p= 0.1 num clusters= 3
linkage completed in  12.303523063659668
silhouette_score of the clusters -0.00817525267904133
#beta= 0.025 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 11: 1, 100: 1} [8, 1, 2, 3, 5, 7, 11, 100]
learned probs for cluster 2 

{1: np.float64(0.09347667644274692), 2: np.float64(0.09116872907807641), 3: np.float64(0.08891776513687367), 4: np.float64(0.21323815054963524), 5: np.float64(0.08672237769340023), 6: np.float64(0.21323815054963524), 0: np.float64(0.21323815054963524)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 5, 7, 11, 100]
learned probs (dictionary):

probs= {1: np.float64(0.01958336371475548), 2: np.float64(0.019099848741857006), 3: np.float64(0.018628271796175034), 4: np.float64(0.04467339254014858), 5: np.float64(0.018168338126767346), 6: np.float64(0.04467339254014858), 0: np.float64(0.04467339254014858)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 11, 100]
learned probs for cluster 1 

{1: np.float64(0.1009964197681003), 2: np.float64(0.09850280927920248), 3: np.float64(0.09607076625264264), 4: np.float64(0.09369877058235943), 5: np.float64(0.09138533969384391), 6: np.float64(0.08912902761748219), 0: np.float64(0.4302168668063694)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 11, 100]
learned probs (dictionary):

probs= {1: np.float64(0.0939167286640773), 2: np.float64(0.09159791637135004), 3: np.float64(0.08933635575812002), 4: np.float64(0.11363568768876511), 5: np.float64(0.08542794814143645), 6: np.float64(0.11027235686661546), 0: np.float64(0.36131300650963644)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 2, 15: 3, 19: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 19]
learned probs for cluster 3 

{1: np.float64(0.1257980842534629), 2: np.float64(0.16930097241981745), 3: np.float64(0.12269211848657766), 4: np.float64(0.16930097241981745), 5: np.float64(0.11161972311827711), 6: np.float64(0.13198715688220883), 0: np.float64(0.16930097241981745)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 19]
learned probs (dictionary):

probs= {1: np.float64(0.10077272425589102), 2: np.float64(0.10082481936823008), 3: np.float64(0.0960230762156385), 4: np.float64(0.12286259068564516), 5: np.float64(0.09151122305138255), 6: np.float64(0.11746565691669585), 0: np.float64(0.3705399095065165)}
choice probs for this beta: {1: np.float64(0.10077272425589102), 2: np.float64(0.10082481936823008), 3: np.float64(0.0960230762156385), 4: np.float64(0.12286259068564516), 5: np.float64(0.09151122305138255), 6: np.float64(0.11746565691669585), 0: np.float64(0.3705399095065165)}
#beta= 0.05 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 12: 1, 100: 1} [8, 1, 3, 4, 7, 10, 12, 100]
learned probs for cluster 2 

{1: np.float64(0.1334494941781613), 2: np.float64(0.15471483113111603), 3: np.float64(0.12694108554700392), 4: np.float64(0.12075009575037239), 5: np.float64(0.15471483113111603), 6: np.float64(0.15471483113111603), 0: np.float64(0.15471483113111603)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 7, 10, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(0.02795766903032479), 2: np.float64(0.03241275712196881), 3: np.float64(0.026594157422097323), 4: np.float64(0.025297145059703013), 5: np.float64(0.03241275712196881), 6: np.float64(0.03241275712196881), 0: np.float64(0.03241275712196881)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{1: np.float64(0.15107601883596652), 2: np.float64(0.1437079544531955), 3: np.float64(0.1366992348106879), 4: np.float64(0.1300323344586587), 5: np.float64(0.12369058267359433), 6: np.float64(0.1176581217727612), 0: np.float64(0.19713575299513827)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(0.13914961889359614), 2: np.float64(0.1381818115995207), 3: np.float64(0.12720479424276362), 4: np.float64(0.12100094322127582), 5: np.float64(0.12344902596973423), 6: np.float64(0.11900913474672106), 0: np.float64(0.17750467132639058)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 15: 4, 16: 7, 17: 6, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 15, 20, 7, 17, 16]
learned probs for cluster 3 

{1: np.float64(0.17529639034785086), 2: np.float64(0.10678520408507138), 3: np.float64(0.1667470845076384), 4: np.float64(0.10678520408507138), 5: np.float64(0.14504742376297042), 6: np.float64(0.19255348912631062), 0: np.float64(0.10678520408507138)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 5, 8, 15, 20, 7, 17, 16]
learned probs (dictionary):

probs= {1: np.float64(0.14870327216755402), 2: np.float64(0.14400160522215708), 3: np.float64(0.13629251034842993), 4: np.float64(0.1268207368439122), 5: np.float64(0.1313541105648161), 6: np.float64(0.129503299904105), 0: np.float64(0.18332446494902696)}
choice probs for this beta: {1: np.float64(0.14870327216755402), 2: np.float64(0.14400160522215708), 3: np.float64(0.13629251034842993), 4: np.float64(0.1268207368439122), 5: np.float64(0.1313541105648161), 6: np.float64(0.129503299904105), 0: np.float64(0.18332446494902696)}
#beta= 0.1 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
learned probs for cluster 2 

