p= 1 num clusters= 3
linkage completed in  13.761894941329956
silhouette_score of the clusters -0.033620198817423556
#beta= 0.025 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 100: 0} [2, 3, 5, 6, 7, 8, 9, 100]
learned probs for cluster 3 

{1: np.float64(0.04930549148459529), 2: np.float64(0.22107446824944527), 3: np.float64(0.21561612018007684), 4: np.float64(0.04930549148459529), 5: np.float64(0.21029253920472124), 6: np.float64(0.2051003979119713), 0: np.float64(0.04930549148459529)}
cluster label 3 learned center: 
 
sigma= [2, 3, 5, 6, 7, 8, 9, 100]
learned probs (dictionary):

probs= {1: np.float64(0.0402456074243009), 2: np.float64(0.1804520347086097), 3: np.float64(0.17599665809698772), 4: np.float64(0.0402456074243009), 5: np.float64(0.17165128512585373), 6: np.float64(0.16741319979564656), 0: np.float64(0.0402456074243009)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 3: 2, 4: 1, 5: 1, 6: 1, 9: 3, 10: 1, 100: 1} [1, 4, 5, 6, 10, 100, 3, 9]
learned probs for cluster 2 

{1: np.float64(0.193586960998408), 2: np.float64(0.04305594850791012), 3: np.float64(0.16774920447881256), 4: np.float64(0.18880728190118953), 5: np.float64(0.18414561350135775), 6: np.float64(0.1795990421044127), 0: np.float64(0.04305594850791012)}
cluster label 2 learned center: 
 
sigma= [1, 4, 5, 6, 10, 100, 3, 9]
learned probs (dictionary):

probs= {1: np.float64(0.06846090698981887), 2: np.float64(0.1867274392036376), 3: np.float64(0.20044610464977466), 4: np.float64(0.06776426876139928), 5: np.float64(0.19849050829367662), 6: np.float64(0.1935897601823647), 0: np.float64(0.0465210119193288)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 2, 3: 2, 4: 6, 6: 0, 7: 0, 8: 0, 9: 1, 10: 7, 11: 0, 14: 6, 16: 7, 19: 4, 21: 9, 26: 8} [6, 7, 8, 11, 9, 1, 3, 19, 4, 14, 10, 16, 26, 21]
learned probs for cluster 1 

{1: np.float64(0.21988227915175154), 2: np.float64(0.03867692131525641), 3: np.float64(0.21445336633608492), 4: np.float64(0.20482928491476649), 5: np.float64(0.03867692131525641), 6: np.float64(0.24480430565165165), 0: np.float64(0.03867692131525641)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 11, 9, 1, 3, 19, 4, 14, 10, 16, 26, 21]
learned probs (dictionary):

probs= {1: np.float64(0.07681643359758543), 2: np.float64(0.18819716221361735), 3: np.float64(0.20859533257054588), 4: np.float64(0.0755477815881604), 5: np.float64(0.19996023130365637), 6: np.float64(0.20289232379712746), 0: np.float64(0.04799073492930855)}
choice probs for this beta: {1: np.float64(0.07681643359758543), 2: np.float64(0.18819716221361735), 3: np.float64(0.20859533257054588), 4: np.float64(0.0755477815881604), 5: np.float64(0.19996023130365637), 6: np.float64(0.20289232379712746), 0: np.float64(0.04799073492930855)}
#beta= 0.05 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 13: 0, 14: 0, 100: 0} [2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 100]
learned probs for cluster 3 

{1: np.float64(0.004184182923786446), 2: np.float64(0.21863750763875048), 3: np.float64(0.20797443056547923), 4: np.float64(0.1978313978976645), 5: np.float64(0.18818304677036699), 6: np.float64(0.17900525128016703), 0: np.float64(0.004184182923786446)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.0034153393115406864), 2: np.float64(0.17846286561013008), 3: np.float64(0.16975912894907244), 4: np.float64(0.16147987853396864), 5: np.float64(0.15360441192631205), 6: np.float64(0.14611303635743633), 0: np.float64(0.0034153393115406864)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 6: 1, 10: 1, 12: 3, 13: 2, 14: 3, 100: 1} [1, 4, 5, 6, 10, 100, 13, 12, 14]
learned probs for cluster 2 

{1: np.float64(0.2650912312607337), 2: np.float64(0.004905195640847986), 3: np.float64(0.004905195640847986), 4: np.float64(0.2521625793523334), 5: np.float64(0.23986446523793578), 6: np.float64(0.22816613722645315), 0: np.float64(0.004905195640847986)}
cluster label 2 learned center: 
 
sigma= [1, 4, 5, 6, 10, 100, 13, 12, 14]
learned probs (dictionary):

probs= {1: np.float64(0.04205238626779262), 2: np.float64(0.1791777978747837), 3: np.float64(0.17047406121372605), 4: np.float64(0.19823257447457124), 5: np.float64(0.18856465773474118), 6: np.float64(0.17936825085819189), 0: np.float64(0.00413027157619428)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 4, 3: 2, 4: 6, 6: 0, 7: 0, 8: 0, 9: 1, 10: 6, 11: 1, 14: 6, 16: 6, 17: 8, 100: 6} [6, 7, 8, 9, 11, 3, 1, 4, 10, 14, 16, 100, 17]
learned probs for cluster 1 

{1: np.float64(0.22856591254110306), 2: np.float64(0.0059362547778373164), 3: np.float64(0.24028473747127171), 4: np.float64(0.2174186214469538), 5: np.float64(0.0059362547778373164), 6: np.float64(0.2959219642071581), 0: np.float64(0.0059362547778373164)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 9, 11, 3, 1, 4, 10, 14, 16, 100, 17]
learned probs (dictionary):

probs= {1: np.float64(0.05073789094435453), 2: np.float64(0.1794033755563415), 3: np.float64(0.17960488123763438), 4: np.float64(0.20649448208955548), 5: np.float64(0.188790235416299), 6: np.float64(0.1906132854980639), 0: np.float64(0.0043558492577520985)}
choice probs for this beta: {1: np.float64(0.05073789094435453), 2: np.float64(0.1794033755563415), 3: np.float64(0.17960488123763438), 4: np.float64(0.20649448208955548), 5: np.float64(0.188790235416299), 6: np.float64(0.1906132854980639), 0: np.float64(0.0043558492577520985)}
#beta= 0.1 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 6: 0, 7: 0, 8: 0, 100: 0} [2, 3, 4, 6, 7, 8, 100]
learned probs for cluster 3 

{1: np.float64(7.350258754875263e-05), 2: np.float64(0.28858775528186636), 3: np.float64(0.2611249993660373), 4: np.float64(0.2362756702110068), 5: np.float64(7.350258754875263e-05), 6: np.float64(0.21379106737844328), 0: np.float64(7.350258754875263e-05)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 6, 7, 8, 100]
learned probs (dictionary):

probs= {1: np.float64(5.999648708666933e-05), 2: np.float64(0.23555975524882342), 3: np.float64(0.21314328073252795), 4: np.float64(0.1928600158097343), 5: np.float64(5.999648708666933e-05), 6: np.float64(0.17450695874765434), 0: np.float64(5.999648708666933e-05)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 4: 2, 5: 1, 6: 1, 10: 1, 15: 3, 100: 1} [1, 5, 6, 10, 100, 4, 15]
learned probs for cluster 2 

{1: np.float64(0.29822423742754284), 2: np.float64(7.589657026091155e-05), 3: np.float64(7.589657026091155e-05), 4: np.float64(0.18753826937683477), 5: np.float64(0.2698444489896808), 6: np.float64(0.244165354495159), 0: np.float64(7.589657026091155e-05)}
cluster label 2 learned center: 
 
sigma= [1, 5, 6, 10, 100, 4, 15]
learned probs (dictionary):

probs= {1: np.float64(0.043526179092151035), 2: np.float64(0.23557081717393893), 3: np.float64(0.21315434265764346), 4: np.float64(0.22019371857140796), 5: np.float64(0.039389824927332645), 6: np.float64(0.21009405916532375), 0: np.float64(7.105841220219719e-05)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 3, 3: 1, 4: 6, 6: 1, 7: 0, 8: 0, 9: 2, 10: 7, 11: 0, 16: 6, 19: 3, 76: 12, 100: 7} [7, 8, 11, 3, 6, 9, 1, 19, 4, 16, 10, 100, 76]
learned probs for cluster 1 

{1: np.float64(0.22960029768306087), 2: np.float64(0.00014806525224651812), 3: np.float64(0.3037513690931232), 4: np.float64(0.19135853293196742), 5: np.float64(0.00014806525224651812), 6: np.float64(0.2748456045351094), 0: np.float64(0.00014806525224651812)}
cluster label 1 learned center: 
 
sigma= [7, 8, 11, 3, 6, 9, 1, 19, 4, 16, 10, 100, 76]
learned probs (dictionary):

probs= {1: np.float64(0.05225099040410735), 2: np.float64(0.23557644365352431), 3: np.float64(0.22469689468318216), 4: np.float64(0.2274653428228227), 5: np.float64(0.03939545140691801), 6: np.float64(0.2205381921376579), 0: np.float64(7.668489178756488e-05)}
choice probs for this beta: {1: np.float64(0.05225099040410735), 2: np.float64(0.23557644365352431), 3: np.float64(0.22469689468318216), 4: np.float64(0.2274653428228227), 5: np.float64(0.03939545140691801), 6: np.float64(0.2205381921376579), 0: np.float64(7.668489178756488e-05)}
#beta= 0.25 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 5: 0, 7: 0, 8: 0, 12: 0, 100: 0} [2, 3, 4, 5, 7, 8, 12, 100]
learned probs for cluster 3 

{1: np.float64(2.6074223186162986e-11), 2: np.float64(0.3499320087313999), 3: np.float64(0.2725273224217639), 4: np.float64(0.21224449211042298), 5: np.float64(0.16529617665819007), 6: np.float64(2.6074223186162986e-11), 0: np.float64(2.6074223186162986e-11)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 5, 7, 8, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(2.1283084675705537e-11), 2: np.float64(0.2856320021270052), 3: np.float64(0.2224504269267648), 4: np.float64(0.17324456668513277), 5: np.float64(0.13492300419724765), 6: np.float64(2.1283084675705537e-11), 0: np.float64(2.1283084675705537e-11)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 4: 2, 5: 1, 6: 1, 10: 1, 11: 3, 12: 3, 13: 2, 14: 3, 100: 1} [1, 5, 6, 10, 100, 4, 13, 11, 12, 14]
learned probs for cluster 2 

{1: np.float64(0.37116259004049795), 2: np.float64(3.091379247105199e-11), 3: np.float64(3.091379247105199e-11), 4: np.float64(0.1146542034984967), 5: np.float64(0.28906171577035056), 6: np.float64(0.22512149059791298), 0: np.float64(3.091379247105199e-11)}
cluster label 2 learned center: 
 
sigma= [1, 5, 6, 10, 100, 4, 13, 11, 12, 14]
learned probs (dictionary):

probs= {1: np.float64(0.05409694751968566), 2: np.float64(0.28563200213151085), 3: np.float64(0.22245042693127048), 4: np.float64(0.18995541684503867), 5: np.float64(0.17705374927077625), 6: np.float64(0.0328114572759289), 0: np.float64(2.5788769928361364e-11)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 5, 3: 1, 4: 6, 5: 7, 6: 0, 7: 0, 8: 0, 9: 2, 11: 0, 14: 7, 16: 6, 19: 4, 100: 7} [6, 7, 8, 11, 3, 9, 19, 1, 4, 16, 5, 14, 100]
learned probs for cluster 1 

{1: np.float64(0.11591815044861063), 2: np.float64(5.222547384039283e-11), 3: np.float64(0.22713812728039554), 4: np.float64(0.09027714634156686), 5: np.float64(0.055889078403883824), 6: np.float64(0.5107774974210915), 0: np.float64(5.222547384039283e-11)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 11, 3, 9, 19, 1, 4, 16, 5, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.05850183723673286), 2: np.float64(0.28563200213349543), 3: np.float64(0.23108167576792552), 4: np.float64(0.1933859484060182), 5: np.float64(0.17917753425012384), 6: np.float64(0.052221002177930374), 0: np.float64(2.777333793429629e-11)}
choice probs for this beta: {1: np.float64(0.05850183723673286), 2: np.float64(0.28563200213349543), 3: np.float64(0.23108167576792552), 4: np.float64(0.1933859484060182), 5: np.float64(0.17917753425012384), 6: np.float64(0.052221002177930374), 0: np.float64(2.777333793429629e-11)}
#beta= 0.5 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 12: 0, 100: 0} [2, 3, 4, 5, 6, 7, 8, 12, 100]
learned probs for cluster 3 

{1: np.float64(3.56119206713024e-22), 2: np.float64(0.4286555287771671), 3: np.float64(0.25999272065868284), 4: np.float64(0.15769355638159335), 5: np.float64(0.09564597678455915), 6: np.float64(0.058012217397997876), 0: np.float64(3.56119206713024e-22)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 5, 6, 7, 8, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(2.9068230247950586e-22), 2: np.float64(0.3498900753643627), 3: np.float64(0.2122190582376499), 4: np.float64(0.12871736539647557), 5: np.float64(0.07807102855039641), 6: np.float64(0.04735247245111577), 0: np.float64(2.9068230247950586e-22)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 3: 3, 5: 1, 6: 1, 7: 3, 9: 3, 10: 1, 11: 3, 13: 3, 100: 1} [1, 5, 6, 10, 100, 3, 7, 9, 11, 13]
learned probs for cluster 2 

{1: np.float64(0.4841735761801217), 2: np.float64(4.443493486778809e-22), 3: np.float64(0.04404280060880265), 4: np.float64(4.443493486778809e-22), 5: np.float64(0.2936661185759542), 6: np.float64(0.1781175046351219), 0: np.float64(4.443493486778809e-22)}
cluster label 2 learned center: 
 
sigma= [1, 5, 6, 10, 100, 3, 7, 9, 11, 13]
learned probs (dictionary):

probs= {1: np.float64(0.07056829872825274), 2: np.float64(0.3498900753643627), 3: np.float64(0.21863829642638288), 4: np.float64(0.12871736539647557), 5: np.float64(0.12087286533284172), 6: np.float64(0.07331309875168479), 0: np.float64(3.55446220049307e-22)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 3, 3: 2, 5: 6, 6: 0, 7: 0, 8: 0, 9: 1, 10: 7, 11: 0, 13: 6, 14: 7, 15: 10, 16: 6, 19: 4, 23: 10, 100: 6} [6, 7, 8, 11, 9, 3, 1, 19, 5, 13, 16, 100, 10, 14, 15, 23]
learned probs for cluster 1 

