{"id":"428.82.4.a","row":1048,"stored":{"file":"master_catalog.json","row":1048,"construction":null,"columns_sha256":null},"parameters":{"n":428,"k":82,"d":4,"N":101,"r":19,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15\u00b7T16\u00b7T17\u00b7T18\u00b7T19\u00b7T20\u00b7T21\u00b7T22\u00b7T23\u00b7T24\u00b7T25\u00b7T26\u00b7T27\u00b7T28\u00b7T29\u00b7T30\u00b7T31\u00b7T32\u00b7T33\u00b7T34\u00b7T35\u00b7T36\u00b7T37\u00b7T38\u00b7T39\u00b7T40\u00b7T41\u00b7T42\u00b7T43\u00b7T44\u00b7T45\u00b7T46\u00b7T47\u00b7T48\u00b7T49\u00b7T50\u00b7T51\u00b7T52\u00b7T53\u00b7T54\u00b7T55\u00b7T56\u00b7T57\u00b7T58\u00b7T59\u00b7T60\u00b7T61\u00b7T62\u00b7T63\u00b7T64\u00b7T65\u00b7T66\u00b7T67\u00b7T68\u00b7T69\u00b7T70\u00b7T71\u00b7T72\u00b7T73\u00b7T74\u00b7T75\u00b7T76\u00b7T77\u00b7T78\u00b7T79\u00b7T80\u00b7T81","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45],[46],[47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],[62],[63],[64],[65],[66],[67],[68],[69],[70],[71],[72],[73],[74],[75],[76],[77],[78],[79],[80],[81]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45],[46],[47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],[62],[63],[64],[65],[66],[67],[68],[69],[70],[71],[72],[73],[74],[75],[76],[77],[78],[79],[80],[81]],"sk_fingerprint":"6e02394f80a8e61b","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2,10,11,12,13,14,15,19,20,21,22,23,26,27,28,29,30,31,32,34,39,43,46,50,52,54,55,56,59,63,68,72,73,75,76,77,78,82,83,87,89,91,93,95,97,99,100],[0,1,4,9,10,19,20,21,22,23,28,29,31,32,33,34,37,38,39,40,42,43,45,47,48,50,53,54,56,58,59,62,63,66,68,71,72,73,74,75,76,77,78,79,81,83,84,85,86,87,89,90,91,93,94,95],[1,4,10,12,15,16,17,18,19,21,22,23,25,30,31,33,34,35,45,46,47,48,50,53,56,58,59,61,64,65,70,71,73,74,75,76,77,78,80,82,86,87,88,90,91,92,95,97,98,99,100],[0,1,2,6,10,12,13,16,17,18,20,23,25,27,29,30,31,33,34,35,36,37,38,41,43,44,45,47,48,49,50,54,59,61,62,63,69,70,71,72,75,76,81,82,85,86,87,89,90,91,93,94,96],[74,92,93,94,95],[4,5,7,8,10,11,12,13,14,15,17,20,23,24,25,30,36,37,38,39,40,41,44,45,46,48,50,51,53,54,55,57,60,61,63,66,67,70,73,74,80,83,86,87,88,89,92,95,99,100],[1,2,6,7,11,12,13,15,17,19,21,25,26,28,29,30,31,36,40,43,44,46,47,49,51,52,53,54,55,57,58,59,61,62,66,69,71,72,73,74,75,77,78,79,80,82,83,85,86,87,89,90,91,93,97,99],[1,2,11,13,14,15,16,17,18,19,20,21,23,25,28,31,33,35,36,38,39,40,42,43,44,47,49,50,53,55,56,57,59,60,61,64,67,69,70,71,73,75,77,78,81,82,84,86,91,92,95,96,100],[2,4,6,9,10,11,15,18,20,22,23,24,25,29,35,36,40,44,46,55,59,61,68,72,73,74,75,79,81,82,83,85,86,88,91,93,94,98],[75,92,95,96],[0,2,4,8,9,10,11,12,14,17,22,28,30,32,34,38,39,40,44,45,46,48,49,55,56,57,58,60,61,63,65,67,69,70,74,76,80,84,85,88,90,91,92,96,97,98],[0,1,4,5,6,9,10,16,19,21,22,23,26,28,29,32,33,34,36,37,38,39,40,43,45,47,48,53,54,56,59,62,63,66,67,68,70,71,72,73,74,76,77,78,79,83,84,87,88,90,95,98,100],[40,60,61,85,86,87,88,89,100],[2,4,5,7,11,13,14,15,17,18,21,23,25,26,28,30,32,33,36,39,40,41,43,46,48,50,55,60,62,63,64,68,69,70,72,73,77,78,79,80,81,82,84,87,88,90,92,93,98,99,100],[0,2,4,6,7,8,9,10,11,12,14,15,17,21,22,23,27,28,29,31,32,34,35,38,39,40,41,42,46,49,52,53,54,55,56,57,58,60,61,62,63,69,71,73,76,77,78,79,80,82,83,85,86,88,89,90,92,93,96,99,100],[0,5,6,9,10,11,12,14,15,17,19,23,24,26,35,37,38,39,40,42,43,44,45,46,48,49,51,54,55,56,58,59,60,61,62,66,67,68,72,73,75,80,81,83,85,86,88,90,94,95,98,99,100],[1,2,3,5,7,8,10,16,17,18,19,20,21,25,29,30,31,32,33,37,39,41,42,44,46,47,48,50,51,52,53,55,57,59,61,64,66,67,69,72,73,74,77,80,81,82,85,90,93,95,96,97],[2,3,5,6,7,9,10,12,15,16,19,23,24,27,29,30,32,34,43,44,47,48,49,52,54,55,56,60,61,62,63,64,65,70,73,75,76,78,79,80,81,85,86,87,90,93,96,97,98,99,100],[0,2,3,4,5,6,7,10,11,13,19,22,23,26,29,31,32,33,36,37,40,41,44,45,46,47,50,52,60,61,63,64,65,68,69,70,74,78,79,83,86,87,88,89,91,95,98,99],[0,1,3,4,9,10,11,13,14,15,16,19,23,26,28,29,31,32,36,37,38,40,47,51,52,53,57,59,60,62,63,66,67,68,70,71,74,78,80,84,85,87,88,93,94,96,97],[1,2,5,7,11,12,13,15,16,19,20,21,25,28,29,30,33,36,38,40,42,43,44,47,48,49,50,51,52,53,54,55,56,57,59,61,62,63,67,69,72,73,74,77,78,82,83,85,88,90,91,92,93,94,96,99],[44,92,94,95,96,97],[1,2,10,11,15,16,22,23,26,27,29,32,33,34,36,39,40,41,43,44,45,46,47,48,49,51,52,53,58,59,61,63,64,65,66,68,69,70,71,76,79,80,81,83,84,85,90,92,95,97,98,100],[3,4,5,6,9,10,12,14,15,16,17,19,20,22,28,29,30,31,35,36,39,40,41,42,44,45,47,52,56,57,59,60,61,63,64,65,67,69,71,75,76,77,78,79,80,82