{{1, -1, 1, 1, -1/4, 1/2, -1, -1, -2, -3, -1, -1, 1, -2, 1/3, 1/2, -1/6, 
  -1/2, 1/3, 2/3, -1/3, -2/3, 1/3, 2/3, 1/3, -2/3, 1/3, -2/3, -2/3, 2/3, 
  -1/9, 1/9, -1/18, 1/9, -1/18, 1/18, -1/9, 1/18, -5/72, 1/36, 1/4, -5/18, 
  1/9, 1/4, -5/18, 1/9, 1/9, 1/9, -2/9, -2/9, 1/9, 1/9, -1/9, 2/9, -1/9, 1/4, 
  -11/18, 1/9, 1/3, 1/18, -1/9, 1/18, 5/72, -1/36, 1/18, 1/18, -1/18, -1/18, 
  1/18, 1/18, -1/2, 1/2, 1/2, -1/4, 7/4, -1/4, -1/4, 1/4, -7/4, -3/2, 1/4, 
  1/4, -1/6, 1/4, -1/4, 1/6, 1/3, 1/2, -7/12, 1/6, 2/3, 2/3, -1/4, 2, 1/3, 
  -13/2, -1/6, -21/8, 13/2, -9/4, 6, -2/3, -2/3, 3/16, -17/4, -61/48, 7/2, 
  71/48, 11/6, -25/6, -7/3, 61/48, -11/4, -31/24, -2/3, -1/3, -5/8, -1/6, 
  -13/24, -5/24, 3/8, 2, -1/2, 1/3, 1/3, 4/3, 4/3, -1/3, -4/3, 2/3, 2/3, 5/2, 
  -5/6, -7/8, -7/3, 3/2, 1/3, 1/12, -47/4, 1/3, 37/4, 3/4, -7/12, 5/3, -1/2, 
  -3/2, 13243/360, 19/24, -155/24, 2/3, -3673/360, -25/8, 155/24, 25/8, 
  -13783/360, 3839/180, -43/12, 3017/360, -3839/180, -2/3, -1, -1/2, 1/3, 
  11/24, 1/6, -1/6, 13/24, 3/8, 11/24, -5839/180, -187/36, -43/12, 589/36, 
  -3839/180, -1/4, -10/27, -2/9, 1/6, 29/36, 2/9, -47/108, 5/4, -43/108, 1/3, 
  -91/27, 173/216, 263/108, -3/4, 37/24, 535/216, -3/8, 10/27, 43/27, 
  -47/108, -37/27, -649/108, -3968/9, 259/108, 39557/108, -37/27, -1/4, 
  -181/216, 25/72, 1/2, 5/12, 17/18, -37/72, -1/6, 407/108, 61/108, -37/24, 
  55/27, -587/216, -623/108, -11/24, -29/108, 127/216, -1087052/5481, 
  -7480688/9135, -437/216, -38916667/54810, -1/6, 8099/216, 31442759/73080, 
  78853409/109620, 100913/216, 1559/216, 22217/90, 36861959/876960, 1/4, 
  79/432, -1/9, -25/72, 7/36, 5/18, 5/36, -527/216, -139/216, -1/6, -61/54, 
  -317/216, 671/216, 1/6, 365/216, -25/432, 43/54, 1/6, -35/216, -23/27, 
  1/18, -671/432, 1/18, 109/216, -7519/216, -37/54, -1/6, 37/54, -5/72, 1/36, 
  1/18, 1/18, -1/18, -1/9, -1/18, 1/9, 1/18, -1/18, 1/18, -1697/90, -2788/45, 
  307/5, -1/18, 1/9, -1/18, 1/6, -1/18, 1/2, -1/6, -1/2, -1/8, -10/27, 
  -13/18, 5/24, 7/72, -16/9, -1/12, 95/216, 1/6, -5/216, 37/216, 317/216, 
  -239/216, 1/6, -41/216, -1/6, -41/108, 337/108, 23/216, 185/27, -506/135, 
  298/9, -152/27, 55/54, -259/108, -21739/540, 7/4, -5/4, 11878/9, -11878/9, 
  -1/4, -115/4, -7/4, 87/4, 57/2, -58607/18, -87/2, 58607/18, 87/2, -7807/6, 
  -39, -87/2, 19511/6, 3/4, 3/2, 1333/15, 11/27, -2/27, 98/27, -3/2, 3/2, 
  17787/20, 3350699/4060, 1/4, 7/4, 1/4, -3/4, -3/2, -258295627/194880, 
  -805310999/175392, 10464277/13920, 259757227/97440, 19606/15, 
  -805310999/175392, -20939/15, 10464277/13920, -197/108, 26/27, -163/216, 
  3/2, -11341/16, -3/2, 10481/16, 11341/16, -348073/406, -13241763/4060, 
  -64291851/16240, -280019189/97440, 6280303/4060, -12773/60, 18, 
  -3776667/4060, 17129527/12180, 8714417/4872, 179/8, -7276247/2436, 