{1: np.float64(0.06839271697174061), 2: np.float64(1.1839968087406308e-21), 3: np.float64(0.1127605272322824), 4: np.float64(1.1839968087406308e-21), 5: np.float64(0.02608468640411927), 6: np.float64(0.7927620693918581), 0: np.float64(1.1839968087406308e-21)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 11, 9, 3, 1, 19, 5, 13, 16, 100, 10, 14, 15]
learned probs (dictionary):

probs= {1: np.float64(0.07316722197317888), 2: np.float64(0.3498900753643627), 3: np.float64(0.22292319646120962), 4: np.float64(0.12871736539647557), 5: np.float64(0.12186408341619825), 6: np.float64(0.1034380573885754), 0: np.float64(4.0043809878145093e-22)}
choice probs for this beta: {1: np.float64(0.07316722197317888), 2: np.float64(0.3498900753643627), 3: np.float64(0.22292319646120962), 4: np.float64(0.12871736539647557), 5: np.float64(0.12186408341619825), 6: np.float64(0.1034380573885754), 0: np.float64(4.0043809878145093e-22)}
#beta= 0.75 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 8: 0, 9: 0, 10: 0, 14: 0, 100: 0} [2, 3, 4, 5, 6, 8, 9, 10, 14, 100]
learned probs for cluster 3 

{1: np.float64(5.894688509885072e-33), 2: np.float64(0.5403410507664803), 3: np.float64(0.25523903945502), 4: np.float64(0.12056638519229564), 5: np.float64(0.05695152774973), 6: np.float64(0.026901996836474193), 0: np.float64(5.894688509885072e-33)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 5, 6, 8, 9, 10, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(4.81153949619369e-33), 2: np.float64(0.4410533826881396), 3: np.float64(0.2083388659551601), 4: np.float64(0.09841231191321131), 5: np.float64(0.046486684525717116), 6: np.float64(0.02195875491777206), 0: np.float64(4.81153949619369e-33)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 4: 2, 5: 1, 6: 1, 10: 1, 12: 3, 25: 4, 100: 1} [1, 5, 6, 10, 100, 4, 12, 25]
learned probs for cluster 2 

{1: np.float64(0.5809202319854944), 2: np.float64(6.878756601228127e-33), 3: np.float64(6.878756601228127e-33), 4: np.float64(0.015051656217620432), 5: np.float64(0.2744072874004985), 6: np.float64(0.12962082439638636), 0: np.float64(6.878756601228127e-33)}
cluster label 2 learned center: 
 
sigma= [1, 5, 6, 10, 100, 4, 12, 25]
learned probs (dictionary):

probs= {1: np.float64(0.0846691238118858), 2: np.float64(0.4410533826881396), 3: np.float64(0.2083388659551601), 4: np.float64(0.10060609080692949), 5: np.float64(0.08648154666433977), 6: np.float64(0.04085099007354537), 0: np.float64(5.81411827082269e-33)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 3, 3: 1, 4: 6, 5: 7, 6: 0, 7: 0, 8: 0, 9: 1, 10: 7, 11: 0, 14: 7, 16: 6, 19: 5, 100: 6} [6, 7, 8, 11, 3, 9, 1, 19, 4, 16, 100, 5, 10, 14]
learned probs for cluster 1 

{1: np.float64(0.02025243173655616), 2: np.float64(2.000378412509192e-32), 3: np.float64(0.08467380247892885), 4: np.float64(0.004621913309297863), 5: np.float64(0.0004915073965090171), 6: np.float64(0.8899603450787082), 0: np.float64(2.000378412509192e-32)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 11, 3, 9, 1, 19, 4, 16, 100, 5, 10, 14]
learned probs (dictionary):

probs= {1: np.float64(0.08543871621787492), 2: np.float64(0.4410533826881396), 3: np.float64(0.2115564704493594), 4: np.float64(0.1007817235126828), 5: np.float64(0.08650022394540711), 6: np.float64(0.07466948318653628), 0: np.float64(6.574262067576183e-33)}
choice probs for this beta: {1: np.float64(0.08543871621787492), 2: np.float64(0.4410533826881396), 3: np.float64(0.2115564704493594), 4: np.float64(0.1007817235126828), 5: np.float64(0.08650022394540711), 6: np.float64(0.07466948318653628), 0: np.float64(6.574262067576183e-33)}
#beta= 1 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 6: 0, 7: 0, 8: 0, 9: 0, 100: 0} [2, 3, 4, 6, 7, 8, 9, 100]
learned probs for cluster 3 

{1: np.float64(1.0516757597336474e-43), 2: np.float64(0.6439142598879724), 3: np.float64(0.23688281808991019), 4: np.float64(0.0871443187420326), 5: np.float64(1.0516757597336474e-43), 6: np.float64(0.03205860328008501), 0: np.float64(1.0516757597336474e-43)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 6, 7, 8, 9, 100]
learned probs (dictionary):

probs= {1: np.float64(8.584303388825897e-44), 2: np.float64(0.5255950146335574), 3: np.float64(0.1933556002658892), 4: np.float64(0.07113155017318411), 5: np.float64(8.584303388825897e-44), 6: np.float64(0.02616783492736939), 0: np.float64(8.584303388825897e-44)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 3: 2, 4: 2, 5: 1, 6: 1, 10: 1, 12: 3, 14: 3, 100: 1} [1, 5, 6, 10, 100, 3, 4, 12, 14]
learned probs for cluster 2 

{1: np.float64(0.6608674065881656), 2: np.float64(1.1306355154250001e-43), 3: np.float64(0.004806259482688419), 4: np.float64(0.0017681240526163614), 5: np.float64(0.2431195322240747), 6: np.float64(0.0894386776524551), 0: np.float64(1.1306355154250001e-43)}
cluster label 2 learned center: 
 
sigma= [1, 5, 6, 10, 100, 3, 4, 12, 14]
learned probs (dictionary):

probs= {1: np.float64(0.09632142451022513), 2: np.float64(0.5255950146335574), 3: np.float64(0.19405611258549102), 4: np.float64(0.07138925425385294), 5: np.float64(0.03543467182165889), 6: np.float64(0.039203522195214724), 0: np.float64(1.0232204652557834e-43)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 3, 3: 1, 4: 6, 5: 7, 6: 0, 7: 0, 8: 0, 9: 1, 10: 7, 11: 0, 16: 7, 17: 8, 19: 5, 22: 9, 27: 12, 100: 7} [6, 7, 8, 11, 3, 9, 1, 19, 4, 5, 10, 16, 100, 17, 22, 27]
learned probs for cluster 1 

{1: np.float64(0.00574724757470046), 2: np.float64(3.720091753464606e-43), 3: np.float64(0.03984541364775042), 4: np.float64(0.0007883084424943616), 5: np.float64(0.00029000246929555585), 6: np.float64(0.9533290278657598), 0: np.float64(3.720091753464606e-43)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 11, 3, 9, 1, 19, 4, 5, 10, 16, 100, 17, 22]
learned probs (dictionary):

probs= {1: np.float64(0.09653981991806375), 2: np.float64(0.5255950146335574), 3: np.float64(0.19557023830410553), 4: np.float64(0.07141920997466772), 5: np.float64(0.03544569191549212), 6: np.float64(0.0754300252541136), 0: np.float64(1.1645839518874385e-43)}
choice probs for this beta: {1: np.float64(0.09653981991806375), 2: np.float64(0.5255950146335574), 3: np.float64(0.19557023830410553), 4: np.float64(0.07141920997466772), 5: np.float64(0.03544569191549212), 6: np.float64(0.0754300252541136), 0: np.float64(1.1645839518874385e-43)}
#beta= 1.25 

#cluster  3 with weight 0.81625
Learned cluster center of cluster 3:  {2: 0, 3: 0, 4: 0, 5: 0, 8: 0, 10: 0, 100: 0} [2, 3, 4, 5, 8, 10, 100]
learned probs for cluster 3 

{1: np.float64(1.8259515047567616e-54), 2: np.float64(0.7183353083752138), 3: np.float64(0.20580651160354266), 4: np.float64(0.05896455279947734), 5: np.float64(0.01689362722176621), 6: np.float64(1.8259515047567616e-54), 0: np.float64(1.8259515047567616e-54)}
cluster label 3 learned center: 
 
sigma= [2, 3, 4, 5, 8, 10, 100]
learned probs (dictionary):

probs= {1: np.float64(1.4904329157577067e-54), 2: np.float64(0.5863411954612683), 3: np.float64(0.1679895650963917), 4: np.float64(0.04812981622257338), 5: np.float64(0.01378942321976667), 6: np.float64(1.4904329157577067e-54), 0: np.float64(1.4904329157577067e-54)}
#cluster  2 with weight 0.14575
Learned cluster center of cluster 2:  {1: 0, 3: 2, 4: 2, 5: 1, 6: 1, 7: 3, 9: 3, 10: 2, 12: 3, 14: 3, 100: 1} [1, 5, 6, 100, 3, 4, 10, 7, 9, 12, 14]
learned probs for cluster 2 

{1: np.float64(0.7258921454244784), 2: np.float64(1.8920127334722523e-54), 3: np.float64(0.005092415641197365), 4: np.float64(0.001459001508808905), 5: np.float64(0.20797158166724777), 6: np.float64(0.05958485575826724), 0: np.float64(1.8920127334722523e-54)}
cluster label 2 learned center: 
 
sigma= [1, 5, 6, 100, 3, 4, 10, 7, 9, 12, 14]
learned probs (dictionary):

probs= {1: np.float64(0.10579878019561773), 2: np.float64(0.5863411954612683), 3: np.float64(0.16873178467609623), 4: np.float64(0.04834246569248228), 5: np.float64(0.044101281247768034), 6: np.float64(0.00868449272676745), 0: np.float64(1.7661937716612875e-54)}
#cluster  1 with weight 0.038
Learned cluster center of cluster 1:  {1: 3, 3: 1, 4: 7, 6: 0, 7: 0, 8: 0, 9: 1, 11: 0, 14: 6, 15: 9, 16: 6, 17: 8, 19: 4, 26: 7, 38: 10, 100: 6} [6, 7, 8, 11, 3, 9, 1, 19, 14, 16, 100, 4, 26, 17, 15, 38]
learned probs for cluster 1 

{1: np.float64(0.001502776055092945), 2: np.float64(6.861941861777995e-54), 3: np.float64(0.017324587444970486), 4: np.float64(2.9329184966655478e-06), 5: np.float64(6.861941861777995e-54), 6: np.float64(0.9811697035814388), 0: np.float64(6.861941861777995e-54)}
cluster label 1 learned center: 
 
sigma= [6, 7, 8, 11, 3, 9, 1, 19, 14, 16, 100, 4, 26, 17, 15]
learned probs (dictionary):