,86,87,89,92,94,95,96,97,98,99,100],[0,2,3,4,8,9,15,19,20,21,24,25,26,27,29,31,38,39,40,44,45,46,47,48,49,50,52,55,57,58,60,61,66,68,69,70,73,74,75,77,78,79,80,83,84,86,88,93,97,99,100],[0,5,8,9,11,13,15,17,19,20,22,23,24,25,28,32,33,34,35,36,38,39,41,48,49,51,53,54,61,63,64,65,66,67,70,71,72,78,81,84,85,86,87,92,93,94,95,97,100],[11,92,94,95,98],[0,1,4,9,11,12,13,16,20,22,24,27,28,30,34,37,38,40,41,42,43,45,46,47,48,49,50,53,55,56,58,62,67,69,70,71,73,74,76,77,79,83,85,89,90,98,100],[0,1,2,6,8,9,10,16,22,23,28,29,31,34,39,40,41,44,45,46,47,48,49,50,51,52,54,59,63,64,65,66,67,69,71,75,76,79,80,83,84,85,88,90,91,92,93,96,97,98,99],[0,1,4,5,6,7,8,9,10,14,16,17,18,19,21,22,25,26,28,29,31,32,34,36,38,43,45,47,48,51,52,56,59,60,62,65,66,67,68,70,71,72,73,75,76,77,78,79,81,82,84,88,91,92,93,96,98,99],[3,4,5,6,7,8,10,11,13,14,16,19,20,22,24,26,27,34,36,37,38,39,40,41,43,44,47,48,49,51,53,54,56,58,61,64,65,68,70,71,72,73,75,78,81,82,84,86,88,92,94,95,98,99,100],[0,3,5,6,8,11,12,13,15,17,22,24,27,28,29,30,32,33,35,36,38,39,40,41,45,46,47,48,52,53,55,57,58,61,67,70,74,75,77,80,81,82,83,86,87,88,91,95,97,98,99,100],[2,4,5,10,12,14,15,18,19,20,23,24,25,30,33,35,39,40,41,44,45,46,51,53,54,55,57,58,60,64,66,69,71,72,74,76,78,80,81,83,86,87,88,90,91,93,94,95,98,100],[6,92,93,94,95,96,98],[0,1,2,5,7,10,11,12,15,16,18,26,27,28,31,34,36,37,43,46,47,49,52,53,56,58,59,61,65,66,68,69,71,72,73,74,75,76,78,79,81,82,84,88,89,90,92,95,97,99],[0,5,6,7,8,9,11,13,14,16,17,18,19,22,24,25,26,29,32,34,35,36,38,41,42,48,49,50,52,53,54,55,58,60,61,62,63,65,71,72,74,78,80,84,86,88,89,91,93,97,98,99,100],[19,35,72,85,87,90,91,92,94,97,98,99],[2,3,4,6,10,12,13,14,15,16,17,20,21,22,24,25,34,35,36,38,40,41,43,51,63,65,66,67,68,69,71,75,76,84,86,88,90,91,92,93,94,97,100],[0,2,3,4,5,6,7,8,9,11,15,17,20,22,23,25,26,27,28,30,31,33,34,39,40,41,42,43,45,49,50,51,52,53,55,57,61,62,63,64,66,68,69,70,76,78,79,80,81,83,84,85,87,88,89,93,96,100],[5,12,15,38,53,54,71,82,83,89],[0,7,9,13,14,16,17,19,20,23,25,26,32,33,35,37,38,39,40,42,44,46,54,55,57,59,60,61,67,68,70,71,74,76,77,79,80,82,84,86,88,89,91,92,93,94,95,98,99,100],[0,1,2,5,8,9,12,14,15,18,21,22,24,30,31,32,34,35,38,40,41,42,43,44,46,47,48,50,51,57,59,60,63,65,66,68,69,73,75,77,80,84,86,87,88,90,92,93,97],[2,3,4,5,7,11,19,20,22,23,25,27,30,32,34,35,38,39,40,41,42,45,51,52,54,55,56,57,58,62,64,66,67,69,70,71,72,75,76,78,81,83,84,85,87,89,90,91,92,93,96,98,100],[5,7,8,10,12,15,16,20,23,24,26,27,28,29,31,32,33,36,37,38,39,41,42,43,44,46,48,50,51,52,53,55,57,61,64,65,66,73,74,80,81,84,85,86,88,89,98,99,100],[0,1,3,5,7,8,9,11,12,14,16,20,21,23,24,25,26,29,30,31,32,33,35,36,39,41,43,44,45,47,49,50,52,57,58,61,62,64,68,71,75,83,85,87,92,93,95,99],[1,4,6,7,8,9,10,11,12,13,14,18,22,23,24,28,29,31,35,36,37,38,39,40,41,45,47,48,49,50,51,53,55,59,60,65,67,69,70,71,73,75,76,79,80,82,85,86,87,88,89,90,91,92,93,94,95,97,98],[32,92,99],[0,1,5,8,11,13,15,16,17,18,22,23,24,26,27,29,30,32,33,34,35,36,37,39,40,41,43,45,47,48,49,50,51,52,55,56,60,61,63,64,66,68,69,70,71,72,73,76,80,84,85,86,87,91,97,99],[0,5,6,7,9,12,14,15,16,17,18,19,20,21,23,24,26,27,33,34,35,37,39,42,44,50,60,61,65,70,74,76,77,78,79,82,85,87,88,89,90,91,92,94,96,97,98],[9,92,96,99],[1,4,9,11,12,13,15,16,20,22,24,26,27,30,31,33,34,36,37,38,40,41,42,45,46,47,48,49,50,53,55,56,62,69,71,73,74,75,76,79,81,83,85,88,89,90,91,92,93,94,98],[1,2,4,11,13,14,15,16,17,18,19,20,21,23,25,28,30,31,33,35,36,38,39,40,42,43,44,47,49,50,53,55,56,57,59,60,61,64,67,69,70,71,73,75,77,78,81,82,84,85,86,87,89,91,92,95,96,100],[0,1,2,5,6,7,9,10,13,14,17,19,21,23,24,28,29,30,31,33,36,37,38,39,41,42,45,47,48,49,50,51,52,53,56,58,59,60,62,67,68,69,71,72,74,77,78,79,81,82,85,88,89,90,93,97,99,100],[0,5,7,10,11,18,19,20,21,25,26,27,31,33,34,35,38,40,41,45,46,48,50,51,54,55,57,58,63,65,66,68,70,73,74,76,77,78,79,80,81,82,83,85,87,88,90,92,94,95,96,97],[14,92,93,95,96,99],[61,92,93,94,95,96,99],[1,2,6,7,9,11,14,15,16,23,27,28,29,30,33,35,37,38,39,42,43,45,46,47,50,53,54,56,59,60,61,64,65,66,69,70,72,74,76,78,79,82,83,85,86,87,89,93,94,95,96,98],[0,1,2,5,6,7,8,9,10,13,14,15,16,17,18,19,23,25,27,33,35,38,39,40,42,43,44,45,46,47,50,51,54,55,59,60,62,64,66,69,70,72,74,78,81,83,84,85,86,88,89,91,95,100],[0,1,2,7,8,9,10,11,16,18,19,20,22,23,25,26,28,29,30,33,37,40,41,42,45,48,52,54,55,57,58,59,61,63,64,65,68,69,74,75,76,79,81,83,87,88,90,95,96,97,99,100],[37,92,93,94,97,99],[2,3,4,5,6,7,8,9,11,13,14,15,17,18,19,21,23,28,30,33,35,38,39,40,43,44,46,48,49,53