Created: Sept-Dec., 2003. This version: Dec. 1, 2003 This is SMCper, a Maple package to implement Doron Zeilberger's Symbolic Moment Calculus applied to patterns in permutations as it is described in his article Symbolic Moment Calculus: I. Foundations and Permutation-Patterns Written by Doron Zeilberger, zeilberg@math.rutgers.edu `` Please report bugs to zeilberg@math.rutgers.edu `` The most current version of this package and paper are available from http://www.math.rutgers.edu/~zeilberg/ For a list of the MAIN procedures type ezra();, for help with a specific procedure, type ezra(procedure_name); For a list of the supporting procedures type ezra1();, for help with a specific supporting procedure, type ezra1(procedure_name); Warning, the protected name Chi has been redefined and unprotected The list of Asymtotic Correlations of patterns of size 2, and , 3, are [[{{[1, 2], [3, 2, 1]}}, -5/26*26^(1/2), -.9805806757], [{{[1, 2], [2, 3, 1]}}, -5/28*14^(1/2), -.6681531049], [{{[1, 2], [1, 3, 2]}}, 5/28*14^(1/2), .66815310\ 49], [{{[1, 2], [1, 2, 3]}}, 5/26*26^(1/2), .9805806757]] The list of Asymtotic Correlations of patterns of size 2, and , 4, are [[{{[1, 2], [4, 3, 2, 1]}}, -21/491*491^(1/2), -.9477167331], [{{[1, 2], [4, 2, 3, 1]}}, -84/1735*347^(1/2), -.9018712535], [{{[1, 2], [3, 4, 2, 1]}}, -84/1795 *359^(1/2), -.8866700874], [{{[1, 2], [3, 4, 1, 2]}}, -63/1175*235^(1/2), -.821\ 9333723], [{{[1, 2], [2, 4, 3, 1]}}, -42/1195*239^(1/2), -.5433508308], [{{[1, 2], [2, 3, 4, 1]}}, -21/1315*263^(1/2), -.2589830947], [{{[1, 2], [2, 4, 1, 3]} }, 0, 0.], [{{[1, 2], [1, 4, 3, 2]}}, 21/1315*263^(1/2), .2589830947], [{{[1, 2 ], [1, 3, 4, 2]}}, 42/1195*239^(1/2), .5433508308], [{{[1, 2], [2, 1, 4, 3]}}, 63/1175*235^(1/2), .8219333723], [{{[1, 2], [1, 2, 4, 3]}}, 84/1795*359^(1/2), .8866700874], [{{[1, 2], [1, 3, 2, 4]}}, 84/1735*347^(1/2), .9018712535], [{{[1 , 2], [1, 2, 3, 4]}}, 21/491*491^(1/2), .9477167331]] The list of Asymtotic Correlations of patterns of size 2, and , 5, are [[{{[1, 2], [4, 5, 3, 1, 2]}}, -168/6605*1321^(1/2), -.9244594551], [{{[1, 2], [4, 5, 3, 2, 1]}}, -63/5675*6810^(1/2), -.9161112992], [{{[1, 2], [5, 4, 3, 2, 1]}}, -42/4217*8434^(1/2), -.9146658988], [{{[1, 2], [4, 5, 2, 3, 1]}}, -168/ 13585*5434^(1/2), -.9116107883], [{{[1, 2], [5, 3, 4, 2, 1]}}, -63/5855*7026^(1 /2), -.9019193881], [{{[1, 2], [5, 2, 4, 3, 1]}}, -49/4355*5226^(1/2), -.813378\ 3779], [{{[1, 2], [3, 5, 4, 2, 1]}}, -147/13735*5494^(1/2), -.7932918611], [{{[ 1, 2], [3, 5, 4, 1, 2]}}, -21/65*6^(1/2), -.7913736093], [{{[1, 2], [5, 2, 3, 4 , 1]}}, -126/12085*4834^(1/2), -.7248985207], [{{[1, 2], [3, 5, 2, 4, 1]}}, -21 /1727*3454^(1/2), -.7146413212], [{{[1, 2], [3, 4, 5, 2, 1]}}, -6/95*114^(1/2), -.6743417842], [{{[1, 2], [3, 4, 5, 1, 2]}}, -21/1051*1051^(1/2), -.6477656832] , [{{[1, 2], [3, 5, 1, 4, 2]}}, -63/2405*481^(1/2), -.5745105484], [{{[1, 2], [ 2, 5, 4, 3, 1]}}, -84/10735*4294^(1/2), -.5127530559], [{{[1, 2], [2, 5, 3, 4, 1]}}, -21/275*30^(1/2), -.4182608621], [{{[1, 2], [2, 4, 5, 3, 1]}}, -63/935*34 ^(1/2), -.3928876678], [{{[1, 2], [2, 5, 4, 1, 3]}}, -7/235*141^(1/2), -.353703\ 8069], [{{[1, 2], [3, 2, 5, 4, 1]}}, -14/3155*3786^(1/2), -.2730354116], [{{[1, 2], [2, 4, 5, 1, 3]}}, -21/2705*541^(1/2), -.1805721038], [{{[1, 2], [2, 4, 3, 5, 1]}}, -7/75*2^(1/2), -.1319932658], [{{[1, 2], [2, 3, 5, 4, 1]}}, -3/1555* 4354^(1/2), -.1273019551], [{{[1, 2], [1, 5, 4, 3, 2]}, {[1, 2], [2, 3, 4, 5, 1 ]}, {[1, 2], [2, 5, 3, 1, 4]}}, 0, 0.], [{{[1, 2], [1, 4, 5, 3, 2]}}, 3/1555* 4354^(1/2), .1273019551], [{{[1, 2], [1, 5, 3, 4, 2]}}, 7/75*2^(1/2), .13199326\ 58], [{{[1, 2], [2, 5, 1, 4, 3]}}, 21/2705*541^(1/2), .1805721038], [{{[1, 2], [1, 4, 5, 2, 3]}}, 14/3155*3786^(1/2), .2730354116], [{{[1, 2], [2, 3, 5, 1, 4] }}, 7/235*141^(1/2), .3537038069], [{{[1, 2], [1, 3, 5, 4, 2]}}, 63/935*34^(1/2 ), .3928876678], [{{[1, 2], [1, 4, 3, 5, 2]}}, 21/275*30^(1/2), .4182608621], [ {{[1, 2], [1, 3, 4, 5, 2]}}, 84/10735*4294^(1/2), .5127530559], [{{[1, 2], [2, 4, 1, 5, 3]}}, 63/2405*481^(1/2), .5745105484], [{{[1, 2], [2, 1, 5, 4, 3]}}, 21/1051*1051^(1/2), .6477656832], [{{[1, 2], [1, 2, 5, 4, 3]}}, 6/95*114^(1/2), .6743417842], [{{[1, 2], [1, 3, 5, 2, 4]}}, 21/1727*3454^(1/2), .7146413212], [ {{[1, 2], [1, 4, 3, 2, 5]}}, 126/12085*4834^(1/2), .7248985207], [{{[1, 2], [2, 1, 4, 5, 3]}}, 21/65*6^(1/2), .7913736093], [{{[1, 2], [1, 2, 4, 5, 3]}}, 147/ 13735*5494^(1/2), .7932918611], [{{[1, 2], [1, 3, 4, 2, 5]}}, 49/4355*5226^(1/2 ), .8133783779], [{{[1, 2], [1, 2, 4, 3, 5]}}, 63/5855*7026^(1/2), .9019193881] , [{{[1, 2], [1, 3, 2, 5, 4]}}, 168/13585*5434^(1/2), .9116107883], [{{[1, 2], [1, 2, 3, 4, 5]}}, 42/4217*8434^(1/2), .9146658988], [{{[1, 2], [1, 2, 3, 5, 4] }}, 63/5675*6810^(1/2), .9161112992], [{{[1, 2], [2, 1, 3, 5, 4]}}, 168/6605* 1321^(1/2), .9244594551]] The list of Asymtotic Correlations of patterns of size 3, and , 4, are [[{{[1, 2, 3], [3, 4, 1, 2]}}, -7/611*6110^(1/2), -.8955244238], [{{[1, 2, 3], [3, 4, 2, 1]}}, -42/4667*9334^(1/2), -.8694515535], [{{[1, 2, 3], [4, 3, 2, 1]} }, -49/6383*12766^(1/2), -.8673585336], [{{[1, 2, 3], [4, 2, 3, 1]}}, -77/9022* 9022^(1/2), -.8106610629], [{{[2, 1, 3], [4, 3, 2, 1]}}, -4/491*6874^(1/2), -.6\ 754345361], [{{[2, 1, 3], [4, 2, 3, 1]}}, -13/1388*4858^(1/2), -.6528037513], [ {{[2, 1, 3], [3, 4, 2, 1]}}, -3/359*5026^(1/2), -.5924313719], [{{[2, 3, 1], [3 , 1, 2, 4]}}, -9/956*3346^(1/2), -.5445623171], [{{[1, 2, 3], [3, 2, 4, 1]}}, -\ 21/3107*6214^(1/2), -.5327993250], [{{[2, 3, 1], [4, 1, 2, 3]}}, -9/1052*3682^( 1/2), -.5191210765], [{{[2, 1, 3], [3, 4, 1, 2]}}, -2/235*3290^(1/2), -.4881576\ 306], [{{[1, 2, 3], [4, 1, 2, 