.07517753446351276), np.float64(0.048194516708945034), np.float64(0.10217753446351276), 0]
beta is  0.75 

err dic= {100: np.float64(0.4130821890265088), 84: np.float64(0.07117753446351276), 77: np.float64(0.07417753446351276), 57: np.float64(0.07517753446351276), 6: np.float64(0.048194516708945034), 49: np.float64(0.10217753446351276), 0: np.float64(0.04217753446351276)} 

err list= [np.float64(0.4130821890265088), np.float64(0.07117753446351276), np.float64(0.07417753446351276), np.float64(0.07517753446351276), np.float64(0.048194516708945034), np.float64(0.10217753446351276), np.float64(0.04217753446351276)]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2849816268365149), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: np.float64(0.07699909280888581), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2849816268365149), np.float64(0.07699909280888581), 0, 0, 0, 0, 0]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: np.float64(0.07699909280888581), 77: np.float64(0.07999909280888581), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2849816268365149), np.float64(0.07699909280888581), np.float64(0.07999909280888581), 0, 0, 0, 0]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: np.float64(0.07699909280888581), 77: np.float64(0.07999909280888581), 57: np.float64(0.08099909280888581), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2849816268365149), np.float64(0.07699909280888581), np.float64(0.07999909280888581), np.float64(0.08099909280888581), 0, 0, 0]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: np.float64(0.07699909280888581), 77: np.float64(0.07999909280888581), 57: np.float64(0.08099909280888581), 6: np.float64(0.6789770908809443), 49: 0, 0: 0} 

err list= [np.float64(0.2849816268365149), np.float64(0.07699909280888581), np.float64(0.07999909280888581), np.float64(0.08099909280888581), np.float64(0.6789770908809443), 0, 0]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: np.float64(0.07699909280888581), 77: np.float64(0.07999909280888581), 57: np.float64(0.08099909280888581), 6: np.float64(0.6789770908809443), 49: np.float64(0.10799909280888581), 0: 0} 

err list= [np.float64(0.2849816268365149), np.float64(0.07699909280888581), np.float64(0.07999909280888581), np.float64(0.08099909280888581), np.float64(0.6789770908809443), np.float64(0.10799909280888581), 0]
beta is  1 

err dic= {100: np.float64(0.2849816268365149), 84: np.float64(0.07699909280888581), 77: np.float64(0.07999909280888581), 57: np.float64(0.08099909280888581), 6: np.float64(0.6789770908809443), 49: np.float64(0.10799909280888581), 0: np.float64(0.047999092808885806)} 

err list= [np.float64(0.2849816268365149), np.float64(0.07699909280888581), np.float64(0.07999909280888581), np.float64(0.08099909280888581), np.float64(0.6789770908809443), np.float64(0.10799909280888581), np.float64(0.047999092808885806)]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: 0, 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2116326461359412), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: np.float64(0.07699965180797075), 77: 0, 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2116326461359412), np.float64(0.07699965180797075), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: np.float64(0.07699965180797075), 77: np.float64(0.07999965180797075), 57: 0, 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2116326461359412), np.float64(0.07699965180797075), np.float64(0.07999965180797075), 0, 0, 0, 0]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: np.float64(0.07699965180797075), 77: np.float64(0.07999965180797075), 57: np.float64(0.08099965180797075), 6: 0, 49: 0, 0: 0} 

err list= [np.float64(0.2116326461359412), np.float64(0.07699965180797075), np.float64(0.07999965180797075), np.float64(0.08099965180797075), 0, 0, 0]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: np.float64(0.07699965180797075), 77: np.float64(0.07999965180797075), 57: np.float64(0.08099965180797075), 6: np.float64(0.6056309051757944), 49: 0, 0: 0} 

err list= [np.float64(0.2116326461359412), np.float64(0.07699965180797075), np.float64(0.07999965180797075), np.float64(0.08099965180797075), np.float64(0.6056309051757944), 0, 0]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: np.float64(0.07699965180797075), 77: np.float64(0.07999965180797075), 57: np.float64(0.08099965180797075), 6: np.float64(0.6056309051757944), 49: np.float64(0.10799965180797075), 0: 0} 

err list= [np.float64(0.2116326461359412), np.float64(0.07699965180797075), np.float64(0.07999965180797075), np.float64(0.08099965180797075), np.float64(0.6056309051757944), np.float64(0.10799965180797075), 0]
beta is  1.25 

err dic= {100: np.float64(0.2116326461359412), 84: np.float64(0.07699965180797075), 77: np.float64(0.07999965180797075), 57: np.float64(0.08099965180797075), 6: np.float64(0.6056309051757944), 49: np.float64(0.10799965180797075), 0: np.float64(0.04799965180797075)} 

err list= [np.float64(0.2116326461359412), np.float64(0.07699965180797075), np.float64(0.07999965180797075), np.float64(0.08099965180797075), np.float64(0.6056309051757944), np.float64(0.10799965180797075), np.float64(0.04799965180797075)]
samppled assortment [4, 21, 99, 14, 63, 38]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{4: np.float64(0.14285714285714307), 21: np.float64(0.14285714285714307), 99: np.float64(0.14285714285714307), 14: np.float64(0.14285714285714307), 63: np.float64(0.14285714285714307), 38: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428577), 21: np.float64(0.03771428571428577), 99: np.float64(0.03771428571428577), 14: np.float64(0.03771428571428577), 63: np.float64(0.03771428571428577), 38: np.float64(0.03771428571428577), 0: np.float64(0.03771428571428577)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.1265085596005645), 21: np.float64(0.14558190673323881), 99: np.float64(0.14558190673323881), 14: np.float64(0.14558190673323881), 63: np.float64(0.14558190673323881), 38: np.float64(0.14558190673323881), 0: np.float64(0.14558190673323881)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.13082458558030124), 21: np.float64(0.14486256906994954), 99: np.float64(0.14486256906994954), 14: np.float64(0.14486256906994954), 63: np.float64(0.14486256906994954), 38: np.float64(0.14486256906994954), 0: np.float64(0.14486256906994954)}
choice probs for this beta: {4: np.float64(0.13082458558030124), 21: np.float64(0.14486256906994954), 99: np.float64(0.14486256906994954), 14: np.float64(0.14486256906994954), 63: np.float64(0.14486256906994954), 38: np.float64(0.14486256906994954), 0: np.float64(0.14486256906994954)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{4: np.float64(0.1428571428571429), 21: np.float64(0.1428571428571429), 99: np.float64(0.1428571428571429), 14: np.float64(0.1428571428571429), 63: np.float64(0.1428571428571429), 38: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428573), 21: np.float64(0.03771428571428573), 99: np.float64(0.03771428571428573), 14: np.float64(0.03771428571428573), 63: np.float64(0.03771428571428573), 38: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 100]
learned probs for cluster 1 

{4: np.float64(0.17850595266049235), 21: np.float64(0.1372567131282653), 99: np.float64(0.1372567131282653), 14: np.float64(0.13521048169818745), 63: np.float64(0.1372567131282653), 38: np.float64(0.1372567131282653), 0: np.float64(0.1372567131282653)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 100]
learned probs (dictionary):

probs= {4: np.float64(0.1690946668724081), 21: np.float64(0.13873522657668896), 99: np.float64(0.13873522657668896), 14: np.float64(0.1372292002441517), 63: np.float64(0.13873522657668896), 38: np.float64(0.13873522657668896), 0: np.float64(0.13873522657668896)}
choice probs for this beta: {4: np.float64(0.1690946668724081), 21: np.float64(0.13873522657668896), 99: np.float64(0.13873522657668896), 14: np.float64(0.1372292002441517), 63: np.float64(0.13873522657668896), 38: np.float64(0.13873522657668896), 0: np.float64(0.13873522657668896)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.22279070542769183), 21: np.float64(0.12953488242871825), 99: np.float64(0.12953488242871825), 14: np.float64(0.12953488242871825), 63: np.float64(0.12953488242871825), 38: np.float64(0.12953488242871825), 0: np.float64(0.12953488242871825)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.058816746232910645), 21: np.float64(0.03419720896118162), 99: np.float64(0.03419720896118162), 14: np.float64(0.03419720896118162), 63: np.float64(0.03419720896118162), 38: np.float64(0.03419720896118162), 0: np.float64(0.03419720896118162)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.2722931931076716), 21: np.float64(0.12128446781538799), 99: np.float64(0.12128446781538799), 14: np.float64(0.12128446781538799), 63: np.float64(0.12128446781538799), 38: np.float64(0.12128446781538799), 0: np.float64(0.12128446781538799)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.2592245363601569), 21: np.float64(0.12346257727330717), 99: np.float64(0.12346257727330717), 14: np.float64(0.12346257727330717), 63: np.float64(0.12346257727330717), 38: np.float64(0.12346257727330717), 0: np.float64(0.12346257727330717)}
choice probs for this beta: {4: np.float64(0.2592245363601569), 21: np.float64(0.12346257727330717), 99: np.float64(0.12346257727330717), 14: np.float64(0.12346257727330717), 63: np.float64(0.12346257727330717), 38: np.float64(0.12346257727330717), 0: np.float64(0.12346257727330717)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.43939945501121486), 21: np.float64(0.09343342416479725), 99: np.float64(0.09343342416479725), 14: np.float64(0.09343342416479725), 63: np.float64(0.09343342416479725), 38: np.float64(0.09343342416479725), 0: np.float64(0.09343342416479725)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.11600145612296073), 21: np.float64(0.024666423979506476), 99: np.float64(0.024666423979506476), 14: np.float64(0.024666423979506476), 63: np.float64(0.024666423979506476), 38: np.float64(0.024666423979506476), 0: np.float64(0.024666423979506476)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.6797960738291976), 21: np.float64(0.053367321028466745), 99: np.float64(0.053367321028466745), 14: np.float64(0.053367321028466745), 63: np.float64(0.053367321028466745), 38: np.float64(0.053367321028466745), 0: np.float64(0.053367321028466745)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.6163313664612502), 21: np.float64(0.063944772256458), 99: np.float64(0.063944772256458), 14: np.float64(0.063944772256458), 63: np.float64(0.063944772256458), 38: np.float64(0.063944772256458), 0: np.float64(0.063944772256458)}
choice probs for this beta: {4: np.float64(0.6163313664612502), 21: np.float64(0.063944772256458), 99: np.float64(0.063944772256458), 14: np.float64(0.063944772256458), 63: np.float64(0.063944772256458), 38: np.float64(0.063944772256458), 0: np.float64(0.063944772256458)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 13, 100]
learned probs for cluster 2 

{4: np.float64(0.9469343068213072), 21: np.float64(0.008844282196448719), 99: np.float64(0.008844282196448719), 14: np.float64(0.008844282196448719), 63: np.float64(0.008844282196448719), 38: np.float64(0.008844282196448719), 0: np.float64(0.008844282196448719)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 13, 100]
learned probs (dictionary):

probs= {4: np.float64(0.24999065700082512), 21: np.float64(0.002334890499862462), 99: np.float64(0.002334890499862462), 14: np.float64(0.002334890499862462), 63: np.float64(0.002334890499862462), 38: np.float64(0.002334890499862462), 0: np.float64(0.002334890499862462)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9772895989949775), 21: np.float64(0.0037850668341706385), 99: np.float64(0.0037850668341706385), 14: np.float64(0.0037850668341706385), 63: np.float64(0.0037850668341706385), 38: np.float64(0.0037850668341706385), 0: np.float64(0.0037850668341706385)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9692758018611285), 21: np.float64(0.0051206996898120515), 99: np.float64(0.0051206996898120515), 14: np.float64(0.0051206996898120515), 63: np.float64(0.0051206996898120515), 38: np.float64(0.0051206996898120515), 0: np.float64(0.0051206996898120515)}
choice probs for this beta: {4: np.float64(0.9692758018611285), 21: np.float64(0.0051206996898120515), 99: np.float64(0.0051206996898120515), 14: np.float64(0.0051206996898120515), 63: np.float64(0.0051206996898120515), 38: np.float64(0.0051206996898120515), 0: np.float64(0.0051206996898120515)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.9765680326971854), 21: np.float64(0.003905327883802409), 99: np.float64(0.003905327883802409), 14: np.float64(0.003905327883802409), 63: np.float64(0.003905327883802409), 38: np.float64(0.003905327883802409), 0: np.float64(0.003905327883802409)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.25781396063205697), 21: np.float64(0.001031006561323836), 99: np.float64(0.001031006561323836), 14: np.float64(0.001031006561323836), 63: np.float64(0.001031006561323836), 38: np.float64(0.001031006561323836), 0: np.float64(0.001031006561323836)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{4: np.float64(0.9992532236310754), 21: np.float64(0.00012446272815416656), 99: np.float64(0.00012446272815416656), 14: np.float64(0.00012446272815416656), 63: np.float64(0.00012446272815416656), 38: np.float64(0.00012446272815416656), 0: np.float64(0.00012446272815416656)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9932643332245285), 21: np.float64(0.0011226111292453027), 99: np.float64(0.0011226111292453027), 14: np.float64(0.0011226111292453027), 63: np.float64(0.0011226111292453027), 38: np.float64(0.0011226111292453027), 0: np.float64(0.0011226111292453027)}
choice probs for this beta: {4: np.float64(0.9932643332245285), 21: np.float64(0.0011226111292453027), 99: np.float64(0.0011226111292453027), 14: np.float64(0.0011226111292453027), 63: np.float64(0.0011226111292453027), 38: np.float64(0.0011226111292453027), 0: np.float64(0.0011226111292453027)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4]
learned probs for cluster 2 

{4: np.float64(0.9958509226380784), 21: np.float64(0.0006915128936536024), 99: np.float64(0.0006915128936536024), 14: np.float64(0.0006915128936536024), 63: np.float64(0.0006915128936536024), 38: np.float64(0.0006915128936536024), 0: np.float64(0.0006915128936536024)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4]
learned probs (dictionary):

probs= {4: np.float64(0.2629046435764527), 21: np.float64(0.00018255940392455106), 99: np.float64(0.00018255940392455106), 14: np.float64(0.00018255940392455106), 63: np.float64(0.00018255940392455106), 38: np.float64(0.00018255940392455106), 0: np.float64(0.00018255940392455106)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 100]
learned probs for cluster 1 

{4: np.float64(0.9914782536423196), 21: np.float64(2.795313958756123e-07), 99: np.float64(2.795313958756123e-07), 14: np.float64(0.00852034870070124), 63: np.float64(2.795313958756123e-07), 38: np.float64(2.795313958756123e-07), 0: np.float64(2.795313958756123e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9926326382571999), 21: np.float64(0.0001827651390319155), 99: np.float64(0.0001827651390319155), 14: np.float64(0.006453536047640664), 63: np.float64(0.0001827651390319155), 38: np.float64(0.0001827651390319155), 0: np.float64(0.0001827651390319155)}
choice probs for this beta: {4: np.float64(0.9926326382571999), 21: np.float64(0.0001827651390319155), 99: np.float64(0.0001827651390319155), 14: np.float64(0.006453536047640664), 63: np.float64(0.0001827651390319155), 38: np.float64(0.0001827651390319155), 0: np.float64(0.0001827651390319155)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 15, 100, 2, 4, 10]
learned probs for cluster 2 

{4: np.float64(0.999885274955843), 21: np.float64(1.9120840692757955e-05), 99: np.float64(1.9120840692757955e-05), 14: np.float64(1.9120840692757955e-05), 63: np.float64(1.9120840692757955e-05), 38: np.float64(1.9120840692757955e-05), 0: np.float64(1.9120840692757955e-05)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 15, 100, 2, 4, 10]
learned probs (dictionary):

probs= {4: np.float64(0.26396971258834256), 21: np.float64(5.0479019428881005e-06), 99: np.float64(5.0479019428881005e-06), 14: np.float64(5.0479019428881005e-06), 63: np.float64(5.0479019428881005e-06), 38: np.float64(5.0479019428881005e-06), 0: np.float64(5.0479019428881005e-06)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9999999028724906), 21: np.float64(1.6187918187443074e-08), 99: np.float64(1.6187918187443074e-08), 14: np.float64(1.6187918187443074e-08), 63: np.float64(1.6187918187443074e-08), 38: np.float64(1.6187918187443074e-08), 0: np.float64(1.6187918187443074e-08)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9999696411024956), 21: np.float64(5.059816250674058e-06), 99: np.float64(5.059816250674058e-06), 14: np.float64(5.059816250674058e-06), 63: np.float64(5.059816250674058e-06), 38: np.float64(5.059816250674058e-06), 0: np.float64(5.059816250674058e-06)}
choice probs for this beta: {4: np.float64(0.9999696411024956), 21: np.float64(5.059816250674058e-06), 99: np.float64(5.059816250674058e-06), 14: np.float64(5.059816250674058e-06), 63: np.float64(5.059816250674058e-06), 38: np.float64(5.059816250674058e-06), 0: np.float64(5.059816250674058e-06)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.10390216445949353), 21: np.float64(0.14934963925675174), 99: np.float64(0.14934963925675174), 14: np.float64(0.14934963925675174), 63: np.float64(0.14934963925675174), 38: np.float64(0.14934963925675174), 0: np.float64(0.14934963925675174)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.027430171417306293), 21: np.float64(0.03942830476378246), 99: np.float64(0.03942830476378246), 14: np.float64(0.03942830476378246), 63: np.float64(0.03942830476378246), 38: np.float64(0.03942830476378246), 0: np.float64(0.03942830476378246)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.1265085596005645), 21: np.float64(0.14558190673323881), 99: np.float64(0.14558190673323881), 14: np.float64(0.14558190673323881), 63: np.float64(0.14558190673323881), 38: np.float64(0.14558190673323881), 0: np.float64(0.14558190673323881)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.12054047128332177), 21: np.float64(0.1465765881194462), 99: np.float64(0.1465765881194462), 14: np.float64(0.1465765881194462), 63: np.float64(0.1465765881194462), 38: np.float64(0.1465765881194462), 0: np.float64(0.1465765881194462)}
choice probs for this beta: {4: np.float64(0.12054047128332177), 21: np.float64(0.1465765881194462), 99: np.float64(0.1465765881194462), 14: np.float64(0.1465765881194462), 63: np.float64(0.1465765881194462), 38: np.float64(0.1465765881194462), 0: np.float64(0.1465765881194462)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4]
learned probs for cluster 2 

{4: np.float64(0.11163176314156685), 21: np.float64(0.14806137280973894), 99: np.float64(0.14806137280973894), 14: np.float64(0.14806137280973894), 63: np.float64(0.14806137280973894), 38: np.float64(0.14806137280973894), 0: np.float64(0.14806137280973894)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4]
learned probs (dictionary):

probs= {4: np.float64(0.02947078546937365), 21: np.float64(0.03908820242177108), 99: np.float64(0.03908820242177108), 14: np.float64(0.03908820242177108), 63: np.float64(0.03908820242177108), 38: np.float64(0.03908820242177108), 0: np.float64(0.03908820242177108)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.18625817372479683), 21: np.float64(0.1356236377125339), 99: np.float64(0.1356236377125339), 14: np.float64(0.1356236377125339), 63: np.float64(0.1356236377125339), 38: np.float64(0.1356236377125339), 0: np.float64(0.1356236377125339)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.16655680133082412), 21: np.float64(0.13890719977819604), 99: np.float64(0.13890719977819604), 14: np.float64(0.13890719977819604), 63: np.float64(0.13890719977819604), 38: np.float64(0.13890719977819604), 0: np.float64(0.13890719977819604)}
choice probs for this beta: {4: np.float64(0.16655680133082412), 21: np.float64(0.13890719977819604), 99: np.float64(0.13890719977819604), 14: np.float64(0.13890719977819604), 63: np.float64(0.13890719977819604), 38: np.float64(0.13890719977819604), 0: np.float64(0.13890719977819604)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 11, 13, 100]
learned probs for cluster 2 

{4: np.float64(0.14285714285714315), 21: np.float64(0.14285714285714315), 99: np.float64(0.14285714285714315), 14: np.float64(0.14285714285714315), 63: np.float64(0.14285714285714315), 38: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 11, 13, 100]
learned probs (dictionary):

probs= {4: np.float64(0.0377142857142858), 21: np.float64(0.0377142857142858), 99: np.float64(0.0377142857142858), 14: np.float64(0.0377142857142858), 63: np.float64(0.0377142857142858), 38: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.2722931931076716), 21: np.float64(0.12128446781538799), 99: np.float64(0.12128446781538799), 14: np.float64(0.12128446781538799), 63: np.float64(0.12128446781538799), 38: np.float64(0.12128446781538799), 0: np.float64(0.12128446781538799)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.23812207584153205), 21: np.float64(0.12697965402641137), 99: np.float64(0.12697965402641137), 14: np.float64(0.12697965402641137), 63: np.float64(0.12697965402641137), 38: np.float64(0.12697965402641137), 0: np.float64(0.12697965402641137)}
choice probs for this beta: {4: np.float64(0.23812207584153205), 21: np.float64(0.12697965402641137), 99: np.float64(0.12697965402641137), 14: np.float64(0.12697965402641137), 63: np.float64(0.12697965402641137), 38: np.float64(0.12697965402641137), 0: np.float64(0.12697965402641137)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 14]
learned probs for cluster 2 

{4: np.float64(0.6903617919329245), 21: np.float64(0.026827911694641878), 99: np.float64(0.026827911694641878), 14: np.float64(0.17549864959386496), 63: np.float64(0.026827911694641878), 38: np.float64(0.026827911694641878), 0: np.float64(0.026827911694641878)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 14]
learned probs (dictionary):

probs= {4: np.float64(0.18225551307029206), 21: np.float64(0.007082568687385456), 99: np.float64(0.007082568687385456), 14: np.float64(0.04633164349278035), 63: np.float64(0.007082568687385456), 38: np.float64(0.007082568687385456), 0: np.float64(0.007082568687385456)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.8140981303510952), 21: np.float64(0.03098364494148539), 99: np.float64(0.03098364494148539), 14: np.float64(0.03098364494148539), 63: np.float64(0.03098364494148539), 38: np.float64(0.03098364494148539), 0: np.float64(0.03098364494148539)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7814317370086982), 21: np.float64(0.0298865313643187), 99: np.float64(0.0298865313643187), 14: np.float64(0.06913560616971359), 63: np.float64(0.0298865313643187), 38: np.float64(0.0298865313643187), 0: np.float64(0.0298865313643187)}
choice probs for this beta: {4: np.float64(0.7814317370086982), 21: np.float64(0.0298865313643187), 99: np.float64(0.0298865313643187), 14: np.float64(0.06913560616971359), 63: np.float64(0.0298865313643187), 38: np.float64(0.0298865313643187), 0: np.float64(0.0298865313643187)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 9]
learned probs for cluster 2 

{4: np.float64(0.14285714285714304), 21: np.float64(0.14285714285714304), 99: np.float64(0.14285714285714304), 14: np.float64(0.14285714285714304), 63: np.float64(0.14285714285714304), 38: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 9]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428576), 21: np.float64(0.03771428571428576), 99: np.float64(0.03771428571428576), 14: np.float64(0.03771428571428576), 63: np.float64(0.03771428571428576), 38: np.float64(0.03771428571428576), 0: np.float64(0.03771428571428576)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9903135381729253), 21: np.float64(0.001614410304512211), 99: np.float64(0.001614410304512211), 14: np.float64(0.001614410304512211), 63: np.float64(0.001614410304512211), 38: np.float64(0.001614410304512211), 0: np.float64(0.001614410304512211)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7665850498095589), 21: np.float64(0.038902491698406746), 99: np.float64(0.038902491698406746), 14: np.float64(0.038902491698406746), 63: np.float64(0.038902491698406746), 38: np.float64(0.038902491698406746), 0: np.float64(0.038902491698406746)}
choice probs for this beta: {4: np.float64(0.7665850498095589), 21: np.float64(0.038902491698406746), 99: np.float64(0.038902491698406746), 14: np.float64(0.038902491698406746), 63: np.float64(0.038902491698406746), 38: np.float64(0.038902491698406746), 0: np.float64(0.038902491698406746)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{4: np.float64(0.14285714285714288), 21: np.float64(0.14285714285714288), 99: np.float64(0.14285714285714288), 14: np.float64(0.14285714285714288), 63: np.float64(0.14285714285714288), 38: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428572), 21: np.float64(0.03771428571428572), 99: np.float64(0.03771428571428572), 14: np.float64(0.03771428571428572), 63: np.float64(0.03771428571428572), 38: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{4: np.float64(0.9992532236310754), 21: np.float64(0.00012446272815416656), 99: np.float64(0.00012446272815416656), 14: np.float64(0.00012446272815416656), 63: np.float64(0.00012446272815416656), 38: np.float64(0.00012446272815416656), 0: np.float64(0.00012446272815416656)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7731646583067572), 21: np.float64(0.03780589028220719), 99: np.float64(0.03780589028220719), 14: np.float64(0.03780589028220719), 63: np.float64(0.03780589028220719), 38: np.float64(0.03780589028220719), 0: np.float64(0.03780589028220719)}
choice probs for this beta: {4: np.float64(0.7731646583067572), 21: np.float64(0.03780589028220719), 99: np.float64(0.03780589028220719), 14: np.float64(0.03780589028220719), 63: np.float64(0.03780589028220719), 38: np.float64(0.03780589028220719), 0: np.float64(0.03780589028220719)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{4: np.float64(0.14285714285714282), 21: np.float64(0.14285714285714282), 99: np.float64(0.14285714285714282), 14: np.float64(0.14285714285714282), 63: np.float64(0.14285714285714282), 38: np.float64(0.14285714285714282), 0: np.float64(0.14285714285714282)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428571), 21: np.float64(0.03771428571428571), 99: np.float64(0.03771428571428571), 14: np.float64(0.03771428571428571), 63: np.float64(0.03771428571428571), 38: np.float64(0.03771428571428571), 0: np.float64(0.03771428571428571)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.999997303031824), 21: np.float64(4.4949469604345615e-07), 99: np.float64(4.4949469604345615e-07), 14: np.float64(4.4949469604345615e-07), 63: np.float64(4.4949469604345615e-07), 38: np.float64(4.4949469604345615e-07), 0: np.float64(4.4949469604345615e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7737123007457082), 21: np.float64(0.03771461654238199), 99: np.float64(0.03771461654238199), 14: np.float64(0.03771461654238199), 63: np.float64(0.03771461654238199), 38: np.float64(0.03771461654238199), 0: np.float64(0.03771461654238199)}
choice probs for this beta: {4: np.float64(0.7737123007457082), 21: np.float64(0.03771461654238199), 99: np.float64(0.03771461654238199), 14: np.float64(0.03771461654238199), 63: np.float64(0.03771461654238199), 38: np.float64(0.03771461654238199), 0: np.float64(0.03771461654238199)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 4, 5, 14]
learned probs for cluster 2 

{4: np.float64(0.8933986142800333), 21: np.float64(6.770933172429693e-07), 99: np.float64(6.770933172429693e-07), 14: np.float64(0.10659800025337982), 63: np.float64(6.770933172429693e-07), 38: np.float64(6.770933172429693e-07), 0: np.float64(6.770933172429693e-07)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 2, 4, 5, 14]
learned probs (dictionary):

probs= {4: np.float64(0.2358572341699288), 21: np.float64(1.787526357521439e-07), 99: np.float64(1.787526357521439e-07), 14: np.float64(0.02814187206689227), 63: np.float64(1.787526357521439e-07), 38: np.float64(1.787526357521439e-07), 0: np.float64(1.787526357521439e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9999997123059303), 21: np.float64(4.7949011578428604e-08), 99: np.float64(4.7949011578428604e-08), 14: np.float64(4.7949011578428604e-08), 63: np.float64(4.7949011578428604e-08), 38: np.float64(4.7949011578428604e-08), 0: np.float64(4.7949011578428604e-08)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9718570224270935), 21: np.float64(2.1404310827386735e-07), 99: np.float64(2.1404310827386735e-07), 14: np.float64(0.028141907357364795), 63: np.float64(2.1404310827386735e-07), 38: np.float64(2.1404310827386735e-07), 0: np.float64(2.1404310827386735e-07)}
choice probs for this beta: {4: np.float64(0.9718570224270935), 21: np.float64(2.1404310827386735e-07), 99: np.float64(2.1404310827386735e-07), 14: np.float64(0.028141907357364795), 63: np.float64(2.1404310827386735e-07), 38: np.float64(2.1404310827386735e-07), 0: np.float64(2.1404310827386735e-07)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 21
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 38
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 14
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 14
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 4
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 21
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 21
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 4
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 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 99
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 21
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 14
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 63
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 63
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 14
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 99
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 4
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 21
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 38
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 38
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 21
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 21
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 4
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 0
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 99
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 4
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 14
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 63
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 63
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 4
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 21
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 21
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 4
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 38
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 4
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 4
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 21
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 21
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 63
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 14
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 14
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 4
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 14
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 63
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 63
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 14
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 21
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 14
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 38
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 14
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 63
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 14
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 21
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 63
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 4
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 99
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 99
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 63
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 4
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 99
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 21
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 21
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 63
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 21
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 63
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 63
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 14
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 4
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 0
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 99
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 99
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 4
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 38
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 63
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 21
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 14
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 4
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 38
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 14
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 38
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 4
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 4
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 38
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 4
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 4
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 99
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 38
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 21
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 21
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 21
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 14
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 99
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 63
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 21
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 21
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 99
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 38
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 4
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 21
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 99
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 14
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 4
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 38
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 4
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 38
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 0
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 63
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 4
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 38
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 4
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 14
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 63
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 21
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 38
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 21
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 14
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 14
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 38
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 99
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 0
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 21
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 21
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 21
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 21
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 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 63
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 63
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 4
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 4
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 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 0
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 21
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 21
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 21
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 14
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 63
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 4
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 38
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 21
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 38
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 38
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 4
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 38
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 63
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 21
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 14
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 99
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 4
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 21
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 99
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 99
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 14
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 38
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 14
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 21
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 99
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 14
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 63
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 63
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 4
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 14
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 14
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 99
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 4
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 38
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 63
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 21
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 38
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 99
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 14
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 38
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 14
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 21
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 21
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 4
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 14
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 4
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 21
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 21
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 14
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 63
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 4
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 99
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 21
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 38
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 14
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 14
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 0
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 21
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 14
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 4
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 63
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 14
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 21
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 14
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 14
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 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 0
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 0
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 38
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 21
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 4
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 14
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 21
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 38
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 21
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 99
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 4
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 63
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 4
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 14
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 14
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 21
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 21
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 21
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 99
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 14
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 99
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 4
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 4
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 21
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 99
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 0
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 14
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 4
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 63
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 14
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 0
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 14
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 4
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 14
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 63
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 4
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 4
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 4
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 63
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 14
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 99
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 14
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 0
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 99
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 21
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 4
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 63
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 99
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 63
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 38
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 21
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 21
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 21
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 63
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 21
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 38
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 21
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 38
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 4
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 21
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 14
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 4
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 14
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 0
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 4
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 21
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 4
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 14
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 99
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 63
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 4
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 4
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 38
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 21
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 4
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 0
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 21
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 21
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 14
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 4
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 63
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 21
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 21
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 0
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 21
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 0
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 38
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 14
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 14
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 38
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 21
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 14
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 0
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 63
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 14
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 21
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 21
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 4
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 0
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 63
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 63
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 14
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 4
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 4
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 21
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 0
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 4
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 14
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 21
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 63
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 38
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 0
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 63
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 4
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 4
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 0
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 99
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 38
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 21
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 21
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 99
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 21
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 99
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 38
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 4
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 99
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 99
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 38
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 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 21
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 4
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 21
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 4
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 14
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 21
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 99
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 0
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 0
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 4
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 14
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 0
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 21
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 63
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 38
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 14
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 14
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 21
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 21
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 0
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 21
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 4
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 14
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 14
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 4
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 4
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 21
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 38
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 38
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 38
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 21
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 0
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 21
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 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 14
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 0
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 38
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 14
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 63
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 14
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 0
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 4
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 4
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 38
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 21
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 14
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 99
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 14
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 14
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 99
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 38
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 4
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 4
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 99
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 4
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 21
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 21
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 38
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 63
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 14
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 63
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 21
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 14
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 63
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 14
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 99
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 63
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 38
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 21
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 99
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 14
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 4
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 99
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 21
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 21
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 0
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 21
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 63
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 21
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 21
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 4
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 4
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 38
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 4
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 21
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 14
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 0
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 38
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 63
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 99
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 14
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 4
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 4
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 63
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 14
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 21
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 21
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 21
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 21
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 63
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 38
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 21
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 4
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 21
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 4
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 0
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 21
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 38
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 21
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 4
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 4
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 14
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 14
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 14
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 4
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 14
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 21
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 38
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 14
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 14
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 4
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 21
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 21
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 0
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 14
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 21
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 38
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 4
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 99
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 99
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 21
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 14
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 14
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 14
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 38
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 14
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 21
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 0
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 0
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 0
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 63
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 38
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 21
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 4
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 0
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 14
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 99
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 63
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 21
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 99
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 4
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 14
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 14
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 4
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 38
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 38
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 4
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 63
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 38
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 21
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 99
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 0
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 14
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 21
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 14
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 38
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 4
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 38
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 21
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 0
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 99
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 21
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 21
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 4
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 4
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 99
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 0
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 4
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 14
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 99
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 4
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 63
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 14
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 63
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 14
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 0
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 38
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 4
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 14
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 21
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 99
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 4
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 4
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 21
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 21
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 14
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 21
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 4
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 0
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 0
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 4
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 63
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 63
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 21
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 21
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 0
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 21
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 21
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 99
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 38
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 14
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 63
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 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 21
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 4
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 4
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 14
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 63
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 99
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 4
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 21
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 21
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 4
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 21
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 4
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 4
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 4
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 38
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 38
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 63
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 99
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 21
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 14
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 99
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 14
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 14
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 38
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 21
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 99
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 4
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 4
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 21
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 21
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 4
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 99
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 21
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 4
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 99
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 14
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 4
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 21
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 21
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 38
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 0
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 14
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 4
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 63
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 4
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 63
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 14
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 0
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 0
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 21
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 63
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 63
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 63
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 4
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 38
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 21
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 14
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 38
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 21
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 14
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 0
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 63
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 14
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 63
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 0
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 99
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 14
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 21
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 38
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 63
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 21
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 14
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 0
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 21
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 14
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 21
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 21
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 99
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 0
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 99
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 63
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 4
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 38
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 14
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 0
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 14
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 38
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 0
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 63
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 99
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 21
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 14
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 4
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 21
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 63
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 0
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 21
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 63
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 21
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 14
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 4
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 21
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 21
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 14
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 4
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 21
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 4
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 21
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 63
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 0
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 4
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 38
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 21
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 63
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 63
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 63
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 99
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 0
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 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 14
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 4
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 4
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 38
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 63
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 21
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 4
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 99
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 4
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 21
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 21
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 38
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 4
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 14
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 4
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 99
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 14
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 21
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 4
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 14
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 0
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 21
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 4
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 38
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 4
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 99
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 14
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 14
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 4
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 4
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 63
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 4
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 14
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 99
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 14
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 21
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 99
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 38
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 4
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 4
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 4
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 14
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 4
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 4
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 4
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 4
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 14
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 21
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 4
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 4
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 14
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 0
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 14
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 21
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 14
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 99
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 14
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 14
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 21
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 21
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 21
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 14
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 38
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 63
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 38
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 38
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 21
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 21
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 21
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 14
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 21
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 14
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 38
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 0
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 14
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 4
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 0
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 21
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 4
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 0
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 21
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 21
emperical probablities from test set: {4: 0.29, 21: 0.215, 99: 0.068, 14: 0.184, 63: 0.079, 38: 0.1, 0: 0.064}
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.16945952871667821), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: np.float64(0.06842341188055379), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.16945952871667821), np.float64(0.06842341188055379), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: np.float64(0.06842341188055379), 99: np.float64(0.0785765881194462), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.16945952871667821), np.float64(0.06842341188055379), np.float64(0.0785765881194462), 0, 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: np.float64(0.06842341188055379), 99: np.float64(0.0785765881194462), 14: np.float64(0.037423411880553786), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.16945952871667821), np.float64(0.06842341188055379), np.float64(0.0785765881194462), np.float64(0.037423411880553786), 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: np.float64(0.06842341188055379), 99: np.float64(0.0785765881194462), 14: np.float64(0.037423411880553786), 63: np.float64(0.06757658811944621), 38: 0, 0: 0} 

err list= [np.float64(0.16945952871667821), np.float64(0.06842341188055379), np.float64(0.0785765881194462), np.float64(0.037423411880553786), np.float64(0.06757658811944621), 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: np.float64(0.06842341188055379), 99: np.float64(0.0785765881194462), 14: np.float64(0.037423411880553786), 63: np.float64(0.06757658811944621), 38: np.float64(0.046576588119446205), 0: 0} 

err list= [np.float64(0.16945952871667821), np.float64(0.06842341188055379), np.float64(0.0785765881194462), np.float64(0.037423411880553786), np.float64(0.06757658811944621), np.float64(0.046576588119446205), 0]
beta is  0.025 

err dic= {4: np.float64(0.16945952871667821), 21: np.float64(0.06842341188055379), 99: np.float64(0.0785765881194462), 14: np.float64(0.037423411880553786), 63: np.float64(0.06757658811944621), 38: np.float64(0.046576588119446205), 0: np.float64(0.08257658811944621)} 

err list= [np.float64(0.16945952871667821), np.float64(0.06842341188055379), np.float64(0.0785765881194462), np.float64(0.037423411880553786), np.float64(0.06757658811944621), np.float64(0.046576588119446205), np.float64(0.08257658811944621)]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.12344319866917586), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: np.float64(0.07609280022180395), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.12344319866917586), np.float64(0.07609280022180395), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: np.float64(0.07609280022180395), 99: np.float64(0.07090719977819604), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.12344319866917586), np.float64(0.07609280022180395), np.float64(0.07090719977819604), 0, 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: np.float64(0.07609280022180395), 99: np.float64(0.07090719977819604), 14: np.float64(0.04509280022180395), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.12344319866917586), np.float64(0.07609280022180395), np.float64(0.07090719977819604), np.float64(0.04509280022180395), 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: np.float64(0.07609280022180395), 99: np.float64(0.07090719977819604), 14: np.float64(0.04509280022180395), 63: np.float64(0.059907199778196044), 38: 0, 0: 0} 

err list= [np.float64(0.12344319866917586), np.float64(0.07609280022180395), np.float64(0.07090719977819604), np.float64(0.04509280022180395), np.float64(0.059907199778196044), 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: np.float64(0.07609280022180395), 99: np.float64(0.07090719977819604), 14: np.float64(0.04509280022180395), 63: np.float64(0.059907199778196044), 38: np.float64(0.03890719977819604), 0: 0} 

err list= [np.float64(0.12344319866917586), np.float64(0.07609280022180395), np.float64(0.07090719977819604), np.float64(0.04509280022180395), np.float64(0.059907199778196044), np.float64(0.03890719977819604), 0]
beta is  0.05 

err dic= {4: np.float64(0.12344319866917586), 21: np.float64(0.07609280022180395), 99: np.float64(0.07090719977819604), 14: np.float64(0.04509280022180395), 63: np.float64(0.059907199778196044), 38: np.float64(0.03890719977819604), 0: np.float64(0.07490719977819604)} 

err list= [np.float64(0.12344319866917586), np.float64(0.07609280022180395), np.float64(0.07090719977819604), np.float64(0.04509280022180395), np.float64(0.059907199778196044), np.float64(0.03890719977819604), np.float64(0.07490719977819604)]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.051877924158467925), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: np.float64(0.08802034597358863), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.051877924158467925), np.float64(0.08802034597358863), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: np.float64(0.08802034597358863), 99: np.float64(0.058979654026411366), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.051877924158467925), np.float64(0.08802034597358863), np.float64(0.058979654026411366), 0, 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: np.float64(0.08802034597358863), 99: np.float64(0.058979654026411366), 14: np.float64(0.057020345973588626), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.051877924158467925), np.float64(0.08802034597358863), np.float64(0.058979654026411366), np.float64(0.057020345973588626), 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: np.float64(0.08802034597358863), 99: np.float64(0.058979654026411366), 14: np.float64(0.057020345973588626), 63: np.float64(0.04797965402641137), 38: 0, 0: 0} 

err list= [np.float64(0.051877924158467925), np.float64(0.08802034597358863), np.float64(0.058979654026411366), np.float64(0.057020345973588626), np.float64(0.04797965402641137), 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: np.float64(0.08802034597358863), 99: np.float64(0.058979654026411366), 14: np.float64(0.057020345973588626), 63: np.float64(0.04797965402641137), 38: np.float64(0.026979654026411365), 0: 0} 

err list= [np.float64(0.051877924158467925), np.float64(0.08802034597358863), np.float64(0.058979654026411366), np.float64(0.057020345973588626), np.float64(0.04797965402641137), np.float64(0.026979654026411365), 0]
beta is  0.1 

err dic= {4: np.float64(0.051877924158467925), 21: np.float64(0.08802034597358863), 99: np.float64(0.058979654026411366), 14: np.float64(0.057020345973588626), 63: np.float64(0.04797965402641137), 38: np.float64(0.026979654026411365), 0: np.float64(0.06297965402641137)} 

err list= [np.float64(0.051877924158467925), np.float64(0.08802034597358863), np.float64(0.058979654026411366), np.float64(0.057020345973588626), np.float64(0.04797965402641137), np.float64(0.026979654026411365), np.float64(0.06297965402641137)]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4914317370086982), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: np.float64(0.1851134686356813), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4914317370086982), np.float64(0.1851134686356813), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: np.float64(0.1851134686356813), 99: np.float64(0.038113468635681304), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4914317370086982), np.float64(0.1851134686356813), np.float64(0.038113468635681304), 0, 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: np.float64(0.1851134686356813), 99: np.float64(0.038113468635681304), 14: np.float64(0.1148643938302864), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4914317370086982), np.float64(0.1851134686356813), np.float64(0.038113468635681304), np.float64(0.1148643938302864), 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: np.float64(0.1851134686356813), 99: np.float64(0.038113468635681304), 14: np.float64(0.1148643938302864), 63: np.float64(0.0491134686356813), 38: 0, 0: 0} 

err list= [np.float64(0.4914317370086982), np.float64(0.1851134686356813), np.float64(0.038113468635681304), np.float64(0.1148643938302864), np.float64(0.0491134686356813), 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: np.float64(0.1851134686356813), 99: np.float64(0.038113468635681304), 14: np.float64(0.1148643938302864), 63: np.float64(0.0491134686356813), 38: np.float64(0.0701134686356813), 0: 0} 

err list= [np.float64(0.4914317370086982), np.float64(0.1851134686356813), np.float64(0.038113468635681304), np.float64(0.1148643938302864), np.float64(0.0491134686356813), np.float64(0.0701134686356813), 0]
beta is  0.25 

err dic= {4: np.float64(0.4914317370086982), 21: np.float64(0.1851134686356813), 99: np.float64(0.038113468635681304), 14: np.float64(0.1148643938302864), 63: np.float64(0.0491134686356813), 38: np.float64(0.0701134686356813), 0: np.float64(0.0341134686356813)} 

err list= [np.float64(0.4914317370086982), np.float64(0.1851134686356813), np.float64(0.038113468635681304), np.float64(0.1148643938302864), np.float64(0.0491134686356813), np.float64(0.0701134686356813), np.float64(0.0341134686356813)]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4765850498095589), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: np.float64(0.17609750830159326), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4765850498095589), np.float64(0.17609750830159326), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: np.float64(0.17609750830159326), 99: np.float64(0.02909750830159326), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4765850498095589), np.float64(0.17609750830159326), np.float64(0.02909750830159326), 0, 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: np.float64(0.17609750830159326), 99: np.float64(0.02909750830159326), 14: np.float64(0.14509750830159324), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4765850498095589), np.float64(0.17609750830159326), np.float64(0.02909750830159326), np.float64(0.14509750830159324), 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: np.float64(0.17609750830159326), 99: np.float64(0.02909750830159326), 14: np.float64(0.14509750830159324), 63: np.float64(0.040097508301593254), 38: 0, 0: 0} 

err list= [np.float64(0.4765850498095589), np.float64(0.17609750830159326), np.float64(0.02909750830159326), np.float64(0.14509750830159324), np.float64(0.040097508301593254), 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: np.float64(0.17609750830159326), 99: np.float64(0.02909750830159326), 14: np.float64(0.14509750830159324), 63: np.float64(0.040097508301593254), 38: np.float64(0.06109750830159326), 0: 0} 

err list= [np.float64(0.4765850498095589), np.float64(0.17609750830159326), np.float64(0.02909750830159326), np.float64(0.14509750830159324), np.float64(0.040097508301593254), np.float64(0.06109750830159326), 0]
beta is  0.5 

err dic= {4: np.float64(0.4765850498095589), 21: np.float64(0.17609750830159326), 99: np.float64(0.02909750830159326), 14: np.float64(0.14509750830159324), 63: np.float64(0.040097508301593254), 38: np.float64(0.06109750830159326), 0: np.float64(0.025097508301593255)} 

err list= [np.float64(0.4765850498095589), np.float64(0.17609750830159326), np.float64(0.02909750830159326), np.float64(0.14509750830159324), np.float64(0.040097508301593254), np.float64(0.06109750830159326), np.float64(0.025097508301593255)]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4831646583067572), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: np.float64(0.1771941097177928), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4831646583067572), np.float64(0.1771941097177928), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: np.float64(0.1771941097177928), 99: np.float64(0.030194109717792815), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4831646583067572), np.float64(0.1771941097177928), np.float64(0.030194109717792815), 0, 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: np.float64(0.1771941097177928), 99: np.float64(0.030194109717792815), 14: np.float64(0.14619410971779281), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4831646583067572), np.float64(0.1771941097177928), np.float64(0.030194109717792815), np.float64(0.14619410971779281), 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: np.float64(0.1771941097177928), 99: np.float64(0.030194109717792815), 14: np.float64(0.14619410971779281), 63: np.float64(0.04119410971779281), 38: 0, 0: 0} 

err list= [np.float64(0.4831646583067572), np.float64(0.1771941097177928), np.float64(0.030194109717792815), np.float64(0.14619410971779281), np.float64(0.04119410971779281), 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: np.float64(0.1771941097177928), 99: np.float64(0.030194109717792815), 14: np.float64(0.14619410971779281), 63: np.float64(0.04119410971779281), 38: np.float64(0.062194109717792816), 0: 0} 

err list= [np.float64(0.4831646583067572), np.float64(0.1771941097177928), np.float64(0.030194109717792815), np.float64(0.14619410971779281), np.float64(0.04119410971779281), np.float64(0.062194109717792816), 0]
beta is  0.75 

err dic= {4: np.float64(0.4831646583067572), 21: np.float64(0.1771941097177928), 99: np.float64(0.030194109717792815), 14: np.float64(0.14619410971779281), 63: np.float64(0.04119410971779281), 38: np.float64(0.062194109717792816), 0: np.float64(0.02619410971779281)} 

err list= [np.float64(0.4831646583067572), np.float64(0.1771941097177928), np.float64(0.030194109717792815), np.float64(0.14619410971779281), np.float64(0.04119410971779281), np.float64(0.062194109717792816), np.float64(0.02619410971779281)]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4837123007457082), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: np.float64(0.17728538345761802), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4837123007457082), np.float64(0.17728538345761802), 0, 0, 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: np.float64(0.17728538345761802), 99: np.float64(0.030285383457618012), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4837123007457082), np.float64(0.17728538345761802), np.float64(0.030285383457618012), 0, 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: np.float64(0.17728538345761802), 99: np.float64(0.030285383457618012), 14: np.float64(0.146285383457618), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.4837123007457082), np.float64(0.17728538345761802), np.float64(0.030285383457618012), np.float64(0.146285383457618), 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: np.float64(0.17728538345761802), 99: np.float64(0.030285383457618012), 14: np.float64(0.146285383457618), 63: np.float64(0.04128538345761801), 38: 0, 0: 0} 

err list= [np.float64(0.4837123007457082), np.float64(0.17728538345761802), np.float64(0.030285383457618012), np.float64(0.146285383457618), np.float64(0.04128538345761801), 0, 0]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: np.float64(0.17728538345761802), 99: np.float64(0.030285383457618012), 14: np.float64(0.146285383457618), 63: np.float64(0.04128538345761801), 38: np.float64(0.06228538345761801), 0: 0} 

err list= [np.float64(0.4837123007457082), np.float64(0.17728538345761802), np.float64(0.030285383457618012), np.float64(0.146285383457618), np.float64(0.04128538345761801), np.float64(0.06228538345761801), 0]
beta is  1 

err dic= {4: np.float64(0.4837123007457082), 21: np.float64(0.17728538345761802), 99: np.float64(0.030285383457618012), 14: np.float64(0.146285383457618), 63: np.float64(0.04128538345761801), 38: np.float64(0.06228538345761801), 0: np.float64(0.02628538345761801)} 

err list= [np.float64(0.4837123007457082), np.float64(0.17728538345761802), np.float64(0.030285383457618012), np.float64(0.146285383457618), np.float64(0.04128538345761801), np.float64(0.06228538345761801), np.float64(0.02628538345761801)]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: 0, 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.6818570224270935), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: np.float64(0.21499978595689173), 99: 0, 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.6818570224270935), np.float64(0.21499978595689173), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: np.float64(0.21499978595689173), 99: np.float64(0.06799978595689173), 14: 0, 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.6818570224270935), np.float64(0.21499978595689173), np.float64(0.06799978595689173), 0, 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: np.float64(0.21499978595689173), 99: np.float64(0.06799978595689173), 14: np.float64(0.1558580926426352), 63: 0, 38: 0, 0: 0} 

err list= [np.float64(0.6818570224270935), np.float64(0.21499978595689173), np.float64(0.06799978595689173), np.float64(0.1558580926426352), 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: np.float64(0.21499978595689173), 99: np.float64(0.06799978595689173), 14: np.float64(0.1558580926426352), 63: np.float64(0.07899978595689172), 38: 0, 0: 0} 

err list= [np.float64(0.6818570224270935), np.float64(0.21499978595689173), np.float64(0.06799978595689173), np.float64(0.1558580926426352), np.float64(0.07899978595689172), 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: np.float64(0.21499978595689173), 99: np.float64(0.06799978595689173), 14: np.float64(0.1558580926426352), 63: np.float64(0.07899978595689172), 38: np.float64(0.09999978595689173), 0: 0} 

err list= [np.float64(0.6818570224270935), np.float64(0.21499978595689173), np.float64(0.06799978595689173), np.float64(0.1558580926426352), np.float64(0.07899978595689172), np.float64(0.09999978595689173), 0]
beta is  1.25 

err dic= {4: np.float64(0.6818570224270935), 21: np.float64(0.21499978595689173), 99: np.float64(0.06799978595689173), 14: np.float64(0.1558580926426352), 63: np.float64(0.07899978595689172), 38: np.float64(0.09999978595689173), 0: np.float64(0.06399978595689172)} 

err list= [np.float64(0.6818570224270935), np.float64(0.21499978595689173), np.float64(0.06799978595689173), np.float64(0.1558580926426352), np.float64(0.07899978595689172), np.float64(0.09999978595689173), np.float64(0.06399978595689172)]
samppled assortment [24, 51, 25, 64, 97, 60]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs for cluster 2 

{24: np.float64(0.14285714285714327), 51: np.float64(0.14285714285714327), 25: np.float64(0.14285714285714327), 64: np.float64(0.14285714285714327), 97: np.float64(0.14285714285714327), 60: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs (dictionary):

probs= {24: np.float64(0.037714285714285825), 51: np.float64(0.037714285714285825), 25: np.float64(0.037714285714285825), 64: np.float64(0.037714285714285825), 97: np.float64(0.037714285714285825), 60: np.float64(0.037714285714285825), 0: np.float64(0.037714285714285825)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714296), 51: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 64: np.float64(0.14285714285714296), 97: np.float64(0.14285714285714296), 60: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
choice probs for this beta: {24: np.float64(0.14285714285714296), 51: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 64: np.float64(0.14285714285714296), 97: np.float64(0.14285714285714296), 60: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714435), 51: np.float64(0.14285714285714435), 25: np.float64(0.14285714285714435), 64: np.float64(0.14285714285714435), 97: np.float64(0.14285714285714435), 60: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428611), 51: np.float64(0.03771428571428611), 25: np.float64(0.03771428571428611), 64: np.float64(0.03771428571428611), 97: np.float64(0.03771428571428611), 60: np.float64(0.03771428571428611), 0: np.float64(0.03771428571428611)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714435), 51: np.float64(0.14285714285714435), 25: np.float64(0.14285714285714435), 64: np.float64(0.14285714285714435), 97: np.float64(0.14285714285714435), 60: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714435), 51: np.float64(0.14285714285714435), 25: np.float64(0.14285714285714435), 64: np.float64(0.14285714285714435), 97: np.float64(0.14285714285714435), 60: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
choice probs for this beta: {24: np.float64(0.14285714285714435), 51: np.float64(0.14285714285714435), 25: np.float64(0.14285714285714435), 64: np.float64(0.14285714285714435), 97: np.float64(0.14285714285714435), 60: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs for cluster 2 

