{{1, 1, -1, -2, -2, 2, 9/4, 1, 3/2, 10, -1/4, 1/4, 1/4, 3/2, 23/4, 9/4, 3/2, 
  -21/8, 1, -19/8, 1/2, -5/4, 7/24, 1/6, -11/24, -55/48, 19/48, 41/48, 1/12, 
  -1/24, 61/48, 1/12, 7/8, 1/3, -1/24, 15/2, 149/48, 61/48, -7/8, 3/2, 5, 
  5/2, 1/8, 19/16, 1, 1, 23/48, -5/16, 1/6, 59/48, 31/16, 1/16, -17/24, 
  -1/16, -1/16, 17/16, 5/8, 17/48, 3/16, -3/16, 3, 13/12, -5/4, -1/8, 17/8, 
  29/16, 23/8, 4, -29/48, -1/2, -77/24, 55/48, -1/12, -19/8, 5/12, -61/48, 
  23/12, 1/4, 1/8, -21/16, -13/16, 7/16, 3/4, -1/4, -17/8, -1/2, 1/24, 1/8, 
  -1/6, 1/16, -41/96, 5/32, 13/32, -7/48, -15/32, -1/24, 1/24, 23/96, -5/32, 
  -115/96, 7/32, -7/32, -39/32, 1/24, 1/8, -1/6, 1/8, -77/96, 15/32, 13/16, 
  -29/96, -15/16, -1/4, -13/24, 7/8, 41/32, -59/96, 25/32, 3/32, -19/32, 
  13/32, 7/16, -1/32, 1/24, -29/96, -9/32, 1/8, -21/32, -1/6, 1/8, 29/24, 
  31/32, -27/32, -19/24, 11/32, 13/16, -59/24, -13/24, -15/16, 3/16, 11/12, 
  -1/32, -3/16, 5/96, 1/24, 87/32, 395/96, 7/32, -17/32, 9/32, -9/32, -7/32, 
  7/32, 1/16, -5/32, 15/32, 1/24, 1/8, -1/6, -17/16, 167/96, 353/96, -15/32, 
  53/96, 13/16, 5/16, -1/48, -19/96, 1/48, -25/96, 19/96, 1/16, 9/32, -1/12, 
  1/16, 17/96, -1/4, -3/8, -7/32, 15/32, 1/16, -5/24, -1/16, 15/32, 1/12, 
  -7/64, -97/192, 7/64, 121/192, -1/16, -67/96, -19/96, -1/16, 37/96, -13/32, 
  227/96, 29/16, 15/32, 1/4, -5/24, -1/8, -11/24, -5/4, 23/96, 7/8, -1/8, 
  -1/8, 5/32, -3/8, -2, 9/4, -3, 7, 2, -127/4, -24, -1, 1, 1, -9/8, 15/16, 
  -6, -20, -1, 1, 1, 9/4, -13/4, -9/4, -15/16, 3/2, -153/64, 15/4, 441/64, 
  -15/16, -28, -7/2, -11/2, -11, 3/2, 14, 253/24, -71/8, 169/24, -19/2, -1, 
  -1/3, 41/24, 1/3, 9/8, -11/24, -269/24, -103/8, 245/24, 203/48, -101/24, 
  -49/12, -3/4, 19/12, 11/2, 1/24, 25/24, -13/12, -1/2, -2, -31/24, 7/3, 
  -2/3, 19/12, -25/8, 37/24, -49/24, 2, 11/24, -1/12, -27/8, 41/12, -101/24, 
  53/8, 103/24, 101/24, -35/8, -101/24, 5/32, -73/96, -11/24, 175/384, 
  -23/32, -61/24, 221/96, -623/64, -5633/384, -125/32, -1291/256, -1/16, 
  -623/128, 3963/256, 623/128, -1/4, -139/24, 125/12, 61/24, 21/4, 331/48, 
  -25/48, 1/2, -51/8, -165/16, 247/12, 199/16, 221/48, -331/96, 3/2, 1843/96, 
  -10, -179/16, 251/48, 2, 475/48, 11/6, 2/3, -715/48, 587/24, 151/12, 
  365/48, -551/96, -13/8, -11/96, -95/6, 95/16, 1/8, 15/4, -33/8, 139/48, 
  -247/16, -125/24, -9/4, 6, 85/6, -9/2, 89/96, 25/96, -89/96, -25/96, -1/8, 
  -23/72, 11/288, 395/144, 59/32, -13/16, -21/16, -175/288, 15/16, -1/3, 
  -299/288, 551/288, 787/288, -31/96, 437/288, -47/96, -371/36, 1243/288, 
  239/288, -1/6, -89/32, 1681/288, 2/3, 19/72, 7/72, -5/18, 107/48, -17/12, 
  -7/72, -13/72, 1/24, 205/72, -11/18, 49/12, 5/24, 209/72, -1/8, -3/8, 1/2, 
  -91/96, 233/96, -61/32, -135/32, -149/96, -1/3, 21/64, 41/96, -21/64, 
  -383/96, -695/192, -547/96, -227/192, -115/48, 95/192, 63/64, 35/36, -7/3, 