3]}}, -21/6838*6838^(1/2), -.2539538180], [{{[2, 3, 1], [2, 3, 1, 4]}, {[2, 3, 1], [4, 1, 3, 2]}}, -3/956*3346^(1/2), -.18152077\ 24], [{{[2, 3, 1], [3, 2, 1, 4]}}, -3/1052*3682^(1/2), -.1730403589], [{{[1, 2, 3], [3, 1, 4, 2]}}, -1/26*14^(1/2), -.1439098995], [{{[2, 3, 1], [2, 4, 1, 3]}} , 1/52*26^(1/2), .9805806757e-1], [{{[1, 2, 3], [3, 2, 1, 4]}}, 21/6838*6838^(1 /2), .2539538180], [{{[2, 1, 3], [1, 2, 4, 3]}}, 3/718*5026^(1/2), .2962156859] , [{{[1, 2, 3], [3, 1, 2, 4]}}, 21/3107*6214^(1/2), .5327993250], [{{[2, 3, 1], [4, 2, 3, 1]}}, 11/1388*4858^(1/2), .5523724049], [{{[1, 3, 2], [1, 2, 3, 4]}}, 7/982*6874^(1/2), .5910052191], [{{[2, 3, 1], [3, 4, 1, 2]}}, 1/94*3290^(1/2), .6101970382], [{{[1, 2, 3], [2, 1, 4, 3]}}, 28/3055*6110^(1/2), .7164195389], [ {{[2, 3, 1], [2, 3, 4, 1]}}, 15/1052*3682^(1/2), .8652017940], [{{[1, 2, 3], [1 , 2, 4, 3]}}, 42/4667*9334^(1/2), .8694515535], [{{[2, 3, 1], [3, 4, 2, 1]}}, 9 /718*5026^(1/2), .8886470577], [{{[2, 3, 1], [2, 4, 3, 1]}}, 15/956*3346^(1/2), .9076038619], [{{[1, 2, 3], [1, 3, 2, 4]}}, 7/694*9022^(1/2), .9580539833], [{{ [1, 2, 3], [1, 2, 3, 4]}}, 56/6383*12766^(1/2), .9912668956]] The list of Asymtotic Correlations of patterns of size 3, and , 5, are [[{{[1, 2, 3], [4, 5, 3, 1, 2]}}, -606/120211*34346^(1/2), -.9342572938], [{{[1 , 2, 3], [5, 4, 3, 1, 2]}}, -426/103285*44265^(1/2), -.8677658992], [{{[1, 2, 3 ], [4, 5, 2, 3, 1]}}, -60/1001*209^(1/2), -.8665433940], [{{[1, 2, 3], [4, 5, 1 , 3, 2]}}, -159/1183*39^(1/2), -.8393530700], [{{[1, 2, 3], [5, 4, 3, 2, 1]}}, -192/54821*54821^(1/2), -.8200262447], [{{[1, 2, 3], [5, 3, 4, 2, 1]}}, -402/ 106561*45669^(1/2), -.8061920602], [{{[1, 2, 3], [4, 3, 5, 2, 1]}}, -1020/ 249977*35711^(1/2), -.7710829956], [{{[1, 2, 3], [4, 5, 1, 2, 3]}}, -417/95641* 27326^(1/2), -.7207422458], [{{[3, 2, 1], [1, 3, 4, 2, 5]}}, -304/6097*201^(1/2 ), -.7068958260], [{{[2, 3, 1], [5, 1, 2, 3, 4]}}, -648/121373*17339^(1/2), -.7\ 030155683], [{{[3, 2, 1], [2, 4, 1, 3, 5]}}, -66/14287*22451^(1/2), -.692182692\ 0], [{{[3, 2, 1], [2, 4, 1, 5, 3]}}, -270/3367*74^(1/2), -.6898211530], [{{[3, 2, 1], [3, 2, 1, 4, 5]}}, -300/12103*741^(1/2), -.6747413495], [{{[1, 3, 2], [5 , 3, 2, 4, 1]}}, -212/42679*18291^(1/2), -.6718005432], [{{[1, 3, 2], [5, 4, 3, 2, 1]}}, -114/29519*29519^(1/2), -.6635200196], [{{[2, 3, 1], [4, 1, 2, 3, 5]}} , -564/105203*15029^(1/2), -.6572279460], [{{[1, 3, 2], [5, 4, 2, 3, 1]}}, -240 /57379*24591^(1/2), -.6559131856], [{{[1, 3, 2], [4, 5, 3, 2, 1]}}, -228/55615* 23835^(1/2), -.6329224254], [{{[1, 3, 2], [5, 3, 4, 1, 2]}}, -606/133133*19019^ (1/2), -.6277413612], [{{[2, 3, 1], [5, 1, 3, 2, 4]}}, -172/735*7^(1/2), -.6191\ 418033], [{{[3, 2, 1], [1, 4, 3, 2, 5]}}, -108/31421*31421^(1/2), -.6092755552] , [{{[2, 3, 1], [3, 1, 2, 4, 5]}}, -582/134603*19229^(1/2), -.5995792506], [{{[ 1, 3, 2], [4, 5, 3, 1, 2]}}, -285/64729*18494^(1/2), -.5987718700], [{{[2, 3, 1 ], [5, 1, 2, 4, 3]}}, -498/15239*311^(1/2), -.5763059034], [{{[2, 3, 1], [3, 1, 2, 5, 4]}}, -6/49*21^(1/2), -.5611317178], [{{[1, 3, 2], [5, 2, 3, 4, 1]}}, -72 /16919*16919^(1/2), -.5535350825], [{{[2, 3, 1], [4, 1, 3, 2, 5]}}, -144/2695* 105^(1/2), -.5475179632], [{{[1, 3, 2], [5, 2, 4, 3, 1]}}, -170/42679*18291^(1/ 2), -.5387079827], [{{[1, 3, 2], [5, 3, 1, 2, 4]}}, -414/9163*119^(1/2), -.4928\ 742567], [{{[2, 3, 1], [3, 1, 4, 2, 5]}, {[1, 3, 2], [3, 5, 2, 4, 1]}}, -372/ 84623*12089^(1/2), -.4833366314], [{{[2, 3, 1], [4, 1, 2, 5, 3]}}, -25/2303* 1974^(1/2), -.4823026462], [{{[3, 2, 1], [2, 3, 4, 1, 5]}}, -552/195377*27911^( 1/2), -.4720123256], [{{[1, 3, 2], [3, 5, 4, 2, 1]}}, -456/134603*19229^(1/2), -.4697734336], [{{[1, 3, 2], [3, 4, 5, 2, 1]}}, -144/6517*399^(1/2), -.44136838\ 24], [{{[2, 3, 1], [5, 2, 1, 4, 3]}}, -116/30919*13251^(1/2), -.4318738189], [{ {[3, 2, 1], [2, 3, 5, 1, 4]}}, -61/8554*3666^(1/2), -.4317743305], [{{[1, 3, 2] , [3, 5, 4, 1, 2]}}, -57/637*21^(1/2), -.4100577937], [{{[2, 3, 1], [3, 1, 5, 2 , 4]}}, -9/1813*6734^(1/2), -.4073627008], [{{[3, 2, 1], [3, 2, 4, 1, 5]}}, -\ 432/17017*221^(1/2), -.3773956456], [{{[1, 3, 2], [3, 4, 5, 1, 2]}}, -159/51499 *14714^(1/2), -.3745102462], [{{[3, 2, 1], [2, 4, 3, 1, 5]}}, -12/455*195^(1/2) , -.3682876494], [{{[2, 1, 3], [1, 3, 5, 4, 2]}}, -288/9163*119^(1/2), -.342869\ 0481], [{{[3, 2, 1], [3, 1, 5, 4, 2]}}, -123/49231*14066^(1/2), -.2963137198], [{{[3, 2, 1], [3, 4, 1, 2, 5]}}, -8/4417*24609^(1/2), -.2841250799], [{{[1, 3, 2], [3, 5, 1, 2, 4]}}, -75/26509*7574^(1/2), -.2462241056], [{{[1, 3, 2], [5, 2 , 1, 3, 4]}}, -204/15239*311^(1/2), -.2360771169], [{{[2, 3, 1], [5, 1, 3, 4, 2 ]}}, -12/539*105^(1/2), -.2281324846], [{{[1, 3, 2], [3, 5, 1, 4, 2]}}, -54/ 23569*6734^(1/2), -.1880135542], [{{[1, 3, 2], [5, 2, 1, 4, 3]}}, -46/30919* 13251^(1/2), -.1712603075], [{{[2, 1, 3], [1, 3, 4, 5, 2]}}, -102/105203*15029^ (1/2), -.1188603732], [{{[3, 2, 1], [1, 5, 4, 2, 3]}}, -138/198107*28301^(1/2), -.1171871941], [{{[1, 3, 2], [5, 1, 3, 2, 4]}}, -32/735*7^(1/2), -.1151891727], [{{[2, 3, 1], [4, 1, 5, 2, 3]}}, -33/26509*7574^(1/2), -.1083386065], [{{[3, 2, 1], [1, 5, 3, 4, 2]}}, -34/1365*13^(1/2), -.8980860319e-1], [{{[1, 3, 2], [2, 5 , 4, 3, 1]}}, -60/105203*15029^(1/2), -.6991786660e-1], [{{[1, 3, 2], [5, 1, 3, 4, 2]}}, -18/2695*105^(1/2), -.6843974540e-1], [{{[1, 3, 2], [3, 2, 1, 4, 5]}}, -18/6517*399^(1/2), -.5517104779e-1], [{{[3, 2, 1], [2, 5, 3, 1, 4]}}, -18/ 38311*10946^(1/2), -.4915602301e-1], [{{[1, 3, 2], [5, 1, 4, 2, 3]}}, -36/9163* 119^(1/2), -.4285863101e-1], [{{[1, 3, 2], [5, 1, 2, 3, 4]}}, -18/121373*17339^ (1/2), -.1952821023e-1], [{{[3, 2, 1], [2, 3, 4, 5, 1]}, {[3, 2, 1], [1, 5, 4, 3, 2]}}, 36/225407*32201^(1/2), .2865957734e-1], [{{[2, 3, 1], [4, 1, 3, 5, 2]} }, 9/20629*5894^(1/2), .3349418381e-1], [{{[1, 3, 2], [5, 1, 2, 4, 3]}}, 48/ 15239*311^(1/2), .5554755695e-1], [{{[3, 2, 1], [2, 4, 5, 1, 3]}}, 24/49231* 14066^(1/2), .5781731118e-1], [{{[1, 3, 2], [3, 1, 4, 2, 5]}}, 48/84623*12089^( 1/2), .6236601695e-1], [{{[1, 3, 2], [3, 2, 1, 5, 4]}}, 51/51499*14714^(1/2), .