{24: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 64: np.float64(0.1428571428571429), 97: np.float64(0.1428571428571429), 60: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428573), 51: np.float64(0.03771428571428573), 25: np.float64(0.03771428571428573), 64: np.float64(0.03771428571428573), 97: np.float64(0.03771428571428573), 60: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714315), 51: np.float64(0.14285714285714315), 25: np.float64(0.14285714285714315), 64: np.float64(0.14285714285714315), 97: np.float64(0.14285714285714315), 60: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714307), 51: np.float64(0.14285714285714307), 25: np.float64(0.14285714285714307), 64: np.float64(0.14285714285714307), 97: np.float64(0.14285714285714307), 60: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
choice probs for this beta: {24: np.float64(0.14285714285714307), 51: np.float64(0.14285714285714307), 25: np.float64(0.14285714285714307), 64: np.float64(0.14285714285714307), 97: np.float64(0.14285714285714307), 60: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{24: np.float64(0.14285714285714293), 51: np.float64(0.14285714285714293), 25: np.float64(0.14285714285714293), 64: np.float64(0.14285714285714293), 97: np.float64(0.14285714285714293), 60: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {24: np.float64(0.037714285714285735), 51: np.float64(0.037714285714285735), 25: np.float64(0.037714285714285735), 64: np.float64(0.037714285714285735), 97: np.float64(0.037714285714285735), 60: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714263), 51: np.float64(0.14285714285714263), 25: np.float64(0.14285714285714263), 64: np.float64(0.14285714285714263), 97: np.float64(0.14285714285714263), 60: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.1428571428571427), 51: np.float64(0.1428571428571427), 25: np.float64(0.1428571428571427), 64: np.float64(0.1428571428571427), 97: np.float64(0.1428571428571427), 60: np.float64(0.1428571428571427), 0: np.float64(0.1428571428571427)}
choice probs for this beta: {24: np.float64(0.1428571428571427), 51: np.float64(0.1428571428571427), 25: np.float64(0.1428571428571427), 64: np.float64(0.1428571428571427), 97: np.float64(0.1428571428571427), 60: np.float64(0.1428571428571427), 0: np.float64(0.1428571428571427)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 100]
learned probs for cluster 2 

{24: np.float64(0.14285714285714277), 51: np.float64(0.14285714285714277), 25: np.float64(0.14285714285714277), 64: np.float64(0.14285714285714277), 97: np.float64(0.14285714285714277), 60: np.float64(0.14285714285714277), 0: np.float64(0.14285714285714277)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 100]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428569), 51: np.float64(0.03771428571428569), 25: np.float64(0.03771428571428569), 64: np.float64(0.03771428571428569), 97: np.float64(0.03771428571428569), 60: np.float64(0.03771428571428569), 0: np.float64(0.03771428571428569)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714304), 51: np.float64(0.14285714285714304), 25: np.float64(0.14285714285714304), 64: np.float64(0.14285714285714304), 97: np.float64(0.14285714285714304), 60: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714296), 51: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 64: np.float64(0.14285714285714296), 97: np.float64(0.14285714285714296), 60: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
choice probs for this beta: {24: np.float64(0.14285714285714296), 51: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 64: np.float64(0.14285714285714296), 97: np.float64(0.14285714285714296), 60: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428572), 51: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 64: np.float64(0.03771428571428572), 97: np.float64(0.03771428571428572), 60: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 64: np.float64(0.1428571428571429), 97: np.float64(0.1428571428571429), 60: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 64: np.float64(0.1428571428571429), 97: np.float64(0.1428571428571429), 60: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {24: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 64: np.float64(0.1428571428571429), 97: np.float64(0.1428571428571429), 60: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428572), 51: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 64: np.float64(0.03771428571428572), 97: np.float64(0.03771428571428572), 60: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
learned probs (dictionary):

probs= {24: np.float64(0.037714285714285714), 51: np.float64(0.037714285714285714), 25: np.float64(0.037714285714285714), 64: np.float64(0.037714285714285714), 97: np.float64(0.037714285714285714), 60: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428572), 51: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 64: np.float64(0.03771428571428572), 97: np.float64(0.03771428571428572), 60: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714327), 51: np.float64(0.14285714285714327), 25: np.float64(0.14285714285714327), 64: np.float64(0.14285714285714327), 97: np.float64(0.14285714285714327), 60: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714315), 51: np.float64(0.14285714285714315), 25: np.float64(0.14285714285714315), 64: np.float64(0.14285714285714315), 97: np.float64(0.14285714285714315), 60: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
choice probs for this beta: {24: np.float64(0.14285714285714315), 51: np.float64(0.14285714285714315), 25: np.float64(0.14285714285714315), 64: np.float64(0.14285714285714315), 97: np.float64(0.14285714285714315), 60: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 4, 5, 6, 7, 10, 13, 100, 14]
learned probs for cluster 2 

{24: np.float64(0.14285714285714313), 51: np.float64(0.14285714285714313), 25: np.float64(0.14285714285714313), 64: np.float64(0.14285714285714313), 97: np.float64(0.14285714285714313), 60: np.float64(0.14285714285714313), 0: np.float64(0.14285714285714313)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 5, 6, 7, 10, 13, 100, 14]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428579), 51: np.float64(0.03771428571428579), 25: np.float64(0.03771428571428579), 64: np.float64(0.03771428571428579), 97: np.float64(0.03771428571428579), 60: np.float64(0.03771428571428579), 0: np.float64(0.03771428571428579)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714435), 51: np.float64(0.14285714285714435), 25: np.float64(0.14285714285714435), 64: np.float64(0.14285714285714435), 97: np.float64(0.14285714285714435), 60: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714401), 51: np.float64(0.14285714285714401), 25: np.float64(0.14285714285714401), 64: np.float64(0.14285714285714401), 97: np.float64(0.14285714285714401), 60: np.float64(0.14285714285714401), 0: np.float64(0.14285714285714401)}
choice probs for this beta: {24: np.float64(0.14285714285714401), 51: np.float64(0.14285714285714401), 25: np.float64(0.14285714285714401), 64: np.float64(0.14285714285714401), 97: np.float64(0.14285714285714401), 60: np.float64(0.14285714285714401), 0: np.float64(0.14285714285714401)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 11, 13, 100]
learned probs for cluster 2 

{24: np.float64(0.14285714285714315), 51: np.float64(0.14285714285714315), 25: np.float64(0.14285714285714315), 64: np.float64(0.14285714285714315), 97: np.float64(0.14285714285714315), 60: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 11, 13, 100]
learned probs (dictionary):

probs= {24: np.float64(0.0377142857142858), 51: np.float64(0.0377142857142858), 25: np.float64(0.0377142857142858), 64: np.float64(0.0377142857142858), 97: np.float64(0.0377142857142858), 60: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 64: np.float64(0.1428571428571429), 97: np.float64(0.1428571428571429), 60: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714296), 51: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 64: np.float64(0.14285714285714296), 97: np.float64(0.14285714285714296), 60: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
choice probs for this beta: {24: np.float64(0.14285714285714296), 51: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 64: np.float64(0.14285714285714296), 97: np.float64(0.14285714285714296), 60: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 14, 100, 4, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714135), 51: np.float64(0.14285714285714135), 25: np.float64(0.14285714285714135), 64: np.float64(0.14285714285714135), 97: np.float64(0.14285714285714135), 60: np.float64(0.14285714285714135), 0: np.float64(0.14285714285714135)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 14, 100, 4, 5]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428532), 51: np.float64(0.03771428571428532), 25: np.float64(0.03771428571428532), 64: np.float64(0.03771428571428532), 97: np.float64(0.03771428571428532), 60: np.float64(0.03771428571428532), 0: np.float64(0.03771428571428532)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 64: np.float64(0.1428571428571429), 97: np.float64(0.1428571428571429), 60: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.1428571428571425), 51: np.float64(0.1428571428571425), 25: np.float64(0.1428571428571425), 64: np.float64(0.1428571428571425), 97: np.float64(0.1428571428571425), 60: np.float64(0.1428571428571425), 0: np.float64(0.1428571428571425)}
choice probs for this beta: {24: np.float64(0.1428571428571425), 51: np.float64(0.1428571428571425), 25: np.float64(0.1428571428571425), 64: np.float64(0.1428571428571425), 97: np.float64(0.1428571428571425), 60: np.float64(0.1428571428571425), 0: np.float64(0.1428571428571425)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714304), 51: np.float64(0.14285714285714304), 25: np.float64(0.14285714285714304), 64: np.float64(0.14285714285714304), 97: np.float64(0.14285714285714304), 60: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428576), 51: np.float64(0.03771428571428576), 25: np.float64(0.03771428571428576), 64: np.float64(0.03771428571428576), 97: np.float64(0.03771428571428576), 60: np.float64(0.03771428571428576), 0: np.float64(0.03771428571428576)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714304), 51: np.float64(0.14285714285714304), 25: np.float64(0.14285714285714304), 64: np.float64(0.14285714285714304), 97: np.float64(0.14285714285714304), 60: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714304), 51: np.float64(0.14285714285714304), 25: np.float64(0.14285714285714304), 64: np.float64(0.14285714285714304), 97: np.float64(0.14285714285714304), 60: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
choice probs for this beta: {24: np.float64(0.14285714285714304), 51: np.float64(0.14285714285714304), 25: np.float64(0.14285714285714304), 64: np.float64(0.14285714285714304), 97: np.float64(0.14285714285714304), 60: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {24: np.float64(0.03771428571428572), 51: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 64: np.float64(0.03771428571428572), 97: np.float64(0.03771428571428572), 60: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {24: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 64: np.float64(0.14285714285714288), 97: np.float64(0.14285714285714288), 60: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 13, 100, 4]
learned probs for cluster 2 

{24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 13, 100, 4]
learned probs (dictionary):

probs= {24: np.float64(0.037714285714285714), 51: np.float64(0.037714285714285714), 25: np.float64(0.037714285714285714), 64: np.float64(0.037714285714285714), 97: np.float64(0.037714285714285714), 60: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {24: np.float64(0.037714285714285714), 51: np.float64(0.037714285714285714), 25: np.float64(0.037714285714285714), 64: np.float64(0.037714285714285714), 97: np.float64(0.037714285714285714), 60: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {24: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 64: np.float64(0.14285714285714285), 97: np.float64(0.14285714285714285), 60: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 0
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 24
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 64
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 97
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 25
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 64
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 25
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 97
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 25
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 24
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 24
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 25
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 25
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 97
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 51
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 97
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 60
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 24
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 64
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 60
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 25
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 51
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 25
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 64
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 0
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 25
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 97
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 24
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 25
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 24
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 51
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 25
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 64
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 60
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 60
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 51
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 0
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 25
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 51
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 97
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 24
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 24
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 51
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 64
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 25
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 64
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 64
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 0
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 25
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 25
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 25
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 60
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 51
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 25
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 25
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 25
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 25
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 25
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 97
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 25
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 25
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 64
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 60
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 60
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 97
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 24
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 60
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 60
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 25
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 64
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 25
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 51
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 25
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 25
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 64
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 64
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 60
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 25
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 64
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 25
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 64
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 97
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 97
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 60
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 60
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 24
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 51
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 64
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 25
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 64
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 25
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 24
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 24
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 97
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 64
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 24
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 97
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 60
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 97
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 51
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 60
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 60
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 24
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 25
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 97
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 25
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 24
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 97
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 51
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 60
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 51
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 60
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 60
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 64
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 25
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 51
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 25
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 25
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 25
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 25
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 24
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 60
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 51
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 64
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 24
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 24
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 64
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 24
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 25
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 24
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 51
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 25
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 51
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 0
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 0
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 25
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 25
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 60
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 25
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 51
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 64
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 25
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 51
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 25
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 60
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 97
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 51
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 25
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 25
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 60
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 64
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 64
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 51
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 97
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 25
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 51
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 24
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 25
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 24
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 25
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 51
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 97
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 64
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 0
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 24
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 0
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 25
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 24
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 97
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 64
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 51
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 51
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 51
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 51
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 64
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 60
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 60
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 25
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 25
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 0
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 60
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 25
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 25
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 64
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 51
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 51
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 51
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 25
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 0
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 60
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 60
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 25
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 24
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 25
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 25
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 60
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 25
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 24
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 60
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 51
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 51
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 25
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 0
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 64
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 0
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 60
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 25
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 24
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 60
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 25
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 51
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 64
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 97
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 51
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 25
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 64
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 0
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 97
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 24
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 25
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 25
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 24
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 64
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 64
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 24
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 0
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 25
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 25
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 60
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 25
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 24
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 51
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 25
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 64
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 24
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 64
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 25
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 25
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 24
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 64
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 51
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 60
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 25
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 24
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 51
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 24
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 51
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 24
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 25
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 25
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 64
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 0
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 25
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 25
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 25
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 24
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 25
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 24
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 97
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 24
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 60
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 25
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 64
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 60
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 25
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 24
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 51
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 25
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 97
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 64
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 51
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 24
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 25
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 51
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 60
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 64
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 25
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 25
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 24
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 60
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 64
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 0
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 24
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 97
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 0
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 60
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 51
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 64
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 25
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 51
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 64
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 51
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 51
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 64
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 24
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 97
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 60
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 64
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 24
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 24
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 0
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 64
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 24
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 0
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 25
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 25
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 64
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 60
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 51
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 0
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 51
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 51
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 25
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 24
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 25
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 24
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 97
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 24
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 25
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 97
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 51
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 60
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 97
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 64
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 51
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 97
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 64
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 25
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 51
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 51
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 25
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 0
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 25
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 24
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 24
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 25
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 51
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 0
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 25
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 25
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 64
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 51
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 51
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 51
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 0
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 51
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 25
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 60
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 60
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 64
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 25
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 97
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 60
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 64
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 64
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 51
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 97
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 60
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 0
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 64
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 51
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 51
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 51
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 25
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 0
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 51
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 60
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 0
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 51
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 51
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 24
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 97
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 60
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 64
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 97
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 97
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 25
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 51
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 24
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 64
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 60
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 25
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 51
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 51
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 97
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 25
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 51
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 25
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 60
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 51
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 25
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 25
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 64
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 64
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 24
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 25
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 60
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 51
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 51
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 64
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 25
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 25
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 60
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 60
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 0
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 51
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 64
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 60
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 51
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 25
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 60
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 64
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 97
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 51
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 51
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 51
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 97
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 51
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 25
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 24
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 24
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 25
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 64
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 0
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 24
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 97
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 64
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 25
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 97
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 64
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 60
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 60
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 25
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 51
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 51
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 97
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 25
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 64
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 60
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 25
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 25
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 60
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 25
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 51
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 64
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 0
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 25
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 64
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 24
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 24
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 60
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 24
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 60
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 51
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 0
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 0
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 24
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 97
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 25
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 97
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 51
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 51
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 24
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 24
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 60
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 64
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 25
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 24
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 0
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 25
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 24
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 0
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 25
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 60
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 25
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 64
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 64
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 64
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 25
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 0
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 25
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 25
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 25
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 64
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 24
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 25
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 25
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 97
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 25
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 51
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 64
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 0
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 25
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 25
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 60
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 64
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 25
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 0
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 97
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 25
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 64
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 24
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 24
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 25
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 25
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 25
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 64
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 25
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 60
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 97
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 64
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 24
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 51
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 64
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 51
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 25
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 25
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 0
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 51
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 97
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 64
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 25
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 97
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 25
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 25
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 51
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 64
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 60
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 25
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 0
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 97
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 60
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 25
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 0
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 64
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 24
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 64
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 64
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 25
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 24
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 0
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 60
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 64
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 24
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 25
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 51
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 97
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 64
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 24
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 64
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 64
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 25
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 25
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 24
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 97
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 25
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 51
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 51
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 24
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 64
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 25
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 25
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 25
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 24
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 64
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 51
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 64
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 51
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 0
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 0
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 25
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 51
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 60
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 51
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 51
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 25
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 64
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 60
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 60
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 97
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 60
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 24
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 64
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 25
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 25
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 60
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 24
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 25
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 60
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 51
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 51
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 24
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 25
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 51
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 64
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 24
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 24
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 25
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 24
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 24
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 97
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 60
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 51
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 60
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 25
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 24
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 60
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 24
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 60
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 64
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 51
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 97
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 60
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 60
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 24
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 97
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 60
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 24
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 64
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 60
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 24
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 24
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 97
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 25
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 51
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 0
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 60
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 24
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 25
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 24
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 51
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 64
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 60
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 60
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 64
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 24
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 60
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 64
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 51
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 64
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 60
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 51
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 51
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 51
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 51
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 97
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 0
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 24
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 24
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 25
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 24
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 97
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 97
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 51
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 51
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 24
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 24
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 24
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 24
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 60
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 60
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 25
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 60
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 51
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 51
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 25
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 64
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 24
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 24
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 0
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 24
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 25
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 0
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 51
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 64
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 25
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 24
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 64
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 51
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 24
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 0
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 64
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 25
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 97
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 51
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 64
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 0
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 25
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 51
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 51
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 64
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 60
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 25
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 51
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 51
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 51
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 25
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 25
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 25
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 25
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 64
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 51
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 97
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 60
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 24
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 64
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 60
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 24
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 60
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 25
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 97
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 25
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 97
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 51
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 97
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 51
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 25
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 97
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 24
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 51
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 25
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 51
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 25
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 24
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 0
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 97
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 25
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 24
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 25
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 24
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 25
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 25
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 97
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 25
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 25
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 24
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 97
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 24
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 0
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 25
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 51
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 24
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 97
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 24
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 0
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 51
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 0
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 64
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 51
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 64
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 0
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 25
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 25
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 51
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 25
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 97
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 25
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 97
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 64
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 64
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 97
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 64
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 60
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 51
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 64
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 64
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 60
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 64
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 24
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 51
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 64
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 64
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 24
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 97
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 97
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 24
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 51
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 24
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 51
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 25
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 60
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 25
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 25
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 24
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 24
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 51
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 51
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 51
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 24
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 0
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 25
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 97
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 64
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 51
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 25
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 97
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 60
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 24
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 24
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 60
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 25
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 51
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 51
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 24
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 25
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 51
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 25
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 51
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 0
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 24
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 51
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 51
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 24
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 0
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 24
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 60
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 25
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 51
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 60
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 64
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 24
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 24
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 24
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 25
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 97
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 25
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 64
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 0
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 24
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 51
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 25
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 97
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 60
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 24
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 97
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 25
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 97
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 25
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 97
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 51
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 0
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 51
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 64
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 25
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 51
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 25
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 97
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 97
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 60
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 64
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 24
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 51
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 60
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 24
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 60
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 64
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 25
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 25
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 60
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 24
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 51
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 25
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 51
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 51
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 25
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 24
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 51
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 0
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 51
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 25
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 25
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 60
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 25
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 64
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 51
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 24
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 25
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 60
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 60
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 25
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 97
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 60
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 60
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 24
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 51
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 97
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 51
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 51
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 25
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 97
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 60
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 60
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 51
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 25
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 60
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 0
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 51
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 25
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 64
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 97
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 60
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 60
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 60
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 97
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 24
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 25
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 97
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 64
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 25
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 64
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 25
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 24
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 64
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 0
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 24
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 25
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 51
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 60
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 24
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 0
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 60
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 24
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 60
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 24
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 24
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 64
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 24
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 64
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 24
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 97
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 25
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 24
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 60
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 24
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 24
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 24
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 25
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 24
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 51
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 64
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 25
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 0
emperical probablities from test set: {24: 0.198, 51: 0.161, 25: 0.226, 64: 0.13, 97: 0.089, 60: 0.12, 0: 0.076}
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856855), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: np.float64(0.01814285714285685), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856855), np.float64(0.01814285714285685), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: np.float64(0.01814285714285685), 25: np.float64(0.08314285714285685), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856855), np.float64(0.01814285714285685), np.float64(0.08314285714285685), 0, 0, 0, 0]
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: np.float64(0.01814285714285685), 25: np.float64(0.08314285714285685), 64: np.float64(0.01285714285714315), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856855), np.float64(0.01814285714285685), np.float64(0.08314285714285685), np.float64(0.01285714285714315), 0, 0, 0]
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: np.float64(0.01814285714285685), 25: np.float64(0.08314285714285685), 64: np.float64(0.01285714285714315), 97: np.float64(0.05385714285714316), 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856855), np.float64(0.01814285714285685), np.float64(0.08314285714285685), np.float64(0.01285714285714315), np.float64(0.05385714285714316), 0, 0]
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: np.float64(0.01814285714285685), 25: np.float64(0.08314285714285685), 64: np.float64(0.01285714285714315), 97: np.float64(0.05385714285714316), 60: np.float64(0.02285714285714316), 0: 0} 

err list= [np.float64(0.055142857142856855), np.float64(0.01814285714285685), np.float64(0.08314285714285685), np.float64(0.01285714285714315), np.float64(0.05385714285714316), np.float64(0.02285714285714316), 0]
beta is  0.025 

err dic= {24: np.float64(0.055142857142856855), 51: np.float64(0.01814285714285685), 25: np.float64(0.08314285714285685), 64: np.float64(0.01285714285714315), 97: np.float64(0.05385714285714316), 60: np.float64(0.02285714285714316), 0: np.float64(0.06685714285714316)} 

err list= [np.float64(0.055142857142856855), np.float64(0.01814285714285685), np.float64(0.08314285714285685), np.float64(0.01285714285714315), np.float64(0.05385714285714316), np.float64(0.02285714285714316), np.float64(0.06685714285714316)]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142855994), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: np.float64(0.01814285714285599), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142855994), np.float64(0.01814285714285599), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: np.float64(0.01814285714285599), 25: np.float64(0.08314285714285599), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142855994), np.float64(0.01814285714285599), np.float64(0.08314285714285599), 0, 0, 0, 0]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: np.float64(0.01814285714285599), 25: np.float64(0.08314285714285599), 64: np.float64(0.01285714285714401), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142855994), np.float64(0.01814285714285599), np.float64(0.08314285714285599), np.float64(0.01285714285714401), 0, 0, 0]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: np.float64(0.01814285714285599), 25: np.float64(0.08314285714285599), 64: np.float64(0.01285714285714401), 97: np.float64(0.05385714285714402), 60: 0, 0: 0} 

err list= [np.float64(0.055142857142855994), np.float64(0.01814285714285599), np.float64(0.08314285714285599), np.float64(0.01285714285714401), np.float64(0.05385714285714402), 0, 0]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: np.float64(0.01814285714285599), 25: np.float64(0.08314285714285599), 64: np.float64(0.01285714285714401), 97: np.float64(0.05385714285714402), 60: np.float64(0.02285714285714402), 0: 0} 

err list= [np.float64(0.055142857142855994), np.float64(0.01814285714285599), np.float64(0.08314285714285599), np.float64(0.01285714285714401), np.float64(0.05385714285714402), np.float64(0.02285714285714402), 0]
beta is  0.05 

err dic= {24: np.float64(0.055142857142855994), 51: np.float64(0.01814285714285599), 25: np.float64(0.08314285714285599), 64: np.float64(0.01285714285714401), 97: np.float64(0.05385714285714402), 60: np.float64(0.02285714285714402), 0: np.float64(0.06685714285714402)} 

err list= [np.float64(0.055142857142855994), np.float64(0.01814285714285599), np.float64(0.08314285714285599), np.float64(0.01285714285714401), np.float64(0.05385714285714402), np.float64(0.02285714285714402), np.float64(0.06685714285714402)]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285705), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: np.float64(0.018142857142857044), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285705), np.float64(0.018142857142857044), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: np.float64(0.018142857142857044), 25: np.float64(0.08314285714285705), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285705), np.float64(0.018142857142857044), np.float64(0.08314285714285705), 0, 0, 0, 0]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: np.float64(0.018142857142857044), 25: np.float64(0.08314285714285705), 64: np.float64(0.012857142857142956), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285705), np.float64(0.018142857142857044), np.float64(0.08314285714285705), np.float64(0.012857142857142956), 0, 0, 0]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: np.float64(0.018142857142857044), 25: np.float64(0.08314285714285705), 64: np.float64(0.012857142857142956), 97: np.float64(0.053857142857142964), 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285705), np.float64(0.018142857142857044), np.float64(0.08314285714285705), np.float64(0.012857142857142956), np.float64(0.053857142857142964), 0, 0]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: np.float64(0.018142857142857044), 25: np.float64(0.08314285714285705), 64: np.float64(0.012857142857142956), 97: np.float64(0.053857142857142964), 60: np.float64(0.022857142857142965), 0: 0} 

err list= [np.float64(0.05514285714285705), np.float64(0.018142857142857044), np.float64(0.08314285714285705), np.float64(0.012857142857142956), np.float64(0.053857142857142964), np.float64(0.022857142857142965), 0]
beta is  0.1 

err dic= {24: np.float64(0.05514285714285705), 51: np.float64(0.018142857142857044), 25: np.float64(0.08314285714285705), 64: np.float64(0.012857142857142956), 97: np.float64(0.053857142857142964), 60: np.float64(0.022857142857142965), 0: np.float64(0.06685714285714296)} 

err list= [np.float64(0.05514285714285705), np.float64(0.018142857142857044), np.float64(0.08314285714285705), np.float64(0.012857142857142956), np.float64(0.053857142857142964), np.float64(0.022857142857142965), np.float64(0.06685714285714296)]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285752), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: np.float64(0.018142857142857516), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285752), np.float64(0.018142857142857516), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: np.float64(0.018142857142857516), 25: np.float64(0.08314285714285752), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285752), np.float64(0.018142857142857516), np.float64(0.08314285714285752), 0, 0, 0, 0]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: np.float64(0.018142857142857516), 25: np.float64(0.08314285714285752), 64: np.float64(0.012857142857142484), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285752), np.float64(0.018142857142857516), np.float64(0.08314285714285752), np.float64(0.012857142857142484), 0, 0, 0]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: np.float64(0.018142857142857516), 25: np.float64(0.08314285714285752), 64: np.float64(0.012857142857142484), 97: np.float64(0.05385714285714249), 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285752), np.float64(0.018142857142857516), np.float64(0.08314285714285752), np.float64(0.012857142857142484), np.float64(0.05385714285714249), 0, 0]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: np.float64(0.018142857142857516), 25: np.float64(0.08314285714285752), 64: np.float64(0.012857142857142484), 97: np.float64(0.05385714285714249), 60: np.float64(0.022857142857142493), 0: 0} 

err list= [np.float64(0.05514285714285752), np.float64(0.018142857142857516), np.float64(0.08314285714285752), np.float64(0.012857142857142484), np.float64(0.05385714285714249), np.float64(0.022857142857142493), 0]
beta is  0.25 

err dic= {24: np.float64(0.05514285714285752), 51: np.float64(0.018142857142857516), 25: np.float64(0.08314285714285752), 64: np.float64(0.012857142857142484), 97: np.float64(0.05385714285714249), 60: np.float64(0.022857142857142493), 0: np.float64(0.06685714285714249)} 

err list= [np.float64(0.05514285714285752), np.float64(0.018142857142857516), np.float64(0.08314285714285752), np.float64(0.012857142857142484), np.float64(0.05385714285714249), np.float64(0.022857142857142493), np.float64(0.06685714285714249)]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856966), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: np.float64(0.01814285714285696), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856966), np.float64(0.01814285714285696), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: np.float64(0.01814285714285696), 25: np.float64(0.08314285714285696), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856966), np.float64(0.01814285714285696), np.float64(0.08314285714285696), 0, 0, 0, 0]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: np.float64(0.01814285714285696), 25: np.float64(0.08314285714285696), 64: np.float64(0.012857142857143039), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856966), np.float64(0.01814285714285696), np.float64(0.08314285714285696), np.float64(0.012857142857143039), 0, 0, 0]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: np.float64(0.01814285714285696), 25: np.float64(0.08314285714285696), 64: np.float64(0.012857142857143039), 97: np.float64(0.05385714285714305), 60: 0, 0: 0} 

err list= [np.float64(0.055142857142856966), np.float64(0.01814285714285696), np.float64(0.08314285714285696), np.float64(0.012857142857143039), np.float64(0.05385714285714305), 0, 0]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: np.float64(0.01814285714285696), 25: np.float64(0.08314285714285696), 64: np.float64(0.012857142857143039), 97: np.float64(0.05385714285714305), 60: np.float64(0.022857142857143048), 0: 0} 

err list= [np.float64(0.055142857142856966), np.float64(0.01814285714285696), np.float64(0.08314285714285696), np.float64(0.012857142857143039), np.float64(0.05385714285714305), np.float64(0.022857142857143048), 0]
beta is  0.5 

err dic= {24: np.float64(0.055142857142856966), 51: np.float64(0.01814285714285696), 25: np.float64(0.08314285714285696), 64: np.float64(0.012857142857143039), 97: np.float64(0.05385714285714305), 60: np.float64(0.022857142857143048), 0: np.float64(0.06685714285714305)} 

err list= [np.float64(0.055142857142856966), np.float64(0.01814285714285696), np.float64(0.08314285714285696), np.float64(0.012857142857143039), np.float64(0.05385714285714305), np.float64(0.022857142857143048), np.float64(0.06685714285714305)]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285713), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: np.float64(0.018142857142857127), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285713), np.float64(0.018142857142857127), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: np.float64(0.018142857142857127), 25: np.float64(0.08314285714285713), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285713), np.float64(0.018142857142857127), np.float64(0.08314285714285713), 0, 0, 0, 0]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: np.float64(0.018142857142857127), 25: np.float64(0.08314285714285713), 64: np.float64(0.012857142857142873), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285713), np.float64(0.018142857142857127), np.float64(0.08314285714285713), np.float64(0.012857142857142873), 0, 0, 0]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: np.float64(0.018142857142857127), 25: np.float64(0.08314285714285713), 64: np.float64(0.012857142857142873), 97: np.float64(0.05385714285714288), 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285713), np.float64(0.018142857142857127), np.float64(0.08314285714285713), np.float64(0.012857142857142873), np.float64(0.05385714285714288), 0, 0]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: np.float64(0.018142857142857127), 25: np.float64(0.08314285714285713), 64: np.float64(0.012857142857142873), 97: np.float64(0.05385714285714288), 60: np.float64(0.02285714285714288), 0: 0} 

err list= [np.float64(0.05514285714285713), np.float64(0.018142857142857127), np.float64(0.08314285714285713), np.float64(0.012857142857142873), np.float64(0.05385714285714288), np.float64(0.02285714285714288), 0]
beta is  0.75 

err dic= {24: np.float64(0.05514285714285713), 51: np.float64(0.018142857142857127), 25: np.float64(0.08314285714285713), 64: np.float64(0.012857142857142873), 97: np.float64(0.05385714285714288), 60: np.float64(0.02285714285714288), 0: np.float64(0.06685714285714288)} 

err list= [np.float64(0.05514285714285713), np.float64(0.018142857142857127), np.float64(0.08314285714285713), np.float64(0.012857142857142873), np.float64(0.05385714285714288), np.float64(0.02285714285714288), np.float64(0.06685714285714288)]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), 0, 0, 0, 0, 0]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), 0, 0, 0, 0]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), 0, 0, 0]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: np.float64(0.05385714285714285), 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), np.float64(0.05385714285714285), 0, 0]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: np.float64(0.05385714285714285), 60: np.float64(0.022857142857142854), 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), np.float64(0.05385714285714285), np.float64(0.022857142857142854), 0]
beta is  1 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: np.float64(0.05385714285714285), 60: np.float64(0.022857142857142854), 0: np.float64(0.06685714285714285)} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), np.float64(0.05385714285714285), np.float64(0.022857142857142854), np.float64(0.06685714285714285)]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: 0, 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: 0, 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: 0, 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), 0, 0, 0, 0]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: 0, 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), 0, 0, 0]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: np.float64(0.05385714285714285), 60: 0, 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), np.float64(0.05385714285714285), 0, 0]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: np.float64(0.05385714285714285), 60: np.float64(0.022857142857142854), 0: 0} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), np.float64(0.05385714285714285), np.float64(0.022857142857142854), 0]
beta is  1.25 

err dic= {24: np.float64(0.05514285714285716), 51: np.float64(0.018142857142857155), 25: np.float64(0.08314285714285716), 64: np.float64(0.012857142857142845), 97: np.float64(0.05385714285714285), 60: np.float64(0.022857142857142854), 0: np.float64(0.06685714285714285)} 

err list= [np.float64(0.05514285714285716), np.float64(0.018142857142857155), np.float64(0.08314285714285716), np.float64(0.012857142857142845), np.float64(0.05385714285714285), np.float64(0.022857142857142854), np.float64(0.06685714285714285)]
samppled assortment [4, 26, 81, 51, 69, 72]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.10390216445949353), 26: np.float64(0.14934963925675174), 81: np.float64(0.14934963925675174), 51: np.float64(0.14934963925675174), 69: np.float64(0.14934963925675174), 72: np.float64(0.14934963925675174), 0: np.float64(0.14934963925675174)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.027430171417306293), 26: np.float64(0.03942830476378246), 81: np.float64(0.03942830476378246), 51: np.float64(0.03942830476378246), 69: np.float64(0.03942830476378246), 72: np.float64(0.03942830476378246), 0: np.float64(0.03942830476378246)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.11598344523321574), 26: np.float64(0.1473360924611305), 81: np.float64(0.1473360924611305), 51: np.float64(0.1473360924611305), 69: np.float64(0.1473360924611305), 72: np.float64(0.1473360924611305), 0: np.float64(0.1473360924611305)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.11279398710895308), 26: np.float64(0.1478676688151745), 81: np.float64(0.1478676688151745), 51: np.float64(0.1478676688151745), 69: np.float64(0.1478676688151745), 72: np.float64(0.1478676688151745), 0: np.float64(0.1478676688151745)}
choice probs for this beta: {4: np.float64(0.11279398710895308), 26: np.float64(0.1478676688151745), 81: np.float64(0.1478676688151745), 51: np.float64(0.1478676688151745), 69: np.float64(0.1478676688151745), 72: np.float64(0.1478676688151745), 0: np.float64(0.1478676688151745)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 14]
learned probs for cluster 2 

{4: np.float64(0.14285714285714435), 26: np.float64(0.14285714285714435), 81: np.float64(0.14285714285714435), 51: np.float64(0.14285714285714435), 69: np.float64(0.14285714285714435), 72: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 14]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428611), 26: np.float64(0.03771428571428611), 81: np.float64(0.03771428571428611), 51: np.float64(0.03771428571428611), 69: np.float64(0.03771428571428611), 72: np.float64(0.03771428571428611), 0: np.float64(0.03771428571428611)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{4: np.float64(0.1428571428571429), 26: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 69: np.float64(0.1428571428571429), 72: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {4: np.float64(0.1428571428571433), 26: np.float64(0.1428571428571433), 81: np.float64(0.1428571428571433), 51: np.float64(0.1428571428571433), 69: np.float64(0.1428571428571433), 72: np.float64(0.1428571428571433), 0: np.float64(0.1428571428571433)}
choice probs for this beta: {4: np.float64(0.1428571428571433), 26: np.float64(0.1428571428571433), 81: np.float64(0.1428571428571433), 51: np.float64(0.1428571428571433), 69: np.float64(0.1428571428571433), 72: np.float64(0.1428571428571433), 0: np.float64(0.1428571428571433)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 5]
learned probs for cluster 2 

{4: np.float64(0.14285714285714315), 26: np.float64(0.14285714285714315), 81: np.float64(0.14285714285714315), 51: np.float64(0.14285714285714315), 69: np.float64(0.14285714285714315), 72: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 2, 5]
learned probs (dictionary):

probs= {4: np.float64(0.0377142857142858), 26: np.float64(0.0377142857142858), 81: np.float64(0.0377142857142858), 51: np.float64(0.0377142857142858), 69: np.float64(0.0377142857142858), 72: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{4: np.float64(0.2722931931076716), 26: np.float64(0.12128446781538799), 81: np.float64(0.12128446781538799), 51: np.float64(0.12128446781538799), 69: np.float64(0.12128446781538799), 72: np.float64(0.12128446781538799), 0: np.float64(0.12128446781538799)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {4: np.float64(0.23812207584153205), 26: np.float64(0.12697965402641137), 81: np.float64(0.12697965402641137), 51: np.float64(0.12697965402641137), 69: np.float64(0.12697965402641137), 72: np.float64(0.12697965402641137), 0: np.float64(0.12697965402641137)}
choice probs for this beta: {4: np.float64(0.23812207584153205), 26: np.float64(0.12697965402641137), 81: np.float64(0.12697965402641137), 51: np.float64(0.12697965402641137), 69: np.float64(0.12697965402641137), 72: np.float64(0.12697965402641137), 0: np.float64(0.12697965402641137)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 16: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 16]
learned probs for cluster 2 

{4: np.float64(0.43939945501121486), 26: np.float64(0.09343342416479725), 81: np.float64(0.09343342416479725), 51: np.float64(0.09343342416479725), 69: np.float64(0.09343342416479725), 72: np.float64(0.09343342416479725), 0: np.float64(0.09343342416479725)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 16]
learned probs (dictionary):

probs= {4: np.float64(0.11600145612296073), 26: np.float64(0.024666423979506476), 81: np.float64(0.024666423979506476), 51: np.float64(0.024666423979506476), 69: np.float64(0.024666423979506476), 72: np.float64(0.024666423979506476), 0: np.float64(0.024666423979506476)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.7318030227068635), 26: np.float64(0.04469949621552271), 81: np.float64(0.04469949621552271), 51: np.float64(0.04469949621552271), 69: np.float64(0.04469949621552271), 72: np.float64(0.04469949621552271), 0: np.float64(0.04469949621552271)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.6546084808352123), 26: np.float64(0.05756525319413119), 81: np.float64(0.05756525319413119), 51: np.float64(0.05756525319413119), 69: np.float64(0.05756525319413119), 72: np.float64(0.05756525319413119), 0: np.float64(0.05756525319413119)}
choice probs for this beta: {4: np.float64(0.6546084808352123), 26: np.float64(0.05756525319413119), 81: np.float64(0.05756525319413119), 51: np.float64(0.05756525319413119), 69: np.float64(0.05756525319413119), 72: np.float64(0.05756525319413119), 0: np.float64(0.05756525319413119)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{4: np.float64(0.1428571428571429), 26: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 51: np.float64(0.1428571428571429), 69: np.float64(0.1428571428571429), 72: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428573), 26: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 51: np.float64(0.03771428571428573), 69: np.float64(0.03771428571428573), 72: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9772895989949775), 26: np.float64(0.0037850668341706385), 81: np.float64(0.0037850668341706385), 51: np.float64(0.0037850668341706385), 69: np.float64(0.0037850668341706385), 72: np.float64(0.0037850668341706385), 0: np.float64(0.0037850668341706385)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7569994305745891), 26: np.float64(0.04050009490423532), 81: np.float64(0.04050009490423532), 51: np.float64(0.04050009490423532), 69: np.float64(0.04050009490423532), 72: np.float64(0.04050009490423532), 0: np.float64(0.04050009490423532)}
choice probs for this beta: {4: np.float64(0.7569994305745891), 26: np.float64(0.04050009490423532), 81: np.float64(0.04050009490423532), 51: np.float64(0.04050009490423532), 69: np.float64(0.04050009490423532), 72: np.float64(0.04050009490423532), 0: np.float64(0.04050009490423532)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.9735841349485691), 26: np.float64(0.004402644175238482), 81: np.float64(0.004402644175238482), 51: np.float64(0.004402644175238482), 69: np.float64(0.004402644175238482), 72: np.float64(0.004402644175238482), 0: np.float64(0.004402644175238482)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.25702621162642225), 26: np.float64(0.0011622980622629593), 81: np.float64(0.0011622980622629593), 51: np.float64(0.0011622980622629593), 69: np.float64(0.0011622980622629593), 72: np.float64(0.0011622980622629593), 0: np.float64(0.0011622980622629593)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9985849553434409), 26: np.float64(0.00023584077609326088), 81: np.float64(0.00023584077609326088), 51: np.float64(0.00023584077609326088), 69: np.float64(0.00023584077609326088), 72: np.float64(0.00023584077609326088), 0: np.float64(0.00023584077609326088)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9919847387591948), 26: np.float64(0.0013358768734675992), 81: np.float64(0.0013358768734675992), 51: np.float64(0.0013358768734675992), 69: np.float64(0.0013358768734675992), 72: np.float64(0.0013358768734675992), 0: np.float64(0.0013358768734675992)}
choice probs for this beta: {4: np.float64(0.9919847387591948), 26: np.float64(0.0013358768734675992), 81: np.float64(0.0013358768734675992), 51: np.float64(0.0013358768734675992), 69: np.float64(0.0013358768734675992), 72: np.float64(0.0013358768734675992), 0: np.float64(0.0013358768734675992)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 14, 100]
learned probs for cluster 2 

{4: np.float64(0.14285714285714285), 26: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 69: np.float64(0.14285714285714285), 72: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 11, 13, 14, 100]
learned probs (dictionary):

probs= {4: np.float64(0.037714285714285714), 26: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 51: np.float64(0.037714285714285714), 69: np.float64(0.037714285714285714), 72: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.9999848820617258), 26: np.float64(2.5196563790753457e-06), 81: np.float64(2.5196563790753457e-06), 51: np.float64(2.5196563790753457e-06), 69: np.float64(2.5196563790753457e-06), 72: np.float64(2.5196563790753457e-06), 0: np.float64(2.5196563790753457e-06)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7737031589117158), 26: np.float64(0.03771614018138071), 81: np.float64(0.03771614018138071), 51: np.float64(0.03771614018138071), 69: np.float64(0.03771614018138071), 72: np.float64(0.03771614018138071), 0: np.float64(0.03771614018138071)}
choice probs for this beta: {4: np.float64(0.7737031589117158), 26: np.float64(0.03771614018138071), 81: np.float64(0.03771614018138071), 51: np.float64(0.03771614018138071), 69: np.float64(0.03771614018138071), 72: np.float64(0.03771614018138071), 0: np.float64(0.03771614018138071)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 2, 16: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 15, 16]
learned probs for cluster 2 

{4: np.float64(0.9999999672571497), 26: np.float64(5.457141659572067e-09), 81: np.float64(5.457141659572067e-09), 51: np.float64(5.457141659572067e-09), 69: np.float64(5.457141659572067e-09), 72: np.float64(5.457141659572067e-09), 0: np.float64(5.457141659572067e-09)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 5, 15, 16]
learned probs (dictionary):

probs= {4: np.float64(0.26399999135588753), 26: np.float64(1.4406853981270258e-09), 81: np.float64(1.4406853981270258e-09), 51: np.float64(1.4406853981270258e-09), 69: np.float64(1.4406853981270258e-09), 72: np.float64(1.4406853981270258e-09), 0: np.float64(1.4406853981270258e-09)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9999997123059303), 26: np.float64(4.7949011578428604e-08), 81: np.float64(4.7949011578428604e-08), 51: np.float64(4.7949011578428604e-08), 69: np.float64(4.7949011578428604e-08), 72: np.float64(4.7949011578428604e-08), 0: np.float64(4.7949011578428604e-08)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9999997796130522), 26: np.float64(3.673115791985048e-08), 81: np.float64(3.673115791985048e-08), 51: np.float64(3.673115791985048e-08), 69: np.float64(3.673115791985048e-08), 72: np.float64(3.673115791985048e-08), 0: np.float64(3.673115791985048e-08)}
choice probs for this beta: {4: np.float64(0.9999997796130522), 26: np.float64(3.673115791985048e-08), 81: np.float64(3.673115791985048e-08), 51: np.float64(3.673115791985048e-08), 69: np.float64(3.673115791985048e-08), 72: np.float64(3.673115791985048e-08), 0: np.float64(3.673115791985048e-08)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{4: np.float64(0.14285714285714307), 26: np.float64(0.14285714285714307), 81: np.float64(0.14285714285714307), 51: np.float64(0.14285714285714307), 69: np.float64(0.14285714285714307), 72: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428577), 26: np.float64(0.03771428571428577), 81: np.float64(0.03771428571428577), 51: np.float64(0.03771428571428577), 69: np.float64(0.03771428571428577), 72: np.float64(0.03771428571428577), 0: np.float64(0.03771428571428577)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.10521250375200171), 26: np.float64(0.14913124937466668), 81: np.float64(0.14913124937466668), 51: np.float64(0.14913124937466668), 69: np.float64(0.14913124937466668), 72: np.float64(0.14913124937466668), 0: np.float64(0.14913124937466668)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.11515068847575903), 26: np.float64(0.14747488525404046), 81: np.float64(0.14747488525404046), 51: np.float64(0.14747488525404046), 69: np.float64(0.14747488525404046), 72: np.float64(0.14747488525404046), 0: np.float64(0.14747488525404046)}
choice probs for this beta: {4: np.float64(0.11515068847575903), 26: np.float64(0.14747488525404046), 81: np.float64(0.14747488525404046), 51: np.float64(0.14747488525404046), 69: np.float64(0.14747488525404046), 72: np.float64(0.14747488525404046), 0: np.float64(0.14747488525404046)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 14: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 11, 100, 5, 14]
learned probs for cluster 2 

{4: np.float64(0.14285714285714313), 26: np.float64(0.14285714285714313), 81: np.float64(0.14285714285714313), 51: np.float64(0.14285714285714313), 69: np.float64(0.14285714285714313), 72: np.float64(0.14285714285714313), 0: np.float64(0.14285714285714313)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 11, 100, 5, 14]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428579), 26: np.float64(0.03771428571428579), 81: np.float64(0.03771428571428579), 51: np.float64(0.03771428571428579), 69: np.float64(0.03771428571428579), 72: np.float64(0.03771428571428579), 0: np.float64(0.03771428571428579)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 10, 100]
learned probs for cluster 1 

{4: np.float64(0.13299650837509924), 26: np.float64(0.14450058193748366), 81: np.float64(0.14450058193748366), 51: np.float64(0.14450058193748366), 69: np.float64(0.14450058193748366), 72: np.float64(0.14450058193748366), 0: np.float64(0.14450058193748366)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 10, 100]
learned probs (dictionary):

probs= {4: np.float64(0.13559971587835884), 26: np.float64(0.14406671402027377), 81: np.float64(0.14406671402027377), 51: np.float64(0.14406671402027377), 69: np.float64(0.14406671402027377), 72: np.float64(0.14406671402027377), 0: np.float64(0.14406671402027377)}
choice probs for this beta: {4: np.float64(0.13559971587835884), 26: np.float64(0.14406671402027377), 81: np.float64(0.14406671402027377), 51: np.float64(0.14406671402027377), 69: np.float64(0.14406671402027377), 72: np.float64(0.14406671402027377), 0: np.float64(0.14406671402027377)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100, 5, 11]
learned probs for cluster 2 

{4: np.float64(0.14285714285714315), 26: np.float64(0.14285714285714315), 81: np.float64(0.14285714285714315), 51: np.float64(0.14285714285714315), 69: np.float64(0.14285714285714315), 72: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100, 5, 11]
learned probs (dictionary):

probs= {4: np.float64(0.0377142857142858), 26: np.float64(0.0377142857142858), 81: np.float64(0.0377142857142858), 51: np.float64(0.0377142857142858), 69: np.float64(0.0377142857142858), 72: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.2722931931076716), 26: np.float64(0.12128446781538799), 81: np.float64(0.12128446781538799), 51: np.float64(0.12128446781538799), 69: np.float64(0.12128446781538799), 72: np.float64(0.12128446781538799), 0: np.float64(0.12128446781538799)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.23812207584153205), 26: np.float64(0.12697965402641137), 81: np.float64(0.12697965402641137), 51: np.float64(0.12697965402641137), 69: np.float64(0.12697965402641137), 72: np.float64(0.12697965402641137), 0: np.float64(0.12697965402641137)}
choice probs for this beta: {4: np.float64(0.23812207584153205), 26: np.float64(0.12697965402641137), 81: np.float64(0.12697965402641137), 51: np.float64(0.12697965402641137), 69: np.float64(0.12697965402641137), 72: np.float64(0.12697965402641137), 0: np.float64(0.12697965402641137)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 14]
learned probs for cluster 2 

{4: np.float64(0.14285714285714263), 26: np.float64(0.14285714285714263), 81: np.float64(0.14285714285714263), 51: np.float64(0.14285714285714263), 69: np.float64(0.14285714285714263), 72: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 14]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428566), 26: np.float64(0.03771428571428566), 81: np.float64(0.03771428571428566), 51: np.float64(0.03771428571428566), 69: np.float64(0.03771428571428566), 72: np.float64(0.03771428571428566), 0: np.float64(0.03771428571428566)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 100]
learned probs for cluster 1 

{4: np.float64(0.6197889019867263), 26: np.float64(0.06336851633554565), 81: np.float64(0.06336851633554565), 51: np.float64(0.06336851633554565), 69: np.float64(0.06336851633554565), 72: np.float64(0.06336851633554565), 0: np.float64(0.06336851633554565)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 100]
learned probs (dictionary):

probs= {4: np.float64(0.4938789175765162), 26: np.float64(0.08435351373724725), 81: np.float64(0.08435351373724725), 51: np.float64(0.08435351373724725), 69: np.float64(0.08435351373724725), 72: np.float64(0.08435351373724725), 0: np.float64(0.08435351373724725)}
choice probs for this beta: {4: np.float64(0.4938789175765162), 26: np.float64(0.08435351373724725), 81: np.float64(0.08435351373724725), 51: np.float64(0.08435351373724725), 69: np.float64(0.08435351373724725), 72: np.float64(0.08435351373724725), 0: np.float64(0.08435351373724725)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 5]
learned probs for cluster 2 

{4: np.float64(0.14285714285714304), 26: np.float64(0.14285714285714304), 81: np.float64(0.14285714285714304), 51: np.float64(0.14285714285714304), 69: np.float64(0.14285714285714304), 72: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 2, 5]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428576), 26: np.float64(0.03771428571428576), 81: np.float64(0.03771428571428576), 51: np.float64(0.03771428571428576), 69: np.float64(0.03771428571428576), 72: np.float64(0.03771428571428576), 0: np.float64(0.03771428571428576)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{4: np.float64(0.9652697216896713), 26: np.float64(0.0057883797183883295), 81: np.float64(0.0057883797183883295), 51: np.float64(0.0057883797183883295), 69: np.float64(0.0057883797183883295), 72: np.float64(0.0057883797183883295), 0: np.float64(0.0057883797183883295)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7481528008778838), 26: np.float64(0.041974533187019575), 81: np.float64(0.041974533187019575), 51: np.float64(0.041974533187019575), 69: np.float64(0.041974533187019575), 72: np.float64(0.041974533187019575), 0: np.float64(0.041974533187019575)}
choice probs for this beta: {4: np.float64(0.7481528008778838), 26: np.float64(0.041974533187019575), 81: np.float64(0.041974533187019575), 51: np.float64(0.041974533187019575), 69: np.float64(0.041974533187019575), 72: np.float64(0.041974533187019575), 0: np.float64(0.041974533187019575)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100]
learned probs for cluster 2 

{4: np.float64(0.14285714285714288), 26: np.float64(0.14285714285714288), 81: np.float64(0.14285714285714288), 51: np.float64(0.14285714285714288), 69: np.float64(0.14285714285714288), 72: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100]
learned probs (dictionary):

probs= {4: np.float64(0.03771428571428572), 26: np.float64(0.03771428571428572), 81: np.float64(0.03771428571428572), 51: np.float64(0.03771428571428572), 69: np.float64(0.03771428571428572), 72: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9992532236310754), 26: np.float64(0.00012446272815416656), 81: np.float64(0.00012446272815416656), 51: np.float64(0.00012446272815416656), 69: np.float64(0.00012446272815416656), 72: np.float64(0.00012446272815416656), 0: np.float64(0.00012446272815416656)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7731646583067572), 26: np.float64(0.03780589028220719), 81: np.float64(0.03780589028220719), 51: np.float64(0.03780589028220719), 69: np.float64(0.03780589028220719), 72: np.float64(0.03780589028220719), 0: np.float64(0.03780589028220719)}
choice probs for this beta: {4: np.float64(0.7731646583067572), 26: np.float64(0.03780589028220719), 81: np.float64(0.03780589028220719), 51: np.float64(0.03780589028220719), 69: np.float64(0.03780589028220719), 72: np.float64(0.03780589028220719), 0: np.float64(0.03780589028220719)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{4: np.float64(0.9980969154049444), 26: np.float64(0.0003171807658426495), 81: np.float64(0.0003171807658426495), 51: np.float64(0.0003171807658426495), 69: np.float64(0.0003171807658426495), 72: np.float64(0.0003171807658426495), 0: np.float64(0.0003171807658426495)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {4: np.float64(0.26349758566690534), 26: np.float64(8.373572218245947e-05), 81: np.float64(8.373572218245947e-05), 51: np.float64(8.373572218245947e-05), 69: np.float64(8.373572218245947e-05), 72: np.float64(8.373572218245947e-05), 0: np.float64(8.373572218245947e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.999997303031824), 26: np.float64(4.4949469604345615e-07), 81: np.float64(4.4949469604345615e-07), 51: np.float64(4.4949469604345615e-07), 69: np.float64(4.4949469604345615e-07), 72: np.float64(4.4949469604345615e-07), 0: np.float64(4.4949469604345615e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.9994956006983278), 26: np.float64(8.406655027874746e-05), 81: np.float64(8.406655027874746e-05), 51: np.float64(8.406655027874746e-05), 69: np.float64(8.406655027874746e-05), 72: np.float64(8.406655027874746e-05), 0: np.float64(8.406655027874746e-05)}
choice probs for this beta: {4: np.float64(0.9994956006983278), 26: np.float64(8.406655027874746e-05), 81: np.float64(8.406655027874746e-05), 51: np.float64(8.406655027874746e-05), 69: np.float64(8.406655027874746e-05), 72: np.float64(8.406655027874746e-05), 0: np.float64(8.406655027874746e-05)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 5: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 11: 2, 13: 1, 14: 2, 100: 1} [8, 1, 6, 7, 10, 13, 100, 5, 9, 11, 14]
learned probs for cluster 2 