probs= {1: np.float64(0.10585588568571126), 2: np.float64(0.5863411954612683), 3: np.float64(0.1693901189990051), 4: np.float64(0.048342577143385156), 5: np.float64(0.044101281247768034), 6: np.float64(0.04596894146286212), 0: np.float64(2.0269475624088513e-54)}
choice probs for this beta: {1: np.float64(0.10585588568571126), 2: np.float64(0.5863411954612683), 3: np.float64(0.1693901189990051), 4: np.float64(0.048342577143385156), 5: np.float64(0.044101281247768034), 6: np.float64(0.04596894146286212), 0: np.float64(2.0269475624088513e-54)}
finding emperical estimations from test set
tau [47, 18, 21, 100, 17, 53, 12, 5, 30, 52] choice 5
tau [16, 8, 22, 47, 31, 28, 1, 12, 24, 30] choice 1
tau [8, 53, 14, 12, 100, 30, 6, 4, 43, 48] choice 6
tau [19, 11, 34, 10, 33, 42, 100, 29, 67, 31] choice 5
tau [11, 32, 5, 16, 41, 10, 25, 47, 39, 33] choice 5
tau [8, 22, 1, 10, 61, 36, 21, 2, 5, 29] choice 1
tau [100, 1, 21, 14, 13, 36, 25, 88, 92, 12] choice 1
tau [100, 34, 20, 5, 74, 9, 82, 2, 58, 4] choice 5
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 5
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 2
tau [4, 1, 9, 10, 25, 41, 11, 43, 30, 40] choice 4
tau [6, 8, 9, 43, 35, 27, 45, 46, 2, 85] choice 6
tau [19, 2, 3, 27, 11, 67, 44, 1, 14, 16] choice 2
tau [8, 22, 3, 1, 63, 100, 36, 7, 4, 97] choice 3
tau [26, 3, 31, 1, 35, 71, 44, 23, 33, 17] choice 3
tau [2, 8, 15, 100, 7, 5, 14, 32, 42, 28] choice 2
tau [100, 59, 22, 65, 10, 16, 7, 24, 39, 52] choice 4
tau [100, 48, 50, 43, 12, 21, 85, 28, 39, 4] choice 4
tau [19, 58, 43, 15, 7, 100, 5, 4, 14, 59] choice 5
tau [12, 36, 45, 20, 50, 18, 72, 5, 76, 75] choice 5
tau [9, 6, 11, 43, 10, 27, 12, 33, 7, 38] choice 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 2
tau [10, 20, 22, 29, 2, 34, 3, 19, 36, 16] choice 2
tau [12, 71, 33, 18, 25, 27, 14, 3, 5, 16] choice 3
tau [10, 8, 13, 16, 100, 26, 7, 1, 23, 4] choice 1
tau [15, 37, 27, 74, 5, 26, 35, 100, 31, 4] choice 5
tau [19, 100, 18, 10, 27, 52, 25, 17, 50, 29] choice 2
tau [4, 20, 41, 14, 10, 21, 100, 5, 23, 69] choice 4
tau [9, 5, 43, 88, 66, 51, 78, 65, 49, 58] choice 5
tau [19, 25, 41, 9, 44, 26, 34, 21, 12, 40] choice 2
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 2
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 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 4
tau [1, 62, 21, 13, 3, 51, 100, 35, 42, 16] choice 1
tau [6, 21, 43, 9, 11, 22, 59, 5, 53, 12] choice 6
tau [15, 79, 10, 17, 27, 73, 42, 5, 3, 49] choice 5
tau [6, 2, 31, 38, 9, 7, 5, 24, 95, 35] choice 6
tau [4, 18, 48, 1, 29, 47, 3, 14, 12, 17] choice 4
tau [31, 19, 6, 18, 20, 10, 73, 33, 55, 7] choice 6
tau [8, 9, 2, 30, 3, 18, 7, 40, 84, 12] choice 2
tau [15, 33, 32, 4, 18, 10, 71, 39, 30, 40] choice 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 1
tau [2, 6, 9, 58, 14, 7, 15, 5, 4, 17] choice 2
tau [10, 41, 3, 13, 18, 8, 35, 11, 40, 39] choice 3
tau [19, 13, 11, 18, 22, 27, 66, 23, 28, 48] choice 0
tau [9, 3, 4, 47, 8, 19, 2, 23, 42, 25] choice 3
tau [62, 8, 4, 18, 2, 16, 60, 12, 33, 68] choice 4
tau [2, 7, 70, 3, 100, 11, 27, 14, 15, 23] choice 2
tau [3, 11, 50, 6, 26, 8, 15, 16, 42, 28] choice 3
tau [11, 13, 1, 100, 6, 15, 27, 3, 22, 25] choice 1
tau [25, 64, 47, 5, 11, 35, 12, 100, 17, 23] choice 5
tau [10, 26, 5, 18, 28, 25, 51, 78, 15, 32] choice 5
tau [8, 10, 100, 25, 48, 71, 21, 43, 29, 30] choice 5
tau [11, 21, 14, 35, 5, 12, 16, 29, 38, 40] choice 5
tau [15, 6, 2, 100, 52, 18, 95, 14, 23, 17] choice 6
tau [17, 25, 43, 27, 21, 4, 3, 37, 16, 72] choice 4
tau [2, 38, 47, 3, 30, 46, 11, 1, 15, 73] choice 2
tau [6, 14, 37, 2, 58, 29, 50, 28, 35, 69] choice 6
tau [36, 15, 19, 11, 5, 39, 49, 1, 56, 60] choice 5
tau [9, 41, 22, 33, 4, 6, 14, 23, 80, 17] choice 4
tau [4, 9, 22, 20, 3, 87, 100, 28, 7, 40] choice 4
tau [1, 19, 11, 48, 22, 7, 9, 17, 24, 33] choice 1
tau [4, 17, 20, 10, 18, 1, 74, 5, 23, 60] choice 4
tau [12, 21, 6, 10, 19, 55, 7, 70, 50, 3] choice 6
tau [61, 2, 5, 15, 26, 16, 100, 20, 7, 95] choice 2
tau [15, 13, 22, 36, 11, 23, 5, 21, 16, 55] choice 5
tau [4, 8, 19, 12, 14, 25, 30, 80, 29, 59] choice 4
tau [19, 34, 41, 20, 14, 30, 1, 13, 49, 42] choice 1
tau [25, 41, 100, 36, 3, 5, 15, 27, 24, 48] choice 3
tau [20, 2, 13, 5, 10, 22, 25, 50, 24, 6] choice 2
tau [4, 2, 26, 30, 16, 22, 23, 34, 73, 29] choice 4
tau [6, 28, 7, 70, 8, 16, 1, 18, 23, 64] choice 6
tau [73, 26, 21, 11, 20, 7, 29, 80, 23, 6] choice 6
tau [11, 100, 31, 98, 23, 16, 30, 7, 12, 4] choice 4
tau [26, 45, 21, 33, 10, 68, 35, 13, 3, 14] choice 3
tau [20, 8, 6, 5, 100, 16, 2, 12, 36, 23] choice 6
tau [8, 4, 13, 18, 2, 12, 14, 1, 52, 7] choice 4
tau [19, 26, 3, 23, 6, 30, 39, 37, 27, 97] choice 3
tau [15, 18, 76, 12, 26, 100, 16, 5, 13, 49] choice 5
tau [8, 1, 100, 41, 5, 87, 93, 16, 7, 29] choice 1
tau [4, 8, 13, 9, 12, 2, 26, 65, 67, 60] choice 4
tau [19, 61, 18, 10, 56, 12, 17, 66, 68, 24] choice 5
tau [19, 1, 42, 4, 13, 16, 43, 63, 10, 80] choice 1
tau [47, 3, 5, 40, 36, 37, 16, 18, 9, 23] choice 3
tau [10, 13, 20, 6, 25, 17, 49, 86, 4, 38] choice 6
tau [15, 1, 22, 18, 34, 10, 26, 39, 40, 16] choice 1
tau [19, 8, 11, 22, 14, 25, 100, 70, 61, 23] choice 5
tau [100, 74, 1, 9, 5, 72, 13, 4, 14, 81] choice 1
tau [13, 9, 27, 22, 4, 20, 34, 24, 23, 18] choice 4
tau [100, 56, 15, 44, 43, 38, 11, 16, 13, 59] choice 4
tau [3, 58, 31, 45, 8, 64, 11, 6, 12, 41] choice 3
tau [9, 12, 48, 100, 52, 27, 7, 23, 31, 5] choice 5
tau [19, 21, 20, 13, 39, 4, 16, 66, 10, 69] choice 4
tau [39, 18, 3, 59, 31, 57, 72, 10, 75, 6] choice 3
tau [44, 8, 7, 4, 13, 11, 36, 60, 15, 14] choice 4
tau [7, 5, 3, 40, 9, 2, 18, 11, 53, 54] choice 5
tau [32, 36, 11, 1, 2, 7, 10, 63, 28, 51] choice 1
tau [10, 12, 60, 20, 13, 54, 8, 18, 31, 21] choice 6
tau [18, 20, 46, 3, 100, 37, 45, 29, 43, 84] choice 3
tau [18, 1, 3, 22, 27, 24, 34, 25, 43, 4] choice 1
tau [27, 13, 1, 2, 7, 92, 8, 28, 93, 38] choice 1
tau [13, 22, 12, 6, 44, 17, 5, 14, 46, 23] choice 6
tau [16, 34, 20, 62, 21, 54, 76, 3, 5, 52] choice 3
tau [2, 79, 41, 38, 100, 3, 71, 31, 10, 1] choice 2
tau [18, 2, 27, 31, 47, 44, 9, 48, 36, 14] choice 2
tau [8, 20, 15, 34, 79, 51, 24, 1, 28, 4] choice 1
tau [29, 72, 24, 26, 78, 4, 15, 6, 67, 22] choice 4
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 4
tau [61, 7, 13, 22, 41, 33, 28, 14, 60, 59] choice 5
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 6
tau [8, 10, 44, 100, 9, 73, 91, 7, 96, 17] choice 6
tau [19, 47, 21, 6, 3, 16, 34, 50, 45, 33] choice 6
tau [27, 13, 21, 15, 50, 28, 7, 5, 3, 23] choice 5
tau [19, 11, 13, 30, 24, 51, 6, 40, 85, 32] choice 6
tau [4, 11, 2, 7, 31, 5, 25, 55, 1, 34] choice 4
tau [4, 37, 41, 8, 75, 5, 6, 17, 92, 25] choice 4
tau [11, 28, 4, 46, 25, 27, 21, 3, 7, 71] choice 4
tau [5, 100, 7, 44, 76, 66, 31, 12, 21, 1] choice 5
tau [2, 37, 11, 20, 13, 100, 45, 60, 24, 6] choice 2
tau [19, 55, 21, 9, 51, 57, 100, 35, 7, 18] choice 2
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 5
tau [100, 3, 15, 1, 24, 28, 37, 26, 16, 56] choice 3
tau [22, 8, 44, 34, 5, 29, 33, 18, 54, 10] choice 5
tau [100, 9, 7, 10, 3, 5, 42, 8, 21, 6] choice 3
tau [5, 25, 31, 21, 28, 10, 23, 59, 48, 72] choice 5
tau [8, 7, 43, 46, 29, 16, 24, 41, 92, 6] choice 6
tau [26, 20, 23, 39, 8, 5, 100, 74, 48, 49] choice 5
tau [25, 62, 20, 7, 9, 5, 4, 16, 17, 14] choice 5
tau [16, 3, 43, 31, 73, 21, 28, 35, 6, 71] choice 3
tau [5, 18, 8, 19, 30, 33, 20, 2, 29, 45] choice 5
tau [24, 16, 8, 14, 5, 3, 4, 17, 32, 23] choice 5
tau [19, 61, 100, 9, 22, 52, 35, 3, 5, 12] choice 3
tau [4, 18, 5, 15, 9, 26, 16, 6, 50, 70] choice 4
tau [1, 11, 12, 39, 24, 26, 5, 19, 49, 15] choice 1
tau [8, 13, 27, 58, 2, 25, 1, 35, 4, 6] choice 2
tau [95, 19, 9, 87, 59, 8, 100, 58, 49, 17] choice 5
tau [36, 7, 14, 20, 8, 2, 27, 26, 25, 55] choice 2
tau [2, 3, 11, 20, 12, 17, 1, 19, 8, 6] choice 2
tau [1, 95, 41, 6, 26, 39, 35, 63, 64, 16] choice 1
tau [14, 46, 79, 18, 26, 17, 8, 31, 66, 55] choice 2
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 2
tau [15, 18, 47, 57, 5, 11, 46, 6, 72, 4] choice 5
tau [9, 36, 11, 3, 2, 18, 7, 45, 80, 81] choice 3
tau [15, 71, 8, 20, 28, 41, 16, 42, 5, 39] choice 5
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 4
tau [43, 47, 9, 27, 10, 66, 5, 18, 21, 42] choice 5
tau [14, 10, 70, 79, 100, 35, 32, 26, 28, 5] choice 5
tau [26, 8, 34, 14, 12, 36, 28, 30, 20, 15] choice 3
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 3
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 1
tau [14, 51, 18, 12, 17, 21, 13, 6, 42, 49] choice 6
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 6
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 5
tau [25, 18, 34, 23, 15, 21, 33, 17, 69, 38] choice 2
tau [19, 1, 6, 21, 100, 5, 44, 30, 7, 69] choice 1
tau [1, 72, 7, 57, 11, 25, 21, 4, 45, 17] choice 1
tau [19, 10, 9, 4, 16, 6, 5, 96, 39, 40] choice 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 6
tau [20, 37, 2, 8, 6, 39, 27, 66, 16, 40] choice 2
tau [8, 62, 7, 15, 5, 100, 63, 24, 16, 1] choice 5
tau [1, 50, 16, 6, 13, 11, 32, 2, 7, 70] choice 1
tau [25, 1, 2, 9, 8, 22, 44, 23, 29, 24] choice 1
tau [4, 2, 1, 11, 30, 24, 23, 40, 12, 52] choice 4
tau [41, 14, 11, 4, 100, 2, 13, 19, 8, 39] choice 4
tau [1, 14, 18, 4, 23, 20, 90, 55, 49, 6] choice 1
tau [7, 45, 18, 41, 94, 28, 12, 39, 36, 59] choice 6
tau [13, 15, 9, 23, 53, 41, 47, 100, 21, 1] choice 1
tau [3, 21, 7, 8, 100, 26, 41, 51, 33, 91] choice 3
tau [32, 44, 19, 51, 16, 71, 24, 59, 30, 2] choice 2
tau [10, 11, 3, 21, 2, 77, 13, 12, 64, 17] choice 3
tau [18, 35, 20, 10, 2, 50, 3, 30, 49, 17] choice 2
tau [22, 2, 4, 19, 48, 58, 98, 12, 3, 100] choice 2
tau [15, 26, 25, 1, 20, 39, 63, 52, 28, 75] choice 1
tau [75, 30, 100, 12, 37, 6, 25, 54, 34, 23] choice 6
tau [1, 38, 58, 19, 2, 3, 26, 21, 36, 10] choice 1
tau [19, 27, 10, 6, 2, 15, 28, 17, 49, 7] choice 6
tau [2, 13, 16, 23, 7, 70, 46, 67, 25, 1] choice 2
tau [37, 38, 41, 31, 12, 1, 18, 92, 17, 45] choice 1
tau [23, 57, 100, 22, 5, 6, 8, 4, 90, 61] choice 5
tau [6, 56, 7, 41, 100, 8, 32, 11, 10, 76] choice 6
tau [20, 100, 2, 3, 5, 45, 10, 17, 48, 63] choice 2
tau [20, 6, 16, 100, 21, 1, 77, 38, 75, 17] choice 6
tau [79, 100, 10, 3, 7, 65, 22, 30, 94, 12] choice 3
tau [13, 2, 55, 26, 48, 11, 41, 54, 7, 14] choice 2
tau [11, 46, 37, 66, 22, 47, 89, 30, 3, 7] choice 3
tau [14, 47, 9, 57, 38, 23, 31, 42, 49, 30] choice 1
tau [4, 100, 20, 26, 7, 33, 16, 52, 85, 63] choice 4
tau [1, 5, 11, 22, 21, 3, 17, 28, 6, 41] choice 1
tau [8, 44, 16, 3, 43, 25, 23, 27, 13, 10] choice 3
tau [7, 29, 44, 20, 25, 18, 23, 12, 66, 35] choice 0
tau [61, 11, 4, 100, 87, 60, 90, 33, 17, 56] choice 4
tau [3, 26, 25, 11, 20, 4, 14, 42, 24, 28] choice 3
tau [19, 37, 2, 17, 3, 24, 14, 66, 29, 69] choice 2
tau [2, 19, 15, 11, 13, 84, 17, 60, 38, 94] choice 2
tau [7, 15, 43, 1, 20, 29, 14, 51, 50, 12] choice 1
tau [26, 18, 31, 13, 23, 6, 100, 46, 27, 37] choice 6
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 0
tau [13, 2, 100, 37, 16, 30, 49, 14, 52, 64] choice 2
tau [11, 7, 1, 22, 44, 23, 13, 84, 4, 12] choice 1
tau [10, 100, 17, 11, 55, 7, 58, 37, 16, 44] choice 6
tau [2, 34, 32, 4, 14, 17, 37, 12, 78, 49] choice 2
tau [15, 19, 8, 17, 9, 2, 68, 24, 63, 5] choice 2
tau [43, 3, 37, 22, 9, 41, 1, 66, 89, 4] choice 3
tau [13, 9, 5, 17, 22, 2, 19, 34, 14, 55] choice 5
tau [6, 100, 4, 40, 46, 47, 11, 51, 29, 3] choice 6
tau [10, 61, 2, 20, 7, 18, 5, 42, 14, 35] choice 2
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 6
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 1
tau [10, 4, 76, 57, 1, 26, 82, 71, 15, 62] choice 4
tau [19, 32, 54, 27, 72, 13, 2, 89, 100, 40] choice 2
tau [6, 17, 20, 24, 10, 33, 70, 18, 28, 44] choice 6
tau [24, 26, 7, 100, 10, 6, 54, 34, 28, 1] choice 6
tau [48, 16, 11, 75, 98, 25, 10, 7, 1, 73] choice 1
tau [100, 13, 7, 8, 27, 25, 9, 41, 11, 14] choice 6
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 1
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 2
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 1
tau [75, 9, 16, 1, 18, 3, 30, 96, 48, 35] choice 1
tau [20, 4, 33, 3, 7, 24, 2, 48, 16, 56] choice 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 2
tau [25, 26, 17, 10, 11, 2, 9, 34, 13, 32] choice 2
tau [8, 84, 13, 77, 100, 12, 7, 56, 67, 29] choice 1
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 2
tau [5, 20, 34, 21, 35, 43, 18, 15, 23, 100] choice 5
tau [1, 2, 13, 21, 30, 25, 11, 23, 10, 12] choice 1
tau [100, 8, 11, 43, 1, 34, 13, 12, 50, 42] choice 1
tau [47, 15, 10, 20, 17, 11, 55, 74, 44, 100] choice 6