\ 1201259280], [{{[1, 3, 2], [2, 5, 4, 1, 3]}}, 13/4606*1974^(1/2), .1253986880], [{{[3, 2, 1], [2, 3, 5, 4, 1]}}, 12/15239*28301^(1/2), .1324724803], [{{[1, 3, 2], [3, 1, 2, 4, 5]}}, 132/134603*19229^(1/2), .1359870465], [{{[2, 3, 1], [3, 1, 5, 4, 2]}}, 51/26509*7574^(1/2), .1674323918], [{{[3, 2, 1], [2, 4, 3, 5, 1] }}, 64/1365*13^(1/2), .1690514884], [{{[2, 3, 1], [4, 1, 5, 3, 2]}}, 10/2303* 1974^(1/2), .1929210585], [{{[3, 2, 1], [3, 2, 5, 4, 1]}}, 92/57421*24609^(1/2) , .2513414167], [{{[3, 2, 1], [2, 5, 4, 1, 3]}}, 37/8554*3666^(1/2), .261895905\ 3], [{{[1, 3, 2], [3, 1, 2, 5, 4]}}, 48/637*21^(1/2), .3453118263], [{{[3, 2, 1 ], [2, 4, 5, 3, 1]}}, 450/17017*221^(1/2), .3931204641], [{{[1, 3, 2], [3, 1, 4 , 5, 2]}}, 41/4606*1974^(1/2), .3954881700], [{{[2, 1, 3], [1, 4, 3, 2, 5]}}, 54/16919*16919^(1/2), .4151513119], [{{[1, 3, 2], [2, 1, 3, 4, 5]}}, 30/11123* 23835^(1/2), .4163963325], [{{[1, 2, 3], [2, 4, 1, 5, 3]}}, 171/3367*74^(1/2), .4368867302], [{{[3, 2, 1], [2, 5, 3, 4, 1]}}, 162/5005*195^(1/2), .4519893879] , [{{[2, 3, 1], [5, 3, 4, 1, 2]}}, 444/133133*19019^(1/2), .4599293142], [{{[2, 3, 1], [4, 2, 5, 1, 3]}}, 135/23569*6734^(1/2), .4700338856], [{{[2, 1, 3], [1, 4, 2, 3, 5]}}, 152/42679*18291^(1/2), .4816683139], [{{[2, 1, 3], [1, 2, 4, 3, 5]}}, 180/57379*24591^(1/2), .4919348892], [{{[1, 3, 2], [3, 1, 5, 4, 2]}}, 156 /26509*7574^(1/2), .5121461398], [{{[3, 2, 1], [2, 5, 4, 3, 1]}}, 48/15029* 27911^(1/2), .5335791506], [{{[1, 2, 3], [2, 1, 5, 4, 3]}}, 318/95641*27326^(1/ 2), .5496307774], [{{[1, 3, 2], [1, 2, 3, 4, 5]}}, 96/29519*29519^(1/2), .55875\ 37007], [{{[2, 3, 1], [5, 3, 4, 2, 1]}}, 222/57379*24591^(1/2), .6067196966], [ {{[1, 3, 2], [2, 1, 3, 5, 4]}}, 303/64729*18494^(1/2), .6365890406], [{{[1, 2, 3], [1, 2, 5, 4, 3]}}, 288/12103*741^(1/2), .6477516956], [{{[1, 3, 2], [1, 5, 4, 3, 2]}}, 612/121373*17339^(1/2), .6639591479], [{{[1, 2, 3], [1, 3, 5, 2, 4] }}, 744/157157*22451^(1/2), .7093442464], [{{[1, 2, 3], [2, 1, 4, 5, 3]}}, 135/ 1183*39^(1/2), .7126582670], [{{[2, 3, 1], [4, 5, 2, 3, 1]}}, 696/133133*19019^ (1/2), .7209702763], [{{[1, 3, 2], [1, 4, 3, 5, 2]}}, 192/2695*105^(1/2), .7300\ 239509], [{{[1, 3, 2], [1, 5, 4, 2, 3]}}, 636/15239*311^(1/2), .7360051295], [{ {[2, 3, 1], [2, 4, 3, 5, 1]}}, 206/735*7^(1/2), .7415302993], [{{[2, 3, 1], [4, 3, 2, 5, 1]}}, 654/105203*15029^(1/2), .7621047460], [{{[1, 3, 2], [1, 2, 3, 5, 4]}}, 276/55615*23835^(1/2), .7661692518], [{{[1, 2, 3], [1, 2, 4, 5, 3]}}, 1038/249977*35711^(1/2), .7846903424], [{{[1, 3, 2], [2, 1, 4, 5, 3]}}, 111/637 *21^(1/2), .7985335983], [{{[1, 2, 3], [1, 4, 3, 2, 5]}}, 144/31421*31421^(1/2) , .8123674069], [{{[2, 3, 1], [3, 2, 5, 4, 1]}}, 220/30919*13251^(1/2), .819071\ 0359], [{{[1, 3, 2], [1, 3, 5, 4, 2]}}, 720/9163*119^(1/2), .8571726202], [{{[2 , 3, 1], [3, 4, 5, 1, 2]}}, 366/51499*14714^(1/2), .8620801894], [{{[1, 2, 3], [2, 1, 3, 5, 4]}}, 570/120211*34346^(1/2), .8787568605], [{{[1, 3, 2], [1, 3, 5 , 2, 4]}}, 678/84623*12089^(1/2), .8809199895], [{{[1, 2, 3], [1, 3, 4, 2, 5]}} , 382/6097*201^(1/2), .8882704131], [{{[2, 3, 1], [4, 3, 5, 2, 1]}}, 888/134603 *19229^(1/2), .9148219495], [{{[1, 2, 3], [1, 3, 2, 5, 4]}}, 1212/19019*209^(1/ 2), .9212724505], [{{[1, 2, 3], [1, 2, 3, 5, 4]}}, 456/103285*44265^(1/2), .928\ 8761740], [{{[1, 2, 3], [1, 2, 4, 3, 5]}}, 480/106561*45669^(1/2), .9626173854] , [{{[1, 2, 3], [1, 2, 3, 4, 5]}}, 228/54821*54821^(1/2), .9737811655], [{{[2, 3, 1], [3, 4, 5, 2, 1]}}, 318/6517*399^(1/2), .9746885110]] The list of Asymtotic Correlations of patterns of size 4, and , 5, are [[{{[2, 1, 4, 3], [5, 4, 3, 2, 1]}}, -261/396398*1981990^(1/2), -.9269574135], [{{[1, 2, 3, 4], [4, 5, 3, 1, 2]}}, -738/648611*648611^(1/2), -.9163559562], [{ {[2, 1, 4, 3], [5, 3, 4, 2, 1]}}, -381/550370*1651110^(1/2), -.8895251395], [{{ [2, 1, 4, 3], [4, 5, 3, 2, 1]}}, -147/42676*64014^(1/2), -.8715074641], [{{[1, 2, 4, 3], [4, 5, 3, 1, 2]}}, -594/474239*474239^(1/2), -.8625570160], [{{[2, 3, 4, 1], [5, 1, 2, 3, 4]}}, -486/651451*1302902^(1/2), -.8515504634], [{{[1, 2, 3 , 4], [3, 5, 4, 1, 2]}}, -399/25532*2946^(1/2), -.8482120369], [{{[2, 1, 4, 3], [4, 5, 2, 3, 1]}}, -9/12220*1276990^(1/2), -.8322715547], [{{[1, 2, 4, 3], [4, 5, 3, 2, 1]}}, -867/1629860*2444790^(1/2), -.8317438077], [{{[1, 3, 2, 4], [4, 5, 3, 1, 2]}}, -558/458387*458387^(1/2), -.8241723733], [{{[2, 3, 4, 1], [5, 1, 3, 2, 4]}}, -47/1315*526^(1/2), -.8197189540], [{{[1, 2, 3, 4], [4, 5, 3, 2, 1] }}, -999/2229140*3343710^(1/2), -.8194877107], [{{[1, 2, 3, 4], [4, 5, 2, 3, 1] }}, -243/485108*2668094^(1/2), -.8182168142], [{{[1, 2, 4, 3], [4, 5, 2, 3, 1]} }, -207/354692*1950806^(1/2), -.8151283418], [{{[1, 2, 4, 3], [5, 4, 3, 2, 1]}} , -1413/3027806*3027806^(1/2), -.8120413399], [{{[2, 1, 4, 3], [4, 5, 3, 1, 2]} }, -90/62087*310435^(1/2), -.8076573951], [{{[1, 2, 4, 3], [5, 3, 4, 2, 1]}}, -\ 417/840778*2522334^(1/2), -.7876912344], [{{[4, 2, 3, 1], [3, 1, 2, 5, 4]}}, -\ 309/18044*2082^(1/2), -.7813867159], [{{[1, 4, 2, 3], [4, 3, 2, 5, 1]}}, -783/ 1026266*1026266^(1/2), -.7729150990], [{{[2, 1, 4, 3], [5, 2, 4, 3, 1]}}, -57/ 81874*1228110^(1/2), -.7715205189], [{{[2, 3, 4, 1], [5, 1, 2, 4, 3]}}, -117/ 163586*1145102^(1/2), -.7653530461], [{{[1, 3, 2, 4], [4, 5, 2, 3, 1]}}, -522/ 942799*1885598^(1/2), -.7602841631], [{{[1, 2, 4, 3], [4, 3, 5, 1, 