{4: np.float64(0.14285714285714285), 26: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 51: np.float64(0.14285714285714285), 69: np.float64(0.14285714285714285), 72: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 6, 7, 10, 13, 100, 5, 9, 11, 14]
learned probs (dictionary):

probs= {4: np.float64(0.037714285714285714), 26: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 51: np.float64(0.037714285714285714), 69: np.float64(0.037714285714285714), 72: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{4: np.float64(0.9999997123059303), 26: np.float64(4.7949011578428604e-08), 81: np.float64(4.7949011578428604e-08), 51: np.float64(4.7949011578428604e-08), 69: np.float64(4.7949011578428604e-08), 72: np.float64(4.7949011578428604e-08), 0: np.float64(4.7949011578428604e-08)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {4: np.float64(0.7737140739714504), 26: np.float64(0.03771432100475824), 81: np.float64(0.03771432100475824), 51: np.float64(0.03771432100475824), 69: np.float64(0.03771432100475824), 72: np.float64(0.03771432100475824), 0: np.float64(0.03771432100475824)}
choice probs for this beta: {4: np.float64(0.7737140739714504), 26: np.float64(0.03771432100475824), 81: np.float64(0.03771432100475824), 51: np.float64(0.03771432100475824), 69: np.float64(0.03771432100475824), 72: np.float64(0.03771432100475824), 0: np.float64(0.03771432100475824)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 0
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 81
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 4
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 81
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 26
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 72
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 4
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 81
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 4
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 4
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 26
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 4
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 4
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 4
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 26
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 69
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 26
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 4
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 72
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 69
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 26
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 4
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 81
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 26
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 26
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 81
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 51
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 26
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 51
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 26
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 72
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 4
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 51
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 51
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 4
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 72
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 26
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 26
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 4
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 51
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 4
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 69
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 69
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 81
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 26
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 72
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 81
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 26
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 4
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 81
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 4
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 51
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 69
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 4
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 4
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 0
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 26
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 72
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 26
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 0
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 4
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 4
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 26
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 26
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 4
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 26
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 26
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 0
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 4
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 69
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 69
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 26
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 81
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 72
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 81
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 81
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 51
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 72
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 4
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 4
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 51
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 26
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 51
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 4
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 81
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 4
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 69
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 69
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 4
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 51
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 72
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 51
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 4
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 51
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 26
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 26
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 72
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 81
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 51
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 51
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 26
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 72
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 51
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 26
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 26
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 26
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 72
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 4
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 72
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 26
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 26
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 4
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 26
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 69
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 72
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 26
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 4
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 81
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 26
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 0
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 26
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 26
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 0
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 72
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 81
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 72
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 81
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 81
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 69
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 26
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 26
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 26
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 51
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 51
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 4
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 51
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 51
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 69
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 69
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 72
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 4
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 72
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 72
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 51
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 72
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 26
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 51
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 69
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 69
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 26
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 4
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 26
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 0
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 4
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 72
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 4
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 26
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 51
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 51
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 69
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 26
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 26
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 26
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 69
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 4
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 81
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 26
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 69
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 69
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 51
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 26
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 0
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 72
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 26
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 4
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 26
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 4
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 4
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 0
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 72
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 26
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 72
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 72
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 26
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 72
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 0
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 26
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 26
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 81
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 0
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 26
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 26
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 81
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 0
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 72
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 72
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 4
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 69
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 4
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 81
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 69
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 26
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 4
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 69
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 26
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 51
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 4
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 26
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 26
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 26
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 69
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 4
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 81
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 72
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 26
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 69
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 26
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 26
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 26
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 81
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 0
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 26
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 81
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 26
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 51
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 51
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 81
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 72
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 51
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 51
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 51
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 69
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 72
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 69
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 72
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 4
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 26
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 51
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 69
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 4
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 26
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 0
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 26
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 81
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 72
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 26
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 51
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 4
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 26
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 4
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 69
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 4
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 4
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 26
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 51
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 51
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 0
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 4
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 26
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 81
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 72
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 81
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 26
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 4
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 51
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 69
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 51
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 0
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 0
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 26
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 69
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 51
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 51
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 26
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 4
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 4
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 69
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 4
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 26
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 81
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 26
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 72
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 51
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 51
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 69
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 72
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 4
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 72
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 0
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 26
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 81
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 26
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 51
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 4
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 4
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 51
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 51
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 26
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 51
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 51
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 51
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 51
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 51
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 51
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 51
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 81
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 0
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 26
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 72
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 26
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 72
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 26
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 69
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 81
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 72
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 26
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 4
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 51
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 26
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 26
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 0
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 51
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 69
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 26
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 4
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 4
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 69
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 4
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 4
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 51
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 26
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 4
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 0
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 26
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 26
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 69
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 4
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 51
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 4
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 51
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 26
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 4
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 81
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 81
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 51
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 51
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 0
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 51
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 51
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 69
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 26
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 4
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 26
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 26
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 72
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 81
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 51
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 51
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 26
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 26
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 4
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 81
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 4
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 26
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 26
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 26
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 81
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 4
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 51
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 26
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 69
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 0
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 0
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 0
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 26
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 26
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 4
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 4
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 72
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 81
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 26
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 26
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 69
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 72
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 26
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 51
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 72
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 69
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 26
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 72
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 0
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 0
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 69
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 26
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 4
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 51
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 4
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 4
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 0
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 72
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 26
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 26
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 51
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 0
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 4
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 26
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 0
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 69
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 0
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 51
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 51
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 0
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 51
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 26
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 72
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 0
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 26
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 72
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 26
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 81
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 26
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 69
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 72
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 81
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 26
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 26
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 4
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 26
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 4
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 26
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 81
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 51
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 26
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 4
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 69
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 4
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 26
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 51
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 69
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 26
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 4
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 72
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 72
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 0
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 69
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 26
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 81
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 81
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 4
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 26
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 26
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 26
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 69
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 72
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 26
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 0
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 72
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 69
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 26
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 81
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 0
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 81
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 26
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 26
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 51
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 26
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 72
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 69
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 26
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 69
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 0
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 72
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 51
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 4
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 4
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 72
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 0
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 4
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 69
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 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 51
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 69
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 4
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 69
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 51
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 69
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 69
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 72
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 4
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 26
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 26
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 72
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 81
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 51
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 26
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 72
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 4
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 69
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 26
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 51
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 69
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 69
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 69
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 4
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 26
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 26
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 69
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 0
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 26
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 0
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 4
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 51
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 69
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 51
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 0
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 51
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 72
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 51
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 72
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 69
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 0
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 4
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 4
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 4
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 4
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 69
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 0
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 4
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 26
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 4
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 26
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 26
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 4
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 0
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 26
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 51
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 69
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 26
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 72
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 51
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 81
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 26
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 51
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 81
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 26
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 26
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 72
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 26
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 0
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 81
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 26
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 4
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 4
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 26
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 4
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 72
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 72
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 51
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 26
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 81
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 81
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 26
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 81
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 26
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 4
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 51
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 51
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 26
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 4
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 26
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 4
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 81
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 51
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 26
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 26
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 26
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 51
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 4
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 81
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 69
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 26
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 51
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 26
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 51
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 72
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 26
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 51
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 26
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 4
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 72
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 81
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 26
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 4
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 72
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 26
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 72
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 26
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 51
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 26
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 26
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 51
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 81
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 26
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 26
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 72
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 51
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 51
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 4
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 0
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 26
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 0
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 4
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 69
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 81
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 26
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 81
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 81
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 26
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 51
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 81
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 72
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 4
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 4
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 72
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 4
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 26
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 72
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 0
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 81
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 51
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 72
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 72
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 69
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 72
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 26
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 26
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 81
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 4
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 69
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 4
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 26
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 26
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 4
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 4
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 26
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 26
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 4
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 26
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 26
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 51
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 51
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 26
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 81
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 51
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 0
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 51
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 26
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 26
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 26
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 0
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 4
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 51
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 51
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 26
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 69
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 72
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 72
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 26
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 51
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 51
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 26
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 72
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 26
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 69
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 81
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 51
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 51
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 72
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 26
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 51
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 4
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 51
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 81
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 26
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 4
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 4
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 26
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 0
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 69
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 72
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 4
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 26
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 72
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 72
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 4
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 26
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 26
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 69
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 69
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 51
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 81
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 0
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 26
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 72
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 4
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 72
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 26
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 26
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 0
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 26
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 51
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 51
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 72
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 51
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 51
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 26
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 4
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 4
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 0
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 72
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 69
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 4
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 26
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 51
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 4
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 26
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 4
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 26
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 51
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 26
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 26
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 51
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 81
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 26
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 26
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 72
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 26
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 51
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 0
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 81
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 4
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 26
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 69
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 26
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 51
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 4
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 4
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 72
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 0
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 81
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 72
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 81
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 51
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 51
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 72
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 4
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 81
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 26
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 4
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 69
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 4
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 4
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 26
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 26
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 4
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 81
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 72
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 26
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 0
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 81
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 0
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 0
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 69
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 72
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 69
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 51
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 72
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 26
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 26
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 69
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 26
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 26
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 26
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 81
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 51
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 26
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 0
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 72
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 26
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 72
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 4
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 72
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 0
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 0
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 69
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 26
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 26
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 0
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 26
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 4
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 51
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 72
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 72
emperical probablities from test set: {4: 0.327, 26: 0.223, 81: 0.077, 51: 0.124, 69: 0.08, 72: 0.099, 0: 0.07}
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.21184931152424097), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: np.float64(0.07552511474595955), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.21184931152424097), np.float64(0.07552511474595955), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: np.float64(0.07552511474595955), 81: np.float64(0.07047488525404046), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.21184931152424097), np.float64(0.07552511474595955), np.float64(0.07047488525404046), 0, 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: np.float64(0.07552511474595955), 81: np.float64(0.07047488525404046), 51: np.float64(0.023474885254040456), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.21184931152424097), np.float64(0.07552511474595955), np.float64(0.07047488525404046), np.float64(0.023474885254040456), 0, 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: np.float64(0.07552511474595955), 81: np.float64(0.07047488525404046), 51: np.float64(0.023474885254040456), 69: np.float64(0.06747488525404045), 72: 0, 0: 0} 

err list= [np.float64(0.21184931152424097), np.float64(0.07552511474595955), np.float64(0.07047488525404046), np.float64(0.023474885254040456), np.float64(0.06747488525404045), 0, 0]
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: np.float64(0.07552511474595955), 81: np.float64(0.07047488525404046), 51: np.float64(0.023474885254040456), 69: np.float64(0.06747488525404045), 72: np.float64(0.04847488525404045), 0: 0} 

err list= [np.float64(0.21184931152424097), np.float64(0.07552511474595955), np.float64(0.07047488525404046), np.float64(0.023474885254040456), np.float64(0.06747488525404045), np.float64(0.04847488525404045), 0]
beta is  0.025 

err dic= {4: np.float64(0.21184931152424097), 26: np.float64(0.07552511474595955), 81: np.float64(0.07047488525404046), 51: np.float64(0.023474885254040456), 69: np.float64(0.06747488525404045), 72: np.float64(0.04847488525404045), 0: np.float64(0.07747488525404045)} 

err list= [np.float64(0.21184931152424097), np.float64(0.07552511474595955), np.float64(0.07047488525404046), np.float64(0.023474885254040456), np.float64(0.06747488525404045), np.float64(0.04847488525404045), np.float64(0.07747488525404045)]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.19140028412164117), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: np.float64(0.07893328597972624), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.19140028412164117), np.float64(0.07893328597972624), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: np.float64(0.07893328597972624), 81: np.float64(0.06706671402027377), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.19140028412164117), np.float64(0.07893328597972624), np.float64(0.06706671402027377), 0, 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: np.float64(0.07893328597972624), 81: np.float64(0.06706671402027377), 51: np.float64(0.020066714020273768), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.19140028412164117), np.float64(0.07893328597972624), np.float64(0.06706671402027377), np.float64(0.020066714020273768), 0, 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: np.float64(0.07893328597972624), 81: np.float64(0.06706671402027377), 51: np.float64(0.020066714020273768), 69: np.float64(0.06406671402027377), 72: 0, 0: 0} 

err list= [np.float64(0.19140028412164117), np.float64(0.07893328597972624), np.float64(0.06706671402027377), np.float64(0.020066714020273768), np.float64(0.06406671402027377), 0, 0]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: np.float64(0.07893328597972624), 81: np.float64(0.06706671402027377), 51: np.float64(0.020066714020273768), 69: np.float64(0.06406671402027377), 72: np.float64(0.04506671402027376), 0: 0} 

err list= [np.float64(0.19140028412164117), np.float64(0.07893328597972624), np.float64(0.06706671402027377), np.float64(0.020066714020273768), np.float64(0.06406671402027377), np.float64(0.04506671402027376), 0]
beta is  0.05 

err dic= {4: np.float64(0.19140028412164117), 26: np.float64(0.07893328597972624), 81: np.float64(0.06706671402027377), 51: np.float64(0.020066714020273768), 69: np.float64(0.06406671402027377), 72: np.float64(0.04506671402027376), 0: np.float64(0.07406671402027376)} 

err list= [np.float64(0.19140028412164117), np.float64(0.07893328597972624), np.float64(0.06706671402027377), np.float64(0.020066714020273768), np.float64(0.06406671402027377), np.float64(0.04506671402027376), np.float64(0.07406671402027376)]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.08887792415846796), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: np.float64(0.09602034597358863), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.08887792415846796), np.float64(0.09602034597358863), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: np.float64(0.09602034597358863), 81: np.float64(0.04997965402641137), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.08887792415846796), np.float64(0.09602034597358863), np.float64(0.04997965402641137), 0, 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: np.float64(0.09602034597358863), 81: np.float64(0.04997965402641137), 51: np.float64(0.0029796540264113713), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.08887792415846796), np.float64(0.09602034597358863), np.float64(0.04997965402641137), np.float64(0.0029796540264113713), 0, 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: np.float64(0.09602034597358863), 81: np.float64(0.04997965402641137), 51: np.float64(0.0029796540264113713), 69: np.float64(0.04697965402641137), 72: 0, 0: 0} 

err list= [np.float64(0.08887792415846796), np.float64(0.09602034597358863), np.float64(0.04997965402641137), np.float64(0.0029796540264113713), np.float64(0.04697965402641137), 0, 0]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: np.float64(0.09602034597358863), 81: np.float64(0.04997965402641137), 51: np.float64(0.0029796540264113713), 69: np.float64(0.04697965402641137), 72: np.float64(0.027979654026411366), 0: 0} 

err list= [np.float64(0.08887792415846796), np.float64(0.09602034597358863), np.float64(0.04997965402641137), np.float64(0.0029796540264113713), np.float64(0.04697965402641137), np.float64(0.027979654026411366), 0]
beta is  0.1 

err dic= {4: np.float64(0.08887792415846796), 26: np.float64(0.09602034597358863), 81: np.float64(0.04997965402641137), 51: np.float64(0.0029796540264113713), 69: np.float64(0.04697965402641137), 72: np.float64(0.027979654026411366), 0: np.float64(0.056979654026411364)} 

err list= [np.float64(0.08887792415846796), np.float64(0.09602034597358863), np.float64(0.04997965402641137), np.float64(0.0029796540264113713), np.float64(0.04697965402641137), np.float64(0.027979654026411366), np.float64(0.056979654026411364)]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.16687891757651618), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: np.float64(0.13864648626275275), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.16687891757651618), np.float64(0.13864648626275275), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: np.float64(0.13864648626275275), 81: np.float64(0.007353513737247255), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.16687891757651618), np.float64(0.13864648626275275), np.float64(0.007353513737247255), 0, 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: np.float64(0.13864648626275275), 81: np.float64(0.007353513737247255), 51: np.float64(0.039646486262752745), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.16687891757651618), np.float64(0.13864648626275275), np.float64(0.007353513737247255), np.float64(0.039646486262752745), 0, 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: np.float64(0.13864648626275275), 81: np.float64(0.007353513737247255), 51: np.float64(0.039646486262752745), 69: np.float64(0.004353513737247253), 72: 0, 0: 0} 

err list= [np.float64(0.16687891757651618), np.float64(0.13864648626275275), np.float64(0.007353513737247255), np.float64(0.039646486262752745), np.float64(0.004353513737247253), 0, 0]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: np.float64(0.13864648626275275), 81: np.float64(0.007353513737247255), 51: np.float64(0.039646486262752745), 69: np.float64(0.004353513737247253), 72: np.float64(0.01464648626275275), 0: 0} 

err list= [np.float64(0.16687891757651618), np.float64(0.13864648626275275), np.float64(0.007353513737247255), np.float64(0.039646486262752745), np.float64(0.004353513737247253), np.float64(0.01464648626275275), 0]
beta is  0.25 

err dic= {4: np.float64(0.16687891757651618), 26: np.float64(0.13864648626275275), 81: np.float64(0.007353513737247255), 51: np.float64(0.039646486262752745), 69: np.float64(0.004353513737247253), 72: np.float64(0.01464648626275275), 0: np.float64(0.014353513737247248)} 

err list= [np.float64(0.16687891757651618), np.float64(0.13864648626275275), np.float64(0.007353513737247255), np.float64(0.039646486262752745), np.float64(0.004353513737247253), np.float64(0.01464648626275275), np.float64(0.014353513737247248)]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4211528008778838), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: np.float64(0.18102546681298043), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4211528008778838), np.float64(0.18102546681298043), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: np.float64(0.18102546681298043), 81: np.float64(0.035025466812980424), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4211528008778838), np.float64(0.18102546681298043), np.float64(0.035025466812980424), 0, 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: np.float64(0.18102546681298043), 81: np.float64(0.035025466812980424), 51: np.float64(0.08202546681298042), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4211528008778838), np.float64(0.18102546681298043), np.float64(0.035025466812980424), np.float64(0.08202546681298042), 0, 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: np.float64(0.18102546681298043), 81: np.float64(0.035025466812980424), 51: np.float64(0.08202546681298042), 69: np.float64(0.03802546681298043), 72: 0, 0: 0} 

err list= [np.float64(0.4211528008778838), np.float64(0.18102546681298043), np.float64(0.035025466812980424), np.float64(0.08202546681298042), np.float64(0.03802546681298043), 0, 0]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: np.float64(0.18102546681298043), 81: np.float64(0.035025466812980424), 51: np.float64(0.08202546681298042), 69: np.float64(0.03802546681298043), 72: np.float64(0.05702546681298043), 0: 0} 

err list= [np.float64(0.4211528008778838), np.float64(0.18102546681298043), np.float64(0.035025466812980424), np.float64(0.08202546681298042), np.float64(0.03802546681298043), np.float64(0.05702546681298043), 0]
beta is  0.5 

err dic= {4: np.float64(0.4211528008778838), 26: np.float64(0.18102546681298043), 81: np.float64(0.035025466812980424), 51: np.float64(0.08202546681298042), 69: np.float64(0.03802546681298043), 72: np.float64(0.05702546681298043), 0: np.float64(0.028025466812980432)} 

err list= [np.float64(0.4211528008778838), np.float64(0.18102546681298043), np.float64(0.035025466812980424), np.float64(0.08202546681298042), np.float64(0.03802546681298043), np.float64(0.05702546681298043), np.float64(0.028025466812980432)]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.44616465830675717), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: np.float64(0.18519410971779282), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.44616465830675717), np.float64(0.18519410971779282), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: np.float64(0.18519410971779282), 81: np.float64(0.03919410971779281), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.44616465830675717), np.float64(0.18519410971779282), np.float64(0.03919410971779281), 0, 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: np.float64(0.18519410971779282), 81: np.float64(0.03919410971779281), 51: np.float64(0.08619410971779282), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.44616465830675717), np.float64(0.18519410971779282), np.float64(0.03919410971779281), np.float64(0.08619410971779282), 0, 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: np.float64(0.18519410971779282), 81: np.float64(0.03919410971779281), 51: np.float64(0.08619410971779282), 69: np.float64(0.04219410971779281), 72: 0, 0: 0} 

err list= [np.float64(0.44616465830675717), np.float64(0.18519410971779282), np.float64(0.03919410971779281), np.float64(0.08619410971779282), np.float64(0.04219410971779281), 0, 0]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: np.float64(0.18519410971779282), 81: np.float64(0.03919410971779281), 51: np.float64(0.08619410971779282), 69: np.float64(0.04219410971779281), 72: np.float64(0.061194109717792815), 0: 0} 

err list= [np.float64(0.44616465830675717), np.float64(0.18519410971779282), np.float64(0.03919410971779281), np.float64(0.08619410971779282), np.float64(0.04219410971779281), np.float64(0.061194109717792815), 0]
beta is  0.75 

err dic= {4: np.float64(0.44616465830675717), 26: np.float64(0.18519410971779282), 81: np.float64(0.03919410971779281), 51: np.float64(0.08619410971779282), 69: np.float64(0.04219410971779281), 72: np.float64(0.061194109717792815), 0: np.float64(0.03219410971779282)} 

err list= [np.float64(0.44616465830675717), np.float64(0.18519410971779282), np.float64(0.03919410971779281), np.float64(0.08619410971779282), np.float64(0.04219410971779281), np.float64(0.061194109717792815), np.float64(0.03219410971779282)]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.6724956006983278), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: np.float64(0.22291593344972124), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.6724956006983278), np.float64(0.22291593344972124), 0, 0, 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: np.float64(0.22291593344972124), 81: np.float64(0.07691593344972125), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.6724956006983278), np.float64(0.22291593344972124), np.float64(0.07691593344972125), 0, 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: np.float64(0.22291593344972124), 81: np.float64(0.07691593344972125), 51: np.float64(0.12391593344972125), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.6724956006983278), np.float64(0.22291593344972124), np.float64(0.07691593344972125), np.float64(0.12391593344972125), 0, 0, 0]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: np.float64(0.22291593344972124), 81: np.float64(0.07691593344972125), 51: np.float64(0.12391593344972125), 69: np.float64(0.07991593344972125), 72: 0, 0: 0} 

err list= [np.float64(0.6724956006983278), np.float64(0.22291593344972124), np.float64(0.07691593344972125), np.float64(0.12391593344972125), np.float64(0.07991593344972125), 0, 0]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: np.float64(0.22291593344972124), 81: np.float64(0.07691593344972125), 51: np.float64(0.12391593344972125), 69: np.float64(0.07991593344972125), 72: np.float64(0.09891593344972126), 0: 0} 

err list= [np.float64(0.6724956006983278), np.float64(0.22291593344972124), np.float64(0.07691593344972125), np.float64(0.12391593344972125), np.float64(0.07991593344972125), np.float64(0.09891593344972126), 0]
beta is  1 

err dic= {4: np.float64(0.6724956006983278), 26: np.float64(0.22291593344972124), 81: np.float64(0.07691593344972125), 51: np.float64(0.12391593344972125), 69: np.float64(0.07991593344972125), 72: np.float64(0.09891593344972126), 0: np.float64(0.06991593344972126)} 

err list= [np.float64(0.6724956006983278), np.float64(0.22291593344972124), np.float64(0.07691593344972125), np.float64(0.12391593344972125), np.float64(0.07991593344972125), np.float64(0.09891593344972126), np.float64(0.06991593344972126)]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: 0, 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4467140739714504), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: np.float64(0.18528567899524176), 81: 0, 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4467140739714504), np.float64(0.18528567899524176), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: np.float64(0.18528567899524176), 81: np.float64(0.03928567899524176), 51: 0, 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4467140739714504), np.float64(0.18528567899524176), np.float64(0.03928567899524176), 0, 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: np.float64(0.18528567899524176), 81: np.float64(0.03928567899524176), 51: np.float64(0.08628567899524175), 69: 0, 72: 0, 0: 0} 

err list= [np.float64(0.4467140739714504), np.float64(0.18528567899524176), np.float64(0.03928567899524176), np.float64(0.08628567899524175), 0, 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: np.float64(0.18528567899524176), 81: np.float64(0.03928567899524176), 51: np.float64(0.08628567899524175), 69: np.float64(0.042285678995241764), 72: 0, 0: 0} 

err list= [np.float64(0.4467140739714504), np.float64(0.18528567899524176), np.float64(0.03928567899524176), np.float64(0.08628567899524175), np.float64(0.042285678995241764), 0, 0]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: np.float64(0.18528567899524176), 81: np.float64(0.03928567899524176), 51: np.float64(0.08628567899524175), 69: np.float64(0.042285678995241764), 72: np.float64(0.06128567899524177), 0: 0} 

err list= [np.float64(0.4467140739714504), np.float64(0.18528567899524176), np.float64(0.03928567899524176), np.float64(0.08628567899524175), np.float64(0.042285678995241764), np.float64(0.06128567899524177), 0]
beta is  1.25 

err dic= {4: np.float64(0.4467140739714504), 26: np.float64(0.18528567899524176), 81: np.float64(0.03928567899524176), 51: np.float64(0.08628567899524175), 69: np.float64(0.042285678995241764), 72: np.float64(0.06128567899524177), 0: np.float64(0.03228567899524177)} 

err list= [np.float64(0.4467140739714504), np.float64(0.18528567899524176), np.float64(0.03928567899524176), np.float64(0.08628567899524175), np.float64(0.042285678995241764), np.float64(0.06128567899524177), np.float64(0.03228567899524177)]
samppled assortment [48, 59, 9, 81, 55, 91]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{48: np.float64(0.14285714285714327), 59: np.float64(0.14285714285714327), 9: np.float64(0.14285714285714327), 81: np.float64(0.14285714285714327), 55: np.float64(0.14285714285714327), 91: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {48: np.float64(0.037714285714285825), 59: np.float64(0.037714285714285825), 9: np.float64(0.037714285714285825), 81: np.float64(0.037714285714285825), 55: np.float64(0.037714285714285825), 91: np.float64(0.037714285714285825), 0: np.float64(0.037714285714285825)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{48: np.float64(0.1473281182227658), 59: np.float64(0.1473281182227658), 9: np.float64(0.11603129066340358), 81: np.float64(0.1473281182227658), 55: np.float64(0.1473281182227658), 91: np.float64(0.1473281182227658), 0: np.float64(0.1473281182227658)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {48: np.float64(0.14614778072624146), 59: np.float64(0.14614778072624146), 9: np.float64(0.12311331564255086), 81: np.float64(0.14614778072624146), 55: np.float64(0.14614778072624146), 91: np.float64(0.14614778072624146), 0: np.float64(0.14614778072624146)}
choice probs for this beta: {48: np.float64(0.14614778072624146), 59: np.float64(0.14614778072624146), 9: np.float64(0.12311331564255086), 81: np.float64(0.14614778072624146), 55: np.float64(0.14614778072624146), 91: np.float64(0.14614778072624146), 0: np.float64(0.14614778072624146)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 14]
learned probs for cluster 2 

{48: np.float64(0.14285714285714313), 59: np.float64(0.14285714285714313), 9: np.float64(0.14285714285714313), 81: np.float64(0.14285714285714313), 55: np.float64(0.14285714285714313), 91: np.float64(0.14285714285714313), 0: np.float64(0.14285714285714313)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 14]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428579), 59: np.float64(0.03771428571428579), 9: np.float64(0.03771428571428579), 81: np.float64(0.03771428571428579), 55: np.float64(0.03771428571428579), 91: np.float64(0.03771428571428579), 0: np.float64(0.03771428571428579)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{48: np.float64(0.14547832979993575), 59: np.float64(0.14547832979993575), 9: np.float64(0.12713002120038702), 81: np.float64(0.14547832979993575), 55: np.float64(0.14547832979993575), 91: np.float64(0.14547832979993575), 0: np.float64(0.14547832979993575)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {48: np.float64(0.1447863364470385), 59: np.float64(0.1447863364470385), 9: np.float64(0.13128198131777064), 81: np.float64(0.1447863364470385), 55: np.float64(0.1447863364470385), 91: np.float64(0.1447863364470385), 0: np.float64(0.1447863364470385)}
choice probs for this beta: {48: np.float64(0.1447863364470385), 59: np.float64(0.1447863364470385), 9: np.float64(0.13128198131777064), 81: np.float64(0.1447863364470385), 55: np.float64(0.1447863364470385), 91: np.float64(0.1447863364470385), 0: np.float64(0.1447863364470385)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5, 14]
learned probs for cluster 2 

{48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 5, 14]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428573), 59: np.float64(0.03771428571428573), 9: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 55: np.float64(0.03771428571428573), 91: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs for cluster 1 

{48: np.float64(0.1235528958071494), 59: np.float64(0.1235528958071494), 9: np.float64(0.25868262515710216), 81: np.float64(0.1235528958071494), 55: np.float64(0.1235528958071494), 91: np.float64(0.1235528958071494), 0: np.float64(0.1235528958071494)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs (dictionary):

probs= {48: np.float64(0.1286492170283477), 59: np.float64(0.1286492170283477), 9: np.float64(0.2281046978299129), 81: np.float64(0.1286492170283477), 55: np.float64(0.1286492170283477), 91: np.float64(0.1286492170283477), 0: np.float64(0.1286492170283477)}
choice probs for this beta: {48: np.float64(0.1286492170283477), 59: np.float64(0.1286492170283477), 9: np.float64(0.2281046978299129), 81: np.float64(0.1286492170283477), 55: np.float64(0.1286492170283477), 91: np.float64(0.1286492170283477), 0: np.float64(0.1286492170283477)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 14]
learned probs for cluster 2 

{48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 14]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428573), 59: np.float64(0.03771428571428573), 9: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 55: np.float64(0.03771428571428573), 91: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 100]
learned probs for cluster 1 

{48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 100]
learned probs (dictionary):

probs= {48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{48: np.float64(0.14285714285714277), 59: np.float64(0.14285714285714277), 9: np.float64(0.14285714285714277), 81: np.float64(0.14285714285714277), 55: np.float64(0.14285714285714277), 91: np.float64(0.14285714285714277), 0: np.float64(0.14285714285714277)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428569), 59: np.float64(0.03771428571428569), 9: np.float64(0.03771428571428569), 81: np.float64(0.03771428571428569), 55: np.float64(0.03771428571428569), 91: np.float64(0.03771428571428569), 0: np.float64(0.03771428571428569)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{48: np.float64(0.014795430294419931), 59: np.float64(0.014795430294419931), 9: np.float64(0.9112274182334799), 81: np.float64(0.014795430294419931), 55: np.float64(0.014795430294419931), 91: np.float64(0.014795430294419931), 0: np.float64(0.014795430294419931)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {48: np.float64(0.04860372241097876), 59: np.float64(0.04860372241097876), 9: np.float64(0.7083776655341268), 81: np.float64(0.04860372241097876), 55: np.float64(0.04860372241097876), 91: np.float64(0.04860372241097876), 0: np.float64(0.04860372241097876)}
choice probs for this beta: {48: np.float64(0.04860372241097876), 59: np.float64(0.04860372241097876), 9: np.float64(0.7083776655341268), 81: np.float64(0.04860372241097876), 55: np.float64(0.04860372241097876), 91: np.float64(0.04860372241097876), 0: np.float64(0.04860372241097876)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{48: np.float64(0.14285714285714288), 59: np.float64(0.14285714285714288), 9: np.float64(0.14285714285714288), 81: np.float64(0.14285714285714288), 55: np.float64(0.14285714285714288), 91: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428572), 59: np.float64(0.03771428571428572), 9: np.float64(0.03771428571428572), 81: np.float64(0.03771428571428572), 55: np.float64(0.03771428571428572), 91: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{48: np.float64(0.003905327883802409), 59: np.float64(0.003905327883802409), 9: np.float64(0.9765680326971854), 81: np.float64(0.003905327883802409), 55: np.float64(0.003905327883802409), 91: np.float64(0.003905327883802409), 0: np.float64(0.003905327883802409)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {48: np.float64(0.04058860703676429), 59: np.float64(0.04058860703676429), 9: np.float64(0.7564683577794141), 81: np.float64(0.04058860703676429), 55: np.float64(0.04058860703676429), 91: np.float64(0.04058860703676429), 0: np.float64(0.04058860703676429)}
choice probs for this beta: {48: np.float64(0.04058860703676429), 59: np.float64(0.04058860703676429), 9: np.float64(0.7564683577794141), 81: np.float64(0.04058860703676429), 55: np.float64(0.04058860703676429), 91: np.float64(0.04058860703676429), 0: np.float64(0.04058860703676429)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{48: np.float64(0.14285714285714285), 59: np.float64(0.14285714285714285), 9: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 91: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {48: np.float64(0.037714285714285714), 59: np.float64(0.037714285714285714), 9: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 91: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{48: np.float64(2.0177328708337483e-05), 59: np.float64(2.0177328708337483e-05), 9: np.float64(0.9998789360277502), 81: np.float64(2.0177328708337483e-05), 55: np.float64(2.0177328708337483e-05), 91: np.float64(2.0177328708337483e-05), 0: np.float64(2.0177328708337483e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {48: np.float64(0.03772913622821505), 59: np.float64(0.03772913622821505), 9: np.float64(0.7736251826307099), 81: np.float64(0.03772913622821505), 55: np.float64(0.03772913622821505), 91: np.float64(0.03772913622821505), 0: np.float64(0.03772913622821505)}
choice probs for this beta: {48: np.float64(0.03772913622821505), 59: np.float64(0.03772913622821505), 9: np.float64(0.7736251826307099), 81: np.float64(0.03772913622821505), 55: np.float64(0.03772913622821505), 91: np.float64(0.03772913622821505), 0: np.float64(0.03772913622821505)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 5, 6, 7, 10, 100, 4, 14]
learned probs for cluster 2 

{48: np.float64(0.14285714285714285), 59: np.float64(0.14285714285714285), 9: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 91: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 100, 4, 14]
learned probs (dictionary):

probs= {48: np.float64(0.037714285714285714), 59: np.float64(0.037714285714285714), 9: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 91: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11]
learned probs for cluster 1 

{48: np.float64(5.7759892810183745e-06), 59: np.float64(5.7759892810183745e-06), 9: np.float64(0.9999653440643135), 81: np.float64(5.7759892810183745e-06), 55: np.float64(5.7759892810183745e-06), 91: np.float64(5.7759892810183745e-06), 0: np.float64(5.7759892810183745e-06)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11]
learned probs (dictionary):

probs= {48: np.float64(0.037718536842396545), 59: np.float64(0.037718536842396545), 9: np.float64(0.7736887789456204), 81: np.float64(0.037718536842396545), 55: np.float64(0.037718536842396545), 91: np.float64(0.037718536842396545), 0: np.float64(0.037718536842396545)}
choice probs for this beta: {48: np.float64(0.037718536842396545), 59: np.float64(0.037718536842396545), 9: np.float64(0.7736887789456204), 81: np.float64(0.037718536842396545), 55: np.float64(0.037718536842396545), 91: np.float64(0.037718536842396545), 0: np.float64(0.037718536842396545)}
#beta= 0.025 

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

{48: np.float64(0.14745907045713627), 59: np.float64(0.14745907045713627), 9: np.float64(0.1152455772571809), 81: np.float64(0.14745907045713627), 55: np.float64(0.14745907045713627), 91: np.float64(0.14745907045713627), 0: np.float64(0.14745907045713627)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 14, 100, 4, 5, 9]
learned probs (dictionary):

probs= {48: np.float64(0.038929194600683975), 59: np.float64(0.038929194600683975), 9: np.float64(0.03042483239589576), 81: np.float64(0.038929194600683975), 55: np.float64(0.038929194600683975), 91: np.float64(0.038929194600683975), 0: np.float64(0.038929194600683975)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 100]
learned probs for cluster 1 

{48: np.float64(0.15026551899360058), 59: np.float64(0.15026551899360058), 9: np.float64(0.09840688603839677), 81: np.float64(0.15026551899360058), 55: np.float64(0.15026551899360058), 91: np.float64(0.15026551899360058), 0: np.float64(0.15026551899360058)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 100]
learned probs (dictionary):

probs= {48: np.float64(0.149524616579974), 59: np.float64(0.149524616579974), 9: np.float64(0.10285230052015579), 81: np.float64(0.149524616579974), 55: np.float64(0.149524616579974), 91: np.float64(0.149524616579974), 0: np.float64(0.149524616579974)}
choice probs for this beta: {48: np.float64(0.149524616579974), 59: np.float64(0.149524616579974), 9: np.float64(0.10285230052015579), 81: np.float64(0.149524616579974), 55: np.float64(0.149524616579974), 91: np.float64(0.149524616579974), 0: np.float64(0.149524616579974)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
learned probs for cluster 2 

{48: np.float64(0.14285714285714313), 59: np.float64(0.14285714285714313), 9: np.float64(0.14285714285714313), 81: np.float64(0.14285714285714313), 55: np.float64(0.14285714285714313), 91: np.float64(0.14285714285714313), 0: np.float64(0.14285714285714313)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 11, 13, 100, 4, 5]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428579), 59: np.float64(0.03771428571428579), 9: np.float64(0.03771428571428579), 81: np.float64(0.03771428571428579), 55: np.float64(0.03771428571428579), 91: np.float64(0.03771428571428579), 0: np.float64(0.03771428571428579)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs for cluster 1 

{48: np.float64(0.1402762628429531), 59: np.float64(0.1402762628429531), 9: np.float64(0.15834242294228618), 81: np.float64(0.1402762628429531), 55: np.float64(0.1402762628429531), 91: np.float64(0.1402762628429531), 0: np.float64(0.1402762628429531)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs (dictionary):

probs= {48: np.float64(0.14095761516669927), 59: np.float64(0.14095761516669927), 9: np.float64(0.1542543089998084), 81: np.float64(0.14095761516669927), 55: np.float64(0.14095761516669927), 91: np.float64(0.14095761516669927), 0: np.float64(0.14095761516669927)}
choice probs for this beta: {48: np.float64(0.14095761516669927), 59: np.float64(0.14095761516669927), 9: np.float64(0.1542543089998084), 81: np.float64(0.14095761516669927), 55: np.float64(0.14095761516669927), 91: np.float64(0.14095761516669927), 0: np.float64(0.14095761516669927)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 14]
learned probs for cluster 2 

{48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 14]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428573), 59: np.float64(0.03771428571428573), 9: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 55: np.float64(0.03771428571428573), 91: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0} [1, 2, 3, 4, 5, 7, 9, 10, 11, 12]
learned probs for cluster 1 

{48: np.float64(0.12539753288130623), 59: np.float64(0.12539753288130623), 9: np.float64(0.24761480271216194), 81: np.float64(0.12539753288130623), 55: np.float64(0.12539753288130623), 91: np.float64(0.12539753288130623), 0: np.float64(0.12539753288130623)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 10, 11, 12]
learned probs (dictionary):

probs= {48: np.float64(0.1300068699149271), 59: np.float64(0.1300068699149271), 9: np.float64(0.2199587805104369), 81: np.float64(0.1300068699149271), 55: np.float64(0.1300068699149271), 91: np.float64(0.1300068699149271), 0: np.float64(0.1300068699149271)}
choice probs for this beta: {48: np.float64(0.1300068699149271), 59: np.float64(0.1300068699149271), 9: np.float64(0.2199587805104369), 81: np.float64(0.1300068699149271), 55: np.float64(0.1300068699149271), 91: np.float64(0.1300068699149271), 0: np.float64(0.1300068699149271)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 2, 14: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 14, 15, 100, 4, 5, 13]
learned probs for cluster 2 

{48: np.float64(0.14285714285714135), 59: np.float64(0.14285714285714135), 9: np.float64(0.14285714285714135), 81: np.float64(0.14285714285714135), 55: np.float64(0.14285714285714135), 91: np.float64(0.14285714285714135), 0: np.float64(0.14285714285714135)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 14, 15, 100, 4, 5, 13]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428532), 59: np.float64(0.03771428571428532), 9: np.float64(0.03771428571428532), 81: np.float64(0.03771428571428532), 55: np.float64(0.03771428571428532), 91: np.float64(0.03771428571428532), 0: np.float64(0.03771428571428532)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{48: np.float64(0.08226359890156987), 59: np.float64(0.08226359890156987), 9: np.float64(0.5064184065905807), 81: np.float64(0.08226359890156987), 55: np.float64(0.08226359890156987), 91: np.float64(0.08226359890156987), 0: np.float64(0.08226359890156987)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {48: np.float64(0.09826029450584074), 59: np.float64(0.09826029450584074), 9: np.float64(0.4104382329649527), 81: np.float64(0.09826029450584074), 55: np.float64(0.09826029450584074), 91: np.float64(0.09826029450584074), 0: np.float64(0.09826029450584074)}
choice probs for this beta: {48: np.float64(0.09826029450584074), 59: np.float64(0.09826029450584074), 9: np.float64(0.4104382329649527), 81: np.float64(0.09826029450584074), 55: np.float64(0.09826029450584074), 91: np.float64(0.09826029450584074), 0: np.float64(0.09826029450584074)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 14]
learned probs for cluster 2 

{48: np.float64(0.1428571428571429), 59: np.float64(0.1428571428571429), 9: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 91: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 14]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428573), 59: np.float64(0.03771428571428573), 9: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 55: np.float64(0.03771428571428573), 91: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{48: np.float64(0.02233634344033635), 59: np.float64(0.02233634344033635), 9: np.float64(0.8659819393579837), 81: np.float64(0.02233634344033635), 55: np.float64(0.02233634344033635), 91: np.float64(0.02233634344033635), 0: np.float64(0.02233634344033635)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {48: np.float64(0.05415383448637328), 59: np.float64(0.05415383448637328), 9: np.float64(0.6750769930817617), 81: np.float64(0.05415383448637328), 55: np.float64(0.05415383448637328), 91: np.float64(0.05415383448637328), 0: np.float64(0.05415383448637328)}
choice probs for this beta: {48: np.float64(0.05415383448637328), 59: np.float64(0.05415383448637328), 9: np.float64(0.6750769930817617), 81: np.float64(0.05415383448637328), 55: np.float64(0.05415383448637328), 91: np.float64(0.05415383448637328), 0: np.float64(0.05415383448637328)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{48: np.float64(0.14285714285714288), 59: np.float64(0.14285714285714288), 9: np.float64(0.14285714285714288), 81: np.float64(0.14285714285714288), 55: np.float64(0.14285714285714288), 91: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {48: np.float64(0.03771428571428572), 59: np.float64(0.03771428571428572), 9: np.float64(0.03771428571428572), 81: np.float64(0.03771428571428572), 55: np.float64(0.03771428571428572), 91: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 15, 100]
learned probs for cluster 1 

{48: np.float64(0.0005378490018400384), 59: np.float64(0.0005378490018400384), 9: np.float64(0.9967729059889602), 81: np.float64(0.0005378490018400384), 55: np.float64(0.0005378490018400384), 91: np.float64(0.0005378490018400384), 0: np.float64(0.0005378490018400384)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 15, 100]
learned probs (dictionary):

probs= {48: np.float64(0.03811014257963999), 59: np.float64(0.03811014257963999), 9: np.float64(0.7713391445221603), 81: np.float64(0.03811014257963999), 55: np.float64(0.03811014257963999), 91: np.float64(0.03811014257963999), 0: np.float64(0.03811014257963999)}
choice probs for this beta: {48: np.float64(0.03811014257963999), 59: np.float64(0.03811014257963999), 9: np.float64(0.7713391445221603), 81: np.float64(0.03811014257963999), 55: np.float64(0.03811014257963999), 91: np.float64(0.03811014257963999), 0: np.float64(0.03811014257963999)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 16: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 16]
learned probs for cluster 2 

{48: np.float64(0.14285714285714285), 59: np.float64(0.14285714285714285), 9: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 91: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5, 16]
learned probs (dictionary):

probs= {48: np.float64(0.037714285714285714), 59: np.float64(0.037714285714285714), 9: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 91: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{48: np.float64(4.345398215840549e-05), 59: np.float64(4.345398215840549e-05), 9: np.float64(0.9997392761070495), 81: np.float64(4.345398215840549e-05), 55: np.float64(4.345398215840549e-05), 91: np.float64(4.345398215840549e-05), 0: np.float64(4.345398215840549e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {48: np.float64(0.0377462678451543), 59: np.float64(0.0377462678451543), 9: np.float64(0.7735223929290741), 81: np.float64(0.0377462678451543), 55: np.float64(0.0377462678451543), 91: np.float64(0.0377462678451543), 0: np.float64(0.0377462678451543)}
choice probs for this beta: {48: np.float64(0.0377462678451543), 59: np.float64(0.0377462678451543), 9: np.float64(0.7735223929290741), 81: np.float64(0.0377462678451543), 55: np.float64(0.0377462678451543), 91: np.float64(0.0377462678451543), 0: np.float64(0.0377462678451543)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 13: 1, 14: 2, 100: 1} [8, 1, 3, 5, 6, 7, 13, 100, 4, 14]
learned probs for cluster 2 

{48: np.float64(0.14285714285714285), 59: np.float64(0.14285714285714285), 9: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 91: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 13, 100, 4, 14]
learned probs (dictionary):

probs= {48: np.float64(0.037714285714285714), 59: np.float64(0.037714285714285714), 9: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 91: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{48: np.float64(5.930958554895353e-07), 59: np.float64(5.930958554895353e-07), 9: np.float64(0.9999964414248669), 81: np.float64(5.930958554895353e-07), 55: np.float64(5.930958554895353e-07), 91: np.float64(5.930958554895353e-07), 0: np.float64(5.930958554895353e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {48: np.float64(0.037714722232835354), 59: np.float64(0.037714722232835354), 9: np.float64(0.7737116666029877), 81: np.float64(0.037714722232835354), 55: np.float64(0.037714722232835354), 91: np.float64(0.037714722232835354), 0: np.float64(0.037714722232835354)}
choice probs for this beta: {48: np.float64(0.037714722232835354), 59: np.float64(0.037714722232835354), 9: np.float64(0.7737116666029877), 81: np.float64(0.037714722232835354), 55: np.float64(0.037714722232835354), 91: np.float64(0.037714722232835354), 0: np.float64(0.037714722232835354)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 9
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 9
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 48
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 48
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 55
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 81
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 48
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 9
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 48
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 55
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 91
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 55
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 91
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 48
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 0
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 48
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 59
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 81
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 55
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 9
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 9
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 55
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 81
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 59
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 9
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 0
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 55
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 48
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 55
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 59
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 9
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 0
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 9
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 48
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 55
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 9
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 91
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 9
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 9
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 55
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 48
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 59
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 48
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 59
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 59
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 9
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 91
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 48
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 55
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 91
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 55
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 59
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 9
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 81
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 48
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 48
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 55
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 48
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 55
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 59
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 81
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 48
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 59
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 9
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 55
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 59
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 48
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 48
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 81
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 59
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 48
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 9
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 9
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 48
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 81
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 0
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 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 59
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 55
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 48
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 59
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 81
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 9
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 48
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 9
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 9
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 0
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 0
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 59
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 9
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 9
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 55
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 81
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 59
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 0
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 81
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 55
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 55
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 55
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 9
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 55
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 91
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 9
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 48
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 55
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 91
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 9
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 59
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 48
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 59
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 81
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 48
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 9
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 55
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 59
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 55
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 55
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 91
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 9
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 55
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 48
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 55
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 55
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 55
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 9
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 48
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 59
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 81
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 91
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 55
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 9
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 91
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 48
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 0
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 0
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 59
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 81
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 55
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 55
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 55
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 59
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 91
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 59
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 48
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 59
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 55
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 59
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 91
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 59
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 81
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 9
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 48
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 55
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 55
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 59
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 9
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 48
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 59
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 0
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 91
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 48
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 81
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 48
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 55
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 81
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 91
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 55
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 48
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 48
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 81
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 81
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 59
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 59
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 9
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 0
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 48
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 81
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 59
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 55
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 48
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 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 81
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 81
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 48
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 91
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 55
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 48
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 0
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 55
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 81
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 9
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 48
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 9
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 55
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 91
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 9
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 48
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 81
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 9
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 9
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 91
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 48
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 48
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 9
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 55
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 9
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 55
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 55
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 9
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 9
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 48
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 9
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 48
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 59
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 9
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 0
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 48
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 55
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 48
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 48
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 55
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 55
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 48
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 9
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 9
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 81
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 55
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 48
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 81
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 81
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 9
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 0
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 59
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 9
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 55
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 55
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 55
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 81
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 91
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 0
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 48
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 81
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 59
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 48
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 55
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 91
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 59
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 59
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 91
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 9
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 0
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 59
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 9
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 55
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 59
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 59
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 9
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 9
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 59
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 59
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 59
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 81
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 59
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 0
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 81
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 48
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 81
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 59
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 81
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 59
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 91
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 81
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 91
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 55
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 81
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 9
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 81
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 9
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 0
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 59
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 59
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 55
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 48
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 55
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 55
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 9
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 81
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 81
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 91
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 59
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 59
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 48
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 59
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 0
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 0
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 81
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 59
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 9
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 81
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 81
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 59
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 59
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 59
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 0
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 55
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 48
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 48
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 48
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 55
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 59
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 91
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 9
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 9
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 9
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 81
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 91
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 91
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 9
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 55
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 48
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 81
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 91
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 48
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 48
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 48
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 48
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 9
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 9
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 0
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 0
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 0
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 48
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 91
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 48
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 81
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 0
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 81
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 9
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 48
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 59
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 0
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 81
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 81
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 59
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 59
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 81
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 48
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 81
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 55
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 48
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 55
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 59
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 0
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 59
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 0
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 0
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 9
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 55
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 59
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 55
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 9
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 9
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 48
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 55
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 9
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 91
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 81
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 81
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 48
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 9
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 48
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 81
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 0
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 48
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 48
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 59
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 48
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 0
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 81
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 48
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 48
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 59
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 59
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 81
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 9
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 55
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 91
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 81
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 59
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 91
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 48
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 91
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 9
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 59
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 55
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 48
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 91
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 59
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 48
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 9
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 55
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 81
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 91
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 59
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 55
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 48
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 48
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 91
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 48
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 9
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 59
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 55
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 81
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 9
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 81
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 91
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 91
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 0
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 9
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 48
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 91
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 0
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 55
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 55
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 55
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 9
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 59
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 59
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 59
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 9
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 59
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 55
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 48
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 81
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 9
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 0
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 48
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 59
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 59
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 48
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 55
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 48
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 0
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 48
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 55
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 9
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 59
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 48
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 59
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 0
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 9
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 48
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 48
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 59
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 59
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 91
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 91
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 59
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 91
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 0
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 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 55
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 9
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 9
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 0
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 81
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 59
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 55
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 91
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 48
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 55
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 55
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 81
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 55
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 9
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 9
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 9
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 81
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 59
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 48
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 0
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 0
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 48
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 48
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 55
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 9
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 9
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 81
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 59
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 9
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 81
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 55
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 48
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 9
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 55
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 59
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 0
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 48
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 81
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 48
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 59
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 0
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 59
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 91
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 9
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 9
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 48
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 81
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 9
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 91
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 55
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 48
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 81
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 48
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 59
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 55
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 55
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 48
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 81
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 55
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 55
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 48
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 48
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 9
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 9
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 91
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 48
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 59
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 0
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 9
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 55
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 81
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 55
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 81
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 55
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 48
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 55
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 55
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 0
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 91
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 9
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 48
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 48
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 48
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 91
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 48
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 91
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 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 59
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 81
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 55
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 48
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 55
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 59
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 91
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 9
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 59
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 55
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 59
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 55
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 91
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 0
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 9
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 48
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 59
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 9
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 59
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 0
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 48
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 9
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 59
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 48
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 48
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 48
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 81
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 0
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 9
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 48
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 9
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 48
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 55
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 0
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 48
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 55
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 91
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 59
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 59
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 48
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 59
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 48
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 55
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 59
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 81
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 55
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 81
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 91
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 59
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 9
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 48
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 9
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 59
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 91
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 9
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 59
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 91
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 9
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 48
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 0
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 9
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 59
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 55
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 55
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 59
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 9
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 0
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 81
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 59
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 9
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 48
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 55
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 55
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 48
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 48
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 48
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 48
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 81
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 55
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 9
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 0
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 55
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 91
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 55
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 0
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 9
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 0
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 48
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 9
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 9
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 91
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 91
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 48
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 55
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 59
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 59
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 91
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 59
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 91
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 91
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 81
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 9
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 55
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 91
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 48
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 48
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 91
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 81
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 91
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 0
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 0
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 9
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 59
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 81
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 9
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 55
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 59
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 55
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 9
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 48
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 91
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 9
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 48
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 59
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 48
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 9
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 0
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 81
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 9
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 91
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 55
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 81
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 55
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 48
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 48
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 55
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 55
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 55
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 48
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 91
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 48
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 9
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 9
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 9
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 48
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 59
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 81
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 48
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 0
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 91
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 81
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 91
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 0
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 0
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 48
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 55
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 9
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 48
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 9
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 0
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 91
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 55
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 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 0
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 81
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 81
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 48
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 55
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 48
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 81
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 59
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 9
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 0
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 91
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 48
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 59
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 48
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 48
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 59
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 48
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 59
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 48
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 48
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 9
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 91
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 91
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 55
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 9
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 0
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 0
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 59
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 9
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 0
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 81
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 0
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 0
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 48
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 0
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 9
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 9
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 48
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 55
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 59
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 91
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 91
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 48
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 55
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 9
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 9
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 48
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 55
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 0
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 48
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 91
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 81
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 91
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 59
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 48
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 55
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 48
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 9
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 59
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 81
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 59
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 59
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 0
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 91
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 0
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 48
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 55
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 91
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 48
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 91
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 91
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 9
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 59
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 0
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 55
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 48
emperical probablities from test set: {48: 0.16, 59: 0.129, 9: 0.321, 81: 0.093, 55: 0.128, 91: 0.084, 0: 0.085}
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.010475383420025991), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: np.float64(0.02052461657997401), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.010475383420025991), np.float64(0.02052461657997401), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: np.float64(0.02052461657997401), 9: np.float64(0.21814769947984422), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.010475383420025991), np.float64(0.02052461657997401), np.float64(0.21814769947984422), 0, 0, 0, 0]
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: np.float64(0.02052461657997401), 9: np.float64(0.21814769947984422), 81: np.float64(0.05652461657997401), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.010475383420025991), np.float64(0.02052461657997401), np.float64(0.21814769947984422), np.float64(0.05652461657997401), 0, 0, 0]
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: np.float64(0.02052461657997401), 9: np.float64(0.21814769947984422), 81: np.float64(0.05652461657997401), 55: np.float64(0.02152461657997401), 91: 0, 0: 0} 

err list= [np.float64(0.010475383420025991), np.float64(0.02052461657997401), np.float64(0.21814769947984422), np.float64(0.05652461657997401), np.float64(0.02152461657997401), 0, 0]
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: np.float64(0.02052461657997401), 9: np.float64(0.21814769947984422), 81: np.float64(0.05652461657997401), 55: np.float64(0.02152461657997401), 91: np.float64(0.06552461657997401), 0: 0} 

err list= [np.float64(0.010475383420025991), np.float64(0.02052461657997401), np.float64(0.21814769947984422), np.float64(0.05652461657997401), np.float64(0.02152461657997401), np.float64(0.06552461657997401), 0]
beta is  0.025 