  49/36, -1/8, -73/144, 49/48, -13/16, 43/72, 15/16, -1/2, -1/2, -1/48, 
  -19/96, -1/16, 19/96, 1/12, 17/96, 1291/256, 1195/256, 1/8, 7/32, 15/16, 
  5/48, -41/64, 623/128, 5/16, 669/128, -5/12, -31/96, -827/256, 2351/192, 
  -195/128, -19/192, 7/128, 341/32, -455/128, -89/16, 319/96, -3/2, 1/48, 
  -105/32, 7/4, 1/16, 5/24, -1/12, 1/8, -397/96, 247/24, 87/32, 1481/96, 
  125/48, 11/16, -395/96, -15/8, -35/48, 173/24, -1/4, 395/64, 13/24, 
  -281/192, 173/96, -887/48, -469/32, -91/96, -857/192, -97/16, -95/64, 
  379/32, 15/32, -175/8, 179/8, 175/8, -43/16, 1609/64, 33/16, -45/32, -1/2, 
  -27/2, -26, 1003/16, 61/8, -243/8, -131/8, 1319/64, 309/16, -45/32, 35/24, 
  343/96, -475/96, -85/48, -79/32, 37/16, 61/48, -61/48, 35/48, -1/8, 51/32, 
  -3/8, -51/32, 1/2, -31/24, -1873/96, -7535/256, 3731/384, -3/16, -3955/192, 
  -3219/128, 3517/128, 4261/192, -97/96, 49/32, -13/48, 103/24, 19/4, 
  -533/48, -823/192, 161/64, -123/32, -97/96, 347/96, -49/16, -41/96, -1/4, 
  961/32, 179/192, 275/32, 89/4, -979/64, -541/48, 23/32, 103/48, -459/256, 
  95/48, -13/8, -283/96, 33/8, 17815/768, 4069/128, 127/32, -341/96, 
  3645/128, 329/8, -6549/256, -7287/256, 149/48, -19/32, -103/16, 19/32, 
  10/3, -341/96, -1291/128, -923/128, 61/96, 771/32, 67/16, -841/16, -63/16, 
  2749/96, -621/16, 27/4, 415/8, 423/32, 1939/96, 2, -821/32, -1795/96, 57/8, 
  -3/8, -67/16, -9/2, 67/16, 41/8, -917/96, -2063/128, -8041/256, 1073/384, 
  37/4, -1221/64, -6185/128, 1361/96, 1551/64, 83/64, -1869/64, -117/4, 
  7129/128, 397/16, -17/16, 1/16, -309/8, 7/4, 3, 1, -21/4, -3189/64, 
  -1115/64, -1, -1/2, 2, -2, 3/4, -27/4, 51/16, 19/24, 51/16, 3, -3/2, 51/8, 
  -2, -211/48, -11/2, -14/3, 25/6, -43/48, -29/48, 277/48, -47/12, 185/48, 
  193/48, -347/48, -229/144, 593/288, -175/144, 1079/288, 9/2, -27/8, 7/96, 
  -41/36, 307/288, -451/192, 1925/576, 437/192, 43/144, -107/32, 731/144, 
  43/144, -329/288, -287/144, -107/32, -1183/288, 1231/576, 731/144, 33/32, 
  -69/8, -205/32, -17, -319/288, 629/576, 15/2, 15/2, -559/576, 277/192, 
  17/36, 47/18, -1439/288, -455/64, 375/64, -863/192, -863/192, 2303/192, 
  -151/96, 185/96, -805/576, 475/192, 215/192, 301/48, 2657/576, -27/8, 
  -851/288, -533/96, -157/192, -443/144, -15, 1493/576, 857/288, 141/64, 
  -11803/576, -295/64, 1171/96, -85/96, 1585/576, -113/72, -121/288, 
  2879/576, 1889/576, -89/576, -271/64, 239/48, -25/8, -235/96, 5, -107/576, 
  -71/576, 89/288, -109/576, 373/288, -11/18, 227/576, -9/8, -59/288, 
  797/288, -797/288, -801/128, 833/1152, -4619/1152, 641/128, -641/128, 
  -1601/128, -107/576, -71/576, 89/288, -139/288, 955/144, -3257/576, 
  781/576, 2101/288, -503/576, 91/96, 6067/576, -2147/192, 1229/1152, 
  8665/1152, 4051/1152, 8975/1152, 707/384, -4943/1152, -51/64, -245/384, 
  -107/576, 211/384, -63/64, -71/576, -63/64, 89/288, -139/288, 755/576, 