{1: np.float64(0.19254924781228377), 2: np.float64(0.17422576423523306), 3: np.float64(0.15764599066595023), 4: np.float64(0.14264399115789922), 5: np.float64(0.1290696206576579), 6: np.float64(0.10193269273548741), 0: np.float64(0.10193269273548741)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 4, 5, 7, 100]
learned probs (dictionary):

probs= {1: np.float64(0.04033906741667345), 2: np.float64(0.03650029760728132), 3: np.float64(0.03302683504451657), 4: np.float64(0.029883916147579886), 5: np.float64(0.02704008552777933), 6: np.float64(0.021354899128084612), 0: np.float64(0.021354899128084612)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs for cluster 1 

{1: np.float64(0.19862939687758122), 2: np.float64(0.17972731061675057), 3: np.float64(0.16262399568900765), 4: np.float64(0.1471482763699327), 5: np.float64(0.13314526645901179), 6: np.float64(0.12047481912648204), 0: np.float64(0.05825093486123686)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 100]
learned probs (dictionary):

probs= {1: np.float64(0.18653030351857322), 2: np.float64(0.16877959822120975), 3: np.float64(0.15271809587162619), 4: np.float64(0.13818504755585034), 5: np.float64(0.125035001641612), 6: np.float64(0.11002436600517539), 0: np.float64(0.06422758718595493)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 14: 5, 15: 3, 20: 5, 26: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 14, 20, 26]
learned probs for cluster 3 

{1: np.float64(0.2422030851273849), 2: np.float64(0.03164385586490684), 3: np.float64(0.21915441418700643), 4: np.float64(0.03164385586490684), 5: np.float64(0.1535839307429592), 6: np.float64(0.29012700234796723), 0: np.float64(0.03164385586490684)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 14, 20, 26]
learned probs (dictionary):

probs= {1: np.float64(0.1997303716580157), 2: np.float64(0.17050418836584716), 3: np.float64(0.16466201144481804), 4: np.float64(0.13990963770048775), 5: np.float64(0.13340532586710327), 6: np.float64(0.1258362876331396), 0: np.float64(0.06595217733059236)}
choice probs for this beta: {1: np.float64(0.1997303716580157), 2: np.float64(0.17050418836584716), 3: np.float64(0.16466201144481804), 4: np.float64(0.13990963770048775), 5: np.float64(0.13340532586710327), 6: np.float64(0.1258362876331396), 0: np.float64(0.06595217733059236)}
#beta= 0.25 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 5, 6, 7, 13, 14, 100]
learned probs for cluster 2 

{1: np.float64(0.30834552295238565), 2: np.float64(0.24013973473188), 3: np.float64(0.18702101345574754), 4: np.float64(0.002703819229201722), 5: np.float64(0.1456521117301439), 6: np.float64(0.11343397867143984), 0: np.float64(0.002703819229201722)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 5, 6, 7, 13, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.06459838705852479), 2: np.float64(0.050309274426328855), 3: np.float64(0.03918090231897911), 4: np.float64(0.0005664501285177607), 5: np.float64(0.030514117407465145), 6: np.float64(0.023764418531666644), 0: np.float64(0.0005664501285177607)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 12: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 12, 14, 100]
learned probs for cluster 1 

{1: np.float64(0.2840595595063671), 2: np.float64(0.2212258073824771), 3: np.float64(0.1722908320250769), 4: np.float64(0.13418023489715375), 5: np.float64(0.10449967201060839), 6: np.float64(0.0813844263925668), 0: np.float64(0.002359467785747463)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 12, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.27366622285521097), 2: np.float64(0.21313146865983199), 3: np.float64(0.1659869546894357), 4: np.float64(0.09932310301282292), 5: np.float64(0.10742587600727291), 6: np.float64(0.0836633563565958), 0: np.float64(0.0023030184188278934)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 3, 12: 9, 13: 2, 15: 3, 19: 5, 20: 3, 31: 7, 100: 0} [6, 100, 1, 3, 10, 13, 11, 15, 20, 5, 7, 8, 19, 4, 31, 12]
learned probs for cluster 3 

{1: np.float64(0.276781980973464), 2: np.float64(0.0010546675641182792), 3: np.float64(0.2155580235221886), 4: np.float64(0.021229110438801435), 5: np.float64(0.05576866089452358), 6: np.float64(0.42855288904285266), 0: np.float64(0.0010546675641182792)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 11, 15, 20, 5, 7, 8, 19, 4, 31]
learned probs (dictionary):

probs= {1: np.float64(0.28875084081826474), 2: np.float64(0.21318894804207644), 3: np.float64(0.17773486697139498), 4: np.float64(0.10048008953173759), 5: np.float64(0.11046526802602444), 6: np.float64(0.10701948880943127), 0: np.float64(0.0023604978010723396)}
choice probs for this beta: {1: np.float64(0.28875084081826474), 2: np.float64(0.21318894804207644), 3: np.float64(0.17773486697139498), 4: np.float64(0.10048008953173759), 5: np.float64(0.11046526802602444), 6: np.float64(0.10701948880943127), 0: np.float64(0.0023604978010723396)}
#beta= 0.5 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
learned probs for cluster 2 

