{{1, -1, 1, 1, -1, -1, -2, -3, -1, -1, 1, -2, -1/2, 1/2, -3/2, 1, -1, 1/2, 1, 
  -1, 1/4, 1/4, -1/2, 1/2, 1/4, 1/4, -3/4, -1, -1/4, 3/4, 1/2, -1/4, 3/4, 
  -3/4, -1, -1, 3/2, 1, -3/4, 3/4, 3/4, -3/4, 1/4, -1/8, 1/8, 1/8, -5/8, 1/8, 
  1/2, 1/4, -1/8, -1/2, -1/8, -1/2, -3/8, 5/8, 3/8, -1/4, 3/4, -3/8, -3/8, 
  -17/16, -1, -3/16, 9/8, 9/8, -3/4, 3/4, 3/8, 7/16, -3/4, 1/4, 1/4, -1/4, 
  -1/8, -3/8, -1/4, 1/8, 1/8, 3/8, 1/2, -1/8, -1/4, 1/8, 1/8, -1/8, -1/8, 
  1/8, 1/8, 1/8, -3/8, 1/4, 3/8, -3/8, -1/2, 3/8, 1/4, -1/8, 3/8, -3/8, -3/4, 
  -1/2, 3/8, 3/4, 1/2, -3/8, 3/8, 3/8, -1/8, -3/8, -1/2, 1/2, 1, 1, -1/2, -1, 
  -1, -1/2, -1, -1/4, 1/4, -1/2, -1, 1, -1/2, 2, -3/2, 1, -1, -1/2, -1/2, 
  1/2, 1, 1, -1, 1, 1, -1, 1/4, 1/4, -1/4, 1/4, -3/2, -3/2, 3/2, -1/2, 1, 
  1/2, -1/2, -1, 1, 1, -1, 2, 3/2, -2, 1/4, -1/4, -1/6, 1/4, -1/4, 1, 1/2, 
  29/4, 27/4, 25/4, 9/4, -9/2, -1/2, -27/4, -27/4, -25/4, -25/4, 4, 25/4, 
  1/2, 1/2, -1/2, 1/2, 5/12, 1/3, 1/6, -5/6, -1/3, 1/3, -3/4, -3/4, 1/12, 
  3/4, 1/2, -1/2, -1/2, -1/2, 1, 1/2, -1/2, 1, 1, -1, -1/2, -1/2, 1/2, 1, -1, 
  -5/4, -5/4, -1, 1, 5/4, 7/4, 7/4, -7/4, 1/4, -1/4, -5/24, -1/24, -1/12, 
  5/12, 1/24, -1/6, 3/8, 3/8, -1/6, -3/8, -1/2, 1/4, 1/4, 1/6, -2/3, 1/3, 
  -3/4, -3/8, 3/4, 19/24, 5/8, 1/4, -19/24, -1/4, 1/24, -1/8, 1/4, -1/24, 
  -1/4, 1/4, 1/4, -1/8, 1/8, 3/8, 1/2, 1/8, -1/4, -3/4, -3/8, 3/4, 5/8, -1/2, 
  5/8, 23/16, 3/16, -25/16, -15/16, -1/2, -1/2, 1/2, -1/8, -1/8, 1/8, 1/4, 
  -1/2, -1/4, 1/4, 1/2, 15/16, -15/16, 15/16, 1/2, 1/2, -1/2, -1/2, 1/4, 
  -1/6, -3/4, -1, -3/2, -1/4, 3/4, 3/2, 2, 7/3, -2, 1, -17/16, -17/16, 
  -51/16, -85/48, 1, -1, 25/16, 45/16, 37/16, 23/16, -1/2, -37/16, -5/8, 
  -19/24, 3/4, 3/4, 5/8, -3/4, -5/4, -17/12, 5/4, -1/2, 7/8, 13/8, -1/8, 7/8, 
  -5/2, -21/8, -1/4, 3/2, 5/4, -7/8, 1/4, 7/8, 5, -13/8, -3/4, -1/8, -19/8, 
  -5/2, 7/8, 33/8, 107/16, 11/4, -59/16, 1, -45/8, -33/8, 3/2, -17/4, -37/8, 
  51/16, 17/4, 1/8, -1/8, 1/8, -1/8, 1/4, 1/8, -1/4, 1/8, 1/8, 1/8, 1/8, 3/8, 
  -3/8, 3/8, 3/8, -1/8, -1/8, 1/4, 7/48, -43/144, -1/8, -7/36, 3/8, -7/48, 
  17/36, 7/36, -3/8, -25/144, 1/8, -5/8, 5/8, 13/16, 31/48, -5/36, 1/12, 
  -7/6, -29/48, 13/24, -3/4, -3/4, 17/72, 3/4, 3/8, -3/8, 3/8, -1/4, -3/4, 
  1/2, -1/4, 3/4, 1/2, -3/4, -1/2, 1/8, 1/8, -1/8, -1/8, -1/2, 1/4, 1/4, 1/2, 