tau [73, 13, 8, 2, 19, 34, 22, 9, 5, 4] choice 2
tau [8, 37, 11, 2, 20, 13, 100, 32, 1, 30] choice 2
tau [6, 70, 15, 13, 80, 22, 3, 10, 78, 52] choice 6
tau [8, 4, 27, 19, 66, 20, 5, 26, 74, 2] choice 4
tau [100, 19, 22, 31, 74, 38, 1, 32, 6, 64] choice 1
tau [48, 10, 49, 8, 18, 13, 14, 17, 59, 4] choice 4
tau [8, 100, 6, 84, 13, 29, 11, 14, 35, 17] choice 6
tau [34, 36, 25, 39, 37, 2, 93, 66, 100, 29] choice 2
tau [21, 1, 5, 9, 20, 4, 22, 10, 12, 33] choice 1
tau [1, 8, 62, 7, 30, 27, 11, 12, 5, 16] choice 1
tau [1, 3, 9, 26, 12, 29, 4, 56, 14, 62] choice 1
tau [51, 26, 63, 9, 52, 43, 62, 84, 17, 59] choice 3
tau [13, 14, 28, 34, 100, 21, 18, 67, 1, 17] choice 1
tau [19, 2, 32, 5, 43, 25, 67, 18, 64, 49] choice 2
tau [6, 53, 100, 25, 14, 26, 22, 31, 5, 45] choice 6
tau [2, 35, 31, 36, 24, 16, 47, 7, 19, 8] choice 2
tau [13, 11, 12, 32, 21, 46, 5, 28, 16, 30] choice 5
tau [4, 37, 88, 21, 11, 7, 31, 48, 30, 49] choice 4
tau [2, 73, 38, 5, 22, 41, 40, 21, 32, 25] choice 2
tau [71, 25, 15, 1, 30, 29, 36, 33, 16, 18] choice 1
tau [25, 15, 47, 18, 62, 31, 24, 72, 33, 56] choice 5
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 1
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 3
tau [6, 9, 11, 57, 22, 100, 12, 21, 1, 39] choice 6
tau [4, 2, 14, 5, 17, 3, 30, 72, 67, 9] choice 4
tau [18, 9, 26, 3, 14, 46, 77, 33, 24, 28] choice 3
tau [6, 26, 7, 22, 21, 60, 16, 10, 63, 18] choice 6
tau [18, 25, 100, 50, 10, 28, 11, 27, 81, 29] choice 2
tau [13, 1, 17, 5, 18, 50, 55, 44, 29, 42] choice 1
tau [1, 11, 7, 4, 30, 29, 48, 23, 99, 38] choice 1
tau [71, 26, 7, 36, 10, 25, 42, 8, 13, 40] choice 2
tau [13, 5, 2, 6, 11, 65, 95, 30, 36, 16] choice 5
tau [4, 6, 3, 16, 7, 20, 5, 41, 67, 56] choice 4
tau [9, 100, 15, 8, 5, 30, 3, 25, 13, 76] choice 5
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 0
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 1
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 6
tau [2, 25, 14, 32, 73, 5, 23, 30, 24, 16] choice 2
tau [7, 72, 57, 50, 21, 18, 38, 73, 23, 17] choice 1
tau [100, 7, 41, 18, 30, 21, 28, 60, 49, 35] choice 3
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 4
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 4
tau [12, 33, 14, 5, 21, 52, 60, 49, 44, 23] choice 5
tau [21, 7, 15, 6, 2, 3, 1, 94, 59, 14] choice 6
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 4
tau [8, 4, 6, 13, 33, 46, 84, 16, 17, 18] choice 4
tau [22, 1, 13, 15, 4, 66, 5, 37, 9, 6] choice 1
tau [10, 47, 35, 8, 9, 26, 7, 55, 66, 39] choice 6
tau [100, 15, 2, 13, 12, 82, 1, 21, 51, 78] choice 2
tau [13, 3, 5, 16, 61, 17, 69, 64, 31, 100] choice 3
tau [1, 4, 20, 59, 40, 19, 3, 17, 45, 12] choice 1
tau [15, 2, 71, 26, 50, 46, 10, 42, 33, 3] choice 2
tau [2, 6, 9, 100, 50, 64, 5, 14, 38, 7] choice 2
tau [58, 21, 15, 41, 6, 11, 4, 27, 17, 84] choice 6
tau [2, 61, 4, 18, 6, 58, 74, 30, 71, 7] choice 2
tau [1, 96, 26, 18, 10, 100, 22, 30, 3, 5] choice 1
tau [59, 41, 9, 1, 5, 14, 18, 10, 24, 29] choice 1
tau [100, 15, 19, 1, 10, 39, 62, 12, 7, 18] choice 1
tau [19, 26, 31, 20, 43, 3, 5, 16, 22, 12] choice 3
tau [100, 9, 2, 19, 30, 20, 40, 6, 17, 34] choice 2
tau [8, 27, 39, 47, 3, 10, 94, 100, 24, 2] choice 3
tau [19, 2, 10, 41, 13, 75, 20, 46, 15, 7] choice 2
tau [21, 4, 35, 2, 37, 53, 19, 28, 49, 42] choice 4
tau [16, 6, 49, 8, 63, 14, 52, 66, 38, 7] choice 6
tau [47, 1, 8, 39, 100, 30, 3, 12, 4, 43] choice 1
tau [13, 8, 6, 15, 69, 100, 22, 59, 98, 45] choice 6
tau [4, 19, 1, 25, 2, 14, 3, 33, 56, 81] choice 4
tau [44, 7, 71, 11, 95, 25, 28, 1, 33, 97] choice 1
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 2
tau [38, 43, 26, 10, 22, 3, 21, 15, 6, 92] choice 3
tau [47, 78, 36, 5, 3, 18, 49, 39, 51, 23] choice 5
tau [2, 54, 39, 9, 11, 29, 22, 3, 51, 4] choice 2
tau [19, 9, 3, 43, 37, 25, 6, 11, 84, 27] choice 3
tau [6, 14, 23, 10, 15, 74, 31, 17, 4, 7] choice 6
tau [21, 34, 23, 15, 26, 12, 14, 68, 3, 30] choice 3
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 4
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 4
tau [3, 34, 4, 10, 19, 81, 8, 44, 5, 66] choice 3
tau [2, 12, 1, 16, 51, 78, 81, 35, 18, 85] choice 2
tau [20, 9, 19, 5, 94, 6, 10, 33, 99, 59] choice 5
tau [21, 13, 2, 22, 6, 24, 28, 51, 14, 29] choice 2
tau [100, 3, 10, 37, 28, 12, 56, 8, 40, 27] choice 3
tau [15, 7, 29, 5, 44, 22, 12, 64, 97, 38] choice 5
tau [37, 21, 4, 2, 13, 44, 10, 36, 59, 92] choice 4
tau [27, 18, 5, 7, 3, 26, 2, 100, 97, 95] choice 5
tau [37, 10, 20, 29, 28, 45, 40, 21, 18, 64] choice 6
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 4
tau [26, 2, 47, 43, 6, 13, 82, 42, 33, 51] choice 2
tau [53, 10, 31, 38, 21, 18, 23, 25, 5, 17] choice 5
tau [11, 34, 4, 6, 1, 27, 18, 23, 5, 3] choice 4
tau [3, 25, 17, 29, 7, 22, 39, 11, 28, 87] choice 3
tau [9, 12, 4, 13, 3, 7, 1, 8, 24, 74] choice 4
tau [54, 21, 31, 38, 17, 1, 30, 4, 9, 47] choice 1
tau [2, 88, 3, 53, 17, 89, 77, 24, 12, 10] choice 2
tau [11, 6, 7, 25, 15, 71, 30, 4, 90, 59] choice 6
tau [3, 15, 4, 32, 33, 17, 14, 16, 51, 25] choice 3
tau [1, 15, 37, 26, 100, 4, 18, 12, 89, 29] choice 1
tau [4, 15, 12, 27, 18, 100, 25, 59, 98, 49] choice 4
tau [83, 11, 3, 49, 7, 10, 33, 12, 6, 35] choice 3
tau [6, 26, 2, 47, 14, 64, 29, 24, 28, 25] choice 6
tau [8, 6, 22, 11, 9, 36, 71, 41, 40, 17] choice 6
tau [8, 51, 79, 3, 20, 27, 4, 60, 45, 17] choice 3
tau [13, 11, 51, 38, 19, 30, 44, 3, 9, 22] choice 3
tau [59, 3, 10, 6, 1, 30, 27, 37, 28, 56] choice 3
tau [10, 100, 2, 11, 78, 12, 80, 68, 28, 86] choice 2
tau [4, 8, 18, 10, 25, 9, 14, 51, 5, 48] choice 4
tau [7, 29, 5, 4, 81, 20, 36, 33, 87, 62] choice 5
tau [34, 27, 13, 100, 42, 15, 5, 33, 43, 29] choice 5
tau [20, 2, 15, 79, 27, 12, 23, 24, 39, 28] choice 2
tau [5, 21, 3, 2, 26, 76, 11, 7, 100, 28] choice 5
tau [24, 14, 11, 9, 18, 6, 36, 31, 27, 76] choice 6
tau [17, 2, 16, 25, 9, 11, 10, 40, 100, 90] choice 2
tau [10, 9, 31, 15, 32, 7, 27, 55, 45, 1] choice 1
tau [2, 19, 9, 11, 55, 3, 6, 4, 28, 40] choice 2
tau [39, 27, 59, 12, 6, 16, 4, 9, 7, 75] choice 6
tau [2, 19, 3, 20, 1, 68, 18, 23, 52, 70] choice 2
tau [9, 40, 49, 21, 36, 3, 16, 1, 14, 66] choice 3
tau [14, 36, 19, 2, 100, 40, 55, 28, 83, 17] choice 2
tau [19, 100, 60, 40, 48, 29, 20, 12, 28, 85] choice 6
tau [37, 9, 3, 29, 22, 40, 41, 54, 27, 39] choice 3
tau [19, 27, 1, 21, 100, 41, 48, 18, 24, 35] choice 1
tau [15, 9, 41, 6, 20, 21, 23, 13, 18, 33] choice 6
tau [8, 13, 15, 11, 1, 100, 30, 17, 28, 48] choice 1
tau [79, 41, 8, 65, 13, 11, 51, 10, 5, 33] choice 5
tau [13, 51, 72, 100, 8, 59, 65, 42, 41, 3] choice 3
tau [21, 13, 4, 57, 6, 7, 3, 65, 35, 25] choice 4
tau [13, 20, 81, 18, 6, 12, 100, 75, 21, 16] choice 6
tau [41, 22, 9, 54, 82, 49, 83, 42, 6, 35] choice 6
tau [3, 2, 30, 43, 26, 5, 11, 23, 27, 13] choice 3
tau [1, 15, 6, 13, 5, 20, 16, 49, 58, 30] choice 1
tau [11, 9, 38, 18, 5, 26, 2, 51, 30, 48] choice 5
tau [72, 52, 17, 71, 7, 30, 6, 51, 29, 8] choice 6
tau [6, 19, 26, 5, 14, 28, 24, 17, 3, 94] choice 6
tau [32, 100, 11, 47, 17, 16, 45, 29, 6, 97] choice 6
tau [18, 15, 34, 20, 79, 67, 2, 100, 5, 29] choice 2
tau [35, 9, 22, 95, 14, 42, 1, 5, 23, 48] choice 1
tau [8, 44, 7, 10, 13, 12, 15, 26, 86, 52] choice 5
tau [6, 7, 39, 54, 32, 34, 12, 41, 8, 30] choice 6
tau [17, 12, 48, 63, 4, 25, 35, 5, 19, 28] choice 4
tau [1, 15, 5, 36, 34, 51, 79, 100, 23, 30] choice 1
tau [1, 11, 100, 18, 5, 21, 24, 33, 30, 26] choice 1
tau [2, 11, 29, 88, 24, 18, 21, 81, 12, 9] choice 2
tau [13, 76, 73, 26, 5, 4, 12, 35, 16, 99] choice 5
tau [15, 10, 3, 2, 11, 17, 7, 68, 45, 70] choice 3
tau [2, 25, 1, 40, 48, 39, 93, 46, 20, 4] choice 2
tau [3, 5, 19, 2, 15, 12, 10, 17, 51, 58] choice 3
tau [4, 35, 6, 22, 100, 7, 9, 15, 73, 3] choice 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 2
tau [16, 31, 11, 95, 80, 33, 23, 17, 4, 9] choice 4
tau [5, 6, 47, 22, 10, 13, 20, 11, 98, 25] choice 5
tau [14, 3, 4, 34, 9, 2, 27, 23, 78, 60] choice 3
tau [62, 15, 9, 100, 17, 11, 88, 43, 18, 4] choice 4
tau [6, 15, 100, 13, 12, 25, 36, 3, 77, 4] choice 6
tau [8, 13, 21, 25, 32, 5, 42, 14, 6, 4] choice 5
tau [37, 2, 1, 10, 11, 100, 28, 6, 46, 16] choice 2
tau [6, 27, 64, 5, 4, 3, 18, 36, 1, 99] choice 6
tau [8, 6, 58, 44, 7, 14, 3, 24, 95, 77] choice 6
tau [38, 5, 11, 20, 14, 36, 18, 71, 61, 1] choice 5
tau [26, 5, 60, 100, 15, 33, 20, 21, 66, 34] choice 5
tau [15, 7, 4, 80, 9, 19, 39, 17, 22, 26] choice 4
tau [1, 22, 10, 19, 13, 61, 39, 12, 16, 48] choice 1
tau [100, 29, 32, 34, 23, 27, 2, 49, 64, 4] choice 2
tau [15, 6, 25, 11, 24, 5, 42, 10, 12, 3] choice 6
tau [26, 100, 22, 5, 25, 23, 6, 15, 35, 77] choice 5
tau [20, 26, 13, 9, 3, 68, 43, 67, 28, 16] choice 3
tau [19, 12, 14, 10, 1, 6, 11, 2, 100, 74] choice 1
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 1
tau [20, 31, 9, 10, 1, 23, 32, 28, 16, 45] choice 1
tau [6, 4, 34, 9, 14, 8, 17, 5, 66, 90] choice 6
tau [27, 96, 2, 16, 51, 26, 4, 30, 10, 6] choice 2
tau [25, 12, 26, 57, 47, 28, 10, 29, 45, 18] choice 3
tau [7, 5, 19, 61, 15, 21, 4, 2, 12, 17] choice 5
tau [19, 47, 100, 20, 38, 44, 18, 23, 55, 17] choice 3
tau [18, 21, 22, 100, 48, 5, 16, 20, 14, 46] choice 5
tau [2, 6, 9, 21, 4, 3, 58, 23, 51, 20] choice 2
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 6
tau [34, 22, 61, 6, 16, 9, 42, 25, 3, 13] choice 6
tau [14, 15, 4, 34, 59, 21, 13, 38, 23, 58] choice 4
tau [100, 3, 43, 37, 12, 44, 32, 2, 28, 6] choice 3
tau [22, 73, 100, 17, 53, 25, 13, 3, 10, 24] choice 3
tau [19, 10, 7, 5, 17, 11, 6, 31, 23, 34] choice 5
tau [67, 46, 44, 6, 22, 10, 5, 17, 33, 38] choice 6
tau [4, 39, 59, 42, 14, 49, 2, 27, 12, 58] choice 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 2
tau [8, 3, 9, 25, 23, 12, 6, 4, 7, 70] choice 3
tau [35, 1, 41, 100, 79, 21, 26, 32, 30, 38] choice 1
tau [19, 2, 26, 100, 4, 6, 3, 40, 48, 97] choice 2
tau [9, 42, 2, 61, 95, 100, 12, 30, 28, 17] choice 2
tau [3, 27, 4, 5, 22, 7, 12, 23, 37, 60] choice 3
tau [6, 19, 5, 60, 13, 31, 17, 24, 35, 18] choice 6
tau [16, 100, 39, 85, 18, 23, 12, 54, 8, 41] choice 1
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 4
tau [16, 1, 20, 13, 49, 65, 2, 26, 3, 32] choice 1
tau [44, 6, 4, 34, 16, 39, 11, 17, 13, 49] choice 6
tau [8, 41, 27, 3, 17, 26, 43, 16, 76, 7] choice 3
tau [53, 15, 19, 4, 25, 100, 61, 14, 22, 5] choice 4
tau [21, 57, 20, 34, 5, 13, 1, 7, 28, 16] choice 5
tau [8, 6, 3, 75, 74, 33, 44, 12, 50, 42] choice 6
tau [9, 2, 10, 48, 7, 44, 100, 24, 34, 95] choice 2
tau [21, 2, 23, 25, 26, 13, 45, 48, 50, 9] choice 2
tau [41, 3, 10, 63, 35, 16, 13, 26, 31, 38] choice 3
tau [32, 18, 12, 36, 33, 50, 5, 23, 3, 60] choice 5
tau [75, 6, 30, 100, 9, 33, 13, 2, 34, 27] choice 6
tau [9, 79, 5, 22, 45, 51, 14, 77, 50, 48] choice 5
tau [6, 11, 18, 7, 39, 46, 27, 4, 29, 10] choice 6
tau [4, 8, 12, 28, 43, 11, 50, 45, 16, 100] choice 4
tau [25, 21, 47, 26, 7, 22, 5, 24, 43, 29] choice 5
tau [100, 10, 12, 64, 14, 74, 18, 27, 42, 17] choice 2
tau [20, 13, 6, 12, 19, 1, 8, 16, 18, 21] choice 6
tau [28, 12, 4, 1, 5, 30, 47, 8, 56, 26] choice 4
tau [37, 19, 1, 29, 45, 8, 23, 18, 56, 17] choice 1
tau [14, 6, 2, 5, 100, 21, 13, 17, 39, 28] choice 6
tau [3, 22, 50, 7, 18, 21, 16, 9, 12, 35] choice 3
tau [11, 8, 4, 15, 36, 13, 26, 12, 30, 49] choice 4
tau [19, 7, 26, 1, 33, 5, 4, 69, 17, 21] choice 1
tau [21, 27, 1, 44, 14, 52, 28, 3, 100, 9] choice 1
tau [29, 13, 2, 14, 1, 3, 34, 98, 24, 42] choice 2
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 6
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 2
tau [26, 22, 43, 10, 1, 17, 3, 4, 100, 83] choice 1
tau [4, 19, 8, 1, 31, 5, 9, 12, 37, 15] choice 4
tau [8, 100, 2, 24, 28, 27, 48, 50, 32, 7] choice 2
tau [13, 90, 12, 3, 5, 68, 2, 30, 36, 17] choice 3
tau [13, 2, 1, 37, 43, 29, 20, 49, 3, 38] choice 2
tau [37, 3, 20, 19, 9, 70, 100, 39, 75, 64] choice 3
tau [2, 13, 9, 25, 5, 12, 24, 56, 59, 35] choice 2
tau [100, 7, 3, 47, 21, 13, 73, 16, 24, 59] choice 3
tau [6, 41, 9, 11, 3, 31, 80, 61, 48, 52] choice 6
tau [3, 21, 31, 2, 22, 15, 25, 63, 97, 42] choice 3
tau [4, 15, 22, 100, 11, 21, 7, 1, 82, 46] choice 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 3
tau [6, 72, 8, 9, 25, 10, 22, 30, 100, 29] choice 6
tau [9, 5, 95, 20, 19, 67, 11, 77, 6, 7] choice 5
tau [37, 45, 10, 34, 14, 13, 48, 2, 7, 3] choice 2
tau [36, 4, 8, 19, 1, 6, 2, 3, 90, 69] choice 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 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 5
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 1
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 6