,55,56,58,60,61,64,65,69,71,73,75,77,78,82,84,85,86,88,89,90,94,97,98],[3,4,6,7,9,10,11,12,16,17,19,20,24,25,26,28,30,31,34,35,39,40,45,47,48,49,51,52,53,55,56,58,60,62,66,67,68,69,71,72,73,74,75,79,81,82,83,87,90,93,94,95],[6,7,8,10,11,13,15,17,18,19,20,24,25,29,30,31,34,36,37,38,40,44,45,46,49,52,53,55,57,58,61,64,67,71,73,74,75,80,81,84,85,87,91,92,93,94,96,97,98],[57,92,93,96,97,99],[0,1,2,3,7,8,9,10,11,13,14,16,17,18,19,21,22,23,27,31,35,37,38,40,42,44,46,50,51,52,54,55,56,57,59,61,62,64,66,69,70,73,75,76,77,78,79,80,81,84,86,88,89,90,91,92,93,98,99],[2,4,5,6,7,11,13,14,15,18,19,21,23,25,28,30,32,33,35,36,37,39,40,43,44,46,48,49,53,55,58,60,63,64,69,70,73,75,77,78,79,80,81,82,84,85,88,91,92,93,94,95,96,97,100],[1,6,7,10,14,15,17,19,20,21,22,26,29,30,31,37,38,39,42,44,45,48,52,53,54,60,62,65,67,68,71,72,73,74,76,77,78,79,81,82,83,84,86,87,88,91,92,98],[1,4,6,9,10,13,14,15,16,18,20,21,22,23,24,26,28,29,31,32,33,34,35,36,37,38,39,40,41,43,46,47,48,50,52,53,54,55,56,59,60,62,64,67,68,69,71,74,75,76,77,79,81,82,83,84,86,87,88,93,95,97,98,99,100],[0,5,7,8,9,10,11,12,14,15,18,20,21,23,24,27,29,30,31,35,36,38,39,42,43,46,51,53,56,58,60,61,62,65,71,74,75,76,77,79,80,84,86,87,88,89,90,91,96,97,99],[0,1,4,6,7,11,12,15,16,17,23,24,30,31,32,38,39,41,47,50,51,53,54,55,56,57,58,59,61,63,66,71,79,83,85,86,88,89,94,95,98,99,100],[0,1,3,5,12,15,17,21,23,24,26,30,32,33,34,35,37,38,39,41,42,43,44,48,50,52,53,54,57,62,65,66,68,69,72,73,74,80,81,82,83,84,85,87,88,89,90,91,92,93,96,97,100],[0,6,8,9,10,14,17,18,19,21,25,28,29,31,32,34,35,36,38,41,43,45,46,48,51,52,53,55,57,60,65,66,67,70,73,76,77,78,79,80,81,82,83,86,87,90,93,96,97,98],[0,10,14,15,18,19,20,21,22,25,26,33,34,35,36,38,41,42,43,45,46,48,50,51,52,54,55,56,57,58,60,61,63,65,66,68,70,73,75,76,77,78,79,80,81,82,83,85,86,88,90,92,93,95,97,99,100],[0,1,4,9,10,15,16,19,21,22,23,26,28,29,31,32,34,37,38,39,40,42,45,47,48,51,52,53,54,58,59,62,63,66,67,68,70,71,72,73,74,75,76,78,79,83,84,85,87,89,90,92,93,99,100],[0,2,3,4,5,7,9,13,17,23,24,28,30,31,33,34,36,42,45,47,48,49,54,55,56,57,60,62,63,69,72,73,75,76,79,89,90,94,95,96,97,98,99,100],[2,4,6,8,10,12,14,17,21,22,24,26,28,29,33,34,35,38,39,41,42,45,50,52,55,57,58,60,62,63,64,68,69,70,71,74,75,77,81,83,84,87,89,91,92,94,95,100],[0,1,2,5,6,7,8,9,10,13,14,16,18,20,22,24,25,28,31,34,37,39,40,41,44,45,46,47,48,49,50,51,59,60,66,67,69,70,71,74,76,79,80,82,84,85,87,89,91,94,95,97,98,100],[1,2,3,4,5,8,11,12,14,15,18,19,22,23,25,26,29,30,31,35,45,52,54,56,58,59,62,65,68,69,73,74,75,76,78,84,85,88,89,90,91,92,96,99,100],[0,6,10,11,12,13,15,19,21,23,24,26,27,29,30,31,32,36,39,41,42,46,49,51,52,54,55,58,59,66,68,69,70,72,75,78,81,84,85,91,92,95,98],[58,92,93,95,96,98,99],[0,2,3,4,6,9,11,13,14,15,17,18,23,24,27,28,30,33,34,36,39,43,45,47,48,49,51,52,53,55,56,57,60,62,63,69,72,73,76,77,79,83,85,88,90,93,95,97,100],[0,1,2,7,9,12,15,16,17,18,19,23,24,31,32,33,35,36,37,39,41,47,48,50,51,53,54,55,56,57,58,59,64,66,67,69,72,73,74,76,78,79,81,83,86,87,88,89,90,91,92,96,100],[41,92,97,98,99],[1,3,4,5,10,11,14,17,24,25,27,28,29,30,42,44,47,48,49,50,51,52,53,54,55,56,58,59,61,62,65,66,68,71,73,75,76,77,78,82,83,84,86,87,90,91,94,95,99,100],[72,92,94,97,98,99],[0,1,2,5,6,7,9,11,12,14,18,21,23,24,27,29,32,38,40,43,45,46,47,48,50,51,52,53,58,59,60,62,63,66,67,68,69,70,71,72,74,77,78,79,80,82,83,87,88,89,90,91,95,96,100],[2,4,5,6,10,12,13,14,19,24,25,26,27,30,31,32,35,36,38,40,42,43,45,46,48,49,50,56,57,60,67,68,69,72,74,75,76,79,80,84,86,87,90,93,94,98,100],[0,5,9,11,13,15,16,18,24,25,26,28,29,30,32,33,35,37,39,40,42,46,48,50,51,52,53,54,56,59,61,62,63,64,65,67,68,71,76,77,80,85,86,88,90,91,92,98,100],[0,2,7,8,10,11,15,17,22,25,27,29,30,31,34,35,37,38,41,42,43,44,50,52,53,56,57,62,63,67,70,71,72,74,75,78,80,82,84,85,90,91,93,95,96,97,98,100],[0,1,2,3,6,8,9,10,11,12,13,16,20,23,29,30,32,33,34,35,38,39,41,42,44,45,46,47,48,49,50,51,52,54,56,59,65,66,69,71,72,75,76,79,80,87,88,92,95,96,97,99,100],[0,1,2,3,10,11,12,13,15,16,23,26,28,29,30,31,34,35,36,39,44,45,46,47,48,49,51,52,53,56,58,59,61,62,65,66,67,68,69,70,72,76,81,87,91,92,94,95,100],[0,1,2,5,8,9,12,14,15,18,21,22,24,30,31,32,34,35,38,40,41,42,43,44,46,47,48,50,51,57,59,60,63,65,66,68,69,75,77,84,85,87,88,89,91,96,98,99,100],[0,7,9,10,12,17,18,20,21,25,28,29,30,35,37,39,40,42,43,45,46,49,52,54,61,63,64,65,66,67,70,72,73,74,79,80,81,82,83,84,86,88,89,94,95,97,98,100],[0,2,4,6,9,13,16,19,22,24,25,27,28,31,33,34,36,37,38,41,42,43,44,46,48,49,62,64,65,67,68,69,73,74