  -1/8, 1/4, 3/8, -1/4, -1/8, 1/8, -3/8, -3/8, 1/8, -1/4, 11/16, 25/48, -3/8, 
  3/8, -3/8, -11/16, -23/24, 3/8, 3/8, 7/16, -1/8, 21/16, -21/16, -11/4, 
  -17/24, 1, -7/8, 7/4, 9/8, -7/16, 7/4, 7/4, -3/2, -7/4, -29/6, -1/4, 1, 
  7/12, 7/12, -7/12, -47/8, -7/6, -11/12, -17/24, 7/6, -1/2, 9/4, -9/4, 
  -11/4, 1/2, 27/8, 9/2, -23/8, -3/4, -3/4, 3/4, 3/8, 21/8, 3/16, -13/16, 
  9/16, -1/2, -27/4, -27/8, 23/8, -1/8, -1/8, -3/8, -1, -43/24, 1, 7/12, 
  -7/24, -7/12, 31/12, 67/24, -31/12, 179/32, -195/32, 1/2, 1/2, -1/2, 
  179/32, -1/2, 15/8, 15/8, 15/32, 1/2, 1/2, -3/2, 1/2, 91/64, 1341/64, 
  -557/128, 147/64, -195/32, -37/32, -151/4, -1611/32, 239/64, -21/32, 29/6, 
  9/2, -9/2, 1/3, -3/4, -13/12, 13/12, 1/3, -1, 1, -1, -29/12, -9/4, 9/4, 
  -1/6, -1/2, -1/2, 1/4, -2, 1/4, 95/36, -35/18, -35/9, -109/36, -7/12, -1/2, 
  1/2, 1/2, -3/4, 1/2, 1/2, -1/2, -1, -1, 7/4, -11/8, 11/8, 1, 4/3, 2/3, 
  -2/3, -4/3, 1/2, 1, 1, -1, 3/4, 25/24, -1, -2/3, -2/3, -11/4, -31/12, 
  31/12, 1/3, 1, -3/2, -5/6, 3/2, -1/2, -3/4, -2/9, -1/6, 2/3, -1/3, 1/2, 1, 
  1/2, -1, -61/24, -67/24, 83/24, 131/24, -13/6, 61/24, 21/4, -143/24, 
  -61/24, 61/24, 8/3, -17/6, -61/24, -1, 27/8, 13/4, 3/4, -29/8, -7/4, -25/4, 
  31/8, 3, -45/8, -19/16, 103/16, 41/16, -53/16, -17/8, -33/8, -3/16, 25/8, 
  53/16, -3/4, 15/8, 3/16, -49/16, 1, -33/8, -53/16, 33/16, 53/16, 25/8, 
  17/4, 29/12, -21/16, 3/4, -1/2, -17/6, -13/8, -17/16, -7/24, -133/48, 
  -63/16, 2, 133/48, -1/4, 1/4, -1/6, -3/8, 1/4, -17/16, 1/8, -3/4, 13/16, 
  11/16, -1/8, 25/16, -3/2, -19/8, 187/64, 13/8, -1/4, 191/64, 5/64, 
  -115/128, -31/16, -9/8, 145/64, -501/64, -1/16, 1/16, 9/32, 349/48, 61/32, 
  -15/16, -5/8, 23/16, 5/32, -255/64, -21/16, -1/2, -281/144, 1/2, 527/144, 
  -41/24, -5/4, 419/144, 17/24, -31/12, -19/12, -19/48, -29/144, 41/72, 1/4, 
  47/144, -1/4, 283/144, 259/144, -77/36, -253/144, 17/72, 37/24, 35/24, 
  -7/6, 23/24, -1/4, -47/24, -29/24, 1/2, -7/24, -5/24, -19/8, 13/24, -1/4, 
  5/24, 7/12, -1/4, -7/12, -3/8, 1/4, -17/16, -43/48, 7/4, 17/16, 41/24, 
  -7/4, -13/16, 7/4, -11/24, -2, 1/24, 5/3, -5/16, -13/144, 1/8, -19/18, 
  -3/16, 1/18, -107/72, 19/36, 2/3, -11/36, -5/3, -89/16, 497/96, 767/144, 
  319/72, 11/6, 7/72, -667/144, -205/72, -95/72, -43/24, 3/4, -133/24, -29/6, 
  11/6, 17/3, 35/16, 25/8, 51/16, 1/2, -11/8, -21/8, -193/144, -49/72, 