{1: np.float64(0.428482739865983), 2: np.float64(0.2598879188863912), 3: np.float64(0.15762999089350624), 4: np.float64(0.09560742236713476), 5: np.float64(0.05798883296176265), 6: np.float64(0.00020154751261108013), 0: np.float64(0.00020154751261108013)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 4, 5, 7, 100]
learned probs (dictionary):

probs= {1: np.float64(0.08976713400192343), 2: np.float64(0.05444651900669895), 3: np.float64(0.033023483092189554), 4: np.float64(0.020029754985914732), 5: np.float64(0.012148660505489276), 6: np.float64(4.222420389202128e-05), 0: np.float64(4.222420389202128e-05)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs for cluster 1 

{1: np.float64(0.41407322412743836), 2: np.float64(0.2511481057993521), 3: np.float64(0.15232902629605927), 4: np.float64(0.0923922248127319), 5: np.float64(0.05603871706798423), 6: np.float64(0.03398920003269405), 0: np.float64(2.950186374094928e-05)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(0.3945250269597181), 2: np.float64(0.2392915248750221), 3: np.float64(0.14513764644608917), 4: np.float64(0.08803043244808542), 5: np.float64(0.053393156267525665), 6: np.float64(0.025058275427954843), 0: np.float64(6.393757560535995e-05)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 3, 15: 3, 16: 6, 20: 5, 23: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 20, 16, 23]
learned probs for cluster 3 

{1: np.float64(0.2459885880140752), 2: np.float64(1.3321114451140936e-05), 3: np.float64(0.14919962056995628), 4: np.float64(1.3321114451140936e-05), 5: np.float64(0.022777244476010913), 6: np.float64(0.5819945835966029), 0: np.float64(1.3321114451140936e-05)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 20, 16, 23]
learned probs (dictionary):

probs= {1: np.float64(0.40793140500648517), 2: np.float64(0.23929225087575967), 3: np.float64(0.1532690257671518), 4: np.float64(0.088031158448823), 5: np.float64(0.05463451609146826), 6: np.float64(0.0567769802339697), 0: np.float64(6.466357634294712e-05)}
choice probs for this beta: {1: np.float64(0.40793140500648517), 2: np.float64(0.23929225087575967), 3: np.float64(0.1532690257671518), 4: np.float64(0.088031158448823), 5: np.float64(0.05463451609146826), 6: np.float64(0.0567769802339697), 0: np.float64(6.466357634294712e-05)}
#beta= 0.75 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 14, 100]
learned probs for cluster 2 

{1: np.float64(0.5403379971541709), 2: np.float64(0.25523759703069987), 3: np.float64(0.12056570383929194), 4: np.float64(0.05695120590136046), 5: np.float64(0.026901844806069372), 6: np.float64(2.8256342036950077e-06), 0: np.float64(2.8256342036950077e-06)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 4, 5, 7, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.11320081040379879), 2: np.float64(0.05347227657793162), 3: np.float64(0.02525851495433166), 4: np.float64(0.011931277636335016), 5: np.float64(0.005635936486871533), 6: np.float64(5.91970365674104e-07), 0: np.float64(5.91970365674104e-07)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{1: np.float64(0.5335605930745879), 2: np.float64(0.25203617802909445), 3: np.float64(0.11905346058162403), 4: np.float64(0.05623687276683001), 5: np.float64(0.02656441772580255), 6: np.float64(0.012548142426709654), 0: np.float64(3.353953515305517e-07)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(0.5059014069066955), 2: np.float64(0.23897090360734513), 3: np.float64(0.11288186194240694), 4: np.float64(0.0533216159927219), 5: np.float64(0.02518734793306221), 6: np.float64(0.00923602479642398), 0: np.float64(8.388213444005901e-07)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 13: 3, 17: 6, 20: 6, 24: 9, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 17, 20, 24]
learned probs for cluster 3 

{1: np.float64(0.19457503948871213), 2: np.float64(5.944826366546365e-07), 3: np.float64(0.09191074065272976), 4: np.float64(5.944826366546365e-07), 5: np.float64(0.01049099208310068), 6: np.float64(0.7030214443275478), 0: np.float64(5.944826366546365e-07)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 5, 7, 17, 20, 24]
learned probs (dictionary):

probs= {1: np.float64(0.5165057465588303), 2: np.float64(0.23897093600664882), 3: np.float64(0.11789099730798072), 4: np.float64(0.0533216483920256), 5: np.float64(0.025759107001591196), 6: np.float64(0.04755069351227533), 0: np.float64(8.712206480982677e-07)}
choice probs for this beta: {1: np.float64(0.5165057465588303), 2: np.float64(0.23897093600664882), 3: np.float64(0.11789099730798072), 4: np.float64(0.0533216483920256), 5: np.float64(0.025759107001591196), 6: np.float64(0.04755069351227533), 0: np.float64(8.712206480982677e-07)}
#beta= 1 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 11: 1, 100: 1} [8, 1, 3, 4, 7, 11, 100]
learned probs for cluster 2 