  -859/288, 713/96, -35/12, -2905/576, 781/576, -3/32, 1037/144, -503/576, 
  37/192, -7831/576, -857/384, 61/24, 12683/1152, -797/288, -83/128, 
  -18155/1152, -2569/1152, 3343/384, -315/128, -2383/384, -641/128, 763/128, 
  757/192, -757/192, -18323/1152, 9689/1152, -109/576, -4315/288, 1141/1152, 
  59/288, -107/576, -37061/1152, -71/576, 26093/576, 89/288, 5365/384, 
  -4025/576, -381/16, 2137/144, 12583/1152, -337/96, -11623/1152, 16177/576, 
  -373/192, 1183/576, -2093/2304, 269/144, -2023/2304, 2093/2304, -107/1152, 
  -301/256, -2045/1152, -109/576, -4841/576, -455/64, 2879/768, 7229/2304, 
  17/72, -4315/576, -91/576, -2371/288, 221/576, 15/64, 253/576, 179/96, 
  -28631/2304, -3377/256, 172/9, 20179/1152, 181/576, 1321/192, -1073/256, 
  1379/576, -9589/768, -109/64, -497/576, 995/144, -11/72, 79/144, 131/96, 
  6293/576, -677/384, -193/192, -12461/1152, -2279/576, 15917/1152, 181/48, 
  -1315/576, 685/192, -907/384, -1357/192, 1/2, -1/2, 3/2, -27/16, -1/2, 7/2, 
  -639/8, 5, -73/6, -2, -101/6, 2321/48, 92, 1/2, -1/2, -1/2, -7/2, 7/2, 
  -3/4, 33/4, -27/16, -1039/192, 139/12, 125/12, -7, -4261/144, 1613/72, 
  -2275/96, -343/48, -3, 3, 3, -139/48, 67/48, -95/48, 1039/192, -47/12, 
  7297/768, 125/16, -12481/768, 1039/192, 743/12, 11, 83/12, -185/24, 20/3, 
  25/4, 67/12, -659/24, -11/2, -39055/288, 401/16, -35167/288, 701/24, 58/3, 
  -13/24, 65/144, -11/18, -1861/288, 307/288, 5659/288, 16583/288, 
  -18041/288, 269/72, 5401/96, 9545/288, 463/48, -163/3, -13, 71/96, -109/96, 
  19/48, 41/36, 1/9, 69/32, -1409/144, 1229/144, -1/4, 119/96, -95/96, 27/32, 
  -19/12, -19/32, -49/144, -109/288, -1/48, 16/9, -17/16, -23/16, 1633/288, 
  -523/96, -1633/288, -1069/1152, 2995/288, 821/288, 601/192, 4471/1152, 
  37/12, -14393/288, 647/32, 2893/768, 1877/96, 11301/1024, 257/576, 647/64, 
  -36281/1024, -647/64, 221/24, 24721/288, 4301/144, 2117/32, -1421/288, 
  1715/576, 2809/576, -109/6, -377/48, 4487/288, -544/3, -20081/1152, 
  14525/576, 8419/1152, 10807/144, 625/36, 6797/128, -479/48, 1297/192, 
  199/96, 971/576, -2371/288, 271/288, 3895/288, -25409/144, -66335/1152, 
  6929/576, 14639/1152, 19169/288, 2653/576, 36155/384, -103/4, -91/24, 
  -409/384, 5305/384, -18655/576, 6067/48, -4301/288, -235/384, -8753/128, 
  -29827/192, 8429/144, -121/288, 16345/3456, 233/864, -16345/3456, 65/432, 
  35/144, 1685/288, 1/18, -107/128, -84685/3456, -26975/1152, 539/576, 
  815/96, 10163/384, -679/576, -2023/288, -991/3456, 1/9, -16753/1152, 
  -68959/3456, 1259/1152, 3337/1152, 15127/3456, 12517/96, -4199/384, 
  -41977/1152, 1781/576, 66263/1152, 23233/1152, -119/12, 5/72, 1/72, -7/72, 
  -139/432, -751/144, 1951/432, 1235/1728, -3319/864, -11899/5184, -197/54, 
  907/288, 3043/864, -2989/216, 3845/432, -2621/288, 42857/2592, -61/96, 