err dic= {48: np.float64(0.010475383420025991), 59: np.float64(0.02052461657997401), 9: np.float64(0.21814769947984422), 81: np.float64(0.05652461657997401), 55: np.float64(0.02152461657997401), 91: np.float64(0.06552461657997401), 0: np.float64(0.064524616579974)} 

err list= [np.float64(0.010475383420025991), np.float64(0.02052461657997401), np.float64(0.21814769947984422), np.float64(0.05652461657997401), np.float64(0.02152461657997401), np.float64(0.06552461657997401), np.float64(0.064524616579974)]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.01904238483330073), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: np.float64(0.01195761516669927), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.01904238483330073), np.float64(0.01195761516669927), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: np.float64(0.01195761516669927), 9: np.float64(0.1667456910001916), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.01904238483330073), np.float64(0.01195761516669927), np.float64(0.1667456910001916), 0, 0, 0, 0]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: np.float64(0.01195761516669927), 9: np.float64(0.1667456910001916), 81: np.float64(0.047957615166699274), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.01904238483330073), np.float64(0.01195761516669927), np.float64(0.1667456910001916), np.float64(0.047957615166699274), 0, 0, 0]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: np.float64(0.01195761516669927), 9: np.float64(0.1667456910001916), 81: np.float64(0.047957615166699274), 55: np.float64(0.012957615166699271), 91: 0, 0: 0} 

err list= [np.float64(0.01904238483330073), np.float64(0.01195761516669927), np.float64(0.1667456910001916), np.float64(0.047957615166699274), np.float64(0.012957615166699271), 0, 0]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: np.float64(0.01195761516669927), 9: np.float64(0.1667456910001916), 81: np.float64(0.047957615166699274), 55: np.float64(0.012957615166699271), 91: np.float64(0.05695761516669927), 0: 0} 

err list= [np.float64(0.01904238483330073), np.float64(0.01195761516669927), np.float64(0.1667456910001916), np.float64(0.047957615166699274), np.float64(0.012957615166699271), np.float64(0.05695761516669927), 0]
beta is  0.05 

err dic= {48: np.float64(0.01904238483330073), 59: np.float64(0.01195761516669927), 9: np.float64(0.1667456910001916), 81: np.float64(0.047957615166699274), 55: np.float64(0.012957615166699271), 91: np.float64(0.05695761516669927), 0: np.float64(0.05595761516669927)} 

err list= [np.float64(0.01904238483330073), np.float64(0.01195761516669927), np.float64(0.1667456910001916), np.float64(0.047957615166699274), np.float64(0.012957615166699271), np.float64(0.05695761516669927), np.float64(0.05595761516669927)]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.0299931300850729), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: np.float64(0.0010068699149270999), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.0299931300850729), np.float64(0.0010068699149270999), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: np.float64(0.0010068699149270999), 9: np.float64(0.1010412194895631), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.0299931300850729), np.float64(0.0010068699149270999), np.float64(0.1010412194895631), 0, 0, 0, 0]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: np.float64(0.0010068699149270999), 9: np.float64(0.1010412194895631), 81: np.float64(0.037006869914927104), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.0299931300850729), np.float64(0.0010068699149270999), np.float64(0.1010412194895631), np.float64(0.037006869914927104), 0, 0, 0]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: np.float64(0.0010068699149270999), 9: np.float64(0.1010412194895631), 81: np.float64(0.037006869914927104), 55: np.float64(0.0020068699149271008), 91: 0, 0: 0} 

err list= [np.float64(0.0299931300850729), np.float64(0.0010068699149270999), np.float64(0.1010412194895631), np.float64(0.037006869914927104), np.float64(0.0020068699149271008), 0, 0]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: np.float64(0.0010068699149270999), 9: np.float64(0.1010412194895631), 81: np.float64(0.037006869914927104), 55: np.float64(0.0020068699149271008), 91: np.float64(0.0460068699149271), 0: 0} 

err list= [np.float64(0.0299931300850729), np.float64(0.0010068699149270999), np.float64(0.1010412194895631), np.float64(0.037006869914927104), np.float64(0.0020068699149271008), np.float64(0.0460068699149271), 0]
beta is  0.1 

err dic= {48: np.float64(0.0299931300850729), 59: np.float64(0.0010068699149270999), 9: np.float64(0.1010412194895631), 81: np.float64(0.037006869914927104), 55: np.float64(0.0020068699149271008), 91: np.float64(0.0460068699149271), 0: np.float64(0.0450068699149271)} 

err list= [np.float64(0.0299931300850729), np.float64(0.0010068699149270999), np.float64(0.1010412194895631), np.float64(0.037006869914927104), np.float64(0.0020068699149271008), np.float64(0.0460068699149271), np.float64(0.0450068699149271)]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.06173970549415926), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: np.float64(0.03073970549415926), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.06173970549415926), np.float64(0.03073970549415926), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: np.float64(0.03073970549415926), 9: np.float64(0.08943823296495268), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.06173970549415926), np.float64(0.03073970549415926), np.float64(0.08943823296495268), 0, 0, 0, 0]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: np.float64(0.03073970549415926), 9: np.float64(0.08943823296495268), 81: np.float64(0.005260294505840743), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.06173970549415926), np.float64(0.03073970549415926), np.float64(0.08943823296495268), np.float64(0.005260294505840743), 0, 0, 0]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: np.float64(0.03073970549415926), 9: np.float64(0.08943823296495268), 81: np.float64(0.005260294505840743), 55: np.float64(0.02973970549415926), 91: 0, 0: 0} 

err list= [np.float64(0.06173970549415926), np.float64(0.03073970549415926), np.float64(0.08943823296495268), np.float64(0.005260294505840743), np.float64(0.02973970549415926), 0, 0]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: np.float64(0.03073970549415926), 9: np.float64(0.08943823296495268), 81: np.float64(0.005260294505840743), 55: np.float64(0.02973970549415926), 91: np.float64(0.014260294505840737), 0: 0} 

err list= [np.float64(0.06173970549415926), np.float64(0.03073970549415926), np.float64(0.08943823296495268), np.float64(0.005260294505840743), np.float64(0.02973970549415926), np.float64(0.014260294505840737), 0]
beta is  0.25 

err dic= {48: np.float64(0.06173970549415926), 59: np.float64(0.03073970549415926), 9: np.float64(0.08943823296495268), 81: np.float64(0.005260294505840743), 55: np.float64(0.02973970549415926), 91: np.float64(0.014260294505840737), 0: np.float64(0.013260294505840736)} 

err list= [np.float64(0.06173970549415926), np.float64(0.03073970549415926), np.float64(0.08943823296495268), np.float64(0.005260294505840743), np.float64(0.02973970549415926), np.float64(0.014260294505840737), np.float64(0.013260294505840736)]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.10584616551362672), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: np.float64(0.07484616551362672), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.10584616551362672), np.float64(0.07484616551362672), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: np.float64(0.07484616551362672), 9: np.float64(0.3540769930817617), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.10584616551362672), np.float64(0.07484616551362672), np.float64(0.3540769930817617), 0, 0, 0, 0]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: np.float64(0.07484616551362672), 9: np.float64(0.3540769930817617), 81: np.float64(0.03884616551362672), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.10584616551362672), np.float64(0.07484616551362672), np.float64(0.3540769930817617), np.float64(0.03884616551362672), 0, 0, 0]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: np.float64(0.07484616551362672), 9: np.float64(0.3540769930817617), 81: np.float64(0.03884616551362672), 55: np.float64(0.07384616551362672), 91: 0, 0: 0} 

err list= [np.float64(0.10584616551362672), np.float64(0.07484616551362672), np.float64(0.3540769930817617), np.float64(0.03884616551362672), np.float64(0.07384616551362672), 0, 0]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: np.float64(0.07484616551362672), 9: np.float64(0.3540769930817617), 81: np.float64(0.03884616551362672), 55: np.float64(0.07384616551362672), 91: np.float64(0.029846165513626725), 0: 0} 

err list= [np.float64(0.10584616551362672), np.float64(0.07484616551362672), np.float64(0.3540769930817617), np.float64(0.03884616551362672), np.float64(0.07384616551362672), np.float64(0.029846165513626725), 0]
beta is  0.5 

err dic= {48: np.float64(0.10584616551362672), 59: np.float64(0.07484616551362672), 9: np.float64(0.3540769930817617), 81: np.float64(0.03884616551362672), 55: np.float64(0.07384616551362672), 91: np.float64(0.029846165513626725), 0: np.float64(0.030846165513626726)} 

err list= [np.float64(0.10584616551362672), np.float64(0.07484616551362672), np.float64(0.3540769930817617), np.float64(0.03884616551362672), np.float64(0.07384616551362672), np.float64(0.029846165513626725), np.float64(0.030846165513626726)]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12188985742036001), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: np.float64(0.09088985742036002), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12188985742036001), np.float64(0.09088985742036002), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: np.float64(0.09088985742036002), 9: np.float64(0.45033914452216034), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12188985742036001), np.float64(0.09088985742036002), np.float64(0.45033914452216034), 0, 0, 0, 0]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: np.float64(0.09088985742036002), 9: np.float64(0.45033914452216034), 81: np.float64(0.05488985742036001), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12188985742036001), np.float64(0.09088985742036002), np.float64(0.45033914452216034), np.float64(0.05488985742036001), 0, 0, 0]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: np.float64(0.09088985742036002), 9: np.float64(0.45033914452216034), 81: np.float64(0.05488985742036001), 55: np.float64(0.08988985742036001), 91: 0, 0: 0} 

err list= [np.float64(0.12188985742036001), np.float64(0.09088985742036002), np.float64(0.45033914452216034), np.float64(0.05488985742036001), np.float64(0.08988985742036001), 0, 0]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: np.float64(0.09088985742036002), 9: np.float64(0.45033914452216034), 81: np.float64(0.05488985742036001), 55: np.float64(0.08988985742036001), 91: np.float64(0.04588985742036002), 0: 0} 

err list= [np.float64(0.12188985742036001), np.float64(0.09088985742036002), np.float64(0.45033914452216034), np.float64(0.05488985742036001), np.float64(0.08988985742036001), np.float64(0.04588985742036002), 0]
beta is  0.75 

err dic= {48: np.float64(0.12188985742036001), 59: np.float64(0.09088985742036002), 9: np.float64(0.45033914452216034), 81: np.float64(0.05488985742036001), 55: np.float64(0.08988985742036001), 91: np.float64(0.04588985742036002), 0: np.float64(0.04688985742036002)} 

err list= [np.float64(0.12188985742036001), np.float64(0.09088985742036002), np.float64(0.45033914452216034), np.float64(0.05488985742036001), np.float64(0.08988985742036001), np.float64(0.04588985742036002), np.float64(0.04688985742036002)]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.1222537321548457), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: np.float64(0.0912537321548457), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.1222537321548457), np.float64(0.0912537321548457), 0, 0, 0, 0, 0]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: np.float64(0.0912537321548457), 9: np.float64(0.4525223929290741), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.1222537321548457), np.float64(0.0912537321548457), np.float64(0.4525223929290741), 0, 0, 0, 0]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: np.float64(0.0912537321548457), 9: np.float64(0.4525223929290741), 81: np.float64(0.0552537321548457), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.1222537321548457), np.float64(0.0912537321548457), np.float64(0.4525223929290741), np.float64(0.0552537321548457), 0, 0, 0]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: np.float64(0.0912537321548457), 9: np.float64(0.4525223929290741), 81: np.float64(0.0552537321548457), 55: np.float64(0.0902537321548457), 91: 0, 0: 0} 

err list= [np.float64(0.1222537321548457), np.float64(0.0912537321548457), np.float64(0.4525223929290741), np.float64(0.0552537321548457), np.float64(0.0902537321548457), 0, 0]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: np.float64(0.0912537321548457), 9: np.float64(0.4525223929290741), 81: np.float64(0.0552537321548457), 55: np.float64(0.0902537321548457), 91: np.float64(0.046253732154845704), 0: 0} 

err list= [np.float64(0.1222537321548457), np.float64(0.0912537321548457), np.float64(0.4525223929290741), np.float64(0.0552537321548457), np.float64(0.0902537321548457), np.float64(0.046253732154845704), 0]
beta is  1 

err dic= {48: np.float64(0.1222537321548457), 59: np.float64(0.0912537321548457), 9: np.float64(0.4525223929290741), 81: np.float64(0.0552537321548457), 55: np.float64(0.0902537321548457), 91: np.float64(0.046253732154845704), 0: np.float64(0.047253732154845705)} 

err list= [np.float64(0.1222537321548457), np.float64(0.0912537321548457), np.float64(0.4525223929290741), np.float64(0.0552537321548457), np.float64(0.0902537321548457), np.float64(0.046253732154845704), np.float64(0.047253732154845705)]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: 0, 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12228527776716465), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: np.float64(0.09128527776716465), 9: 0, 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12228527776716465), np.float64(0.09128527776716465), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: np.float64(0.09128527776716465), 9: np.float64(0.45271166660298773), 81: 0, 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12228527776716465), np.float64(0.09128527776716465), np.float64(0.45271166660298773), 0, 0, 0, 0]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: np.float64(0.09128527776716465), 9: np.float64(0.45271166660298773), 81: np.float64(0.055285277767164645), 55: 0, 91: 0, 0: 0} 

err list= [np.float64(0.12228527776716465), np.float64(0.09128527776716465), np.float64(0.45271166660298773), np.float64(0.055285277767164645), 0, 0, 0]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: np.float64(0.09128527776716465), 9: np.float64(0.45271166660298773), 81: np.float64(0.055285277767164645), 55: np.float64(0.09028527776716465), 91: 0, 0: 0} 

err list= [np.float64(0.12228527776716465), np.float64(0.09128527776716465), np.float64(0.45271166660298773), np.float64(0.055285277767164645), np.float64(0.09028527776716465), 0, 0]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: np.float64(0.09128527776716465), 9: np.float64(0.45271166660298773), 81: np.float64(0.055285277767164645), 55: np.float64(0.09028527776716465), 91: np.float64(0.04628527776716465), 0: 0} 

err list= [np.float64(0.12228527776716465), np.float64(0.09128527776716465), np.float64(0.45271166660298773), np.float64(0.055285277767164645), np.float64(0.09028527776716465), np.float64(0.04628527776716465), 0]
beta is  1.25 

err dic= {48: np.float64(0.12228527776716465), 59: np.float64(0.09128527776716465), 9: np.float64(0.45271166660298773), 81: np.float64(0.055285277767164645), 55: np.float64(0.09028527776716465), 91: np.float64(0.04628527776716465), 0: np.float64(0.04728527776716465)} 

err list= [np.float64(0.12228527776716465), np.float64(0.09128527776716465), np.float64(0.45271166660298773), np.float64(0.055285277767164645), np.float64(0.09028527776716465), np.float64(0.04628527776716465), np.float64(0.04728527776716465)]
samppled assortment [2, 37, 88, 81, 26, 62]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 5, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{2: np.float64(0.11853896787131495), 37: np.float64(0.14691017202144746), 88: np.float64(0.14691017202144746), 81: np.float64(0.14691017202144746), 26: np.float64(0.14691017202144746), 62: np.float64(0.14691017202144746), 0: np.float64(0.14691017202144746)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 5, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {2: np.float64(0.031294287518027146), 37: np.float64(0.038784285413662134), 88: np.float64(0.038784285413662134), 81: np.float64(0.038784285413662134), 26: np.float64(0.038784285413662134), 62: np.float64(0.038784285413662134), 0: np.float64(0.038784285413662134)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.12114213220786123), 37: np.float64(0.14647631129869046), 88: np.float64(0.14647631129869046), 81: np.float64(0.14647631129869046), 26: np.float64(0.14647631129869046), 62: np.float64(0.14647631129869046), 0: np.float64(0.14647631129869046)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.120454896823013), 37: np.float64(0.14659085052949833), 88: np.float64(0.14659085052949833), 81: np.float64(0.14659085052949833), 26: np.float64(0.14659085052949833), 62: np.float64(0.14659085052949833), 0: np.float64(0.14659085052949833)}
choice probs for this beta: {2: np.float64(0.120454896823013), 37: np.float64(0.14659085052949833), 88: np.float64(0.14659085052949833), 81: np.float64(0.14659085052949833), 26: np.float64(0.14659085052949833), 62: np.float64(0.14659085052949833), 0: np.float64(0.14659085052949833)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 5]
learned probs for cluster 2 

{2: np.float64(0.12713002120038702), 37: np.float64(0.14547832979993575), 88: np.float64(0.14547832979993575), 81: np.float64(0.14547832979993575), 26: np.float64(0.14547832979993575), 62: np.float64(0.14547832979993575), 0: np.float64(0.14547832979993575)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 2, 5]
learned probs (dictionary):

probs= {2: np.float64(0.03356232559690218), 37: np.float64(0.03840627906718304), 88: np.float64(0.03840627906718304), 81: np.float64(0.03840627906718304), 26: np.float64(0.03840627906718304), 62: np.float64(0.03840627906718304), 0: np.float64(0.03840627906718304)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
learned probs for cluster 1 

{2: np.float64(0.14491012417085858), 37: np.float64(0.14251497930485704), 88: np.float64(0.14251497930485704), 81: np.float64(0.14251497930485704), 26: np.float64(0.14251497930485704), 62: np.float64(0.14251497930485704), 0: np.float64(0.14251497930485704)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 100]
learned probs (dictionary):

probs= {2: np.float64(0.1402161769866541), 37: np.float64(0.14329730383555783), 88: np.float64(0.14329730383555783), 81: np.float64(0.14329730383555783), 26: np.float64(0.14329730383555783), 62: np.float64(0.14329730383555783), 0: np.float64(0.14329730383555783)}
choice probs for this beta: {2: np.float64(0.1402161769866541), 37: np.float64(0.14329730383555783), 88: np.float64(0.14329730383555783), 81: np.float64(0.14329730383555783), 26: np.float64(0.14329730383555783), 62: np.float64(0.14329730383555783), 0: np.float64(0.14329730383555783)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{2: np.float64(0.1428571428571429), 37: np.float64(0.1428571428571429), 88: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 26: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {2: np.float64(0.03771428571428573), 37: np.float64(0.03771428571428573), 88: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 26: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.3493968123803352), 37: np.float64(0.1084338646032774), 88: np.float64(0.1084338646032774), 81: np.float64(0.1084338646032774), 26: np.float64(0.1084338646032774), 62: np.float64(0.1084338646032774), 0: np.float64(0.1084338646032774)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.29487033962621245), 37: np.float64(0.1175216100622979), 88: np.float64(0.1175216100622979), 81: np.float64(0.1175216100622979), 26: np.float64(0.1175216100622979), 62: np.float64(0.1175216100622979), 0: np.float64(0.1175216100622979)}
choice probs for this beta: {2: np.float64(0.29487033962621245), 37: np.float64(0.1175216100622979), 88: np.float64(0.1175216100622979), 81: np.float64(0.1175216100622979), 26: np.float64(0.1175216100622979), 62: np.float64(0.1175216100622979), 0: np.float64(0.1175216100622979)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 10, 100]
learned probs for cluster 2 

{2: np.float64(0.14285714285714293), 37: np.float64(0.14285714285714293), 88: np.float64(0.14285714285714293), 81: np.float64(0.14285714285714293), 26: np.float64(0.14285714285714293), 62: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 10, 100]
learned probs (dictionary):

probs= {2: np.float64(0.037714285714285735), 37: np.float64(0.037714285714285735), 88: np.float64(0.037714285714285735), 81: np.float64(0.037714285714285735), 26: np.float64(0.037714285714285735), 62: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{2: np.float64(0.8132067157120869), 37: np.float64(0.031132214047985614), 88: np.float64(0.031132214047985614), 81: np.float64(0.031132214047985614), 26: np.float64(0.031132214047985614), 62: np.float64(0.031132214047985614), 0: np.float64(0.031132214047985614)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {2: np.float64(0.6362344284783816), 37: np.float64(0.060627595253603145), 88: np.float64(0.060627595253603145), 81: np.float64(0.060627595253603145), 26: np.float64(0.060627595253603145), 62: np.float64(0.060627595253603145), 0: np.float64(0.060627595253603145)}
choice probs for this beta: {2: np.float64(0.6362344284783816), 37: np.float64(0.060627595253603145), 88: np.float64(0.060627595253603145), 81: np.float64(0.060627595253603145), 26: np.float64(0.060627595253603145), 62: np.float64(0.060627595253603145), 0: np.float64(0.060627595253603145)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 7, 13, 100, 2]
learned probs for cluster 2 

{2: np.float64(0.7100749265234687), 37: np.float64(0.048320845579421984), 88: np.float64(0.048320845579421984), 81: np.float64(0.048320845579421984), 26: np.float64(0.048320845579421984), 62: np.float64(0.048320845579421984), 0: np.float64(0.048320845579421984)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 7, 13, 100, 2]
learned probs (dictionary):

probs= {2: np.float64(0.18745978060219576), 37: np.float64(0.012756703232967403), 88: np.float64(0.012756703232967403), 81: np.float64(0.012756703232967403), 26: np.float64(0.012756703232967403), 62: np.float64(0.012756703232967403), 0: np.float64(0.012756703232967403)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.9908217773685968), 37: np.float64(0.0015297037719008571), 88: np.float64(0.0015297037719008571), 81: np.float64(0.0015297037719008571), 26: np.float64(0.0015297037719008571), 62: np.float64(0.0015297037719008571), 0: np.float64(0.0015297037719008571)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.9167046087454829), 37: np.float64(0.013882565209086435), 88: np.float64(0.013882565209086435), 81: np.float64(0.013882565209086435), 26: np.float64(0.013882565209086435), 62: np.float64(0.013882565209086435), 0: np.float64(0.013882565209086435)}
choice probs for this beta: {2: np.float64(0.9167046087454829), 37: np.float64(0.013882565209086435), 88: np.float64(0.013882565209086435), 81: np.float64(0.013882565209086435), 26: np.float64(0.013882565209086435), 62: np.float64(0.013882565209086435), 0: np.float64(0.013882565209086435)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 14: 2, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 5, 11, 14]
learned probs for cluster 2 

{2: np.float64(0.14285714285714285), 37: np.float64(0.14285714285714285), 88: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 26: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 5, 11, 14]
learned probs (dictionary):

probs= {2: np.float64(0.037714285714285714), 37: np.float64(0.037714285714285714), 88: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 26: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.9998172398393688), 37: np.float64(3.0460026771860668e-05), 88: np.float64(3.0460026771860668e-05), 81: np.float64(3.0460026771860668e-05), 26: np.float64(3.0460026771860668e-05), 62: np.float64(3.0460026771860668e-05), 0: np.float64(3.0460026771860668e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.7735797742360611), 37: np.float64(0.0377367042939898), 88: np.float64(0.0377367042939898), 81: np.float64(0.0377367042939898), 26: np.float64(0.0377367042939898), 62: np.float64(0.0377367042939898), 0: np.float64(0.0377367042939898)}
choice probs for this beta: {2: np.float64(0.7735797742360611), 37: np.float64(0.0377367042939898), 88: np.float64(0.0377367042939898), 81: np.float64(0.0377367042939898), 26: np.float64(0.0377367042939898), 62: np.float64(0.0377367042939898), 0: np.float64(0.0377367042939898)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 20: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5, 20]
learned probs for cluster 2 

{2: np.float64(0.14285714285714285), 37: np.float64(0.14285714285714285), 88: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 26: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5, 20]
learned probs (dictionary):

probs= {2: np.float64(0.037714285714285714), 37: np.float64(0.037714285714285714), 88: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 26: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.9999990546003826), 37: np.float64(1.5756660286391724e-07), 88: np.float64(1.5756660286391724e-07), 81: np.float64(1.5756660286391724e-07), 26: np.float64(1.5756660286391724e-07), 62: np.float64(1.5756660286391724e-07), 0: np.float64(1.5756660286391724e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.7737135899001673), 37: np.float64(0.03771440168330542), 88: np.float64(0.03771440168330542), 81: np.float64(0.03771440168330542), 26: np.float64(0.03771440168330542), 62: np.float64(0.03771440168330542), 0: np.float64(0.03771440168330542)}
choice probs for this beta: {2: np.float64(0.7737135899001673), 37: np.float64(0.03771440168330542), 88: np.float64(0.03771440168330542), 81: np.float64(0.03771440168330542), 26: np.float64(0.03771440168330542), 62: np.float64(0.03771440168330542), 0: np.float64(0.03771440168330542)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{2: np.float64(0.14285714285714285), 37: np.float64(0.14285714285714285), 88: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 26: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {2: np.float64(0.037714285714285714), 37: np.float64(0.037714285714285714), 88: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 26: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{2: np.float64(0.999999974111687), 37: np.float64(4.314718807217836e-09), 88: np.float64(4.314718807217836e-09), 81: np.float64(4.314718807217836e-09), 26: np.float64(4.314718807217836e-09), 62: np.float64(4.314718807217836e-09), 0: np.float64(4.314718807217836e-09)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {2: np.float64(0.7737142666604873), 37: np.float64(0.037714288889918755), 88: np.float64(0.037714288889918755), 81: np.float64(0.037714288889918755), 26: np.float64(0.037714288889918755), 62: np.float64(0.037714288889918755), 0: np.float64(0.037714288889918755)}
choice probs for this beta: {2: np.float64(0.7737142666604873), 37: np.float64(0.037714288889918755), 88: np.float64(0.037714288889918755), 81: np.float64(0.037714288889918755), 26: np.float64(0.037714288889918755), 62: np.float64(0.037714288889918755), 0: np.float64(0.037714288889918755)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 15: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 15, 100, 5, 14]
learned probs for cluster 2 

{2: np.float64(0.12924814871445733), 37: np.float64(0.14512530854759062), 88: np.float64(0.14512530854759062), 81: np.float64(0.14512530854759062), 26: np.float64(0.14512530854759062), 62: np.float64(0.14512530854759062), 0: np.float64(0.14512530854759062)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 15, 100, 5, 14]
learned probs (dictionary):

probs= {2: np.float64(0.03412151126061674), 37: np.float64(0.038313081456563924), 88: np.float64(0.038313081456563924), 81: np.float64(0.038313081456563924), 26: np.float64(0.038313081456563924), 62: np.float64(0.038313081456563924), 0: np.float64(0.038313081456563924)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.13203675248313484), 37: np.float64(0.14466054125281103), 88: np.float64(0.14466054125281103), 81: np.float64(0.14466054125281103), 26: np.float64(0.14466054125281103), 62: np.float64(0.14466054125281103), 0: np.float64(0.14466054125281103)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.13130056108820398), 37: np.float64(0.14478323981863284), 88: np.float64(0.14478323981863284), 81: np.float64(0.14478323981863284), 26: np.float64(0.14478323981863284), 62: np.float64(0.14478323981863284), 0: np.float64(0.14478323981863284)}
choice probs for this beta: {2: np.float64(0.13130056108820398), 37: np.float64(0.14478323981863284), 88: np.float64(0.14478323981863284), 81: np.float64(0.14478323981863284), 26: np.float64(0.14478323981863284), 62: np.float64(0.14478323981863284), 0: np.float64(0.14478323981863284)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4]
learned probs for cluster 2 

{2: np.float64(0.1428571428571429), 37: np.float64(0.1428571428571429), 88: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 26: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4]
learned probs (dictionary):

probs= {2: np.float64(0.03771428571428573), 37: np.float64(0.03771428571428573), 88: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 26: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 10, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.18285033221559574), 37: np.float64(0.1361916112974028), 88: np.float64(0.1361916112974028), 81: np.float64(0.1361916112974028), 26: np.float64(0.1361916112974028), 62: np.float64(0.1361916112974028), 0: np.float64(0.1361916112974028)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 10, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.1722921302249642), 37: np.float64(0.13795131162917418), 88: np.float64(0.13795131162917418), 81: np.float64(0.13795131162917418), 26: np.float64(0.13795131162917418), 62: np.float64(0.13795131162917418), 0: np.float64(0.13795131162917418)}
choice probs for this beta: {2: np.float64(0.1722921302249642), 37: np.float64(0.13795131162917418), 88: np.float64(0.13795131162917418), 81: np.float64(0.13795131162917418), 26: np.float64(0.13795131162917418), 62: np.float64(0.13795131162917418), 0: np.float64(0.13795131162917418)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 17: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 17]
learned probs for cluster 2 

{2: np.float64(0.14285714285714315), 37: np.float64(0.14285714285714315), 88: np.float64(0.14285714285714315), 81: np.float64(0.14285714285714315), 26: np.float64(0.14285714285714315), 62: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 17]
learned probs (dictionary):

probs= {2: np.float64(0.0377142857142858), 37: np.float64(0.0377142857142858), 88: np.float64(0.0377142857142858), 81: np.float64(0.0377142857142858), 26: np.float64(0.0377142857142858), 62: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.3493968123803352), 37: np.float64(0.1084338646032774), 88: np.float64(0.1084338646032774), 81: np.float64(0.1084338646032774), 26: np.float64(0.1084338646032774), 62: np.float64(0.1084338646032774), 0: np.float64(0.1084338646032774)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.2948703396262125), 37: np.float64(0.11752161006229797), 88: np.float64(0.11752161006229797), 81: np.float64(0.11752161006229797), 26: np.float64(0.11752161006229797), 62: np.float64(0.11752161006229797), 0: np.float64(0.11752161006229797)}
choice probs for this beta: {2: np.float64(0.2948703396262125), 37: np.float64(0.11752161006229797), 88: np.float64(0.11752161006229797), 81: np.float64(0.11752161006229797), 26: np.float64(0.11752161006229797), 62: np.float64(0.11752161006229797), 0: np.float64(0.11752161006229797)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 2, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 13, 100, 10]
learned probs for cluster 2 

{2: np.float64(0.14285714285714263), 37: np.float64(0.14285714285714263), 88: np.float64(0.14285714285714263), 81: np.float64(0.14285714285714263), 26: np.float64(0.14285714285714263), 62: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 13, 100, 10]
learned probs (dictionary):

probs= {2: np.float64(0.03771428571428566), 37: np.float64(0.03771428571428566), 88: np.float64(0.03771428571428566), 81: np.float64(0.03771428571428566), 26: np.float64(0.03771428571428566), 62: np.float64(0.03771428571428566), 0: np.float64(0.03771428571428566)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{2: np.float64(0.773640823342681), 37: np.float64(0.03772652944288633), 88: np.float64(0.03772652944288633), 81: np.float64(0.03772652944288633), 26: np.float64(0.03772652944288633), 62: np.float64(0.03772652944288633), 0: np.float64(0.03772652944288633)}
cluster label 1 learned center: 
 
sigma= [1, 2, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {2: np.float64(0.6071139316944989), 37: np.float64(0.06548101138425), 88: np.float64(0.06548101138425), 81: np.float64(0.06548101138425), 26: np.float64(0.06548101138425), 62: np.float64(0.06548101138425), 0: np.float64(0.06548101138425)}
choice probs for this beta: {2: np.float64(0.6071139316944989), 37: np.float64(0.06548101138425), 88: np.float64(0.06548101138425), 81: np.float64(0.06548101138425), 26: np.float64(0.06548101138425), 62: np.float64(0.06548101138425), 0: np.float64(0.06548101138425)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{2: np.float64(0.1428571428571429), 37: np.float64(0.1428571428571429), 88: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 26: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {2: np.float64(0.03771428571428573), 37: np.float64(0.03771428571428573), 88: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 26: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{2: np.float64(0.9859246696846666), 37: np.float64(0.0023458883858890377), 88: np.float64(0.0023458883858890377), 81: np.float64(0.0023458883858890377), 26: np.float64(0.0023458883858890377), 62: np.float64(0.0023458883858890377), 0: np.float64(0.0023458883858890377)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {2: np.float64(0.7633548426022003), 37: np.float64(0.03944085956630006), 88: np.float64(0.03944085956630006), 81: np.float64(0.03944085956630006), 26: np.float64(0.03944085956630006), 62: np.float64(0.03944085956630006), 0: np.float64(0.03944085956630006)}
choice probs for this beta: {2: np.float64(0.7633548426022003), 37: np.float64(0.03944085956630006), 88: np.float64(0.03944085956630006), 81: np.float64(0.03944085956630006), 26: np.float64(0.03944085956630006), 62: np.float64(0.03944085956630006), 0: np.float64(0.03944085956630006)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs for cluster 2 

{2: np.float64(0.1428571428571429), 37: np.float64(0.1428571428571429), 88: np.float64(0.1428571428571429), 81: np.float64(0.1428571428571429), 26: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs (dictionary):

probs= {2: np.float64(0.03771428571428573), 37: np.float64(0.03771428571428573), 88: np.float64(0.03771428571428573), 81: np.float64(0.03771428571428573), 26: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.9998172398393688), 37: np.float64(3.0460026771860668e-05), 88: np.float64(3.0460026771860668e-05), 81: np.float64(3.0460026771860668e-05), 26: np.float64(3.0460026771860668e-05), 62: np.float64(3.0460026771860668e-05), 0: np.float64(3.0460026771860668e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.7735797742360611), 37: np.float64(0.037736704293989815), 88: np.float64(0.037736704293989815), 81: np.float64(0.037736704293989815), 26: np.float64(0.037736704293989815), 62: np.float64(0.037736704293989815), 0: np.float64(0.037736704293989815)}
choice probs for this beta: {2: np.float64(0.7735797742360611), 37: np.float64(0.037736704293989815), 88: np.float64(0.037736704293989815), 81: np.float64(0.037736704293989815), 26: np.float64(0.037736704293989815), 62: np.float64(0.037736704293989815), 0: np.float64(0.037736704293989815)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{2: np.float64(0.14285714285714285), 37: np.float64(0.14285714285714285), 88: np.float64(0.14285714285714285), 81: np.float64(0.14285714285714285), 26: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {2: np.float64(0.037714285714285714), 37: np.float64(0.037714285714285714), 88: np.float64(0.037714285714285714), 81: np.float64(0.037714285714285714), 26: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.9999990546003826), 37: np.float64(1.5756660286391724e-07), 88: np.float64(1.5756660286391724e-07), 81: np.float64(1.5756660286391724e-07), 26: np.float64(1.5756660286391724e-07), 62: np.float64(1.5756660286391724e-07), 0: np.float64(1.5756660286391724e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.7737135899001673), 37: np.float64(0.03771440168330542), 88: np.float64(0.03771440168330542), 81: np.float64(0.03771440168330542), 26: np.float64(0.03771440168330542), 62: np.float64(0.03771440168330542), 0: np.float64(0.03771440168330542)}
choice probs for this beta: {2: np.float64(0.7737135899001673), 37: np.float64(0.03771440168330542), 88: np.float64(0.03771440168330542), 81: np.float64(0.03771440168330542), 26: np.float64(0.03771440168330542), 62: np.float64(0.03771440168330542), 0: np.float64(0.03771440168330542)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 15: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 5, 14, 15]
learned probs for cluster 2 

{2: np.float64(0.9999851809865727), 37: np.float64(2.4698355711467735e-06), 88: np.float64(2.4698355711467735e-06), 81: np.float64(2.4698355711467735e-06), 26: np.float64(2.4698355711467735e-06), 62: np.float64(2.4698355711467735e-06), 0: np.float64(2.4698355711467735e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 5, 14, 15]
learned probs (dictionary):

probs= {2: np.float64(0.2639960877804552), 37: np.float64(6.520365907827483e-07), 88: np.float64(6.520365907827483e-07), 81: np.float64(6.520365907827483e-07), 26: np.float64(6.520365907827483e-07), 62: np.float64(6.520365907827483e-07), 0: np.float64(6.520365907827483e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs for cluster 1 

{2: np.float64(0.999999974111687), 37: np.float64(4.314718807217836e-09), 88: np.float64(4.314718807217836e-09), 81: np.float64(4.314718807217836e-09), 26: np.float64(4.314718807217836e-09), 62: np.float64(4.314718807217836e-09), 0: np.float64(4.314718807217836e-09)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs (dictionary):

probs= {2: np.float64(0.9999960687266567), 37: np.float64(6.552122238248606e-07), 88: np.float64(6.552122238248606e-07), 81: np.float64(6.552122238248606e-07), 26: np.float64(6.552122238248606e-07), 62: np.float64(6.552122238248606e-07), 0: np.float64(6.552122238248606e-07)}
choice probs for this beta: {2: np.float64(0.9999960687266567), 37: np.float64(6.552122238248606e-07), 88: np.float64(6.552122238248606e-07), 81: np.float64(6.552122238248606e-07), 26: np.float64(6.552122238248606e-07), 62: np.float64(6.552122238248606e-07), 0: np.float64(6.552122238248606e-07)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 88
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 81
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 88
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 37
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 26
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 88
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 0
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 2
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 26
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 81
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 26
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 81
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 2
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 37
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 88
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 2
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 37
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 62
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 26
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 2
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 62
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 88
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 26
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 88
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 2
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 0
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 62
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 2
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 37
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 81
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 62
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 26
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 62
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 0
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 2
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 26
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 37
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 2
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 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 26
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 37
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 62
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 26
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 81
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 81
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 37
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 37
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 88
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 26
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 62
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 37
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 81
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 2
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 88
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 37
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 37
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 88
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 88
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 26
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 81
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 26
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 26
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 26
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 2
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 62
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 62
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 37
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 37
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 26
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 81
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 81
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 0
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 81
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 37
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 0
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 0
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 26
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 62
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 2
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 88
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 37
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 0
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 2
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 37
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 26
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 26
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 88
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 0
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 26
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 81
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 2
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 37
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 2
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 2
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 26
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 2
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 81
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 62
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 81
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 26
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 37
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 81
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 62
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 26
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 26
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 26
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 37
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 62
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 62
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 26
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 26
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 81
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 26
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 26
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 62
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 88
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 2
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 2
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 2
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 26
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 26
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 26
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 62
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 2
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 81
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 2
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 2
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 2
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 2
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 26
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 88
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 62
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 37
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 37
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 26
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 37
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 81
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 26
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 2
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 2
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 2
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 2
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 26
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 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 37
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 2
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 2
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 26
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 26
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 37
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 88
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 26
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 26
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 62
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 81
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 88
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 26
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 2
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 37
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 26
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 37
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 62
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 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 37
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 62
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 37
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 88
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 62
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 0
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 26
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 26
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 0
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 26
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 81
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 88
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 26
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 81
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 62
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 2
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 37
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 26
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 37
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 2
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 26
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 26
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 81
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 37
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 81
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 26
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 2
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 37
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 26
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 0
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 26
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 26
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 81
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 26
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 88
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 2
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 26
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 37
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 0
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 37
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 26
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 26
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 81
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 81
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 0
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 26
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 2
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 2
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 37
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 88
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 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 26
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 26
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 26
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 2
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 2
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 37
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 37
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 37
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 26
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 0
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 81
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 26
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 26
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 26
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 26
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 2
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 2
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 2
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 2
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 62
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 0
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 81
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 0
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 81
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 26
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 2
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 37
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 2
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 26
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 37
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 26
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 81
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 26
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 37
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 62
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 26
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 62
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 62
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 26
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 26
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 26
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 2
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 26
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 2
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 37
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 37
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 81
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 81
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 26
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 0
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 26
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 26
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 37
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 88
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 81
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 37
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 2
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 2
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 26
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 88
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 2
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 62
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 81
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 62
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 88
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 88
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 81
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 88
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 37
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 26
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 62
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 26
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 88
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 26
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 26
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 88
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 62
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 26
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 26
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 0
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 88
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 37
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 37
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 2
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 62
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 37
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 62
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 81
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 37
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 81
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 26
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 26
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 37
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 62
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 26
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 26
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 2
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 0
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 2
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 2
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 88
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 26
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 2
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 62
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 37
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 37
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 81
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 88
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 62
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 81
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 2
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 37
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 62
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 2
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 2
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 81
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 37
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 26
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 37
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 37
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 62
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 2
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 0
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 26
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 26
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 37
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 81
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 26
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 26
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 26
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 37
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 0
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 26
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 0
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 88
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 26
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 2
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 26
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 26
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 26
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 88
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 88
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 81
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 26
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 37
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 2
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 2
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 2
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 37
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 81
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 37
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 26
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 26
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 2
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 37
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 88
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 88
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 2
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 37
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 37
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 0
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 88
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 37
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 37
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 37
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 37
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 26
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 88
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 37
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 88
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 26
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 37
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 37
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 0
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 26
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 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 81
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 26
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 88
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 26
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 88
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 0
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 26
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 26
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 26
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 2
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 26
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 37
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 88
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 26
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 88
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 26
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 26
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 37
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 88
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 88
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 88
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 26
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 26
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 0
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 2
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 37
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 81
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 26
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 26
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 2
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 2
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 2
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 0
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 2
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 26
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 2
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 2
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 26
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 62
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 62
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 26
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 26
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 62
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 88
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 26
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 26
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 0
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 26
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 88
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 2
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 81
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 62
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 37
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 88
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 62
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 37
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 62
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 37
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 26
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 37
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 2
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 81
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 88
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 88
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 26
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 62
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 26
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 26
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 88
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 62
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 26
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 88
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 26
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 26
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 0
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 88
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 62
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 0
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 0
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 26
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 0
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 62
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 62
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 0
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 0
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 26
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 81
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 88
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 37
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 81
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 37
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 88
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 0
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 2
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 88
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 37
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 26
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 26
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 88
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 88
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 2
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 26
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 26
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 88
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 62
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 88
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 88
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 2
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 26
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 81
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 0
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 62
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 0
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 2
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 88
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 2
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 37
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 88
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 81
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 37
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 26
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 26
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 88
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 37
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 62
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 26
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 37
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 0
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 2
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 0
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 2
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 0
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 26
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 81
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 26
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 88
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 2
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 26
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 0
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 26
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 2
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 88
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 37
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 2
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 2
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 26
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 26
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 26
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 62
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 2
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 37
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 37
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 26
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 37
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 37
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 88
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 26
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 62
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 26
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 37
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 26
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 81
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 26
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 26
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 81
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 0
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 2
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 2
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 2
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 81
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 37
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 26
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 0
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 26
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 2
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 2
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 62
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 26
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 88
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 2
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 26
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 2
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 88
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 26
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 0
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 62
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 2
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 2
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 81
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 37
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 2
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 26
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 37
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 26
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 81
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 26
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 26
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 37
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 88
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 62
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 62
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 88
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 37
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 37
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 62
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 26
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 26
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 81
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 37
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 37
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 0
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 88
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 62
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 26
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 62
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 2
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 2
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 37
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 62
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 88
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 26
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 88
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 88
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 37
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 62
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 26
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 62
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 2
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 2
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 2
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 2
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 26
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 2
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 62
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 37
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 62
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 26
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 0
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 26
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 37
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 2
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 81
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 37
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 62
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 37
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 88
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 26
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 81
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 62
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 26
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 26
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 81
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 81
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 0
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 26
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 26
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 62
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 26
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 26
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 88
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 37
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 81
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 26
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 0
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 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 62
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 26
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 26
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 88
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 2
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 88
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 26
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 26
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 0
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 26
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 62
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 62
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 62
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 26
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 81
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 37
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 81
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 26
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 62
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 26
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 37
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 26
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 26
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 37
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 26
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 2
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 88
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 37
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 26
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 62
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 88
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 62
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 2
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 37
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 37
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 88
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 62
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 26
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 0
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 0
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 2
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 2
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 88
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 62
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 2
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 2
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 62
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 26
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 37
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 81
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 81
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 2
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 37
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 2
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 2
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 2
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 88
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 62
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 81
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 88
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 37
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 88
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 26
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 62
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 62
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 0
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 88
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 26
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 26
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 62
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 26
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 2
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 2
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 2
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 2
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 0
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 88
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 26
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 26
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 0
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 0
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 26
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 0
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 37
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 26
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 81
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 26
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 2
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 37
emperical probablities from test set: {2: 0.32, 37: 0.157, 88: 0.088, 81: 0.07, 26: 0.204, 62: 0.099, 0: 0.062}
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.18869943891179602), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: np.float64(0.012216760181367164), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.18869943891179602), np.float64(0.012216760181367164), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: np.float64(0.012216760181367164), 88: np.float64(0.05678323981863284), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.18869943891179602), np.float64(0.012216760181367164), np.float64(0.05678323981863284), 0, 0, 0, 0]
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: np.float64(0.012216760181367164), 88: np.float64(0.05678323981863284), 81: np.float64(0.07478323981863283), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.18869943891179602), np.float64(0.012216760181367164), np.float64(0.05678323981863284), np.float64(0.07478323981863283), 0, 0, 0]
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: np.float64(0.012216760181367164), 88: np.float64(0.05678323981863284), 81: np.float64(0.07478323981863283), 26: np.float64(0.05921676018136715), 62: 0, 0: 0} 

err list= [np.float64(0.18869943891179602), np.float64(0.012216760181367164), np.float64(0.05678323981863284), np.float64(0.07478323981863283), np.float64(0.05921676018136715), 0, 0]
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: np.float64(0.012216760181367164), 88: np.float64(0.05678323981863284), 81: np.float64(0.07478323981863283), 26: np.float64(0.05921676018136715), 62: np.float64(0.04578323981863283), 0: 0} 

err list= [np.float64(0.18869943891179602), np.float64(0.012216760181367164), np.float64(0.05678323981863284), np.float64(0.07478323981863283), np.float64(0.05921676018136715), np.float64(0.04578323981863283), 0]
beta is  0.025 

err dic= {2: np.float64(0.18869943891179602), 37: np.float64(0.012216760181367164), 88: np.float64(0.05678323981863284), 81: np.float64(0.07478323981863283), 26: np.float64(0.05921676018136715), 62: np.float64(0.04578323981863283), 0: np.float64(0.08278323981863284)} 

err list= [np.float64(0.18869943891179602), np.float64(0.012216760181367164), np.float64(0.05678323981863284), np.float64(0.07478323981863283), np.float64(0.05921676018136715), np.float64(0.04578323981863283), np.float64(0.08278323981863284)]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1477078697750358), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: np.float64(0.019048688370825823), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1477078697750358), np.float64(0.019048688370825823), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: np.float64(0.019048688370825823), 88: np.float64(0.04995131162917418), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1477078697750358), np.float64(0.019048688370825823), np.float64(0.04995131162917418), 0, 0, 0, 0]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: np.float64(0.019048688370825823), 88: np.float64(0.04995131162917418), 81: np.float64(0.06795131162917417), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1477078697750358), np.float64(0.019048688370825823), np.float64(0.04995131162917418), np.float64(0.06795131162917417), 0, 0, 0]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: np.float64(0.019048688370825823), 88: np.float64(0.04995131162917418), 81: np.float64(0.06795131162917417), 26: np.float64(0.06604868837082581), 62: 0, 0: 0} 

err list= [np.float64(0.1477078697750358), np.float64(0.019048688370825823), np.float64(0.04995131162917418), np.float64(0.06795131162917417), np.float64(0.06604868837082581), 0, 0]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: np.float64(0.019048688370825823), 88: np.float64(0.04995131162917418), 81: np.float64(0.06795131162917417), 26: np.float64(0.06604868837082581), 62: np.float64(0.03895131162917417), 0: 0} 

err list= [np.float64(0.1477078697750358), np.float64(0.019048688370825823), np.float64(0.04995131162917418), np.float64(0.06795131162917417), np.float64(0.06604868837082581), np.float64(0.03895131162917417), 0]
beta is  0.05 

err dic= {2: np.float64(0.1477078697750358), 37: np.float64(0.019048688370825823), 88: np.float64(0.04995131162917418), 81: np.float64(0.06795131162917417), 26: np.float64(0.06604868837082581), 62: np.float64(0.03895131162917417), 0: np.float64(0.07595131162917418)} 

err list= [np.float64(0.1477078697750358), np.float64(0.019048688370825823), np.float64(0.04995131162917418), np.float64(0.06795131162917417), np.float64(0.06604868837082581), np.float64(0.03895131162917417), np.float64(0.07595131162917418)]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.0251296603737875), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: np.float64(0.03947838993770203), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.0251296603737875), np.float64(0.03947838993770203), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: np.float64(0.03947838993770203), 88: np.float64(0.029521610062297976), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.0251296603737875), np.float64(0.03947838993770203), np.float64(0.029521610062297976), 0, 0, 0, 0]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: np.float64(0.03947838993770203), 88: np.float64(0.029521610062297976), 81: np.float64(0.047521610062297964), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.0251296603737875), np.float64(0.03947838993770203), np.float64(0.029521610062297976), np.float64(0.047521610062297964), 0, 0, 0]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: np.float64(0.03947838993770203), 88: np.float64(0.029521610062297976), 81: np.float64(0.047521610062297964), 26: np.float64(0.08647838993770202), 62: 0, 0: 0} 

err list= [np.float64(0.0251296603737875), np.float64(0.03947838993770203), np.float64(0.029521610062297976), np.float64(0.047521610062297964), np.float64(0.08647838993770202), 0, 0]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: np.float64(0.03947838993770203), 88: np.float64(0.029521610062297976), 81: np.float64(0.047521610062297964), 26: np.float64(0.08647838993770202), 62: np.float64(0.018521610062297966), 0: 0} 

err list= [np.float64(0.0251296603737875), np.float64(0.03947838993770203), np.float64(0.029521610062297976), np.float64(0.047521610062297964), np.float64(0.08647838993770202), np.float64(0.018521610062297966), 0]
beta is  0.1 

err dic= {2: np.float64(0.0251296603737875), 37: np.float64(0.03947838993770203), 88: np.float64(0.029521610062297976), 81: np.float64(0.047521610062297964), 26: np.float64(0.08647838993770202), 62: np.float64(0.018521610062297966), 0: np.float64(0.05552161006229797)} 

err list= [np.float64(0.0251296603737875), np.float64(0.03947838993770203), np.float64(0.029521610062297976), np.float64(0.047521610062297964), np.float64(0.08647838993770202), np.float64(0.018521610062297966), np.float64(0.05552161006229797)]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.2871139316944989), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: np.float64(0.09151898861575), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.2871139316944989), np.float64(0.09151898861575), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: np.float64(0.09151898861575), 88: np.float64(0.022518988615749996), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.2871139316944989), np.float64(0.09151898861575), np.float64(0.022518988615749996), 0, 0, 0, 0]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: np.float64(0.09151898861575), 88: np.float64(0.022518988615749996), 81: np.float64(0.004518988615750008), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.2871139316944989), np.float64(0.09151898861575), np.float64(0.022518988615749996), np.float64(0.004518988615750008), 0, 0, 0]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: np.float64(0.09151898861575), 88: np.float64(0.022518988615749996), 81: np.float64(0.004518988615750008), 26: np.float64(0.13851898861575), 62: 0, 0: 0} 

err list= [np.float64(0.2871139316944989), np.float64(0.09151898861575), np.float64(0.022518988615749996), np.float64(0.004518988615750008), np.float64(0.13851898861575), 0, 0]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: np.float64(0.09151898861575), 88: np.float64(0.022518988615749996), 81: np.float64(0.004518988615750008), 26: np.float64(0.13851898861575), 62: np.float64(0.033518988615750006), 0: 0} 

err list= [np.float64(0.2871139316944989), np.float64(0.09151898861575), np.float64(0.022518988615749996), np.float64(0.004518988615750008), np.float64(0.13851898861575), np.float64(0.033518988615750006), 0]
beta is  0.25 

err dic= {2: np.float64(0.2871139316944989), 37: np.float64(0.09151898861575), 88: np.float64(0.022518988615749996), 81: np.float64(0.004518988615750008), 26: np.float64(0.13851898861575), 62: np.float64(0.033518988615750006), 0: np.float64(0.003481011384249999)} 

err list= [np.float64(0.2871139316944989), np.float64(0.09151898861575), np.float64(0.022518988615749996), np.float64(0.004518988615750008), np.float64(0.13851898861575), np.float64(0.033518988615750006), np.float64(0.003481011384249999)]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.4433548426022003), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: np.float64(0.11755914043369994), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.4433548426022003), np.float64(0.11755914043369994), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: np.float64(0.11755914043369994), 88: np.float64(0.04855914043369994), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.4433548426022003), np.float64(0.11755914043369994), np.float64(0.04855914043369994), 0, 0, 0, 0]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: np.float64(0.11755914043369994), 88: np.float64(0.04855914043369994), 81: np.float64(0.03055914043369995), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.4433548426022003), np.float64(0.11755914043369994), np.float64(0.04855914043369994), np.float64(0.03055914043369995), 0, 0, 0]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: np.float64(0.11755914043369994), 88: np.float64(0.04855914043369994), 81: np.float64(0.03055914043369995), 26: np.float64(0.16455914043369993), 62: 0, 0: 0} 

err list= [np.float64(0.4433548426022003), np.float64(0.11755914043369994), np.float64(0.04855914043369994), np.float64(0.03055914043369995), np.float64(0.16455914043369993), 0, 0]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: np.float64(0.11755914043369994), 88: np.float64(0.04855914043369994), 81: np.float64(0.03055914043369995), 26: np.float64(0.16455914043369993), 62: np.float64(0.05955914043369995), 0: 0} 

err list= [np.float64(0.4433548426022003), np.float64(0.11755914043369994), np.float64(0.04855914043369994), np.float64(0.03055914043369995), np.float64(0.16455914043369993), np.float64(0.05955914043369995), 0]
beta is  0.5 

err dic= {2: np.float64(0.4433548426022003), 37: np.float64(0.11755914043369994), 88: np.float64(0.04855914043369994), 81: np.float64(0.03055914043369995), 26: np.float64(0.16455914043369993), 62: np.float64(0.05955914043369995), 0: np.float64(0.022559140433699942)} 

err list= [np.float64(0.4433548426022003), np.float64(0.11755914043369994), np.float64(0.04855914043369994), np.float64(0.03055914043369995), np.float64(0.16455914043369993), np.float64(0.05955914043369995), np.float64(0.022559140433699942)]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45357977423606105), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: np.float64(0.11926329570601019), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45357977423606105), np.float64(0.11926329570601019), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: np.float64(0.11926329570601019), 88: np.float64(0.05026329570601018), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45357977423606105), np.float64(0.11926329570601019), np.float64(0.05026329570601018), 0, 0, 0, 0]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: np.float64(0.11926329570601019), 88: np.float64(0.05026329570601018), 81: np.float64(0.03226329570601019), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45357977423606105), np.float64(0.11926329570601019), np.float64(0.05026329570601018), np.float64(0.03226329570601019), 0, 0, 0]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: np.float64(0.11926329570601019), 88: np.float64(0.05026329570601018), 81: np.float64(0.03226329570601019), 26: np.float64(0.16626329570601017), 62: 0, 0: 0} 

err list= [np.float64(0.45357977423606105), np.float64(0.11926329570601019), np.float64(0.05026329570601018), np.float64(0.03226329570601019), np.float64(0.16626329570601017), 0, 0]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: np.float64(0.11926329570601019), 88: np.float64(0.05026329570601018), 81: np.float64(0.03226329570601019), 26: np.float64(0.16626329570601017), 62: np.float64(0.06126329570601019), 0: 0} 

err list= [np.float64(0.45357977423606105), np.float64(0.11926329570601019), np.float64(0.05026329570601018), np.float64(0.03226329570601019), np.float64(0.16626329570601017), np.float64(0.06126329570601019), 0]
beta is  0.75 

err dic= {2: np.float64(0.45357977423606105), 37: np.float64(0.11926329570601019), 88: np.float64(0.05026329570601018), 81: np.float64(0.03226329570601019), 26: np.float64(0.16626329570601017), 62: np.float64(0.06126329570601019), 0: np.float64(0.024263295706010185)} 

err list= [np.float64(0.45357977423606105), np.float64(0.11926329570601019), np.float64(0.05026329570601018), np.float64(0.03226329570601019), np.float64(0.16626329570601017), np.float64(0.06126329570601019), np.float64(0.024263295706010185)]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45371358990016725), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: np.float64(0.11928559831669458), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45371358990016725), np.float64(0.11928559831669458), 0, 0, 0, 0, 0]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: np.float64(0.11928559831669458), 88: np.float64(0.050285598316694574), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45371358990016725), np.float64(0.11928559831669458), np.float64(0.050285598316694574), 0, 0, 0, 0]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: np.float64(0.11928559831669458), 88: np.float64(0.050285598316694574), 81: np.float64(0.032285598316694586), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.45371358990016725), np.float64(0.11928559831669458), np.float64(0.050285598316694574), np.float64(0.032285598316694586), 0, 0, 0]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: np.float64(0.11928559831669458), 88: np.float64(0.050285598316694574), 81: np.float64(0.032285598316694586), 26: np.float64(0.16628559831669457), 62: 0, 0: 0} 

err list= [np.float64(0.45371358990016725), np.float64(0.11928559831669458), np.float64(0.050285598316694574), np.float64(0.032285598316694586), np.float64(0.16628559831669457), 0, 0]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: np.float64(0.11928559831669458), 88: np.float64(0.050285598316694574), 81: np.float64(0.032285598316694586), 26: np.float64(0.16628559831669457), 62: np.float64(0.061285598316694584), 0: 0} 

err list= [np.float64(0.45371358990016725), np.float64(0.11928559831669458), np.float64(0.050285598316694574), np.float64(0.032285598316694586), np.float64(0.16628559831669457), np.float64(0.061285598316694584), 0]
beta is  1 

err dic= {2: np.float64(0.45371358990016725), 37: np.float64(0.11928559831669458), 88: np.float64(0.050285598316694574), 81: np.float64(0.032285598316694586), 26: np.float64(0.16628559831669457), 62: np.float64(0.061285598316694584), 0: np.float64(0.02428559831669458)} 

err list= [np.float64(0.45371358990016725), np.float64(0.11928559831669458), np.float64(0.050285598316694574), np.float64(0.032285598316694586), np.float64(0.16628559831669457), np.float64(0.061285598316694584), np.float64(0.02428559831669458)]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: 0, 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.6799960687266566), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: np.float64(0.15699934478777616), 88: 0, 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.6799960687266566), np.float64(0.15699934478777616), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: np.float64(0.15699934478777616), 88: np.float64(0.08799934478777617), 81: 0, 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.6799960687266566), np.float64(0.15699934478777616), np.float64(0.08799934478777617), 0, 0, 0, 0]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: np.float64(0.15699934478777616), 88: np.float64(0.08799934478777617), 81: np.float64(0.06999934478777618), 26: 0, 62: 0, 0: 0} 

err list= [np.float64(0.6799960687266566), np.float64(0.15699934478777616), np.float64(0.08799934478777617), np.float64(0.06999934478777618), 0, 0, 0]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: np.float64(0.15699934478777616), 88: np.float64(0.08799934478777617), 81: np.float64(0.06999934478777618), 26: np.float64(0.20399934478777615), 62: 0, 0: 0} 

err list= [np.float64(0.6799960687266566), np.float64(0.15699934478777616), np.float64(0.08799934478777617), np.float64(0.06999934478777618), np.float64(0.20399934478777615), 0, 0]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: np.float64(0.15699934478777616), 88: np.float64(0.08799934478777617), 81: np.float64(0.06999934478777618), 26: np.float64(0.20399934478777615), 62: np.float64(0.09899934478777618), 0: 0} 

err list= [np.float64(0.6799960687266566), np.float64(0.15699934478777616), np.float64(0.08799934478777617), np.float64(0.06999934478777618), np.float64(0.20399934478777615), np.float64(0.09899934478777618), 0]
beta is  1.25 

err dic= {2: np.float64(0.6799960687266566), 37: np.float64(0.15699934478777616), 88: np.float64(0.08799934478777617), 81: np.float64(0.06999934478777618), 26: np.float64(0.20399934478777615), 62: np.float64(0.09899934478777618), 0: np.float64(0.061999344787776176)} 

err list= [np.float64(0.6799960687266566), np.float64(0.15699934478777616), np.float64(0.08799934478777617), np.float64(0.06999934478777618), np.float64(0.20399934478777615), np.float64(0.09899934478777618), np.float64(0.061999344787776176)]
samppled assortment [22, 86, 92, 52, 24, 62]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{22: np.float64(0.14285714285714327), 86: np.float64(0.14285714285714327), 92: np.float64(0.14285714285714327), 52: np.float64(0.14285714285714327), 24: np.float64(0.14285714285714327), 62: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285825), 86: np.float64(0.037714285714285825), 92: np.float64(0.037714285714285825), 52: np.float64(0.037714285714285825), 24: np.float64(0.037714285714285825), 62: np.float64(0.037714285714285825), 0: np.float64(0.037714285714285825)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714327), 86: np.float64(0.14285714285714327), 92: np.float64(0.14285714285714327), 52: np.float64(0.14285714285714327), 24: np.float64(0.14285714285714327), 62: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714327), 86: np.float64(0.14285714285714327), 92: np.float64(0.14285714285714327), 52: np.float64(0.14285714285714327), 24: np.float64(0.14285714285714327), 62: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
choice probs for this beta: {22: np.float64(0.14285714285714327), 86: np.float64(0.14285714285714327), 92: np.float64(0.14285714285714327), 52: np.float64(0.14285714285714327), 24: np.float64(0.14285714285714327), 62: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 14: 2, 100: 1} [8, 1, 3, 5, 6, 7, 10, 11, 100, 14]
learned probs for cluster 2 