tau [76, 33, 5, 9, 47, 73, 38, 16, 52, 80] choice 5
tau [10, 5, 1, 19, 7, 25, 11, 29, 28, 23] choice 5
tau [8, 27, 19, 26, 20, 18, 7, 30, 97, 100] choice 2
tau [25, 28, 33, 19, 29, 3, 22, 59, 9, 14] choice 3
tau [31, 19, 8, 14, 27, 5, 46, 35, 1, 29] choice 5
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 1
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 6
tau [11, 5, 3, 7, 12, 100, 50, 16, 69, 54] choice 5
tau [41, 37, 22, 25, 15, 64, 40, 20, 24, 28] choice 3
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 2
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 3
tau [1, 20, 9, 14, 34, 73, 64, 47, 31, 37] choice 1
tau [41, 100, 33, 20, 13, 25, 95, 35, 70, 10] choice 2
tau [100, 41, 45, 16, 3, 26, 95, 27, 61, 31] choice 3
tau [37, 6, 20, 10, 38, 3, 5, 30, 54, 7] choice 6
tau [2, 19, 10, 57, 25, 27, 11, 47, 100, 32] choice 2
tau [19, 2, 26, 100, 41, 22, 12, 59, 70, 78] choice 2
tau [33, 5, 15, 42, 61, 63, 24, 72, 29, 21] choice 5
tau [9, 79, 21, 26, 96, 2, 8, 12, 80, 3] choice 2
tau [20, 37, 6, 18, 4, 25, 12, 38, 43, 16] choice 6
tau [14, 12, 22, 88, 66, 32, 59, 37, 3, 42] choice 3
tau [13, 20, 9, 10, 12, 79, 63, 31, 5, 26] choice 5
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 5
tau [8, 20, 54, 9, 46, 29, 60, 24, 17, 77] choice 2
tau [100, 5, 26, 1, 9, 68, 97, 24, 78, 85] choice 5
tau [41, 36, 47, 64, 27, 18, 21, 26, 6, 38] choice 6
tau [7, 100, 6, 2, 99, 24, 19, 63, 27, 25] choice 6
tau [26, 11, 5, 7, 22, 47, 9, 15, 52, 87] choice 5
tau [2, 30, 20, 40, 14, 18, 43, 6, 17, 4] choice 2
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 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 4
tau [15, 6, 19, 8, 71, 39, 85, 52, 78, 9] choice 6
tau [19, 13, 47, 4, 8, 41, 12, 7, 2, 17] choice 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 2
tau [38, 10, 58, 5, 33, 12, 68, 69, 17, 23] choice 5
tau [17, 10, 25, 4, 26, 39, 75, 50, 16, 5] choice 4
tau [15, 30, 3, 11, 26, 21, 32, 10, 66, 97] choice 3
tau [19, 20, 11, 63, 22, 9, 27, 52, 53, 17] choice 1
tau [21, 18, 15, 22, 2, 28, 100, 20, 58, 69] choice 2
tau [3, 100, 41, 6, 31, 49, 21, 23, 44, 40] choice 3
tau [2, 4, 13, 26, 16, 7, 10, 14, 41, 43] choice 2
tau [6, 18, 10, 16, 43, 5, 40, 17, 4, 7] choice 6
tau [7, 25, 9, 2, 28, 27, 24, 93, 33, 38] choice 2
tau [19, 100, 14, 13, 23, 2, 10, 7, 31, 52] choice 2
tau [8, 2, 100, 66, 3, 12, 42, 31, 39, 40] choice 2
tau [27, 45, 20, 15, 53, 16, 35, 59, 33, 86] choice 6
tau [100, 26, 5, 76, 1, 32, 14, 62, 12, 28] choice 5
tau [4, 10, 6, 28, 26, 3, 17, 52, 7, 94] choice 4
tau [9, 43, 15, 48, 3, 76, 77, 52, 19, 8] choice 3
tau [20, 19, 15, 9, 38, 1, 6, 4, 23, 49] choice 1
tau [47, 63, 39, 1, 18, 16, 8, 35, 7, 13] choice 1
tau [77, 52, 13, 79, 17, 15, 47, 100, 48, 54] choice 5
tau [8, 19, 100, 9, 2, 20, 32, 5, 30, 59] choice 2
tau [6, 9, 26, 29, 7, 5, 49, 4, 28, 24] choice 6
tau [4, 2, 17, 31, 16, 33, 5, 12, 14, 29] choice 4
tau [28, 100, 23, 7, 17, 26, 22, 62, 89, 35] choice 5
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 2
tau [1, 5, 34, 27, 76, 2, 33, 31, 25, 18] choice 1
tau [6, 14, 45, 100, 5, 56, 28, 21, 32, 18] choice 6
tau [8, 19, 11, 2, 27, 39, 37, 29, 3, 22] choice 2
tau [8, 21, 46, 20, 26, 19, 69, 42, 58, 1] choice 1
tau [3, 1, 8, 21, 45, 13, 100, 12, 20, 30] choice 3
tau [9, 19, 21, 10, 33, 28, 22, 15, 36, 78] choice 5
tau [22, 16, 6, 41, 42, 9, 2, 68, 20, 15] choice 6
tau [3, 15, 100, 41, 22, 43, 26, 4, 78, 46] choice 3
tau [6, 2, 5, 9, 48, 100, 11, 65, 25, 81] choice 6
tau [19, 9, 25, 29, 36, 7, 50, 21, 17, 44] choice 5
tau [6, 100, 3, 11, 32, 1, 41, 35, 24, 33] choice 6
tau [44, 1, 10, 8, 26, 5, 12, 30, 80, 82] choice 1
tau [7, 13, 29, 26, 27, 49, 24, 53, 14, 35] choice 2
tau [4, 25, 34, 64, 5, 32, 63, 6, 67, 92] choice 4
tau [91, 16, 56, 49, 30, 71, 17, 5, 33, 12] choice 5
tau [21, 45, 26, 22, 17, 32, 6, 11, 12, 100] choice 6
tau [6, 8, 53, 1, 9, 28, 33, 3, 16, 7] choice 6
tau [3, 15, 2, 8, 21, 37, 14, 34, 49, 90] choice 3
tau [10, 8, 25, 39, 64, 24, 46, 97, 4, 35] choice 4
tau [100, 26, 10, 12, 19, 8, 49, 31, 6, 56] choice 6
tau [31, 2, 15, 25, 6, 88, 84, 14, 3, 69] choice 2
tau [6, 8, 2, 36, 70, 23, 17, 13, 14, 3] choice 6
tau [20, 22, 5, 10, 23, 15, 27, 67, 42, 46] choice 5
tau [11, 50, 10, 51, 1, 39, 19, 13, 18, 86] choice 1
tau [8, 2, 9, 22, 100, 33, 87, 5, 64, 4] choice 2
tau [1, 13, 31, 74, 5, 14, 65, 33, 28, 90] choice 1
tau [4, 47, 19, 27, 14, 36, 59, 62, 10, 11] choice 4
tau [4, 20, 36, 38, 8, 13, 44, 18, 23, 48] choice 4
tau [25, 1, 3, 37, 100, 11, 33, 21, 23, 30] choice 1
tau [19, 58, 6, 11, 23, 79, 31, 34, 12, 71] choice 6
tau [34, 61, 15, 37, 4, 8, 30, 10, 17, 26] choice 4
tau [32, 53, 6, 13, 100, 49, 22, 38, 19, 69] choice 6
tau [10, 34, 46, 6, 4, 42, 68, 33, 14, 17] choice 6
tau [4, 9, 22, 13, 84, 10, 33, 25, 17, 62] choice 4
tau [7, 37, 16, 12, 14, 23, 17, 39, 18, 9] choice 3
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 6
tau [1, 3, 47, 11, 6, 10, 9, 28, 4, 39] choice 1
tau [11, 57, 3, 31, 18, 7, 20, 21, 16, 30] choice 3
tau [100, 17, 7, 3, 24, 51, 8, 11, 21, 4] choice 3
tau [19, 32, 100, 3, 5, 27, 45, 10, 89, 1] choice 3
tau [22, 61, 27, 24, 30, 5, 17, 14, 19, 8] choice 5
tau [32, 31, 11, 5, 8, 13, 20, 25, 1, 6] choice 5
tau [6, 9, 25, 1, 8, 22, 27, 11, 62, 3] choice 6
tau [31, 3, 9, 22, 26, 100, 1, 30, 29, 35] choice 3
tau [13, 11, 32, 22, 6, 26, 18, 29, 17, 5] choice 6
tau [11, 34, 22, 19, 37, 30, 25, 72, 23, 24] choice 2
tau [1, 7, 27, 41, 17, 22, 21, 30, 39, 38] choice 1
tau [8, 1, 14, 5, 100, 11, 51, 21, 39, 30] choice 1
tau [1, 90, 40, 26, 48, 3, 44, 14, 13, 4] choice 1
tau [11, 13, 73, 37, 2, 34, 12, 16, 23, 7] choice 2
tau [21, 6, 14, 43, 44, 100, 15, 7, 45, 35] choice 6
tau [37, 47, 38, 43, 100, 3, 80, 59, 36, 12] choice 3
tau [7, 26, 100, 23, 6, 33, 12, 24, 17, 35] choice 6
tau [27, 1, 6, 3, 16, 21, 34, 30, 49, 71] choice 1
tau [8, 2, 30, 34, 27, 32, 100, 11, 35, 24] choice 2
tau [2, 13, 9, 22, 1, 3, 57, 33, 12, 24] choice 2
tau [100, 7, 40, 3, 25, 10, 9, 35, 6, 19] choice 3
tau [22, 37, 58, 5, 30, 8, 34, 24, 1, 23] choice 5
tau [10, 35, 20, 57, 38, 98, 24, 32, 83, 71] choice 5
tau [19, 17, 1, 100, 5, 22, 7, 11, 9, 68] choice 1
tau [15, 20, 4, 8, 1, 2, 100, 38, 5, 56] choice 4
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 1
tau [8, 6, 76, 15, 29, 1, 42, 12, 17, 93] choice 6
tau [2, 4, 21, 22, 73, 53, 15, 27, 42, 58] choice 2
tau [8, 9, 3, 5, 43, 56, 78, 82, 49, 18] choice 3
tau [4, 16, 13, 32, 37, 3, 24, 11, 21, 31] choice 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 2
tau [8, 19, 42, 51, 45, 55, 5, 23, 6, 33] choice 5
tau [63, 18, 7, 32, 14, 66, 27, 97, 20, 39] choice 4
tau [21, 13, 31, 14, 10, 17, 22, 7, 3, 36] choice 3
tau [15, 22, 3, 28, 6, 45, 49, 40, 7, 60] choice 3
tau [14, 3, 6, 15, 55, 21, 42, 24, 95, 77] choice 3
tau [4, 14, 1, 22, 10, 5, 6, 30, 17, 97] choice 4
tau [8, 37, 1, 9, 22, 29, 7, 12, 14, 17] choice 1
tau [19, 8, 22, 10, 18, 11, 44, 48, 23, 17] choice 5
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 1
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 5
tau [1, 6, 15, 80, 22, 48, 45, 17, 3, 24] choice 1
tau [18, 52, 7, 4, 2, 10, 97, 44, 69, 64] choice 4
tau [11, 100, 15, 65, 9, 7, 25, 36, 14, 10] choice 3
tau [39, 73, 19, 76, 2, 11, 29, 1, 16, 43] choice 2
tau [3, 12, 2, 6, 31, 1, 38, 21, 15, 100] choice 3
tau [2, 1, 20, 10, 55, 13, 94, 12, 60, 32] choice 2
tau [2, 14, 18, 31, 30, 35, 16, 24, 43, 28] choice 2
tau [19, 8, 22, 24, 12, 18, 10, 55, 56, 17] choice 3
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 4
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 1
tau [10, 19, 26, 50, 42, 45, 53, 3, 51, 52] choice 3
tau [100, 8, 58, 6, 22, 5, 27, 40, 16, 14] choice 6
tau [38, 10, 13, 20, 11, 8, 14, 39, 23, 3] choice 3
tau [37, 26, 22, 8, 45, 7, 31, 89, 55, 28] choice 1
tau [20, 8, 13, 6, 5, 17, 100, 39, 14, 7] choice 6
tau [11, 5, 34, 10, 24, 46, 28, 80, 7, 18] choice 5
tau [39, 26, 9, 13, 67, 10, 17, 6, 35, 59] choice 6
tau [19, 11, 2, 20, 7, 54, 27, 17, 23, 4] choice 2
tau [15, 19, 48, 12, 1, 34, 51, 5, 35, 3] choice 1
tau [27, 48, 18, 43, 17, 35, 12, 50, 33, 4] choice 4
tau [37, 8, 9, 44, 60, 21, 6, 15, 95, 35] choice 6
tau [1, 12, 44, 40, 30, 43, 6, 27, 15, 23] choice 1
tau [8, 19, 100, 20, 13, 41, 9, 10, 35, 29] choice 6
tau [9, 20, 32, 23, 5, 22, 27, 61, 51, 13] choice 5
tau [100, 18, 1, 12, 54, 36, 7, 22, 6, 16] choice 1
tau [35, 27, 47, 26, 43, 7, 30, 10, 12, 28] choice 2
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 0
tau [3, 33, 20, 2, 9, 75, 5, 1, 65, 81] choice 3
tau [21, 8, 11, 61, 9, 17, 38, 12, 24, 33] choice 0
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 5
tau [5, 100, 45, 44, 8, 12, 2, 18, 7, 13] choice 5
tau [1, 4, 3, 7, 70, 40, 44, 16, 17, 21] choice 1
tau [10, 13, 3, 5, 6, 40, 7, 22, 2, 26] choice 3
tau [4, 41, 100, 5, 31, 39, 34, 38, 51, 44] choice 4
tau [4, 6, 79, 100, 36, 59, 5, 29, 54, 1] choice 4
tau [10, 46, 13, 9, 24, 6, 17, 16, 18, 43] choice 6
tau [14, 6, 37, 11, 5, 46, 68, 35, 17, 1] choice 6
tau [8, 20, 1, 18, 3, 12, 9, 100, 35, 56] choice 1
tau [4, 8, 11, 61, 18, 87, 52, 24, 33, 5] choice 4
tau [8, 19, 32, 22, 100, 55, 40, 63, 24, 28] choice 3
tau [1, 15, 10, 34, 24, 59, 76, 3, 5, 14] choice 1
tau [8, 4, 34, 11, 49, 3, 12, 5, 55, 60] choice 4
tau [3, 26, 15, 100, 71, 34, 29, 32, 1, 63] choice 3
tau [7, 79, 6, 14, 63, 24, 89, 73, 13, 4] choice 6
tau [27, 6, 76, 3, 11, 1, 79, 25, 72, 7] choice 6
tau [37, 2, 23, 6, 29, 90, 13, 67, 72, 38] choice 2
tau [37, 4, 8, 17, 7, 14, 2, 51, 12, 33] choice 4
tau [13, 27, 39, 2, 23, 14, 35, 51, 16, 29] choice 2
tau [9, 18, 3, 73, 100, 25, 31, 30, 17, 14] choice 3
tau [19, 2, 23, 18, 34, 6, 21, 40, 76, 58] choice 2
tau [47, 8, 6, 84, 7, 5, 12, 24, 17, 89] choice 6
tau [19, 26, 21, 15, 22, 5, 39, 7, 33, 77] choice 5
tau [27, 7, 46, 2, 100, 49, 50, 29, 4, 57] choice 2
tau [1, 3, 13, 30, 11, 24, 28, 8, 44, 42] choice 1
tau [6, 13, 31, 12, 73, 18, 26, 1, 92, 25] choice 6
tau [1, 29, 92, 15, 17, 5, 6, 78, 30, 68] choice 1
tau [7, 16, 37, 14, 51, 1, 41, 23, 33, 28] choice 1
tau [47, 41, 45, 39, 2, 8, 19, 42, 53, 64] choice 2
tau [1, 13, 3, 7, 10, 5, 100, 26, 45, 4] choice 1
tau [7, 1, 16, 15, 22, 8, 18, 27, 24, 17] choice 1
tau [53, 9, 26, 17, 100, 18, 23, 46, 20, 40] choice 5
tau [10, 12, 15, 5, 45, 6, 30, 48, 4, 38] choice 5
tau [7, 19, 4, 20, 9, 21, 13, 24, 18, 97] choice 4
tau [7, 22, 61, 37, 29, 4, 34, 17, 48, 41] choice 4
tau [1, 43, 13, 22, 29, 78, 35, 12, 61, 9] choice 1
tau [9, 20, 17, 23, 25, 87, 1, 27, 66, 74] choice 1
tau [3, 5, 2, 26, 52, 27, 55, 6, 21, 8] choice 3
tau [10, 3, 13, 73, 100, 79, 7, 61, 26, 12] choice 3
tau [1, 11, 6, 100, 4, 27, 30, 50, 7, 29] choice 1
tau [11, 4, 10, 22, 28, 2, 21, 45, 7, 17] choice 4
tau [13, 27, 9, 25, 17, 26, 29, 18, 51, 36] choice 6
tau [6, 9, 2, 8, 47, 21, 17, 51, 1, 4] choice 6
tau [13, 27, 2, 21, 8, 18, 73, 14, 4, 12] choice 2
tau [16, 61, 43, 6, 34, 49, 23, 10, 39, 99] choice 6
tau [21, 15, 31, 23, 16, 7, 45, 43, 60, 29] choice 1
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 5
tau [26, 13, 10, 2, 7, 67, 3, 29, 28, 17] choice 2
tau [6, 16, 19, 31, 100, 4, 25, 67, 12, 24] choice 6
tau [7, 16, 58, 100, 11, 25, 31, 14, 51, 34] choice 5
tau [14, 53, 19, 13, 6, 20, 46, 16, 49, 25] choice 6
tau [26, 73, 2, 3, 23, 5, 21, 39, 17, 16] choice 2
tau [13, 10, 12, 14, 58, 39, 54, 11, 91, 5] choice 5
tau [26, 10, 11, 54, 29, 42, 23, 35, 3, 4] choice 3
tau [3, 22, 7, 4, 9, 6, 55, 16, 28, 29] choice 3
tau [61, 48, 58, 29, 57, 60, 12, 25, 41, 23] choice 3
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 3
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 5
tau [61, 31, 65, 39, 10, 38, 22, 60, 16, 72] choice 5
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 2
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 1
tau [100, 5, 2, 13, 26, 30, 27, 8, 12, 70] choice 5
tau [9, 2, 3, 22, 53, 55, 77, 7, 23, 39] choice 2
tau [3, 20, 13, 8, 2, 26, 1, 52, 90, 16] choice 3
tau [8, 19, 9, 7, 32, 11, 10, 50, 33, 97] choice 0
tau [13, 27, 15, 7, 20, 3, 10, 44, 51, 4] choice 3
tau [12, 22, 3, 4, 25, 11, 100, 35, 45, 38] choice 3
tau [1, 9, 3, 10, 7, 28, 34, 18, 32, 27] choice 1
tau [1, 24, 11, 52, 26, 36, 38, 46, 79, 49] choice 1
tau [3, 2, 10, 32, 35, 75, 26, 24, 63, 21] choice 3
tau [8, 2, 22, 100, 20, 1, 78, 49, 10, 89] choice 2
tau [6, 9, 4, 35, 36, 15, 11, 10, 32, 7] choice 6
tau [21, 34, 51, 10, 6, 29, 63, 5, 23, 59] choice 6
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 4
tau [10, 8, 34, 14, 47, 23, 18, 54, 1, 30] choice 1
tau [41, 15, 3, 26, 14, 47, 33, 90, 31, 69] choice 3