  -459841/3045, -2889097/8120, -7/4, 93/16, -7/8, -60949/360, -56561/360, 
  6865/72, -5/8, -129/8, -10137287/219240, -6127/45, -11321/45, 15883/90, 
  -10137287/219240, -16/27, -28/27, -7/54, 85/54, 7807/4, 7/8, 7/8, 9, 
  -237/16, -9, -7/4, 51/16, -51/16, -79/16, 1057/24, 517/24, -517/24, 281/16, 
  4301/72, -4547/72, 44971/360, 5/8, -10493/120, -2227/18, -2968207/24360, 
  -3996918923/876960, 225052969/58464, 71326147/146160, 12119/90, 9269/45, 
  -3996918923/876960, 120778517/32480, 71326147/146160, 55/27, -271/54, 
  -40/27, -11/108, 1/4, -7/12, -1316, 29/24, 33/2, -7/6, 43/2, 7901/12, 
  -373/12, -87/4, 5/6, 11807/9, -2, 11639/18, 37/9, -2/9, 1075310947/876960, 
  8321333/3045, -205/72, 197239/1080, -1/6, -533921999/526176, 
  -899422829/46980, -25001/216, 36688794973/2630880, 5416/45, -194317/378, 
  3441707/7560, -695/972, -97/243, -1/3, 637/243, -559/1944, -449/243, 
  1189/972, -1319/648, -5989/1944, 3737/1944, 5/3, 1/3, -263980543/19488, 
  -37/2, 553/12, -4/3, 15361/12, 43/6, 603, -14/3, -275/6, 1266659501/876960, 
  -52692431/48720, -603, -1266440261/876960, -173/72, 3589027/25920, 
  -142944127/18270, 529/72, -1787137249/1753920, 1/6, 91147703/131544, 
  20690427259/2630880, -130929209/97440, 398923673/164430, -260704831/292320, 
  -1675491019/1753920, 329371513/438480, 4165/1944, -9679/1944, -1693/648, 
  -205/243, 253/1944, 1111/1944, 3/2, 73689089/48720, 23421319/6960, 3/8, 
  128974477/48720, -19/3, -12689/120, -4548191/1740, -64299971/24360, 
  -11233/8, -156883/240, -5817541/9744, 53137001/48720, 85301507/36540, 
  -2337568/3045, 149/144, -37561/160, -989333/8640, -91/36, 30353/270, 
  54198205/263088, 113089381/164430, -17347/216, -983521355/526176, 
  44023/360, -5176553/27405, 3352403/73080, -6007/3888, -89/243, 7753/1944, 
  89/243, -88/243, 362/243, 1/2, 80/243, 68/243, -20527/96, 5351/864, 
  1542461/1296, 3947/18, -3/2, 17573/360, 102, 7/48, -595/24, 19/4, -923/360, 
  -1657/8, 185/8, 841/8, -9079/180, -8429/45, -265/24, 42761/180, 3839/45, 
  23/72, -179634967/2630880, 7230371/9135, 1/9, 2687/216, 1581364369/5261760, 
  -10527031/657720, -1358350937/584640, 804110207/328860, -4793/180, 
  24237949/109620, 74842219/876960, -1147/1944, 4067/1944, 4/3, 271/108, 
  913/1944, -9839/1944, -86/243, -1301/324, -521/243, 379/243, 
  1391239441/584640, 476209309/194880, -68, -13935713437/584640, 
  -184953253/219240, -621/16, 125813/96, 3785/288, -695081/432, 2455/4, 
  8911/9, 68, 3966216731/97440, 157681/180, -2838454027/1753920, 
  -19726073/3045, -7247/360, 72162695977/1753920, 625649/2436, -6119111/3654, 
  -4218797813/125280, -14948743/438480, 580758907/292320, 1782756299/438480, 
  7/4, -49563707/41760, 600233/8120, -93/16, -70741651/292320, 
  343833103/97440, 14522461/928, 275761463/58464, -175781933/32480, 