,76,78,79,80,81,84,87,89,90,95,96,100],[0,5,10,12,13,18,19,20,22,23,24,25,27,28,31,33,34,35,37,40,41,42,43,48,49,53,55,61,62,64,65,67,71,72,78,79,80,85,86,87,88,91,92,95,99],[0,2,4,6,8,10,11,12,13,16,17,19,20,22,25,26,27,29,34,36,37,41,43,44,49,52,53,54,56,57,58,62,63,68,72,73,74,78,81,83,84,85,88,90,92,93,94,95,98,99,100],[1,3,6,7,11,13,16,18,21,22,24,27,32,34,41,42,44,45,47,48,50,53,54,56,60,61,62,72,75,84,85,86,88,90,91,94,98,100],[62,92,93,94,95,96,97,98,99],[2,7,9,12,14,15,17,19,21,22,23,24,25,27,30,31,32,33,34,35,37,39,41,43,44,45,46,48,57,59,62,64,70,74,75,76,77,78,79,82,83,84,85,87,88,89,90,93,94,98],[0,1,4,9,10,16,19,20,21,22,23,28,29,31,32,33,34,37,38,39,40,42,43,45,47,48,50,53,54,56,58,59,62,63,66,71,72,73,74,75,76,77,78,79,81,83,84,87,89,90,91,93,94,95],[0,1,2,5,6,7,8,9,11,12,13,16,18,19,20,21,25,26,29,31,32,39,40,42,44,46,47,49,51,52,55,56,57,58,59,62,63,66,68,69,70,71,72,73,74,75,77,78,79,80,81,82,83,85,90,92,93,97],[0,5,6,7,9,12,14,15,16,17,18,19,20,21,23,24,27,33,34,35,37,39,42,44,50,60,61,65,67,70,74,76,77,78,79,82,86,88,89,90,91,92,94,96,97,98],[18,92,93,95,100],[15,33,54,85,87,88,92,94,95,99,100],[0,1,4,6,7,8,9,10,14,15,16,18,19,21,22,23,26,28,29,31,32,34,36,37,38,40,43,45,47,48,51,52,53,54,56,59,60,61,62,63,66,67,68,70,71,72,73,74,75,76,77,78,79,83,84,85,87,90,94,95,98,99],[0,2,10,11,13,17,18,22,25,26,29,32,33,34,35,36,37,39,44,45,48,49,51,52,54,55,57,58,62,63,64,66,68,69,70,72,74,76,79,82,83,85,88,90,94,96,100],[0,2,4,5,7,10,11,12,14,16,17,19,21,22,23,26,27,29,33,34,36,39,40,42,46,50,55,59,60,67,68,70,72,73,75,76,77,78,81,82,83,86,87,89,92,93,96,97,100],[0,5,7,10,11,18,19,20,21,25,26,27,33,34,35,38,40,41,45,46,48,50,51,54,55,57,58,63,65,66,68,70,73,74,75,76,77,78,79,80,81,82,83,87,89,90,92,94,95,96,97,99,100],[39,92,93,95,96,100],[0,1,4,6,9,10,16,19,21,22,23,26,28,29,32,33,34,36,37,38,39,40,43,45,47,48,54,56,59,62,63,66,67,68,70,71,72,73,74,76,77,78,79,83,84,85,89,90,92,94,96,98,99],[1,2,7,8,9,11,12,16,21,23,28,29,33,34,37,38,40,41,43,44,46,48,50,51,52,56,57,59,61,63,65,66,67,69,70,72,73,74,77,82,83,84,85,86,87,88,90,91,92,93,94,96,98,99],[0,1,4,6,8,9,10,11,16,19,21,26,27,28,30,32,35,36,38,41,42,44,45,47,48,51,54,59,63,66,68,73,74,76,77,79,80,82,83,87,89,91,95,97,98,100],[0,2,4,5,6,7,8,9,10,11,13,15,20,22,23,26,29,30,32,33,34,39,40,42,44,45,49,50,51,52,53,55,57,61,62,63,64,65,66,68,69,76,79,83,84,85,86,87,88,90,91,92,93,94,95,97,100],[0,2,4,6,7,8,9,10,11,12,14,15,17,21,22,27,28,29,31,32,34,35,37,38,39,40,41,42,46,49,52,53,54,55,56,57,58,60,61,62,63,69,71,73,76,77,78,79,80,82,83,87,88,89,92,93,96,99],[1,4,6,7,8,9,10,13,14,17,21,22,25,28,29,31,32,34,36,38,41,45,46,47,48,49,51,52,55,57,60,66,67,68,70,71,72,73,76,77,78,79,81,82,83,88,91,97,100],[0,2,4,8,9,10,11,12,13,14,17,18,22,28,30,32,34,38,40,44,45,48,49,56,57,58,60,61,63,65,66,67,69,70,74,76,80,82,84,85,88,90,91,92,97,98],[2,3,4,6,8,10,11,12,13,16,20,21,22,23,27,28,29,31,34,37,41,43,44,49,52,53,56,58,62,63,65,68,69,72,73,74,77,78,81,83,84,86,87,88,89,92,93,96,99],[2,3,5,8,9,11,12,13,16,17,18,20,23,25,27,31,32,36,37,38,40,43,45,46,47,48,53,54,56,57,58,60,62,63,65,67,70,71,74,76,79,84,85,87,88,91,92,94,99,100],[1,2,3,6,11,14,15,16,17,18,19,21,23,25,26,30,31,36,37,40,43,44,46,49,51,53,54,55,58,59,61,63,64,66,68,69,70,72,73,74,76,77,78,79,80,82,85,86,87,88,90,91,93,94,95,97,98,100],[1,3,4,5,8,12,13,15,16,18,19,21,27,28,30,32,33,35,37,39,40,42,45,47,49,50,51,58,59,61,62,63,64,66,67,73,74,75,76,77,78,79,81,85,92,93,94,95,96,97],[5,7,12,14,18,23,29,31,39,48,51,52,54,60,62,63,64,70,71,74,75,82,83,85,86,88,92,93,95,97,98,100],[0,2,4,6,8,15,16,17,22,24,25,28,30,32,34,35,39,41,42,46,49,51,54,55,56,65,66,68,70,72,73,74,76,83,90,93,94,95,96,98,100],[1,4,6,7,11,12,13,15,17,18,19,22,23,25,27,28,30,32,33,34,39,42,43,44,46,47,48,49,50,51,53,54,55,56,57,58,59,61,62,63,64,65,66,67,68,78,80,83,84,85,86,87,88,90,94,99],[0,4,9,11,13,14,16,17,20,21,22,23,24,25,26,28,30,32,40,43,44,46,47,48,49,51,54,55,56,57,58,59,60,61,62,63,64,66,68,70,72,74,76,77,79,80,81,82,83,89,91,94,96,97,99,100],[0,1,4,6,7,11,12,15,16,17,20,23,24,30,31,32,38,39,41,47,51,53,54,55,56,57,58,59,61,63,66,71,79,83,86,88,89,91,94,95,98,99,100],[24,92,93,98,100],[17,70,81,85,87,91],[0,3,4,5,8,12,15,16,18,20,21,22,25,30,32,34,38,39,40,42,43,44,46,47,48,51,53,55,56,59,61,63,66,69,70,71,73,75,81,83,85,86,87,89,90,91,95,98],[1,2,3,5,9,10,20,21,24,26,27,31,32,34,35,36,41,48,51,53,55,56,57,58,59,60,61,63,64,67,69,70,72,77,81,82,83,85,86,88,90,91,93,95,96,99,100],[1,