  13/144, -7/24, 203/144, -59/24, -4/9, 10063/576, 1775/288, -13747/576, 
  -637/192, -407/192, -295/384, -95/64, -59/16, 19, 67/16, 45/32, -153/8, 
  -73/32, -517/36, -7111/192, -207/64, 6871/192, 83/16, -169/48, -101/96, 
  353/72, 82/9, -959/144, 17/6, -1, -43/12, -1391/144, 15/8, 5/12, -23/6, 
  -13/4, -5/6, -2, 2, -2, -1/2, -5/4, -2, 1/2, 2, 2, 1/2, 1, 1/2, 3/4, 4, 6, 
  1, -17/8, 1, 1, 1, -1/4, 3/2, 2, 2, -2, 4, 1/2, 3/2, 5/4, -5/4, -5/4, -5/4, 
  5/4, 1/2, -1/2, -1/2, 3/4, -3/4, -5/4, 5/4, 7/2, 1/2, -3/2, -1/2, 9/4, 
  -1/4, 1/4, 17/8, 1/4, 17/8, 43/8, -3/2, 11/4, -43/8, -7/4, -13/4, -41/8, 
  1/4, 15/8, -15/8, 1, 1, -1, -1, -3/4, -11/4, 11/4, 5/4, -1/4, 1/4, 3/2, 1, 
  -1/4, -1/4, 5/4, 1, -1, 1/2, 1/2, -3/2, -1/2, 45/8, 43/8, 53/8, 39/8, 
  -43/8, -43/8, -15/8, -13/8, 9/4, 15/8, 1/2, -1/2, 1/2, 45/8, 43/8, -1, 
  -5/4, -45/8, -43/4, 5/4, 43/8, -37/8, -41/8, 1/4, 41/8, 1/4, -1/4, -1/4, 
  1/2, 45/8, 39/8, -1/4, -5/4, 3/4, -45/8, -39/4, 5/4, -3/4, 39/8, 1/4, -3/4, 
  3/4, -37/8, -33/8, 1, -3/2, 33/8, 3/4, -3/4, -3/4, -1/4, 3/4, -1/4, -1/4, 
  1, 7/2, -1/2, -1, -4, 3/4, -45/8, -35/8, 17/4, -3/4, 39/8, 1/4, -3/4, 3/4, 
  1/8, 3/4, -3/4, -3/2, 5/2, 3/4, -3/4, -3/4, 19/8, 3/4, -1/4, -1/4, 1/4, 
  31/8, 19/2, 45/8, -31/8, -41/8, -19/2, -45/4, 41/8, 45/8, -7/4, -7/4, 5/4, 
  7/4, 1/4, -1/4, -1/4, -1/4, 3/4, -1/2, -3/4, 3/4, 1, -3/4, -1/2, 1/4, -3/4, 
  3/4, 3/2, 1, -3/4, -3/2, -1, 3/4, -3/4, -3/4, 1/4, 3/4, 2, 5/4, -5/4, -5/4, 
  5/4, -2, 3/2, -3/2, -15/8, -75/64, -1063/1152, -1/2, 1/2, 1/2, -1/2, -1/2, 
  1/2, 1/2, -1/2, -11/4, -1/2, 1/2, -9/4, 3/4, 5/4, -5/4, 3/2, 5/4, 3/2, 3/4, 
  3/4, -3/4, 3/4, 3/4, 13/24, -13/24, 5/24, -5/12, -1, -1, 1, -5/4, 1/4, 3/2, 
  -1/4, -3/2, 3/4, -3/4, 15/4, 21/4, 3/2, -15/4, -27/8, 7/4, 21/8, -29/8, 
  1/2, 1, 3/4, 11/4, -11/4, -3/2, 27/8, 1/8, 15/4, 3/2, -11/4, -29/8, -1, 2, 
  3/2, -3/2, -1/6, 1/6, 1/12, 1/4, -17/24, 1, 21/8, -7/6, 1, 1, -1, 9/4, -3, 
  3, 57/16, 57/16, -57/8, -57/8, 57/8, -57/8, -57/16, 57/16, 57/8, -35/128, 
  2475/32, 105/32, 1319/1152, 5217/16, 291/8, 105/32, 193/144, -19/24, 1/4, 
  1/4, -1/4, -1, 1, 1, 11/4, 15/4, -13/4, -1/2, -1, 1, 3/2, 1/2, -1, 1/2, 
  1/2, 1/2, 1/2, -5/2, -3/2, 3/2, -3/2, -11/12, -11/12, 11/12, 1/2, 1/12, 
  -1/2, 3/2, 3/2, -3/2, 7/24, -5/24, -5/24, 5/24, -1/4, -19/24, -35/24, 1/4, 
