{{1, 2, -2, -2, 2, 3, -1, -3, -19/4, 19/4, -27/4, 27/4, -27/4, 19/4, -2, 
  17/6, -3, 31/6, 1/2, -9/4, 11/12, -13/4, 23/12, -1, 1/6, -3/8, 5/24, 13/4, 
  -59/12, 5/3, -17/4, -5, -7/3, 1, 25/12, -47/24, -1/8, 25/12, -71/24, 5/24, 
  -1/4, -7/2, 7/2, -11/2, 5, -29/4, 9/4, 77/12, -9/4, -7/4, 31/6, -105/8, 
  -55/12, 105/8, -7/12, 31/6, -17/4, -41/6, -7/3, 5/3, -4, 1, 29/4, 29/2, 
  29/4, -29/4, -29/2, -29/4, 29/2, 29/2, -29/8, -211/8, -1, -275/12, 5/6, 
  79/8, 29/4, -29/12, 31/12, 49/8, 27/8, 3/2, 59/16, 269/16, 29/2, 475/24, 
  311/16, -83/48, 59/16, 7/8, -107/8, 227/48, -191/8, -29/8, 107/8, 191/8, 
  29/8, -47/16, -27/16, -3/4, 37/12, -6, 29/4, -79/24, 53/4, 5/24, -15/8, 
  -53/4, -9/4, -163/8, 25/12, 29/8, -25/12, 4, 9/16, 23/12, 35/8, 39/16, 
  -1/2, 43/16, -3/16, 31/16, -9/16, 27/16, 9/16, 3/4, 29/4, 29/2, 29/4, 87/4, 
  29/4, -29/4, -203/8, -29/4, -145/4, -87/8, 87/8, 29/2, 29/8, -229/96, 
  11/32, 991/32, -85/24, 5465/96, 495/32, -47/32, 9/32, -159/16, 39/16, 
  -787/48, -147/32, -13/32, -69/32, 47/16, 3/2, -1/32, 27/16, 15/32, -35/16, 
  -5/16, -15/32, 11/32, 3/4, 3/8, -3/8, -3, 3, 1, -2, -39/8, 39/8, -9/2, 9/2, 
  -9/2, 7, -7, -18, -9, -39/8, 39/8, -189/32, -189/32, -9/4, 9/4, 1, 109/4, 
  -109/4, 12, 9, 575/3, 927/16, -47/2, -575/12, 155/16, -47/16, -1085/16, 
  -369/16, 35/12, 927/4, -34/3, -94, 101/12, -1257/32, -7373/32, 1923/32, 
  541/32, -2117/32, -15401/32, 9869/96, 3143/160, 231/4, 3075/8, 927/16, 
  -545/4, -3263/8, -261/4, -5919/160, -6135/16, 20089/160, -3581/160, 
  -4281/160, -57/16, 2731/160, 7821/160, -9/4, -41/6, 51/8, 927/8, 16/3, 
  -427/8, 3/2, -71/8, -465/16, -80/3, -57/16, -353/4, -4333/8, 2245/24, 
  -2283/64, 5897/320, 2, -5/3, -365/16, 9/2, 3443/96, -9/2, 10, 45/16, -9/8, 
  -703/96, -2, 9/8, 35/6, -31/6, -1/2, 17/6, -23/6, 2, -217/6, -213/8, 
  229/24, 43, 477/8, 2, 121/12, 127/6, -217/6, -107/24, -93/8, -45/8, 41/6, 
  317/6, 595/24, 2/3, -277/6, -365/8, 5/4, -31/3, 375/16, 1995/16, 811/8, 
  -209/4, -3443/16, -4609/48, 141/32, -157/4, -3187/16, -335/32, -279/32, 
  227/24, 65/16, -13/16, -911/16, -12645/32, -7267/16, 6703/96, 8215/48, 
  603/32, 977/20, 21453/64, -105211/960, 667/80, 2561/320, 1969/80, -45/32, 
  -8411/320, -9/8, 47/32, 805/32, 2053/32, 5/4, 104, 1493/48, -789/32, 
  -1013/32, -29/4, 141/32, 165/32, -10, -3/4, -1053/32, -201/32, -7/4, 69/32, 
  47/16, 39/32, 15/32, -11/32, 3/8, -47/8, -27/8, -3/2, -365/48, -25, -125/8, 
  139/24, -289/6, -547/48, -37/6, 905/48, 3/8, 161/16, 89/8, 6, 443/24, 
  -16/3, -19/4, -91/8, 19/9, -469/36, -29/2, 19/9, -353/24, -575/36, -121/72, 
  -137/72, -31/72, 217/24, 505/24, 217/24, 1259/72, -32/9, -269/24, -269/24, 
  803/144, 685/144, 217/12, 1619/72, 179/36, -217/16, -1249/144, -99/4, 