4,6,7,13,17,18,19,22,23,25,27,28,30,32,33,34,38,39,42,43,46,47,48,49,50,51,53,55,56,57,58,59,61,62,63,64,65,66,67,68,78,80,86,90,94],[2,4,6,8,10,12,14,17,21,22,24,26,28,29,33,34,35,38,39,41,42,43,45,50,52,55,57,58,60,62,63,64,68,69,70,71,74,75,81,83,84,85,86,88,89,92,94,95,100],[0,2,4,5,6,7,8,10,11,12,14,18,25,27,30,31,38,39,42,43,44,51,53,55,56,58,59,60,62,66,73,77,80,82,83,84,85,87,89,90,92,94,95,96,97,98,99,100],[0,1,2,7,8,9,12,13,16,17,19,21,24,25,27,28,29,30,32,33,40,44,46,47,49,50,51,52,55,57,59,62,66,67,69,70,71,72,73,74,77,78,79,80,81,82,87,88,89,90,92,93,95,96,97,98],[0,3,4,5,7,9,11,13,16,17,18,20,21,22,23,24,26,27,28,29,31,32,35,39,40,44,45,46,47,49,52,54,55,56,57,58,60,61,65,66,67,68,71,72,75,76,77,79,80,82,84,87,88,91,95,96,97,98,100],[2,3,4,5,7,10,16,21,22,23,24,25,26,27,28,29,31,33,34,36,37,40,43,46,47,48,50,52,56,62,63,64,65,69,70,71,74,75,80,83,84,87,88,90,91,93,97,98],[1,4,5,6,7,11,13,15,17,18,19,22,23,25,28,30,32,33,34,38,39,42,43,46,47,48,49,50,51,54,55,56,57,58,59,61,62,63,64,65,66,67,68,78,80,83,86,89,90,92,95,96,98],[0,1,2,6,7,9,12,15,16,17,18,19,23,24,31,32,33,35,36,37,39,41,42,47,48,50,51,53,54,55,56,57,58,59,64,66,67,69,72,73,74,76,78,79,81,83,85,90,92,96,99],[1,4,5,6,8,12,13,16,18,21,25,27,28,30,32,35,36,37,39,40,41,45,47,49,50,52,57,59,61,62,63,64,66,67,72,73,74,75,76,77,78,79,81,87,90,91,93,94,95,96,98],[79,92,93,97,98,100],[2,3,4,5,6,7,8,13,14,17,21,22,26,27,28,29,31,32,33,34,35,39,40,42,44,45,46,48,50,52,53,55,57,61,63,64,65,67,68,69,71,73,74,75,76,80,81,83,86,87,89,91,92,93,94,97,98,99,100],[0,1,6,7,11,16,17,18,20,21,22,24,25,26,27,28,29,30,33,34,35,36,41,42,44,46,47,48,51,52,53,57,58,59,64,66,67,68,69,73,74,75,77,82,85,87,89,90,91,93,98,99],[0,3,6,7,8,9,10,11,12,13,14,17,19,22,24,26,27,28,31,34,35,36,42,43,44,49,50,52,54,55,58,60,61,62,63,68,70,71,72,74,79,82,83,85,86,89,90,91,92,93,94,96,98,100],[71,92,94,95,97,98,100],[1,2,6,7,8,10,11,12,14,17,19,26,29,30,34,37,40,41,45,47,48,49,50,51,52,55,56,57,60,61,66,67,68,69,70,72,74,75,77,82,84,86,87,88,93,94,96,97,98],[5,6,7,9,12,14,17,18,22,23,26,28,31,35,37,38,39,41,43,44,48,49,50,54,55,60,61,62,64,65,68,70,71,74,76,77,80,82,83,86,93,94,99,100],[0,1,2,3,6,8,9,10,11,14,16,18,20,21,23,26,27,28,29,30,31,36,39,40,41,42,43,47,48,54,55,57,58,59,60,63,64,65,68,69,72,73,77,79,81,83,85,87,88,89,92,94,97,98,100],[1,3,7,8,9,11,13,14,16,18,19,21,22,26,27,28,29,30,32,34,36,37,39,40,42,44,45,47,48,50,52,53,55,57,58,65,67,68,72,75,78,79,80,83,85,86,89,90,92,93,95,96,97,98,99,100],[0,5,8,9,11,15,17,18,19,20,22,23,24,25,28,32,33,34,35,36,38,39,41,46,48,51,53,54,55,56,61,63,64,65,66,67,70,71,72,78,81,83,85,86,87,94,97],[38,92,94,95,96,97,98,100],[1,2,6,8,9,10,15,19,20,21,23,24,25,26,29,30,33,38,40,42,43,44,45,46,47,48,51,55,59,62,63,65,68,71,75,76,77,78,79,84,85,89,92,94,96],[7,9,10,11,13,17,20,24,25,26,28,29,32,33,35,37,41,44,45,48,50,52,54,55,56,57,62,63,64,68,70,72,73,74,79,84,88,90,91,92,94,95,97,98,100],[1,2,4,6,7,9,10,16,18,20,24,27,36,37,41,42,43,44,47,53,56,57,60,62,65,70,71,73,79,80,81,83,84,85,87,88,93,95,97,98,100],[0,1,2,6,10,12,13,16,17,18,20,23,25,27,29,30,31,33,34,35,36,37,38,41,43,44,45,47,48,49,50,51,52,54,59,61,62,63,69,70,71,72,75,76,81,82,86,87,88,89,90,91,93,94,96],[7,13,18,85,86,88,92,93,95,100],[15,92,94,95,99,100],[0,1,4,6,7,9,10,14,15,16,18,19,21,22,23,26,28,29,31,32,34,36,37,38,40,43,45,47,48,51,52,53,54,56,59,60,61,62,63,66,67,68,70,71,72,73,75,76,77,78,79,83,84,86,88,90,92,93,98,99],[0,2,4,5,7,8,9,12,14,15,18,20,22,23,24,26,29,30,32,33,34,35,38,40,41,46,49,50,52,53,58,60,61,62,64,67,68,69,72,73,76,79,80,82,86,87,90,94,95],[2,4,6,7,9,16,17,19,20,21,22,24,25,27,29,33,34,37,38,41,42,43,44,45,48,50,51,52,54,56,57,58,59,61,66,72,76,77,78,80,81,82,85,87,88,89,92,94,97,98,99],[1,2,10,12,13,15,16,18,20,23,25,26,27,28,29,30,31,34,35,36,37,38,41,44,45,47,48,49,51,52,53,56,58,59,61,62,68,69,70,71,72,76,81,82,85,86,89,90,91,92,93,94,96,98,99],[31,92,95,96,99,100],[0,2,4,8,9,10,11,12,17,22,28,30,32,34,38,40,44,45,46,48,49,55,56,57,58,60,61,63,65,67,69,70,74,76,80,84,86,89,90,91,92,96,97,98,99,100],[5,92,94,95,96,99,100],[40,92,93,94,95,96,99,100],[6,8,12,14,15,21,27,30,34,35,39,40,41,42,44,45,48,51,52,53,54,57,60,63,64,67,73,76,77,78,79,84,85,88,89,91,92,95,99],[76,92,93,97,99,100],[1,4,5,6,13,15,16,18,19,25,28,32,34,37,39,41,44,49,50,51,53,54,58,59,62,66,74,75,81,84,86,87,90,91,92,93,94,96,99],[23,92,93,94,97,99,100],[0,1,2,3,6,9,12,14,17,18,22,24,25,26,29,30,31,32,33,34,36,37,38,41,42,46,47,48,49,52