2]}}, -303/ 18668*2154^(1/2), -.7532995113], [{{[1, 2, 3, 4], [3, 4, 5, 1, 2]}}, -540/ 516041*516041^(1/2), -.7517122983], [{{[4, 2, 3, 1], [3, 1, 5, 2, 4]}}, -306/ 166907*166907^(1/2), -.7490040238], [{{[1, 2, 3, 4], [5, 4, 3, 2, 1]}}, -1521/ 4141094*4141094^(1/2), -.7474319693], [{{[1, 2, 3, 4], [3, 5, 4, 2, 1]}}, -2439 /5395108*2697554^(1/2), -.7425004669], [{{[1, 2, 3, 4], [3, 5, 1, 4, 2]}}, -360 /236171*236171^(1/2), -.7407799454], [{{[1, 3, 2, 4], [4, 5, 3, 2, 1]}}, -189/ 393845*2363070^(1/2), -.7376914693], [{{[1, 2, 3, 4], [5, 3, 4, 2, 1]}}, -453/ 1149922*3449766^(1/2), -.7316858189], [{{[1, 2, 4, 3], [4, 3, 5, 2, 1]}}, -2043 /3944692*1972346^(1/2), -.7273556541], [{{[1, 2, 4, 3], [3, 5, 4, 1, 2]}}, -291 /18668*2154^(1/2), -.7234658672], [{{[1, 4, 2, 3], [4, 2, 3, 5, 1]}}, -219/ 26290*7170^(1/2), -.7053637011], [{{[1, 2, 4, 3], [5, 3, 2, 4, 1]}}, -321/ 625378*1876134^(1/2), -.7030631895], [{{[1, 2, 4, 3], [3, 5, 4, 2, 1]}}, -1971/ 3944692*1972346^(1/2), -.7017219746], [{{[2, 1, 4, 3], [3, 5, 4, 2, 1]}}, -315/ 516436*1291090^(1/2), -.6930623454], [{{[1, 3, 2, 4], [3, 4, 5, 1, 2]}}, -414/ 364697*364697^(1/2), -.6855422820], [{{[1, 3, 2, 4], [3, 5, 4, 2, 1]}}, -945/ 1906418*1906418^(1/2), -.6844200814], [{{[2, 1, 4, 3], [5, 2, 3, 4, 1]}}, -729/ 1135990*1135990^(1/2), -.6839750723], [{{[1, 3, 2, 4], [5, 3, 4, 2, 1]}}, -177/ 406337*2438022^(1/2), -.6801515726], [{{[1, 4, 2, 3], [4, 3, 1, 5, 2]}}, -165/ 44932*33699^(1/2), -.6741192063], [{{[1, 3, 2, 4], [5, 4, 3, 2, 1]}}, -576/ 1463299*2926598^(1/2), -.6733966371], [{{[1, 4, 2, 3], [3, 4, 2, 5, 1]}}, -333/ 44693*8126^(1/2), -.6716501793], [{{[2, 3, 4, 1], [5, 2, 1, 4, 3]}}, -111/ 165953*995718^(1/2), -.6674305017], [{{[4, 2, 3, 1], [3, 1, 4, 2, 5]}}, -729/ 1198538*1198538^(1/2), -.6658886681], [{{[1, 2, 3, 4], [3, 4, 5, 2, 1]}}, -105/ 37316*55974^(1/2), -.6657135341], [{{[1, 2, 3, 4], [3, 5, 2, 4, 1]}}, -1719/ 3391828*1695914^(1/2), -.6600000499], [{{[1, 4, 2, 3], [4, 3, 2, 1, 5]}}, -711/ 1184006*1184006^(1/2), -.6534203400], [{{[1, 2, 4, 3], [5, 2, 4, 3, 1]}}, -297/ 625378*1876134^(1/2), -.6504977174], [{{[2, 3, 4, 1], [5, 1, 4, 2, 3]}}, -675/ 98362*8942^(1/2), -.6489238781], [{{[1, 3, 2, 4], [5, 2, 4, 3, 1]}}, -141/ 302237*1813422^(1/2), -.6282332566], [{{[1, 2, 4, 3], [3, 5, 2, 4, 1]}}, -1395/ 2479972*1239986^(1/2), -.6263770266], [{{[1, 2, 3, 4], [5, 2, 4, 3, 1]}}, -333/ 855322*2565966^(1/2), -.6236487260], [{{[1, 2, 4, 3], [3, 4, 5, 1, 2]}}, -378/ 377309*377309^(1/2), -.6153797733], [{{[1, 2, 4, 3], [3, 4, 5, 2, 1]}}, -579/ 190988*40926^(1/2), -.6132988252], [{{[1, 4, 2, 3], [4, 3, 5, 2, 1]}}, -351/ 656533*1313066^(1/2), -.6126237568], [{{[4, 2, 3, 1], [3, 2, 1, 4, 5]}}, -141/ 46151*39558^(1/2), -.6076523195], [{{[2, 1, 4, 3], [3, 5, 4, 1, 2]}}, -3/188* 1410^(1/2), -.5992015965], [{{[1, 4, 2, 3], [4, 2, 3, 1, 5]}}, -13/478*478^(1/2 ), -.5946061599], [{{[1, 4, 2, 3], [4, 3, 5, 1, 2]}}, -15/956*1434^(1/2), -.594\ 1661997], [{{[1, 2, 4, 3], [4, 2, 5, 3, 1]}}, -1323/2479972*1239986^(1/2), -.59\ 40478897], [{{[1, 4, 2, 3], [3, 4, 2, 1, 5]}}, -297/520303*1040606^(1/2), -.582\ 2952963], [{{[1, 2, 4, 3], [5, 2, 3, 4, 1]}}, -765/1735406*1735406^(1/2), -.580\ 7121169], [{{[2, 3, 4, 1], [4, 1, 2, 3, 5]}}, -297/564661*1129322^(1/2), -.5589\ 559077], [{{[1, 3, 2, 4], [5, 2, 3, 4, 1]}}, -360/838699*1677398^(1/2), -.55592\ 27357], [{{[1, 2, 4, 3], [4, 3, 2, 5, 1]}}, -1377/3083092*1541546^(1/2), -.5545\ 308346], [{{[2, 1, 4, 3], [3, 5, 2, 4, 1]}}, -999/1623380*811690^(1/2), -.55442\ 19230], [{{[2, 1, 4, 3], [3, 4, 5, 2, 1]}}, -9/2660*26790^(1/2), -.5537927037], [{{[1, 4, 2, 3], [5, 3, 2, 4, 1]}}, -102/208169*1249014^(1/2), -.5476054591], [ {{[1, 4, 2, 3], [4, 2, 5, 3, 1]}}, -243/412753*825506^(1/2), -.5349043777], [{{ [1, 4, 2, 3], [4, 3, 1, 2, 5]}}, -270/520303*1040606^(1/2), -.5293593603], [{{[ 1, 4, 2, 3], [5, 3, 4, 2, 1]}}, -114/279869*1679214^(1/2), -.5278409483], [{{[1 , 4, 2, 3], [3, 4, 1, 5, 2]}}, -189/129299*129299^(1/2), -.5256107282], [{{[1, 2, 3, 4], [5, 2, 3, 4, 1]}}, -801/2373494*2373494^(1/2), -.5199223020], [{{[1, 2, 4, 3], [3, 5, 1, 4, 2]}, {[1, 2, 4, 3], [4, 2, 5, 1, 3]}}, -216/172679* 172679^(1/2), -.5197972634], [{{[1, 4, 2, 3], [3, 2, 4, 5, 1]}}, -261/520303* 1040606^(1/2), -.5117140483], [{{[1, 4, 2, 3], [3, 4, 5, 2, 1]}}, -195/63574* 27246^(1/2), -.5062982776], [{{[1, 4, 2, 3], [4, 5, 3, 2, 1]}}, -213/542530* 1627590^(1/2), -.5008738426], [{{[1, 4, 2, 3], [5, 3, 4, 1, 2]}}, -567/1298726* 1298726^(1/2), -.4975357491], [{{[4, 1, 3, 2], [1, 2, 3, 4, 5]}}, -351/1007863* 2015726^(1/2), -.4944488410], [{{[2, 3, 4, 1], [5, 4, 1, 2, 3]}}, -99/34979* 29982^(1/2), -.4900699856], [{{[1, 4, 2, 3], [4, 5, 2, 3, 1]}}, -549/1298726* 1298726^(1/2), -.4817409634], [{{[2, 3, 4, 1], [2, 5, 1, 3, 4]}}, -123/49444* 37083^(1/2), -.4790479039], [{{[2, 3, 4, 1], [4, 1, 3, 2, 5]}}, -78/14465*7890^ (1/2), -.4789770075], [{{[1, 4, 2, 3], [3, 5, 2, 4, 1]}}, -216/412753*825506^(1 /2), -.4754705580], [{{[1, 4, 2, 3], [5, 4, 2, 3, 1]}}, -102/279869*1679214^(1/ 2), -.4722787432], [{{[1, 2, 3, 4], [3, 5, 2, 1, 4]}}, -165/92308*69231^(1/2), -.4703215790], [{{[2, 1, 3, 4], [4, 1, 5, 3, 2]}}, -3/1436*50619^(1/2), -.47002\ 78543], [{{[1, 4, 2, 3], [3, 4, 5, 1, 2]}}, -234/251189*251189^(1/2), -.4668910\ 500], [{{[1, 4, 2, 3], [4, 5, 3, 1, 2]}}, -261/315719*315719^(1/2), -.464504737\ 8], [{{[4, 1, 2, 3], [4, 2, 3, 5, 1]}}, -15/2893*7890^(1/2), -.4605548148], [{{ [3, 1, 4, 2], [2, 5, 3, 1, 4]}}, -90/38311*38311^(1/2), -.4598124915], [{{[1, 4 , 2, 3], [5, 4, 3, 1, 2]}}, -39/108506*1627590^(1/2), -.4585464757], [{{[4, 2, 3, 1], [3, 1, 4, 5, 2]}}, -135/65236*48927^(1/2), -.4577419740], [{{[1, 4, 2, 3 ], [3, 2, 4, 1, 