{22: np.float64(0.14285714285714435), 86: np.float64(0.14285714285714435), 92: np.float64(0.14285714285714435), 52: np.float64(0.14285714285714435), 24: np.float64(0.14285714285714435), 62: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 11, 100, 14]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428611), 86: np.float64(0.03771428571428611), 92: np.float64(0.03771428571428611), 52: np.float64(0.03771428571428611), 24: np.float64(0.03771428571428611), 62: np.float64(0.03771428571428611), 0: np.float64(0.03771428571428611)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714293), 86: np.float64(0.14285714285714293), 92: np.float64(0.14285714285714293), 52: np.float64(0.14285714285714293), 24: np.float64(0.14285714285714293), 62: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 1 learned center: 
 
sigma= [1, 2, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.1428571428571433), 86: np.float64(0.1428571428571433), 92: np.float64(0.1428571428571433), 52: np.float64(0.1428571428571433), 24: np.float64(0.1428571428571433), 62: np.float64(0.1428571428571433), 0: np.float64(0.1428571428571433)}
choice probs for this beta: {22: np.float64(0.1428571428571433), 86: np.float64(0.1428571428571433), 92: np.float64(0.1428571428571433), 52: np.float64(0.1428571428571433), 24: np.float64(0.1428571428571433), 62: np.float64(0.1428571428571433), 0: np.float64(0.1428571428571433)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428573), 86: np.float64(0.03771428571428573), 92: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 24: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 19: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 19]
learned probs for cluster 2 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5, 19]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428573), 86: np.float64(0.03771428571428573), 92: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 24: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 100]
learned probs for cluster 1 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 100]
learned probs (dictionary):

probs= {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs for cluster 2 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428573), 86: np.float64(0.03771428571428573), 92: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 24: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 20: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5, 20]
learned probs for cluster 2 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 5, 20]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428573), 86: np.float64(0.03771428571428573), 92: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 24: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 19: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 19]
learned probs for cluster 2 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 19]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285714), 86: np.float64(0.037714285714285714), 92: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 24: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714288), 86: np.float64(0.14285714285714288), 92: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 24: np.float64(0.14285714285714288), 62: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285714), 86: np.float64(0.037714285714285714), 92: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 24: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{22: np.float64(0.14285714285714307), 86: np.float64(0.14285714285714307), 92: np.float64(0.14285714285714307), 52: np.float64(0.14285714285714307), 24: np.float64(0.14285714285714307), 62: np.float64(0.14285714285714307), 0: np.float64(0.14285714285714307)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428577), 86: np.float64(0.03771428571428577), 92: np.float64(0.03771428571428577), 52: np.float64(0.03771428571428577), 24: np.float64(0.03771428571428577), 62: np.float64(0.03771428571428577), 0: np.float64(0.03771428571428577)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714196), 86: np.float64(0.14285714285714196), 92: np.float64(0.14285714285714196), 52: np.float64(0.14285714285714196), 24: np.float64(0.14285714285714196), 62: np.float64(0.14285714285714196), 0: np.float64(0.14285714285714196)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714224), 86: np.float64(0.14285714285714224), 92: np.float64(0.14285714285714224), 52: np.float64(0.14285714285714224), 24: np.float64(0.14285714285714224), 62: np.float64(0.14285714285714224), 0: np.float64(0.14285714285714224)}
choice probs for this beta: {22: np.float64(0.14285714285714224), 86: np.float64(0.14285714285714224), 92: np.float64(0.14285714285714224), 52: np.float64(0.14285714285714224), 24: np.float64(0.14285714285714224), 62: np.float64(0.14285714285714224), 0: np.float64(0.14285714285714224)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{22: np.float64(0.14285714285714293), 86: np.float64(0.14285714285714293), 92: np.float64(0.14285714285714293), 52: np.float64(0.14285714285714293), 24: np.float64(0.14285714285714293), 62: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285735), 86: np.float64(0.037714285714285735), 92: np.float64(0.037714285714285735), 52: np.float64(0.037714285714285735), 24: np.float64(0.037714285714285735), 62: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 15: 0, 100: 0} [1, 2, 4, 5, 6, 9, 10, 11, 15, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714435), 86: np.float64(0.14285714285714435), 92: np.float64(0.14285714285714435), 52: np.float64(0.14285714285714435), 24: np.float64(0.14285714285714435), 62: np.float64(0.14285714285714435), 0: np.float64(0.14285714285714435)}
cluster label 1 learned center: 
 
sigma= [1, 2, 4, 5, 6, 9, 10, 11, 15, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714396), 86: np.float64(0.14285714285714396), 92: np.float64(0.14285714285714396), 52: np.float64(0.14285714285714396), 24: np.float64(0.14285714285714396), 62: np.float64(0.14285714285714396), 0: np.float64(0.14285714285714396)}
choice probs for this beta: {22: np.float64(0.14285714285714396), 86: np.float64(0.14285714285714396), 92: np.float64(0.14285714285714396), 52: np.float64(0.14285714285714396), 24: np.float64(0.14285714285714396), 62: np.float64(0.14285714285714396), 0: np.float64(0.14285714285714396)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 11]
learned probs for cluster 2 

{22: np.float64(0.14285714285714315), 86: np.float64(0.14285714285714315), 92: np.float64(0.14285714285714315), 52: np.float64(0.14285714285714315), 24: np.float64(0.14285714285714315), 62: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 11]
learned probs (dictionary):

probs= {22: np.float64(0.0377142857142858), 86: np.float64(0.0377142857142858), 92: np.float64(0.0377142857142858), 52: np.float64(0.0377142857142858), 24: np.float64(0.0377142857142858), 62: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 100]
learned probs for cluster 1 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714296), 86: np.float64(0.14285714285714296), 92: np.float64(0.14285714285714296), 52: np.float64(0.14285714285714296), 24: np.float64(0.14285714285714296), 62: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
choice probs for this beta: {22: np.float64(0.14285714285714296), 86: np.float64(0.14285714285714296), 92: np.float64(0.14285714285714296), 52: np.float64(0.14285714285714296), 24: np.float64(0.14285714285714296), 62: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 12, 14]
learned probs for cluster 2 

{22: np.float64(0.14285714285714263), 86: np.float64(0.14285714285714263), 92: np.float64(0.14285714285714263), 52: np.float64(0.14285714285714263), 24: np.float64(0.14285714285714263), 62: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 12, 14]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428566), 86: np.float64(0.03771428571428566), 92: np.float64(0.03771428571428566), 52: np.float64(0.03771428571428566), 24: np.float64(0.03771428571428566), 62: np.float64(0.03771428571428566), 0: np.float64(0.03771428571428566)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 10, 11, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714263), 86: np.float64(0.14285714285714263), 92: np.float64(0.14285714285714263), 52: np.float64(0.14285714285714263), 24: np.float64(0.14285714285714263), 62: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 10, 11, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714263), 86: np.float64(0.14285714285714263), 92: np.float64(0.14285714285714263), 52: np.float64(0.14285714285714263), 24: np.float64(0.14285714285714263), 62: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
choice probs for this beta: {22: np.float64(0.14285714285714263), 86: np.float64(0.14285714285714263), 92: np.float64(0.14285714285714263), 52: np.float64(0.14285714285714263), 24: np.float64(0.14285714285714263), 62: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 100, 4, 14]
learned probs for cluster 2 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 13, 100, 4, 14]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285714), 86: np.float64(0.037714285714285714), 92: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 24: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714207), 86: np.float64(0.14285714285714207), 92: np.float64(0.14285714285714207), 52: np.float64(0.14285714285714207), 24: np.float64(0.14285714285714207), 62: np.float64(0.14285714285714207), 0: np.float64(0.14285714285714207)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
learned probs (dictionary):

probs= {22: np.float64(0.1428571428571423), 86: np.float64(0.1428571428571423), 92: np.float64(0.1428571428571423), 52: np.float64(0.1428571428571423), 24: np.float64(0.1428571428571423), 62: np.float64(0.1428571428571423), 0: np.float64(0.1428571428571423)}
choice probs for this beta: {22: np.float64(0.1428571428571423), 86: np.float64(0.1428571428571423), 92: np.float64(0.1428571428571423), 52: np.float64(0.1428571428571423), 24: np.float64(0.1428571428571423), 62: np.float64(0.1428571428571423), 0: np.float64(0.1428571428571423)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100, 5, 11]
learned probs for cluster 2 

{22: np.float64(0.1428571428571429), 86: np.float64(0.1428571428571429), 92: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 24: np.float64(0.1428571428571429), 62: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100, 5, 11]
learned probs (dictionary):

probs= {22: np.float64(0.03771428571428573), 86: np.float64(0.03771428571428573), 92: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 24: np.float64(0.03771428571428573), 62: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714288), 86: np.float64(0.14285714285714288), 92: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 24: np.float64(0.14285714285714288), 62: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714288), 86: np.float64(0.14285714285714288), 92: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 24: np.float64(0.14285714285714288), 62: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {22: np.float64(0.14285714285714288), 86: np.float64(0.14285714285714288), 92: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 24: np.float64(0.14285714285714288), 62: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285714), 86: np.float64(0.037714285714285714), 92: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 24: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714288), 86: np.float64(0.14285714285714288), 92: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 24: np.float64(0.14285714285714288), 62: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 13, 100, 5]
learned probs for cluster 2 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 13, 100, 5]
learned probs (dictionary):

probs= {22: np.float64(0.037714285714285714), 86: np.float64(0.037714285714285714), 92: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 24: np.float64(0.037714285714285714), 62: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {22: np.float64(0.14285714285714285), 86: np.float64(0.14285714285714285), 92: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 24: np.float64(0.14285714285714285), 62: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 52
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 22
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 22
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 62
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 92
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 22
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 92
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 24
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 22
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 24
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 22
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 52
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 62
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 62
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 62
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 22
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 22
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 0
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 22
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 52
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 0
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 22
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 0
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 52
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 24
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 62
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 62
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 52
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 24
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 86
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 22
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 0
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 86
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 86
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 24
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 52
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 52
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 22
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 0
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 24
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 62
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 0
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 0
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 92
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 24
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 86
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 52
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 22
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 52
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 0
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 22
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 22
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 0
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 86
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 86
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 22
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 52
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 0
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 52
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 52
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 22
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 22
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 22
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 22
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 24
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 22
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 22
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 86
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 22
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 24
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 22
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 92
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 22
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 62
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 52
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 62
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 22
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 62
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 24
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 0
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 22
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 86
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 22
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 22
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 22
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 62
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 52
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 62
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 22
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 92
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 24
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 22
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 52
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 24
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 22
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 92
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 62
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 24
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 92
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 24
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 52
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 0
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 24
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 22
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 92
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 24
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 52
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 86
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 22
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 92
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 86
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 24
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 86
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 52
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 24
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 24
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 22
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 22
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 24
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 22
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 62
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 52
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 22
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 24
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 52
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 52
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 22
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 0
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 52
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 92
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 62
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 92
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 0
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 86
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 62
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 86
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 62
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 92
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 24
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 62
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 62
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 24
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 62
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 86
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 24
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 62
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 92
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 22
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 92
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 0
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 22
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 52
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 0
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 22
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 24
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 86
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 22
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 24
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 0
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 24
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 62
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 62
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 22
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 52
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 24
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 52
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 22
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 22
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 0
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 92
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 0
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 22
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 22
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 0
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 52
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 22
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 22
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 86
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 22
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 24
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 24
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 22
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 86
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 62
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 22
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 52
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 22
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 92
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 86
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 24
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 92
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 86
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 62
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 22
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 86
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 24
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 52
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 52
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 52
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 22
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 62
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 24
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 52
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 0
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 24
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 62
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 22
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 92
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 52
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 0
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 52
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 22
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 52
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 22
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 92
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 24
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 92
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 22
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 22
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 62
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 62
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 52
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 22
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 22
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 24
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 22
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 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 24
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 62
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 22
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 0
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 24
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 22
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 52
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 24
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 24
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 22
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 24
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 92
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 52
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 86
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 0
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 24
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 52
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 24
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 0
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 62
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 92
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 92
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 52
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 52
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 52
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 86
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 0
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 22
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 22
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 92
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 22
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 92
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 52
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 92
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 22
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 52
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 52
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 22
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 24
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 22
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 86
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 24
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 52
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 22
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 52
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 0
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 22
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 24
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 92
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 62
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 22
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 22
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 52
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 24
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 0
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 24
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 22
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 24
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 92
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 92
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 0
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 62
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 0
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 22
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 92
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 22
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 86
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 62
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 52
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 52
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 92
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 24
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 22
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 24
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 24
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 52
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 24
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 52
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 22
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 92
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 24
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 22
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 92
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 24
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 86
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 52
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 62
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 0
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 52
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 52
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 22
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 24
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 24
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 52
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 0
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 92
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 24
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 24
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 52
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 86
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 62
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 24
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 62
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 0
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 22
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 22
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 0
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 52
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 24
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 22
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 0
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 22
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 86
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 62
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 62
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 0
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 24
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 24
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 52
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 24
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 0
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 22
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 62
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 62
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 22
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 22
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 24
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 52
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 92
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 22
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 62
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 24
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 22
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 0
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 22
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 22
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 22
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 24
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 86
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 92
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 22
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 62
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 0
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 22
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 24
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 62
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 92
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 52
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 24
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 52
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 24
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 92
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 92
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 62
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 22
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 92
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 22
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 86
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 24
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 62
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 62
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 22
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 62
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 24
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 52
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 24
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 24
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 92
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 22
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 22
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 62
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 24
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 92
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 0
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 22
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 86
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 86
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 86
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 22
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 52
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 62
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 86
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 92
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 52
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 52
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 52
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 52
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 24
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 52
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 22
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 86
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 0
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 22
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 52
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 24
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 86
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 62
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 62
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 24
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 24
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 52
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 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 86
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 0
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 22
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 0
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 92
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 0
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 92
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 24
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 22
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 92
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 62
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 52
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 52
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 24
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 52
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 62
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 92
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 92
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 22
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 24
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 0
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 52
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 24
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 24
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 92
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 24
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 92
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 24
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 92
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 92
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 22
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 86
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 86
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 24
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 24
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 52
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 22
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 86
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 86
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 62
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 0
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 24
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 52
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 92
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 52
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 22
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 24
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 52
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 86
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 24
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 22
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 52
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 86
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 86
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 52
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 52
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 86
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 92
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 52
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 52
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 24
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 62
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 22
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 52
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 92
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 86
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 24
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 22
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 62
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 22
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 0
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 86
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 24
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 92
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 92
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 22
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 24
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 86
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 24
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 92
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 22
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 0
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 86
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 22
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 92
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 22
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 86
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 22
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 62
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 22
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 0
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 22
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 22
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 22
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 0
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 62
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 24
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 62
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 86
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 22
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 22
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 22
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 22
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 22
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 24
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 92
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 62
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 0
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 92
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 24
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 62
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 24
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 22
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 22
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 22
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 22
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 0
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 22
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 24
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 0
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 62
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 92
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 86
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 24
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 22
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 22
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 22
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 22
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 24
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 24
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 22
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 52
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 62
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 52
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 24
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 22
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 22
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 24
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 52
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 22
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 22
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 24
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 24
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 86
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 0
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 86
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 0
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 86
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 62
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 52
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 22
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 22
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 22
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 22
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 92
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 24
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 24
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 52
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 0
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 0
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 22
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 22
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 24
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 92
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 86
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 52
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 22
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 0
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 86
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 62
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 62
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 92
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 62
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 0
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 24
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 24
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 22
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 24
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 22
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 52
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 86
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 22
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 22
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 92
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 24
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 22
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 22
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 52
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 52
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 0
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 52
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 92
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 0
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 86
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 22
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 52
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 86
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 24
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 0
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 24
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 24
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 52
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 22
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 62
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 22
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 62
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 24
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 52
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 24
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 0
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 24
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 92
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 52
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 24
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 22
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 22
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 22
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 24
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 22
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 52
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 24
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 52
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 62
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 52
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 52
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 24
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 0
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 24
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 52
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 22
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 92
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 0
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 22
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 22
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 22
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 92
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 52
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 62
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 92
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 24
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 22
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 52
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 0
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 52
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 22
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 62
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 22
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 92
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 86
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 0
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 52
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 52
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 62
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 52
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 92
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 52
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 0
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 22
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 22
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 52
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 0
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 62
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 86
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 52
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 22
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 24
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 24
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 24
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 92
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 24
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 24
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 86
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 22
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 86
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 22
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 22
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 62
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 22
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 92
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 62
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 24
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 0
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 24
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 22
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 0
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 24
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 52
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 22
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 62
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 24
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 22
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 86
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 24
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 24
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 92
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 52
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 86
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 86
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 52
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 22
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 24
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 52
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 22
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 0
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 22
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 52
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 86
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 22
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 22
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 52
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 52
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 22
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 22
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 86
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 22
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 92
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 92
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 92
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 24
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 92
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 92
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 62
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 86
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 86
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 52
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 52
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 24
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 52
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 52
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 22
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 52
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 86
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 62
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 92
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 24
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 62
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 24
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 24
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 92
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 86
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 52
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 92
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 86
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 52
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 62
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 62
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 22
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 86
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 22
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 86
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 52
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 24
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 86
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 24
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 0
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 24
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 24
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 86
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 24
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 86
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 52
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 92
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 52
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 22
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 62
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 86
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 62
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 22
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 86
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 86
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 52
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 92
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 52
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 92
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 62
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 62
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 24
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 24
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 22
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 22
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 52
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 0
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 62
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 62
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 0
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 24
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 22
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 86
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 22
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 62
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 62
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 62
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 92
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 24
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 52
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 52
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 22
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 24
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 62
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 24
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 0
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 92
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 24
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 92
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 62
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 22
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 62
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 24
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 86
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 52
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 92
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 52
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 92
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 22
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 24
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 24
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 86
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 24
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 22
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 24
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 92
emperical probablities from test set: {22: 0.287, 86: 0.084, 92: 0.098, 52: 0.136, 24: 0.198, 62: 0.111, 0: 0.086}
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285774), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: np.float64(0.05885714285714223), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285774), np.float64(0.05885714285714223), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: np.float64(0.05885714285714223), 92: np.float64(0.044857142857142235), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285774), np.float64(0.05885714285714223), np.float64(0.044857142857142235), 0, 0, 0, 0]
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: np.float64(0.05885714285714223), 92: np.float64(0.044857142857142235), 52: np.float64(0.006857142857142229), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285774), np.float64(0.05885714285714223), np.float64(0.044857142857142235), np.float64(0.006857142857142229), 0, 0, 0]
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: np.float64(0.05885714285714223), 92: np.float64(0.044857142857142235), 52: np.float64(0.006857142857142229), 24: np.float64(0.05514285714285777), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285774), np.float64(0.05885714285714223), np.float64(0.044857142857142235), np.float64(0.006857142857142229), np.float64(0.05514285714285777), 0, 0]
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: np.float64(0.05885714285714223), 92: np.float64(0.044857142857142235), 52: np.float64(0.006857142857142229), 24: np.float64(0.05514285714285777), 62: np.float64(0.03185714285714224), 0: 0} 

err list= [np.float64(0.14414285714285774), np.float64(0.05885714285714223), np.float64(0.044857142857142235), np.float64(0.006857142857142229), np.float64(0.05514285714285777), np.float64(0.03185714285714224), 0]
beta is  0.025 

err dic= {22: np.float64(0.14414285714285774), 86: np.float64(0.05885714285714223), 92: np.float64(0.044857142857142235), 52: np.float64(0.006857142857142229), 24: np.float64(0.05514285714285777), 62: np.float64(0.03185714285714224), 0: np.float64(0.056857142857142245)} 

err list= [np.float64(0.14414285714285774), np.float64(0.05885714285714223), np.float64(0.044857142857142235), np.float64(0.006857142857142229), np.float64(0.05514285714285777), np.float64(0.03185714285714224), np.float64(0.056857142857142245)]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285602), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: np.float64(0.058857142857143954), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285602), np.float64(0.058857142857143954), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: np.float64(0.058857142857143954), 92: np.float64(0.044857142857143956), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285602), np.float64(0.058857142857143954), np.float64(0.044857142857143956), 0, 0, 0, 0]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: np.float64(0.058857142857143954), 92: np.float64(0.044857142857143956), 52: np.float64(0.00685714285714395), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285602), np.float64(0.058857142857143954), np.float64(0.044857142857143956), np.float64(0.00685714285714395), 0, 0, 0]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: np.float64(0.058857142857143954), 92: np.float64(0.044857142857143956), 52: np.float64(0.00685714285714395), 24: np.float64(0.05514285714285605), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285602), np.float64(0.058857142857143954), np.float64(0.044857142857143956), np.float64(0.00685714285714395), np.float64(0.05514285714285605), 0, 0]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: np.float64(0.058857142857143954), 92: np.float64(0.044857142857143956), 52: np.float64(0.00685714285714395), 24: np.float64(0.05514285714285605), 62: np.float64(0.03185714285714396), 0: 0} 

err list= [np.float64(0.14414285714285602), np.float64(0.058857142857143954), np.float64(0.044857142857143956), np.float64(0.00685714285714395), np.float64(0.05514285714285605), np.float64(0.03185714285714396), 0]
beta is  0.05 

err dic= {22: np.float64(0.14414285714285602), 86: np.float64(0.058857142857143954), 92: np.float64(0.044857142857143956), 52: np.float64(0.00685714285714395), 24: np.float64(0.05514285714285605), 62: np.float64(0.03185714285714396), 0: np.float64(0.056857142857143966)} 

err list= [np.float64(0.14414285714285602), np.float64(0.058857142857143954), np.float64(0.044857142857143956), np.float64(0.00685714285714395), np.float64(0.05514285714285605), np.float64(0.03185714285714396), np.float64(0.056857142857143966)]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285702), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: np.float64(0.058857142857142955), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285702), np.float64(0.058857142857142955), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: np.float64(0.058857142857142955), 92: np.float64(0.044857142857142956), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285702), np.float64(0.058857142857142955), np.float64(0.044857142857142956), 0, 0, 0, 0]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: np.float64(0.058857142857142955), 92: np.float64(0.044857142857142956), 52: np.float64(0.0068571428571429505), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285702), np.float64(0.058857142857142955), np.float64(0.044857142857142956), np.float64(0.0068571428571429505), 0, 0, 0]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: np.float64(0.058857142857142955), 92: np.float64(0.044857142857142956), 52: np.float64(0.0068571428571429505), 24: np.float64(0.05514285714285705), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285702), np.float64(0.058857142857142955), np.float64(0.044857142857142956), np.float64(0.0068571428571429505), np.float64(0.05514285714285705), 0, 0]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: np.float64(0.058857142857142955), 92: np.float64(0.044857142857142956), 52: np.float64(0.0068571428571429505), 24: np.float64(0.05514285714285705), 62: np.float64(0.03185714285714296), 0: 0} 

err list= [np.float64(0.14414285714285702), np.float64(0.058857142857142955), np.float64(0.044857142857142956), np.float64(0.0068571428571429505), np.float64(0.05514285714285705), np.float64(0.03185714285714296), 0]
beta is  0.1 

err dic= {22: np.float64(0.14414285714285702), 86: np.float64(0.058857142857142955), 92: np.float64(0.044857142857142956), 52: np.float64(0.0068571428571429505), 24: np.float64(0.05514285714285705), 62: np.float64(0.03185714285714296), 0: np.float64(0.05685714285714297)} 

err list= [np.float64(0.14414285714285702), np.float64(0.058857142857142955), np.float64(0.044857142857142956), np.float64(0.0068571428571429505), np.float64(0.05514285714285705), np.float64(0.03185714285714296), np.float64(0.05685714285714297)]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285735), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: np.float64(0.05885714285714262), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285735), np.float64(0.05885714285714262), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: np.float64(0.05885714285714262), 92: np.float64(0.04485714285714262), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285735), np.float64(0.05885714285714262), np.float64(0.04485714285714262), 0, 0, 0, 0]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: np.float64(0.05885714285714262), 92: np.float64(0.04485714285714262), 52: np.float64(0.006857142857142617), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285735), np.float64(0.05885714285714262), np.float64(0.04485714285714262), np.float64(0.006857142857142617), 0, 0, 0]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: np.float64(0.05885714285714262), 92: np.float64(0.04485714285714262), 52: np.float64(0.006857142857142617), 24: np.float64(0.05514285714285738), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285735), np.float64(0.05885714285714262), np.float64(0.04485714285714262), np.float64(0.006857142857142617), np.float64(0.05514285714285738), 0, 0]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: np.float64(0.05885714285714262), 92: np.float64(0.04485714285714262), 52: np.float64(0.006857142857142617), 24: np.float64(0.05514285714285738), 62: np.float64(0.031857142857142626), 0: 0} 

err list= [np.float64(0.14414285714285735), np.float64(0.05885714285714262), np.float64(0.04485714285714262), np.float64(0.006857142857142617), np.float64(0.05514285714285738), np.float64(0.031857142857142626), 0]
beta is  0.25 

err dic= {22: np.float64(0.14414285714285735), 86: np.float64(0.05885714285714262), 92: np.float64(0.04485714285714262), 52: np.float64(0.006857142857142617), 24: np.float64(0.05514285714285738), 62: np.float64(0.031857142857142626), 0: np.float64(0.056857142857142634)} 

err list= [np.float64(0.14414285714285735), np.float64(0.05885714285714262), np.float64(0.04485714285714262), np.float64(0.006857142857142617), np.float64(0.05514285714285738), np.float64(0.031857142857142626), np.float64(0.056857142857142634)]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285768), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: np.float64(0.05885714285714229), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285768), np.float64(0.05885714285714229), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: np.float64(0.05885714285714229), 92: np.float64(0.04485714285714229), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285768), np.float64(0.05885714285714229), np.float64(0.04485714285714229), 0, 0, 0, 0]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: np.float64(0.05885714285714229), 92: np.float64(0.04485714285714229), 52: np.float64(0.006857142857142284), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285768), np.float64(0.05885714285714229), np.float64(0.04485714285714229), np.float64(0.006857142857142284), 0, 0, 0]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: np.float64(0.05885714285714229), 92: np.float64(0.04485714285714229), 52: np.float64(0.006857142857142284), 24: np.float64(0.055142857142857715), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285768), np.float64(0.05885714285714229), np.float64(0.04485714285714229), np.float64(0.006857142857142284), np.float64(0.055142857142857715), 0, 0]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: np.float64(0.05885714285714229), 92: np.float64(0.04485714285714229), 52: np.float64(0.006857142857142284), 24: np.float64(0.055142857142857715), 62: np.float64(0.03185714285714229), 0: 0} 

err list= [np.float64(0.14414285714285768), np.float64(0.05885714285714229), np.float64(0.04485714285714229), np.float64(0.006857142857142284), np.float64(0.055142857142857715), np.float64(0.03185714285714229), 0]
beta is  0.5 

err dic= {22: np.float64(0.14414285714285768), 86: np.float64(0.05885714285714229), 92: np.float64(0.04485714285714229), 52: np.float64(0.006857142857142284), 24: np.float64(0.055142857142857715), 62: np.float64(0.03185714285714229), 0: np.float64(0.0568571428571423)} 

err list= [np.float64(0.14414285714285768), np.float64(0.05885714285714229), np.float64(0.04485714285714229), np.float64(0.006857142857142284), np.float64(0.055142857142857715), np.float64(0.03185714285714229), np.float64(0.0568571428571423)]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1441428571428571), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: np.float64(0.05885714285714287), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1441428571428571), np.float64(0.05885714285714287), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: np.float64(0.05885714285714287), 92: np.float64(0.04485714285714287), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1441428571428571), np.float64(0.05885714285714287), np.float64(0.04485714285714287), 0, 0, 0, 0]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: np.float64(0.05885714285714287), 92: np.float64(0.04485714285714287), 52: np.float64(0.006857142857142867), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.1441428571428571), np.float64(0.05885714285714287), np.float64(0.04485714285714287), np.float64(0.006857142857142867), 0, 0, 0]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: np.float64(0.05885714285714287), 92: np.float64(0.04485714285714287), 52: np.float64(0.006857142857142867), 24: np.float64(0.05514285714285713), 62: 0, 0: 0} 

err list= [np.float64(0.1441428571428571), np.float64(0.05885714285714287), np.float64(0.04485714285714287), np.float64(0.006857142857142867), np.float64(0.05514285714285713), 0, 0]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: np.float64(0.05885714285714287), 92: np.float64(0.04485714285714287), 52: np.float64(0.006857142857142867), 24: np.float64(0.05514285714285713), 62: np.float64(0.031857142857142876), 0: 0} 

err list= [np.float64(0.1441428571428571), np.float64(0.05885714285714287), np.float64(0.04485714285714287), np.float64(0.006857142857142867), np.float64(0.05514285714285713), np.float64(0.031857142857142876), 0]
beta is  0.75 

err dic= {22: np.float64(0.1441428571428571), 86: np.float64(0.05885714285714287), 92: np.float64(0.04485714285714287), 52: np.float64(0.006857142857142867), 24: np.float64(0.05514285714285713), 62: np.float64(0.031857142857142876), 0: np.float64(0.056857142857142884)} 

err list= [np.float64(0.1441428571428571), np.float64(0.05885714285714287), np.float64(0.04485714285714287), np.float64(0.006857142857142867), np.float64(0.05514285714285713), np.float64(0.031857142857142876), np.float64(0.056857142857142884)]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), 0, 0, 0, 0, 0]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), 0, 0, 0, 0]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), 0, 0, 0]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: np.float64(0.05514285714285716), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), np.float64(0.05514285714285716), 0, 0]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: np.float64(0.05514285714285716), 62: np.float64(0.03185714285714285), 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), np.float64(0.05514285714285716), np.float64(0.03185714285714285), 0]
beta is  1 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: np.float64(0.05514285714285716), 62: np.float64(0.03185714285714285), 0: np.float64(0.056857142857142856)} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), np.float64(0.05514285714285716), np.float64(0.03185714285714285), np.float64(0.056857142857142856)]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: 0, 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: 0, 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: 0, 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), 0, 0, 0, 0]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: 0, 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), 0, 0, 0]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: np.float64(0.05514285714285716), 62: 0, 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), np.float64(0.05514285714285716), 0, 0]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: np.float64(0.05514285714285716), 62: np.float64(0.03185714285714285), 0: 0} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), np.float64(0.05514285714285716), np.float64(0.03185714285714285), 0]
beta is  1.25 

err dic= {22: np.float64(0.14414285714285713), 86: np.float64(0.058857142857142844), 92: np.float64(0.044857142857142845), 52: np.float64(0.0068571428571428394), 24: np.float64(0.05514285714285716), 62: np.float64(0.03185714285714285), 0: np.float64(0.056857142857142856)} 

err list= [np.float64(0.14414285714285713), np.float64(0.058857142857142844), np.float64(0.044857142857142845), np.float64(0.0068571428571428394), np.float64(0.05514285714285716), np.float64(0.03185714285714285), np.float64(0.056857142857142856)]
samppled assortment [14, 55, 28, 53, 87, 44]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 14: 2, 15: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 11, 13, 100, 5, 14, 15]
learned probs for cluster 2 

{14: np.float64(0.12401998752860088), 55: np.float64(0.14599666874523354), 28: np.float64(0.14599666874523354), 53: np.float64(0.14599666874523354), 87: np.float64(0.14599666874523354), 44: np.float64(0.14599666874523354), 0: np.float64(0.14599666874523354)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 11, 13, 100, 5, 14, 15]
learned probs (dictionary):

probs= {14: np.float64(0.032741276707550636), 55: np.float64(0.038543120548741656), 28: np.float64(0.038543120548741656), 53: np.float64(0.038543120548741656), 87: np.float64(0.038543120548741656), 44: np.float64(0.038543120548741656), 0: np.float64(0.038543120548741656)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 100]
learned probs for cluster 1 

{14: np.float64(0.11107459718183935), 55: np.float64(0.14815423380302833), 28: np.float64(0.14815423380302833), 53: np.float64(0.14815423380302833), 87: np.float64(0.14815423380302833), 44: np.float64(0.14815423380302833), 0: np.float64(0.14815423380302833)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 100]
learned probs (dictionary):

probs= {14: np.float64(0.1144921802333844), 55: np.float64(0.14758463662777052), 28: np.float64(0.14758463662777052), 53: np.float64(0.14758463662777052), 87: np.float64(0.14758463662777052), 44: np.float64(0.14758463662777052), 0: np.float64(0.14758463662777052)}
choice probs for this beta: {14: np.float64(0.1144921802333844), 55: np.float64(0.14758463662777052), 28: np.float64(0.14758463662777052), 53: np.float64(0.14758463662777052), 87: np.float64(0.14758463662777052), 44: np.float64(0.14758463662777052), 0: np.float64(0.14758463662777052)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs for cluster 2 

{14: np.float64(0.14285714285714293), 55: np.float64(0.14285714285714293), 28: np.float64(0.14285714285714293), 53: np.float64(0.14285714285714293), 87: np.float64(0.14285714285714293), 44: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285735), 55: np.float64(0.037714285714285735), 28: np.float64(0.037714285714285735), 53: np.float64(0.037714285714285735), 87: np.float64(0.037714285714285735), 44: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
learned probs for cluster 1 

{14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 100]
learned probs (dictionary):

probs= {14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 2, 5, 15]
learned probs for cluster 2 

{14: np.float64(0.14285714285714315), 55: np.float64(0.14285714285714315), 28: np.float64(0.14285714285714315), 53: np.float64(0.14285714285714315), 87: np.float64(0.14285714285714315), 44: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 2, 5, 15]
learned probs (dictionary):

probs= {14: np.float64(0.0377142857142858), 55: np.float64(0.0377142857142858), 28: np.float64(0.0377142857142858), 53: np.float64(0.0377142857142858), 87: np.float64(0.0377142857142858), 44: np.float64(0.0377142857142858), 0: np.float64(0.0377142857142858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.1428571428571438), 55: np.float64(0.1428571428571438), 28: np.float64(0.1428571428571438), 53: np.float64(0.1428571428571438), 87: np.float64(0.1428571428571438), 44: np.float64(0.1428571428571438), 0: np.float64(0.1428571428571438)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714363), 55: np.float64(0.14285714285714363), 28: np.float64(0.14285714285714363), 53: np.float64(0.14285714285714363), 87: np.float64(0.14285714285714363), 44: np.float64(0.14285714285714363), 0: np.float64(0.14285714285714363)}
choice probs for this beta: {14: np.float64(0.14285714285714363), 55: np.float64(0.14285714285714363), 28: np.float64(0.14285714285714363), 53: np.float64(0.14285714285714363), 87: np.float64(0.14285714285714363), 44: np.float64(0.14285714285714363), 0: np.float64(0.14285714285714363)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{14: np.float64(0.14285714285714263), 55: np.float64(0.14285714285714263), 28: np.float64(0.14285714285714263), 53: np.float64(0.14285714285714263), 87: np.float64(0.14285714285714263), 44: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {14: np.float64(0.03771428571428566), 55: np.float64(0.03771428571428566), 28: np.float64(0.03771428571428566), 53: np.float64(0.03771428571428566), 87: np.float64(0.03771428571428566), 44: np.float64(0.03771428571428566), 0: np.float64(0.03771428571428566)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714263), 55: np.float64(0.14285714285714263), 28: np.float64(0.14285714285714263), 53: np.float64(0.14285714285714263), 87: np.float64(0.14285714285714263), 44: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714263), 55: np.float64(0.14285714285714263), 28: np.float64(0.14285714285714263), 53: np.float64(0.14285714285714263), 87: np.float64(0.14285714285714263), 44: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
choice probs for this beta: {14: np.float64(0.14285714285714263), 55: np.float64(0.14285714285714263), 28: np.float64(0.14285714285714263), 53: np.float64(0.14285714285714263), 87: np.float64(0.14285714285714263), 44: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5, 9]
learned probs for cluster 2 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 5, 9]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 28: np.float64(0.037714285714285714), 53: np.float64(0.037714285714285714), 87: np.float64(0.037714285714285714), 44: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714304), 55: np.float64(0.14285714285714304), 28: np.float64(0.14285714285714304), 53: np.float64(0.14285714285714304), 87: np.float64(0.14285714285714304), 44: np.float64(0.14285714285714304), 0: np.float64(0.14285714285714304)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {14: np.float64(0.142857142857143), 55: np.float64(0.142857142857143), 28: np.float64(0.142857142857143), 53: np.float64(0.142857142857143), 87: np.float64(0.142857142857143), 44: np.float64(0.142857142857143), 0: np.float64(0.142857142857143)}
choice probs for this beta: {14: np.float64(0.142857142857143), 55: np.float64(0.142857142857143), 28: np.float64(0.142857142857143), 53: np.float64(0.142857142857143), 87: np.float64(0.142857142857143), 44: np.float64(0.142857142857143), 0: np.float64(0.142857142857143)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 28: np.float64(0.037714285714285714), 53: np.float64(0.037714285714285714), 87: np.float64(0.037714285714285714), 44: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 19: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 19]
learned probs for cluster 2 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 19]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 28: np.float64(0.037714285714285714), 53: np.float64(0.037714285714285714), 87: np.float64(0.037714285714285714), 44: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 28: np.float64(0.037714285714285714), 53: np.float64(0.037714285714285714), 87: np.float64(0.037714285714285714), 44: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 2, 11: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5, 10, 11]
learned probs for cluster 2 

{14: np.float64(0.14285714285714288), 55: np.float64(0.14285714285714288), 28: np.float64(0.14285714285714288), 53: np.float64(0.14285714285714288), 87: np.float64(0.14285714285714288), 44: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 5, 10, 11]
learned probs (dictionary):

probs= {14: np.float64(0.03771428571428572), 55: np.float64(0.03771428571428572), 28: np.float64(0.03771428571428572), 53: np.float64(0.03771428571428572), 87: np.float64(0.03771428571428572), 44: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714288), 55: np.float64(0.14285714285714288), 28: np.float64(0.14285714285714288), 53: np.float64(0.14285714285714288), 87: np.float64(0.14285714285714288), 44: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714288), 55: np.float64(0.14285714285714288), 28: np.float64(0.14285714285714288), 53: np.float64(0.14285714285714288), 87: np.float64(0.14285714285714288), 44: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {14: np.float64(0.14285714285714288), 55: np.float64(0.14285714285714288), 28: np.float64(0.14285714285714288), 53: np.float64(0.14285714285714288), 87: np.float64(0.14285714285714288), 44: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 14, 100, 5]
learned probs for cluster 2 

{14: np.float64(0.14272022219869748), 55: np.float64(0.14287996296688568), 28: np.float64(0.14287996296688568), 53: np.float64(0.14287996296688568), 87: np.float64(0.14287996296688568), 44: np.float64(0.14287996296688568), 0: np.float64(0.14287996296688568)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 14, 100, 5]
learned probs (dictionary):

probs= {14: np.float64(0.037678138660456134), 55: np.float64(0.03772031022325782), 28: np.float64(0.03772031022325782), 53: np.float64(0.03772031022325782), 87: np.float64(0.03772031022325782), 44: np.float64(0.03772031022325782), 0: np.float64(0.03772031022325782)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 7: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 5, 7, 10, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714293), 55: np.float64(0.14285714285714293), 28: np.float64(0.14285714285714293), 53: np.float64(0.14285714285714293), 87: np.float64(0.14285714285714293), 44: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 5, 7, 10, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.1428209958033133), 55: np.float64(0.142863167366115), 28: np.float64(0.142863167366115), 53: np.float64(0.142863167366115), 87: np.float64(0.142863167366115), 44: np.float64(0.142863167366115), 0: np.float64(0.142863167366115)}
choice probs for this beta: {14: np.float64(0.1428209958033133), 55: np.float64(0.142863167366115), 28: np.float64(0.142863167366115), 53: np.float64(0.142863167366115), 87: np.float64(0.142863167366115), 44: np.float64(0.142863167366115), 0: np.float64(0.142863167366115)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5]
learned probs for cluster 2 

{14: np.float64(0.1428571428571427), 55: np.float64(0.1428571428571427), 28: np.float64(0.1428571428571427), 53: np.float64(0.1428571428571427), 87: np.float64(0.1428571428571427), 44: np.float64(0.1428571428571427), 0: np.float64(0.1428571428571427)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 5]
learned probs (dictionary):

probs= {14: np.float64(0.03771428571428568), 55: np.float64(0.03771428571428568), 28: np.float64(0.03771428571428568), 53: np.float64(0.03771428571428568), 87: np.float64(0.03771428571428568), 44: np.float64(0.03771428571428568), 0: np.float64(0.03771428571428568)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs for cluster 1 

{14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs for cluster 2 

{14: np.float64(0.14285714285714263), 55: np.float64(0.14285714285714263), 28: np.float64(0.14285714285714263), 53: np.float64(0.14285714285714263), 87: np.float64(0.14285714285714263), 44: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 4, 5]
learned probs (dictionary):

probs= {14: np.float64(0.03771428571428566), 55: np.float64(0.03771428571428566), 28: np.float64(0.03771428571428566), 53: np.float64(0.03771428571428566), 87: np.float64(0.03771428571428566), 44: np.float64(0.03771428571428566), 0: np.float64(0.03771428571428566)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714135), 55: np.float64(0.14285714285714135), 28: np.float64(0.14285714285714135), 53: np.float64(0.14285714285714135), 87: np.float64(0.14285714285714135), 44: np.float64(0.14285714285714135), 0: np.float64(0.14285714285714135)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714168), 55: np.float64(0.14285714285714168), 28: np.float64(0.14285714285714168), 53: np.float64(0.14285714285714168), 87: np.float64(0.14285714285714168), 44: np.float64(0.14285714285714168), 0: np.float64(0.14285714285714168)}
choice probs for this beta: {14: np.float64(0.14285714285714168), 55: np.float64(0.14285714285714168), 28: np.float64(0.14285714285714168), 53: np.float64(0.14285714285714168), 87: np.float64(0.14285714285714168), 44: np.float64(0.14285714285714168), 0: np.float64(0.14285714285714168)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 6, 7, 100, 5]
learned probs for cluster 2 

{14: np.float64(0.1428571428571429), 55: np.float64(0.1428571428571429), 28: np.float64(0.1428571428571429), 53: np.float64(0.1428571428571429), 87: np.float64(0.1428571428571429), 44: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 100, 5]
learned probs (dictionary):

probs= {14: np.float64(0.03771428571428573), 55: np.float64(0.03771428571428573), 28: np.float64(0.03771428571428573), 53: np.float64(0.03771428571428573), 87: np.float64(0.03771428571428573), 44: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 2, 4, 11]
learned probs for cluster 2 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 2, 4, 11]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 28: np.float64(0.037714285714285714), 53: np.float64(0.037714285714285714), 87: np.float64(0.037714285714285714), 44: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs for cluster 2 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs (dictionary):

probs= {14: np.float64(0.037714285714285714), 55: np.float64(0.037714285714285714), 28: np.float64(0.037714285714285714), 53: np.float64(0.037714285714285714), 87: np.float64(0.037714285714285714), 44: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 17: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5, 14, 17]
learned probs for cluster 2 

{14: np.float64(0.9998713775373935), 55: np.float64(2.14370771010356e-05), 28: np.float64(2.14370771010356e-05), 53: np.float64(2.14370771010356e-05), 87: np.float64(2.14370771010356e-05), 44: np.float64(2.14370771010356e-05), 0: np.float64(2.14370771010356e-05)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 5, 14, 17]
learned probs (dictionary):

probs= {14: np.float64(0.2639660436698719), 55: np.float64(5.659388354673398e-06), 28: np.float64(5.659388354673398e-06), 53: np.float64(5.659388354673398e-06), 87: np.float64(5.659388354673398e-06), 44: np.float64(5.659388354673398e-06), 0: np.float64(5.659388354673398e-06)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 100]
learned probs for cluster 1 