,53,54,55,57,59,60,62,64,65,69,70,73,76,79,80,84,85,89,90,91,95,99],[0,2,3,6,7,8,13,14,16,18,19,20,22,24,25,26,31,32,35,38,39,44,47,51,52,53,55,57,61,62,63,65,66,68,70,71,72,73,75,76,79,80,81,83,84,86,87,90,91,92,93,94,95,97,98],[1,4,5,6,7,11,12,13,17,18,19,22,23,25,27,28,30,32,33,34,39,42,43,46,47,48,49,50,51,55,56,57,58,61,62,63,64,65,66,67,68,78,80,82,83,84,86,89,92,95,97,99],[0,1,4,5,7,10,13,14,15,16,17,18,21,22,25,29,30,32,33,34,41,43,45,47,49,50,51,52,53,54,55,58,59,60,65,66,72,73,76,77,80,82,83,93,94,97,99,100],[0,5,8,9,10,11,12,14,18,21,23,26,27,29,30,31,33,35,36,38,39,42,45,49,50,52,53,58,60,61,64,68,70,71,73,75,76,77,79,80,81,84,85,86,87,88,89,90,93,95,96,97,99],[0,3,7,8,9,10,15,17,20,22,25,27,28,30,33,35,36,37,39,43,46,47,49,51,52,53,54,60,62,66,67,71,72,76,79,80,81,84,85,87,88,90,92,93,94,95,96,97,100],[0,5,7,8,11,13,14,16,17,18,19,21,22,23,24,33,34,36,37,40,41,42,43,44,48,51,53,54,56,58,60,63,64,65,66,68,72,74,75,76,77,78,79,80,81,82,83,84,89,91,92,97,98],[1,6,7,10,14,15,17,19,20,21,22,26,29,30,31,37,38,39,42,44,45,46,48,52,53,54,55,60,62,65,67,68,71,72,73,74,76,77,78,79,81,82,83,84,85,87,89,90,91,92,98],[7,9,10,11,12,14,16,17,19,20,21,24,25,26,27,29,30,31,35,36,37,38,40,41,42,49,51,52,57,58,60,61,63,65,66,69,71,74,75,76,77,78,79,80,81,82,87,88,89,92,93,96,98,100],[1,4,5,7,8,10,12,13,15,16,17,18,22,25,26,27,28,29,31,32,35,36,38,39,40,42,44,47,48,49,53,54,55,57,59,63,64,65,66,68,70,71,72,75,81,82,83,84,85,89,94,100],[0,2,3,5,10,11,12,16,17,21,22,27,29,30,35,36,37,38,40,42,45,46,47,49,50,51,54,57,58,59,61,62,63,64,70,71,72,73,74,76,79,82,85,86,87,88,89,92,95,96,100],[64,92,93,94,98,99,100],[1,4,5,8,14,18,20,21,22,26,29,32,33,39,40,42,43,44,47,48,49,53,54,55,57,58,59,60,61,64,65,67,70,72,74,76,77,83,84,85,86,92,93,96,99,100],[1,4,5,8,10,11,13,16,17,20,21,24,25,26,29,31,33,35,36,37,40,41,42,45,47,49,52,56,58,59,61,62,64,65,68,73,74,75,76,79,81,83,85,88,89,90,91,94,95,97,99],[0,1,2,3,5,6,9,11,18,19,22,24,25,27,31,32,36,38,39,43,45,46,50,51,53,54,58,59,60,61,64,65,66,67,68,69,72,73,75,76,78,79,80,85,86,87,88,89,91,92,94,96,97,99,100],[0,92,96,98,99,100],[1,2,3,4,5,6,7,8,10,11,13,14,15,17,18,21,24,26,27,29,32,33,34,35,39,41,48,52,55,56,57,58,59,63,64,68,69,70,72,77,81,82,83,85,86,87,88,89,90,91,92,95,96,100],[1,4,5,7,8,9,11,12,13,14,15,16,17,18,22,23,24,25,27,28,30,34,38,39,41,42,43,45,46,47,48,49,54,55,56,58,60,62,63,65,67,69,71,73,76,77,79,82,87,88,89,91,93,95,96,99],[0,6,8,9,10,14,17,18,19,21,23,28,31,32,34,35,36,37,38,41,43,45,46,48,51,52,53,55,57,60,64,66,67,70,73,76,77,78,79,80,81,85,89,92,94,96,97,99],[0,2,4,6,7,8,10,11,12,13,15,16,17,21,22,23,25,26,30,31,32,34,35,37,38,39,41,43,45,50,53,55,56,57,58,61,62,63,64,65,67,69,71,77,81,82,84,85,86,88,89,90,91,93,95,99,100],[2,4,5,10,12,14,15,18,19,20,23,24,25,30,33,35,36,39,40,41,44,45,46,51,53,54,55,57,60,64,66,69,71,72,74,76,78,80,81,83,85,87,89,90,92,94,96,99,100],[0,1,2,3,5,7,9,14,19,22,24,25,32,36,38,42,45,46,50,52,53,54,58,59,60,61,64,65,66,67,68,69,72,73,76,77,78,79,80,86,87,91,92,93,96,97,98,100],[42,92,93,94,95,96,98,99,100],[0,2,4,6,7,8,10,11,13,15,21,25,26,30,31,32,34,35,39,40,43,45,46,50,53,56,57,58,62,63,64,65,67,68,69,71,77,82,84,85,87,88,89,90,93,94,96],[0,1,3,4,6,7,8,9,10,13,16,18,19,22,26,27,28,30,32,34,35,36,38,41,44,47,51,56,59,60,63,66,68,72,73,74,75,76,77,79,80,82,83,85,86,87,88,89,91,92,94,95,100],[0,1,2,6,8,9,10,11,14,15,16,18,20,21,23,25,26,28,31,33,36,39,40,41,42,44,47,55,57,58,59,60,61,62,63,64,67,68,69,70,71,72,73,77,78,79,81,82,84,85,86,87,90,95,96,98,99,100],[0,1,4,5,7,10,11,12,13,14,16,17,18,19,20,21,22,28,29,31,32,33,34,38,40,41,43,44,45,47,49,50,51,52,53,56,58,59,60,64,66,72,73,76,77,79,80,82,84,86,88,89,90,94,99,100],[0,2,4,9,10,11,12,14,16,18,19,20,23,26,28,29,32,36,37,41,42,44,45,46,48,50,52,56,57,58,59,60,61,62,63,65,66,67,68,69,72,74,77,78,81,82,84,86,87,88,90,91,94,100],[0,2,5,7,8,10,11,12,17,22,25,27,29,30,31,34,35,37,41,42,43,44,50,52,54,56,57,62,63,67,70,71,72,74,75,78,80,83,84,87,88,89,92,93,94,96],[0,1,2,3,5,6,7,9,10,11,13,14,15,16,17,18,21,22,29,30,34,36,37,38,41,43,45,46,47,50,51,52,53,54,55,56,58,59,60,64,66,67,69,71,72,74,77,80,81,82,83,85,86,87,89,90,92,93,95,99],[73,92,93,96,97,98,99,100],[1,4,5,6,8,12,14,16,17,19,20,22,26,30,31,32,34,36,37,38,39,40,42,46,47,48,49,51,54,56,59,60,61,62,64,68,71,72,74,75,76,77,78,80,81,82,83,85,86,87,93,95,96,98,100],[0,2,4,5,6,7,8,9,10,12,13,15,19,20,22,23,25,26,29,32,34,39,45,49,50,51,52,53,55,57,61,62,66,67,68,69,76,78,79,88,89,91,95,96