{{1, 2, -3, -2, 2, -1, -1, -1, 1, -6, -3, 3, 6, -3, 6, 3, 1, 1, -4, 4, 3, -7, 
  4, -3, -6, -3, -3, 6, -3, -6, -6, 6, -6, -2, -2, 2, 2, 5, -2, 5, 2, 2, -4, 
  2, -3, -3, 3, -3, 3, -3, -3, 3, 6, -3, -3, -2, -2, 2, 2, 2, 2, 2, 1, -1, 
  -2, -2, 2, 2, -1, -1, -2, 2, -2, 2, 2, 2, -1, -2, 4, 1, -2, -4, 1, 2, -2, 
  -3, 2, -3, -6, 6, -3, 3, 6, -6, -3, 1, 2, 1, 2, -2, -2, 2, 2, 2, 6, 2, -2, 
  -4, -4, -4, 2, 2, 2, 2, -2, -2, -4, -2, 2, 2, -2, 2, 4, 2, -2, -2, -4, 2, 
  4, -2, -4, -4, 4, -2, 2, -1, 1, -2, 2, 2, 2, -3, -2, 6, -6, -6, 2, 3, -4, 
  -2, 2, 2, -4, 3, 6, 3, 3, -6, 3, -2, 2, -6, 6, 2, -2, 4, -3, -6, -3, -3, 6, 
  -3, 6, 1, 1, -1, -1, -10, 3, -3, -6, 3, 3, 2, 106/9, 4, 6, 3, -812/11, 
  862/11, -6, -1, -1, 2, 2, 538/11, 8841/32, -486/11, -9129/32, -1, -3, 4, 9, 
  -10, -6, -406/11, 52565/96, -140/11, 370681/1056, 684/11, 570271/1056, 
  412759/1056, -327673/1056, -492319/528, -121475/352, 61989/176, 46451/44, 
  -236035/1056, -964933/1056, 3, 6, 3, 3, -6, 3, 6, -6, -2, -2, 6, 2, -2, 2, 
  2, -2, -2, 3, 3, 3, 3, -3, -3, 3, -3, -6, 3, 3, 6, -12, -6, -6, 6, 2, 2, 
  -6, -2, 2, -2, -2, 5, -7, 2, -3, -3, -3, -3, 3, 3, -3, 3, 3, 3, -2, 2, 5, 
  4, -3, -8, -7, 8, 12, -2, 3, 6, -10, 3, 16, 12, -6, -5, 3, 8, 11, -8, -16, 
  2, -6, -6, 10, 4, -16, -16, 6, 6, -6, 6, 2, 2, 8, 3, 162751/528, 
  -642173/1056, 161695/528, -645341/1056, -857755/1056, -62321/44, -6, 6, 
  162751/528, -812/11, 6, -856/11, -59249/44, 4, 2, 9, 4, 162751/528, 
  -642173/1056, 161695/528, -649565/1056, -857755/1056, -62145/44, -6, 9, 
  162751/528, -812/11, 6, -933/11, -59249/44, 8, -6, -6, 6, -6, 20/3, 20/3, 
  -46/3, -46/3, -14/3, -46/9, 92/9, 106/9, 64/9, 20/3, 2/3, 17/3, -47/3, -20, 
  -16/3, -20/3, -8/3, 44/3, -1/9, 23/9, 5/9, 103/9, 41/9, 2/3, 23/3, -10/3, 
  -20/3, -8/3, 55/3, -2/3, -133/9, 4/3, 70/9, 82/9, 406/11, -52565/96, 
  140/11, -370681/1056, -684/11, -570271/1056, -412759/1056, 327673/1056, 
  492319/528, 121475/352, -61989/176, -46451/44, 236035/1056, 962821/1056, 
  -812/11, 1350/11, 529459/528, 664/11, 96961/66, 287/11, 531295/528, 
  -3315/44, -96475/66, -492319/528, -162563/176, 21367/176, 53299/88, 
  92543/96, -82165/96, -406/11, 530515/528, 617/11, 812/11, -3315/44, 
  -1004/11, -492319/528, 1624/11, -275491/132, -2009/11, -505405/1056, 
  285475/352, 812/11, -1350/11, -529459/528, -664/11, -97027/66, -298/11, 
  -531295/528, 3315/44, 96475/66, 492319/528, 162563/176, -21367/176, 
  -52947/88, -92543/96, 81781/96, 406/11, -530515/528, -650/11, -812/11, 
  3315/44, 1004/11, 492319/528, -1624/11, 275491/132, 2086/11, 505405/1056, 
  -286883/352, 6, 6, -6, 6, 2, -2, 2, -8, -8, 11, 11, 14, 6, -11, -6, -2, -2, 