{1: np.float64(0.66524020310147), 2: np.float64(2.828574163327212e-07), 3: np.float64(0.24472819416174563), 4: np.float64(0.09003047130711922), 5: np.float64(2.828574163327212e-07), 6: np.float64(2.828574163327212e-07), 0: np.float64(2.828574163327212e-07)}
cluster label 2 learned center: 
 
sigma= [8, 1, 3, 4, 7, 11, 100]
learned probs (dictionary):

probs= {1: np.float64(0.13936782254975796), 2: np.float64(5.925862872170509e-08), 3: np.float64(0.05127055667688571), 4: np.float64(0.018861383738841477), 5: np.float64(5.925862872170509e-08), 6: np.float64(5.925862872170509e-08), 0: np.float64(5.925862872170509e-08)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 2, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs for cluster 1 

{1: np.float64(0.636408638661047), 2: np.float64(0.2341216543473044), 3: np.float64(6.2049627272961526e-09), 4: np.float64(0.0861285433674199), 5: np.float64(0.031684920402916775), 6: np.float64(0.011656230811386656), 0: np.float64(6.2049627272961526e-09)}
cluster label 1 learned center: 
 
sigma= [1, 2, 4, 5, 6, 7, 9, 11, 12, 100]
learned probs (dictionary):

probs= {1: np.float64(0.6077645806042886), 2: np.float64(0.17231359685824477), 3: np.float64(0.05127056124373828), 4: np.float64(0.08225199165726252), 5: np.float64(0.023320160675175467), 6: np.float64(0.0085790451358093), 0: np.float64(6.382548128899506e-08)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 1, 13: 2, 15: 3, 17: 6, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 17]
learned probs for cluster 3 

{1: np.float64(0.07794335049430202), 2: np.float64(1.5823398127291407e-08), 3: np.float64(0.0286737562228737), 4: np.float64(1.5823398127291407e-08), 5: np.float64(0.0014931527598748685), 6: np.float64(0.8918896930527549), 0: np.float64(1.5823398127291407e-08)}
cluster label 3 learned center: 
 
sigma= [6, 100, 10, 1, 3, 13, 15, 5, 7, 17]
learned probs (dictionary):

probs= {1: np.float64(0.6120124932062281), 2: np.float64(0.17231359772061997), 3: np.float64(0.05283328095788489), 4: np.float64(0.08225199251963772), 5: np.float64(0.023401537500588647), 6: np.float64(0.057187033407184444), 0: np.float64(6.468785648693244e-08)}
choice probs for this beta: {1: np.float64(0.6120124932062281), 2: np.float64(0.17231359772061997), 3: np.float64(0.05283328095788489), 4: np.float64(0.08225199251963772), 5: np.float64(0.023401537500588647), 6: np.float64(0.057187033407184444), 0: np.float64(6.468785648693244e-08)}
#beta= 1.25 

#cluster  2 with weight 0.2095
Learned cluster center of cluster 2:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 10: 1, 13: 1, 14: 1, 100: 1} [8, 1, 2, 3, 7, 10, 13, 14, 100]
learned probs for cluster 2 

{1: np.float64(0.7306791273439033), 2: np.float64(0.20934307494964605), 3: np.float64(0.05997779516253588), 4: np.float64(6.359786864904995e-10), 5: np.float64(6.359786864904995e-10), 6: np.float64(6.359786864904995e-10), 0: np.float64(6.359786864904995e-10)}
cluster label 2 learned center: 
 
sigma= [8, 1, 2, 3, 7, 10, 13, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.15307727717854774), 2: np.float64(0.04385737420195084), 3: np.float64(0.012565348086551267), 4: np.float64(1.3323753481975965e-10), 5: np.float64(1.3323753481975965e-10), 6: np.float64(1.3323753481975965e-10), 0: np.float64(1.3323753481975965e-10)}
#cluster  1 with weight 0.736
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 100]
learned probs for cluster 1 

{1: np.float64(0.7138900445613706), 2: np.float64(0.20453292219756752), 3: np.float64(0.05859966332543515), 4: np.float64(0.01678908463712932), 5: np.float64(0.004810153283429275), 6: np.float64(0.0013781319893352811), 0: np.float64(5.7323838755105325e-12)}
cluster label 1 learned center: 
 
sigma= [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 100]
learned probs (dictionary):

probs= {1: np.float64(0.6785003499757165), 2: np.float64(0.19439360493936053), 3: np.float64(0.05569470029407153), 4: np.float64(0.012356766426164716), 5: np.float64(0.003540272949841481), 6: np.float64(0.0010143052773883016), 0: np.float64(1.374565693521354e-10)}
#cluster  3 with weight 0.0545
Learned cluster center of cluster 3:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 7, 4]
learned probs for cluster 3 