5]}}, -225/44693*8126^(1/2), -.4538176887], [{{[3, 4, 1, 2], [4 , 1, 2, 3, 5]}}, -909/2018180*1009090^(1/2), -.4524482745], [{{[1, 4, 2, 3], [5 , 2, 3, 4, 1]}}, -243/577663*1155326^(1/2), -.4521515205], [{{[1, 4, 2, 3], [3, 4, 1, 2, 5]}}, -141/301618*904854^(1/2), -.4446835992], [{{[1, 2, 4, 3], [3, 4, 2, 5, 1]}}, -63/15796*12206^(1/2), -.4406361331], [{{[1, 4, 2, 3], [3, 5, 4, 2, 1]}}, -252/656533*1313066^(1/2), -.4398324408], [{{[1, 2, 3, 4], [4, 3, 2, 5, 1 ]}}, -1269/4216708*2108354^(1/2), -.4369782896], [{{[2, 1, 4, 3], [3, 4, 5, 1, 2]}}, -216/246985*246985^(1/2), -.4346287612], [{{[1, 2, 4, 3], [4, 2, 3, 5, 1] }}, -327/78980*10770^(1/2), -.4296734064], [{{[1, 3, 2, 4], [4, 3, 2, 5, 1]}}, -261/745009*1490018^(1/2), -.4276364796], [{{[2, 3, 4, 1], [4, 2, 1, 3, 5]}}, -\ 441/98362*8942^(1/2), -.4239636003], [{{[1, 4, 2, 3], [5, 2, 4, 3, 1]}}, -6/ 16013*1249014^(1/2), -.4187571158], [{{[4, 1, 2, 3], [4, 3, 2, 5, 1]}}, -216/ 564661*1129322^(1/2), -.4065133874], [{{[2, 3, 4, 1], [3, 5, 1, 2, 4]}}, -153/ 142283*142283^(1/2), -.4056158562], [{{[1, 4, 2, 3], [4, 2, 5, 1, 3]}}, -135/ 114959*114959^(1/2), -.3981642650], [{{[1, 4, 2, 3], [3, 5, 4, 1, 2]}}, -129/ 12428*1434^(1/2), -.3930637938], [{{[1, 2, 4, 3], [4, 3, 2, 1, 5]}}, -1035/ 3556972*1778486^(1/2), -.3880477134], [{{[1, 4, 2, 3], [3, 2, 5, 4, 1]}}, -123/ 301618*904854^(1/2), -.3879154802], [{{[1, 4, 2, 3], [5, 3, 2, 1, 4]}}, -387/ 1026266*1026266^(1/2), -.3820155086], [{{[3, 1, 4, 2], [1, 4, 3, 2, 5]}}, -18/ 31421*439894^(1/2), -.3799500637], [{{[2, 3, 4, 1], [4, 5, 1, 2, 3]}}, -198/ 276413*276413^(1/2), -.3766048928], [{{[3, 1, 4, 2], [2, 4, 3, 1, 5]}}, -36/ 5005*2730^(1/2), -.3758198739], [{{[1, 2, 3, 4], [3, 4, 1, 5, 2]}}, -189/265631 *265631^(1/2), -.3667097234], [{{[1, 2, 3, 4], [3, 4, 2, 5, 1]}}, -1035/367268* 16694^(1/2), -.3641140729], [{{[1, 3, 2, 4], [5, 2, 1, 4, 3]}}, -69/218957* 1313742^(1/2), -.3611979685], [{{[1, 4, 2, 3], [5, 3, 1, 4, 2]}}, -162/412753* 825506^(1/2), -.3566029184], [{{[3, 4, 1, 2], [4, 1, 3, 2, 5]}}, -219/10340*282 ^(1/2), -.3556707332], [{{[1, 3, 2, 4], [3, 4, 2, 5, 1]}}, -423/129778*11798^(1 /2), -.3540327890], [{{[2, 3, 4, 1], [1, 4, 2, 3, 5]}}, -69/229073*1374438^(1/2 ), -.3531325612], [{{[4, 2, 3, 1], [3, 1, 5, 4, 2]}}, -153/187727*187727^(1/2), -.3531246713], [{{[4, 2, 3, 1], [2, 4, 3, 1, 5]}}, -6/1735*10410^(1/2), -.35283\ 94495], [{{[1, 4, 2, 3], [5, 4, 2, 1, 3]}}, -198/656533*1313066^(1/2), -.345582\ 6320], [{{[3, 1, 4, 2], [1, 4, 2, 3, 5]}}, -3/469*2814^(1/2), -.3393207815], [{ {[1, 4, 2, 3], [2, 4, 3, 5, 1]}}, -37/2390*478^(1/2), -.3384681218], [{{[1, 4, 2, 3], [4, 5, 2, 1, 3]}}, -111/12428*1434^(1/2), -.3382176829], [{{[1, 2, 3, 4] , [4, 2, 3, 5, 1]}}, -291/108020*14730^(1/2), -.3269566610], [{{[1, 4, 2, 3], [ 4, 2, 1, 3, 5]}}, -162/44693*8126^(1/2), -.3267487359], [{{[1, 2, 4, 3], [2, 5, 4, 3, 1]}}, -801/3083092*1541546^(1/2), -.3225702241], [{{[3, 1, 4, 2], [2, 5, 4, 3, 1]}}, -99/195377*390754^(1/2), -.3167477029], [{{[3, 4, 1, 2], [4, 2, 1, 3, 5]}}, -603/175780*7990^(1/2), -.3066346589], [{{[2, 1, 3, 4], [4, 1, 5, 2, 3 ]}}, -135/194219*194219^(1/2), -.3063288578], [{{[2, 3, 4, 1], [3, 1, 5, 2, 4]} }, -108/126503*126503^(1/2), -.3036500403], [{{[4, 1, 2, 3], [4, 2, 5, 3, 1]}}, -279/908402*908402^(1/2), -.2927286045], [{{[2, 4, 1, 3], [1, 2, 4, 3, 5]}}, -3 /8197*639366^(1/2), -.2926449866], [{{[4, 1, 2, 3], [4, 3, 5, 2, 1]}, {[2, 3, 4 , 1], [3, 1, 2, 4, 5]}}, -351/1444922*1444922^(1/2), -.2920013872], [{{[1, 2, 4 , 3], [3, 4, 2, 1, 5]}}, -729/3126172*1563086^(1/2), -.2915453346], [{{[4, 1, 3 , 2], [4, 3, 2, 1, 5]}}, 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1], [1, 2 , 4, 3, 5]}}, -57/307973*1847838^(1/2), -.2515904542], [{{[1, 4, 2, 3], [4, 2, 1, 5, 3]}}, -90/129299*129299^(1/2), -.2502908230], [{{[2, 3, 4, 1], [1, 2, 3, 4, 5]}}, -180/1109071*2218142^(1/2), -.2417173521], [{{[1, 2, 4, 3], [2, 5, 3, 4, 1]}}, -183/78980*10770^(1/2), -.2404594292], [{{[4, 1, 3, 2], [4, 3, 2, 5, 1 ]}}, -243/1026266*1026266^(1/2), -.2398702031], [{{[1, 2, 4, 3], [2, 4, 5, 3, 1 ]}}, -567/268532*12206^(1/2), -.2332779528], [{{[2, 3, 4, 1], [1, 3, 2, 5, 4]}} , -135/714571*1429142^(1/2), -.2258531088], [{{[1, 4, 2, 3], [5, 3, 1, 2, 4]}}, -108/44693*8126^(1/2), -.2178324906], [{{[2, 3, 4, 1], [3, 1, 4, 2, 5]}}, -207/ 908402*908402^(1/2), -.2171857388], [{{[2, 3, 4, 1], [1, 2, 3, 5, 4]}}, -48/ 298505*1791030^(1/2), -.2151994007], [{{[2, 1, 4, 3], [3, 5, 1, 4, 2]}}, -72/ 113035*113035^(1/2), -.2141539194], [{{[1, 4, 2, 3], [3, 5, 1, 4, 2]}}, -72/ 114959*114959^(1/2), -.2123542747], [{{[1, 4, 2, 3], [3, 2, 5, 1, 4]}}, -72/ 129299*129299^(1/2), -.2002326584], [{{[4, 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4, 3], [4, 3, 2, 1, 5]}}, -351/2328380*1164190^ (1/2), -.1626541650], [{{[1, 4, 2, 3], [4, 5, 1, 2, 3]}}, -81/251189*251189^(1/ 2), -.1616161327], [{{[4, 1, 3, 2], [4, 3, 1, 2, 5]}}, -81/520303*1040606^(1/2) , -.1588078081], [{{[3, 1, 4, 2], [2, 4, 3, 5, 1]}}, -1/91*182^(1/2), -.1482498\ 633], [{{[4, 1, 2, 3], [4, 3, 5, 1, 2]}}, -51/13676*1578^(1/2), -.1481373541], [{{[3, 1, 4, 2], [2, 4, 1, 3, 5]}}, -81/314314*314314^(1/2), -.1444784774], [{{ [1, 2, 4, 3], [3, 2, 4, 5, 1]}}, -351/3126172*1563086^(1/2), -.1403736796], [{{ [3, 4, 1, 2], [4, 1, 2, 5, 3]}}, -33/940*15^(1/2), -.1359664366], [{{[3, 4, 1, 2], [4, 2, 3, 1, 5]}}, -29/4700*470^(1/2), -.1337670252], [{{[3, 1, 4, 2], [3, 2, 4, 1, 5]}}, -81/34034*3094^(1/2), -.1323829879], [{{[3, 1, 4, 2], [2, 3, 5, 4, 1]}}, -81/56602*8086^(1/2), -.1286826839], [{{[2, 3, 4, 1], [3, 4, 1, 2, 5]} }, -21/165953*995718^(1/2), -.1262706354], [{{[2, 3, 4, 1], [3, 2, 1, 5, 4]}}, -63/276413*276413^(1/2), -.1198288295], [{{[3, 