  -1054049/4060, -16876903/12180, 80605715/29232, 56714239/29232, 
  12162575/9744, -1248382657/1753920, -28101555037/1753920, 
  -3779920043/1753920, 7869337393/438480, 99651317/125280, 285/4, 
  26898449/19488, 6818951/6496, -197255/108, -1513499/3045, -2, 2, 5/3, -5/3, 
  -5/12, -2, -2, -1, -1, 3/4, -3/4, -5/4, 1/3, 1/3, -1/3, -1/2, -7/3, 7/3, 
  -5/4, 2, 2, 4, 6, 2, 2, -2, 4, 1/3, 1/3, -1/3, -3/2, -1/6, -1/2, 1/6, 1/4, 
  5/64, -4/9, 4/9, 4/9, -4/9, -19/18, 1/2, 1/18, -43/48, -1/3, -1/3, 1/3, 
  3/4, 371/192, 5/4, -1/6, 131/192, -1/3, -1/3, 1/3, 1/2, 5/2, -1/6, -1/2, 
  1/6, 5/4, 5/6, 251/192, -7/8, 1, -679/72, -1, 1/9, 1/9, -1/9, -1/9, -1/9, 
  1/9, 1, -1, -1, -25/24, -1, 1/3, 1/3, -5/8, -5/8, -1/3, 5/8, 7/18, -1/3, 
  -1/18, 1/9, -1/6, 1/18, 1/9, -1/2, 1/18, -3703/2160, -1/54, 103/2160, 
  89/54, 1/9, -2/9, 1/9, -1/9, 2/9, -1/9, 5/36, -1/18, 19/30, -23/45, -4/9, 
  -1559/1440, -151/36, -1/4, 2/9, 1/6, 1/3, 1/9, -38/45, 51/40, 16/27, -2/27, 
  -1/9, 17/24, -49/30, -7/27, 49/360, -1/4, -4/9, 1/6, -1/3, -1/9, 4919/1080, 
  4817/270, 1/3, -27893/1080, 1, 2/9, -4009/180, -1/9, -1/9, 1/9, 1/9, 1/9, 
  -1/9, -1/4, 1, -2/9, 7/6, -1/3, -1/9, -1661/1080, -1273/540, -2/3, 
  1661/1080, 1, 2/9, -4009/180, -1/9, 2/9, -1/9, -5/36, 1/18, -4/5, 17/180, 
  -7/12, 25/36, -7/36, -1/9, 91/96, -541/720, -1/4, -373/1440, 187/72, -11/8, 
  -13357/720, -1/2, 5/16, -5/12, -25/16, -1/6, -127/48, 127/48, 13/6, 2/3, 
  -2/3, 95/48, -3/2, 5/12, -5/16, -100759659083/2630880, -5/12, -3/4, 
  355/192, -21518672317/526176, 2902940729/65772, -81724555729/2630880, 
  -81525188617/2630880, 11636596/435, -693680305/37584, -4675136/435, 5/12, 
  3/4, -355/192, 4088539471/263088, -982056967/65772, -3888049423/263088, 
  -11300158837/657720, -1/2, 167/48, -187/48, -167/48, -9/4, -209/96, 3/4, 
  1/4, 113/96, 1, 1, -5/4, -5/4, 5/2, -1, 1, 2, 1, 491/120, -29/24, 1/12, 
  15/4, 3/4, 7/16, -7/16, -25/24, 154361861/75168, -154361861/75168, 
  -154515329/75168, 154515329/75168, 154515329/75168, -154515329/75168, 
  -25/24, 154455821/75168, -154455821/75168, -154515329/75168, -29/48, 
  1892/15, -1/6, -5/24, 2/3, -1/3, -1/3, 1/3, -3/2, 1/3, -1/3, -5/2, 5/12, 
  3/2, -3/4, 185/96, 1, 3, -1/2, 1/2, -1, 1/4, 5/4, 5/4, 2, -2, -2, -57/40, 
  -1/12, 29/24, 2614510891/328860, 5119323359/876960, -2614510891/328860, 
  45257702977/876960, 7170128711/164430, -2699953939/328860, 1/2, 
  -20701082371/10523520, 23/30, 29883115567/1169280, -2/3, 
  -89093709683/2630880, -361/90, 154934089/15660, -80168864849/2630880, 
  11086641553/328860, -81624872173/1315440, 242606881/21924, 
  -30307962389/526176, 302896207/9072, 21486400277/526176, -1803293806/82215, 
  1882128157/93960, 21474272741/526176, -1/2, -12204849521/876960, 348073/36, 