  -1/2, 25/8, -23/8, -3/2, 1/2, 2, -3/2, -1, 15/8, -5/4, 29/8, 3/2, 9/4, 9/4, 
  3/2, -5/4, 1, 13/12, 5/6, -13/12, -11/12, -11/12, 11/12, -1, -7/4, 1/12, 1, 
  -1/4, -15/16, 3/2, 31/16, -69/16, -69/16, 3/16, 69/16, 3/16, -25/8, -49/16, 
  35/16, 23/8, 1/4, 45557/3584, 5033/1536, -3/2, -277/128, -212043/896, 
  264977/3584, -4203/28, 650423/3456, -3/4, -245/48, -277/48, 3/4, 11/8, 
  245/48, 541/48, -11/8, -11/2, 161/48, 95/16, -7/24, -35/6, -17/12, -1, 1, 
  1, 5/4, -5/4, -1/4, -3/4, -29/8, -27/8, 3/4, 27/8, -1/4, -3/4, 5/2, 25/6, 
  -5/4, -20/3, 5/2, -13/4, -3, 1, 43/12, -7/6, -25/8, -111/16, -29/8, -95/16, 
  111/16, 99/16, -3/16, 29/8, 17/4, 3/16, 69/16, 195/16, 57/8, -5/2, 9/16, 
  -45/16, -183/16, -57/4, -13/16, 57/8, -45/16, -33/16, -61/16, 45/16, 73/16, 
  67/16, -51/16, -33/4, -2, 63/16, -187/16, -63/16, 9, 57/8, 13/16, 29/8, 
  -21/8, -13/16, 69/16, 105/16, -65/8, -183/16, -45/16, -69/8, -69/16, 67/8, 
  69/16, 17/8, 35/8, -1, -17/8, -1/4, 43021/448, 207339/448, -94209/224, 
  -202049/512, 3398149/10752, 627841/896, -70393/224, -5423801/12096, 
  -202561/512, 2805289/10752, 207227/448, -70393/224, -354775/1512, 
  -370031/3584, 5033/1536, -445937/3584, 20290799/96768, -277/128, -9173/112, 
  121993/448, 2988511/13824, -2559113/96768, -242061/896, 2243/1152, 1/2, 
  -1/2, -5/12, -5/8, -1/6, 5/6, 5/8, -1/3, 3/4, 3/4, 5/24, -3/4, -1/2, -45/8, 
  -39/8, 1/2, 5/2, 45/8, 39/4, -5/2, -39/8, 37/8, 33/8, -2, -33/8, 1/4, 
  -15/8, -13/8, 3/4, -3/4, -1, 13/8, 3/4, -17/8, -13/8, 3/2, 13/8, -1/4, 1/4, 
  3/4, 5/4, 5/3, 1/4, -1/2, -5/3, -1/4, -1/2, -1, 1/12, 1/2, -1/2, 1/2, 5/12, 
  1/12, 1/6, -5/6, -1/12, 1/3, -3/4, -3/4, 1/3, 3/4, 1/2, -1/2, -7/6, -1/4, 
  -1/6, 5/6, 1/4, -1/3, 3/4, 3/4, -23/24, -3/4, -197/48, -79/8, -277/48, 
  11/8, 19/8, -1, 461/48, 541/48, -19/8, -11/2, 29/12, 29/12, -37/24, -29/12, 
  1/2, -1/2, -1/2, 1/4, -1/4, -3/4, -1, -7/2, 1/2, 7/4, 9/8, 45/8, 35/8, 
  -13/8, -39/8, 29/8, 17/4, 9/4, -15/2, -29/8, 1/2, 1/2, -1/2, 31/8, 41/8, 
  -41/8, -5/4, -1/4, -1/4, -1/4, -11/8, 15/8, 13/4, -13/8, -1, 13/8, 17/8, 
  9/4, 15/8, 7/8, 13/8, 29/8, -29/8, -39/8, 3/2, 39/8, 5/4, -27/4, -275/24, 
  -107/24, 1, 5/12, 81/8, 47/6, -5/12, -27/8, 13/12, 5/6, -13/12, -1, -47/8, 
  -37/8, -31/8, -13/4, -1, 5/4, 39/8, 25/12, -1/4, 9/4, 2, 19/12, -9/4, 29/4, 
