{{1, -1, 1, 1, -1, -1, -2, -3, -1, -1, 1, -2, 1/2, -1/2, -1/2, -1/2, -1, 1/2, 
  1, 1, -1, -1/4, 1/4, -25/96, 1/32, 3/16, -11/64, 1/96, 143/192, -11/96, 
  -19/32, 17/64, -29/192, 5/32, 1/8, 1/16, 19/96, 7/32, 7/64, -23/48, -11/32, 
  1/4, 1/8, -1/8, -1/16, -19/48, 3/16, 23/32, -11/32, 11/48, 5/8, -19/32, 
  3/16, -11/48, 5/32, 1/8, 1/8, 1/16, 19/48, -9/32, 11/32, -11/48, 5/32, 1/4, 
  1/4, -1/4, 1/8, 1/8, 1/16, 19/48, 7/32, 11/32, -11/48, -11/32, 1/8, 7/32, 
  3/32, 11/96, 19/96, -19/64, 11/64, -11/96, 5/64, -1/2, 1/2, -1/2, -1, 1, 
  1/2, 1/2, -1/4, 1/2, 1/2, 1, -1, -9/4, -9/4, -2, -2, -3/2, 1/2, 1/4, -1/4, 
  -1/2, 1/4, 2/3, -1/4, -1/4, -3/4, -1/4, 1/2, 3/4, 5/12, 2/3, 2/3, -2/3, 
  -1/2, -5/4, -1/4, -1/4, 1/4, 1/2, 1/2, -1/2, -1/2, -1, -1, 1, 2, 5/2, 5/4, 
  -2, 5/2, 5/2, -5/2, 1/4, 1/6, -1/4, 1/2, 3/8, -3/8, -1/2, -15/8, -3/4, 
  -15/8, -11/8, -1, 1/2, 15/8, 15/8, 11/8, 3/4, 1, -11/8, -17/8, -19/8, -1, 
  -1, 7/4, 1, -1/2, 1/2, -1/2, 1, -1, -1/2, 1/2, -1/2, 9/16, 1/6, -43/96, 
  -9/16, 43/48, -43/48, -7/48, 13/192, -3/32, 5/64, 1/12, 49/96, 3/64, 
  -79/192, -35/96, -1/6, -29/192, 1/3, 35/96, -1/6, -1/2, 7/24, 5/24, -1/24, 
  -1/3, 7/12, 1/2, -1/4, -11/24, -7/96, 1/6, -3/2, 31/64, 49/48, -211/192, 
  -1/6, 5/32, -117/64, 83/192, 43/32, -3/4, -31/64, 1/4, 3/4, 55/96, 55/96, 
  -17/32, -53/48, 17/32, 9/16, -1/3, -55/48, 1/6, 1/6, 1/2, 53/24, -1/6, 
  -17/16, 43/48, 55/48, -43/48, 9/16, 9/16, 1/6, 1/6, -17/16, -1/2, -1/6, 
  1/2, 55/48, 55/48, -55/48, 5/192, 13/192, 1/12, 35/192, -1/12, -7/48, 
  -1/96, 13/96, -1/6, 1/6, 1/96, 11/48, -1/6, -35/96, -13/96, -29/96, -1/6, 
  -19/96, 1/6, -77/96, -13/96, -1/6, 61/96, 1/6, 5/24, -1/12, -5/24, 1/12, 
  1/24, 1/8, -1/2, -1/4, 1/12, 1/6, -1/3, -13/12, 1/3, 1, -1/4, 1/12, 1/2, 
  7/12, -1/6, -5/12, -5/12, 1/6, 1/6, 5/12, -1/6, -1/4, -1/12, 1/2, 5/12, 
  -1/6, 3/4, 37/64, 3/32, -29/48, 65/64, 1/6, 1/64, 43/64, -67/192, -49/64, 
  -37/64, -3/32, -1/4, 37/64, -3/2, 19/32, 43/32, 7/12, 1/3, 5/32, -43/16, 
  -1/3, 43/32, -67/32, -43/32, 67/32, -7/16, -7/16, 3/4, 1/2, 15/16, 1/2, 
  -1/2, -1/2, -27/32, -43/32, 27/32, -1/4, -3/4, 17/48, 19/48, 23/16, -3/32, 
  -17/16, -5/6, -103/96, -17/16, -27/32, 11/32, 53/96, -11/32, 3/4, 19/48, 
  39/32, 7/8, 5/48, -63/32, -1/4, -1/8, 5/8, -3/16, 23/32, -1/2, 5/24, 11/48, 
  19/32, -11/32, 7/96, -5/32, -1/8, -1/16, -23/32, 43/48, 27/32, 1/6, -1/6, 
  25/288, -7/72, 1/3, 19/96, -7/32, 49/576, 11/64, -11/96, -5/16, 19/64, 