  2, -6, 6, 6, 6, -6, -6, 6, -6, -6, 6, 8, 13, -12, -23, -6, -6, -17, 6, 2, 
  -4, -6, 6, -9, -2, -6, -5, -6, 9, 4, 3, 6, 3, -6, -3, -3, -6, 3, 3, 5, -10, 
  -11, -3, -5/2, 5, 5, -10, -5/2, -9/2, 5/2, -6, 5, -10, 5, 4, 4, -8, -4, 4, 
  -6, -4, -4, 4, 1, 5, 4, -1, -5, -3, -1, -4, 3, -3, -3, -6, -3, 6, 3, -3, 3, 
  3, 2, -2, -2, 2, -2, 2, -4, -4, -2, -4, 2, 2, -2, 2, 2, -2, -2, 5, 2, 2, 
  -2, -2, 2, -2, -4, 4, 2, 4, -2, -2, 2/3, -65/6, 35/3, 10/3, 5/3, -35/3, 
  43/6, 4/3, 205/18, -29/3, 119/18, -23/9, 2, -4, -4, 2, 2, -2, -6, 4, 2, 
  406/11, 8521/32, -332/11, 620/11, -326527/352, -679/11, 55359/88, -812/11, 
  -8665/16, 818/11, 2035075/2112, 4, -5, 5, -5, -3, 2, 5/2, -2, 1/2, 33/2, 4, 
  -37/2, -5, 3, 5, 2, 3/2, -9, -15/2, -39/2, -4, 14, 17/2, -11, 15, 1, -2, 3, 
  3, -3, -3, -2, 2, -2, -3, 1, 2, 2, 3, 2, -2, 1/2, -11/2, -9/2, -39/2, 
  -31/2, 11, 17/2, -9, -1, 11, 1, 5, -5, -2, 2, -1, 2, -7, 3/2, -1, -27/2, 
  -3/2, 13/2, 2, -5, -1/2, 25/2, 9, 2, -3, -2, 3, -2, -6, -2, 2, 9, 10, 2, 
  -3, -10, 3, -16, -2, 26, 8, -12, 12, -2, 2, -3, -2, 3, -2, -4, -1, 
  -909547/1056, 10, 2, -5, -10, 8, -16, -2, -883147/1056, 8, -10, 8, -6, 12, 
  6, -12, 2, 4, 2, -6, 2, -2, -2, -1756/11, -161167/264, 2, 3413/11, 
  164335/264, -1613/11, 460387/352, 161695/264, 401981/1056, -177415/528, 
  2412643/1056, 161695/528, -641117/1056, -885235/528, -62497/44, -2, 2, 2, 
  4, -8, -2, -2, 4, 856/11, 161167/264, -1668/11, -176359/528, 4, -812/11, 
  -2332579/1056, -6, 13/2, 13, 6, -10, -13, 7/2, 6, -13/2, -13, 7/2, 2, -9, 
  17/2, 20, -2, -12, -9, 25/2, 10, 2, 5/3, -77/6, -40/3, -28/3, -2, 27/2, 8, 
  -8, 26/9, 20/3, 4, 2, -14, -7, 3, -2, 7, -3, -20/3, -121/6, -41/6, 94/3, 
  -67/6, -29, -71/6, 5/3, -11/6, 43/6, 16/9, -49/9, 29/3, -95/9, 23/9, 2, -7, 
  -2, 7, -10/3, -65/6, 59/3, 10/3, 5/3, -38/3, 43/6, 10/3, 205/18, -38/3, 
  83/18, -23/9, -1426/11, 39175/264, -14, 1645/11, -94183/66, -331/11, 
  -23455/264, 16, -252/11, 92119/33, 386/11, -4, -89989/66, 2342/11, 
  -599899/352, -115657/48, -3369/11, 297163/96, 1171/11, 383417/528, 
  616237/132, -259147/96, -1126145/528, 1893245/704, 37826/11, -646875/352, 
  -4277215/1056, 933253/1056, 510/11, -175915/352, 2, -733/11, 94579/66, 
  331/11, 164203/352, -4, 252/11, -92317/33, -441/11, 4, 89989/66, -1728/11, 
  234041/192, 130501/96, 2267/11, -7582/3, -542/11, 23247/32, 26399/264, 
  80216/33, -1572019/1056, -211433/192, 28663/176, 1019891/352, -493183/704, 
  -948037/528, 1, 4, 1, -4, -2, -2, -6, -2, 1, 1, 2, 2, 302/11, -33263/264, 
  -124133/264, -260/11, -102793/66, -265/11, -1549439/1056, -489581/352, 
  95977/66, 1931195/1056, -92767/2112, -211997/176, -53651/88, 1151357/2112, 
  82549/96, -1, 4, -4, -2, -6, 3, 2, 1273/11, -124661/264, -1391/11, -686/11, 