  -23/30, -3401362529/657720, 2/3, 7184575945/233856, 4407787973/187920, 
  -21914464847/657720, -766541249/46980, 3158416313/187920, 
  -42040564789/1315440, -1/2, -253/45, -283/48, 1/2, 967/180, 
  529986641/2630880, 12155/1728, 1039/540, 197009647/375840, -121727/756, 
  1/2, -109/18, -1, -1/2, 109/18, 127/60, 16/9, -1, -1259/72, -3/4, 1, 3, 
  1/2, -1/2, 162808517/93960, 162808517/93960, -162808517/93960, 
  162808517/93960, 162808517/93960, -162808517/93960, -1, 
  -8160490993/3946320, 8160490993/3946320, 162698897/93960, -1, 
  -8157202393/3946320, 8157202393/3946320, 162698897/93960, 154515329/75168, 
  154515329/75168, -154515329/75168, -53/108, -77/48, -29/54, -13/54, 
  109/108, 125/48, 17/24, 11/8, 2/3, -17/24, -1/6, 3/2, -3/2, 139/15, 1/2, 1, 
  59/9, 1, -13/15, 241/18, 1, 167/72, -43/18, -1, 510649673/2630880, 
  -271721/8640, 12109/540, 209500063/375840, -263903/1890, 1, -3, -1, 3/4, 
  -931/320, 29883115567/1169280, 25/96, -89086639193/2630880, 
  -180434554057/5011200, 9/5, -3401362529/657720, -1/2, -1, -371/192, 
  7183947457/233856, 71/96, -13/10, 1447470619/62640, -4/3, 
  -405875436167/35078400, -2672459003/187920, 1/4, -81/64, -419/288, 19/36, 
  1511/960, -1/9, 371/192, -553/72, -539/1440, -31/64, 71/288, -1/9, 
  10309/960, -7/24, -7/36, -1/18, 1/6, -162761537/187920, -5/9, -1/9, 5/9, 
  1/9, 1/9, -1/9, -1, 82/45, 2/9, -82/45, 1/9, -3043/2880, 1087/144, 
  1793/2880, 457/288, -37/45, -349/60, -88539347723/8769600, 
  88539347723/8769600, 88539347723/2505600, -554999489/1753920, 
  54497448433/2630880, 88539347723/8769600, -364411517209/26308800, -1/2, 
  29/90, 17/9, 7/12, -19/90, -1/6, -3601/1440, -63569/1440, 1903/1080, 
  5901/160, -119/90, -371/18, -1/9, 180716580217/7516800, 337/18, -1/2, 
  -276577329589/17539200, -95126208493/5846400, -4/15, -361/45, 2/3, 
  293084282689/26308800, -16248383839/3507840, 15467/2160, 
  106240083997/8769600, 276577329589/17539200, 96645196013/5846400, 361/45, 
  -330419603417/8769600, -81842/315, -1/2, -29883115567/1169280, -4/15, -1, 
  -1/3, 89088941213/2630880, 29883115567/1169280, 37/16, 
  -89087625773/2630880, 276647681269/17539200, 95126208493/5846400, 361/45, 
  -5210654519/139200, -81842/315, -2243054519/604800, -4/15, 
  -14286333421/907200, 2/3, -51973552889/2923200, -9871256971/3758400, 
  191127286487/13154400, 62261949989/2923200, 8005679/1044, 
  155015293691/17539200, 5758644517/187920, 248015137/90720, -1808023/3915, 
  -403/180, -1273/36, -1/12, 589/90, 1/6, 391/90, 634/15, -8743/1080, 
  -551/360, 493/180, 163177421/43848, -47/9, -128809449967/5846400, 20377/72, 
  -12826986233/751680, -14436780859/1753920, 3/5, 103529683/109620, -2/3, 
  51973552889/2923200, 4425142747/243600, -312403349/146160, 
  -62261949989/2923200, 7062521513/751680, 5776602443/584640, 