  -497/72, -1183/36, 565/48, 11/18, 97/9, -929/144, 7/16, -983/16, -547/48, 
  -8309/72, -261/8, 85/9, 47/36, 1181/144, -181/144, -4/9, -3/16, 27/16, 
  463/144, 3/4, 453/8, -379/8, -579/32, -99/32, -87/8, -475/8, 15, -27/2, 
  243/8, -325/8, -12, 17/2, -603/8, -69879/160, -7821/32, 719/4, 91909/160, 
  -2137/32, 5919/160, 66879/160, -15049/160, 3581/160, -99/4, 207/32, 233/4, 
  -51/16, 225/16, 705/8, 66309/160, 5859/32, -265/2, -108329/160, -5065/24, 
  -13713/320, -131463/320, 11749/160, -9367/320, 33/64, -1191/64, -421/8, 
  1191/64, -261/16, -53/24, 155, -1045/96, -5185/48, 1487/24, 299/48, 
  5587/160, 23275/48, -104957/960, -4443/160, -141/32, -99/8, 1485/32, 
  207/32, 69/16, 45/32, -33/32, 9/8, -421/24, 979/16, -391/8, -28/3, 
  -14335/96, -289/48, 173/8, -89/8, 557/24, -29/8, 103/16, 17/2, 1235/96, 
  9/2, 17/8, 1065/32, 5705/32, 1017/16, -117/2, -31159/96, -2379/32, -423/8, 
  -5641/32, 813/8, 439/32, -141/16, -2533/48, -1167/16, 1183/48, -4639/48, 
  -1041/32, 1813/48, 1013/48, 17/6, -649/48, 455/48, 113/48, 17/6, 131/6, 
  345/16, -5/8, 115/24, -16983/320, -711/64, 19443/320, 27963/320, -27/4, 
  1115/64, -5481/64, -99/2, 71/64, -10009/160, -2315/32, 9107/32, 16787/32, 
  521/32, -869/32, -1/2, -3/2, 3, 3, -59/48, 59/48, -25/8, 25/8, 2, 11/2, 
  15/2, -59/24, 59/24, 19/16, -19/16, -1/6, 1/6, 65/12, -29/12, 389/144, 
  -397/144, 175/144, -431/144, -1/2, 827/288, 101/288, 127/36, -11/36, 5/2, 
  -91/288, 19/96, 17/144, -109/144, 8/3, -275/144, -107/144, 1/2, 13/144, 
  3/2, -7/24, -109/96, 137/96, -7/24, 233/144, 17/144, 7/8, 5/3, -5/3, 
  607/96, -101/32, 937/144, -63/8, -521/144, 55/8, 43/8, -365/288, 717/64, 
  15/16, -717/64, 95/288, -365/288, -395/144, 305/96, 13/144, -275/144, 2, 
  -5/2, 3/2, 3, 3/2, -3/2, -3, -3/2, -6, -5/8, 5/4, 43/8, -5/4, 2503/288, 
  77/16, 163/288, -3077/288, -35/288, -35/16, 95/16, 391/144, -611/144, 5/4, 
  -433/32, -139/32, 5/4, -10327/1152, -821/128, -5/8, 5/8, 17/64, 389/128, 
  6853/1152, -5/8, -16117/576, -1683/64, 10829/576, -3595/96, -187/8, 
  -10327/1152, 53/16, 63/16, 5/8, -1177/1152, 113/16, -5/8, -33/16, -63/16, 
  -113/16, 33/16, 117/16, 5099/1152, -17/64, 83/32, 97/48, -97/48, 17/64, 
  -7/16, -13/16, 13/16, -487/288, -9/4, 3/2, 135/32, 15/4, -91/36, 403/96, 
  -1/2, 379/288, -221/32, -251/288, 3, 31/8, 305/144, 983/128, -177/64, 
  -331/144, -203/128, 5/8, -1447/192, -2471/1152, 997/192, 5441/1152, -91/32, 
  137/64, -7/4, 4073/1152, 13/16, -3, -65/8, -5/8, 5/8, -7/8, 55/8, 13/4, 
  -5/8, 159/16, 69/16, 33/16, -171/16, -5/8, -57/8, 5/8, -59/16, 61/16, 31/8, 
  -3725/288, -21551/2304, -3/2, -5/8, 2941/288, 6245/768, 5/8, 3, 19483/1152, 
  23495/2304, 56795/2304, -10595/1152, 4063/144, 183/16, -9581/2304, 
  -1927/2304, 17/128, -117/16, -15161/2304, 1/2, -83/32, -165/32, 10661/2304, 