tau [6, 7, 38, 18, 2, 12, 31, 28, 65, 99] choice 6
tau [8, 25, 5, 18, 79, 20, 93, 24, 10, 39] choice 5
tau [8, 19, 3, 53, 47, 36, 7, 71, 12, 23] choice 3
tau [14, 27, 48, 7, 24, 50, 2, 3, 39, 67] choice 2
tau [9, 7, 29, 56, 11, 4, 13, 49, 16, 46] choice 4
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 4
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 3
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 1
tau [4, 1, 13, 100, 74, 22, 20, 14, 9, 11] choice 4
tau [1, 41, 15, 2, 70, 100, 67, 16, 49, 5] choice 1
tau [61, 11, 5, 29, 52, 27, 34, 28, 21, 35] choice 5
tau [9, 18, 13, 31, 4, 14, 40, 12, 33, 28] choice 4
tau [47, 13, 9, 20, 6, 16, 34, 5, 49, 25] choice 6
tau [38, 3, 2, 5, 100, 93, 53, 23, 22, 84] choice 3
tau [1, 37, 13, 14, 3, 24, 18, 11, 40, 21] choice 1
tau [4, 10, 7, 29, 26, 22, 34, 23, 5, 3] choice 4
tau [45, 11, 1, 10, 2, 6, 8, 52, 27, 4] choice 1
tau [11, 21, 2, 26, 18, 31, 10, 12, 72, 49] choice 2
tau [15, 2, 13, 21, 27, 100, 3, 52, 28, 12] choice 2
tau [32, 91, 8, 27, 17, 82, 3, 22, 38, 75] choice 3
tau [12, 47, 9, 16, 64, 20, 50, 35, 5, 48] choice 5
tau [7, 10, 2, 51, 36, 11, 9, 5, 65, 3] choice 2
tau [32, 24, 73, 72, 26, 10, 94, 3, 6, 45] choice 3
tau [28, 1, 24, 15, 13, 52, 17, 29, 6, 23] choice 1
tau [18, 100, 10, 5, 30, 49, 58, 31, 48, 89] choice 5
tau [36, 27, 11, 2, 100, 5, 12, 55, 29, 43] choice 2
tau [3, 6, 36, 20, 5, 14, 25, 47, 28, 59] choice 3
tau [9, 2, 1, 11, 26, 16, 25, 15, 100, 49] choice 2
tau [13, 10, 33, 100, 1, 44, 49, 16, 29, 40] choice 1
tau [4, 20, 46, 1, 5, 10, 25, 38, 7, 78] choice 4
tau [8, 1, 9, 73, 50, 5, 30, 59, 18, 36] choice 1
tau [22, 9, 30, 8, 2, 39, 33, 4, 35, 23] choice 2
tau [19, 13, 5, 11, 59, 16, 23, 32, 40, 48] choice 5
tau [64, 13, 45, 50, 15, 9, 22, 33, 24, 75] choice 6
tau [47, 22, 41, 37, 15, 91, 63, 12, 50, 6] choice 6
tau [4, 20, 31, 9, 26, 23, 12, 49, 17, 7] choice 4
tau [8, 26, 7, 3, 66, 35, 29, 4, 77, 38] choice 3
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 1
tau [11, 3, 100, 65, 13, 5, 12, 18, 54, 28] choice 3
tau [17, 21, 70, 22, 9, 3, 64, 32, 10, 35] choice 3
tau [14, 1, 17, 77, 9, 16, 43, 44, 27, 13] choice 1
tau [12, 4, 41, 100, 36, 1, 73, 9, 17, 62] choice 4
tau [6, 9, 18, 17, 28, 5, 43, 12, 44, 48] choice 6
tau [19, 1, 50, 11, 21, 26, 12, 9, 51, 28] choice 1
tau [47, 14, 38, 52, 74, 36, 99, 62, 7, 1] choice 1
tau [1, 2, 100, 20, 34, 9, 41, 39, 30, 78] choice 1
tau [61, 1, 36, 9, 2, 16, 5, 15, 24, 63] choice 1
tau [13, 20, 14, 37, 8, 26, 3, 18, 43, 32] choice 3
tau [2, 22, 6, 32, 11, 20, 5, 48, 40, 17] choice 2
tau [19, 4, 6, 32, 11, 9, 47, 36, 56, 24] choice 4
tau [100, 19, 36, 6, 54, 27, 82, 33, 28, 16] choice 6
tau [4, 8, 34, 26, 47, 1, 14, 38, 17, 24] choice 4
tau [9, 99, 30, 8, 3, 20, 51, 4, 24, 40] choice 3
tau [8, 3, 5, 30, 14, 17, 23, 1, 57, 36] choice 3
tau [15, 8, 9, 3, 37, 18, 23, 58, 28, 35] choice 3
tau [6, 100, 9, 1, 25, 3, 5, 21, 7, 48] choice 6
tau [1, 6, 26, 9, 46, 22, 35, 49, 33, 23] choice 1
tau [23, 63, 1, 3, 28, 11, 16, 22, 10, 49] choice 1
tau [23, 19, 58, 3, 1, 62, 52, 41, 5, 7] choice 3
tau [1, 9, 2, 22, 100, 11, 5, 14, 23, 92] choice 1
tau [13, 21, 2, 29, 11, 32, 36, 51, 18, 9] choice 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 2
tau [45, 10, 100, 25, 47, 23, 39, 35, 38, 94] choice 5
tau [19, 12, 21, 28, 22, 70, 17, 15, 42, 1] choice 1
tau [5, 9, 64, 15, 7, 1, 73, 8, 93, 35] choice 5
tau [8, 19, 9, 100, 16, 6, 18, 12, 36, 51] choice 6
tau [100, 10, 21, 6, 38, 8, 35, 2, 56, 45] choice 6
tau [61, 26, 3, 5, 12, 43, 7, 22, 50, 17] choice 3
tau [47, 100, 17, 5, 9, 3, 39, 20, 34, 59] choice 5
tau [100, 63, 24, 14, 26, 5, 13, 42, 12, 1] choice 5
tau [6, 4, 49, 36, 34, 31, 33, 19, 8, 89] choice 6
tau [20, 1, 62, 100, 28, 15, 10, 38, 18, 27] choice 1
tau [22, 5, 8, 10, 45, 14, 36, 34, 28, 33] choice 5
tau [36, 35, 6, 2, 8, 28, 7, 100, 25, 16] choice 6
tau [8, 1, 100, 51, 30, 14, 24, 89, 28, 6] choice 1
tau [22, 48, 8, 11, 16, 6, 19, 1, 2, 51] choice 6
tau [8, 27, 3, 100, 1, 24, 33, 28, 29, 59] choice 3
tau [47, 22, 14, 25, 24, 31, 48, 5, 17, 16] choice 5
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 6
tau [4, 1, 18, 100, 65, 52, 58, 3, 13, 61] choice 4
tau [9, 7, 40, 16, 10, 42, 3, 20, 23, 11] choice 3
tau [78, 18, 47, 5, 62, 14, 15, 51, 10, 80] choice 5
tau [7, 57, 20, 100, 24, 28, 11, 3, 31, 39] choice 3
tau [9, 100, 8, 4, 29, 34, 17, 11, 14, 27] choice 4
tau [8, 1, 22, 2, 21, 36, 39, 17, 41, 33] choice 1
tau [2, 10, 1, 18, 89, 5, 3, 57, 29, 7] choice 2
tau [8, 1, 17, 22, 33, 25, 89, 35, 44, 42] choice 1
tau [13, 1, 20, 52, 26, 22, 10, 100, 44, 35] choice 1
tau [47, 31, 5, 2, 8, 60, 40, 63, 34, 48] choice 5
tau [8, 100, 5, 21, 32, 18, 35, 65, 12, 98] choice 5
tau [9, 5, 15, 14, 18, 8, 30, 22, 11, 29] choice 5
tau [58, 3, 12, 7, 30, 4, 16, 55, 39, 52] choice 3
tau [36, 79, 9, 14, 5, 58, 23, 22, 6, 40] choice 5
tau [11, 8, 2, 20, 15, 21, 32, 23, 52, 12] choice 2
tau [21, 3, 30, 5, 7, 39, 6, 14, 99, 61] choice 3
tau [33, 24, 54, 32, 18, 37, 20, 11, 19, 13] choice 2
tau [21, 22, 1, 100, 70, 43, 30, 9, 17, 4] choice 1
tau [26, 10, 4, 44, 11, 13, 27, 33, 23, 64] choice 4
tau [19, 14, 24, 26, 10, 16, 21, 25, 64, 33] choice 6
tau [2, 6, 71, 5, 69, 7, 21, 10, 19, 4] choice 2
tau [15, 11, 62, 47, 14, 78, 3, 69, 72, 84] choice 3
tau [51, 33, 23, 5, 46, 85, 9, 29, 16, 4] choice 5
tau [47, 8, 17, 33, 23, 43, 57, 18, 21, 65] choice 5
tau [8, 21, 6, 99, 100, 14, 1, 23, 35, 17] choice 6
tau [34, 20, 30, 1, 26, 9, 6, 29, 71, 48] choice 1
tau [19, 31, 22, 17, 56, 72, 11, 5, 100, 24] choice 5
tau [19, 50, 6, 2, 92, 39, 5, 49, 48, 16] choice 6
tau [12, 24, 3, 22, 1, 25, 2, 27, 72, 64] choice 3
tau [4, 27, 2, 30, 32, 37, 19, 72, 47, 5] choice 4
tau [1, 17, 11, 21, 32, 41, 54, 18, 50, 6] choice 1
tau [30, 25, 11, 3, 100, 86, 6, 23, 12, 29] choice 3
tau [8, 2, 73, 47, 6, 33, 100, 3, 5, 20] choice 2
tau [3, 10, 26, 46, 77, 76, 2, 18, 22, 8] choice 3
tau [20, 95, 32, 9, 52, 23, 3, 47, 22, 40] choice 3
tau [2, 19, 51, 16, 27, 98, 47, 11, 18, 52] choice 2
tau [38, 15, 16, 17, 18, 46, 6, 73, 14, 24] choice 6
tau [4, 36, 9, 100, 74, 19, 13, 14, 40, 89] choice 4
tau [10, 50, 9, 15, 12, 82, 5, 23, 100, 52] choice 5
tau [19, 14, 15, 8, 2, 12, 18, 32, 23, 100] choice 2
tau [6, 8, 100, 26, 7, 5, 50, 10, 78, 32] choice 6
tau [6, 12, 11, 3, 36, 1, 4, 26, 61, 32] choice 6
tau [6, 100, 19, 7, 13, 11, 43, 5, 27, 1] choice 6
tau [9, 19, 41, 29, 17, 13, 46, 36, 3, 1] choice 3
tau [32, 45, 12, 64, 50, 1, 20, 3, 7, 17] choice 1
tau [1, 10, 4, 28, 35, 11, 17, 55, 24, 52] choice 1
tau [90, 1, 9, 8, 10, 100, 18, 62, 15, 47] choice 1
tau [1, 100, 17, 3, 32, 16, 10, 12, 9, 8] choice 1
tau [9, 31, 3, 10, 35, 24, 100, 28, 1, 5] choice 3
tau [4, 2, 5, 39, 60, 1, 10, 33, 25, 69] choice 4
tau [8, 9, 100, 48, 7, 20, 18, 16, 17, 64] choice 6
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 5
tau [19, 8, 16, 26, 35, 7, 30, 76, 25, 42] choice 4
tau [20, 3, 52, 15, 53, 68, 1, 4, 71, 23] choice 3
tau [2, 20, 6, 26, 23, 48, 14, 59, 42, 17] choice 2
tau [11, 14, 62, 33, 7, 16, 17, 1, 6, 4] choice 1
tau [14, 20, 25, 10, 16, 6, 51, 5, 12, 13] choice 6
tau [4, 91, 6, 1, 87, 5, 31, 2, 12, 37] choice 4
tau [16, 12, 5, 8, 20, 50, 9, 18, 34, 94] choice 5
tau [41, 14, 6, 26, 20, 5, 22, 45, 63, 1] choice 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 4
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 5
tau [6, 45, 2, 35, 72, 8, 12, 23, 11, 18] choice 6
tau [15, 48, 6, 19, 16, 80, 71, 29, 10, 1] choice 6
tau [19, 2, 100, 9, 29, 34, 22, 25, 3, 51] choice 2
tau [8, 41, 54, 21, 10, 5, 27, 7, 46, 85] choice 5
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 2
tau [100, 9, 33, 21, 80, 27, 64, 30, 15, 3] choice 3
tau [10, 3, 11, 4, 1, 15, 32, 21, 59, 72] choice 3
tau [19, 20, 11, 9, 10, 5, 24, 29, 28, 30] choice 5
tau [53, 15, 1, 73, 28, 17, 18, 31, 68, 43] choice 1
tau [4, 6, 1, 43, 5, 3, 10, 63, 70, 48] choice 4
tau [8, 15, 14, 18, 28, 90, 5, 16, 7, 71] choice 5
tau [8, 16, 1, 100, 11, 7, 5, 57, 12, 37] choice 1
tau [88, 9, 13, 82, 1, 19, 24, 100, 4, 53] choice 1
tau [53, 32, 18, 63, 22, 14, 2, 10, 17, 56] choice 2
tau [4, 19, 14, 36, 7, 40, 62, 39, 55, 11] choice 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 6
tau [17, 5, 10, 28, 13, 21, 7, 16, 15, 2] choice 5
tau [15, 7, 100, 2, 57, 18, 39, 34, 35, 59] choice 2
tau [8, 13, 53, 10, 18, 7, 15, 21, 30, 17] choice 3
tau [25, 1, 8, 13, 41, 46, 19, 10, 30, 18] choice 1
tau [34, 19, 6, 5, 38, 52, 14, 22, 84, 40] choice 6
tau [4, 37, 14, 49, 44, 20, 42, 26, 100, 1] choice 4
tau [32, 27, 8, 5, 75, 43, 65, 30, 7, 4] choice 5
tau [79, 100, 5, 7, 48, 28, 55, 62, 15, 53] choice 5
tau [6, 28, 11, 25, 14, 38, 26, 32, 29, 30] choice 6
tau [9, 7, 8, 47, 2, 4, 3, 5, 44, 28] choice 2
tau [6, 37, 2, 3, 53, 11, 16, 18, 1, 49] choice 6
tau [1, 22, 12, 39, 54, 45, 29, 5, 48, 4] choice 1
tau [41, 3, 44, 61, 100, 52, 25, 18, 5, 55] choice 3
tau [8, 43, 2, 11, 26, 10, 1, 15, 41, 12] choice 2
tau [10, 19, 54, 2, 21, 36, 33, 53, 30, 50] choice 2
tau [36, 67, 8, 6, 4, 95, 5, 28, 29, 93] choice 6
tau [19, 7, 2, 34, 68, 16, 29, 42, 60, 48] choice 2
tau [1, 60, 7, 8, 58, 10, 14, 24, 31, 34] choice 1
tau [19, 8, 11, 15, 2, 9, 3, 30, 42, 97] choice 2
tau [8, 12, 35, 3, 9, 2, 86, 24, 98, 38] choice 3
tau [2, 42, 38, 13, 1, 18, 31, 17, 48, 12] choice 2
tau [9, 5, 10, 15, 8, 33, 14, 73, 44, 6] choice 5
tau [12, 31, 5, 11, 23, 3, 94, 18, 53, 39] choice 5
tau [4, 6, 11, 76, 100, 21, 10, 16, 56, 25] choice 4
tau [100, 17, 48, 14, 22, 56, 15, 40, 16, 1] choice 1
tau [6, 5, 32, 2, 19, 15, 98, 100, 17, 25] choice 6
tau [19, 53, 10, 12, 3, 18, 42, 17, 45, 69] choice 3
tau [64, 13, 2, 38, 7, 77, 51, 20, 52, 6] choice 2
tau [14, 31, 13, 54, 21, 18, 27, 32, 29, 85] choice 4
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 2
tau [4, 8, 22, 5, 27, 34, 18, 12, 24, 48] choice 4
tau [15, 37, 1, 11, 10, 26, 9, 25, 24, 5] choice 1
tau [47, 14, 44, 62, 32, 28, 69, 55, 43, 48] choice 1
tau [1, 48, 21, 14, 39, 15, 46, 23, 50, 60] choice 1
tau [8, 33, 14, 46, 39, 4, 24, 23, 9, 52] choice 4
tau [9, 1, 76, 12, 17, 78, 80, 55, 100, 75] choice 1
tau [27, 26, 41, 72, 3, 40, 36, 66, 4, 7] choice 3
tau [19, 2, 36, 20, 10, 7, 81, 80, 16, 69] choice 2
tau [31, 21, 34, 79, 10, 32, 3, 43, 27, 93] choice 3
tau [9, 19, 26, 15, 5, 50, 38, 85, 21, 4] choice 5
tau [100, 18, 9, 31, 23, 32, 8, 13, 2, 49] choice 2
tau [19, 3, 23, 5, 45, 72, 10, 77, 59, 22] choice 3
tau [2, 6, 11, 21, 38, 17, 23, 31, 4, 39] choice 2
tau [6, 8, 15, 11, 21, 32, 2, 23, 49, 7] choice 6
tau [59, 41, 9, 10, 100, 14, 5, 18, 58, 29] choice 5
tau [6, 41, 10, 13, 15, 21, 12, 24, 70, 5] choice 6
tau [1, 32, 2, 8, 48, 20, 77, 65, 12, 14] choice 1
tau [23, 4, 12, 28, 9, 53, 26, 21, 29, 25] choice 4
tau [1, 8, 38, 10, 7, 11, 14, 20, 55, 42] choice 1
tau [22, 52, 10, 60, 7, 11, 46, 15, 17, 84] choice 2
tau [100, 3, 20, 7, 17, 46, 14, 83, 15, 53] choice 3
tau [8, 6, 22, 19, 26, 20, 36, 12, 24, 28] choice 6
tau [1, 14, 24, 12, 11, 20, 100, 35, 7, 3] choice 1
tau [53, 9, 16, 27, 24, 65, 6, 11, 36, 97] choice 6
tau [19, 10, 6, 100, 26, 25, 13, 31, 59, 28] choice 6
tau [27, 14, 30, 8, 24, 45, 98, 5, 2, 37] choice 5
tau [8, 9, 40, 22, 4, 14, 57, 15, 18, 81] choice 4
tau [100, 16, 6, 49, 87, 19, 64, 8, 42, 29] choice 6
tau [22, 13, 21, 6, 75, 16, 3, 5, 52, 30] choice 6
tau [100, 3, 20, 37, 48, 10, 21, 13, 18, 6] choice 3
emperical probablities from test set: {1: 0.166, 2: 0.188, 3: 0.155, 4: 0.163, 5: 0.143, 6: 0.176, 0: 0.009}
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08918356640241458), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: np.float64(0.00019716221361734676), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08918356640241458), np.float64(0.00019716221361734676), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: np.float64(0.00019716221361734676), 3: np.float64(0.053595332570545884), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08918356640241458), np.float64(0.00019716221361734676), np.float64(0.053595332570545884), 0, 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: np.float64(0.00019716221361734676), 3: np.float64(0.053595332570545884), 4: np.float64(0.0874522184118396), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08918356640241458), np.float64(0.00019716221361734676), np.float64(0.053595332570545884), np.float64(0.0874522184118396), 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: np.float64(0.00019716221361734676), 3: np.float64(0.053595332570545884), 4: np.float64(0.0874522184118396), 5: np.float64(0.05696023130365638), 6: 0, 0: 0} 