,98,99],[10,92,95,96,97,98,99,100],[2,4,5,6,9,10,12,13,15,16,18,23,24,26,27,28,29,32,33,35,37,38,39,43,44,46,48,51,52,55,57,58,61,62,64,65,66,67,68,70,71,73,74,84,85,87,89,91,92,93,95,97,98,99,100],[1,3,6,7,11,12,13,16,18,21,22,24,27,32,34,38,41,42,44,45,47,48,50,53,54,56,60,61,62,72,75,84,86,87,89,92,95,96,97],[2,4,7,11,12,13,14,15,18,19,20,21,22,25,26,28,30,31,33,35,36,37,39,41,42,43,44,46,49,50,53,60,63,67,68,69,70,73,77,78,80,82,84,85,89,92,94,99],[2,10,11,12,13,14,15,19,20,21,22,23,26,27,28,29,30,31,32,34,39,43,46,50,52,54,55,56,59,63,68,72,73,75,76,77,78,82,83,87,89,91,92,93,95,97,99,100],[0,1,4,9,10,19,20,21,22,23,28,29,31,32,33,34,37,38,39,40,42,43,45,47,48,50,53,54,56,58,59,62,63,66,68,71,72,73,74,75,76,77,78,79,81,83,84,85,86,87,89,90,91,92,94,95],[1,4,10,12,15,16,17,18,19,21,22,23,25,30,31,33,34,35,45,46,47,48,50,53,56,58,59,61,64,65,70,71,73,74,75,76,77,78,80,82,86,87,88,90,91,94,95,97,98,99,100],[26,92,93,94],[0,1,2,6,10,12,13,16,17,18,20,23,25,27,29,30,31,33,34,35,36,37,38,41,43,44,45,47,48,49,50,54,59,61,62,63,69,70,71,72,75,76,81,82,85,86,87,89,90,91,92,93,94,95,96],[13,92,93,95],[33,92,94,95],[4,5,7,8,10,11,12,13,14,15,17,20,23,24,25,30,36,37,38,39,40,41,44,45,46,48,50,51,53,54,55,57,60,61,63,66,67,70,73,74,80,83,86,87,88,89,95,96,99,100],[1,2,6,7,11,12,13,15,17,19,21,25,26,28,29,30,31,36,40,43,44,46,47,49,51,52,53,54,55,57,58,59,61,62,66,69,71,72,73,74,75,77,78,79,80,82,83,85,86,87,89,90,91,92,96,97,99],[1,2,11,13,14,15,16,17,18,19,20,21,23,25,28,31,33,35,36,38,39,40,42,43,44,47,49,50,53,55,56,57,59,60,61,64,67,69,70,71,73,75,77,78,81,82,84,86,91,94,95,100],[2,4,6,9,10,11,15,18,20,22,23,24,25,29,35,36,40,44,46,55,59,61,68,72,73,74,75,79,81,82,83,85,86,88,91,92,96,98],[0,2,4,8,9,10,11,12,14,17,22,28,30,32,34,38,39,40,44,45,46,48,49,55,56,57,58,60,61,63,65,67,69,70,74,76,80,84,85,88,90,91,93,95,97,98],[0,1,4,5,6,9,10,16,19,21,22,23,26,28,29,32,33,34,36,37,38,39,40,43,45,47,48,53,54,56,59,62,63,66,67,68,70,71,72,73,74,76,77,78,79,83,84,87,88,90,92,94,96,98,100],[40,60,61,85,86,87,88,89,92,93,94,95,96,100],[47,92,97],[2,4,5,7,11,13,14,15,17,18,21,23,25,26,28,30,32,33,36,39,40,41,43,46,48,50,55,60,62,63,64,68,69,70,72,73,77,78,79,80,81,82,84,87,88,90,97,98,99,100],[48,92,94,97],[0,2,4,6,7,8,9,10,11,12,14,15,17,21,22,23,27,28,29,31,32,34,35,38,39,40,41,42,46,49,52,53,54,55,56,57,58,60,61,62,63,69,71,73,76,77,78,79,80,82,83,85,86,88,89,90,94,96,97,99,100],[0,5,6,9,10,11,12,14,15,17,19,23,24,26,35,37,38,39,40,42,43,44,45,46,48,49,51,54,55,56,58,59,60,61,62,66,67,68,72,73,75,80,81,83,85,86,88,90,92,94,97,98,99,100],[66,92,93,95,97],[1,2,3,5,7,8,10,16,17,18,19,20,21,25,29,30,31,32,33,37,39,41,42,44,46,47,48,50,51,52,53,55,57,59,61,64,66,67,69,72,73,74,77,80,81,82,85,90,92,93,94,96],[2,3,5,6,7,9,10,12,15,16,19,23,24,27,29,30,32,34,43,44,47,48,49,52,54,55,56,60,61,62,63,64,65,70,73,75,76,78,79,80,81,85,86,87,90,92,94,95,96,98,99,100],[0,2,3,4,5,6,7,10,11,13,19,22,23,26,29,31,32,33,36,37,40,41,44,45,46,47,50,52,60,61,63,64,65,68,69,70,74,78,79,83,86,87,88,89,91,92,95,96,97,98,99],[0,1,3,4,9,10,11,13,14,15,16,19,23,26,28,29,31,32,36,37,38,40,47,51,52,53,57,59,60,62,63,66,67,68,70,71,74,78,80,84,85,87,88,92,94],[1,2,5,7,11,12,13,15,16,19,20,21,25,28,29,30,33,36,38,40,42,43,44,47,48,49,50,51,52,53,54,55,56,57,59,61,62,63,67,69,72,73,74,77,78,82,83,85,88,90,91,93,97,99],[25,92,93,94,96,97],[69,92,95,96,97],[46,92,93,95,96,97],[1,92,93,94,95,96,97],[50,92,98],[1,2,10,11,15,16,22,23,26,27,29,32,33,34,36,39,40,41,43,44,45,46,47,48,49,51,52,53,58,59,61,63,64,65,66,68,69,70,71,76,79,80,81,83,84,85,90,93,95,97,100],[70,92,94,98],[3,4,5,6,9,10,12,14,15,16,17,19,20,22,28,29,30,31,35,36,39,40,41,42,44,45,47,52,56,57,59,60,61,63,64,65,67,69,71,75,76,77,78,79,80,82,86,87,89,93,95,96,97,99,100],[0,2,3,4,8,9,15,19,20,21,24,25,26,27,29,31,38,39,40,44,45,46,47,48,49,50,52,55,57,58,60,61,66,68,69,70,73,74,75,77,78,79,80,83,84,86,88,92,93,95,97,98,99,100],[0,5,8,9,11,13,15,17,19,20,22,23,24,25,28,32,33,34,35,36,38,39,41,48,49,51,53,54,61,63,64,65,66,67,70,71,72,78,81,84,85,86,87,94,97,98,100],[77,92,93,94,95,98],[0,1,4,9,11,12,13,16,20,22,24,27,28,30,34,37,38,40,41,42,43,45,46,47,48,49,50,53,55,56,58,62,67,69,70,71,73,74,76,77,79,83,85,89,90,92,96,100],[0,1,2,6,8,9,10,16,22,23,28,29,31,34,39,40,41,44,45,46,47,48,49,50,51,52,54,59,63,64,65,66,67,69,71,75,76,79,80,83,84,85,88,90,91,97,99],[0,1,4,5,6,7,8,9,10,14,16,17,18,19,21,22,25,26,28,29,31,32,34,36,38,43,45,47,48,51,52,56,59,60,62,65,66,67