1, 4, 2], [2, 3, 1, 4, 5]}}, 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[{{[1, 2, 3, 4], [4, 1, 3, 5 , 2]}}, -36/206711*206711^(1/2), -.7918094978e-1], [{{[1, 3, 2, 4], [5, 1, 3, 2 , 4]}}, -1/347*694^(1/2), -.7591896178e-1], [{{[4, 1, 2, 3], [4, 2, 3, 1, 5]}}, -4/1315*526^(1/2), -.6976331522e-1], [{{[1, 2, 3, 4], [5, 1, 3, 2, 4]}}, -21/ 9820*982^(1/2), -.6701369286e-1], [{{[2, 1, 4, 3], [3, 2, 5, 4, 1]}}, -39/ 593140*889710^(1/2), -.6201998118e-1], [{{[2, 1, 3, 4], [3, 4, 1, 5, 2]}}, -27/ 194219*194219^(1/2), -.6126577158e-1], [{{[1, 4, 2, 3], [3, 2, 1, 5, 4]}}, -27/ 251189*251189^(1/2), -.5387204421e-1], [{{[2, 1, 4, 3], [4, 2, 3, 1, 5]}}, -11/ 4700*470^(1/2), -.5073921645e-1], [{{[1, 4, 2, 3], [3, 5, 1, 2, 4]}}, -18/ 129299*129299^(1/2), -.5005816462e-1], [{{[4, 1, 2, 3], [4, 3, 2, 1, 5]}}, -27/ 651451*1302902^(1/2), -.4730835907e-1], [{{[2, 3, 4, 1], [2, 1, 4, 5, 3]}}, -15 /13676*1578^(1/2), -.4356981002e-1], [{{[1, 4, 2, 3], [3, 1, 4, 2, 5]}}, -18/ 412753*825506^(1/2), -.3962254649e-1], [{{[2, 1, 4, 3], [3, 4, 2, 1, 5]}}, -9/ 409276*1023190^(1/2), -.2224356403e-1], [{{[1, 2, 3, 4], [3, 2, 5, 1, 4]}}, -9/ 265631*265631^(1/2), -.1746236778e-1], [{{[3, 4, 1, 2], [4, 3, 1, 2, 5]}}, -27/ 2046380*1023190^(1/2), -.1334613842e-1], [{{[1, 4, 2, 3], [5, 2, 1, 4, 3]}}, -3 /301618*904854^(1/2), -.9461353174e-2], [{{[1, 2, 4, 3], [3, 2, 4, 1, 5]}}, -9/ 268532*12206^(1/2), -.3702824648e-2], [{{[4, 1, 3, 2], [4, 3, 5, 2, 1]}, {[2, 1 , 3, 4], [4, 1, 3, 5, 2]}, {[4, 1, 2, 3], [4, 1, 3, 5, 2]}, {[4, 1, 3, 2], [4, 2, 5, 3, 1]}, {[1, 4, 2, 3], [5, 2, 1, 3, 4]}, {[1, 3, 2, 4], [5, 1, 2, 3, 4]}} , 0, 0.], [{{[2, 1, 3, 4], [3, 2, 4, 5, 1]}}, 9/3126172*1563086^(1/2), .\ 3599325118e-2], [{{[1, 4, 2, 3], [3, 1, 4, 5, 2]}}, 3/44932*33699^(1/2), .\ 1225671284e-1], [{{[1, 4, 3, 2], [2, 1, 3, 4, 5]}}, 3/298505*1791030^(1/2), .\ 1344996254e-1], [{{[3, 4, 1, 2], [4, 3, 2, 1, 5]}}, 63/2328380*1164190^(1/2), .\ 2919433732e-1], [{{[1, 4, 2, 3], [3, 1, 2, 4, 5]}}, 18/656533*1313066^(1/2), .\ 3141660291e-1], [{{[1, 2, 4, 3], [2, 3, 4, 5, 1]}}, 99/3556972*1778486^(1/2), .\ 3711760736e-1], [{{[1, 2, 3, 4], [5, 1, 2, 3, 4]}}, 135/4864828*2432414^(1/2), .4327977810e-1], [{{[4, 2, 1, 3], [4, 1, 3, 2, 5]}}, 3/5258*7170^(1/2), .\ 4831258227e-1], [{{[1, 2, 3, 4], [4, 3, 2, 1, 5]}}, 153/4864828*2432414^(1/2), .4905041518e-1], [{{[3, 1, 4, 2], [3, 2, 1, 4, 5]}}, 6/12103*10374^(1/2), .\ 5049301908e-1], [{{[2, 3, 4, 1], [2, 4, 1, 5, 3]}}, 18/126503*126503^(1/2), .\ 5060834006e-1], [{{[1, 2, 4, 3], [2, 4, 3, 1, 5]}}, 39/78980*10770^(1/2), .\ 5124545213e-1], [{{[2, 1, 3, 4], [3, 1, 5, 4, 2]}}, 27/194219*194219^(1/2), .\ 6126577158e-1], [{{[4, 2, 1, 3], [4, 1, 2, 5, 3]}}, 15/44932*33699^(1/2), .\ 6128356420e-1], [{{[3, 1, 4, 2], [1, 4, 5, 2, 3]}}, 6/57421*344526^(1/2), .\ 6133261755e-1], [{{[4, 2, 1, 3], [4, 1, 2, 3, 5]}}, 63/1026266*1026266^(1/2), .\ 6218857118e-1], [{{[3, 1, 4, 2], [1, 4, 3, 5, 2]}}, 6/5005*2730^(1/2), .\ 6263664566e-1], [{{[3, 1, 4, 2], [3, 1, 2, 4, 5]}}, 45/499954*499954^(1/2), .\ 6364253793e-1], [{{[3, 1, 4, 2], [3, 2, 4, 5, 1]}}, 45/56602*8086^(1/2), .\ 7149037996e-1], [{{[3, 1, 4, 2], [1, 3, 5, 4, 2]}}, 45/34034*3094^(1/2), .\ 7354610443e-1], [{{[1, 4, 2, 3], [2, 4, 5, 1, 3]}}, 27/129299*129299^(1/2), .\ 7508724690e-1], [{{[3, 4, 1, 2], [4, 2, 1, 5, 3]}}, 27/127135*127135^(1/2), .\ 7572359089e-1], [{{[3, 1, 4, 2], [1, 4, 2, 5, 3]}}, 45/314314*314314^(1/2), .\ 8026582078e-1], [{{[4, 1, 3, 2], [4, 3, 1, 5, 2]}, {[1, 4, 2, 3], [4, 1, 2, 5, 3]}}, 21/44932*33699^(1/2), .8579698990e-1], [{{[2, 4, 1, 3], [1, 5, 2, 3, 4]}} , 27/195377*390754^(1/2), .8638573717e-1], [{{[1, 4, 3, 2], [2, 1, 4, 3, 5]}}, 54/714571*1429142^(1/2), .9034124354e-1], [{{[2, 4, 1, 3], [2, 1, 3, 5, 4]}}, 36/120211*120211^(1/2), .1038318031], [{{[4, 1, 2, 3], [4, 3, 1, 2, 5]}}, 117/ 1145102*1145102^(1/2), .1093361494], [{{[1, 3, 2, 4], [4, 3, 2, 1, 5]}}, 72/ 859519*1719038^(1/2), .1098296890], [{{[3, 4, 1, 2], [4, 1, 3, 5, 2]}}, 36/ 98935*98935^(1/2), .1144530898], [{{[4, 1, 2, 3], [4, 2, 5, 1, 3]}}, 45/126503* 126503^(1/2), .1265208501], [{{[4, 2, 3, 1], [3, 5, 2, 1, 4]}}, 39/65236*48927^ (1/2), .1322365703], [{{[1, 2, 3, 4], [3, 4, 2, 1, 5]}}, 387/4275628*2137814^(1 /2), .1323414873], [{{[3, 1, 4, 2], [2, 1, 5, 3, 4]}}, 27/4732*546^(1/2), .1333\ 261534], [{{[2, 1, 4, 3], [3, 4, 1, 2, 5]}}, 87/593140*889710^(1/2), .138352265\ 7], [{{[4, 2, 1, 3], [3, 5, 4, 1, 2]}}, 51/12428*1434^(1/2), .1553973138], [{{[ 1, 4, 2, 3], [5, 1, 3, 2, 4]}}, 17/2390*478^(1/2), .1555123803], [{{[3, 4, 1, 2 ], [4, 2, 3, 5, 1]}}, 9/940*282^(1/2), .1607826602], [{{[3, 1, 4, 2], [2, 4, 5, 1, 3]}}, 36/49231*49231^(1/2), .1622494271], [{{[1, 4, 2, 3], [5, 1, 4, 2, 3]}} , 81/44693*8126^(1/2), .1633743679], [{{[4, 1, 2, 3], [5, 3, 4, 2, 1]}}, 39/ 307973*1847838^(1/2), .1721408371], [{{[4, 3, 1, 2], [4, 3, 2, 5, 1]}}, 441/ 3083092*1541546^(1/2), .1775948425], [{{[4, 1, 2, 3], [4, 2, 1, 3, 5]}}, 189/ 98362*8942^(1/2), .1816986859], [{{[1, 4, 3, 2], [2, 1, 3, 5, 4]}}, 108/347423* 347423^(1/2), .1832291102], [{{[1, 4, 2, 3], [2, 5, 4, 1, 3]}}, 45/44932*33699^ (1/2), .1838506926], [{{[4, 1, 2, 3], [4, 1, 3, 2, 5]}}, 6/2893*7890^(1/2), .18\ 42219260], [{{[1, 4, 2, 3], [3, 1, 2, 5, 4]}}, 63/12428*1434^(1/2), .1919613876 ], [{{[1, 2, 3, 4], [4, 2, 3, 1, 5]}}, 61/9820*982^(1/2), .1946588221], [{{[1, 2, 3, 4], [4, 1, 2, 5, 3]}}, 69/92308*69231^(1/2), .1966799330], [{{[1, 3, 2, 4 ], [3, 4, 2, 1, 5]}}, 243/1510838*1510838^(1/2), .1976957458], [{{[1, 4, 2, 3], [2, 5, 3, 1, 4]}}, 63/100619*100619^(1/2), .1986097437], [{{[1, 4, 2, 3], [4, 1 , 5, 2, 3]}}, 72/129299*129299^(1/2), .2002326584], [{{[2, 1, 4, 3], [1, 4, 3, 2, 