err list= [np.float64(0.08918356640241458), np.float64(0.00019716221361734676), np.float64(0.053595332570545884), np.float64(0.0874522184118396), np.float64(0.05696023130365638), 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: np.float64(0.00019716221361734676), 3: np.float64(0.053595332570545884), 4: np.float64(0.0874522184118396), 5: np.float64(0.05696023130365638), 6: np.float64(0.02689232379712747), 0: 0} 

err list= [np.float64(0.08918356640241458), np.float64(0.00019716221361734676), np.float64(0.053595332570545884), np.float64(0.0874522184118396), np.float64(0.05696023130365638), np.float64(0.02689232379712747), 0]
beta is  0.025 

err dic= {1: np.float64(0.08918356640241458), 2: np.float64(0.00019716221361734676), 3: np.float64(0.053595332570545884), 4: np.float64(0.0874522184118396), 5: np.float64(0.05696023130365638), 6: np.float64(0.02689232379712747), 0: np.float64(0.038990734929308546)} 

err list= [np.float64(0.08918356640241458), np.float64(0.00019716221361734676), np.float64(0.053595332570545884), np.float64(0.0874522184118396), np.float64(0.05696023130365638), np.float64(0.02689232379712747), np.float64(0.038990734929308546)]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11526210905564548), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: np.float64(0.008596624443658496), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11526210905564548), np.float64(0.008596624443658496), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: np.float64(0.008596624443658496), 3: np.float64(0.02460488123763438), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11526210905564548), np.float64(0.008596624443658496), np.float64(0.02460488123763438), 0, 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: np.float64(0.008596624443658496), 3: np.float64(0.02460488123763438), 4: np.float64(0.043494482089555475), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11526210905564548), np.float64(0.008596624443658496), np.float64(0.02460488123763438), np.float64(0.043494482089555475), 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: np.float64(0.008596624443658496), 3: np.float64(0.02460488123763438), 4: np.float64(0.043494482089555475), 5: np.float64(0.04579023541629901), 6: 0, 0: 0} 