  -3/32, 11/96, -5/64, 55/288, 17/32, 55/96, -17/32, -1/8, -13/96, -3/32, 
  -11/96, -19/96, 13/48, -23/96, 1/32, -25/96, 1/12, 1/12, -1/3, 1/12, 1/8, 
  -1/24, -35/96, 1/96, 1/4, 17/32, -1/6, -1/8, -1/8, 31/96, -19/96, -3/32, 
  19/64, 1/6, -59/192, 9/32, 19/64, -11/64, -5/192, -5/64, -5/8, -19/96, 
  -17/32, -43/64, 9/32, 37/32, -1/4, 5/4, 1/4, -3, -1/4, 1/2, 1/4, -1/4, 1/4, 
  1/16, 1/4, -55/16, 55/16, -21/8, 1/2, -21/8, -1/2, -1/2, -2/3, -143/96, 
  -43/96, 1/6, 7/96, -1/2, -5/8, 1/48, -1/2, 1/16, 5/6, 167/48, 91/48, 1/6, 
  -5/16, -1/2, -1/16, 1/4, -15/16, 1/16, 1/2, 17/4, 15/8, -15/4, 1/4, 1, -1, 
  -27/8, -51/16, -3/8, -5, -91/16, 3/8, -1297/112, 1/4, 1297/112, 201/32, 
  -1/2, 1/2, 1/2, 109/18, -3971/1008, 1/2, -1/2, -13/12, 1, 3/4, -91/9, -1/2, 
  101/16, 3719/504, -343/48, 1/2, -1/4, -1/2, -1/2, 21/16, -45/8, -11/7, 9/4, 
  189/16, 189/16, 1297/112, 3/4, 97/48, 511/32, 617/64, 421/168, 5/4, 23/9, 
  83/72, -13/12, -187/72, -73/36, 1/8, -1, -7/8, 43/24, 2, 1, 3/2, -27/16, 
  3/4, 1/6, -1/6, 1/2, -1/2, 1/4, 1/2, 1/6, -1/6, 1/3, 1/2, 1/2, -1/2, 1/12, 
  1/2, 7/16, 1/2, 1, 7/16, -1/2, -23/16, -11/16, 11/16, 23/16, -9/8, -5/6, 
  -1/9, 13/18, 5/6, 1/2, -1/8, -1/4, -43/24, -7/8, -1, -9/4, -5/2, -2/3, 5/2, 
  1/4, 1/2, -1/4, -1/2, -1/4, 5/6, -3/4, -3/4, -9/8, 45/16, 9/8, 3/2, 9/16, 
  -9/16, 15/16, 5/12, -2/3, -2/3, 17/48, -1/8, -103/48, -11/16, 29/48, 31/48, 
  11/16, -53/48, -17/12, -9/16, 5/24, 1/2, -5/24, -11/24, -29/96, 17/16, 
  -1/48, 161/96, 2/3, 167/96, 65/48, -17/24, -1/32, 13/48, -7/8, -1/6, 89/48, 
  1/2, 15/16, -7/8, -5/16, 5/16, 49/24, -23/16, -15/16, -37/8, -9/4, -37/32, 
  -3/8, -7/24, -65/32, -1/3, 33/32, -43/32, 7/96, 39/32, -35/32, 3/8, 1/2, 
  35/32, -9/16, -1/6, 1/2, 35/48, 1/16, -43/48, 43/48, 19/48, -1963/288, 3/8, 
  13/96, -31/48, -97/96, 9223/2016, -5/8, 35/96, 1567/288, -5/32, -959/192, 
  -1555/504, 329/64, 1/4, 407/288, -1/4, 31/192, -653/2016, -5/6, 263/144, 
  -177/128, -1681/504, 3/8, 3/2, 91/96, 483/64, -11/6, 393/128, -17/48, 
  -5/32, 2837/672, 1/3, -43/32, -289/96, 103/64, 363/128, 95/84, -7/4, 
  -13/192, 157/288, -1/12, -77/192, -11/96, 1/12, 35/192, 5/12, -47/96, 
  43/96, 1/24, -31/288, 29/144, 1/32, 139/288, 5/48, -1/32, -11/36, -103/288, 
  163/288, 107/96, -43/64, -13/32, -61/96, -17/24, 347/192, 59/48, -13/32, 
  -1, 1, 5/24, -1/12, -67/288, 31/96, 17/36, -41/288, 1/12, 19/96, -25/192, 
  -23/96, 1/192, -1/12, -73/192, 13/192, 21/64, 35/192, -41/48, 43/64, -1/6, 