  -488877/352, 833/11, 1929083/1056, -1668/11, 265037/264, 1965/11, 
  1404299/704, -284067/352, -2, -2, 1, -2, -2, 2, 2, -8, -2, 6, -2, -6, -2, 
  4, 6, -6, 4, 4, -4, -2, 6, 6, -9, -9, -10, -4, 9, 4, 2, 2, -2, 2, -2, -4, 
  -2, 6, 2, 4, -4, -2, 2, -4, -2, -2, 2, 2, -4, 6, 4, -5/2, 5/2, 5/2, 2, -2, 
  -5, 3/2, -3/2, 1/2, -4, -3, -1, -2, 1, 2, -2, 1/2, -1, -3, -2, 3/2, -7/2, 
  -3/2, -2, 3/4, -2, 1/2, 3/2, -3, 2, -5/4, -15/4, -4, 5/4, -10, 20, 10, 5, 
  -10, 5, 9, -15, 6, -9, 7, 3, 8, -5, -9, 17, 8, 3, 1, 4, -5, -7, 5, 3, 2, 2, 
  2, -3, -3, -4, -4, -2, 2, -22, -3, 23, 4, 24, 3, 17, -2, -5, 5, -2, 2, -3, 
  -2, -4, -2, 2, 2, -3, 2, 3, 7, -2, 3, -3, 2, -4, 2, -2, 2, 2, -2, -1, -4, 
  2, 2, -2, 2, 2, 6, 2, -2, -8, -2, -12, -2, 10, 2, 2, 2, -4, -3, -12, 10, 
  -6, 2, -8, -2, 2, -2, -2, -1, 2, 2, -3, -2, 3, -2, -10, -2, 3, 11, 10, 2, 
  -5, -10, 3, -16, -2, 26, 8, -10, 12, -2, 2, -2, 2, 4, -2, -2, -4, 2, -8/3, 
  64/3, 4/3, -4/3, -59/3, -10/3, 1/3, 2/3, -197/9, -10/3, 8/9, 23/9, -2, 2, 
  -4, 6, 2, 2, -8, -2, 4, 8, 1, -4, 982/11, -10273/44, 2, -2009/11, 
  475439/528, 1061/11, -450/11, -20915/88, -4, 634/11, -1406897/1056, 
  -149/11, 3487/8, 10, 480595/1056, -6, -1366/11, 130061/192, 4871/6, 
  2495/11, -1895765/1056, -1171/11, 389665/528, -307163/1056, 871513/704, 
  -593717/1056, -1596913/2112, -16663/88, 649691/352, -91589/192, 
  -945925/1056, -5/4, 5/4, -1/2, 5/4, 1/2, -5/2, 5/4, -5/4, -11/4, -4, 8, -4, 
  -3, 3, 1, 13, -18, 5, -10, -13, 17, -3, -5, 10, 3, -9, 10, 8, 10, 1, -10, 
  8, 9, 7, -2, -20, 2, 3, -2, 2, -2, 2, -1624/11, -4, 1679/11, 479/11, 
  -1756/11, 1844/11, 616541/528, 53287/48, 8/3, -23/6, -4/3, 10/3, 16/3, 4/3, 
  -3/2, -6, -4/9, 13, 31/9, 170/11, -536851/1056, -160/11, -214/11, 
  517699/528, 160/11, -498547/1056, -642/11, 846685/704, 602/11, -824669/704, 
  -889183/2112, 6, -12, -14, -10, 24, 16, 2, 40/3, 4, 40/3, -92/3, -92/3, 
  -40/3, -92/9, 184/9, 38/9, -4/3, -34/3, 11/3, 40/3, 16/3, -137/3, 4/3, 
  446/9, -41/3, -428/9, -362/9, 1888/11, -2019/11, -1756/11, -444919/264, 
  492319/264, -1218/11, -56579/352, 9865/32, 1888/11, 13563/4, 142833/44, 
  1756/11, -492319/264, -1876/11, -492319/264, -670/11, -153517/22, -13443/4, 
  2215045/1056, 1165829/352, -2, 2, -32, -4, 40, 16, 2, -2, -4, -2, 2, -2, 
  16, 2, -20, -8, 2, 2, 2, -3, -12, -19/2, 20, 39/2, -11/2, 8, 18, 1/2, -17, 
  -14, 16, 9, 8, -6, -2, 9, -1, 10, 17/2, 1/2, 6, -10, -3, 1, 12, 1, 3, -4, 
  -2, -1, 1, -2, 4, -2, 2, -12, 7, 8, 2, 4, 4, 2, -8, 2, -4, -15, -5, 7, 8, 
  6, 8, 6, 10, -5, -6, -8, 6, 2, -3, 6, 3, -6, 12, -2, -16, -14, -424219/288, 
  -4, 12, 4, -10, -53383/48, -62761/22, -1756/11, -910603/528, -59029/22, 