err list= [np.float64(0.11526210905564548), np.float64(0.008596624443658496), np.float64(0.02460488123763438), np.float64(0.043494482089555475), np.float64(0.04579023541629901), 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: np.float64(0.008596624443658496), 3: np.float64(0.02460488123763438), 4: np.float64(0.043494482089555475), 5: np.float64(0.04579023541629901), 6: np.float64(0.0146132854980639), 0: 0} 

err list= [np.float64(0.11526210905564548), np.float64(0.008596624443658496), np.float64(0.02460488123763438), np.float64(0.043494482089555475), np.float64(0.04579023541629901), np.float64(0.0146132854980639), 0]
beta is  0.05 

err dic= {1: np.float64(0.11526210905564548), 2: np.float64(0.008596624443658496), 3: np.float64(0.02460488123763438), 4: np.float64(0.043494482089555475), 5: np.float64(0.04579023541629901), 6: np.float64(0.0146132854980639), 0: np.float64(0.004644150742247901)} 

err list= [np.float64(0.11526210905564548), np.float64(0.008596624443658496), np.float64(0.02460488123763438), np.float64(0.043494482089555475), np.float64(0.04579023541629901), np.float64(0.0146132854980639), np.float64(0.004644150742247901)]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11374900959589265), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: np.float64(0.047576443653524314), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11374900959589265), np.float64(0.047576443653524314), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: np.float64(0.047576443653524314), 3: np.float64(0.06969689468318216), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11374900959589265), np.float64(0.047576443653524314), np.float64(0.06969689468318216), 0, 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: np.float64(0.047576443653524314), 3: np.float64(0.06969689468318216), 4: np.float64(0.06446534282282271), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.11374900959589265), np.float64(0.047576443653524314), np.float64(0.06969689468318216), np.float64(0.06446534282282271), 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: np.float64(0.047576443653524314), 3: np.float64(0.06969689468318216), 4: np.float64(0.06446534282282271), 5: np.float64(0.10360454859308198), 6: 0, 0: 0} 

err list= [np.float64(0.11374900959589265), np.float64(0.047576443653524314), np.float64(0.06969689468318216), np.float64(0.06446534282282271), np.float64(0.10360454859308198), 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: np.float64(0.047576443653524314), 3: np.float64(0.06969689468318216), 4: np.float64(0.06446534282282271), 5: np.float64(0.10360454859308198), 6: np.float64(0.04453819213765792), 0: 0} 

err list= [np.float64(0.11374900959589265), np.float64(0.047576443653524314), np.float64(0.06969689468318216), np.float64(0.06446534282282271), np.float64(0.10360454859308198), np.float64(0.04453819213765792), 0]
beta is  0.1 

err dic= {1: np.float64(0.11374900959589265), 2: np.float64(0.047576443653524314), 3: np.float64(0.06969689468318216), 4: np.float64(0.06446534282282271), 5: np.float64(0.10360454859308198), 6: np.float64(0.04453819213765792), 0: np.float64(0.008923315108212435)} 

err list= [np.float64(0.11374900959589265), np.float64(0.047576443653524314), np.float64(0.06969689468318216), np.float64(0.06446534282282271), np.float64(0.10360454859308198), np.float64(0.04453819213765792), np.float64(0.008923315108212435)]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.10749816276326715), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: np.float64(0.09763200213349543), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.10749816276326715), np.float64(0.09763200213349543), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: np.float64(0.09763200213349543), 3: np.float64(0.07608167576792552), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.10749816276326715), np.float64(0.09763200213349543), np.float64(0.07608167576792552), 0, 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: np.float64(0.09763200213349543), 3: np.float64(0.07608167576792552), 4: np.float64(0.030385948406018187), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.10749816276326715), np.float64(0.09763200213349543), np.float64(0.07608167576792552), np.float64(0.030385948406018187), 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: np.float64(0.09763200213349543), 3: np.float64(0.07608167576792552), 4: np.float64(0.030385948406018187), 5: np.float64(0.03617753425012385), 6: 0, 0: 0} 

err list= [np.float64(0.10749816276326715), np.float64(0.09763200213349543), np.float64(0.07608167576792552), np.float64(0.030385948406018187), np.float64(0.03617753425012385), 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: np.float64(0.09763200213349543), 3: np.float64(0.07608167576792552), 4: np.float64(0.030385948406018187), 5: np.float64(0.03617753425012385), 6: np.float64(0.12377899782206961), 0: 0} 

err list= [np.float64(0.10749816276326715), np.float64(0.09763200213349543), np.float64(0.07608167576792552), np.float64(0.030385948406018187), np.float64(0.03617753425012385), np.float64(0.12377899782206961), 0]
beta is  0.25 

err dic= {1: np.float64(0.10749816276326715), 2: np.float64(0.09763200213349543), 3: np.float64(0.07608167576792552), 4: np.float64(0.030385948406018187), 5: np.float64(0.03617753425012385), 6: np.float64(0.12377899782206961), 0: np.float64(0.008999999972226662)} 

err list= [np.float64(0.10749816276326715), np.float64(0.09763200213349543), np.float64(0.07608167576792552), np.float64(0.030385948406018187), np.float64(0.03617753425012385), np.float64(0.12377899782206961), np.float64(0.008999999972226662)]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.09283277802682113), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: np.float64(0.16189007536436267), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.09283277802682113), np.float64(0.16189007536436267), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: np.float64(0.16189007536436267), 3: np.float64(0.06792319646120962), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.09283277802682113), np.float64(0.16189007536436267), np.float64(0.06792319646120962), 0, 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: np.float64(0.16189007536436267), 3: np.float64(0.06792319646120962), 4: np.float64(0.03428263460352443), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.09283277802682113), np.float64(0.16189007536436267), np.float64(0.06792319646120962), np.float64(0.03428263460352443), 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: np.float64(0.16189007536436267), 3: np.float64(0.06792319646120962), 4: np.float64(0.03428263460352443), 5: np.float64(0.021135916583801734), 6: 0, 0: 0} 

err list= [np.float64(0.09283277802682113), np.float64(0.16189007536436267), np.float64(0.06792319646120962), np.float64(0.03428263460352443), np.float64(0.021135916583801734), 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: np.float64(0.16189007536436267), 3: np.float64(0.06792319646120962), 4: np.float64(0.03428263460352443), 5: np.float64(0.021135916583801734), 6: np.float64(0.0725619426114246), 0: 0} 

err list= [np.float64(0.09283277802682113), np.float64(0.16189007536436267), np.float64(0.06792319646120962), np.float64(0.03428263460352443), np.float64(0.021135916583801734), np.float64(0.0725619426114246), 0]
beta is  0.5 

err dic= {1: np.float64(0.09283277802682113), 2: np.float64(0.16189007536436267), 3: np.float64(0.06792319646120962), 4: np.float64(0.03428263460352443), 5: np.float64(0.021135916583801734), 6: np.float64(0.0725619426114246), 0: np.float64(0.009)} 

err list= [np.float64(0.09283277802682113), np.float64(0.16189007536436267), np.float64(0.06792319646120962), np.float64(0.03428263460352443), np.float64(0.021135916583801734), np.float64(0.0725619426114246), np.float64(0.009)]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08056128378212508), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: np.float64(0.2530533826881396), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08056128378212508), np.float64(0.2530533826881396), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: np.float64(0.2530533826881396), 3: np.float64(0.05655647044935941), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08056128378212508), np.float64(0.2530533826881396), np.float64(0.05655647044935941), 0, 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: np.float64(0.2530533826881396), 3: np.float64(0.05655647044935941), 4: np.float64(0.0622182764873172), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.08056128378212508), np.float64(0.2530533826881396), np.float64(0.05655647044935941), np.float64(0.0622182764873172), 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: np.float64(0.2530533826881396), 3: np.float64(0.05655647044935941), 4: np.float64(0.0622182764873172), 5: np.float64(0.05649977605459287), 6: 0, 0: 0} 

err list= [np.float64(0.08056128378212508), np.float64(0.2530533826881396), np.float64(0.05655647044935941), np.float64(0.0622182764873172), np.float64(0.05649977605459287), 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: np.float64(0.2530533826881396), 3: np.float64(0.05655647044935941), 4: np.float64(0.0622182764873172), 5: np.float64(0.05649977605459287), 6: np.float64(0.10133051681346371), 0: 0} 

err list= [np.float64(0.08056128378212508), np.float64(0.2530533826881396), np.float64(0.05655647044935941), np.float64(0.0622182764873172), np.float64(0.05649977605459287), np.float64(0.10133051681346371), 0]
beta is  0.75 

err dic= {1: np.float64(0.08056128378212508), 2: np.float64(0.2530533826881396), 3: np.float64(0.05655647044935941), 4: np.float64(0.0622182764873172), 5: np.float64(0.05649977605459287), 6: np.float64(0.10133051681346371), 0: np.float64(0.009)} 

err list= [np.float64(0.08056128378212508), np.float64(0.2530533826881396), np.float64(0.05655647044935941), np.float64(0.0622182764873172), np.float64(0.05649977605459287), np.float64(0.10133051681346371), np.float64(0.009)]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06946018008193626), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: np.float64(0.3375950146335574), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06946018008193626), np.float64(0.3375950146335574), 0, 0, 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: np.float64(0.3375950146335574), 3: np.float64(0.04057023830410553), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06946018008193626), np.float64(0.3375950146335574), np.float64(0.04057023830410553), 0, 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: np.float64(0.3375950146335574), 3: np.float64(0.04057023830410553), 4: np.float64(0.09158079002533229), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06946018008193626), np.float64(0.3375950146335574), np.float64(0.04057023830410553), np.float64(0.09158079002533229), 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: np.float64(0.3375950146335574), 3: np.float64(0.04057023830410553), 4: np.float64(0.09158079002533229), 5: np.float64(0.10755430808450786), 6: 0, 0: 0} 

err list= [np.float64(0.06946018008193626), np.float64(0.3375950146335574), np.float64(0.04057023830410553), np.float64(0.09158079002533229), np.float64(0.10755430808450786), 0, 0]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: np.float64(0.3375950146335574), 3: np.float64(0.04057023830410553), 4: np.float64(0.09158079002533229), 5: np.float64(0.10755430808450786), 6: np.float64(0.10056997474588639), 0: 0} 

err list= [np.float64(0.06946018008193626), np.float64(0.3375950146335574), np.float64(0.04057023830410553), np.float64(0.09158079002533229), np.float64(0.10755430808450786), np.float64(0.10056997474588639), 0]
beta is  1 

err dic= {1: np.float64(0.06946018008193626), 2: np.float64(0.3375950146335574), 3: np.float64(0.04057023830410553), 4: np.float64(0.09158079002533229), 5: np.float64(0.10755430808450786), 6: np.float64(0.10056997474588639), 0: np.float64(0.009)} 

err list= [np.float64(0.06946018008193626), np.float64(0.3375950146335574), np.float64(0.04057023830410553), np.float64(0.09158079002533229), np.float64(0.10755430808450786), np.float64(0.10056997474588639), np.float64(0.009)]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.060144114314288746), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: np.float64(0.3983411954612683), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.060144114314288746), np.float64(0.3983411954612683), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: np.float64(0.3983411954612683), 3: np.float64(0.014390118999005108), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.060144114314288746), np.float64(0.3983411954612683), np.float64(0.014390118999005108), 0, 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: np.float64(0.3983411954612683), 3: np.float64(0.014390118999005108), 4: np.float64(0.11465742285661484), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.060144114314288746), np.float64(0.3983411954612683), np.float64(0.014390118999005108), np.float64(0.11465742285661484), 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: np.float64(0.3983411954612683), 3: np.float64(0.014390118999005108), 4: np.float64(0.11465742285661484), 5: np.float64(0.09889871875223195), 6: 0, 0: 0} 

err list= [np.float64(0.060144114314288746), np.float64(0.3983411954612683), np.float64(0.014390118999005108), np.float64(0.11465742285661484), np.float64(0.09889871875223195), 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: np.float64(0.3983411954612683), 3: np.float64(0.014390118999005108), 4: np.float64(0.11465742285661484), 5: np.float64(0.09889871875223195), 6: np.float64(0.13003105853713787), 0: 0} 

err list= [np.float64(0.060144114314288746), np.float64(0.3983411954612683), np.float64(0.014390118999005108), np.float64(0.11465742285661484), np.float64(0.09889871875223195), np.float64(0.13003105853713787), 0]
beta is  1.25 

err dic= {1: np.float64(0.060144114314288746), 2: np.float64(0.3983411954612683), 3: np.float64(0.014390118999005108), 4: np.float64(0.11465742285661484), 5: np.float64(0.09889871875223195), 6: np.float64(0.13003105853713787), 0: np.float64(0.009)} 

err list= [np.float64(0.060144114314288746), np.float64(0.3983411954612683), np.float64(0.014390118999005108), np.float64(0.11465742285661484), np.float64(0.09889871875223195), np.float64(0.13003105853713787), np.float64(0.009)]
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25]
err_list means for all beta: [np.float64(0.05046736708978711), np.float64(0.03671510978330066), np.float64(0.06465053522776773), np.float64(0.0686506173021609), np.float64(0.06566093480730631), np.float64(0.08845995803928541), np.float64(0.10804721512504653), np.float64(0.11792323270293525)]