  4307/2304, 55/24, -4235/2304, 7/16, 5/4, -13/16, 27/4, -27/4, 59/24, 
  -59/24, -1, -59/24, 59/24, 1/2, 203/48, -59/48, -59/32, 57/8, -57/8, 9/8, 
  -9/8, 9/8, 29/24, -29/24, 15, 21/2, 57/8, -57/8, 75/16, 75/16, -25/8, 
  27/16, 17/8, -27/16, 7/2, 59/24, -473/72, -727/12, 727/12, -33, -24, 
  1003/48, -1003/48, 10, -575/6, -927/32, 47/4, 575/24, 11347/1152, 
  10241/288, -995/384, -3239/160, -791/288, -927/8, 527/48, 47, -2371/288, 
  53399/576, 179081/2304, -20353/576, 14369/1152, 1057/192, 50809/256, 
  -165/64, -163427/9600, 29227/192, 9635/96, -927/32, -23735/96, -8507/96, 
  10681/64, -1105349/9600, -9797/96, 1244861/14400, 808727/28800, 61649/9600, 
  21/32, 7723/800, 142567/3200, 9/8, 419/96, -289/64, -927/16, -155/48, 
  1793/64, -109/96, 8813/192, 9995/1152, -2221/192, 4631/144, -26357/192, 
  -10285/384, 17669/192, -1745/192, 787/200, -173/72, 121/72, 2023/72, -13/4, 
  -14267/1152, 13/4, -3/2, 19/18, 19/4, -449/1152, -1/2, -5/2, -451/288, 
  803/288, 1/2, -13/96, 157/96, 1, -5, 11791/288, 3325/96, -227/36, 
  -5881/144, -7609/96, -349/288, -1217/96, -4391/144, 11791/288, -13/96, 
  387/16, 205/16, -47/4, -9905/144, -1265/36, 883/288, 11723/144, -125/16, 
  -133/72, -4411/288, 50719/1152, -46369/1152, -2761/32, 5/6, -2011/64, 
  22393/1152, -25/12, 41591/1152, 5/4, -19483/384, 89143/2304, 9395/768, 
  88235/1152, -77935/1152, -27029/576, 86957/2304, 30013/2304, -51/128, 
  -22891/1152, 104749/1152, 57661/256, -2005/1152, 35357/768, 173/8, 
  2010581/57600, -129685/1152, 395969/57600, -129269/6400, 20471/19200, 
  -174227/9600, 13/16, 19853/6400, -19483/1152, -29293/2304, -49/64, 499/18, 
  6199/2304, 5/4, -911/576, -5/4, -3479/2304, -187/256, -95/16, -17/128, 
  -20047/384, 383/1152, -2803/64, 9755/384, -134971/2304, -307/8, -11/16, 
  6583/2304, -51/128, -9653/2304, -13/8, -13/48, 1751/2304, 5/4, -5/4, 
  421/32, 139/32, -5/4, -139/24, 2399/72, 25655/1152, -101/16, 249/32, 
  -2897/1152, -149197/4608, -7/4, -9827/576, 85/384, 159/16, -16021/576, 
  35/16, -7715/576, 1577/144, 1465/576, -11/8, -27/8, 33/16, -3/4, -19/18, 
  2795/864, 2323/432, 5/8, -1195/864, -2695/864, -4403/1296, 125/32, 319/162, 
  -239/324, 71/36, -2533/432, -157/144, 1243/216, 539/48, -61/48, -3/4, 
  395/144, -617/144, -1/6, -15649/1152, 1851/128, -11791/576, -13/8, 
  3533/1152, -13747/1152, 13/8, 2849/288, -27857/3456, 6097/288, -1235/96, 
  179027/3456, -3691/288, 973/576, -23833/1728, 8341/288, 17323/1152, 355/64, 
  83/16, 14137/1152, -161/16, -44095/1152, -12733/1152, 11/6, 26797/3456, 
  -10219/1152, -9/32, 21/8, -181/384, -19/8, -10847/96, -129/32, -1/2, -39/4, 
  -6277/48, 1613/16, 19/2, 54, -7669/192, 1637/192, 2, -9/2, -1091/48, 59/48, 
  23647/192, 2870641/9600, 68105/192, -20165/96, -3009091/9600, 11749/384, 