  942043/528, 62497/22, -40/3, -40/3, 92/3, 92/3, 40/3, 92/9, -184/9, -38/9, 
  -32/3, 46/3, 7/3, -40/3, 53781/88, -3761/33, 32/3, -266/9, -4751/33, 
  -530161/198, 182/9, -2634/11, 3843/22, -1888/11, -415831/264, 2052/11, 
  1756/11, 415769/528, 3696691/1056, -492319/264, 3984/11, 16659/32, 
  1743237/352, -116605/176, 407771/176, 944/11, -532627/264, -1289/11, 
  -1756/11, -135879/176, 410, 492319/264, -2294/11, 4131943/1056, 5095/11, 
  5569547/1056, -286531/176, -2, 2, 12372485/3168, 2, -2, 424219/288, 
  -12372485/3168, -2, -424795/288, 13961455/704, 12359813/3168, -2, 
  -12394661/3168, -13965679/704, -40168855/2112, -158527/528, 
  -102195281/6336, -65205241/6336, -160639/528, 39518185/2112, 79351339/6336, 
  62497/44, 12, -12, -4672549/704, -163807/528, -4581477/704, -12, 878/11, 
  22056629/6336, 20, -15, 325/99, -20, -5, -356/33, -26/99, -1042/99, 50/11, 
  380/33, -212/11, -20, -10, -26/99, -599/198, 10, 380/33, -15/2, -20, 11, 
  -4, -4, -13, 8, 4, -59469/22, -53383/48, -1613/11, 563693/528, -62453/22, 
  -912715/528, -4, 2, 1756/11, -4, -3292/11, 4, 1613/11, -2471299/1056, 
  -53575/48, -549677/1056, 53383/96, -753677/1056, -910603/528, 
  -2246179/1056, -528557/1056, 62497/22, 1690/11, 6, 2, -3270/11, 6, 1657/11, 
  -94817/96, 158527/528, 195655/528, 479/22, 828427/1056, 162751/528, 
  -61275/44, -2328355/1056, -12, 6, -812/11, 158527/528, -5, 479/22, -812/11, 
  9, -805435/1056, 53383/96, 20/3, -37/6, -29/6, -52/3, 2, 101/6, 17/3, -2, 
  -5/6, 200/9, 58/3, -58/3, -14/3, -46/9, 44/3, 217/3, 51, -28/3, -14, 20/3, 
  -40/9, -87/2, 76/9, -110/9, 20/3, -4/3, -12, -70/3, -33, -13, 17, 33, -5, 
  337/18, 121/6, 29/3, -55/2, 23/9, 10/3, -14/3, -35/3, -10/3, 19/3, 35/3, 
  -5/3, -10/3, 263/18, 35/3, -209/18, -179/18, -839/132, -13855/198, 
  1381/198, -40675/396, 761/18, 18845/396, -965/66, 2885/99, -125/396, 
  -2755/66, -67075/1188, -2205/22, 1381/198, 5455/99, -15, 2885/99, 
  -2975/396, -2755/66, -1405/99, -4819/396, -2762/297, -2, 26/3, 20/3, 13, 
  10/3, -29/3, -7, -10/3, 1/3, -23/9, 23/9, -20/3, -37/6, -31/6, 40/3, 118/3, 
  17, 47/2, 4, -97/3, -5/6, 283/9, 77/3, -33, 35/3, -17/3, 2/3, -9/2, -7/6, 
  -22/3, 7/3, 91/6, 17/3, -7/3, -9/2, 200/9, 151/9, -58/3, -19/9, -46/9, 1/3, 
  -7/6, 16/3, 8/3, 17/3, -16/3, -9/2, 9, 58/9, -26, -58/9, 4630661/176, 
  24312487/3168, -489151/1056, 2527/11, -1989771/176, -4668069/176, 
  -3170813/132, 858095/352, -60342233/3168, -1039399/528, -90864535/6336, 
  929905/352, 92472089/3168, 5906971/396, -14263585/6336, 3032/99, -14891/99, 
  3967/44, 14350937/3168, 1925021/792, 14710/99, -308707/264, 1142/11, 
  -270251/528, -53717/96, -1476/11, -2870695/1056, 4, -1293671/1056, 