5]}}, 45/227198*1135990^(1/2), .2111034174], [{{[1, 4, 2, 3], [2, 4, 1, 5, 3 ]}}, 72/114959*114959^(1/2), .2123542747], [{{[4, 1, 2, 3], [4, 1, 5, 3, 2]}}, 57/49444*37083^(1/2), .2219978091], [{{[1, 4, 2, 3], [5, 1, 2, 3, 4]}}, 243/ 1184006*1184006^(1/2), .2233208756], [{{[1, 4, 2, 3], [3, 1, 5, 4, 2]}}, 81/ 129299*129299^(1/2), .2252617407], [{{[1, 2, 3, 4], [3, 4, 1, 2, 5]}}, 207/ 1239284*1858926^(1/2), .2277354049], [{{[4, 2, 3, 1], [2, 4, 3, 5, 1]}}, 3/347* 694^(1/2), .2277568854], [{{[1, 4, 2, 3], [5, 1, 2, 4, 3]}}, 117/520303*1040606 ^(1/2), .2293890562], [{{[4, 1, 2, 3], [4, 2, 1, 5, 3]}}, 90/142283*142283^(1/2 ), .2385975625], [{{[4, 1, 2, 3], [5, 4, 3, 2, 1]}}, 180/1109071*2218142^(1/2), .2417173521], [{{[4, 1, 2, 3], [4, 1, 2, 3, 5]}}, 135/564661*1129322^(1/2), .25\ 40708672], [{{[1, 4, 3, 2], [1, 4, 3, 2, 5]}}, 144/635671*1271342^(1/2), .25542\ 37581], [{{[4, 1, 2, 3], [5, 3, 2, 4, 1]}}, 51/229073*1374438^(1/2), .261011023\ 4], [{{[4, 2, 3, 1], [3, 5, 1, 4, 2]}}, 108/166907*166907^(1/2), .2643543614], [{{[2, 1, 4, 3], [3, 2, 4, 1, 5]}}, 531/175780*7990^(1/2), .2700215653], [{{[1, 4, 2, 3], [2, 1, 3, 4, 5]}}, 123/542530*1627590^(1/2), .2892370077], [{{[1, 3, 2, 4], [1, 4, 5, 2, 3]}}, 57/218957*1313742^(1/2), .2983809305], [{{[2, 1, 3, 4 ], [3, 2, 5, 1, 4]}}, 135/194219*194219^(1/2), .3063288578], [{{[1, 2, 4, 3], [ 3, 2, 1, 4, 5]}}, 291/190988*40926^(1/2), .3082382696], [{{[2, 1, 4, 3], [4, 1, 2, 3, 5]}}, 621/2018180*1009090^(1/2), .3090983261], [{{[2, 1, 3, 4], [3, 1, 4, 5, 2]}}, 93/67492*50619^(1/2), .3100183720], [{{[4, 3, 1, 2], [5, 1, 2, 3, 4]}} , 837/3556972*1778486^(1/2), .3138124987], [{{[3, 1, 4, 2], [3, 2, 1, 5, 4]}}, 99/95641*95641^(1/2), .3201202449], [{{[4, 1, 2, 3], [5, 4, 2, 3, 1]}}, 75/ 307973*1847838^(1/2), .3310400713], [{{[1, 2, 3, 4], [3, 1, 5, 2, 4]}}, 162/ 236171*236171^(1/2), .3333509755], [{{[1, 2, 4, 3], [2, 4, 1, 3, 5]}}, 747/ 2479972*1239986^(1/2), .3354147949], [{{[4, 1, 2, 3], [4, 1, 2, 5, 3]}}, 87/ 49444*37083^(1/2), .3388387613], [{{[4, 1, 3, 2], [4, 5, 2, 3, 1]}}, 387/ 1298726*1298726^(1/2), .3395878922], [{{[3, 1, 4, 2], [3, 1, 2, 5, 4]}}, 69/ 4732*546^(1/2), .3407223920], [{{[2, 1, 4, 3], [1, 3, 4, 2, 5]}}, 129/409370* 1228110^(1/2), .3492145507], [{{[2, 1, 3, 4], [4, 1, 2, 5, 3]}}, 105/67492* 50619^(1/2), .3500207427], [{{[1, 3, 2, 4], [2, 1, 5, 4, 3]}}, 216/364697* 364697^(1/2), .3576742340], [{{[4, 1, 2, 3], [5, 3, 4, 1, 2]}}, 216/714571* 1429142^(1/2), .3613649742], [{{[4, 2, 3, 1], [2, 4, 5, 3, 1]}}, 27/7634*11798^ (1/2), .3841632391], [{{[1, 2, 3, 4], [4, 2, 1, 3, 5]}}, 1107/367268*16694^(1/2 ), .3894437475], [{{[1, 4, 2, 3], [3, 1, 5, 2, 4]}}, 135/114959*114959^(1/2), .\ 3981642650], [{{[4, 1, 2, 3], [5, 4, 3, 1, 2]}}, 93/298505*1791030^(1/2), .4169\ 488389], [{{[2, 1, 3, 4], [3, 4, 2, 1, 5]}}, 153/446596*1563086^(1/2), .4283196\ 890], [{{[1, 2, 4, 3], [3, 2, 1, 5, 4]}}, 270/377309*377309^(1/2), .4395569810] , [{{[1, 4, 2, 3], [1, 3, 2, 4, 5]}}, 96/279869*1679214^(1/2), .4444976407], [{ {[1, 3, 4, 2], [1, 4, 2, 3, 5]}}, 84/208169*1249014^(1/2), .4509692015], [{{[1, 2, 4, 3], [1, 5, 3, 4, 2]}}, 121/7180*718^(1/2), .4515679894], [{{[1, 3, 4, 2], [1, 4, 3, 2, 5]}}, 243/577663*1155326^(1/2), .4521515205], [{{[4, 1, 2, 3], [4, 1, 5, 2, 3]}}, 171/142283*142283^(1/2), .4533353686], [{{[1, 2, 3, 4], [4, 1, 3 , 2, 5]}}, 411/108020*14730^(1/2), .4617841501], [{{[1, 4, 3, 2], [2, 1, 4, 5, 3]}}, 159/13676*1578^(1/2), .4618399862], [{{[4, 1, 3, 2], [4, 5, 3, 1, 2]}}, 261/315719*315719^(1/2), .4645047378], [{{[4, 3, 1, 2], [4, 3, 5, 2, 1]}}, 1323 /3944692*1972346^(1/2), .4710188597], [{{[3, 1, 4, 2], [2, 4, 1, 5, 3]}}, 99/ 3367*259^(1/2), .4731969756], [{{[1, 2, 3, 4], [2, 1, 5, 4, 3]}}, 342/516041* 516041^(1/2), .4760844558], [{{[3, 4, 1, 2], [4, 1, 5, 2, 3]}}, 171/127135* 127135^(1/2), .4795827424], [{{[1, 4, 2, 3], [1, 2, 3, 4, 5]}}, 351/1007863* 2015726^(1/2), .4944488410], [{{[1, 3, 2, 4], [1, 4, 3, 5, 2]}}, 96/19085*10410 ^(1/2), .5132210175], [{{[3, 4, 1, 2], [3, 5, 2, 4, 1]}}, 927/1623380*811690^(1 /2), .5144635862], [{{[1, 4, 2, 3], [1, 4, 2, 3, 5]}}, 96/208169*1249014^(1/2), .5153933732], [{{[2, 1, 3, 4], [3, 1, 5, 2, 4]}}, 216/172679*172679^(1/2), .519\ 7972634], [{{[2, 1, 4, 3], [1, 2, 4, 3, 5]}}, 45/110074*1651110^(1/2), .5253101\ 217], [{{[1, 4, 2, 3], [2, 5, 1, 4, 3]}}, 189/129299*129299^(1/2), .5256107282] , [{{[1, 4, 2, 3], [2, 5, 1, 3, 4]}}, 129/44932*33699^(1/2), .5270386521], [{{[ 3, 4, 1, 2], [3, 5, 2, 1, 4]}}, 129/940*15^(1/2), .5315051615], [{{[1, 2, 3, 4] , [4, 1, 2, 3, 5]}}, 1557/4216708*2108354^(1/2), .5361506674], [{{[4, 2, 3, 1], [3, 5, 4, 1, 2]}}, 213/18044*2082^(1/2), .5386257943], [{{[4, 1, 3, 2], [4, 5, 2, 1, 3]}}, 177/12428*1434^(1/2), .5393200891], [{{[1, 3, 4, 2], [1, 5, 2, 3, 4 ]}}, 549/1026266*1026266^(1/2), .5419289774], [{{[1, 3, 2, 4], [1, 3, 4, 5, 2]} }, 333/745009*1490018^(1/2), .5456051637], [{{[1, 4, 2, 3], [1, 2, 4, 3, 5]}}, 120/279869*1679214^(1/2), .5556220508], [{{[4, 2, 3, 1], [3, 4, 5, 2, 1]}}, 129 /46151*39558^(1/2), .5559372286], [{{[2, 1, 3, 4], [3, 4, 1, 2, 5]}}, 435/ 906116*1359174^(1/2), .5596841229], [{{[2, 1, 4, 3], [1, 2, 3, 4, 5]}}, 801/ 1981990*1981990^(1/2), .5689600677], [{{[1, 3, 4, 2], [1, 5, 3, 2, 4]}}, 177/ 26290*7170^(1/2), .5700884708], [{{[2, 1, 3, 4], [1, 4, 3, 2, 5]}}, 765/1735406 *1735406^(1/2), .5807121169], [{{[1, 4, 3, 2], [2, 1, 5, 4, 3]}}, 324/276413* 276413^(1/2), .6162625520], [{{[2, 1, 4, 3], [3, 2, 1, 4, 5]}}, 471/125020* 26790^(1/2), .6166344289], [{{[2, 1, 3, 4], [4, 1, 3, 2, 5]}}, 471/78980*10770^ (1/2), .6188873834], [{{[4, 3, 2, 1], [5, 4, 1, 2, 3]}}, 687/261212*55974^(1/2) , .6222383645], [{{[4, 3, 1, 2], [4, 3, 5, 1, 