  41/32, 119/192, -151/192, 391/384, -179/8, 14599/576, -273/128, -6707/384, 
  -4177/1152, 8335/2304, -33743/1152, 11411/768, -67793/2304, 923/48, 
  -30995/1152, -21767/2304, 17279/576, -215791/4608, -4865/768, -221/864, 
  541/288, -701/432, 25/72, -2155/1728, -269/576, -571/576, 1555/864, 
  371/576, -7/2, -7/2, 1727/288, -2093/2304, 35/1152, 2093/2304, -6943/1152, 
  -9335/384, -11301/1024, 10351/9216, -25/72, -27473/1152, 371/576, 443/288, 
  -37615/1152, -647/64, -247/1152, 42125/768, -1525/1152, -9361/576, 
  -19501/9216, -124633/2304, 341/24, -2181/256, -865/96, -1249/72, 
  138275/2304, 1271/192, -15871/1152, 343/192, -1733/288, 24637/2304, 
  -2111/192, -107/1152, -14111/2304, 7039/1152, -41/144, 5687/192, -1533/16, 
  27133/1152, -62035/576, -25975/2304, 389/192, 9557/288, 1023/64, -587/288, 
  -247/96, 150425/2304, 11599/288, 105259/2304, -12585/256, -9203/144, 
  -45397/1152, 17695/192, 59783/1152, -515/96, -27719/768, -10627/288, 
  48745/1152, -113563/2304, 1195/64, -61/32, -19/32, 1495/32, -5/2, 
  11567/192, -6097/768, -717/32, 1069/128, -95/12, 87/4, 7, -4061/48, 
  -8211/64, 13775/96, 8849/32, 17381/96, 39205/768, -663/8, 1069/128, 
  -1301/96, 7081/1152, 10115/1152, 553/288, 19483/1152, 3619/144, -5923/144, 
  5923/144, 7867/144, -539/48, 5261/576, 95/192, -5261/576, 687/64, 
  102109/1152, 60295/1152, 110925/1024, 52429/1152, 7609/144, 119527/2304, 
  -3817/144, -362759/4608, -75967/2304, 2449/1152, 4015/768, -38159/2304, 
  -61685/1152, -28177/256, -12863/192, -1781/576, -62899/2304, -182635/2304, 
  -925/192, 1471/1152, 859/128, -4069/576, -17275/1152, -823/9, -21883/3456, 
  -5431/1152, -23035/1152, 42229/576, -12467/864, 16775/1152, -4913/384, 
  5817/1024, 451/192, -167/32, -27403/1152, -102787/1152, -645725/9216, 
  -113651/1536, -235925/2304, -11249/192, -52915/768, 138055/1152, 
  43989/1024, 72617/3072, -967/96, -571/256, 1349/128, 571/256, -179/384, 
  3693/128, 11301/512, 439/512, 2811/128, 8795/384, -1345/384, 6095/192, 
  955/128, -19961/384, -19983/128, -511/64, 4573/64, -43/192, -83227/384, 
  -1217/96, 109223/384, 6007/384, -581/16, -445/24, 235/384, 743/128, 
  -235/384, 1355/384, 80635/576, 64295/1536, 9619/1024, 9355/96, 123, 
  38845/768, -5825/128, -3683/384, -179795/2304, 26951/256, 641/8, 
  -62099/384, -77155/512, -53, -28175/768, 46735/768, 61153/192, -11503/96, 
  -1841/192, -3, 2335/64, 287275/768, -3209/48, 1/2, 5/16, -1/2, -139/72, 
  49/72, 863/144, -25/18, 605/144, 5/2, -25/18, 11/8, 605/144, 9/2, -89/36, 
  269/36, 365/72, 55/72, -401/72, -215/48, -113/36, 5/2, 889/288, -61/96, 
  -353/96, -91/24, -11/96, 5, -61/96, -353/96, -55/12, -11/96, 4, -889/288, 
  13/4, -5/2, 401/144, -353/96, -1285/288, -869/144, 5/2, 889/288, 55/72, 
  -365/72, -53/32, -113/36, 5, -421/144, 835/288, 163/144, 17/96, -1523/144, 
  -265/36, 49/96, -353/96, -55/16, -283/96, 5, -185/96, -185/96, -889/288, 