{14: np.float64(0.14285714285714285), 55: np.float64(0.14285714285714285), 28: np.float64(0.14285714285714285), 53: np.float64(0.14285714285714285), 87: np.float64(0.14285714285714285), 44: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 100]
learned probs (dictionary):

probs= {14: np.float64(0.36910890081272907), 55: np.float64(0.10514851653121181), 28: np.float64(0.10514851653121181), 53: np.float64(0.10514851653121181), 87: np.float64(0.10514851653121181), 44: np.float64(0.10514851653121181), 0: np.float64(0.10514851653121181)}
choice probs for this beta: {14: np.float64(0.36910890081272907), 55: np.float64(0.10514851653121181), 28: np.float64(0.10514851653121181), 53: np.float64(0.10514851653121181), 87: np.float64(0.10514851653121181), 44: np.float64(0.10514851653121181), 0: np.float64(0.10514851653121181)}
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 28
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 53
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 28
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 44
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 44
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 0
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 53
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 55
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 44
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 87
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 87
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 44
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 14
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 44
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 14
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 53
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 28
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 14
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 87
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 28
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 44
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 44
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 87
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 55
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 87
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 55
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 44
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 44
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 55
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 28
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 53
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 28
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 28
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 87
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 14
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 53
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 28
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 28
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 14
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 55
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 0
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 87
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 87
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 14
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 14
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 55
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 28
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 87
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 87
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 14
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 28
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 87
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 28
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 28
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 0
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 14
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 14
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 44
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 55
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 14
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 28
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 14
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 87
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 0
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 28
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 55
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 14
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 55
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 14
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 44
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 44
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 0
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 28
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 87
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 28
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 14
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 14
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 14
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 87
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 53
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 87
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 55
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 14
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 14
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 53
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 53
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 87
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 14
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 14
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 28
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 44
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 44
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 14
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 44
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 53
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 44
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 53
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 28
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 55
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 44
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 87
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 28
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 44
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 55
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 44
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 44
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 28
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 87
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 28
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 53
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 14
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 28
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 55
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 55
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 44
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 44
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 28
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 53
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 55
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 28
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 28
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 44
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 28
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 55
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 44
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 28
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 44
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 55
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 28
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 28
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 14
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 14
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 28
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 53
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 14
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 0
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 44
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 55
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 53
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 87
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 53
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 53
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 55
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 28
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 55
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 28
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 28
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 44
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 28
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 14
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 28
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 87
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 87
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 28
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 28
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 28
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 44
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 87
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 0
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 55
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 53
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 14
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 0
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 28
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 44
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 55
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 28
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 87
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 44
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 55
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 44
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 28
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 28
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 87
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 87
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 28
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 55
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 87
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 14
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 87
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 87
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 14
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 87
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 55
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 44
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 53
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 28
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 44
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 44
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 87
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 14
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 14
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 55
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 14
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 44
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 55
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 14
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 44
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 55
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 28
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 53
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 14
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 87
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 14
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 14
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 0
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 55
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 44
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 55
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 14
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 28
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 28
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 14
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 14
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 55
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 28
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 14
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 0
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 28
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 55
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 44
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 53
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 14
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 28
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 87
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 28
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 14
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 0
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 55
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 0
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 55
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 55
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 0
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 87
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 14
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 14
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 53
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 0
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 14
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 14
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 14
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 0
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 53
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 44
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 28
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 55
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 53
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 28
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 87
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 28
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 14
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 28
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 14
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 28
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 28
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 55
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 55
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 14
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 53
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 0
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 87
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 44
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 28
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 14
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 14
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 53
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 28
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 28
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 0
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 55
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 28
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 14
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 28
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 44
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 87
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 55
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 87
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 28
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 28
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 55
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 14
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 44
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 87
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 87
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 14
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 53
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 87
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 44
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 14
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 44
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 14
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 87
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 55
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 44
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 44
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 14
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 55
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 87
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 53
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 14
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 53
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 14
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 0
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 44
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 14
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 28
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 28
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 44
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 87
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 55
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 28
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 28
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 44
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 44
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 44
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 28
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 0
tau [20, 51, 44, 4, 13, 34, 8, 31, 64, 56] choice 44
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 0
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 28
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 28
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 0
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 0
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 87
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 14
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 44
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 28
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 87
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 14
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 53
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 55
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 44
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 28
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 28
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 14
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 87
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 53
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 28
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 28
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 44
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 55
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 55
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 55
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 44
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 14
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 28
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 55
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 87
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 0
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 28
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 0
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 44
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 53
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 87
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 53
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 87
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 14
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 28
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 28
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 14
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 87
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 28
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 44
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 0
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 28
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 14
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 14
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 53
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 53
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 0
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 87
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 0
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 53
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 28
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 14
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 87
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 87
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 44
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 53
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 14
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 28
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 0
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 44
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 14
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 14
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 87
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 55
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 53
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 28
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 44
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 28
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 87
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 55
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 28
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 14
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 44
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 28
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 0
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 44
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 14
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 44
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 55
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 44
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 44
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 53
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 0
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 44
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 53
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 0
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 44
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 14
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 55
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 55
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 0
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 28
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 87
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 28
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 55
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 14
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 55
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 53
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 53
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 44
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 14
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 28
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 44
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 44
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 14
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 14
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 87
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 55
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 14
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 87
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 28
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 53
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 53
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 28
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 44
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 53
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 55
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 0
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 44
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 14
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 14
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 14
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 44
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 0
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 14
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 28
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 53
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 14
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 44
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 53
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 14
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 14
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 14
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 87
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 53
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 44
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 44
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 0
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 14
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 87
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 53
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 44
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 28
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 44
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 87
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 55
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 28
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 53
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 28
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 0
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 28
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 14
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 28
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 14
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 53
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 28
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 14
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 28
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 87
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 28
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 44
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 14
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 55
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 14
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 44
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 44
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 0
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 55
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 28
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 28
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 44
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 0
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 53
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 0
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 87
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 87
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 28
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 44
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 53
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 55
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 0
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 0
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 53
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 53
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 87
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 14
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 28
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 44
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 14
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 0
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 28
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 55
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 14
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 28
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 0
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 53
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 44
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 0
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 87
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 28
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 14
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 28
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 0
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 55
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 14
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 55
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 44
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 87
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 28
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 0
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 87
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 44
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 44
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 44
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 44
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 53
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 87
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 14
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 28
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 53
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 14
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 28
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 44
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 14
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 14
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 53
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 87
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 14
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 44
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 14
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 87
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 0
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 14
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 55
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 14
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 55
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 14
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 28
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 44
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 44
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 44
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 14
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 0
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 28
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 14
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 14
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 87
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 14
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 44
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 53
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 14
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 14
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 28
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 55
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 28
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 28
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 0
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 14
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 14
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 44
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 87
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 53
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 14
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 55
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 55
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 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 28
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 14
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 44
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 44
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 28
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 87
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 55
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 44
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 14
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 87
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 55
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 55
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 55
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 44
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 44
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 14
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 14
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 55
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 14
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 28
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 55
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 87
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 55
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 28
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 44
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 44
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 28
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 0
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 28
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 28
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 87
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 55
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 53
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 53
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 44
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 44
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 14
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 44
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 87
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 87
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 55
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 87
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 55
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 14
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 55
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 44
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 14
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 28
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 44
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 14
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 14
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 28
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 44
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 53
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 55
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 28
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 53
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 28
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 14
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 53
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 53
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 0
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 53
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 53
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 28
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 0
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 87
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 55
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 44
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 28
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 28
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 0
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 14
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 14
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 53
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 87
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 28
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 55
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 28
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 55
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 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 53
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 87
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 55
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 53
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 28
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 14
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 55
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 53
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 28
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 28
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 53
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 44
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 53
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 44
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 53
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 44
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 28
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 28
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 55
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 14
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 53
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 55
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 87
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 14
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 44
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 55
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 14
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 14
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 28
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 55
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 53
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 14
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 28
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 55
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 87
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 0
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 53
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 28
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 44
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 53
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 14
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 28
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 53
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 44
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 28
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 28
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 87
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 28
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 28
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 28
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 55
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 14
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 55
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 44
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 53
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 44
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 28
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 14
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 28
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 14
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 28
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 87
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 55
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 28
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 53
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 53
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 28
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 28
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 0
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 44
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 14
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 53
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 53
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 28
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 14
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 87
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 14
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 28
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 28
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 14
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 28
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 87
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 14
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 55
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 28
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 28
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 53
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 44
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 28
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 44
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 14
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 87
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 28
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 14
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 28
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 14
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 53
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 28
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 28
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 28
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 28
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 44
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 14
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 14
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 28
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 14
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 14
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 87
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 44
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 44
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 87
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 0
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 14
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 55
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 14
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 44
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 14
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 55
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 53
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 44
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 14
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 87
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 55
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 0
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 14
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 44
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 44
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 87
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 28
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 55
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 55
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 14
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 14
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 55
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 0
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 44
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 14
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 87
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 28
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 53
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 14
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 87
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 28
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 28
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 28
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 53
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 28
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 0
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 14
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 87
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 53
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 28
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 14
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 87
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 53
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 14
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 28
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 28
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 87
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 87
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 44
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 0
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 14
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 28
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 28
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 28
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 53
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 0
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 14
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 28
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 53
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 53
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 14
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 14
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 28
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 28
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 28
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 14
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 53
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 0
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 14
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 14
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 87
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 28
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 28
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 44
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 53
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 0
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 44
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 28
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 28
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 55
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 14
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 0
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 87
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 0
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 14
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 87
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 44
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 0
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 0
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 87
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 14
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 14
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 55
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 87
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 28
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 55
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 87
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 55
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 55
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 87
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 14
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 55
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 14
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 28
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 14
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 28
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 14
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 28
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 53
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 28
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 14
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 87
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 28
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 55
emperical probablities from test set: {14: 0.254, 55: 0.109, 28: 0.195, 53: 0.119, 87: 0.112, 44: 0.135, 0: 0.076}
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285713), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: np.float64(0.03385714285714288), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285713), np.float64(0.03385714285714288), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: np.float64(0.03385714285714288), 28: np.float64(0.05214285714285713), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285713), np.float64(0.03385714285714288), np.float64(0.05214285714285713), 0, 0, 0, 0]
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: np.float64(0.03385714285714288), 28: np.float64(0.05214285714285713), 53: np.float64(0.023857142857142882), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285713), np.float64(0.03385714285714288), np.float64(0.05214285714285713), np.float64(0.023857142857142882), 0, 0, 0]
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: np.float64(0.03385714285714288), 28: np.float64(0.05214285714285713), 53: np.float64(0.023857142857142882), 87: np.float64(0.030857142857142875), 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285713), np.float64(0.03385714285714288), np.float64(0.05214285714285713), np.float64(0.023857142857142882), np.float64(0.030857142857142875), 0, 0]
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: np.float64(0.03385714285714288), 28: np.float64(0.05214285714285713), 53: np.float64(0.023857142857142882), 87: np.float64(0.030857142857142875), 44: np.float64(0.007857142857142868), 0: 0} 

err list= [np.float64(0.11114285714285713), np.float64(0.03385714285714288), np.float64(0.05214285714285713), np.float64(0.023857142857142882), np.float64(0.030857142857142875), np.float64(0.007857142857142868), 0]
beta is  0.025 

err dic= {14: np.float64(0.11114285714285713), 55: np.float64(0.03385714285714288), 28: np.float64(0.05214285714285713), 53: np.float64(0.023857142857142882), 87: np.float64(0.030857142857142875), 44: np.float64(0.007857142857142868), 0: np.float64(0.06685714285714288)} 

err list= [np.float64(0.11114285714285713), np.float64(0.03385714285714288), np.float64(0.05214285714285713), np.float64(0.023857142857142882), np.float64(0.030857142857142875), np.float64(0.007857142857142868), np.float64(0.06685714285714288)]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11117900419668669), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: np.float64(0.03386316736611501), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11117900419668669), np.float64(0.03386316736611501), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: np.float64(0.03386316736611501), 28: np.float64(0.052136832633884994), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11117900419668669), np.float64(0.03386316736611501), np.float64(0.052136832633884994), 0, 0, 0, 0]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: np.float64(0.03386316736611501), 28: np.float64(0.052136832633884994), 53: np.float64(0.023863167366115018), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11117900419668669), np.float64(0.03386316736611501), np.float64(0.052136832633884994), np.float64(0.023863167366115018), 0, 0, 0]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: np.float64(0.03386316736611501), 28: np.float64(0.052136832633884994), 53: np.float64(0.023863167366115018), 87: np.float64(0.03086316736611501), 44: 0, 0: 0} 

err list= [np.float64(0.11117900419668669), np.float64(0.03386316736611501), np.float64(0.052136832633884994), np.float64(0.023863167366115018), np.float64(0.03086316736611501), 0, 0]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: np.float64(0.03386316736611501), 28: np.float64(0.052136832633884994), 53: np.float64(0.023863167366115018), 87: np.float64(0.03086316736611501), 44: np.float64(0.007863167366115004), 0: 0} 

err list= [np.float64(0.11117900419668669), np.float64(0.03386316736611501), np.float64(0.052136832633884994), np.float64(0.023863167366115018), np.float64(0.03086316736611501), np.float64(0.007863167366115004), 0]
beta is  0.05 

err dic= {14: np.float64(0.11117900419668669), 55: np.float64(0.03386316736611501), 28: np.float64(0.052136832633884994), 53: np.float64(0.023863167366115018), 87: np.float64(0.03086316736611501), 44: np.float64(0.007863167366115004), 0: np.float64(0.06686316736611501)} 

err list= [np.float64(0.11117900419668669), np.float64(0.03386316736611501), np.float64(0.052136832633884994), np.float64(0.023863167366115018), np.float64(0.03086316736611501), np.float64(0.007863167366115004), np.float64(0.06686316736611501)]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), 0, 0, 0, 0]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), 0, 0, 0]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), 0, 0]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), 0]
beta is  0.1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: np.float64(0.06685714285714285)} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), np.float64(0.06685714285714285)]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285832), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: np.float64(0.033857142857141684), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285832), np.float64(0.033857142857141684), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: np.float64(0.033857142857141684), 28: np.float64(0.05214285714285832), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285832), np.float64(0.033857142857141684), np.float64(0.05214285714285832), 0, 0, 0, 0]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: np.float64(0.033857142857141684), 28: np.float64(0.05214285714285832), 53: np.float64(0.02385714285714169), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285832), np.float64(0.033857142857141684), np.float64(0.05214285714285832), np.float64(0.02385714285714169), 0, 0, 0]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: np.float64(0.033857142857141684), 28: np.float64(0.05214285714285832), 53: np.float64(0.02385714285714169), 87: np.float64(0.03085714285714168), 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285832), np.float64(0.033857142857141684), np.float64(0.05214285714285832), np.float64(0.02385714285714169), np.float64(0.03085714285714168), 0, 0]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: np.float64(0.033857142857141684), 28: np.float64(0.05214285714285832), 53: np.float64(0.02385714285714169), 87: np.float64(0.03085714285714168), 44: np.float64(0.007857142857141675), 0: 0} 

err list= [np.float64(0.11114285714285832), np.float64(0.033857142857141684), np.float64(0.05214285714285832), np.float64(0.02385714285714169), np.float64(0.03085714285714168), np.float64(0.007857142857141675), 0]
beta is  0.25 

err dic= {14: np.float64(0.11114285714285832), 55: np.float64(0.033857142857141684), 28: np.float64(0.05214285714285832), 53: np.float64(0.02385714285714169), 87: np.float64(0.03085714285714168), 44: np.float64(0.007857142857141675), 0: np.float64(0.06685714285714169)} 

err list= [np.float64(0.11114285714285832), np.float64(0.033857142857141684), np.float64(0.05214285714285832), np.float64(0.02385714285714169), np.float64(0.03085714285714168), np.float64(0.007857142857141675), np.float64(0.06685714285714169)]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), 0, 0, 0, 0]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), 0, 0, 0]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), 0, 0]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), 0]
beta is  0.5 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: np.float64(0.06685714285714285)} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), np.float64(0.06685714285714285)]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), 0, 0, 0, 0]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), 0, 0, 0]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), 0, 0]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), 0]
beta is  0.75 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: np.float64(0.06685714285714285)} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), np.float64(0.06685714285714285)]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), 0, 0, 0, 0, 0]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), 0, 0, 0, 0]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), 0, 0, 0]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: 0, 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), 0, 0]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: 0} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), 0]
beta is  1 

err dic= {14: np.float64(0.11114285714285715), 55: np.float64(0.03385714285714285), 28: np.float64(0.05214285714285716), 53: np.float64(0.023857142857142855), 87: np.float64(0.030857142857142847), 44: np.float64(0.00785714285714284), 0: np.float64(0.06685714285714285)} 

err list= [np.float64(0.11114285714285715), np.float64(0.03385714285714285), np.float64(0.05214285714285716), np.float64(0.023857142857142855), np.float64(0.030857142857142847), np.float64(0.00785714285714284), np.float64(0.06685714285714285)]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: 0, 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11510890081272906), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: np.float64(0.0038514834687881916), 28: 0, 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11510890081272906), np.float64(0.0038514834687881916), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: np.float64(0.0038514834687881916), 28: np.float64(0.0898514834687882), 53: 0, 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11510890081272906), np.float64(0.0038514834687881916), np.float64(0.0898514834687882), 0, 0, 0, 0]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: np.float64(0.0038514834687881916), 28: np.float64(0.0898514834687882), 53: np.float64(0.013851483468788187), 87: 0, 44: 0, 0: 0} 

err list= [np.float64(0.11510890081272906), np.float64(0.0038514834687881916), np.float64(0.0898514834687882), np.float64(0.013851483468788187), 0, 0, 0]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: np.float64(0.0038514834687881916), 28: np.float64(0.0898514834687882), 53: np.float64(0.013851483468788187), 87: np.float64(0.006851483468788194), 44: 0, 0: 0} 

err list= [np.float64(0.11510890081272906), np.float64(0.0038514834687881916), np.float64(0.0898514834687882), np.float64(0.013851483468788187), np.float64(0.006851483468788194), 0, 0]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: np.float64(0.0038514834687881916), 28: np.float64(0.0898514834687882), 53: np.float64(0.013851483468788187), 87: np.float64(0.006851483468788194), 44: np.float64(0.0298514834687882), 0: 0} 

err list= [np.float64(0.11510890081272906), np.float64(0.0038514834687881916), np.float64(0.0898514834687882), np.float64(0.013851483468788187), np.float64(0.006851483468788194), np.float64(0.0298514834687882), 0]
beta is  1.25 

err dic= {14: np.float64(0.11510890081272906), 55: np.float64(0.0038514834687881916), 28: np.float64(0.0898514834687882), 53: np.float64(0.013851483468788187), 87: np.float64(0.006851483468788194), 44: np.float64(0.0298514834687882), 0: np.float64(0.02914851653121181)} 

err list= [np.float64(0.11510890081272906), np.float64(0.0038514834687881916), np.float64(0.0898514834687882), np.float64(0.013851483468788187), np.float64(0.006851483468788194), np.float64(0.0298514834687882), np.float64(0.02914851653121181)]
samppled assortment [35, 82, 67, 71, 100, 80]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 11]
learned probs for cluster 2 

{35: np.float64(0.15199705103857505), 82: np.float64(0.15199705103857505), 67: np.float64(0.15199705103857505), 71: np.float64(0.15199705103857505), 100: np.float64(0.08801769376855098), 80: np.float64(0.15199705103857505), 0: np.float64(0.15199705103857505)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 11]
learned probs (dictionary):

probs= {35: np.float64(0.040127221474183815), 82: np.float64(0.040127221474183815), 67: np.float64(0.040127221474183815), 71: np.float64(0.040127221474183815), 100: np.float64(0.02323667115489746), 80: np.float64(0.040127221474183815), 0: np.float64(0.040127221474183815)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
learned probs for cluster 1 

{35: np.float64(0.15232707412547067), 82: np.float64(0.15232707412547067), 67: np.float64(0.15232707412547067), 71: np.float64(0.15232707412547067), 100: np.float64(0.08603755524717617), 80: np.float64(0.15232707412547067), 0: np.float64(0.15232707412547067)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 100]
learned probs (dictionary):

probs= {35: np.float64(0.15223994803053023), 82: np.float64(0.15223994803053023), 67: np.float64(0.15223994803053023), 71: np.float64(0.15223994803053023), 100: np.float64(0.08656031181681911), 80: np.float64(0.15223994803053023), 0: np.float64(0.15223994803053023)}
choice probs for this beta: {35: np.float64(0.15223994803053023), 82: np.float64(0.15223994803053023), 67: np.float64(0.15223994803053023), 71: np.float64(0.15223994803053023), 100: np.float64(0.08656031181681911), 80: np.float64(0.15223994803053023), 0: np.float64(0.15223994803053023)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{35: np.float64(0.14387022677173347), 82: np.float64(0.14387022677173347), 67: np.float64(0.14387022677173347), 71: np.float64(0.14387022677173347), 100: np.float64(0.13677863936960732), 80: np.float64(0.14387022677173347), 0: np.float64(0.14387022677173347)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {35: np.float64(0.03798173986773764), 82: np.float64(0.03798173986773764), 67: np.float64(0.03798173986773764), 71: np.float64(0.03798173986773764), 100: np.float64(0.036109560793576335), 80: np.float64(0.03798173986773764), 0: np.float64(0.03798173986773764)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0} [1, 2, 3, 4, 5, 6, 9, 11]
learned probs for cluster 1 

{35: np.float64(0.1428571428571429), 82: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 71: np.float64(0.1428571428571429), 100: np.float64(0.1428571428571429), 80: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11]
learned probs (dictionary):

probs= {35: np.float64(0.14312459701059482), 82: np.float64(0.14312459701059482), 67: np.float64(0.14312459701059482), 71: np.float64(0.14312459701059482), 100: np.float64(0.1412524179364335), 80: np.float64(0.14312459701059482), 0: np.float64(0.14312459701059482)}
choice probs for this beta: {35: np.float64(0.14312459701059482), 82: np.float64(0.14312459701059482), 67: np.float64(0.14312459701059482), 71: np.float64(0.14312459701059482), 100: np.float64(0.1412524179364335), 80: np.float64(0.14312459701059482), 0: np.float64(0.14312459701059482)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 14: 2, 17: 3, 100: 1} [8, 1, 3, 6, 7, 13, 100, 2, 4, 5, 14, 17]
learned probs for cluster 2 

{35: np.float64(0.11531074277470042), 82: np.float64(0.11531074277470042), 67: np.float64(0.11531074277470042), 71: np.float64(0.11531074277470042), 100: np.float64(0.3081355433518115), 80: np.float64(0.11531074277470042), 0: np.float64(0.11531074277470042)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 2, 4, 5, 14, 17]
learned probs (dictionary):

probs= {35: np.float64(0.030442036092520913), 82: np.float64(0.030442036092520913), 67: np.float64(0.030442036092520913), 71: np.float64(0.030442036092520913), 100: np.float64(0.08134778344487824), 80: np.float64(0.030442036092520913), 0: np.float64(0.030442036092520913)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 100]
learned probs for cluster 1 

{35: np.float64(0.13784085046903546), 82: np.float64(0.13784085046903546), 67: np.float64(0.13784085046903546), 71: np.float64(0.13784085046903546), 100: np.float64(0.1729548971857855), 80: np.float64(0.13784085046903546), 0: np.float64(0.13784085046903546)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 100]
learned probs (dictionary):

probs= {35: np.float64(0.13189290203773102), 82: np.float64(0.13189290203773102), 67: np.float64(0.13189290203773102), 71: np.float64(0.13189290203773102), 100: np.float64(0.20864258777361638), 80: np.float64(0.13189290203773102), 0: np.float64(0.13189290203773102)}
choice probs for this beta: {35: np.float64(0.13189290203773102), 82: np.float64(0.13189290203773102), 67: np.float64(0.13189290203773102), 71: np.float64(0.13189290203773102), 100: np.float64(0.20864258777361638), 80: np.float64(0.13189290203773102), 0: np.float64(0.13189290203773102)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{35: np.float64(0.09343342416479725), 82: np.float64(0.09343342416479725), 67: np.float64(0.09343342416479725), 71: np.float64(0.09343342416479725), 100: np.float64(0.43939945501121486), 80: np.float64(0.09343342416479725), 0: np.float64(0.09343342416479725)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {35: np.float64(0.024666423979506476), 82: np.float64(0.024666423979506476), 67: np.float64(0.024666423979506476), 71: np.float64(0.024666423979506476), 100: np.float64(0.11600145612296073), 80: np.float64(0.024666423979506476), 0: np.float64(0.024666423979506476)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.1026047304600985), 82: np.float64(0.1026047304600985), 67: np.float64(0.1026047304600985), 71: np.float64(0.1026047304600985), 100: np.float64(0.38437161723940777), 80: np.float64(0.1026047304600985), 0: np.float64(0.1026047304600985)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.10018350559813899), 82: np.float64(0.10018350559813899), 67: np.float64(0.10018350559813899), 71: np.float64(0.10018350559813899), 100: np.float64(0.39889896641116485), 80: np.float64(0.10018350559813899), 0: np.float64(0.10018350559813899)}
choice probs for this beta: {35: np.float64(0.10018350559813899), 82: np.float64(0.10018350559813899), 67: np.float64(0.10018350559813899), 71: np.float64(0.10018350559813899), 100: np.float64(0.39889896641116485), 80: np.float64(0.10018350559813899), 0: np.float64(0.10018350559813899)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 15, 100, 5]
learned probs for cluster 2 

{35: np.float64(0.03481654763892304), 82: np.float64(0.03481654763892304), 67: np.float64(0.03481654763892304), 71: np.float64(0.03481654763892304), 100: np.float64(0.7911007141664625), 80: np.float64(0.03481654763892304), 0: np.float64(0.03481654763892304)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 15, 100, 5]
learned probs (dictionary):

probs= {35: np.float64(0.009191568576675684), 82: np.float64(0.009191568576675684), 67: np.float64(0.009191568576675684), 71: np.float64(0.009191568576675684), 100: np.float64(0.20885058853994612), 80: np.float64(0.009191568576675684), 0: np.float64(0.009191568576675684)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{35: np.float64(0.050017506683635644), 82: np.float64(0.050017506683635644), 67: np.float64(0.050017506683635644), 71: np.float64(0.050017506683635644), 100: np.float64(0.6998949598981872), 80: np.float64(0.050017506683635644), 0: np.float64(0.050017506683635644)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {35: np.float64(0.046004453495831515), 82: np.float64(0.046004453495831515), 67: np.float64(0.046004453495831515), 71: np.float64(0.046004453495831515), 100: np.float64(0.7239732790250119), 80: np.float64(0.046004453495831515), 0: np.float64(0.046004453495831515)}
choice probs for this beta: {35: np.float64(0.046004453495831515), 82: np.float64(0.046004453495831515), 67: np.float64(0.046004453495831515), 71: np.float64(0.046004453495831515), 100: np.float64(0.7239732790250119), 80: np.float64(0.046004453495831515), 0: np.float64(0.046004453495831515)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs for cluster 2 

{35: np.float64(0.0019325626405954088), 82: np.float64(0.0019325626405954088), 67: np.float64(0.0019325626405954088), 71: np.float64(0.0019325626405954088), 100: np.float64(0.9884046241564274), 80: np.float64(0.0019325626405954088), 0: np.float64(0.0019325626405954088)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 5]
learned probs (dictionary):

probs= {35: np.float64(0.0005101965371171879), 82: np.float64(0.0005101965371171879), 67: np.float64(0.0005101965371171879), 71: np.float64(0.0005101965371171879), 100: np.float64(0.26093882077729685), 80: np.float64(0.0005101965371171879), 0: np.float64(0.0005101965371171879)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.007905687539770199), 82: np.float64(0.007905687539770199), 67: np.float64(0.007905687539770199), 71: np.float64(0.007905687539770199), 100: np.float64(0.9525658747613788), 80: np.float64(0.007905687539770199), 0: np.float64(0.007905687539770199)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.0063287825663880535), 82: np.float64(0.0063287825663880535), 67: np.float64(0.0063287825663880535), 71: np.float64(0.0063287825663880535), 100: np.float64(0.9620273046016716), 80: np.float64(0.0063287825663880535), 0: np.float64(0.0063287825663880535)}
choice probs for this beta: {35: np.float64(0.0063287825663880535), 82: np.float64(0.0063287825663880535), 67: np.float64(0.0063287825663880535), 71: np.float64(0.0063287825663880535), 100: np.float64(0.9620273046016716), 80: np.float64(0.0063287825663880535), 0: np.float64(0.0063287825663880535)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 20: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 20]
learned probs for cluster 2 

{35: np.float64(0.00011214343113081357), 82: np.float64(0.00011214343113081357), 67: np.float64(0.00011214343113081357), 71: np.float64(0.00011214343113081357), 100: np.float64(0.9993271394132154), 80: np.float64(0.00011214343113081357), 0: np.float64(0.00011214343113081357)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 20]
learned probs (dictionary):

probs= {35: np.float64(2.9605865818534783e-05), 82: np.float64(2.9605865818534783e-05), 67: np.float64(2.9605865818534783e-05), 71: np.float64(2.9605865818534783e-05), 100: np.float64(0.26382236480508886), 80: np.float64(2.9605865818534783e-05), 0: np.float64(2.9605865818534783e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 100]
learned probs for cluster 1 

{35: np.float64(0.0006328271487551007), 82: np.float64(0.0006328271487551007), 67: np.float64(0.0006328271487551007), 71: np.float64(0.0006328271487551007), 100: np.float64(0.9962030371074694), 80: np.float64(0.0006328271487551007), 0: np.float64(0.0006328271487551007)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 100]
learned probs (dictionary):

probs= {35: np.float64(0.0004953666473022888), 82: np.float64(0.0004953666473022888), 67: np.float64(0.0004953666473022888), 71: np.float64(0.0004953666473022888), 100: np.float64(0.9970278001161863), 80: np.float64(0.0004953666473022888), 0: np.float64(0.0004953666473022888)}
choice probs for this beta: {35: np.float64(0.0004953666473022888), 82: np.float64(0.0004953666473022888), 67: np.float64(0.0004953666473022888), 71: np.float64(0.0004953666473022888), 100: np.float64(0.9970278001161863), 80: np.float64(0.0004953666473022888), 0: np.float64(0.0004953666473022888)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 14: 2, 15: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 11, 14, 15]
learned probs for cluster 2 

{35: np.float64(2.201046131648008e-06), 82: np.float64(2.201046131648008e-06), 67: np.float64(2.201046131648008e-06), 71: np.float64(2.201046131648008e-06), 100: np.float64(0.9999867937232098), 80: np.float64(2.201046131648008e-06), 0: np.float64(2.201046131648008e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 11, 14, 15]
learned probs (dictionary):

probs= {35: np.float64(5.810761787550742e-07), 82: np.float64(5.810761787550742e-07), 67: np.float64(5.810761787550742e-07), 71: np.float64(5.810761787550742e-07), 100: np.float64(0.2639965135429274), 80: np.float64(5.810761787550742e-07), 0: np.float64(5.810761787550742e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{35: np.float64(6.368445453814637e-05), 82: np.float64(6.368445453814637e-05), 67: np.float64(6.368445453814637e-05), 71: np.float64(6.368445453814637e-05), 100: np.float64(0.999617893272771), 80: np.float64(6.368445453814637e-05), 0: np.float64(6.368445453814637e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {35: np.float64(4.7452834718830805e-05), 82: np.float64(4.7452834718830805e-05), 67: np.float64(4.7452834718830805e-05), 71: np.float64(4.7452834718830805e-05), 100: np.float64(0.9997152829916868), 80: np.float64(4.7452834718830805e-05), 0: np.float64(4.7452834718830805e-05)}
choice probs for this beta: {35: np.float64(4.7452834718830805e-05), 82: np.float64(4.7452834718830805e-05), 67: np.float64(4.7452834718830805e-05), 71: np.float64(4.7452834718830805e-05), 100: np.float64(0.9997152829916868), 80: np.float64(4.7452834718830805e-05), 0: np.float64(4.7452834718830805e-05)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{35: np.float64(0.15062900064257054), 82: np.float64(0.15062900064257054), 67: np.float64(0.15062900064257054), 71: np.float64(0.15062900064257054), 100: np.float64(0.09622599614458027), 80: np.float64(0.15062900064257054), 0: np.float64(0.15062900064257054)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {35: np.float64(0.039766056169638624), 82: np.float64(0.039766056169638624), 67: np.float64(0.039766056169638624), 71: np.float64(0.039766056169638624), 100: np.float64(0.025403662982169194), 80: np.float64(0.039766056169638624), 0: np.float64(0.039766056169638624)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.14855583724948668), 82: np.float64(0.14855583724948668), 67: np.float64(0.14855583724948668), 71: np.float64(0.14855583724948668), 100: np.float64(0.1086649765030859), 80: np.float64(0.14855583724948668), 0: np.float64(0.14855583724948668)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.1491031523852608), 82: np.float64(0.1491031523852608), 67: np.float64(0.1491031523852608), 71: np.float64(0.1491031523852608), 100: np.float64(0.10538108568844043), 80: np.float64(0.1491031523852608), 0: np.float64(0.1491031523852608)}
choice probs for this beta: {35: np.float64(0.1491031523852608), 82: np.float64(0.1491031523852608), 67: np.float64(0.1491031523852608), 71: np.float64(0.1491031523852608), 100: np.float64(0.10538108568844043), 80: np.float64(0.1491031523852608), 0: np.float64(0.1491031523852608)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{35: np.float64(0.14387022677173347), 82: np.float64(0.14387022677173347), 67: np.float64(0.14387022677173347), 71: np.float64(0.14387022677173347), 100: np.float64(0.13677863936960732), 80: np.float64(0.14387022677173347), 0: np.float64(0.14387022677173347)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {35: np.float64(0.03798173986773764), 82: np.float64(0.03798173986773764), 67: np.float64(0.03798173986773764), 71: np.float64(0.03798173986773764), 100: np.float64(0.036109560793576335), 80: np.float64(0.03798173986773764), 0: np.float64(0.03798173986773764)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.14482621723511838), 82: np.float64(0.14482621723511838), 67: np.float64(0.14482621723511838), 71: np.float64(0.14482621723511838), 100: np.float64(0.1310426965893054), 80: np.float64(0.14482621723511838), 0: np.float64(0.14482621723511838)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.14457383575278476), 82: np.float64(0.14457383575278476), 67: np.float64(0.14457383575278476), 71: np.float64(0.14457383575278476), 100: np.float64(0.1325569854833051), 80: np.float64(0.14457383575278476), 0: np.float64(0.14457383575278476)}
choice probs for this beta: {35: np.float64(0.14457383575278476), 82: np.float64(0.14457383575278476), 67: np.float64(0.14457383575278476), 71: np.float64(0.14457383575278476), 100: np.float64(0.1325569854833051), 80: np.float64(0.14457383575278476), 0: np.float64(0.14457383575278476)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100]
learned probs for cluster 2 

{35: np.float64(0.14022107334162845), 82: np.float64(0.14022107334162845), 67: np.float64(0.14022107334162845), 71: np.float64(0.14022107334162845), 100: np.float64(0.15867355995022941), 80: np.float64(0.14022107334162845), 0: np.float64(0.14022107334162845)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100]
learned probs (dictionary):

probs= {35: np.float64(0.037018363362189916), 82: np.float64(0.037018363362189916), 67: np.float64(0.037018363362189916), 71: np.float64(0.037018363362189916), 100: np.float64(0.04188981982686057), 80: np.float64(0.037018363362189916), 0: np.float64(0.037018363362189916)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{35: np.float64(0.13391267069095358), 82: np.float64(0.13391267069095358), 67: np.float64(0.13391267069095358), 71: np.float64(0.13391267069095358), 100: np.float64(0.19652397585428202), 80: np.float64(0.13391267069095358), 0: np.float64(0.13391267069095358)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {35: np.float64(0.13557808899073176), 82: np.float64(0.13557808899073176), 67: np.float64(0.13557808899073176), 71: np.float64(0.13557808899073176), 100: np.float64(0.18653146605561213), 80: np.float64(0.13557808899073176), 0: np.float64(0.13557808899073176)}
choice probs for this beta: {35: np.float64(0.13557808899073176), 82: np.float64(0.13557808899073176), 67: np.float64(0.13557808899073176), 71: np.float64(0.13557808899073176), 100: np.float64(0.18653146605561213), 80: np.float64(0.13557808899073176), 0: np.float64(0.13557808899073176)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 5]
learned probs for cluster 2 

{35: np.float64(0.09443889372090622), 82: np.float64(0.09443889372090622), 67: np.float64(0.09443889372090622), 71: np.float64(0.09443889372090622), 100: np.float64(0.43336663767456335), 80: np.float64(0.09443889372090622), 0: np.float64(0.09443889372090622)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 5]
learned probs (dictionary):

probs= {35: np.float64(0.024931867942319243), 82: np.float64(0.024931867942319243), 67: np.float64(0.024931867942319243), 71: np.float64(0.024931867942319243), 100: np.float64(0.11440879234608473), 80: np.float64(0.024931867942319243), 0: np.float64(0.024931867942319243)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 100]
learned probs for cluster 1 

{35: np.float64(0.10372261081141593), 82: np.float64(0.10372261081141593), 67: np.float64(0.10372261081141593), 71: np.float64(0.10372261081141593), 100: np.float64(0.37766433513150277), 80: np.float64(0.10372261081141593), 0: np.float64(0.10372261081141593)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 100]
learned probs (dictionary):

probs= {35: np.float64(0.10127170949952137), 82: np.float64(0.10127170949952137), 67: np.float64(0.10127170949952137), 71: np.float64(0.10127170949952137), 100: np.float64(0.39236974300287075), 80: np.float64(0.10127170949952137), 0: np.float64(0.10127170949952137)}
choice probs for this beta: {35: np.float64(0.10127170949952137), 82: np.float64(0.10127170949952137), 67: np.float64(0.10127170949952137), 71: np.float64(0.10127170949952137), 100: np.float64(0.39236974300287075), 80: np.float64(0.10127170949952137), 0: np.float64(0.10127170949952137)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 5]
learned probs for cluster 2 

{35: np.float64(0.022843006481697667), 82: np.float64(0.022843006481697667), 67: np.float64(0.022843006481697667), 71: np.float64(0.022843006481697667), 100: np.float64(0.8629419611098132), 80: np.float64(0.022843006481697667), 0: np.float64(0.022843006481697667)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 4, 5]
learned probs (dictionary):

probs= {35: np.float64(0.006030553711168184), 82: np.float64(0.006030553711168184), 67: np.float64(0.006030553711168184), 71: np.float64(0.006030553711168184), 100: np.float64(0.22781667773299072), 80: np.float64(0.006030553711168184), 0: np.float64(0.006030553711168184)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.05094093352952595), 82: np.float64(0.05094093352952595), 67: np.float64(0.05094093352952595), 71: np.float64(0.05094093352952595), 100: np.float64(0.694354398822846), 80: np.float64(0.05094093352952595), 0: np.float64(0.05094093352952595)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.043523080788899285), 82: np.float64(0.043523080788899285), 67: np.float64(0.043523080788899285), 71: np.float64(0.043523080788899285), 100: np.float64(0.7388615152666054), 80: np.float64(0.043523080788899285), 0: np.float64(0.043523080788899285)}
choice probs for this beta: {35: np.float64(0.043523080788899285), 82: np.float64(0.043523080788899285), 67: np.float64(0.043523080788899285), 71: np.float64(0.043523080788899285), 100: np.float64(0.7388615152666054), 80: np.float64(0.043523080788899285), 0: np.float64(0.043523080788899285)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs for cluster 2 

{35: np.float64(0.002053700626242238), 82: np.float64(0.002053700626242238), 67: np.float64(0.002053700626242238), 71: np.float64(0.002053700626242238), 100: np.float64(0.9876777962425464), 80: np.float64(0.002053700626242238), 0: np.float64(0.002053700626242238)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 5]
learned probs (dictionary):

probs= {35: np.float64(0.0005421769653279508), 82: np.float64(0.0005421769653279508), 67: np.float64(0.0005421769653279508), 71: np.float64(0.0005421769653279508), 100: np.float64(0.26074693820803224), 80: np.float64(0.0005421769653279508), 0: np.float64(0.0005421769653279508)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.007905687539770199), 82: np.float64(0.007905687539770199), 67: np.float64(0.007905687539770199), 71: np.float64(0.007905687539770199), 100: np.float64(0.9525658747613788), 80: np.float64(0.007905687539770199), 0: np.float64(0.007905687539770199)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.006360762994598816), 82: np.float64(0.006360762994598816), 67: np.float64(0.006360762994598816), 71: np.float64(0.006360762994598816), 100: np.float64(0.961835422032407), 80: np.float64(0.006360762994598816), 0: np.float64(0.006360762994598816)}
choice probs for this beta: {35: np.float64(0.006360762994598816), 82: np.float64(0.006360762994598816), 67: np.float64(0.006360762994598816), 71: np.float64(0.006360762994598816), 100: np.float64(0.961835422032407), 80: np.float64(0.006360762994598816), 0: np.float64(0.006360762994598816)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 14]
learned probs for cluster 2 

{35: np.float64(0.0002428385891113634), 82: np.float64(0.0002428385891113634), 67: np.float64(0.0002428385891113634), 71: np.float64(0.0002428385891113634), 100: np.float64(0.9985429684653319), 80: np.float64(0.0002428385891113634), 0: np.float64(0.0002428385891113634)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 14]
learned probs (dictionary):

probs= {35: np.float64(6.410938752539993e-05), 82: np.float64(6.410938752539993e-05), 67: np.float64(6.410938752539993e-05), 71: np.float64(6.410938752539993e-05), 100: np.float64(0.2636153436748476), 80: np.float64(6.410938752539993e-05), 0: np.float64(6.410938752539993e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{35: np.float64(0.0008252984820937543), 82: np.float64(0.0008252984820937543), 67: np.float64(0.0008252984820937543), 71: np.float64(0.0008252984820937543), 100: np.float64(0.9950482091074375), 80: np.float64(0.0008252984820937543), 0: np.float64(0.0008252984820937543)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {35: np.float64(0.0006715290703464031), 82: np.float64(0.0006715290703464031), 67: np.float64(0.0006715290703464031), 71: np.float64(0.0006715290703464031), 100: np.float64(0.9959708255779216), 80: np.float64(0.0006715290703464031), 0: np.float64(0.0006715290703464031)}
choice probs for this beta: {35: np.float64(0.0006715290703464031), 82: np.float64(0.0006715290703464031), 67: np.float64(0.0006715290703464031), 71: np.float64(0.0006715290703464031), 100: np.float64(0.9959708255779216), 80: np.float64(0.0006715290703464031), 0: np.float64(0.0006715290703464031)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 11, 14]
learned probs for cluster 2 

{35: np.float64(1.961311078861308e-06), 82: np.float64(1.961311078861308e-06), 67: np.float64(1.961311078861308e-06), 71: np.float64(1.961311078861308e-06), 100: np.float64(0.9999882321335266), 80: np.float64(1.961311078861308e-06), 0: np.float64(1.961311078861308e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 11, 14]
learned probs (dictionary):

probs= {35: np.float64(5.177861248193853e-07), 82: np.float64(5.177861248193853e-07), 67: np.float64(5.177861248193853e-07), 71: np.float64(5.177861248193853e-07), 100: np.float64(0.26399689328325104), 80: np.float64(5.177861248193853e-07), 0: np.float64(5.177861248193853e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
learned probs for cluster 1 

{35: np.float64(8.957139374940886e-05), 82: np.float64(8.957139374940886e-05), 67: np.float64(8.957139374940886e-05), 71: np.float64(8.957139374940886e-05), 100: np.float64(0.9994625716375032), 80: np.float64(8.957139374940886e-05), 0: np.float64(8.957139374940886e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 100]
learned probs (dictionary):

probs= {35: np.float64(6.644233192438431e-05), 82: np.float64(6.644233192438431e-05), 67: np.float64(6.644233192438431e-05), 71: np.float64(6.644233192438431e-05), 100: np.float64(0.9996013460084534), 80: np.float64(6.644233192438431e-05), 0: np.float64(6.644233192438431e-05)}
choice probs for this beta: {35: np.float64(6.644233192438431e-05), 82: np.float64(6.644233192438431e-05), 67: np.float64(6.644233192438431e-05), 71: np.float64(6.644233192438431e-05), 100: np.float64(0.9996013460084534), 80: np.float64(6.644233192438431e-05), 0: np.float64(6.644233192438431e-05)}
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 67
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 100
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 100
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 67
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 80
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 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 67
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 100
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 71
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 71
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 35
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 67
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 100
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 35
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 100
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 100
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 100
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 100
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 100
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 100
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 100
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 71
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 67
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 71
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 100
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 35
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 35
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 71
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 100
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 71
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 71
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 100
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 71
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 100
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 82
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 71
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 35
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 82
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 82
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 100
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 71
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 100
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 67
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 35
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 71
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 80
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 82
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 100
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 35
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 35
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 35
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 100
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 35
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 100
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 67
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 82
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 35
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 0
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 80
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 100
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 71
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 100
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 35
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 0
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 80
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 67
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 71
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 71
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 100
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 80
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 100
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 100
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 82
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 82
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 100
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 100
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 67
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 71
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 80
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 100
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 35
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 100
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 100
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 100
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 67
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 67
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 82
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 80
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 100
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 82
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 82
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 100
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 35
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 35
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 0
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 82
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 35
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 35
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 67
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 100
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 100
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 35
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 35
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 82
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 80
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 100
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 67
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 80
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 82
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 80
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 67
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 71
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 82
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 71
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 80
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 0
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 0
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 100
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 0
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 67
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 80
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 67
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 71
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 35
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 100
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 80
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 82
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 35
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 35
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 80
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 67
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 100
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 80
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 71
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 0
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 100
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 82
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 67
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 67
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 100
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 35
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 35
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 67
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 100
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 80
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 0
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 82
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 100
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 100
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 100
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 80
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 82
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 67
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 67
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 100
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 100
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 71
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 71
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 100
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 67
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 82
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 80
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 67
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 67
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 100
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 100
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 100
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 100
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 100
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 67
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 35
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 100
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 100
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 0
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 100
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 35
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 100
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 100
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 100
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 100
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 100
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 100
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 0
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 0
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 80
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 80
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 71
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 35
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 100
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 35
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 0
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 67
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 80
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 35
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 82
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 100
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 35
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 100
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 0
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 35
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 35
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 35
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 82
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 82
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 35
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 100
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 67
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 100
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 82
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 35
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 100
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 80
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 82
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 82
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 100
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 100
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 67
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 80
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 67
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 100
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 67
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 100
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 35
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 67
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 71
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 100
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 71
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 67
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 0
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 82
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 100
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 67
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 35
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 67
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 35
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 82
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 71
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 0
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 67
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 35
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 82
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 71
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 71
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 67
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 67
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 35
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 71
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 35
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 100
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 82
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 35
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 100
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 100
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 100
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 82
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 71
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 100
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 82
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 71
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 35
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 82
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 100
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 71
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 35
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 100
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 100
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 100
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 71
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 35
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 35
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 80
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 67
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 35
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 71
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 35
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 100
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 35
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 100
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 100
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 35
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 71
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 35
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 0
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 35
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 67
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 35
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 100
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 100
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 71
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 82
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 71
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 67
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 67
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 67
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 100
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 0
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 71
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 80
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 35
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 82
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 71
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 71
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 82
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 82
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 71
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 82
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 0
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 100
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 82
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 71
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 100
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 71
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 82
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 0
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 100
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 100
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 82
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 71
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 100
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 71
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 35
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 100
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 82
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 35
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 67
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 0
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 71
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 80
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 100
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 67
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 67
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 82
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 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 71
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 67
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 80
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 35
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 67
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 71
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 80
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 67
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 80
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 100
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 100
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 82
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 71
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 71
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 80
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 67
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 67
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 100
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 100
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 71
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 80
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 67
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 80
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 0
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 67
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 35
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 80
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 100
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 71
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 0
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 35
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 0
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 67
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 80
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 35
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 0
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 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 67
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 35
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 100
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 0
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 35
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 71
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 0
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 100
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 0
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 100
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 67
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 35
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 100
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 35
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 0
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 100
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 0
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 100
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 35
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 100
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 100
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 35
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 71
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 100
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 100
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 35
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 71
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 67
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 35
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 80
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 100
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 80
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 100
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 80
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 82
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 100
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 35
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 80
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 100
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 82
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 71
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 100
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 100
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 67
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 67
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 67
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 35
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 0
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 100
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 100
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 71
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 35
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 67
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 80
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 35
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 100
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 35
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 67
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 71
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 80
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 100
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 67
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 67
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 35
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 82
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 71
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 82
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 80
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 82
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 0
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 100
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 71
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 80
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 100
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 71
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 35
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 35
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 0
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 71
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 35
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 80
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 71
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 0
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 71
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 100
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 100
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 67
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 0
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 67
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 100
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 100
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 35
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 0
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 82
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 35
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 35
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 100
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 100
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 71
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 67
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 100
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 71
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 82
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 100
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 100
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 35
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 71
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 100
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 100
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 71
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 100
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 100
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 82
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 100
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 80
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 35
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 67
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 71
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 100
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 0
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 82
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 100
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 82
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 71
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 67
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 71
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 100
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 35
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 80
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 0
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 100
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 71
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 71
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 100
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 80
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 80
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 71
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 100
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 100
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 100
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 71
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 100
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 100
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 0
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 71
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 67
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 100
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 67
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 100
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 35
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 100
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 35
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 0
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 100
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 100
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 71
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 100
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 80
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 82
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 100
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 100
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 82
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 67
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 71
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 80
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 82
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 71
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 100
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 35
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 100
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 100
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 0
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 100
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 0
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 80
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 67
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 100
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 35
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 80
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 0
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 80
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 71
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 0
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 100
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 0
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 35
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 0
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 71
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 35
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 82
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 0
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 82
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 100
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 80
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 67
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 35
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 35
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 35
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 71
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 100
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 0
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 35
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 82
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 71
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 80
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 35
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 35
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 82
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 100
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 100
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 100
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 35
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 100
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 80
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 100
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 82
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 71
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 100
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 82
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 0
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 67
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 0
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 100
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 71
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 82
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 67
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 100
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 71
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 100
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 82
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 67
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 0
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 100
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 35
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 35
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 80
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 67
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 35
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 71
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 35
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 100
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 100
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 0
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 71
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 71
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 80
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 80
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 100
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 35
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 82
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 35
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 67
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 100
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 100
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 71
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 67
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 67
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 100
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 0
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 82
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 67
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 82
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 67
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 100
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 67
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 82
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 80
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 0
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 0
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 100
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 80
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 0
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 35
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 100
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 35
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 35
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 82
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 71
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 82
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 71
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 35
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 100
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 71
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 67
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 35
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 71
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 35
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 80
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 82
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 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 35
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 67
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 35
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 100
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 67
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 82
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 35
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 100
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 82
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 100
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 71
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 80
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 80
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 0
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 71
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 35
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 71
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 67
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 67
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 67
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 35
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 82
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 71
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 100
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 35
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 82
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 35
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 80
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 100
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 82
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 35
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 80
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 71
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 0
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 0
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 82
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 35
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 100
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 35
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 35
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 71
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 67
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 0
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 71
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 100
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 35
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 100
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 100
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 35
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 71
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 35
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 100
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 67
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 100
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 35
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 100
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 71
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 82
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 67
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 80
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 100
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 100
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 0
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 100
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 35
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 0
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 100
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 67
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 71
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 71
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 100
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 67
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 67
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 71
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 71
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 71
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 67
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 71
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 71
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 100
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 71
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 35
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 80
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 82
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 0
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 100
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 100
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 80
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 82
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 67
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 35
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 82
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 100
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 100
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 82
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 100
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 100
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 0
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 35
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 100
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 100
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 35
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 71
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 100
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 35
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 35
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 71
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 35
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 71
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 82
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 80
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 67
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 67
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 67
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 80
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 0
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 35
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 35
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 80
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 35
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 82
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 0
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 100
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 100
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 0
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 35
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 35
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 71
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 100
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 82
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 100
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 71
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 67
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 71
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 80
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 100
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 35
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 82
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 67
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 80
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 71
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 67
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 71
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 80
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 100
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 71
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 67
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 67
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 80
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 80
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 0
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 35
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 0
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 80
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 100
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 100
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 100
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 35
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 35
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 0
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 71
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 82
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 100
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 80
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 67
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 82
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 80
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 100
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 80
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 80
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 67
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 0
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 35
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 0
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 82
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 80
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 35
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 80
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 0
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 82
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 71
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 100
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 80
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 80
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 71
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 100
emperical probablities from test set: {35: 0.166, 82: 0.09, 67: 0.108, 71: 0.122, 100: 0.351, 80: 0.085, 0: 0.078}
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.016896847614739197), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: np.float64(0.059103152385260815), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.016896847614739197), np.float64(0.059103152385260815), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: np.float64(0.059103152385260815), 67: np.float64(0.04110315238526081), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.016896847614739197), np.float64(0.059103152385260815), np.float64(0.04110315238526081), 0, 0, 0, 0]
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: np.float64(0.059103152385260815), 67: np.float64(0.04110315238526081), 71: np.float64(0.027103152385260815), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.016896847614739197), np.float64(0.059103152385260815), np.float64(0.04110315238526081), np.float64(0.027103152385260815), 0, 0, 0]
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: np.float64(0.059103152385260815), 67: np.float64(0.04110315238526081), 71: np.float64(0.027103152385260815), 100: np.float64(0.24561891431155955), 80: 0, 0: 0} 

err list= [np.float64(0.016896847614739197), np.float64(0.059103152385260815), np.float64(0.04110315238526081), np.float64(0.027103152385260815), np.float64(0.24561891431155955), 0, 0]
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: np.float64(0.059103152385260815), 67: np.float64(0.04110315238526081), 71: np.float64(0.027103152385260815), 100: np.float64(0.24561891431155955), 80: np.float64(0.0641031523852608), 0: 0} 

err list= [np.float64(0.016896847614739197), np.float64(0.059103152385260815), np.float64(0.04110315238526081), np.float64(0.027103152385260815), np.float64(0.24561891431155955), np.float64(0.0641031523852608), 0]
beta is  0.025 

err dic= {35: np.float64(0.016896847614739197), 82: np.float64(0.059103152385260815), 67: np.float64(0.04110315238526081), 71: np.float64(0.027103152385260815), 100: np.float64(0.24561891431155955), 80: np.float64(0.0641031523852608), 0: np.float64(0.07110315238526081)} 

err list= [np.float64(0.016896847614739197), np.float64(0.059103152385260815), np.float64(0.04110315238526081), np.float64(0.027103152385260815), np.float64(0.24561891431155955), np.float64(0.0641031523852608), np.float64(0.07110315238526081)]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.021426164247215246), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: np.float64(0.054573835752784766), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.021426164247215246), np.float64(0.054573835752784766), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: np.float64(0.054573835752784766), 67: np.float64(0.036573835752784764), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.021426164247215246), np.float64(0.054573835752784766), np.float64(0.036573835752784764), 0, 0, 0, 0]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: np.float64(0.054573835752784766), 67: np.float64(0.036573835752784764), 71: np.float64(0.022573835752784766), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.021426164247215246), np.float64(0.054573835752784766), np.float64(0.036573835752784764), np.float64(0.022573835752784766), 0, 0, 0]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: np.float64(0.054573835752784766), 67: np.float64(0.036573835752784764), 71: np.float64(0.022573835752784766), 100: np.float64(0.21844301451669487), 80: 0, 0: 0} 

err list= [np.float64(0.021426164247215246), np.float64(0.054573835752784766), np.float64(0.036573835752784764), np.float64(0.022573835752784766), np.float64(0.21844301451669487), 0, 0]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: np.float64(0.054573835752784766), 67: np.float64(0.036573835752784764), 71: np.float64(0.022573835752784766), 100: np.float64(0.21844301451669487), 80: np.float64(0.05957383575278476), 0: 0} 

err list= [np.float64(0.021426164247215246), np.float64(0.054573835752784766), np.float64(0.036573835752784764), np.float64(0.022573835752784766), np.float64(0.21844301451669487), np.float64(0.05957383575278476), 0]
beta is  0.05 

err dic= {35: np.float64(0.021426164247215246), 82: np.float64(0.054573835752784766), 67: np.float64(0.036573835752784764), 71: np.float64(0.022573835752784766), 100: np.float64(0.21844301451669487), 80: np.float64(0.05957383575278476), 0: np.float64(0.06657383575278476)} 

err list= [np.float64(0.021426164247215246), np.float64(0.054573835752784766), np.float64(0.036573835752784764), np.float64(0.022573835752784766), np.float64(0.21844301451669487), np.float64(0.05957383575278476), np.float64(0.06657383575278476)]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.03042191100926825), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: np.float64(0.04557808899073176), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.03042191100926825), np.float64(0.04557808899073176), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: np.float64(0.04557808899073176), 67: np.float64(0.02757808899073176), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.03042191100926825), np.float64(0.04557808899073176), np.float64(0.02757808899073176), 0, 0, 0, 0]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: np.float64(0.04557808899073176), 67: np.float64(0.02757808899073176), 71: np.float64(0.013578088990731763), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.03042191100926825), np.float64(0.04557808899073176), np.float64(0.02757808899073176), np.float64(0.013578088990731763), 0, 0, 0]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: np.float64(0.04557808899073176), 67: np.float64(0.02757808899073176), 71: np.float64(0.013578088990731763), 100: np.float64(0.16446853394438785), 80: 0, 0: 0} 