  -1/96, 1/4, 1/24, -1/8, -1/24, -1/4, -11/24, -1/2, 35/24, -15/32, 37/64, 
  157/144, -17/144, 31/24, 319/144, -109/144, -31/48, -271/144, -71/144, 1/2, 
  -7/16, 13/16, -13/18, -31/18, 9/8, -295/96, -25/16, 5/8, 281/96, 29/16, 
  -3/8, 9/4, 19/8, 23/16, -13/9, -1/8, 7795/576, -1/128, -2077/192, 
  -57343/4032, 13/9, -175/96, -1019/192, -313/84, -37/48, -305/48, -443/64, 
  -2219/384, -2815/336, -1209/128, -287/32, 141/128, 405/128, 205/28, 
  -285/128, 139/24, 517/192, 13/72, -2431/576, -23/24, -143/36, 841/576, 
  13/12, -1/64, 253/144, 29/12, -1475/288, -2171/288, -29/12, -213/32, -2, 2, 
  -1/2, -5/4, -2, -2, 1/2, 1, -13/16, 1/2, 1, 1/2, 3/4, 1, 1, 1, -1/4, 3/2, 
  2, 2, 4, 6, 2, 2, -2, 4, 1/2, 3/2, -5/4, -3/4, -27/16, -27/16, -1/6, 27/16, 
  9/16, 9/8, 1/3, -9/16, 1/4, -33/16, 43/48, 3/2, -5/16, -61/24, 21/16, 5/12, 
  -1/2, 1/2, -1/2, 3/4, 5/4, 3/2, 1, -1, 3/4, 11/4, -3/4, 3/2, -19/16, 
  -27/16, 1/2, -1/6, 27/16, 17/16, 17/16, 1/3, -17/16, 4/3, -1/6, -1/2, 1/2, 
  1/2, 25/16, 67/48, 1/3, -25/16, -1, -3/2, -3/2, 3/2, 3/2, -3/2, 1/2, 1/4, 
  -1/2, -1/16, 7/16, 1/16, -1/6, -1/4, 3/8, 23/16, 11/48, -1/6, -1/6, -3/16, 
  -7/32, 27/32, -11/48, -5/16, 19/32, -19/16, 11/48, -5/32, -1/8, -23/12, 
  -11/48, -19/48, -25/32, -3/32, 11/48, 29/32, 1/6, -1/6, -1/4, -1/8, 13/8, 
  11/48, 19/48, -3/16, -39/32, 11/32, -11/48, -5/8, 19/32, -3/16, 11/48, 
  -5/32, -1/8, -19/24, -11/48, -19/48, 7/32, 3/32, 11/48, -3/32, 1/6, -1/6, 
  -1/4, -1/4, 1/4, -1/8, -5/8, -11/48, -19/48, -41/32, 3/32, 11/48, 45/32, 
  1/6, -1/6, -1/4, -7/16, -3/16, -11/48, -19/48, 19/32, -11/32, 11/48, -5/32, 
  2, 5/4, -5/4, -3/2, 5/4, -1/2, 295/4, 107/28, -119/576, 107/28, 1651/576, 
  12695/168, 107/28, -5045/4032, 1/2, -475/288, -209/112, -28121/24192, 1/2, 
  3/8, 1/8, -1/2, 9/8, 11/8, -1/3, -7/8, -13/16, -9/8, -13/8, 9/8, 17/16, 
  -1/2, 37/16, -1/2, -3/4, -1, 79/48, -7/4, -1/12, 37/16, -21/16, 3/16, 1/2, 
  1/4, 5/16, 3/8, -3/8, -1/2, -1/2, 1/2, 3/4, -3/4, 3/4, -1, -1, 1, 3, -3, 
  1/2, 1/2, 1/2, -5/4, -3/2, 1, -2, -3/2, 7/12, -7/12, 1/6, 1/2, -1/2, -1/2, 
  -3/4, -5/4, 5/4, -1, -3/4, -11/4, 11/4, 33/16, -1/4, -1/2, 9/4, -1/2, 13/4, 
  -1/2, 3, 1, -1, -1, 5/2, 1/4, 1/2, 1, -295/4, -107/14, -383/144, 
  -25085/168, -107/14, 2939/2016, 475/288, -219/112, 33119/24192, 12695/168, 
  -1/2, 107/14, 407/252, -763/288, 219/112, 41221/24192, 865793/504, 
  -475/288, 219/112, -58391/24192, -3/8, 1/4, 3/8, 1/2, 1/8, -5/4, 1/8, 3/8, 