{1: np.float64(0.10201741037295259), 2: np.float64(3.203826871921763e-11), 3: np.float64(0.02922847743510543), 4: np.float64(4.8330724418872185e-06), 5: np.float64(0.00020543738372917346), 6: np.float64(0.8685438416716941), 0: np.float64(3.203826871921763e-11)}
cluster label 3 learned center: 
 
sigma= [6, 100, 1, 3, 10, 13, 15, 5, 8, 7, 4]
learned probs (dictionary):

probs= {1: np.float64(0.6840602988410425), 2: np.float64(0.1943936049411066), 3: np.float64(0.05728765231428477), 4: np.float64(0.012357029828612798), 5: np.float64(0.003551469287254721), 6: np.float64(0.048349944648495624), 0: np.float64(1.3920265499733277e-10)}
choice probs for this beta: {1: np.float64(0.6840602988410425), 2: np.float64(0.1943936049411066), 3: np.float64(0.05728765231428477), 4: np.float64(0.012357029828612798), 5: np.float64(0.003551469287254721), 6: np.float64(0.048349944648495624), 0: np.float64(1.3920265499733277e-10)}
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 3
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 6
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 1
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 2
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 3
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 4
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 4
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 6
tau [22, 3, 47, 5, 7, 18, 79, 10, 34, 1] choice 3
tau [8, 27, 37, 23, 80, 21, 74, 40, 17, 46] choice 5
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 1
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 4
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 3
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 0
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 0
tau [61, 100, 3, 30, 74, 67, 62, 26, 4, 32] choice 3
tau [19, 13, 1, 23, 50, 16, 17, 33, 24, 64] choice 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 4
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 5
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 6
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 1
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 5
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 5
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 4
tau [20, 11, 26, 55, 52, 38, 69, 78, 35, 24] choice 2
tau [8, 11, 2, 32, 26, 20, 31, 28, 1, 18] choice 2
tau [1, 11, 81, 13, 27, 98, 57, 70, 14, 64] choice 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 4
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 1
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 2
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 6
tau [8, 27, 24, 21, 23, 89, 1, 84, 42, 99] choice 1
tau [25, 3, 9, 34, 69, 17, 83, 7, 78, 38] choice 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 5
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 3
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 3
tau [16, 37, 39, 32, 36, 23, 14, 51, 24, 74] choice 2
tau [6, 10, 19, 4, 2, 18, 3, 14, 52, 12] choice 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 2
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 1
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 4
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 1
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 3
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 4
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 2
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 2
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 6
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 5
tau [8, 53, 15, 94, 17, 51, 39, 24, 18, 30] choice 3
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 5
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 5
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 4
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 0
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 2
tau [24, 46, 9, 92, 28, 19, 17, 70, 23, 13] choice 5
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 2
tau [25, 37, 2, 27, 3, 23, 60, 16, 40, 45] choice 2
tau [16, 36, 23, 18, 19, 3, 28, 52, 5, 65] choice 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 4
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 0
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 1
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 1
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 0
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 2
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 0
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 0
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 1
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 5
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 0
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 0
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 3
tau [2, 20, 36, 15, 76, 4, 16, 7, 44, 35] choice 2
tau [32, 56, 11, 37, 7, 12, 9, 60, 10, 28] choice 2
tau [8, 11, 24, 5, 50, 38, 3, 23, 87, 17] choice 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 4
tau [4, 6, 2, 19, 44, 26, 74, 25, 34, 51] choice 4
tau [16, 1, 35, 49, 4, 9, 31, 56, 18, 6] choice 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 2
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 0
tau [43, 34, 54, 20, 100, 74, 15, 56, 28, 33] choice 4
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 1
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 6
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 0
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 1
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 0
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 0
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 6
tau [20, 2, 5, 85, 83, 24, 39, 54, 16, 4] choice 2
tau [100, 11, 15, 8, 12, 96, 46, 45, 70, 58] choice 0
tau [22, 19, 8, 31, 6, 3, 26, 78, 67, 1] choice 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 1
tau [45, 30, 2, 26, 16, 21, 25, 12, 38, 28] choice 2
tau [11, 36, 65, 20, 9, 8, 67, 100, 21, 32] choice 5
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 5
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 3
tau [15, 35, 19, 76, 12, 11, 17, 25, 27, 21] choice 6
tau [12, 13, 18, 6, 5, 11, 7, 22, 25, 84] choice 6
tau [7, 15, 22, 10, 14, 70, 82, 55, 90, 1] choice 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 5
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 3
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 3
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 3
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 0
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 4
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 0
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 0
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 1
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 3
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 5
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 3
tau [9, 7, 52, 24, 26, 27, 13, 20, 23, 16] choice 6
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 2
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 1
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: 0.168, 2: 0.185, 3: 0.157, 4: 0.166, 5: 0.139, 6: 0.168, 0: 0.017}
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06722727574410899), 0, 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: np.float64(0.08417518063176992), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06722727574410899), np.float64(0.08417518063176992), 0, 0, 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: np.float64(0.08417518063176992), 3: np.float64(0.060976923784361495), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06722727574410899), np.float64(0.08417518063176992), np.float64(0.060976923784361495), 0, 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: np.float64(0.08417518063176992), 3: np.float64(0.060976923784361495), 4: np.float64(0.04313740931435485), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.06722727574410899), np.float64(0.08417518063176992), np.float64(0.060976923784361495), np.float64(0.04313740931435485), 0, 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: np.float64(0.08417518063176992), 3: np.float64(0.060976923784361495), 4: np.float64(0.04313740931435485), 5: np.float64(0.04748877694861746), 6: 0, 0: 0} 

err list= [np.float64(0.06722727574410899), np.float64(0.08417518063176992), np.float64(0.060976923784361495), np.float64(0.04313740931435485), np.float64(0.04748877694861746), 0, 0]
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: np.float64(0.08417518063176992), 3: np.float64(0.060976923784361495), 4: np.float64(0.04313740931435485), 5: np.float64(0.04748877694861746), 6: np.float64(0.050534343083304165), 0: 0} 