  125/12, 25/6, -3/4, 7/4, -39/4, -20/3, -7/4, 5/2, 23/12, 11/12, 1/12, 
  -23/12, 1/4, -1, -5/2, 1/4, -1/2, 35/8, 9/2, 1/4, -21/8, -1, 7/4, -1/2, 
  -1/8, -53/8, 9/4, 3/4, 1/4, 17/8, 15/4, 15/4, -3, -35/4, -13/4, 51/8, -9/2, 
  9/4, 41/8, 3/4, 7/2, 5, -41/8, -7/2, -1/4, 1/4, -1/4, 1/4, -18023/1792, 
  1495/2304, -1/4, 65/24, -1/4, 1/2, -1/4, -73/64, 69001/448, -1/4, -1/4, 
  -3/4, 3/4, -69925/224, 3269125/16128, 206499/448, -3/4, -11939/112, -3/4, 
  -5091185/12096, 1/4, 1/4, -1/2, -25/48, 43/48, 1/4, -1/8, -3/4, 25/48, 
  -73/48, 1/8, 3/4, 5/8, -1/4, 5/4, -5/4, -67/48, -39/16, 19/24, -1/6, 7/3, 
  7/3, -13/12, 3/2, 3/2, 3/8, -3/2, -3/4, 3/4, -3/4, 1/2, 3/2, -1, 1/2, -3/2, 
  -1, 3/2, 1, -1/4, -1/4, 9/4, 9/4, 1/4, -9/4, -5/4, -1/4, -9/4, -1/2, 5/4, 
  1/4, 9/4, 7/4, -1, -7/4, 1/4, 1/4, -13/8, -15/8, -1/4, -1/4, 3/2, 4/3, 
  -1/4, -1/2, 15/8, 3/4, -5/4, -43/12, 1/4, -3/4, 9/4, 1/4, -7/8, -47/8, 
  -9/2, 3/8, -23/24, -1, 9/2, 65/8, 9/8, -29/8, 9/4, 2, 3/2, -9/4, 49/16, 
  45/16, -1/2, 51/16, -7/4, -9/2, 19/8, -1/2, -51/16, -73/8, -69/16, 113/16, 
  37/8, -1/4, 191/24, -1, -83/16, -145/48, 7/4, -212860639/580608, 
  346797/896, 215763679/580608, -111427/128, -5392609/64512, 88520987/96768, 
  419871/896, -39782327/193536, 246379/256, 1895021/4032, -47419261/96768, 
  -132525/128, -4361527/13824, -1/2, -13/12, 3/2, -5/4, 5/4, -41/24, 
  -587/576, -3/2, -1/2, 3/4, 1/2, 3/4, -3/4, -1/2, 3/2, 3/2, 47/12, 1/4, 1/2, 
  -35/16, -1/4, 129/16, 41/16, 35/16, -131/48, -57/16, -11/24, 25/16, -3, 
  45/16, 13/4, 77/16, -191/16, -57/8, -25/16, 57/8, -77/16, 23/4, 11/2, 
  -7/12, -23/4, 1/4, 85/16, 97/16, 257/48, 25/48, -97/16, 3/4, -41/8, 9/2, 
  11/2, 9/16, -173/16, -87/16, 13/4, 31/4, 115/16, 33/4, 45/16, -83/16, 
  27/16, -3/2, -3/8, 13/8, -11/8, -175/16, 33/16, 141/16, 57/8, -31/4, 
  -145/16, -131/16, -7/8, 113/16, -27/16, 89/16, 109/16, -89/16, 23/4, 19/6, 
  -199/48, -23/4, -143/16, -39/4, -7/12, 143/16, 1/4, -69169/224, -69113/224, 
  68791/224, -1/4, -180071/448, 73593/224, -68791/224, 26093/32, -6555/64, 
  5/64, -22085/256, -2223665/4032, -255788861/580608, 490759/896, 
  34814845/96768, -128285/128, -41765155/96768, 230223641/193536, 481443/896, 
  -32919847/96768, 36535/32, 36543/32, -1579049/1792, -73045/64, -1319/2304, 
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