  -459463/352, 2845351/1056, 492319/264, -143643/352, -2662651/1056, -4, 
  66971/132, 2, 494/11, 13001/528, -221893/528, -519/11, -21, 2, -12473/528, 
  219253/264, 21, -216613/528, -265051/1056, 729203/1056, -288/11, 
  -717587/1056, -8665/16, -4628997/176, -12259553/1584, -134429/1056, 
  -2599/11, 1986411/176, 4668069/176, 8467099/352, -465095/352, 
  60402713/3168, 761689/528, 12017591/792, -1101137/1056, -8364139/288, 
  -26147647/1584, 4619431/1584, -576/11, 5093/96, 526291/1056, 272/11, 
  182/11, 23, -34615/1056, -510307/528, 137/11, 500659/1056, -473799/704, 
  -572779/704, -321/11, 581227/704, -8665/16, -203/11, 528403/1056, 237/11, 
  126/11, -511363/528, -83/11, 500659/1056, 1015/11, -1030627/704, -1055/11, 
  1017059/704, 880735/2112, -10, -26/33, 25/2, 248/99, -5/2, -60/11, -217/66, 
  -1706993/1056, -547/198, 14545513/9504, -115/33, -14621785/9504, 1394/11, 
  -41383/144, -1547/198, -8682029/7128, -1577/44, 158107/792, 2119/22, 
  64222967/28512, -4441/132, -444841/264, -7026221/14256, 22784071/14256, 
  -74594153/28512, -781859/1296, -30, 7759/198, -15/2, 49585/396, -7933/198, 
  -2453/36, 415/6, -100/9, -15817/396, 775/66, -2791625/3168, -831659/3168, 
  -2422591/9504, 308105/1056, 1186637/3168, 1545/22, -15/2, -3343/66, 55, 
  -100/9, -8905/396, 775/66, -2950/33, -787531/3168, 5407/66, 916979/3168, 
  -12143/594, -13, -2, 30, 12, -17, -1822/11, -176305/528, 52565/96, 1997/11, 
  2858023/1056, -4, 2174111/1056, 463687/352, -2825287/1056, -492319/264, 
  139419/352, 950149/1056, 4, 597871/528, -2, 340/11, 3471/8, 13, -277/11, 9, 
  -3359/8, -12, -8, 5, 8649/16, -8745/16, -3, 13, 4, 6, -12, 3, 8505/16, 
  -8841/16, 4, -88907/396, 56675/176, -35872531/3168, -55267/176, 901/72, 4, 
  52531/176, -88907/396, 56675/176, -11720425/1056, -56675/176, 6, -2, -21, 
  18, 2, 21, -2, 2, 4, 4, -11, -11, -6, -2, 11, 2, 2, 2, -2, 12, -6, -2, -2, 
  6, 2, -6, 6, 6, 50771/176, 620/99, -887155/5544, -109/66, -675373/11088, 
  -248/33, -698/33, -448/99, 3017/66, 103889/396, -115642/2079, -181193/528, 
  -5777789/7128, -8343293/7128, 108402161/9504, 7950137/7128, -1097/33, 
  33701249/14784, -11/18, -980898911/399168, 1186139/11088, -29281/33, 
  24085/88, 1171936741/99792, -391/11, -612976211/14784, 799196089/199584, 
  18208222889/399168, 347451619/12474, -215084845/12474, 10, -456107/1584, 
  -1016/99, 203161/792, 363145/1386, -1720639/11088, 148873/264, 8785/36, 
  -1236575/3696, -58787/176, -90322655/22176, 127775297/14784, -307631/324, 
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  47251/176, 8785/36, -100157/336, -58787/176, 168281/528, 373216883/44352, 
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