  5/4, 29/16, 1/4, 1/4, -1/4, 83/48, 5/8, 7/8, -4/3, -7/8, -1/4, 5/4, 3/4, 
  -2, -9/4, -13/12, -1/2, -37/16, 1/4, -1/16, 21/8, -1/8, -9/8, -19/48, 5/8, 
  1/2, -11/12, -151/48, -35/48, 23/12, 4/3, 1/2, -1, -5/4, -3/4, -1/4, 5/4, 
  -3/8, -3/8, 3/8, 3/8, 3/8, -3/8, -9/4, -9/4, 9/4, 1, 1/2, 2, 5/2, 3/2, 
  -3/2, 3/2, -29/48, 29/48, -19/48, -1/6, -1/6, 1/6, -19/48, 1, -1, -3/2, 
  1/2, -2, -5/2, -3/4, 2, -13/4, -15/4, -3/2, 13/4, 3/4, -7/4, 1/2, 
  -48035/588, -6849715/56448, 2413321/4704, -29776/147, 270556067/207360, 
  45781381/56448, -4006345/20736, 13/16, 15/32, -1/16, 1/8, -19/32, 5/48, 
  17/48, -3/4, 19/48, -7/16, -9/16, -13/12, 1/3, 1/12, 1/2, -1, 5/16, 7/16, 
  3, -49/48, -3/2, 3/8, -1/6, 23/48, -9/16, 9/16, -3/4, 19/16, 45/16, 61/48, 
  3/4, 1/16, 7/16, -17/48, -7/16, -1/4, 45/16, 9/8, 45/16, 33/16, 3/2, 1/4, 
  -45/16, -37/16, -33/16, -9/8, -3/2, 33/16, -1/2, 51/16, 57/16, 3/2, 3/2, 1, 
  1/2, -21/8, -3/2, -70481/441, -43/48, 905404313/6773760, -7913/4608, 
  52917773/28224, -3722987/6272, 1610591/7056, -1032755/20736, 
  -195246443/207360, -3202471/14112, 3143/1728, 1137839/7056, -1303973/882, 
  43/48, -5113218713/6773760, 8681/4608, -52965401/28224, 3722987/6272, 
  -100910/441, 1409336939/1016064, 195177323/207360, 3210409/14112, 
  -3143/1728, 282365/1764, -1093139/1176, 43/48, -7205271833/6773760, 
  7913/4608, -52917773/28224, 3722987/6272, -1614119/7056, 852214259/1016064, 
  195246443/207360, 3209527/14112, -3143/1728, 2556803/2352, 43/48, 
  -7220602463/6773760, 7913/4608, -3/2, -7007719/56448, 3722987/6272, 3/2, 
  -1617647/7056, 394380865/112896, 195246443/207360, 3216583/14112, 
  -3143/1728, -11/16, 275/96, 401/96, 17/24, 39/32, -169/48, -17/32, -2/3, 
  -13/12, -1/4, 2/3, -17/48, -299/96, -37/96, 7/48, 1/6, -49/96, -23/48, 
  -7/48, 131/96, 193/96, -137/96, -59/96, 1/3, 1, -1/12, -139/48, 5/6, 
  -73/48, 1/12, -7/12, 1/48, -11/48, 85/24, -1/6, -11/12, -1/3, 3/8, 43/32, 
  37/32, 7/6, 5/3, 1/6, 85/32, 15/8, -7/6, -97/32, 53/32, 35/32, -19/12, 
  -53/32, -55/48, -55/48, 17/16, 53/24, -17/16, -11/16, 53/96, 155/96, 7/32, 
  -25/12, 15/32, -2/3, -25/24, 2/3, -11/16, -7/32, 15/32, 89/32, 13/8, 
  -67/32, -17/12, -25/24, 17/12, -5/96, -13/96, -1/6, -35/96, 1/6, 7/48, 
  -239/96, -13/96, -1/6, 47/96, -11/48, 1/6, 35/96, 67/96, -13/96, 1/6, 
  -35/96, -1/6, 211/96, -29/96, 1/6, -307/96, -1/6, -5/12, 1/6, 5/12, -1/6, 
  -1/12, -43/48, 1/2, 121/48, 1/4, 1/2, -73/48, -13/48, -1/2, 1/48, -49/48, 