2]}}, 255/18668*2154^(1/2), .6339\ 649353], [{{[1, 3, 4, 2], [1, 3, 2, 5, 4]}}, 729/1298726*1298726^(1/2), .639688\ 8203], [{{[1, 2, 3, 4], [2, 1, 4, 5, 3]}}, 303/25532*2946^(1/2), .6441309452], [{{[3, 4, 1, 2], [3, 5, 4, 2, 1]}}, 1503/2582180*1291090^(1/2), .6613794954], [ {{[1, 4, 2, 3], [1, 2, 3, 5, 4]}}, 57/108506*1627590^(1/2), .6701833106], [{{[1 , 3, 4, 2, 5], [2, 1, 3, 4]}}, 309/625378*1876134^(1/2), .6767804534], [{{[2, 1 , 3, 4], [3, 2, 4, 1, 5]}}, 1647/268532*12206^(1/2), .6776169106], [{{[4, 1, 2, 3], [5, 4, 2, 1, 3]}}, 819/1444922*1444922^(1/2), .6813365702], [{{[4, 1, 3, 2] , [4, 5, 1, 2, 3]}}, 342/251189*251189^(1/2), .6823792269], [{{[4, 3, 1, 2], [4 , 5, 2, 3, 1]}}, 1917/3901612*1950806^(1/2), .6862542955], [{{[1, 2, 3, 4], [1, 3, 5, 2, 4]}}, 1791/3391828*1695914^(1/2), .6876440311], [{{[1, 4, 2, 3], [1, 4 , 5, 3, 2]}}, 351/520303*1040606^(1/2), .6881671684], [{{[4, 3, 1, 2], [4, 5, 3 , 2, 1]}}, 723/1629860*2444790^(1/2), .6935995075], [{{[4, 2, 3, 1], [3, 5, 2, 4, 1]}}, 765/1198538*1198538^(1/2), .6987720592], [{{[1, 2, 4, 3], [1, 5, 2, 3, 4]}}, 1737/3083092*1541546^(1/2), .6995062163], [{{[4, 1, 3, 2], [4, 5, 1, 3, 2 ]}}, 231/12428*1434^(1/2), .7038584210], [{{[2, 1, 4, 3], [1, 3, 2, 5, 4]}}, 1593/2553980*1276990^(1/2), .7048424172], [{{[1, 3, 4, 2], [1, 5, 2, 4, 3]}}, 351/44693*8126^(1/2), .7079555944], [{{[4, 1, 2, 3], [5, 2, 4, 1, 3]}}, 675/ 908402*908402^(1/2), .7082143658], [{{[1, 3, 2, 4], [2, 3, 1, 4, 5]}}, 981/ 1906418*1906418^(1/2), .7104932274], [{{[4, 1, 2, 3], [5, 3, 2, 1, 4]}}, 378/ 564661*1129322^(1/2), .7113984280], [{{[1, 3, 2, 4], [2, 1, 3, 5, 4]}}, 486/ 458387*458387^(1/2), .7178275511], [{{[1, 4, 2, 3], [1, 5, 4, 3, 2]}}, 783/ 1184006*1184006^(1/2), .7195894882], [{{[2, 1, 4, 3], [1, 2, 3, 5, 4]}}, 123/ 42676*64014^(1/2), .7292205312], [{{[3, 1, 4, 2], [3, 1, 5, 4, 2]}}, 162/49231* 49231^(1/2), .7301224219], [{{[3, 1, 4, 2], [3, 1, 4, 5, 2]}}, 111/17108*12831^ (1/2), .7349435617], [{{[1, 4, 2, 3], [1, 2, 4, 5, 3]}}, 432/656533*1313066^(1/ 2), .7539984699], [{{[1, 4, 3, 2], [1, 4, 3, 5, 2]}}, 123/14465*7890^(1/2), .75\ 53098963], [{{[4, 3, 2, 1], [5, 4, 1, 3, 2]}}, 2511/5395108*2697554^(1/2), .764\ 4192999], [{{[1, 2, 4, 3], [1, 3, 2, 4, 5]}}, 405/840778*2522334^(1/2), .765023\ 8607], [{{[1, 4, 2, 3], [1, 5, 3, 4, 2]}}, 17/478*478^(1/2), .7775619015], [{{[ 2, 1, 3, 4], [3, 2, 1, 5, 4]}}, 486/377309*377309^(1/2), .7912025656], [{{[1, 3 , 4, 2], [1, 3, 5, 2, 4]}}, 360/412753*825506^(1/2), .7924509299], [{{[3, 4, 1, 2], [4, 2, 5, 1, 3]}}, 54/22607*113035^(1/2), .8030771978], [{{[1, 2, 4, 3], [1 , 2, 4, 3, 5]}}, 429/840778*2522334^(1/2), .8103586080], [{{[1, 2, 4, 3], [1, 2 , 3, 4, 5]}}, 1413/3027806*3027806^(1/2), .8120413399], [{{[4, 1, 2, 3], [5, 4, 1, 2, 3]}}, 165/34979*29982^(1/2), .8167833095], [{{[1, 2, 3, 4], [2, 1, 3, 5, 4]}}, 666/648611*648611^(1/2), .8269553751], [{{[2, 4, 1, 3], [2, 5, 3, 1, 4]}} , 162/38311*38311^(1/2), .8276624848], [{{[3, 4, 1, 2], [4, 5, 1, 2, 3]}}, 414/ 246985*246985^(1/2), .8330384590], [{{[1, 4, 2, 3], [1, 4, 5, 2, 3]}}, 267/ 301618*904854^(1/2), .8420604324], [{{[4, 3, 1, 2], [4, 5, 1, 3, 2]}}, 339/ 18668*2154^(1/2), .8428004432], [{{[1, 2, 3, 4], [1, 4, 3, 2, 5]}}, 1305/ 2373494*2373494^(1/2), .8470644246], [{{[1, 3, 2, 4], [2, 1, 3, 4, 5]}}, 219/ 393845*2363070^(1/2), .8547853534], [{{[4, 3, 1, 2], [4, 5, 3, 1, 2]}}, 594/ 474239*474239^(1/2), .8625570160], [{{[1, 4, 2, 3], [1, 5, 4, 2, 3]}}, 63/74329 *1040606^(1/2), .8646202886], [{{[1, 3, 2, 4], [1, 3, 2, 5, 4]}}, 54/85709* 1885598^(1/2), .8651509443], [{{[1, 4, 2, 3], [1, 2, 5, 4, 3]}}, 339/63574* 27246^(1/2), .8801800825], [{{[2, 1, 3, 4], [2, 4, 1, 3, 5]}}, 1971/2479972* 1239986^(1/2), .8850101215], [{{[4, 1, 2, 3], [5, 3, 1, 2, 4]}}, 927/98362*8942 ^(1/2), .8911887925], [{{[1, 3, 4, 2], [1, 4, 2, 5, 3]}}, 405/412753*825506^(1/ 2), .8915072961], [{{[3, 4, 1, 2], [3, 5, 4, 1, 2]}}, 291/12220*1410^(1/2), .89\ 41931515], [{{[1, 4, 2, 3], [1, 2, 5, 3, 4]}}, 513/656533*1313066^(1/2), .89537\ 31830], [{{[4, 3, 2, 1], [5, 3, 4, 1, 2]}}, 2961/5336188*2668094^(1/2), .906374\ 8549], [{{[1, 2, 3, 4], [1, 3, 4, 2, 5]}}, 489/855322*2565966^(1/2), .915808489\ 5], [{{[4, 3, 2, 1], [5, 4, 3, 1, 2]}}, 1119/2229140*3343710^(1/2), .9179246730 ], [{{[1, 2, 4, 3], [1, 2, 5, 4, 3]}}, 867/190988*40926^(1/2), .9183593807], [{ {[1, 4, 3, 2], [1, 4, 5, 2, 3]}}, 153/165953*995718^(1/2), .9199717726], [{{[1, 4, 3, 2], [1, 4, 5, 3, 2]}}, 999/1145102*1145102^(1/2), .9335625068], [{{[2, 1, 4, 3], [2, 1, 3, 5, 4]}}, 522/310435*310435^(1/2), .9368825784], [{{[1, 4, 2, 3 ], [1, 5, 3, 2, 4]}}, 291/26290*7170^(1/2), .9372640959], [{{[1, 2, 4, 3], [1, 3, 2, 5, 4]}}, 2637/3901612*1950806^(1/2), .9440023878], [{{[1, 3, 2, 4], [1, 4 , 3, 2, 5]}}, 612/838699*1677398^(1/2), .9450686508], [{{[1, 4, 3, 2], [1, 5, 4 , 3, 2]}}, 540/651451*1302902^(1/2), .9461671815], [{{[1, 4, 2, 3], [1, 5, 2, 3 , 4]}}, 963/1026266*1026266^(1/2), .9505967309], [{{[1, 2, 4, 3], [1, 2, 5, 3, 4]}}, 2691/3944692*1972346^(1/2), .9580587690], [{{[1, 4, 3, 2], [1, 5, 3, 4, 2 ]}}, 11/263*526^(1/2), .9592455844], [{{[1, 4, 2, 3], [1, 5, 2, 4, 3]}}, 477/ 44693*8126^(1/2), .9620935003], [{{[1, 3, 2, 4], [1, 2, 3, 4, 5]}}, 828/1463299 *2926598^(1/2), .9680076659], [{{[1, 2, 4, 3], [1, 2, 3, 5, 4]}}, 1011/1629860* 2444790^(1/2), .9698881080], [{{[1, 3, 2, 4], [1, 3, 4, 2, 5]}}, 219/302237* 1813422^(1/2), .9757665475], [{{[1, 3, 2, 4], [1, 3, 2, 4, 5]}}, 255/406337* 2438022^(1/2), .9798793842], [{{[4, 3, 2, 1], [5, 4, 2, 3, 1]}}, 609/1149922* 3449766^(1/2), .9836570943], [{{[4, 3, 2, 1], [5, 4, 3, 2, 1]}}, 2025/4141094* 4141094^(1/2), .9951017343]] The whole thing took, 2.839, of CPU time