  750209/9600, -3483431/9600, 469849/14400, -1407407/28800, 13861/192, 
  -37339/960, -25429/384, 40609/960, 749/160, -10465/48, -182651/600, 
  -29089/96, 16465/96, 244801/600, 379/4, 43611/1600, 27827/75, 
  -771199/14400, 275933/7200, -165/128, 15751/240, 25777/384, -57041/640, 
  -1229/160, 16571/1152, -6565/128, -10067/288, 26123/1152, -144539/1152, 
  1025/64, 2850787/57600, -464509/2304, -60877/9600, 69609/3200, 20893/384, 
  -5087/384, 1545/64, -6869/768, 51/128, -15293/768, -903/64, 7379/768, 
  63/16, -21473/288, -14057/1152, -109/2, 5057/64, -36673/1152, -58289/576, 
  -39011/576, -6593/144, -1751/144, 5573/192, -4901/128, -26, -7927/2304, 
  2527/144, 9/8, -55/8, -151243/2304, -2973/64, -2951/72, 293939/2304, 
  30443/576, 3005/64, 15887/256, -32521/1152, 17879/576, 20893/192, 
  81199/1152, 7091/64, -56845/576, 165113/1152, 11847/128, -17333/1152, 
  -25763/1152, 51/64, -20911/1152, 5779/576, -581/576, -6571/1152, -179/72, 
  -33781/576, -2429/192, 1657/144, 3439/576, 70043/800, 2037/64, 
  -317047/3200, -15701/1600, 45/8, 10347/64, 10537/256, -113425/768, 
  -1009/48, -356621/6400, 71923/768, -2377/8, -155729/256, 5777/768, 179/8, 
  -1/2, -1, -1, 25/96, -25/96, 59/48, -59/48, 85/48, -85/48, -95/72, 55/72, 
  -2, -2, -5/2, -3, 1, -1, 1, 59/32, -59/32, -1, -1, -59/288, -2, 59/96, -3, 
  -59/96, -1, 175/96, -175/96, 2, 2, 1, -1, 1, -59/288, -2, 379/96, -379/96, 
  1, 1, -107/288, -3, -53/288, 1, 2, 1, -347/288, -2, 1, -101/144, -11/144, 
  3/4, -163/288, -2, -205/288, -137/144, 21/16, -47/144, 15/16, -17/16, 
  251/576, -73/64, 203/288, -85/288, -1, -11393/2304, 1539/256, 1, -1, -1/2, 
  1/2, 1, 1/2, -1/2, 229/288, 59/48, -4/3, -59/48, 155/288, 59/288, 1, 
  509/288, -1, -1661/384, -169/4608, 203/48, -707/576, 793/192, 613/192, 
  -793/192, -283/144, -21821/2304, 9089/2304, 13343/2304, -41/16, -707/576, 
  365/96, 31/4, -19/576, -37/192, 203/288, -31/4, -13841/2304, -6259/2304, 
  1539/256, -18415/2304, -1/6, 1/6, -221/288, -371/288, -305/144, 63/16, 
  -23/144, -47/16, -51/16, 1/2, 1, -1/2, 19/72, 201/32, 1/16, -201/32, 
  -47/144, -565/96, -5/2, 103/192, 3/2, -1197/128, 1489/512, 125/32, -2, 
  -57/16, 19/72, 3203/288, 25/4, -77/96, -29/288, 155/288, -565/96, -35/4, 
  103/192, 3/2, -1253/384, -4997/1536, 203/48, -19567/2304, 1/2, 1/2, -1/4, 
  -3/4, -1/2, 1/4, 1/4, 1/2, 3/2, 7/4, -1/4, -1/2, -5/4, -2069/384, 
  -2473/4608, 1465/288, -685/512, -19351/2304, -61057/4608, 685/512, 
  31765/2304, -29605/4608, 29605/4608, 3/2, -3/4, -5/16, -9/4, 5/16, 
  -163/288, 21/8, -145/288, 1361/288, 65/288, -15/8, -31/16, -279/64, 
  -8383/4608, 5/16, 11/8, -5/16, -705/128, 1337/1152, 889/768, 183/64, 
  13711/4608, 7/8, 961/768, -13/32, -157/288, 389/128, -3/4, -9/16, 