err list= [np.float64(0.03042191100926825), np.float64(0.04557808899073176), np.float64(0.02757808899073176), np.float64(0.013578088990731763), np.float64(0.16446853394438785), 0, 0]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: np.float64(0.04557808899073176), 67: np.float64(0.02757808899073176), 71: np.float64(0.013578088990731763), 100: np.float64(0.16446853394438785), 80: np.float64(0.050578088990731754), 0: 0} 

err list= [np.float64(0.03042191100926825), np.float64(0.04557808899073176), np.float64(0.02757808899073176), np.float64(0.013578088990731763), np.float64(0.16446853394438785), np.float64(0.050578088990731754), 0]
beta is  0.1 

err dic= {35: np.float64(0.03042191100926825), 82: np.float64(0.04557808899073176), 67: np.float64(0.02757808899073176), 71: np.float64(0.013578088990731763), 100: np.float64(0.16446853394438785), 80: np.float64(0.050578088990731754), 0: np.float64(0.05757808899073176)} 

err list= [np.float64(0.03042191100926825), np.float64(0.04557808899073176), np.float64(0.02757808899073176), np.float64(0.013578088990731763), np.float64(0.16446853394438785), np.float64(0.050578088990731754), np.float64(0.05757808899073176)]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.06472829050047864), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: np.float64(0.011271709499521373), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.06472829050047864), np.float64(0.011271709499521373), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: np.float64(0.011271709499521373), 67: np.float64(0.006728290500478629), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.06472829050047864), np.float64(0.011271709499521373), np.float64(0.006728290500478629), 0, 0, 0, 0]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: np.float64(0.011271709499521373), 67: np.float64(0.006728290500478629), 71: np.float64(0.020728290500478627), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.06472829050047864), np.float64(0.011271709499521373), np.float64(0.006728290500478629), np.float64(0.020728290500478627), 0, 0, 0]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: np.float64(0.011271709499521373), 67: np.float64(0.006728290500478629), 71: np.float64(0.020728290500478627), 100: np.float64(0.041369743002870774), 80: 0, 0: 0} 

err list= [np.float64(0.06472829050047864), np.float64(0.011271709499521373), np.float64(0.006728290500478629), np.float64(0.020728290500478627), np.float64(0.041369743002870774), 0, 0]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: np.float64(0.011271709499521373), 67: np.float64(0.006728290500478629), 71: np.float64(0.020728290500478627), 100: np.float64(0.041369743002870774), 80: np.float64(0.016271709499521364), 0: 0} 

err list= [np.float64(0.06472829050047864), np.float64(0.011271709499521373), np.float64(0.006728290500478629), np.float64(0.020728290500478627), np.float64(0.041369743002870774), np.float64(0.016271709499521364), 0]
beta is  0.25 

err dic= {35: np.float64(0.06472829050047864), 82: np.float64(0.011271709499521373), 67: np.float64(0.006728290500478629), 71: np.float64(0.020728290500478627), 100: np.float64(0.041369743002870774), 80: np.float64(0.016271709499521364), 0: np.float64(0.02327170949952137)} 

err list= [np.float64(0.06472829050047864), np.float64(0.011271709499521373), np.float64(0.006728290500478629), np.float64(0.020728290500478627), np.float64(0.041369743002870774), np.float64(0.016271709499521364), np.float64(0.02327170949952137)]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.12247691921110072), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: np.float64(0.04647691921110071), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.12247691921110072), np.float64(0.04647691921110071), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: np.float64(0.04647691921110071), 67: np.float64(0.06447691921110071), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.12247691921110072), np.float64(0.04647691921110071), np.float64(0.06447691921110071), 0, 0, 0, 0]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: np.float64(0.04647691921110071), 67: np.float64(0.06447691921110071), 71: np.float64(0.07847691921110071), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.12247691921110072), np.float64(0.04647691921110071), np.float64(0.06447691921110071), np.float64(0.07847691921110071), 0, 0, 0]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: np.float64(0.04647691921110071), 67: np.float64(0.06447691921110071), 71: np.float64(0.07847691921110071), 100: np.float64(0.3878615152666054), 80: 0, 0: 0} 

err list= [np.float64(0.12247691921110072), np.float64(0.04647691921110071), np.float64(0.06447691921110071), np.float64(0.07847691921110071), np.float64(0.3878615152666054), 0, 0]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: np.float64(0.04647691921110071), 67: np.float64(0.06447691921110071), 71: np.float64(0.07847691921110071), 100: np.float64(0.3878615152666054), 80: np.float64(0.04147691921110072), 0: 0} 

err list= [np.float64(0.12247691921110072), np.float64(0.04647691921110071), np.float64(0.06447691921110071), np.float64(0.07847691921110071), np.float64(0.3878615152666054), np.float64(0.04147691921110072), 0]
beta is  0.5 

err dic= {35: np.float64(0.12247691921110072), 82: np.float64(0.04647691921110071), 67: np.float64(0.06447691921110071), 71: np.float64(0.07847691921110071), 100: np.float64(0.3878615152666054), 80: np.float64(0.04147691921110072), 0: np.float64(0.034476919211100715)} 

err list= [np.float64(0.12247691921110072), np.float64(0.04647691921110071), np.float64(0.06447691921110071), np.float64(0.07847691921110071), np.float64(0.3878615152666054), np.float64(0.04147691921110072), np.float64(0.034476919211100715)]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1596392370054012), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: np.float64(0.08363923700540118), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1596392370054012), np.float64(0.08363923700540118), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: np.float64(0.08363923700540118), 67: np.float64(0.10163923700540119), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1596392370054012), np.float64(0.08363923700540118), np.float64(0.10163923700540119), 0, 0, 0, 0]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: np.float64(0.08363923700540118), 67: np.float64(0.10163923700540119), 71: np.float64(0.11563923700540119), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1596392370054012), np.float64(0.08363923700540118), np.float64(0.10163923700540119), np.float64(0.11563923700540119), 0, 0, 0]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: np.float64(0.08363923700540118), 67: np.float64(0.10163923700540119), 71: np.float64(0.11563923700540119), 100: np.float64(0.610835422032407), 80: 0, 0: 0} 

err list= [np.float64(0.1596392370054012), np.float64(0.08363923700540118), np.float64(0.10163923700540119), np.float64(0.11563923700540119), np.float64(0.610835422032407), 0, 0]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: np.float64(0.08363923700540118), 67: np.float64(0.10163923700540119), 71: np.float64(0.11563923700540119), 100: np.float64(0.610835422032407), 80: np.float64(0.0786392370054012), 0: 0} 

err list= [np.float64(0.1596392370054012), np.float64(0.08363923700540118), np.float64(0.10163923700540119), np.float64(0.11563923700540119), np.float64(0.610835422032407), np.float64(0.0786392370054012), 0]
beta is  0.75 

err dic= {35: np.float64(0.1596392370054012), 82: np.float64(0.08363923700540118), 67: np.float64(0.10163923700540119), 71: np.float64(0.11563923700540119), 100: np.float64(0.610835422032407), 80: np.float64(0.0786392370054012), 0: np.float64(0.07163923700540119)} 

err list= [np.float64(0.1596392370054012), np.float64(0.08363923700540118), np.float64(0.10163923700540119), np.float64(0.11563923700540119), np.float64(0.610835422032407), np.float64(0.0786392370054012), np.float64(0.07163923700540119)]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1653284709296536), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: np.float64(0.0893284709296536), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1653284709296536), np.float64(0.0893284709296536), 0, 0, 0, 0, 0]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: np.float64(0.0893284709296536), 67: np.float64(0.1073284709296536), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1653284709296536), np.float64(0.0893284709296536), np.float64(0.1073284709296536), 0, 0, 0, 0]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: np.float64(0.0893284709296536), 67: np.float64(0.1073284709296536), 71: np.float64(0.1213284709296536), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.1653284709296536), np.float64(0.0893284709296536), np.float64(0.1073284709296536), np.float64(0.1213284709296536), 0, 0, 0]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: np.float64(0.0893284709296536), 67: np.float64(0.1073284709296536), 71: np.float64(0.1213284709296536), 100: np.float64(0.6449708255779216), 80: 0, 0: 0} 

err list= [np.float64(0.1653284709296536), np.float64(0.0893284709296536), np.float64(0.1073284709296536), np.float64(0.1213284709296536), np.float64(0.6449708255779216), 0, 0]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: np.float64(0.0893284709296536), 67: np.float64(0.1073284709296536), 71: np.float64(0.1213284709296536), 100: np.float64(0.6449708255779216), 80: np.float64(0.0843284709296536), 0: 0} 

err list= [np.float64(0.1653284709296536), np.float64(0.0893284709296536), np.float64(0.1073284709296536), np.float64(0.1213284709296536), np.float64(0.6449708255779216), np.float64(0.0843284709296536), 0]
beta is  1 

err dic= {35: np.float64(0.1653284709296536), 82: np.float64(0.0893284709296536), 67: np.float64(0.1073284709296536), 71: np.float64(0.1213284709296536), 100: np.float64(0.6449708255779216), 80: np.float64(0.0843284709296536), 0: np.float64(0.0773284709296536)} 

err list= [np.float64(0.1653284709296536), np.float64(0.0893284709296536), np.float64(0.1073284709296536), np.float64(0.1213284709296536), np.float64(0.6449708255779216), np.float64(0.0843284709296536), np.float64(0.0773284709296536)]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: 0, 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.16593355766807563), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: np.float64(0.0899335576680756), 67: 0, 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.16593355766807563), np.float64(0.0899335576680756), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: np.float64(0.0899335576680756), 67: np.float64(0.10793355766807561), 71: 0, 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.16593355766807563), np.float64(0.0899335576680756), np.float64(0.10793355766807561), 0, 0, 0, 0]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: np.float64(0.0899335576680756), 67: np.float64(0.10793355766807561), 71: np.float64(0.1219335576680756), 100: 0, 80: 0, 0: 0} 

err list= [np.float64(0.16593355766807563), np.float64(0.0899335576680756), np.float64(0.10793355766807561), np.float64(0.1219335576680756), 0, 0, 0]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: np.float64(0.0899335576680756), 67: np.float64(0.10793355766807561), 71: np.float64(0.1219335576680756), 100: np.float64(0.6486013460084534), 80: 0, 0: 0} 

err list= [np.float64(0.16593355766807563), np.float64(0.0899335576680756), np.float64(0.10793355766807561), np.float64(0.1219335576680756), np.float64(0.6486013460084534), 0, 0]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: np.float64(0.0899335576680756), 67: np.float64(0.10793355766807561), 71: np.float64(0.1219335576680756), 100: np.float64(0.6486013460084534), 80: np.float64(0.08493355766807562), 0: 0} 

err list= [np.float64(0.16593355766807563), np.float64(0.0899335576680756), np.float64(0.10793355766807561), np.float64(0.1219335576680756), np.float64(0.6486013460084534), np.float64(0.08493355766807562), 0]
beta is  1.25 

err dic= {35: np.float64(0.16593355766807563), 82: np.float64(0.0899335576680756), 67: np.float64(0.10793355766807561), 71: np.float64(0.1219335576680756), 100: np.float64(0.6486013460084534), 80: np.float64(0.08493355766807562), 0: np.float64(0.07793355766807561)} 

err list= [np.float64(0.16593355766807563), np.float64(0.0899335576680756), np.float64(0.10793355766807561), np.float64(0.1219335576680756), np.float64(0.6486013460084534), np.float64(0.08493355766807562), np.float64(0.07793355766807561)]
samppled assortment [40, 52, 47, 15, 25, 67]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 11, 13, 100]
learned probs for cluster 2 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 11, 13, 100]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428572), 52: np.float64(0.03771428571428572), 47: np.float64(0.03771428571428572), 15: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 67: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 47: np.float64(0.03771428571428573), 15: np.float64(0.03771428571428573), 25: np.float64(0.03771428571428573), 67: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714554), 52: np.float64(0.14285714285714554), 47: np.float64(0.14285714285714554), 15: np.float64(0.14285714285714554), 25: np.float64(0.14285714285714554), 67: np.float64(0.14285714285714554), 0: np.float64(0.14285714285714554)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714485), 52: np.float64(0.14285714285714485), 47: np.float64(0.14285714285714485), 15: np.float64(0.14285714285714485), 25: np.float64(0.14285714285714485), 67: np.float64(0.14285714285714485), 0: np.float64(0.14285714285714485)}
choice probs for this beta: {40: np.float64(0.14285714285714485), 52: np.float64(0.14285714285714485), 47: np.float64(0.14285714285714485), 15: np.float64(0.14285714285714485), 25: np.float64(0.14285714285714485), 67: np.float64(0.14285714285714485), 0: np.float64(0.14285714285714485)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428572), 52: np.float64(0.03771428571428572), 47: np.float64(0.03771428571428572), 15: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 67: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 14: 2, 100: 1} [8, 1, 3, 6, 7, 100, 14]
learned probs for cluster 2 

{40: np.float64(0.14285714285714293), 52: np.float64(0.14285714285714293), 47: np.float64(0.14285714285714293), 15: np.float64(0.14285714285714293), 25: np.float64(0.14285714285714293), 67: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 100, 14]
learned probs (dictionary):

probs= {40: np.float64(0.037714285714285735), 52: np.float64(0.037714285714285735), 47: np.float64(0.037714285714285735), 15: np.float64(0.037714285714285735), 25: np.float64(0.037714285714285735), 67: np.float64(0.037714285714285735), 0: np.float64(0.037714285714285735)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714135), 52: np.float64(0.14285714285714135), 47: np.float64(0.14285714285714135), 15: np.float64(0.14285714285714135), 25: np.float64(0.14285714285714135), 67: np.float64(0.14285714285714135), 0: np.float64(0.14285714285714135)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714177), 52: np.float64(0.14285714285714177), 47: np.float64(0.14285714285714177), 15: np.float64(0.14285714285714177), 25: np.float64(0.14285714285714177), 67: np.float64(0.14285714285714177), 0: np.float64(0.14285714285714177)}
choice probs for this beta: {40: np.float64(0.14285714285714177), 52: np.float64(0.14285714285714177), 47: np.float64(0.14285714285714177), 15: np.float64(0.14285714285714177), 25: np.float64(0.14285714285714177), 67: np.float64(0.14285714285714177), 0: np.float64(0.14285714285714177)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 3, 6, 7, 10, 14, 100]
learned probs for cluster 2 

{40: np.float64(0.14285714285714277), 52: np.float64(0.14285714285714277), 47: np.float64(0.14285714285714277), 15: np.float64(0.14285714285714277), 25: np.float64(0.14285714285714277), 67: np.float64(0.14285714285714277), 0: np.float64(0.14285714285714277)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 14, 100]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428569), 52: np.float64(0.03771428571428569), 47: np.float64(0.03771428571428569), 15: np.float64(0.03771428571428569), 25: np.float64(0.03771428571428569), 67: np.float64(0.03771428571428569), 0: np.float64(0.03771428571428569)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428572), 52: np.float64(0.03771428571428572), 47: np.float64(0.03771428571428572), 15: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 67: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
choice probs for this beta: {40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 17: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4, 17]
learned probs for cluster 2 

{40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4, 17]
learned probs (dictionary):

probs= {40: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 47: np.float64(0.037714285714285714), 15: np.float64(0.037714285714285714), 25: np.float64(0.037714285714285714), 67: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5]
learned probs for cluster 2 

{40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 5]
learned probs (dictionary):

probs= {40: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 47: np.float64(0.037714285714285714), 15: np.float64(0.037714285714285714), 25: np.float64(0.037714285714285714), 67: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 14: 1, 100: 1} [8, 1, 3, 6, 7, 10, 14, 100, 12]
learned probs for cluster 2 

{40: np.float64(0.14285714285714327), 52: np.float64(0.14285714285714327), 47: np.float64(0.14285714285714327), 15: np.float64(0.14285714285714327), 25: np.float64(0.14285714285714327), 67: np.float64(0.14285714285714327), 0: np.float64(0.14285714285714327)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 14, 100, 12]
learned probs (dictionary):

probs= {40: np.float64(0.037714285714285825), 52: np.float64(0.037714285714285825), 47: np.float64(0.037714285714285825), 15: np.float64(0.037714285714285825), 25: np.float64(0.037714285714285825), 67: np.float64(0.037714285714285825), 0: np.float64(0.037714285714285825)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714296), 52: np.float64(0.14285714285714296), 47: np.float64(0.14285714285714296), 15: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 67: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
choice probs for this beta: {40: np.float64(0.14285714285714296), 52: np.float64(0.14285714285714296), 47: np.float64(0.14285714285714296), 15: np.float64(0.14285714285714296), 25: np.float64(0.14285714285714296), 67: np.float64(0.14285714285714296), 0: np.float64(0.14285714285714296)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
learned probs for cluster 2 

{40: np.float64(0.14287996296688568), 52: np.float64(0.14287996296688568), 47: np.float64(0.14287996296688568), 15: np.float64(0.14272022219869748), 25: np.float64(0.14287996296688568), 67: np.float64(0.14287996296688568), 0: np.float64(0.14287996296688568)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
learned probs (dictionary):

probs= {40: np.float64(0.03772031022325782), 52: np.float64(0.03772031022325782), 47: np.float64(0.03772031022325782), 15: np.float64(0.037678138660456134), 25: np.float64(0.03772031022325782), 67: np.float64(0.03772031022325782), 0: np.float64(0.03772031022325782)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714293), 52: np.float64(0.14285714285714293), 47: np.float64(0.14285714285714293), 15: np.float64(0.14285714285714293), 25: np.float64(0.14285714285714293), 67: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 100]
learned probs (dictionary):

probs= {40: np.float64(0.142863167366115), 52: np.float64(0.142863167366115), 47: np.float64(0.142863167366115), 15: np.float64(0.1428209958033133), 25: np.float64(0.142863167366115), 67: np.float64(0.142863167366115), 0: np.float64(0.142863167366115)}
choice probs for this beta: {40: np.float64(0.142863167366115), 52: np.float64(0.142863167366115), 47: np.float64(0.142863167366115), 15: np.float64(0.1428209958033133), 25: np.float64(0.142863167366115), 67: np.float64(0.142863167366115), 0: np.float64(0.142863167366115)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 19: 2, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 15, 100, 4, 19]
learned probs for cluster 2 

{40: np.float64(0.12195199852449416), 52: np.float64(0.12195199852449416), 47: np.float64(0.12195199852449416), 15: np.float64(0.2682880088530429), 25: np.float64(0.12195199852449416), 67: np.float64(0.12195199852449416), 0: np.float64(0.12195199852449416)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 13, 15, 100, 4, 19]
learned probs (dictionary):

probs= {40: np.float64(0.03219532761046646), 52: np.float64(0.03219532761046646), 47: np.float64(0.03219532761046646), 15: np.float64(0.07082803433720332), 25: np.float64(0.03219532761046646), 67: np.float64(0.03219532761046646), 0: np.float64(0.03219532761046646)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714315), 52: np.float64(0.14285714285714315), 47: np.float64(0.14285714285714315), 15: np.float64(0.14285714285714315), 25: np.float64(0.14285714285714315), 67: np.float64(0.14285714285714315), 0: np.float64(0.14285714285714315)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.13733818475332382), 52: np.float64(0.13733818475332382), 47: np.float64(0.13733818475332382), 15: np.float64(0.17597089148006068), 25: np.float64(0.13733818475332382), 67: np.float64(0.13733818475332382), 0: np.float64(0.13733818475332382)}
choice probs for this beta: {40: np.float64(0.13733818475332382), 52: np.float64(0.13733818475332382), 47: np.float64(0.13733818475332382), 15: np.float64(0.17597089148006068), 25: np.float64(0.13733818475332382), 67: np.float64(0.13733818475332382), 0: np.float64(0.13733818475332382)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs for cluster 2 

{40: np.float64(0.1428571428571429), 52: np.float64(0.1428571428571429), 47: np.float64(0.1428571428571429), 15: np.float64(0.1428571428571429), 25: np.float64(0.1428571428571429), 67: np.float64(0.1428571428571429), 0: np.float64(0.1428571428571429)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428573), 52: np.float64(0.03771428571428573), 47: np.float64(0.03771428571428573), 15: np.float64(0.03771428571428573), 25: np.float64(0.03771428571428573), 67: np.float64(0.03771428571428573), 0: np.float64(0.03771428571428573)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714263), 52: np.float64(0.14285714285714263), 47: np.float64(0.14285714285714263), 15: np.float64(0.14285714285714263), 25: np.float64(0.14285714285714263), 67: np.float64(0.14285714285714263), 0: np.float64(0.14285714285714263)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714268), 52: np.float64(0.14285714285714268), 47: np.float64(0.14285714285714268), 15: np.float64(0.14285714285714268), 25: np.float64(0.14285714285714268), 67: np.float64(0.14285714285714268), 0: np.float64(0.14285714285714268)}
choice probs for this beta: {40: np.float64(0.14285714285714268), 52: np.float64(0.14285714285714268), 47: np.float64(0.14285714285714268), 15: np.float64(0.14285714285714268), 25: np.float64(0.14285714285714268), 67: np.float64(0.14285714285714268), 0: np.float64(0.14285714285714268)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 1, 3, 4, 6, 7, 10, 11, 13, 100, 5]
learned probs for cluster 2 

{40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 11, 13, 100, 5]
learned probs (dictionary):

probs= {40: np.float64(0.037714285714285714), 52: np.float64(0.037714285714285714), 47: np.float64(0.037714285714285714), 15: np.float64(0.037714285714285714), 25: np.float64(0.037714285714285714), 67: np.float64(0.037714285714285714), 0: np.float64(0.037714285714285714)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
learned probs for cluster 2 

{40: np.float64(0.002053700626242238), 52: np.float64(0.002053700626242238), 47: np.float64(0.002053700626242238), 15: np.float64(0.9876777962425464), 25: np.float64(0.002053700626242238), 67: np.float64(0.002053700626242238), 0: np.float64(0.002053700626242238)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 15, 100, 5]
learned probs (dictionary):

probs= {40: np.float64(0.0005421769653279508), 52: np.float64(0.0005421769653279508), 47: np.float64(0.0005421769653279508), 15: np.float64(0.26074693820803224), 25: np.float64(0.0005421769653279508), 67: np.float64(0.0005421769653279508), 0: np.float64(0.0005421769653279508)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 100]
learned probs (dictionary):

probs= {40: np.float64(0.1056850341081851), 52: np.float64(0.1056850341081851), 47: np.float64(0.1056850341081851), 15: np.float64(0.3658897953508894), 25: np.float64(0.1056850341081851), 67: np.float64(0.1056850341081851), 0: np.float64(0.1056850341081851)}
choice probs for this beta: {40: np.float64(0.1056850341081851), 52: np.float64(0.1056850341081851), 47: np.float64(0.1056850341081851), 15: np.float64(0.3658897953508894), 25: np.float64(0.1056850341081851), 67: np.float64(0.1056850341081851), 0: np.float64(0.1056850341081851)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100, 4]
learned probs for cluster 2 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 4]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428572), 52: np.float64(0.03771428571428572), 47: np.float64(0.03771428571428572), 15: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 67: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
choice probs for this beta: {40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 13, 100, 5, 12]
learned probs for cluster 2 

{40: np.float64(0.14285714285714288), 52: np.float64(0.14285714285714288), 47: np.float64(0.14285714285714288), 15: np.float64(0.14285714285714288), 25: np.float64(0.14285714285714288), 67: np.float64(0.14285714285714288), 0: np.float64(0.14285714285714288)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 4, 6, 7, 10, 13, 100, 5, 12]
learned probs (dictionary):

probs= {40: np.float64(0.03771428571428572), 52: np.float64(0.03771428571428572), 47: np.float64(0.03771428571428572), 15: np.float64(0.03771428571428572), 25: np.float64(0.03771428571428572), 67: np.float64(0.03771428571428572), 0: np.float64(0.03771428571428572)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs for cluster 1 

{40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 100]
learned probs (dictionary):

probs= {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
choice probs for this beta: {40: np.float64(0.14285714285714285), 52: np.float64(0.14285714285714285), 47: np.float64(0.14285714285714285), 15: np.float64(0.14285714285714285), 25: np.float64(0.14285714285714285), 67: np.float64(0.14285714285714285), 0: np.float64(0.14285714285714285)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 47
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 47
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 52
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 67
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 25
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 25
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 25
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 25
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 25
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 25
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 15
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 40
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 25
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 47
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 67
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 40
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 15
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 15
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 52
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 40
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 15
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 40
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 52
tau [6, 2, 25, 100, 33, 26, 11, 13, 3, 38] choice 25
tau [8, 37, 39, 9, 71, 94, 98, 29, 2, 21] choice 52
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 52
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 25
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 67
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 15
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 52
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 52
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 47
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 25
tau [27, 4, 1, 41, 9, 11, 10, 100, 88, 3] choice 0
tau [37, 2, 6, 5, 15, 7, 46, 1, 17, 42] choice 15
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 40
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 47
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 67
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 47
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 47
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 67
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 15
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 47
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 47
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 47
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 40
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 15
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 15
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 25
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 15
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 40
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 25
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 47
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 67
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 15
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 15
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 15
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 25
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 25
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 25
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 40
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 15
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 25
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 47
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 47
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 15
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 47
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 40
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 25
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 15
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 52
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 15
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 15
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 25
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 40
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 25
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 25
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 47
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 15
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 47
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 47
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 52
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 0
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 52
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 0
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 15
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 67
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 67
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 47
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 47
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 47
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 25
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 15
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 25
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 47
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 52
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 15
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 52
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 52
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 67
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 15
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 40
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 67
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 67
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 40
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 25
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 52
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 67
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 52
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 0
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 47
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 15
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 15
tau [6, 4, 11, 28, 8, 38, 31, 100, 36, 60] choice 0
tau [8, 6, 3, 96, 66, 17, 43, 100, 51, 40] choice 40
tau [39, 32, 24, 15, 19, 16, 35, 80, 4, 8] choice 15
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 25
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 47
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 40
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 25
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 47
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 15
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 40
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 25
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 25
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 25
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 25
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 25
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 47
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 0
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 15
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 67
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 0
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 25
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 15
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 67
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 25
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 15
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 47
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 52
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 52
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 15
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 15
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 25
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 67
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 25
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 40
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 15
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 52
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 25
tau [2, 9, 3, 11, 41, 46, 33, 43, 75, 48] choice 67
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 15
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 47
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 15
tau [3, 5, 1, 21, 18, 34, 39, 6, 12, 66] choice 52
tau [100, 9, 10, 36, 25, 34, 24, 38, 37, 64] choice 25
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 47
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 67
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 15
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 67
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 25
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 52
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 47
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 25
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 25
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 67
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 25
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 25
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 25
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 40
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 67
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 47
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 40
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 15
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 47
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 25
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 40
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 67
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 40
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 40
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 15
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 25
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 52
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 15
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 15
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 15
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 25
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 67
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 15
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 67
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 25
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 40
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 67
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 25
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 25
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 52
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 40
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 47
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 47
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 52
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 15
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 25
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 25
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 40
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 25
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 15
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 15
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 47
tau [10, 100, 19, 2, 3, 50, 25, 56, 15, 18] choice 25
tau [21, 9, 11, 22, 36, 8, 33, 7, 30, 40] choice 40
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 52
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 47
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 15
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 47
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 15
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 40
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 52
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 40
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 40
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 47
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 40
tau [15, 14, 61, 62, 25, 12, 52, 68, 92, 100] choice 15
tau [19, 22, 4, 31, 55, 53, 12, 3, 23, 43] choice 47
tau [8, 13, 26, 94, 29, 10, 20, 77, 1, 22] choice 40
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 15
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 40
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 52
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 67
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 25
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 25
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 52
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 25
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 40
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 15
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 15
tau [100, 17, 4, 57, 5, 1, 61, 37, 75, 15] choice 15
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 25
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 25
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 67
tau [25, 47, 33, 12, 28, 37, 4, 10, 11, 9] choice 25
tau [2, 13, 27, 3, 7, 30, 6, 100, 22, 12] choice 40
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 15
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 25
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 15
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 47
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 15
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 0
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 15
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 15
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 67
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 25
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 52
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 25
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 67
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 15
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 67
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 52
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 67
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 25
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 25
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 47
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 47
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 0
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 40
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 25
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 25
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 0
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 25
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 25
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 67
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 15
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 52
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 25
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 47
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 0
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 25
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 15
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 67
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 15
tau [8, 42, 4, 6, 36, 13, 33, 23, 12, 15] choice 15
tau [8, 59, 13, 11, 28, 19, 95, 7, 29, 43] choice 67
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 47
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 52
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 25
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 25
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 25
tau [28, 91, 32, 17, 9, 2, 35, 49, 42, 29] choice 15
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 25
tau [30, 52, 15, 2, 27, 3, 1, 25, 19, 35] choice 52
tau [4, 35, 10, 52, 12, 24, 40, 2, 50, 3] choice 52
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 52
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 15
tau [36, 2, 10, 5, 100, 49, 33, 98, 6, 32] choice 52
tau [14, 9, 29, 37, 23, 13, 22, 35, 58, 40] choice 40
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 52
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 15
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 47
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 15
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 67
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 40
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 15
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 15
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 15
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 0
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 25
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 67
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 15
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 15
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 40
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 47
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 15
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 47
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 52
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 47
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 15
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 25
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 25
tau [4, 33, 19, 2, 17, 44, 100, 3, 56, 35] choice 25
tau [4, 22, 13, 15, 35, 99, 30, 14, 81, 42] choice 15
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 40
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 15
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 47
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 0
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 25
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 15
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 15
tau [2, 8, 3, 24, 57, 1, 18, 7, 75, 100] choice 67
tau [42, 10, 44, 2, 50, 45, 35, 12, 28, 34] choice 67
tau [19, 14, 11, 100, 7, 24, 23, 46, 60, 30] choice 47
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 0
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 40
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 25
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 47
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 25
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 40
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 15
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 52
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 0
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 40
tau [8, 25, 71, 48, 3, 13, 62, 30, 74, 36] choice 25
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 47
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 25
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 47
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 25
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 40
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 47
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 15
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 25
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 15
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 15
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 15
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 47
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 47
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 40
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 67
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 25
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 52
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 47
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 25
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 67
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 15
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 15
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 25
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 67
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 25
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 15
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 40
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 40
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 52
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 40
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 40
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 40
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 40
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 47
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 15
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 15
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 52
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 47
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 25
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 47
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 52
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 52
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 15
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 67
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 52
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 0
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 47
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 15
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 25
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 15
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 15
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 25
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 15
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 25
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 15
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 25
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 15
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 25
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 15
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 15
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 0
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 15
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 52
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 47
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 52
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 15
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 15
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 25
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 67
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 25
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 25
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 52
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 15
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 15
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 40
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 52
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 15
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 25
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 67
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 47
tau [4, 6, 16, 10, 8, 100, 36, 3, 22, 87] choice 47
tau [10, 20, 15, 51, 17, 45, 71, 13, 7, 1] choice 15
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 52
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 52
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 15
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 25
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 15
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 47
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 0
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 52
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 52
tau [4, 3, 19, 13, 77, 18, 1, 21, 51, 25] choice 25
tau [75, 21, 11, 44, 12, 13, 15, 4, 1, 17] choice 15
tau [100, 15, 51, 6, 31, 84, 50, 42, 54, 23] choice 15
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 25
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 15
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 25
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 25
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 67
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 67
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 40
tau [7, 20, 17, 36, 55, 4, 3, 16, 27, 6] choice 67
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 25
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 25
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 25
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 40
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 40
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 40
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 52
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 15
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 15
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 40
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 15
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 15
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 15
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 52
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 0
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 25
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 47
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 67
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 67
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 0
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 40
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 47
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 25
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 15
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 52
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 47
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 25
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 40
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 52
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 15
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 15
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 52
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 47
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 40
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 47
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 15
tau [19, 29, 41, 10, 17, 44, 28, 49, 34, 81] choice 0
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 52
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 15
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 47
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 47
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 47
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 67
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 25
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 47
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 52
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 15
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 15
tau [29, 9, 16, 30, 10, 12, 26, 37, 17, 4] choice 47
tau [10, 71, 25, 11, 4, 6, 13, 35, 98, 92] choice 25
tau [13, 8, 44, 14, 100, 3, 32, 42, 23, 4] choice 47
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 25
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 67
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 47
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 0
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 52
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 67
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 25
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 15
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 15
tau [19, 15, 18, 3, 55, 44, 4, 42, 35, 1] choice 15
tau [7, 1, 3, 5, 28, 35, 27, 94, 16, 48] choice 0
tau [100, 4, 31, 17, 76, 7, 52, 13, 5, 53] choice 52
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 15
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 47
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 25
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 47
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 25
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 40
tau [62, 13, 21, 23, 39, 12, 4, 67, 49, 56] choice 67
tau [71, 37, 13, 79, 22, 29, 30, 42, 24, 16] choice 25
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 40
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 52
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 25
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 25
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 52
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 47
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 25
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 25
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 25
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 25
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 40
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 15
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 25
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 25
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 47
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 67
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 40
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 25
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 52
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 40
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 47
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 25
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 47
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 40
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 25
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 47
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 0
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 25
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 15
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 47
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 15
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 15
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 0
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 25
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 15
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 52
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 15
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 40
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 52
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 40
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 25
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 52
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 40
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 15
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 25
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 52
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 15
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 15
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 47
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 52
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 67
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 67
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 47
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 25
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 15
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 15
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 25
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 25
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 25
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 40
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 15
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 15
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 15
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 15
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 25
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 25
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 25
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 52
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 25
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 52
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 52
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 25
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 15
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 25
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 25
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 15
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 52
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 15
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 15
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 25
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 47
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 47
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 67
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 25
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 25
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 15
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 15
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 15
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 25
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 67
tau [22, 100, 33, 16, 70, 76, 3, 45, 1, 68] choice 0
tau [18, 6, 4, 20, 100, 79, 29, 12, 39, 65] choice 47
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 47
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 15
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 40
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 47
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 40
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 25
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 25
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 40
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 52
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 25
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 25
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 40
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 40
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 67
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 15
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 47
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 0
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 52
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 47
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 15
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 40
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 47
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 25
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 67
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 15
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 52
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 67
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 15
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 15
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 52
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 25
tau [14, 8, 19, 12, 4, 79, 100, 13, 30, 16] choice 40
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 67
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 40
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 15
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 40
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 15
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 15
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 47
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 52
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 67
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 15
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 52
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 40
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 15
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 52
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 15
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 47
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 15
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 0
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 15
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 0
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 25
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 52
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 52
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 40
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 25
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 15
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 40
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 15
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 67
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 0
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 15
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 25
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 15
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 40
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 40
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 15
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 47
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 15
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 25
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 40
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 47
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 25
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 0
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 40
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 40
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 40
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 15
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 15
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 15
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 52
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 52
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 40
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 15
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 0
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 15
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 47
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 25
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 67
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 25
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 52
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 25
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 40
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 47
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 15
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 15
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 25
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 25
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 15
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 47
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 47
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 47
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 15
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 40
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 15
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 47
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 0
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 40
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 25
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 52
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 67
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 15
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 25
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 25
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 47
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 25
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 52
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 15
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 25
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 15
tau [51, 14, 20, 96, 10, 5, 3, 12, 48, 35] choice 15
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 67
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 25
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 25
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 25
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 15
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 0
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 52
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 47
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 25
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 25
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 15
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 67
tau [15, 7, 12, 5, 27, 24, 65, 18, 17, 39] choice 15
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 52
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 25
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 67
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 52
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 15
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 52
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 47
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 15
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 25
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 0
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 52
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 0
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 0
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 15
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 25
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 25
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 15
tau [4, 8, 3, 69, 29, 54, 30, 52, 46, 33] choice 52
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 47
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 15
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 0
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 25
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 47
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 67
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 0
tau [8, 19, 21, 2, 11, 25, 26, 20, 3, 22] choice 25
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 15
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 15
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 25
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 15
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 40
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 15
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 52
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 40
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 47
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 0
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 40
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 67
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 52
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 67
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 15
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 40
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 47
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 0
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 40
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 15
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 47
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 52
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 25
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 25
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 40
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 25
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 67
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 52
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 40
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 15
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 47
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 25
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 40
tau [20, 19, 4, 6, 1, 49, 5, 43, 22, 23] choice 0
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 47
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 40
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 0
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 15
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 15
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 40
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 67
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 47
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 52
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 15
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 15
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 40
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 47
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 47
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 40
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 25
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 15
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 25
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 67
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 67
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 52
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 15
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 52
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 15
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 15
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 40
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 25
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 15
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 15
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 15
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 15
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 52
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 47
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 15
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 0
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 15
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 25
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 25
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 25
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 15
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 67
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 47
tau [29, 11, 15, 63, 33, 100, 32, 37, 23, 4] choice 15
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 25
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 47
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 40
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 52
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 40
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 47
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 25
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 25
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 15
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 15
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 25
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 52
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 47
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 52
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 15
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 52
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 40
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 15
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 40
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 52
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 0
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 47
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 25
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 15
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 15
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 67
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 47
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 40
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 52
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 40
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 15
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 25
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 47
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 47
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 25
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 47
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 40
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 52
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 47
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 15
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 40
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 15
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 15
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 25
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 67
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 0
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 40
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 0
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 52
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 15
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 25
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 67
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 25
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 47
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 25
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 25
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 52
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 25
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 40
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 25
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 0
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 67
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 40
tau [6, 10, 14, 18, 28, 12, 3, 46, 54, 96] choice 15
tau [19, 27, 14, 22, 24, 52, 23, 17, 77, 30] choice 52
tau [28, 26, 19, 9, 10, 6, 11, 21, 29, 32] choice 52
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 47
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 0
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 15
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 25
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 67
tau [22, 61, 10, 82, 33, 27, 25, 34, 8, 59] choice 25
tau [61, 12, 2, 24, 52, 1, 28, 18, 49, 96] choice 52
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 15
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 15
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 52
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 15
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 0
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 15
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 0
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 67
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 40
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 40
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 0
tau [19, 100, 73, 10, 11, 15, 32, 21, 4, 3] choice 15
tau [6, 11, 9, 15, 99, 18, 28, 17, 12, 78] choice 15
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 15
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 15
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 15
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 25
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 52
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 25
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 67
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 15
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 25
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 47
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 40
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 40
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 52
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 15
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 40
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 67
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 67
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 0
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 15
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 15
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 25
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 15
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 0
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 25
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 15
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 15
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 47
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 52
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 40
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 52
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 52
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 15
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 47
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 15
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 52
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 25
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 40
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 25
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 25
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 15
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 25
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 47
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 0
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 15
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 67
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 15
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 67
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 25
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 0
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 52
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 15
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 0
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 25
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 25
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 40
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 40
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 15
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 52
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 47
emperical probablities from test set: {40: 0.123, 52: 0.122, 47: 0.135, 15: 0.247, 25: 0.217, 67: 0.087, 0: 0.069}
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142962), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: np.float64(0.020857142857142963), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142962), np.float64(0.020857142857142963), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: np.float64(0.020857142857142963), 47: np.float64(0.007857142857142951), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142962), np.float64(0.020857142857142963), np.float64(0.007857142857142951), 0, 0, 0, 0]
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: np.float64(0.020857142857142963), 47: np.float64(0.007857142857142951), 15: np.float64(0.10414285714285704), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142962), np.float64(0.020857142857142963), np.float64(0.007857142857142951), np.float64(0.10414285714285704), 0, 0, 0]
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: np.float64(0.020857142857142963), 47: np.float64(0.007857142857142951), 15: np.float64(0.10414285714285704), 25: np.float64(0.07414285714285704), 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142962), np.float64(0.020857142857142963), np.float64(0.007857142857142951), np.float64(0.10414285714285704), np.float64(0.07414285714285704), 0, 0]
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: np.float64(0.020857142857142963), 47: np.float64(0.007857142857142951), 15: np.float64(0.10414285714285704), 25: np.float64(0.07414285714285704), 67: np.float64(0.055857142857142966), 0: 0} 

err list= [np.float64(0.019857142857142962), np.float64(0.020857142857142963), np.float64(0.007857142857142951), np.float64(0.10414285714285704), np.float64(0.07414285714285704), np.float64(0.055857142857142966), 0]
beta is  0.025 

err dic= {40: np.float64(0.019857142857142962), 52: np.float64(0.020857142857142963), 47: np.float64(0.007857142857142951), 15: np.float64(0.10414285714285704), 25: np.float64(0.07414285714285704), 67: np.float64(0.055857142857142966), 0: np.float64(0.07385714285714295)} 

err list= [np.float64(0.019857142857142962), np.float64(0.020857142857142963), np.float64(0.007857142857142951), np.float64(0.10414285714285704), np.float64(0.07414285714285704), np.float64(0.055857142857142966), np.float64(0.07385714285714295)]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019863167366115014), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: np.float64(0.020863167366115015), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019863167366115014), np.float64(0.020863167366115015), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: np.float64(0.020863167366115015), 47: np.float64(0.007863167366115004), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019863167366115014), np.float64(0.020863167366115015), np.float64(0.007863167366115004), 0, 0, 0, 0]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: np.float64(0.020863167366115015), 47: np.float64(0.007863167366115004), 15: np.float64(0.10417900419668669), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019863167366115014), np.float64(0.020863167366115015), np.float64(0.007863167366115004), np.float64(0.10417900419668669), 0, 0, 0]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: np.float64(0.020863167366115015), 47: np.float64(0.007863167366115004), 15: np.float64(0.10417900419668669), 25: np.float64(0.07413683263388499), 67: 0, 0: 0} 

err list= [np.float64(0.019863167366115014), np.float64(0.020863167366115015), np.float64(0.007863167366115004), np.float64(0.10417900419668669), np.float64(0.07413683263388499), 0, 0]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: np.float64(0.020863167366115015), 47: np.float64(0.007863167366115004), 15: np.float64(0.10417900419668669), 25: np.float64(0.07413683263388499), 67: np.float64(0.05586316736611502), 0: 0} 

err list= [np.float64(0.019863167366115014), np.float64(0.020863167366115015), np.float64(0.007863167366115004), np.float64(0.10417900419668669), np.float64(0.07413683263388499), np.float64(0.05586316736611502), 0]
beta is  0.05 

err dic= {40: np.float64(0.019863167366115014), 52: np.float64(0.020863167366115015), 47: np.float64(0.007863167366115004), 15: np.float64(0.10417900419668669), 25: np.float64(0.07413683263388499), 67: np.float64(0.05586316736611502), 0: np.float64(0.073863167366115)} 

err list= [np.float64(0.019863167366115014), np.float64(0.020863167366115015), np.float64(0.007863167366115004), np.float64(0.10417900419668669), np.float64(0.07413683263388499), np.float64(0.05586316736611502), np.float64(0.073863167366115)]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.014338184753323824), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: np.float64(0.015338184753323825), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.014338184753323824), np.float64(0.015338184753323825), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: np.float64(0.015338184753323825), 47: np.float64(0.002338184753323813), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.014338184753323824), np.float64(0.015338184753323825), np.float64(0.002338184753323813), 0, 0, 0, 0]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: np.float64(0.015338184753323825), 47: np.float64(0.002338184753323813), 15: np.float64(0.07102910851993932), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.014338184753323824), np.float64(0.015338184753323825), np.float64(0.002338184753323813), np.float64(0.07102910851993932), 0, 0, 0]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: np.float64(0.015338184753323825), 47: np.float64(0.002338184753323813), 15: np.float64(0.07102910851993932), 25: np.float64(0.07966181524667618), 67: 0, 0: 0} 

err list= [np.float64(0.014338184753323824), np.float64(0.015338184753323825), np.float64(0.002338184753323813), np.float64(0.07102910851993932), np.float64(0.07966181524667618), 0, 0]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: np.float64(0.015338184753323825), 47: np.float64(0.002338184753323813), 15: np.float64(0.07102910851993932), 25: np.float64(0.07966181524667618), 67: np.float64(0.05033818475332383), 0: 0} 

err list= [np.float64(0.014338184753323824), np.float64(0.015338184753323825), np.float64(0.002338184753323813), np.float64(0.07102910851993932), np.float64(0.07966181524667618), np.float64(0.05033818475332383), 0]
beta is  0.1 

err dic= {40: np.float64(0.014338184753323824), 52: np.float64(0.015338184753323825), 47: np.float64(0.002338184753323813), 15: np.float64(0.07102910851993932), 25: np.float64(0.07966181524667618), 67: np.float64(0.05033818475332383), 0: np.float64(0.06833818475332382)} 

err list= [np.float64(0.014338184753323824), np.float64(0.015338184753323825), np.float64(0.002338184753323813), np.float64(0.07102910851993932), np.float64(0.07966181524667618), np.float64(0.05033818475332383), np.float64(0.06833818475332382)]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142684), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: np.float64(0.020857142857142685), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142684), np.float64(0.020857142857142685), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: np.float64(0.020857142857142685), 47: np.float64(0.007857142857142674), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142684), np.float64(0.020857142857142685), np.float64(0.007857142857142674), 0, 0, 0, 0]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: np.float64(0.020857142857142685), 47: np.float64(0.007857142857142674), 15: np.float64(0.10414285714285731), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142684), np.float64(0.020857142857142685), np.float64(0.007857142857142674), np.float64(0.10414285714285731), 0, 0, 0]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: np.float64(0.020857142857142685), 47: np.float64(0.007857142857142674), 15: np.float64(0.10414285714285731), 25: np.float64(0.07414285714285732), 67: 0, 0: 0} 

err list= [np.float64(0.019857142857142684), np.float64(0.020857142857142685), np.float64(0.007857142857142674), np.float64(0.10414285714285731), np.float64(0.07414285714285732), 0, 0]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: np.float64(0.020857142857142685), 47: np.float64(0.007857142857142674), 15: np.float64(0.10414285714285731), 25: np.float64(0.07414285714285732), 67: np.float64(0.05585714285714269), 0: 0} 

err list= [np.float64(0.019857142857142684), np.float64(0.020857142857142685), np.float64(0.007857142857142674), np.float64(0.10414285714285731), np.float64(0.07414285714285732), np.float64(0.05585714285714269), 0]
beta is  0.25 

err dic= {40: np.float64(0.019857142857142684), 52: np.float64(0.020857142857142685), 47: np.float64(0.007857142857142674), 15: np.float64(0.10414285714285731), 25: np.float64(0.07414285714285732), 67: np.float64(0.05585714285714269), 0: np.float64(0.07385714285714268)} 

err list= [np.float64(0.019857142857142684), np.float64(0.020857142857142685), np.float64(0.007857142857142674), np.float64(0.10414285714285731), np.float64(0.07414285714285732), np.float64(0.05585714285714269), np.float64(0.07385714285714268)]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), 0, 0, 0, 0]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), 0, 0, 0]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: np.float64(0.07414285714285715), 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), np.float64(0.07414285714285715), 0, 0]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: np.float64(0.07414285714285715), 67: np.float64(0.055857142857142855), 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), np.float64(0.07414285714285715), np.float64(0.055857142857142855), 0]
beta is  0.5 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: np.float64(0.07414285714285715), 67: np.float64(0.055857142857142855), 0: np.float64(0.07385714285714284)} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), np.float64(0.07414285714285715), np.float64(0.055857142857142855), np.float64(0.07385714285714284)]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.0173149658918149), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: np.float64(0.0163149658918149), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.0173149658918149), np.float64(0.0163149658918149), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: np.float64(0.0163149658918149), 47: np.float64(0.029314965891814912), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.0173149658918149), np.float64(0.0163149658918149), np.float64(0.029314965891814912), 0, 0, 0, 0]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: np.float64(0.0163149658918149), 47: np.float64(0.029314965891814912), 15: np.float64(0.1188897953508894), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.0173149658918149), np.float64(0.0163149658918149), np.float64(0.029314965891814912), np.float64(0.1188897953508894), 0, 0, 0]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: np.float64(0.0163149658918149), 47: np.float64(0.029314965891814912), 15: np.float64(0.1188897953508894), 25: np.float64(0.1113149658918149), 67: 0, 0: 0} 

err list= [np.float64(0.0173149658918149), np.float64(0.0163149658918149), np.float64(0.029314965891814912), np.float64(0.1188897953508894), np.float64(0.1113149658918149), 0, 0]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: np.float64(0.0163149658918149), 47: np.float64(0.029314965891814912), 15: np.float64(0.1188897953508894), 25: np.float64(0.1113149658918149), 67: np.float64(0.018685034108185103), 0: 0} 

err list= [np.float64(0.0173149658918149), np.float64(0.0163149658918149), np.float64(0.029314965891814912), np.float64(0.1188897953508894), np.float64(0.1113149658918149), np.float64(0.018685034108185103), 0]
beta is  0.75 

err dic= {40: np.float64(0.0173149658918149), 52: np.float64(0.0163149658918149), 47: np.float64(0.029314965891814912), 15: np.float64(0.1188897953508894), 25: np.float64(0.1113149658918149), 67: np.float64(0.018685034108185103), 0: np.float64(0.03668503410818509)} 

err list= [np.float64(0.0173149658918149), np.float64(0.0163149658918149), np.float64(0.029314965891814912), np.float64(0.1188897953508894), np.float64(0.1113149658918149), np.float64(0.018685034108185103), np.float64(0.03668503410818509)]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714288), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: np.float64(0.02085714285714288), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714288), np.float64(0.02085714285714288), 0, 0, 0, 0, 0]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: np.float64(0.02085714285714288), 47: np.float64(0.007857142857142868), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714288), np.float64(0.02085714285714288), np.float64(0.007857142857142868), 0, 0, 0, 0]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: np.float64(0.02085714285714288), 47: np.float64(0.007857142857142868), 15: np.float64(0.10414285714285712), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714288), np.float64(0.02085714285714288), np.float64(0.007857142857142868), np.float64(0.10414285714285712), 0, 0, 0]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: np.float64(0.02085714285714288), 47: np.float64(0.007857142857142868), 15: np.float64(0.10414285714285712), 25: np.float64(0.07414285714285712), 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714288), np.float64(0.02085714285714288), np.float64(0.007857142857142868), np.float64(0.10414285714285712), np.float64(0.07414285714285712), 0, 0]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: np.float64(0.02085714285714288), 47: np.float64(0.007857142857142868), 15: np.float64(0.10414285714285712), 25: np.float64(0.07414285714285712), 67: np.float64(0.05585714285714288), 0: 0} 

err list= [np.float64(0.01985714285714288), np.float64(0.02085714285714288), np.float64(0.007857142857142868), np.float64(0.10414285714285712), np.float64(0.07414285714285712), np.float64(0.05585714285714288), 0]
beta is  1 

err dic= {40: np.float64(0.01985714285714288), 52: np.float64(0.02085714285714288), 47: np.float64(0.007857142857142868), 15: np.float64(0.10414285714285712), 25: np.float64(0.07414285714285712), 67: np.float64(0.05585714285714288), 0: np.float64(0.07385714285714287)} 

err list= [np.float64(0.01985714285714288), np.float64(0.02085714285714288), np.float64(0.007857142857142868), np.float64(0.10414285714285712), np.float64(0.07414285714285712), np.float64(0.05585714285714288), np.float64(0.07385714285714287)]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: 0, 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: 0, 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: 0, 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), 0, 0, 0, 0]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: 0, 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), 0, 0, 0]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: np.float64(0.07414285714285715), 67: 0, 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), np.float64(0.07414285714285715), 0, 0]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: np.float64(0.07414285714285715), 67: np.float64(0.055857142857142855), 0: 0} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), np.float64(0.07414285714285715), np.float64(0.055857142857142855), 0]
beta is  1.25 

err dic= {40: np.float64(0.01985714285714285), 52: np.float64(0.020857142857142852), 47: np.float64(0.00785714285714284), 15: np.float64(0.10414285714285715), 25: np.float64(0.07414285714285715), 67: np.float64(0.055857142857142855), 0: np.float64(0.07385714285714284)} 

err list= [np.float64(0.01985714285714285), np.float64(0.020857142857142852), np.float64(0.00785714285714284), np.float64(0.10414285714285715), np.float64(0.07414285714285715), np.float64(0.055857142857142855), np.float64(0.07385714285714284)]
samppled assortment [42, 68, 69, 72, 29, 3]
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs for cluster 2 

{42: np.float64(0.14691017202144746), 68: np.float64(0.14691017202144746), 69: np.float64(0.14691017202144746), 72: np.float64(0.14691017202144746), 29: np.float64(0.14691017202144746), 3: np.float64(0.11853896787131495), 0: np.float64(0.14691017202144746)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs (dictionary):

probs= {42: np.float64(0.038784285413662134), 68: np.float64(0.038784285413662134), 69: np.float64(0.038784285413662134), 72: np.float64(0.038784285413662134), 29: np.float64(0.038784285413662134), 3: np.float64(0.031294287518027146), 0: np.float64(0.038784285413662134)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.14691017202144746), 68: np.float64(0.14691017202144746), 69: np.float64(0.14691017202144746), 72: np.float64(0.14691017202144746), 29: np.float64(0.14691017202144746), 3: np.float64(0.11853896787131495), 0: np.float64(0.14691017202144746)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.14691017202144746), 68: np.float64(0.14691017202144746), 69: np.float64(0.14691017202144746), 72: np.float64(0.14691017202144746), 29: np.float64(0.14691017202144746), 3: np.float64(0.11853896787131493), 0: np.float64(0.14691017202144746)}
choice probs for this beta: {42: np.float64(0.14691017202144746), 68: np.float64(0.14691017202144746), 69: np.float64(0.14691017202144746), 72: np.float64(0.14691017202144746), 29: np.float64(0.14691017202144746), 3: np.float64(0.11853896787131493), 0: np.float64(0.14691017202144746)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 15: 1, 100: 1} [8, 1, 2, 3, 6, 7, 15, 100, 5]
learned probs for cluster 2 