err list= [np.float64(0.06722727574410899), np.float64(0.08417518063176992), np.float64(0.060976923784361495), np.float64(0.04313740931435485), np.float64(0.04748877694861746), np.float64(0.050534343083304165), 0]
beta is  0.025 

err dic= {1: np.float64(0.06722727574410899), 2: np.float64(0.08417518063176992), 3: np.float64(0.060976923784361495), 4: np.float64(0.04313740931435485), 5: np.float64(0.04748877694861746), 6: np.float64(0.050534343083304165), 0: np.float64(0.3535399095065165)} 

err list= [np.float64(0.06722727574410899), np.float64(0.08417518063176992), np.float64(0.060976923784361495), np.float64(0.04313740931435485), np.float64(0.04748877694861746), np.float64(0.050534343083304165), np.float64(0.3535399095065165)]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.019296727832445987), 0, 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: np.float64(0.04099839477784292), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.019296727832445987), np.float64(0.04099839477784292), 0, 0, 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: np.float64(0.04099839477784292), 3: np.float64(0.02070748965157007), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.019296727832445987), np.float64(0.04099839477784292), np.float64(0.02070748965157007), 0, 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: np.float64(0.04099839477784292), 3: np.float64(0.02070748965157007), 4: np.float64(0.0391792631560878), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.019296727832445987), np.float64(0.04099839477784292), np.float64(0.02070748965157007), np.float64(0.0391792631560878), 0, 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: np.float64(0.04099839477784292), 3: np.float64(0.02070748965157007), 4: np.float64(0.0391792631560878), 5: np.float64(0.007645889435183906), 6: 0, 0: 0} 

err list= [np.float64(0.019296727832445987), np.float64(0.04099839477784292), np.float64(0.02070748965157007), np.float64(0.0391792631560878), np.float64(0.007645889435183906), 0, 0]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: np.float64(0.04099839477784292), 3: np.float64(0.02070748965157007), 4: np.float64(0.0391792631560878), 5: np.float64(0.007645889435183906), 6: np.float64(0.03849670009589501), 0: 0} 

err list= [np.float64(0.019296727832445987), np.float64(0.04099839477784292), np.float64(0.02070748965157007), np.float64(0.0391792631560878), np.float64(0.007645889435183906), np.float64(0.03849670009589501), 0]
beta is  0.05 

err dic= {1: np.float64(0.019296727832445987), 2: np.float64(0.04099839477784292), 3: np.float64(0.02070748965157007), 4: np.float64(0.0391792631560878), 5: np.float64(0.007645889435183906), 6: np.float64(0.03849670009589501), 0: np.float64(0.16632446494902697)} 

err list= [np.float64(0.019296727832445987), np.float64(0.04099839477784292), np.float64(0.02070748965157007), np.float64(0.0391792631560878), np.float64(0.007645889435183906), np.float64(0.03849670009589501), np.float64(0.16632446494902697)]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.03173037165801568), 0, 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: np.float64(0.014495811634152839), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.03173037165801568), np.float64(0.014495811634152839), 0, 0, 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: np.float64(0.014495811634152839), 3: np.float64(0.00766201144481804), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.03173037165801568), np.float64(0.014495811634152839), np.float64(0.00766201144481804), 0, 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: np.float64(0.014495811634152839), 3: np.float64(0.00766201144481804), 4: np.float64(0.026090362299512254), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.03173037165801568), np.float64(0.014495811634152839), np.float64(0.00766201144481804), np.float64(0.026090362299512254), 0, 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: np.float64(0.014495811634152839), 3: np.float64(0.00766201144481804), 4: np.float64(0.026090362299512254), 5: np.float64(0.005594674132896743), 6: 0, 0: 0} 

err list= [np.float64(0.03173037165801568), np.float64(0.014495811634152839), np.float64(0.00766201144481804), np.float64(0.026090362299512254), np.float64(0.005594674132896743), 0, 0]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: np.float64(0.014495811634152839), 3: np.float64(0.00766201144481804), 4: np.float64(0.026090362299512254), 5: np.float64(0.005594674132896743), 6: np.float64(0.04216371236686042), 0: 0} 

err list= [np.float64(0.03173037165801568), np.float64(0.014495811634152839), np.float64(0.00766201144481804), np.float64(0.026090362299512254), np.float64(0.005594674132896743), np.float64(0.04216371236686042), 0]
beta is  0.1 

err dic= {1: np.float64(0.03173037165801568), 2: np.float64(0.014495811634152839), 3: np.float64(0.00766201144481804), 4: np.float64(0.026090362299512254), 5: np.float64(0.005594674132896743), 6: np.float64(0.04216371236686042), 0: np.float64(0.04895217733059236)} 