  -479/1152, -677/128, 1/4, -69/128, 5/16, 49045/4608, -49/16, 3/2, 
  -19591/2304, -45/16, -1/8, 8453/1536, 4991/576, -52715/4608, 65417/4608, 
  -5041/1152, 102353/4608, 187/16, -24365/9216, 48787/4608, 118853/9216, 
  17411/9216, 409/32, 27997/9216, -157/288, -36949/4608, 115/16, -9/16, 
  -413/384, 31255/2304, 9/16, 19/4, 49045/4608, -113/16, 3/2, -87869/4608, 
  -19/4, -1/8, 8453/1536, -3167/384, 13609/3072, 1211/576, 1213/288, 
  -3607/1536, -24365/9216, -132397/9216, 3607/1536, 117629/9216, -27733/4608, 
  13/32, 27733/4608, -9/64, 59/48, 11/192, -59/48, 1/12, 41/36, 2, -163/288, 
  749/288, 83/288, -1, -5/144, -2987/256, -6217/2304, -35/144, 1799/768, 
  213/32, -30469/2304, -23/192, 23845/2304, -17/8, 2515/2304, 12905/576, 3/2, 
  3/4, -3/4, -5/16, -41/16, -9/4, 5/16, 5/16, -1/8, 17/8, 7/2, 87/16, -5/16, 
  -11/8, -51/16, -279/64, -28471/4608, -8383/4608, 5/16, 27/16, 11/8, -5/16, 
  -5/16, 1361/2304, 31273/4608, 30373/4608, 9/2, 169/768, -757/2304, 183/64, 
  26887/4608, 13711/4608, 7/8, 7/8, 2057/3072, 10727/4608, -97/96, 
  -5531/1024, -13/32, -13/32, 13/32, -59/16, 59/16, 3/4, -1/4, -59/32, 59/32, 
  1, 1, 5/32, 1/2, -5/32, 59/48, 3, -59/48, -1, -1, -283/1152, 283/1152, 
  -155/96, -3, 59/96, -1, 3, 59/32, 2, 1, -587/288, 815/864, 2, 57/32, 
  -57/32, -2, -5/2, 11/16, -11/16, 11/16, 19/32, -19/32, -55897/4608, 
  -46825/4608, 4585/384, -47/64, -473/48, -473/24, -13/4, 13/4, -1, 15/32, 
  -15/32, -40057/4608, -31561/4608, 1487/192, 5045/576, -11765/1152, 
  9421/768, -145/32, 145/32, -11/4, -11/4, 473/48, -47/64, -473/48, -13/4, 
  13/4, 39/32, 7/32, -29/32, 53431/2304, 29/32, -4771/4608, -22375/4608, 
  14383/4608, 37087/6912, 14383/4608, -31025/13824, -31025/6912, 
  105199/13824, 2, -5849/1152, -229/144, -3377/6912, -26347/6912, 445/144, 
  -9/32, -437/144, 9/32, 2, -41981/4608, -229/144, -24113/1728, 
  -133645/13824, 2, -41981/4608, -229/144, -24113/1728, -133645/13824, 
  14383/4608, -473/48, -283/576, -3817/2304, -59/144, -791/2304, -743/288, 
  283/1152, 295/288, -283/1152, -473/48, 14383/4608, -283/576, -18947/4608, 
  -59/144, -15965/4608, -283/576, -3817/2304, -59/144, -791/2304, 37/256, 
  -15/512, 31/8, -2459/256, 195/2, -185/768, -49/6, 36539/4608, -475/6, 
  -127/24, 31363/12288, -128251/12288, 5653/1536, 26153/9216, 250507/36864, 
  -1501627/36864, 667/3072, 693/32, -15061/9216, -167485/4608, 465/64, 
  -201659/9216, -583/768, 49/6, -3443/512, 487/6, 103/24, -293/256, -137/12, 
  29135/4608, -176/3, -31/24, -37/384, 13/4, 407/1152, -37/2, -5, -25/96, 
  25/96, 10/9, 17/9, 407/96, -407/96, -2/9, -43/18, 1351/288, 3515/864, -10, 
  -10, -1, -1, 1, -17, -5125/288, 1, 1/9, -13/36, 2363/96, -2363/96, 18, 14, 
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