{42: np.float64(0.14152873601137828), 68: np.float64(0.14152873601137828), 69: np.float64(0.14152873601137828), 72: np.float64(0.14152873601137828), 29: np.float64(0.14152873601137828), 3: np.float64(0.1508275839317304), 0: np.float64(0.14152873601137828)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 15, 100, 5]
learned probs (dictionary):

probs= {42: np.float64(0.037363586307003864), 68: np.float64(0.037363586307003864), 69: np.float64(0.037363586307003864), 72: np.float64(0.037363586307003864), 29: np.float64(0.037363586307003864), 3: np.float64(0.03981848215797683), 0: np.float64(0.037363586307003864)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.14285714285714293), 68: np.float64(0.14285714285714293), 69: np.float64(0.14285714285714293), 72: np.float64(0.14285714285714293), 29: np.float64(0.14285714285714293), 3: np.float64(0.14285714285714293), 0: np.float64(0.14285714285714293)}
cluster label 1 learned center: 
 
sigma= [1, 2, 4, 5, 6, 7, 9, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.14250644344986105), 68: np.float64(0.14250644344986105), 69: np.float64(0.14250644344986105), 72: np.float64(0.14250644344986105), 29: np.float64(0.14250644344986105), 3: np.float64(0.14496133930083402), 0: np.float64(0.14250644344986105)}
choice probs for this beta: {42: np.float64(0.14250644344986105), 68: np.float64(0.14250644344986105), 69: np.float64(0.14250644344986105), 72: np.float64(0.14250644344986105), 29: np.float64(0.14250644344986105), 3: np.float64(0.14496133930083402), 0: np.float64(0.14250644344986105)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 13, 100]
learned probs for cluster 2 

{42: np.float64(0.11795304125404495), 68: np.float64(0.11795304125404495), 69: np.float64(0.11795304125404495), 72: np.float64(0.11795304125404495), 29: np.float64(0.11795304125404495), 3: np.float64(0.29228175247573024), 0: np.float64(0.11795304125404495)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 5, 6, 7, 10, 13, 100]
learned probs (dictionary):

probs= {42: np.float64(0.031139602891067868), 68: np.float64(0.031139602891067868), 69: np.float64(0.031139602891067868), 72: np.float64(0.031139602891067868), 29: np.float64(0.031139602891067868), 3: np.float64(0.07716238265359279), 0: np.float64(0.031139602891067868)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 12, 14, 100]
learned probs for cluster 1 

{42: np.float64(0.10632394700514), 68: np.float64(0.10632394700514), 69: np.float64(0.10632394700514), 72: np.float64(0.10632394700514), 29: np.float64(0.10632394700514), 3: np.float64(0.3620563179691614), 0: np.float64(0.10632394700514)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 12, 14, 100]
learned probs (dictionary):

probs= {42: np.float64(0.1093940278868509), 68: np.float64(0.1093940278868509), 69: np.float64(0.1093940278868509), 72: np.float64(0.1093940278868509), 29: np.float64(0.1093940278868509), 3: np.float64(0.3436358326788955), 0: np.float64(0.1093940278868509)}
choice probs for this beta: {42: np.float64(0.1093940278868509), 68: np.float64(0.1093940278868509), 69: np.float64(0.1093940278868509), 72: np.float64(0.1093940278868509), 29: np.float64(0.1093940278868509), 3: np.float64(0.3436358326788955), 0: np.float64(0.1093940278868509)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 6, 7, 10, 100]
learned probs for cluster 2 

{42: np.float64(0.0645676824839331), 68: np.float64(0.0645676824839331), 69: np.float64(0.0645676824839331), 72: np.float64(0.0645676824839331), 29: np.float64(0.0645676824839331), 3: np.float64(0.6125939050964015), 0: np.float64(0.0645676824839331)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100]
learned probs (dictionary):

probs= {42: np.float64(0.01704586817575834), 68: np.float64(0.01704586817575834), 69: np.float64(0.01704586817575834), 72: np.float64(0.01704586817575834), 29: np.float64(0.01704586817575834), 3: np.float64(0.16172479094545), 0: np.float64(0.01704586817575834)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs for cluster 1 

{42: np.float64(0.04506151119952957), 68: np.float64(0.04506151119952957), 69: np.float64(0.04506151119952957), 72: np.float64(0.04506151119952957), 29: np.float64(0.04506151119952957), 3: np.float64(0.7296309328028207), 0: np.float64(0.04506151119952957)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 11, 100]
learned probs (dictionary):

probs= {42: np.float64(0.050211140418612105), 68: np.float64(0.050211140418612105), 69: np.float64(0.050211140418612105), 72: np.float64(0.050211140418612105), 29: np.float64(0.050211140418612105), 3: np.float64(0.698733157488326), 0: np.float64(0.050211140418612105)}
choice probs for this beta: {42: np.float64(0.050211140418612105), 68: np.float64(0.050211140418612105), 69: np.float64(0.050211140418612105), 72: np.float64(0.050211140418612105), 29: np.float64(0.050211140418612105), 3: np.float64(0.698733157488326), 0: np.float64(0.050211140418612105)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs for cluster 2 

{42: np.float64(0.0036888031523014467), 68: np.float64(0.0036888031523014467), 69: np.float64(0.0036888031523014467), 72: np.float64(0.0036888031523014467), 29: np.float64(0.0036888031523014467), 3: np.float64(0.9778671810861923), 0: np.float64(0.0036888031523014467)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4]
learned probs (dictionary):

probs= {42: np.float64(0.000973844032207582), 68: np.float64(0.000973844032207582), 69: np.float64(0.000973844032207582), 72: np.float64(0.000973844032207582), 29: np.float64(0.000973844032207582), 3: np.float64(0.2581569358067548), 0: np.float64(0.000973844032207582)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.0036888031523014467), 68: np.float64(0.0036888031523014467), 69: np.float64(0.0036888031523014467), 72: np.float64(0.0036888031523014467), 29: np.float64(0.0036888031523014467), 3: np.float64(0.9778671810861923), 0: np.float64(0.0036888031523014467)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.0036888031523014467), 68: np.float64(0.0036888031523014467), 69: np.float64(0.0036888031523014467), 72: np.float64(0.0036888031523014467), 29: np.float64(0.0036888031523014467), 3: np.float64(0.9778671810861923), 0: np.float64(0.0036888031523014467)}
choice probs for this beta: {42: np.float64(0.0036888031523014467), 68: np.float64(0.0036888031523014467), 69: np.float64(0.0036888031523014467), 72: np.float64(0.0036888031523014467), 29: np.float64(0.0036888031523014467), 3: np.float64(0.9778671810861923), 0: np.float64(0.0036888031523014467)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 2, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 12, 14]
learned probs for cluster 2 

{42: np.float64(6.16236290394169e-05), 68: np.float64(6.16236290394169e-05), 69: np.float64(6.16236290394169e-05), 72: np.float64(6.16236290394169e-05), 29: np.float64(6.16236290394169e-05), 3: np.float64(0.9996302582257639), 0: np.float64(6.16236290394169e-05)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 12, 14]
learned probs (dictionary):

probs= {42: np.float64(1.626863806640606e-05), 68: np.float64(1.626863806640606e-05), 69: np.float64(1.626863806640606e-05), 72: np.float64(1.626863806640606e-05), 29: np.float64(1.626863806640606e-05), 3: np.float64(0.26390238817160167), 0: np.float64(1.626863806640606e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 15, 100]
learned probs for cluster 1 

{42: np.float64(3.244752596718773e-05), 68: np.float64(3.244752596718773e-05), 69: np.float64(3.244752596718773e-05), 72: np.float64(3.244752596718773e-05), 29: np.float64(3.244752596718773e-05), 3: np.float64(0.9998053148441969), 0: np.float64(3.244752596718773e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 15, 100]
learned probs (dictionary):

probs= {42: np.float64(4.015001717825623e-05), 68: np.float64(4.015001717825623e-05), 69: np.float64(4.015001717825623e-05), 72: np.float64(4.015001717825623e-05), 29: np.float64(4.015001717825623e-05), 3: np.float64(0.9997590998969306), 0: np.float64(4.015001717825623e-05)}
choice probs for this beta: {42: np.float64(4.015001717825623e-05), 68: np.float64(4.015001717825623e-05), 69: np.float64(4.015001717825623e-05), 72: np.float64(4.015001717825623e-05), 29: np.float64(4.015001717825623e-05), 3: np.float64(0.9997590998969306), 0: np.float64(4.015001717825623e-05)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100, 4, 5]
learned probs for cluster 2 

{42: np.float64(2.5196563790753457e-06), 68: np.float64(2.5196563790753457e-06), 69: np.float64(2.5196563790753457e-06), 72: np.float64(2.5196563790753457e-06), 29: np.float64(2.5196563790753457e-06), 3: np.float64(0.9999848820617258), 0: np.float64(2.5196563790753457e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 100, 4, 5]
learned probs (dictionary):

probs= {42: np.float64(6.651892840758913e-07), 68: np.float64(6.651892840758913e-07), 69: np.float64(6.651892840758913e-07), 72: np.float64(6.651892840758913e-07), 29: np.float64(6.651892840758913e-07), 3: np.float64(0.26399600886429564), 0: np.float64(6.651892840758913e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(4.1003600127328426e-07), 68: np.float64(4.1003600127328426e-07), 69: np.float64(4.1003600127328426e-07), 72: np.float64(4.1003600127328426e-07), 29: np.float64(4.1003600127328426e-07), 3: np.float64(0.9999975397839926), 0: np.float64(4.1003600127328426e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(9.669757810130286e-07), 68: np.float64(9.669757810130286e-07), 69: np.float64(9.669757810130286e-07), 72: np.float64(9.669757810130286e-07), 29: np.float64(9.669757810130286e-07), 3: np.float64(0.9999941981453142), 0: np.float64(9.669757810130286e-07)}
choice probs for this beta: {42: np.float64(9.669757810130286e-07), 68: np.float64(9.669757810130286e-07), 69: np.float64(9.669757810130286e-07), 72: np.float64(9.669757810130286e-07), 29: np.float64(9.669757810130286e-07), 3: np.float64(0.9999941981453142), 0: np.float64(9.669757810130286e-07)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 2, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 15: 2, 100: 1} [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 15]
learned probs for cluster 2 

{42: np.float64(4.852579226080844e-09), 68: np.float64(4.852579226080844e-09), 69: np.float64(4.852579226080844e-09), 72: np.float64(4.852579226080844e-09), 29: np.float64(4.852579226080844e-09), 3: np.float64(0.9999999708845244), 0: np.float64(4.852579226080844e-09)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 6, 7, 10, 13, 100, 2, 15]
learned probs (dictionary):

probs= {42: np.float64(1.2810809156853428e-09), 68: np.float64(1.2810809156853428e-09), 69: np.float64(1.2810809156853428e-09), 72: np.float64(1.2810809156853428e-09), 29: np.float64(1.2810809156853428e-09), 3: np.float64(0.26399999231351445), 0: np.float64(1.2810809156853428e-09)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 15: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 100]
learned probs for cluster 1 

{42: np.float64(1.633190174138468e-09), 68: np.float64(1.633190174138468e-09), 69: np.float64(1.633190174138468e-09), 72: np.float64(1.633190174138468e-09), 29: np.float64(1.633190174138468e-09), 3: np.float64(0.9999999902008586), 0: np.float64(1.633190174138468e-09)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 100]
learned probs (dictionary):

probs= {42: np.float64(2.4831088838512554e-09), 68: np.float64(2.4831088838512554e-09), 69: np.float64(2.4831088838512554e-09), 72: np.float64(2.4831088838512554e-09), 29: np.float64(2.4831088838512554e-09), 3: np.float64(0.9999999851013464), 0: np.float64(2.4831088838512554e-09)}
choice probs for this beta: {42: np.float64(2.4831088838512554e-09), 68: np.float64(2.4831088838512554e-09), 69: np.float64(2.4831088838512554e-09), 72: np.float64(2.4831088838512554e-09), 29: np.float64(2.4831088838512554e-09), 3: np.float64(0.9999999851013464), 0: np.float64(2.4831088838512554e-09)}
#beta= 0.025 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 12: 3, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 100, 11, 14, 12]
learned probs for cluster 2 

{42: np.float64(0.14691017202144746), 68: np.float64(0.14691017202144746), 69: np.float64(0.14691017202144746), 72: np.float64(0.14691017202144746), 29: np.float64(0.14691017202144746), 3: np.float64(0.11853896787131495), 0: np.float64(0.14691017202144746)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 100, 11, 14, 12]
learned probs (dictionary):

probs= {42: np.float64(0.038784285413662134), 68: np.float64(0.038784285413662134), 69: np.float64(0.038784285413662134), 72: np.float64(0.038784285413662134), 29: np.float64(0.038784285413662134), 3: np.float64(0.031294287518027146), 0: np.float64(0.038784285413662134)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.14338471088486907), 68: np.float64(0.14338471088486907), 69: np.float64(0.14338471088486907), 72: np.float64(0.14338471088486907), 29: np.float64(0.14338471088486907), 3: np.float64(0.1396917346907737), 0: np.float64(0.14338471088486907)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.14431543262492577), 68: np.float64(0.14431543262492577), 69: np.float64(0.14431543262492577), 72: np.float64(0.14431543262492577), 29: np.float64(0.14431543262492577), 3: np.float64(0.13410740425043657), 0: np.float64(0.14431543262492577)}
choice probs for this beta: {42: np.float64(0.14431543262492577), 68: np.float64(0.14431543262492577), 69: np.float64(0.14431543262492577), 72: np.float64(0.14431543262492577), 29: np.float64(0.14431543262492577), 3: np.float64(0.13410740425043657), 0: np.float64(0.14431543262492577)}
#beta= 0.05 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 4, 14]
learned probs for cluster 2 

{42: np.float64(0.13739710927755933), 68: np.float64(0.13739710927755933), 69: np.float64(0.13739710927755933), 72: np.float64(0.13739710927755933), 29: np.float64(0.13739710927755933), 3: np.float64(0.1756173443346552), 0: np.float64(0.13739710927755933)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 4, 14]
learned probs (dictionary):

probs= {42: np.float64(0.036272836849275666), 68: np.float64(0.036272836849275666), 69: np.float64(0.036272836849275666), 72: np.float64(0.036272836849275666), 29: np.float64(0.036272836849275666), 3: np.float64(0.04636297890434898), 0: np.float64(0.036272836849275666)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 7, 9, 10, 100]
learned probs for cluster 1 

{42: np.float64(0.14045288882643184), 68: np.float64(0.14045288882643184), 69: np.float64(0.14045288882643184), 72: np.float64(0.14045288882643184), 29: np.float64(0.14045288882643184), 3: np.float64(0.1572826670414092), 0: np.float64(0.14045288882643184)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 7, 9, 10, 100]
learned probs (dictionary):

probs= {42: np.float64(0.1396461630255295), 68: np.float64(0.1396461630255295), 69: np.float64(0.1396461630255295), 72: np.float64(0.1396461630255295), 29: np.float64(0.1396461630255295), 3: np.float64(0.16212302184682614), 0: np.float64(0.1396461630255295)}
choice probs for this beta: {42: np.float64(0.1396461630255295), 68: np.float64(0.1396461630255295), 69: np.float64(0.1396461630255295), 72: np.float64(0.1396461630255295), 29: np.float64(0.1396461630255295), 3: np.float64(0.16212302184682614), 0: np.float64(0.1396461630255295)}
#beta= 0.1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 1, 3, 6, 7, 10, 15, 100, 5]
learned probs for cluster 2 

{42: np.float64(0.11795304125404495), 68: np.float64(0.11795304125404495), 69: np.float64(0.11795304125404495), 72: np.float64(0.11795304125404495), 29: np.float64(0.11795304125404495), 3: np.float64(0.29228175247573024), 0: np.float64(0.11795304125404495)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 15, 100, 5]
learned probs (dictionary):

probs= {42: np.float64(0.031139602891067868), 68: np.float64(0.031139602891067868), 69: np.float64(0.031139602891067868), 72: np.float64(0.031139602891067868), 29: np.float64(0.031139602891067868), 3: np.float64(0.07716238265359279), 0: np.float64(0.031139602891067868)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.11206375533471546), 68: np.float64(0.11206375533471546), 69: np.float64(0.11206375533471546), 72: np.float64(0.11206375533471546), 29: np.float64(0.11206375533471546), 3: np.float64(0.3276174679917087), 0: np.float64(0.11206375533471546)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.11361852681741844), 68: np.float64(0.11361852681741844), 69: np.float64(0.11361852681741844), 72: np.float64(0.11361852681741844), 29: np.float64(0.11361852681741844), 3: np.float64(0.31828883909549044), 0: np.float64(0.11361852681741844)}
choice probs for this beta: {42: np.float64(0.11361852681741844), 68: np.float64(0.11361852681741844), 69: np.float64(0.11361852681741844), 72: np.float64(0.11361852681741844), 29: np.float64(0.11361852681741844), 3: np.float64(0.31828883909549044), 0: np.float64(0.11361852681741844)}
#beta= 0.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 2, 100: 1} [8, 1, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs for cluster 2 

{42: np.float64(0.03743413092381321), 68: np.float64(0.03743413092381321), 69: np.float64(0.03743413092381321), 72: np.float64(0.03743413092381321), 29: np.float64(0.03743413092381321), 3: np.float64(0.775395214457121), 0: np.float64(0.03743413092381321)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 10, 13, 100, 5, 14]
learned probs (dictionary):

probs= {42: np.float64(0.009882610563886687), 68: np.float64(0.009882610563886687), 69: np.float64(0.009882610563886687), 72: np.float64(0.009882610563886687), 29: np.float64(0.009882610563886687), 3: np.float64(0.20470433661667994), 0: np.float64(0.009882610563886687)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.025643520666954453), 68: np.float64(0.025643520666954453), 69: np.float64(0.025643520666954453), 72: np.float64(0.025643520666954453), 29: np.float64(0.025643520666954453), 3: np.float64(0.8461388759982803), 0: np.float64(0.025643520666954453)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.028756241774765164), 68: np.float64(0.028756241774765164), 69: np.float64(0.028756241774765164), 72: np.float64(0.028756241774765164), 29: np.float64(0.028756241774765164), 3: np.float64(0.8274625493514143), 0: np.float64(0.028756241774765164)}
choice probs for this beta: {42: np.float64(0.028756241774765164), 68: np.float64(0.028756241774765164), 69: np.float64(0.028756241774765164), 72: np.float64(0.028756241774765164), 29: np.float64(0.028756241774765164), 3: np.float64(0.8274625493514143), 0: np.float64(0.028756241774765164)}
#beta= 0.5 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 9: 2, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 9]
learned probs for cluster 2 

{42: np.float64(0.0024730633653320473), 68: np.float64(0.0024730633653320473), 69: np.float64(0.0024730633653320473), 72: np.float64(0.0024730633653320473), 29: np.float64(0.0024730633653320473), 3: np.float64(0.9851616198080078), 0: np.float64(0.0024730633653320473)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 6, 7, 10, 13, 100, 5, 9]
learned probs (dictionary):

probs= {42: np.float64(0.0006528887284476605), 68: np.float64(0.0006528887284476605), 69: np.float64(0.0006528887284476605), 72: np.float64(0.0006528887284476605), 29: np.float64(0.0006528887284476605), 3: np.float64(0.26008266762931403), 0: np.float64(0.0006528887284476605)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(0.0015714848663064467), 68: np.float64(0.0015714848663064467), 69: np.float64(0.0015714848663064467), 72: np.float64(0.0015714848663064467), 29: np.float64(0.0015714848663064467), 3: np.float64(0.9905710908021621), 0: np.float64(0.0015714848663064467)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(0.001809501590049205), 68: np.float64(0.001809501590049205), 69: np.float64(0.001809501590049205), 72: np.float64(0.001809501590049205), 29: np.float64(0.001809501590049205), 3: np.float64(0.9891429904597053), 0: np.float64(0.001809501590049205)}
choice probs for this beta: {42: np.float64(0.001809501590049205), 68: np.float64(0.001809501590049205), 69: np.float64(0.001809501590049205), 72: np.float64(0.001809501590049205), 29: np.float64(0.001809501590049205), 3: np.float64(0.9891429904597053), 0: np.float64(0.001809501590049205)}
#beta= 0.75 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 4, 5]
learned probs for cluster 2 

{42: np.float64(0.00011688876728339326), 68: np.float64(0.00011688876728339326), 69: np.float64(0.00011688876728339326), 72: np.float64(0.00011688876728339326), 29: np.float64(0.00011688876728339326), 3: np.float64(0.9992986673962997), 0: np.float64(0.00011688876728339326)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 4, 5]
learned probs (dictionary):

probs= {42: np.float64(3.085863456281582e-05), 68: np.float64(3.085863456281582e-05), 69: np.float64(3.085863456281582e-05), 72: np.float64(3.085863456281582e-05), 29: np.float64(3.085863456281582e-05), 3: np.float64(0.26381484819262313), 0: np.float64(3.085863456281582e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(3.244752596718773e-05), 68: np.float64(3.244752596718773e-05), 69: np.float64(3.244752596718773e-05), 72: np.float64(3.244752596718773e-05), 29: np.float64(3.244752596718773e-05), 3: np.float64(0.9998053148441969), 0: np.float64(3.244752596718773e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(5.474001367466599e-05), 68: np.float64(5.474001367466599e-05), 69: np.float64(5.474001367466599e-05), 72: np.float64(5.474001367466599e-05), 29: np.float64(5.474001367466599e-05), 3: np.float64(0.999671559917952), 0: np.float64(5.474001367466599e-05)}
choice probs for this beta: {42: np.float64(5.474001367466599e-05), 68: np.float64(5.474001367466599e-05), 69: np.float64(5.474001367466599e-05), 72: np.float64(5.474001367466599e-05), 29: np.float64(5.474001367466599e-05), 3: np.float64(0.999671559917952), 0: np.float64(5.474001367466599e-05)}
#beta= 1 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 2, 6: 1, 7: 1, 8: 0, 10: 2, 100: 1} [8, 1, 3, 6, 7, 100, 4, 10]
learned probs for cluster 2 

{42: np.float64(5.434942979722524e-06), 68: np.float64(5.434942979722524e-06), 69: np.float64(5.434942979722524e-06), 72: np.float64(5.434942979722524e-06), 29: np.float64(5.434942979722524e-06), 3: np.float64(0.9999673903421217), 0: np.float64(5.434942979722524e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 100, 4, 10]
learned probs (dictionary):

probs= {42: np.float64(1.4348249466467464e-06), 68: np.float64(1.4348249466467464e-06), 69: np.float64(1.4348249466467464e-06), 72: np.float64(1.4348249466467464e-06), 29: np.float64(1.4348249466467464e-06), 3: np.float64(0.26399139105032016), 0: np.float64(1.4348249466467464e-06)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{42: np.float64(1.7278486564876806e-07), 68: np.float64(1.7278486564876806e-07), 69: np.float64(1.7278486564876806e-07), 72: np.float64(1.7278486564876806e-07), 29: np.float64(1.7278486564876806e-07), 3: np.float64(0.9999989632908062), 0: np.float64(1.7278486564876806e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {42: np.float64(1.5619946077642398e-06), 68: np.float64(1.5619946077642398e-06), 69: np.float64(1.5619946077642398e-06), 72: np.float64(1.5619946077642398e-06), 29: np.float64(1.5619946077642398e-06), 3: np.float64(0.9999906280323534), 0: np.float64(1.5619946077642398e-06)}
choice probs for this beta: {42: np.float64(1.5619946077642398e-06), 68: np.float64(1.5619946077642398e-06), 69: np.float64(1.5619946077642398e-06), 72: np.float64(1.5619946077642398e-06), 29: np.float64(1.5619946077642398e-06), 3: np.float64(0.9999906280323534), 0: np.float64(1.5619946077642398e-06)}
#beta= 1.25 

#cluster  2 with weight 0.264
Learned cluster center of cluster 2:  {1: 1, 3: 1, 5: 2, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 6, 7, 13, 100, 5]
learned probs for cluster 2 

{42: np.float64(1.2621274372369536e-07), 68: np.float64(1.2621274372369536e-07), 69: np.float64(1.2621274372369536e-07), 72: np.float64(1.2621274372369536e-07), 29: np.float64(1.2621274372369536e-07), 3: np.float64(0.9999992427235378), 0: np.float64(1.2621274372369536e-07)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 6, 7, 13, 100, 5]
learned probs (dictionary):

probs= {42: np.float64(3.332016434305557e-08), 68: np.float64(3.332016434305557e-08), 69: np.float64(3.332016434305557e-08), 72: np.float64(3.332016434305557e-08), 29: np.float64(3.332016434305557e-08), 3: np.float64(0.26399980007901397), 0: np.float64(3.332016434305557e-08)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs for cluster 1 

{42: np.float64(4.852579226080844e-09), 68: np.float64(4.852579226080844e-09), 69: np.float64(4.852579226080844e-09), 72: np.float64(4.852579226080844e-09), 29: np.float64(4.852579226080844e-09), 3: np.float64(0.9999999708845244), 0: np.float64(4.852579226080844e-09)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 100]
learned probs (dictionary):

probs= {42: np.float64(3.689166265345107e-08), 68: np.float64(3.689166265345107e-08), 69: np.float64(3.689166265345107e-08), 72: np.float64(3.689166265345107e-08), 29: np.float64(3.689166265345107e-08), 3: np.float64(0.9999997786500239), 0: np.float64(3.689166265345107e-08)}
choice probs for this beta: {42: np.float64(3.689166265345107e-08), 68: np.float64(3.689166265345107e-08), 69: np.float64(3.689166265345107e-08), 72: np.float64(3.689166265345107e-08), 29: np.float64(3.689166265345107e-08), 3: np.float64(0.9999997786500239), 0: np.float64(3.689166265345107e-08)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 42
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 42
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 72
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 0
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 29
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 42
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 0
tau [20, 100, 14, 25, 2, 8, 60, 17, 23, 32] choice 69
tau [19, 8, 9, 21, 5, 34, 24, 16, 53, 25] choice 42
tau [8, 31, 100, 7, 36, 21, 15, 18, 55, 4] choice 42
tau [2, 11, 5, 99, 44, 26, 10, 17, 71, 7] choice 69
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 68
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 3
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 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 42
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 3
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 72
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 68
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 72
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 68
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 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 3
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 42
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 3
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 29
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 69
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 29
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 42
tau [8, 4, 23, 16, 11, 19, 71, 2, 3, 32] choice 3
tau [47, 15, 7, 71, 11, 27, 28, 33, 17, 48] choice 42
tau [32, 2, 1, 100, 13, 28, 7, 17, 29, 50] choice 29
tau [19, 8, 10, 4, 21, 54, 5, 87, 16, 7] choice 42
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 69
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 3
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 29
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 42
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 3
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 0
tau [7, 9, 21, 50, 18, 41, 34, 33, 24, 4] choice 72
tau [100, 36, 35, 27, 54, 77, 76, 1, 18, 80] choice 29
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 72
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 42
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 68
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 0
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 0
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 29
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 29
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 68
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 29
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 42
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 72
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 0
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 68
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 69
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 72
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 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 29
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 29
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 68
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 29
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 68
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 29
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 3
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 3
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 29
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 72
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 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 3
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 72
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 0
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 72
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 42
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 72
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 29
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 69
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 3
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 42
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 29
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 29
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 42
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 3
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 72
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 72
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 68
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 3
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 69
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 0
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 3
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 3
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 3
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 0
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 29
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 0
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 72
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 42
tau [41, 8, 26, 6, 57, 21, 91, 64, 97, 38] choice 69
tau [14, 5, 24, 11, 2, 26, 79, 9, 43, 73] choice 42
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 72
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 3
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 3
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 29
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 29
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 69
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 29
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 72
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 3
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 29
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 0
tau [8, 18, 4, 36, 20, 31, 5, 55, 9, 51] choice 68
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 72
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 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 42
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 42
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 68
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 3
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 0
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 42
tau [48, 2, 9, 19, 12, 33, 99, 23, 81, 17] choice 72
tau [21, 6, 4, 25, 53, 2, 13, 51, 63, 7] choice 0
tau [9, 2, 76, 20, 11, 1, 100, 46, 27, 30] choice 42
tau [100, 5, 7, 1, 2, 21, 8, 39, 10, 24] choice 68
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 69
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 69
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 72
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 29
tau [4, 11, 2, 29, 5, 12, 63, 31, 23, 21] choice 29
tau [6, 4, 1, 2, 12, 100, 47, 22, 29, 64] choice 29
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 68
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 29
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 29
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 29
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 42
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 0
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 69
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 29
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 0
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 69
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 0
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 72
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 0
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 29
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 42
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 42
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 68
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 72
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 42
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 68
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 29
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 42
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 29
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 29
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 68
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 3
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 69
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 69
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 29
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 42
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 68
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 68
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 29
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 42
tau [4, 37, 61, 13, 31, 32, 9, 47, 40, 75] choice 3
tau [22, 88, 20, 10, 99, 12, 49, 94, 4, 17] choice 0
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 29
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 42
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 72
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 72
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 3
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 69
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 3
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 69
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 42
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 68
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 42
tau [8, 2, 73, 13, 10, 56, 25, 16, 82, 44] choice 0
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 69
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 72
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 29
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 72
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 0
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 0
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 69
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 42
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 0
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 42
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 29
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 29
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 68
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 72
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 0
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 69
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 69
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 42
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 0
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 72
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 42
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 68
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 29
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 72
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 42
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 3
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 3
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 68
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 29
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 29
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 29
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 42
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 68
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 42
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 3
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 68
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 72
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 42
tau [20, 8, 4, 2, 68, 31, 6, 17, 16, 75] choice 68
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 42
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 72
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 68
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 29
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 42
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 42
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 42
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 69
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 3
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 42
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 29
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 72
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 3
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 42
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 42
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 0
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 69
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 0
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 42
tau [2, 33, 100, 63, 5, 20, 89, 16, 29, 17] choice 29
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 29
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 68
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 3
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 69
tau [6, 26, 21, 11, 10, 5, 23, 28, 24, 43] choice 68
tau [9, 58, 7, 28, 48, 4, 27, 54, 2, 18] choice 42
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 72
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 29
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 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 3
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 3
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 3
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 42
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 72
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 3
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 3
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 68
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 29
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 42
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 29
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 29
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 68
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 69
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 42
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 29
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 72
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 29
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 68
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 68
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 3
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 72
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 3
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 69
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 72
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 3
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 3
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 42
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 0
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 42
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 72
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 29
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 29
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 42
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 42
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 3
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 72
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 69
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 0
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 29
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 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 0
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 3
tau [9, 11, 4, 28, 18, 46, 14, 69, 98, 17] choice 69
tau [10, 27, 2, 33, 17, 18, 32, 63, 15, 1] choice 29
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 68
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 29
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 42
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 68
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 3
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 72
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 42
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 72
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 29
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 68
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 29
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 3
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 69
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 68
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 72
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 42
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 3
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 69
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 3
tau [19, 37, 10, 52, 27, 65, 7, 33, 36, 55] choice 69
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 29
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 42
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 68
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 69
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 29
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 3
tau [9, 11, 100, 2, 22, 26, 21, 33, 35, 38] choice 0
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 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 3
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 42
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 0
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 72
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 3
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 29
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 0
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 3
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 69
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 3
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 68
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 0
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 29
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 29
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 29
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 42
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 29
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 69
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 29
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 72
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 69
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 29
tau [4, 71, 19, 2, 9, 45, 27, 23, 36, 17] choice 3
tau [9, 41, 12, 17, 38, 16, 22, 6, 13, 72] choice 72
tau [4, 27, 18, 8, 21, 2, 37, 15, 45, 49] choice 68
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 3
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 29
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 29
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 29
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 29
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 68
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 29
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 72
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 68
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 3
tau [9, 20, 4, 6, 46, 35, 83, 30, 43, 85] choice 72
tau [19, 2, 1, 32, 63, 39, 77, 12, 29, 69] choice 29
tau [8, 34, 100, 25, 10, 2, 28, 26, 29, 56] choice 29
tau [19, 15, 18, 2, 100, 24, 5, 46, 49, 3] choice 3
tau [15, 8, 5, 25, 1, 29, 51, 4, 23, 69] choice 29
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 69
tau [7, 20, 15, 18, 17, 12, 24, 23, 94, 89] choice 72
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 3
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 29
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 69
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 29
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 29
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 29
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 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 3
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 68
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 69
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 0
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 42
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 3
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 72
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 0
tau [14, 8, 33, 19, 53, 18, 44, 23, 6, 69] choice 69
tau [9, 13, 10, 25, 20, 12, 24, 5, 43, 100] choice 29
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 68
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 0
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 69
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 0
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 68
tau [8, 87, 4, 28, 33, 16, 32, 10, 1, 12] choice 42
tau [47, 11, 2, 26, 10, 5, 17, 42, 56, 28] choice 42
tau [10, 66, 33, 16, 44, 11, 2, 13, 96, 23] choice 3
tau [13, 25, 20, 4, 2, 50, 100, 12, 24, 43] choice 0
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 29
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 3
tau [15, 26, 100, 4, 6, 16, 57, 52, 42, 58] choice 42
tau [41, 2, 100, 8, 88, 53, 59, 15, 73, 1] choice 42
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 68
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 69
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 42
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 69
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 69
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 0
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 68
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 42
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 3
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 72
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 69
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 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 42
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 3
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 69
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 29
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 29
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 68
tau [4, 20, 14, 34, 13, 5, 17, 7, 2, 49] choice 42
tau [11, 15, 2, 9, 6, 37, 58, 4, 3, 16] choice 3
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 69
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 72
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 29
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 69
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 0
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 68
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 3
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 69
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 29
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 29
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 3
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 42
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 72
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 3
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 42
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 72
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 69
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 69
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 68
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 3
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 69
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 72
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 69
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 42
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 68
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 69
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 29
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 29
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 68
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 3
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 29
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 72
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 29
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 0
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 3
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 72
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 0
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 0
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 69
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 68
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 68
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 68
tau [13, 53, 41, 7, 23, 28, 22, 18, 29, 6] choice 29
tau [53, 41, 9, 19, 7, 61, 60, 22, 1, 14] choice 68
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 29
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 42
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 72
tau [21, 2, 37, 76, 4, 10, 17, 55, 50, 7] choice 42
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 72
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 72
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 29
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 42
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 68
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 42
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 69
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 42
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 29
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 3
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 72
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 68
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 29
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 68
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 69
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 29
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 42
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 68
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 69
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 29
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 29
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 68
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 29
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 42
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 29
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 68
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 69
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 68
tau [4, 8, 5, 24, 21, 47, 9, 31, 23, 40] choice 3
tau [13, 25, 53, 18, 34, 20, 5, 74, 11, 16] choice 69
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 3
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 29
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 0
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 3
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 42
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 42
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 29
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 29
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 29
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 3
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 69
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 29
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 72
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 29
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 3
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 0
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 29
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 29
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 42
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 3
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 29
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 3
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 0
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 72
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 29
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 29
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 29
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 42
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 68
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 68
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 29
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 29
tau [6, 18, 37, 3, 8, 1, 25, 7, 28, 35] choice 3
tau [22, 10, 15, 21, 23, 89, 37, 26, 6, 12] choice 68
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 3
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 29
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 68
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 3
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 3
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 29
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 42
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 68
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 72
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 68
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 72
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 72
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 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 3
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 69
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 69
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 42
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 29
tau [22, 2, 31, 70, 25, 18, 14, 6, 24, 17] choice 3
tau [2, 23, 5, 99, 44, 22, 71, 49, 16, 36] choice 3
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 69
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 42
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 3
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 3
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 3
tau [15, 13, 92, 20, 22, 76, 100, 16, 62, 97] choice 69
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 68
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 29
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 68
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 72
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 42
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 42
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 72
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 29
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 0
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 72
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 3
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 42
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 3
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 72
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 29
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 29
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 29
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 3
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 29
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 29
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 72
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 68
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 42
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 3
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 42
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 3
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 42
tau [8, 22, 37, 1, 38, 10, 9, 13, 5, 23] choice 29
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 3
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 69
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 69
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 72
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 42
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 29
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 68
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 68
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 3
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 29
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 3
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 0
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 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 69
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 29
tau [2, 36, 53, 100, 51, 7, 45, 65, 78, 16] choice 29
tau [2, 27, 8, 21, 34, 26, 10, 24, 63, 4] choice 72
tau [14, 40, 9, 10, 70, 20, 50, 34, 71, 69] choice 69
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 72
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 29
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 0
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 0
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 42
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 69
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 3
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 72
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 29
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 29
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 42
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 29
tau [4, 9, 33, 6, 54, 45, 18, 25, 38, 46] choice 42
tau [11, 4, 9, 46, 34, 10, 36, 33, 14, 95] choice 72
tau [19, 6, 2, 5, 16, 3, 95, 28, 18, 86] choice 3
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 42
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 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 72
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 42
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 0
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 3
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 42
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 29
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 69
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 0
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 3
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 72
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 0
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 68
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 69
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 69
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 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 42
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 72
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 29
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 72
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 68
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 72
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 29
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 3
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 69
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 69
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 3
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 72
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 72
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 69
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 3
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 68
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 0
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 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 69
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 42
tau [7, 2, 45, 25, 37, 17, 12, 20, 10, 4] choice 0
tau [21, 61, 100, 5, 3, 45, 4, 98, 6, 92] choice 3
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 42
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 3
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 42
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 42
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 29
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 0
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 69
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 29
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 29
tau [37, 9, 46, 96, 20, 16, 66, 5, 28, 30] choice 68
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 72
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 29
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 29
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 0
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 42
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 29
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 68
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 42
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 29
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 42
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 42
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 3
tau [20, 11, 36, 74, 34, 8, 14, 86, 60, 16] choice 69
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 29
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 3
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 42
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 72
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 3
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 42
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 0
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 72
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 29
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 3
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 29
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 69
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 3
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 29
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 68
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 29
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 3
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 42
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 29
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 69
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 68
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 69
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 72
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 29
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 0
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 72
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 68
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 69
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 72
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 42
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 68
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 72
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 69
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 72
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 69
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 29
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 3
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 29
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 42
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 68
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 29
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 42
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 69
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 3
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 3
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 29
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 29
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 29
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 72
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
emperical probablities from test set: {42: 0.136, 68: 0.093, 69: 0.085, 72: 0.09, 29: 0.189, 3: 0.332, 0: 0.075}
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.008315432624925762), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: np.float64(0.05131543262492577), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.008315432624925762), np.float64(0.05131543262492577), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: np.float64(0.05131543262492577), 69: np.float64(0.059315432624925765), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.008315432624925762), np.float64(0.05131543262492577), np.float64(0.059315432624925765), 0, 0, 0, 0]
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: np.float64(0.05131543262492577), 69: np.float64(0.059315432624925765), 72: np.float64(0.054315432624925775), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.008315432624925762), np.float64(0.05131543262492577), np.float64(0.059315432624925765), np.float64(0.054315432624925775), 0, 0, 0]
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: np.float64(0.05131543262492577), 69: np.float64(0.059315432624925765), 72: np.float64(0.054315432624925775), 29: np.float64(0.04468456737507423), 3: 0, 0: 0} 

err list= [np.float64(0.008315432624925762), np.float64(0.05131543262492577), np.float64(0.059315432624925765), np.float64(0.054315432624925775), np.float64(0.04468456737507423), 0, 0]
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: np.float64(0.05131543262492577), 69: np.float64(0.059315432624925765), 72: np.float64(0.054315432624925775), 29: np.float64(0.04468456737507423), 3: np.float64(0.19789259574956344), 0: 0} 

err list= [np.float64(0.008315432624925762), np.float64(0.05131543262492577), np.float64(0.059315432624925765), np.float64(0.054315432624925775), np.float64(0.04468456737507423), np.float64(0.19789259574956344), 0]
beta is  0.025 

err dic= {42: np.float64(0.008315432624925762), 68: np.float64(0.05131543262492577), 69: np.float64(0.059315432624925765), 72: np.float64(0.054315432624925775), 29: np.float64(0.04468456737507423), 3: np.float64(0.19789259574956344), 0: np.float64(0.06931543262492577)} 

err list= [np.float64(0.008315432624925762), np.float64(0.05131543262492577), np.float64(0.059315432624925765), np.float64(0.054315432624925775), np.float64(0.04468456737507423), np.float64(0.19789259574956344), np.float64(0.06931543262492577)]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.003646163025529503), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: np.float64(0.04664616302552951), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.003646163025529503), np.float64(0.04664616302552951), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: np.float64(0.04664616302552951), 69: np.float64(0.05464616302552951), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.003646163025529503), np.float64(0.04664616302552951), np.float64(0.05464616302552951), 0, 0, 0, 0]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: np.float64(0.04664616302552951), 69: np.float64(0.05464616302552951), 72: np.float64(0.049646163025529516), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.003646163025529503), np.float64(0.04664616302552951), np.float64(0.05464616302552951), np.float64(0.049646163025529516), 0, 0, 0]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: np.float64(0.04664616302552951), 69: np.float64(0.05464616302552951), 72: np.float64(0.049646163025529516), 29: np.float64(0.04935383697447049), 3: 0, 0: 0} 

err list= [np.float64(0.003646163025529503), np.float64(0.04664616302552951), np.float64(0.05464616302552951), np.float64(0.049646163025529516), np.float64(0.04935383697447049), 0, 0]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: np.float64(0.04664616302552951), 69: np.float64(0.05464616302552951), 72: np.float64(0.049646163025529516), 29: np.float64(0.04935383697447049), 3: np.float64(0.16987697815317387), 0: 0} 

err list= [np.float64(0.003646163025529503), np.float64(0.04664616302552951), np.float64(0.05464616302552951), np.float64(0.049646163025529516), np.float64(0.04935383697447049), np.float64(0.16987697815317387), 0]
beta is  0.05 

err dic= {42: np.float64(0.003646163025529503), 68: np.float64(0.04664616302552951), 69: np.float64(0.05464616302552951), 72: np.float64(0.049646163025529516), 29: np.float64(0.04935383697447049), 3: np.float64(0.16987697815317387), 0: np.float64(0.06464616302552952)} 

err list= [np.float64(0.003646163025529503), np.float64(0.04664616302552951), np.float64(0.05464616302552951), np.float64(0.049646163025529516), np.float64(0.04935383697447049), np.float64(0.16987697815317387), np.float64(0.06464616302552952)]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.022381473182581574), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: np.float64(0.020618526817418437), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.022381473182581574), np.float64(0.020618526817418437), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: np.float64(0.020618526817418437), 69: np.float64(0.02861852681741843), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.022381473182581574), np.float64(0.020618526817418437), np.float64(0.02861852681741843), 0, 0, 0, 0]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: np.float64(0.020618526817418437), 69: np.float64(0.02861852681741843), 72: np.float64(0.02361852681741844), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.022381473182581574), np.float64(0.020618526817418437), np.float64(0.02861852681741843), np.float64(0.02361852681741844), 0, 0, 0]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: np.float64(0.020618526817418437), 69: np.float64(0.02861852681741843), 72: np.float64(0.02361852681741844), 29: np.float64(0.07538147318258157), 3: 0, 0: 0} 

err list= [np.float64(0.022381473182581574), np.float64(0.020618526817418437), np.float64(0.02861852681741843), np.float64(0.02361852681741844), np.float64(0.07538147318258157), 0, 0]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: np.float64(0.020618526817418437), 69: np.float64(0.02861852681741843), 72: np.float64(0.02361852681741844), 29: np.float64(0.07538147318258157), 3: np.float64(0.013711160904509578), 0: 0} 

err list= [np.float64(0.022381473182581574), np.float64(0.020618526817418437), np.float64(0.02861852681741843), np.float64(0.02361852681741844), np.float64(0.07538147318258157), np.float64(0.013711160904509578), 0]
beta is  0.1 

err dic= {42: np.float64(0.022381473182581574), 68: np.float64(0.020618526817418437), 69: np.float64(0.02861852681741843), 72: np.float64(0.02361852681741844), 29: np.float64(0.07538147318258157), 3: np.float64(0.013711160904509578), 0: np.float64(0.03861852681741844)} 

err list= [np.float64(0.022381473182581574), np.float64(0.020618526817418437), np.float64(0.02861852681741843), np.float64(0.02361852681741844), np.float64(0.07538147318258157), np.float64(0.013711160904509578), np.float64(0.03861852681741844)]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.10724375822523485), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: np.float64(0.06424375822523484), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.10724375822523485), np.float64(0.06424375822523484), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: np.float64(0.06424375822523484), 69: np.float64(0.05624375822523484), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.10724375822523485), np.float64(0.06424375822523484), np.float64(0.05624375822523484), 0, 0, 0, 0]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: np.float64(0.06424375822523484), 69: np.float64(0.05624375822523484), 72: np.float64(0.06124375822523483), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.10724375822523485), np.float64(0.06424375822523484), np.float64(0.05624375822523484), np.float64(0.06124375822523483), 0, 0, 0]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: np.float64(0.06424375822523484), 69: np.float64(0.05624375822523484), 72: np.float64(0.06124375822523483), 29: np.float64(0.16024375822523484), 3: 0, 0: 0} 

err list= [np.float64(0.10724375822523485), np.float64(0.06424375822523484), np.float64(0.05624375822523484), np.float64(0.06124375822523483), np.float64(0.16024375822523484), 0, 0]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: np.float64(0.06424375822523484), 69: np.float64(0.05624375822523484), 72: np.float64(0.06124375822523483), 29: np.float64(0.16024375822523484), 3: np.float64(0.49546254935141426), 0: 0} 

err list= [np.float64(0.10724375822523485), np.float64(0.06424375822523484), np.float64(0.05624375822523484), np.float64(0.06124375822523483), np.float64(0.16024375822523484), np.float64(0.49546254935141426), 0]
beta is  0.25 

err dic= {42: np.float64(0.10724375822523485), 68: np.float64(0.06424375822523484), 69: np.float64(0.05624375822523484), 72: np.float64(0.06124375822523483), 29: np.float64(0.16024375822523484), 3: np.float64(0.49546254935141426), 0: np.float64(0.046243758225234834)} 

err list= [np.float64(0.10724375822523485), np.float64(0.06424375822523484), np.float64(0.05624375822523484), np.float64(0.06124375822523483), np.float64(0.16024375822523484), np.float64(0.49546254935141426), np.float64(0.046243758225234834)]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13419049840995081), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: np.float64(0.09119049840995079), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13419049840995081), np.float64(0.09119049840995079), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: np.float64(0.09119049840995079), 69: np.float64(0.0831904984099508), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13419049840995081), np.float64(0.09119049840995079), np.float64(0.0831904984099508), 0, 0, 0, 0]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: np.float64(0.09119049840995079), 69: np.float64(0.0831904984099508), 72: np.float64(0.08819049840995079), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13419049840995081), np.float64(0.09119049840995079), np.float64(0.0831904984099508), np.float64(0.08819049840995079), 0, 0, 0]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: np.float64(0.09119049840995079), 69: np.float64(0.0831904984099508), 72: np.float64(0.08819049840995079), 29: np.float64(0.1871904984099508), 3: 0, 0: 0} 

err list= [np.float64(0.13419049840995081), np.float64(0.09119049840995079), np.float64(0.0831904984099508), np.float64(0.08819049840995079), np.float64(0.1871904984099508), 0, 0]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: np.float64(0.09119049840995079), 69: np.float64(0.0831904984099508), 72: np.float64(0.08819049840995079), 29: np.float64(0.1871904984099508), 3: np.float64(0.6571429904597053), 0: 0} 

err list= [np.float64(0.13419049840995081), np.float64(0.09119049840995079), np.float64(0.0831904984099508), np.float64(0.08819049840995079), np.float64(0.1871904984099508), np.float64(0.6571429904597053), 0]
beta is  0.5 

err dic= {42: np.float64(0.13419049840995081), 68: np.float64(0.09119049840995079), 69: np.float64(0.0831904984099508), 72: np.float64(0.08819049840995079), 29: np.float64(0.1871904984099508), 3: np.float64(0.6571429904597053), 0: np.float64(0.07319049840995079)} 

err list= [np.float64(0.13419049840995081), np.float64(0.09119049840995079), np.float64(0.0831904984099508), np.float64(0.08819049840995079), np.float64(0.1871904984099508), np.float64(0.6571429904597053), np.float64(0.07319049840995079)]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13594525998632534), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: np.float64(0.09294525998632533), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13594525998632534), np.float64(0.09294525998632533), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: np.float64(0.09294525998632533), 69: np.float64(0.08494525998632534), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13594525998632534), np.float64(0.09294525998632533), np.float64(0.08494525998632534), 0, 0, 0, 0]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: np.float64(0.09294525998632533), 69: np.float64(0.08494525998632534), 72: np.float64(0.08994525998632533), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13594525998632534), np.float64(0.09294525998632533), np.float64(0.08494525998632534), np.float64(0.08994525998632533), 0, 0, 0]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: np.float64(0.09294525998632533), 69: np.float64(0.08494525998632534), 72: np.float64(0.08994525998632533), 29: np.float64(0.18894525998632533), 3: 0, 0: 0} 

err list= [np.float64(0.13594525998632534), np.float64(0.09294525998632533), np.float64(0.08494525998632534), np.float64(0.08994525998632533), np.float64(0.18894525998632533), 0, 0]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: np.float64(0.09294525998632533), 69: np.float64(0.08494525998632534), 72: np.float64(0.08994525998632533), 29: np.float64(0.18894525998632533), 3: np.float64(0.6676715599179519), 0: 0} 

err list= [np.float64(0.13594525998632534), np.float64(0.09294525998632533), np.float64(0.08494525998632534), np.float64(0.08994525998632533), np.float64(0.18894525998632533), np.float64(0.6676715599179519), 0]
beta is  0.75 

err dic= {42: np.float64(0.13594525998632534), 68: np.float64(0.09294525998632533), 69: np.float64(0.08494525998632534), 72: np.float64(0.08994525998632533), 29: np.float64(0.18894525998632533), 3: np.float64(0.6676715599179519), 0: np.float64(0.07494525998632533)} 

err list= [np.float64(0.13594525998632534), np.float64(0.09294525998632533), np.float64(0.08494525998632534), np.float64(0.08994525998632533), np.float64(0.18894525998632533), np.float64(0.6676715599179519), np.float64(0.07494525998632533)]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599843800539224), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: np.float64(0.09299843800539223), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599843800539224), np.float64(0.09299843800539223), 0, 0, 0, 0, 0]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: np.float64(0.09299843800539223), 69: np.float64(0.08499843800539224), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599843800539224), np.float64(0.09299843800539223), np.float64(0.08499843800539224), 0, 0, 0, 0]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: np.float64(0.09299843800539223), 69: np.float64(0.08499843800539224), 72: np.float64(0.08999843800539223), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599843800539224), np.float64(0.09299843800539223), np.float64(0.08499843800539224), np.float64(0.08999843800539223), 0, 0, 0]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: np.float64(0.09299843800539223), 69: np.float64(0.08499843800539224), 72: np.float64(0.08999843800539223), 29: np.float64(0.18899843800539223), 3: 0, 0: 0} 

err list= [np.float64(0.13599843800539224), np.float64(0.09299843800539223), np.float64(0.08499843800539224), np.float64(0.08999843800539223), np.float64(0.18899843800539223), 0, 0]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: np.float64(0.09299843800539223), 69: np.float64(0.08499843800539224), 72: np.float64(0.08999843800539223), 29: np.float64(0.18899843800539223), 3: np.float64(0.6679906280323533), 0: 0} 

err list= [np.float64(0.13599843800539224), np.float64(0.09299843800539223), np.float64(0.08499843800539224), np.float64(0.08999843800539223), np.float64(0.18899843800539223), np.float64(0.6679906280323533), 0]
beta is  1 

err dic= {42: np.float64(0.13599843800539224), 68: np.float64(0.09299843800539223), 69: np.float64(0.08499843800539224), 72: np.float64(0.08999843800539223), 29: np.float64(0.18899843800539223), 3: np.float64(0.6679906280323533), 0: np.float64(0.07499843800539223)} 

err list= [np.float64(0.13599843800539224), np.float64(0.09299843800539223), np.float64(0.08499843800539224), np.float64(0.08999843800539223), np.float64(0.18899843800539223), np.float64(0.6679906280323533), np.float64(0.07499843800539223)]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: 0, 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599996310833737), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: np.float64(0.09299996310833734), 69: 0, 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599996310833737), np.float64(0.09299996310833734), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: np.float64(0.09299996310833734), 69: np.float64(0.08499996310833735), 72: 0, 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599996310833737), np.float64(0.09299996310833734), np.float64(0.08499996310833735), 0, 0, 0, 0]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: np.float64(0.09299996310833734), 69: np.float64(0.08499996310833735), 72: np.float64(0.08999996310833734), 29: 0, 3: 0, 0: 0} 

err list= [np.float64(0.13599996310833737), np.float64(0.09299996310833734), np.float64(0.08499996310833735), np.float64(0.08999996310833734), 0, 0, 0]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: np.float64(0.09299996310833734), 69: np.float64(0.08499996310833735), 72: np.float64(0.08999996310833734), 29: np.float64(0.18899996310833736), 3: 0, 0: 0} 

err list= [np.float64(0.13599996310833737), np.float64(0.09299996310833734), np.float64(0.08499996310833735), np.float64(0.08999996310833734), np.float64(0.18899996310833736), 0, 0]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: np.float64(0.09299996310833734), 69: np.float64(0.08499996310833735), 72: np.float64(0.08999996310833734), 29: np.float64(0.18899996310833736), 3: np.float64(0.6679997786500238), 0: 0} 

err list= [np.float64(0.13599996310833737), np.float64(0.09299996310833734), np.float64(0.08499996310833735), np.float64(0.08999996310833734), np.float64(0.18899996310833736), np.float64(0.6679997786500238), 0]
beta is  1.25 

err dic= {42: np.float64(0.13599996310833737), 68: np.float64(0.09299996310833734), 69: np.float64(0.08499996310833735), 72: np.float64(0.08999996310833734), 29: np.float64(0.18899996310833736), 3: np.float64(0.6679997786500238), 0: np.float64(0.07499996310833734)} 

err list= [np.float64(0.13599996310833737), np.float64(0.09299996310833734), np.float64(0.08499996310833735), np.float64(0.08999996310833734), np.float64(0.18899996310833736), np.float64(0.6679997786500238), np.float64(0.07499996310833734)]