err list= [np.float64(0.03173037165801568), np.float64(0.014495811634152839), np.float64(0.00766201144481804), np.float64(0.026090362299512254), np.float64(0.005594674132896743), np.float64(0.04216371236686042), np.float64(0.04895217733059236)]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.12075084081826473), 0, 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: np.float64(0.028188948042076445), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.12075084081826473), np.float64(0.028188948042076445), 0, 0, 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: np.float64(0.028188948042076445), 3: np.float64(0.020734866971394983), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.12075084081826473), np.float64(0.028188948042076445), np.float64(0.020734866971394983), 0, 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: np.float64(0.028188948042076445), 3: np.float64(0.020734866971394983), 4: np.float64(0.06551991046826242), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.12075084081826473), np.float64(0.028188948042076445), np.float64(0.020734866971394983), np.float64(0.06551991046826242), 0, 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: np.float64(0.028188948042076445), 3: np.float64(0.020734866971394983), 4: np.float64(0.06551991046826242), 5: np.float64(0.028534731973975574), 6: 0, 0: 0} 

err list= [np.float64(0.12075084081826473), np.float64(0.028188948042076445), np.float64(0.020734866971394983), np.float64(0.06551991046826242), np.float64(0.028534731973975574), 0, 0]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: np.float64(0.028188948042076445), 3: np.float64(0.020734866971394983), 4: np.float64(0.06551991046826242), 5: np.float64(0.028534731973975574), 6: np.float64(0.06098051119056874), 0: 0} 

err list= [np.float64(0.12075084081826473), np.float64(0.028188948042076445), np.float64(0.020734866971394983), np.float64(0.06551991046826242), np.float64(0.028534731973975574), np.float64(0.06098051119056874), 0]
beta is  0.25 

err dic= {1: np.float64(0.12075084081826473), 2: np.float64(0.028188948042076445), 3: np.float64(0.020734866971394983), 4: np.float64(0.06551991046826242), 5: np.float64(0.028534731973975574), 6: np.float64(0.06098051119056874), 0: np.float64(0.014639502198927661)} 

err list= [np.float64(0.12075084081826473), np.float64(0.028188948042076445), np.float64(0.020734866971394983), np.float64(0.06551991046826242), np.float64(0.028534731973975574), np.float64(0.06098051119056874), np.float64(0.014639502198927661)]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.23993140500648516), 0, 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: np.float64(0.05429225087575967), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.23993140500648516), np.float64(0.05429225087575967), 0, 0, 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: np.float64(0.05429225087575967), 3: np.float64(0.003730974232848211), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.23993140500648516), np.float64(0.05429225087575967), np.float64(0.003730974232848211), 0, 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: np.float64(0.05429225087575967), 3: np.float64(0.003730974232848211), 4: np.float64(0.077968841551177), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.23993140500648516), np.float64(0.05429225087575967), np.float64(0.003730974232848211), np.float64(0.077968841551177), 0, 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: np.float64(0.05429225087575967), 3: np.float64(0.003730974232848211), 4: np.float64(0.077968841551177), 5: np.float64(0.08436548390853175), 6: 0, 0: 0} 

err list= [np.float64(0.23993140500648516), np.float64(0.05429225087575967), np.float64(0.003730974232848211), np.float64(0.077968841551177), np.float64(0.08436548390853175), 0, 0]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: np.float64(0.05429225087575967), 3: np.float64(0.003730974232848211), 4: np.float64(0.077968841551177), 5: np.float64(0.08436548390853175), 6: np.float64(0.1112230197660303), 0: 0} 

err list= [np.float64(0.23993140500648516), np.float64(0.05429225087575967), np.float64(0.003730974232848211), np.float64(0.077968841551177), np.float64(0.08436548390853175), np.float64(0.1112230197660303), 0]
beta is  0.5 

err dic= {1: np.float64(0.23993140500648516), 2: np.float64(0.05429225087575967), 3: np.float64(0.003730974232848211), 4: np.float64(0.077968841551177), 5: np.float64(0.08436548390853175), 6: np.float64(0.1112230197660303), 0: np.float64(0.016935336423657053)} 

err list= [np.float64(0.23993140500648516), np.float64(0.05429225087575967), np.float64(0.003730974232848211), np.float64(0.077968841551177), np.float64(0.08436548390853175), np.float64(0.1112230197660303), np.float64(0.016935336423657053)]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.34850574655883026), 0, 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: np.float64(0.05397093600664882), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.34850574655883026), np.float64(0.05397093600664882), 0, 0, 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: np.float64(0.05397093600664882), 3: np.float64(0.03910900269201928), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.34850574655883026), np.float64(0.05397093600664882), np.float64(0.03910900269201928), 0, 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: np.float64(0.05397093600664882), 3: np.float64(0.03910900269201928), 4: np.float64(0.1126783516079744), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.34850574655883026), np.float64(0.05397093600664882), np.float64(0.03910900269201928), np.float64(0.1126783516079744), 0, 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: np.float64(0.05397093600664882), 3: np.float64(0.03910900269201928), 4: np.float64(0.1126783516079744), 5: np.float64(0.11324089299840881), 6: 0, 0: 0} 

err list= [np.float64(0.34850574655883026), np.float64(0.05397093600664882), np.float64(0.03910900269201928), np.float64(0.1126783516079744), np.float64(0.11324089299840881), 0, 0]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: np.float64(0.05397093600664882), 3: np.float64(0.03910900269201928), 4: np.float64(0.1126783516079744), 5: np.float64(0.11324089299840881), 6: np.float64(0.12044930648772467), 0: 0} 