  -52229657/21924, -31626674249/1753920, 262044985/175392, -1/2, 
  -3401362529/657720, 3/5, 4/3, 1/3, 5/8, 7184181313/233856, -127/48, -5/8, 
  -213209479213/5261760, -145242050671/5261760, -52229657/21924, 
  1974306959/64960, 262044985/175392, 527355761/5261760, -436673/17280, 
  59/160, -7957/480, 35/108, 529986641/5261760, 399306719/1503360, 
  43279/4320, 197009647/751680, -529986641/5261760, -4781873/120960, 
  -988/135, -1802677489/5261760, 976043/15120, 1/2, -1781/1440, 37/16, -7/12, 
  -2689/1440, 1/6, -259/360, -1753/180, 17327/4320, 569/1440, 1781/1440, 
  -1549/144, -61/36, -43157/4320, 76/9, -527355761/5261760, -48731/3456, 
  -173/1440, -37147/4320, 1/3, 529986641/5261760, -388731869/1503360, 
  11833/1080, 197009647/751680, 529986641/5261760, 2288749/24192, -1903/540, 
  955457569/5261760, -121727/1512, -19/15, -13/160, -305/288, -57/160, 
  -4757/1440, -1/6, 7/16, -5347/720, 3593/360, 109/240, 578731001/5261760, 
  24491/3456, -1903/540, 166061311/751680, -121727/1512, -12743/144, 
  180078713/250560, 224549633/250560, -202376813/250560, 4/5, 
  -1589067001/10523520, -1/2, -4/5, -2819/180, 1/2, 1753877017/10523520, 
  24781/720, 34303513/50112, -319/360, 823929133/394632, 68323/720, 11/18, 
  11/18, -10466009/11745, -199180433/187920, -11/18, 18134813/18792, 
  -165042677/93960, -5879/60, 171905411/93960, -319/360, 815313001/394632, 
  41/48, -7/18, -7/18, 2093/720, 7/6, 7/18, -97/48, -165042677/93960, 
  -5879/60, 171905411/93960, -4813/1728, -14633/4860, -90887/19440, -197/144, 
  491033/77760, -4325/48, 103/120, -63167/58320, -22973/5832, -7/27, 
  -847/432, -132043/58320, 31115/11664, 847/432, 20555/11664, 165629/23328, 
  -7650341/116640, 559/432, 23516243/116640, 4439/60, -1/9, -1/9, 1/9, 1/9, 
  1/9, -1/9, 26479/11664, 79723/11664, 1279/432, -25993/11664, 4439/60, -1/2, 
  -62/45, -13/36, 7/12, 263/180, -1/6, 53/45, 4127/720, -3893/1080, 797/480, 
  79/90, -89/72, -5/36, 5881/2160, 115/72, -1/2, 4/9, -13/36, 5/36, 
  511965113/2630880, -271721/8640, 26813/2160, 203503849/375840, -115/72, 
  -269573/1890, 61839469/1052352, -271721/17280, -116/45, 5849/540, -1/3, 
  -100951885/1052352, 447337853/1503360, -56977/4320, -203893783/751680, 
  -62365645/1052352, -9122657/120960, -5869/1080, -1140613057/5261760, 
  172261/1890, 167/72, -101/20, 5/6, -823/360, -2627/360, 1/6, -767/480, 
  679/90, 893/1440, -499/1440, -67788181/1052352, 355721/17280, -5869/1080, 
  -197959687/751680, 172261/1890, 1/4, 13/270, -13/18, -1/6, -97/180, -7/6, 
  41/108, -71/45, 7511/540, -19/18, 23447/4320, 120479/4320, -361/108, 55/48, 
  -143/360, -35023/1440, 221/720, 257/270, 941/108, 53/108, 1159/108, 
  -78416174819/5846400, 63641408057/5846400, -71/216, 260910792917/17539200, 
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