  19/12, -269/48, -331/96, 85/144, 7/72, -53/72, 23/288, 341/288, 197/576, 
  -7/72, 413/72, -305/288, -5, -185/192, -185/192, -185/192, -185/192, 
  185/192, 185/192, 193/288, 193/576, -193/576, -193/288, 6, 1/192, 5/4, 
  1295/192, 371/32, -5/4, -185/192, 185/192, -889/576, 187/144, 529/288, 
  -193/576, -2305/1152, -4147/576, -547/128, -533/576, 889/96, 2125/192, 
  369/128, -8363/1152, 4405/1152, 535/576, -13081/1152, 5/4, -79/64, 47/1152, 
  1439/288, -27887/2304, -3661/576, 2117/384, -39461/3456, -2609/384, -1, 
  -79/64, 43/144, -53/72, 205/192, -599/1152, 835/1152, 1439/288, -635/288, 
  -33229/2304, -3661/576, 9239/1152, 109/36, -7649/864, -8555/1152, 13/2, 
  -979/144, 185/192, 2095/2304, 2191/1152, 3331/288, 239/1152, -2767/384, 
  4045/1152, 16613/1152, 27089/3456, -8605/384, -26119/1152, 371/144, -29/9, 
  -61/192, -347/144, 2513/864, 11/6, 2341/1728, 203/144, -3637/1728, -5/2, 
  3947/1152, 2905/576, -269/96, 337/1152, -911/288, -3577/576, -1733/576, 
  12197/3456, 1837/384, 8537/3456, 3481/576, -193/576, 17707/3456, -5/4, 
  -185/192, -185/96, -185/192, 889/576, 185/96, -167/288, -889/576, 185/192, 
  187/72, 1561/576, -443/576, 1/192, -9/32, -353/96, 565/1152, -3677/1152, 
  -239/1152, 5/4, -283/96, -2801/1152, 2447/192, 697/288, 971/288, 201/128, 
  3191/288, 11/4, 22333/2304, -10103/2304, 2471/576, -136985/13824, 
  -17185/2304, -15359/3456, 22333/2304, 1417/288, -269/96, -1921/768, 
  -4619/768, -519/64, -3091/1152, 6559/1152, 90211/13824, -1639/128, 
  -25931/3456, 41585/2304, 16685/1728, -49/288, 439/96, -269/64, 6959/1152, 
  893/288, 199/144, 39/16, 119/1152, -385/576, -185/384, -3205/1152, 
  -883/576, 49/288, 37/32, 13861/1152, -85/64, -21727/4608, -3661/1152, 
  -773/576, -349/72, 1667/384, 203/64, -275/48, -3835/1152, 7441/1152, 
  439/96, -9/2, 20989/4608, 7571/1536, 7/12, 24553/4608, 35/1152, 23209/4608, 
  -65/576, 91/1152, -12515/2304, -25751/27648, -5035/768, -67867/13824, 
  -28829/9216, -43/144, 1985/512, 2441/512, 253/1152, -8089/1152, 27/32, 
  20497/13824, -2413/576, -62713/4608, -56/27, 5377/384, 6745/1536, 
  97261/13824, -5173/576, 2093/1728, -1259/4608, 9625/4608, -15215/1728, 5/4, 
  45113/4608, -251/9216, 185/192, 7571/1536, -24599/4608, 58237/9216, 
  35/1152, 5483/1152, -65/576, -83/576, -8327/768, 25081/27648, -3635/768, 
  -61829/27648, -197887/27648, -45/64, 46321/4608, 35921/4608, 61/72, 
  277/128, 131923/9216, 42505/13824, -9701/864, -2047/144, -2227/3456, 
  -419/288, -39775/3072, 91459/13824, -15325/1152, 5465/3456, -483/512, 
  -54485/13824, -33437/3456, -7/2, 46769/4608, 17087/3072, -353/192, 
  7571/1536, -1729/1536, 57439/9216, 35/1152, 39133/4608, -65/576, -83/576, 
  -29959/2304, -58103/27648, -12035/2304, -74909/27648, -192151/27648, 
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