err list= [np.float64(0.34850574655883026), np.float64(0.05397093600664882), np.float64(0.03910900269201928), np.float64(0.1126783516079744), np.float64(0.11324089299840881), np.float64(0.12044930648772467), 0]
beta is  0.75 

err dic= {1: np.float64(0.34850574655883026), 2: np.float64(0.05397093600664882), 3: np.float64(0.03910900269201928), 4: np.float64(0.1126783516079744), 5: np.float64(0.11324089299840881), 6: np.float64(0.12044930648772467), 0: np.float64(0.0169991287793519)} 

err list= [np.float64(0.34850574655883026), np.float64(0.05397093600664882), np.float64(0.03910900269201928), np.float64(0.1126783516079744), np.float64(0.11324089299840881), np.float64(0.12044930648772467), np.float64(0.0169991287793519)]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.44401249320622804), 0, 0, 0, 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: np.float64(0.012686402279380032), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.44401249320622804), np.float64(0.012686402279380032), 0, 0, 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: np.float64(0.012686402279380032), 3: np.float64(0.10416671904211511), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.44401249320622804), np.float64(0.012686402279380032), np.float64(0.10416671904211511), 0, 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: np.float64(0.012686402279380032), 3: np.float64(0.10416671904211511), 4: np.float64(0.08374800748036229), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.44401249320622804), np.float64(0.012686402279380032), np.float64(0.10416671904211511), np.float64(0.08374800748036229), 0, 0, 0]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: np.float64(0.012686402279380032), 3: np.float64(0.10416671904211511), 4: np.float64(0.08374800748036229), 5: np.float64(0.11559846249941136), 6: 0, 0: 0} 

err list= [np.float64(0.44401249320622804), np.float64(0.012686402279380032), np.float64(0.10416671904211511), np.float64(0.08374800748036229), np.float64(0.11559846249941136), 0, 0]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: np.float64(0.012686402279380032), 3: np.float64(0.10416671904211511), 4: np.float64(0.08374800748036229), 5: np.float64(0.11559846249941136), 6: np.float64(0.11081296659281556), 0: 0} 

err list= [np.float64(0.44401249320622804), np.float64(0.012686402279380032), np.float64(0.10416671904211511), np.float64(0.08374800748036229), np.float64(0.11559846249941136), np.float64(0.11081296659281556), 0]
beta is  1 

err dic= {1: np.float64(0.44401249320622804), 2: np.float64(0.012686402279380032), 3: np.float64(0.10416671904211511), 4: np.float64(0.08374800748036229), 5: np.float64(0.11559846249941136), 6: np.float64(0.11081296659281556), 0: np.float64(0.016999935312143513)} 

err list= [np.float64(0.44401249320622804), np.float64(0.012686402279380032), np.float64(0.10416671904211511), np.float64(0.08374800748036229), np.float64(0.11559846249941136), np.float64(0.11081296659281556), np.float64(0.016999935312143513)]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.5160602988410424), 0, 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: np.float64(0.00939360494110661), 3: 0, 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.5160602988410424), np.float64(0.00939360494110661), 0, 0, 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: np.float64(0.00939360494110661), 3: np.float64(0.09971234768571523), 4: 0, 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.5160602988410424), np.float64(0.00939360494110661), np.float64(0.09971234768571523), 0, 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: np.float64(0.00939360494110661), 3: np.float64(0.09971234768571523), 4: np.float64(0.1536429701713872), 5: 0, 6: 0, 0: 0} 

err list= [np.float64(0.5160602988410424), np.float64(0.00939360494110661), np.float64(0.09971234768571523), np.float64(0.1536429701713872), 0, 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: np.float64(0.00939360494110661), 3: np.float64(0.09971234768571523), 4: np.float64(0.1536429701713872), 5: np.float64(0.1354485307127453), 6: 0, 0: 0} 

err list= [np.float64(0.5160602988410424), np.float64(0.00939360494110661), np.float64(0.09971234768571523), np.float64(0.1536429701713872), np.float64(0.1354485307127453), 0, 0]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: np.float64(0.00939360494110661), 3: np.float64(0.09971234768571523), 4: np.float64(0.1536429701713872), 5: np.float64(0.1354485307127453), 6: np.float64(0.11965005535150439), 0: 0} 

err list= [np.float64(0.5160602988410424), np.float64(0.00939360494110661), np.float64(0.09971234768571523), np.float64(0.1536429701713872), np.float64(0.1354485307127453), np.float64(0.11965005535150439), 0]
beta is  1.25 

err dic= {1: np.float64(0.5160602988410424), 2: np.float64(0.00939360494110661), 3: np.float64(0.09971234768571523), 4: np.float64(0.1536429701713872), 5: np.float64(0.1354485307127453), 6: np.float64(0.11965005535150439), 0: np.float64(0.016999999860797345)} 

err list= [np.float64(0.5160602988410424), np.float64(0.00939360494110661), np.float64(0.09971234768571523), np.float64(0.1536429701713872), np.float64(0.1354485307127453), np.float64(0.11965005535150439), np.float64(0.016999999860797345)]
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(0.10101140271614763), np.float64(0.04752127569972181), np.float64(0.025241302980978337), np.float64(0.04847847309478152), np.float64(0.0840639016806413), np.float64(0.11499333787585117), np.float64(0.12686071234463653), np.float64(0.15012968679489977)]