  -17/12, -1/2, 11/16, 1/6, 5/12, 5/12, -5/12, -49/48, -5/4, -1/2, 97/48, 
  1/6, 33/16, -1/4, -73/16, -5/2, -1/2, 5/2, 9/4, -9/4, 11/8, -103/32, 
  -43/32, 7/6, 7/6, 1/6, 53/32, 35/8, -5/3, -97/32, 131/32, 43/32, -1/3, 
  -131/32, 2, 1/2, 4/3, 1, 1/6, -3/2, -1/2, -7/3, -1/2, 65/96, 43/32, -1/3, 
  -65/96, 1/4, 23/16, -43/24, -19/48, -35/16, -19/32, 17/8, 49/48, 211/96, 
  67/48, 67/32, 5/32, -71/96, -5/32, -1/8, -11/48, -101/32, -7/4, -29/48, 
  105/32, 1/4, -1/8, 5482451/7056, 71/144, -7211165063/10160640, 9497/6912, 
  3/16, -39/32, -97/224, -5/24, 1559483/28224, -11/48, -19/32, 43/32, -7/96, 
  5/32, 1/8, -1117295/1764, 5863729/6912, 11/48, -8355611/34560, 57/32, 
  -22044905/14112, -35/48, -61/32, -1/6, -17012605/20736, 1/6, -13/16, 
  -37/32, -11/48, -19/48, 7/16, 29/16, -11/32, 11/48, 5/8, -19/32, 3/16, 
  -11/48, 5/32, 13/48, -17/16, -55/48, 17/16, 1/4, 13/48, 3/16, 11/48, 19/48, 
  -13/24, 23/48, -1/16, 25/48, -1/6, -1/6, 2/3, -1/6, -1/4, 1/12, -7/24, 
  -27/16, -1/2, -1/24, 1/3, 1/2, 5/16, 7/16, -1/2, 3/16, 5/16, 9/16, 1/6, -1, 
  -1/2, -5/16, 1, -1/8, -1/6, 57/32, 43/32, -1/6, -53/32, 1/4, -3/4, 1/2, 
  -1/2, -3/4, 5/4, -41425/48, 682841137/5080320, 8215656931/10160640, 
  68753371/28224, 1690266773/7620480, 3/4, 1543405369/2540160, 
  -12078365/9408, -1543405369/2540160, 2555/3, -53208523/207360, 
  -8278495021/10160640, -2552549/4032, 154785953/207360, -47/48, 47/48, -1/4, 
  3/4, 1/6, -1/6, 31/48, -49/16, 3/2, 3/4, -55/48, 1, 1/12, -37/16, -3/16, 
  9/2, 3/8, -3/4, -3/8, 3/8, -3/8, 1/2, 23/8, 1/8, -1/2, 7/8, 9/8, -11/24, 
  -9/8, -9/16, -7/8, -9/8, -49/24, 9/8, 9/16, 13/8, -3/8, 1/4, 3/8, -1/2, 
  63/16, 1/2, -7/4, 63/16, 3/4, 7/4, 151/48, 155/48, 55/48, -7/12, 19/12, 
  1/4, 15/16, -17/32, 3/4, -3/32, -3/4, -167/32, -123/32, -3/4, 15/32, 1/2, 
  55/48, -1/4, -11/48, -5/6, 1/4, -51/8, -45/16, -1/2, 45/8, 1/2, -3/8, -3/2, 
  1, 81/16, 153/32, 9/16, 15/2, 273/32, -9/16, -174501305357/40642560, 
  312605/168, 3138635897/2257920, 123611/144, -5/12, -400665883/414720, 
  -27172037/14112, 135078053/1244160, -565/4, 50045573/1244160, 879403/7680, 
  34330703/28224, -128356853/1244160, -16525/48, 285/4, 140668003/248832, 
  117701/336, -11389/6912, -1/2, -312521/168, -51431369467/162570240, 
  -123737/144, 4935515/7056, 51293677867/20321280, 27177329/14112, 
  -101500276277/60963840, 1137/8, -96976157237/60963840, 343338533/376320, 
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