,68,70,71,72,73,75,76,77,78,79,81,82,84,88,91,93,94,99],[3,4,5,6,7,8,10,11,13,14,16,19,20,22,24,26,27,34,36,37,38,39,40,41,43,44,47,48,49,51,53,54,56,58,61,64,65,68,70,71,72,73,75,78,81,82,84,86,88,93,95,96,99,100],[0,3,5,6,8,11,12,13,15,17,22,24,27,28,29,30,32,33,35,36,38,39,40,41,45,46,47,48,52,53,55,57,58,61,67,70,74,75,77,80,81,82,83,86,87,88,91,92,96,97,99,100],[2,4,5,10,12,14,15,18,19,20,23,24,25,30,33,35,39,40,41,44,45,46,51,53,54,55,57,58,60,64,66,69,71,72,74,76,78,80,81,83,86,87,88,90,91,92,94,96,100],[27,92,94,95,96,98],[0,1,2,5,7,10,11,12,15,16,18,26,27,28,31,34,36,37,43,46,47,49,52,53,56,58,59,61,65,66,68,69,71,72,73,74,75,76,78,79,81,82,84,88,89,90,95,98,99],[0,5,6,7,8,9,11,13,14,16,17,18,19,22,24,25,26,29,32,34,35,36,38,41,42,48,49,50,52,53,54,55,58,60,61,62,63,65,71,72,74,78,80,84,86,88,89,91,92,99,100],[19,35,72,85,87,90,91,99],[2,3,4,6,10,12,13,14,15,16,17,20,21,22,24,25,34,35,36,38,40,41,43,51,63,65,66,67,68,69,71,75,76,84,86,88,90,91,98,100],[2,92,95,97,98],[0,2,3,4,5,6,7,8,9,11,15,17,20,22,23,25,26,27,28,30,31,33,34,39,40,41,42,43,45,49,50,51,52,53,55,57,61,62,63,64,66,68,69,70,76,78,79,80,81,83,84,85,87,88,89,92,95,96,97,98,100],[5,12,15,38,53,54,71,82,83,89,92,94,95,97,98],[0,7,9,13,14,16,17,19,20,23,25,26,32,33,35,37,38,39,40,42,44,46,54,55,57,59,60,61,67,68,70,71,74,76,77,79,80,82,84,86,88,89,91,97,99,100],[21,92,96,97,98],[0,1,2,5,8,9,12,14,15,18,21,22,24,30,31,32,34,35,38,40,41,42,43,44,46,47,48,50,51,57,59,60,63,65,66,68,69,73,75,77,80,84,86,87,88,90,96,98],[2,3,4,5,7,11,19,20,22,23,25,27,30,32,34,35,38,39,40,41,42,45,51,52,54,55,56,57,58,62,64,66,67,69,70,71,72,75,76,78,81,83,84,85,87,89,90,91,93,94,97,100],[5,7,8,10,12,15,16,20,23,24,26,27,28,29,31,32,33,36,37,38,39,41,42,43,44,46,48,50,51,52,53,55,57,61,64,65,66,73,74,80,81,84,85,86,88,89,92,93,94,96,97,99,100],[0,1,3,5,7,8,9,11,12,14,16,20,21,23,24,25,26,29,30,31,32,33,35,36,39,41,43,44,45,47,49,50,52,57,58,61,62,64,68,71,75,83,85,87,93,96,97,98,99],[49,92,93,95,96,97,98],[12,92,94,95,96,97,98],[1,4,6,7,8,9,10,11,12,13,14,18,22,23,24,28,29,31,35,36,37,38,39,40,41,45,47,48,49,50,51,53,55,59,60,65,67,69,70,71,73,75,76,79,80,82,85,86,87,88,89,90,91,96],[68,92,93,99],[0,1,5,8,11,13,15,16,17,18,22,23,24,26,27,29,30,32,33,34,35,36,37,39,40,41,43,45,47,48,49,50,51,52,55,56,60,61,63,64,66,68,69,70,71,72,73,76,80,84,85,86,87,91,92,94,97],[0,5,6,7,9,12,14,15,16,17,18,19,20,21,23,24,26,27,33,34,35,37,39,42,44,50,60,61,65,70,74,76,77,78,79,82,85,87,88,89,90,91,93,96,97,98,99],[51,92,95,99],[7,92,93,95,99],[54,92,94,95,99],[8,92,93,94,95,99],[1,4,9,11,12,13,15,16,20,22,24,26,27,30,31,33,34,36,37,38,40,41,42,45,46,47,48,49,50,53,55,56,62,69,71,73,74,75,76,79,81,83,85,88,89,90,91,94,96,98,99],[1,2,4,11,13,14,15,16,17,18,19,20,21,23,25,28,30,31,33,35,36,38,39,40,42,43,44,47,49,50,53,55,56,57,59,60,61,64,67,69,70,71,73,75,77,78,81,82,84,85,86,87,89,91,94,95,99,100],[0,1,2,5,6,7,9,10,13,14,17,19,21,23,24,28,29,30,31,33,36,37,38,39,41,42,45,47,48,49,50,51,52,53,56,58,59,60,62,67,68,69,71,72,74,77,78,79,81,82,85,88,89,90,92,94,96,97,100],[0,5,7,10,11,18,19,20,21,25,26,27,31,33,34,35,38,40,41,45,46,48,50,51,54,55,57,58,63,65,66,68,70,73,74,76,77,78,79,80,81,82,83,85,87,88,90,94,97,99],[53,92,94,95,96,99],[1,2,6,7,9,11,14,15,16,23,27,28,29,30,33,35,37,38,39,42,43,45,46,47,50,53,54,56,59,60,61,64,65,66,69,70,72,74,76,78,79,82,83,85,86,87,89,92,93,94,95,96,97,98,99],[0,1,2,5,6,7,8,9,10,13,14,15,16,17,18,19,23,25,27,33,35,38,39,40,42,43,44,45,46,47,50,51,54,55,59,60,62,64,66,69,70,72,74,78,81,83,84,85,86,88,89,91,92,93,95,97,99,100],[0,1,2,7,8,9,10,11,16,18,19,20,22,23,25,26,28,29,30,33,37,40,41,42,45,48,52,54,55,57,58,59,61,63,64,65,68,69,74,75,76,79,81,83,87,88,90,92,94,95,96,100],[2,3,4,5,6,7,8,9,11,13,14,15,17,18,19,21,23,28,30,33,35,38,39,40,43,44,46,48,49,53,55,56,58,60,61,64,65,69,71,73,75,77,78,82,84,85,86,88,89,90,92,94,95,98,99],[3,4,6,7,9,10,11,12,16,17,19,20,24,25,26,28,30,31,34,35,39,40,45,47,48,49,51,52,53,55,56,58,60,62,66,67,68,69,71,72,73,74,75,79,81,82,83,87,90,92,94,97,99],[59,92,94,95,97,99],[6,7,8,10,11,13,15,17,18,19,20,24,25,29,30,31,34,36,37,38,40,44,45,46,49,52,53,55,57,58,61,64,67,71,73,74,75,80,81,84,85,87,91,95,96,98,99],[34,92,96,97,99],[0,1,2,3,7,8,9,10,11,13,14,16,17,18,19,21,22,23,27,31,35,37,38,40,42,44,46,50,51,52,54,55,56,57,59,61,62,64,66,69,70,73,75,76,77,78,79,80,81,84,86,88,89,90,91,93,94,96,97,98],[3,25,65,85,86,87,89,90,92,93,94,96,97,99],[2,4,5,6,7,11,13,14,15,18,19,21,23,25,28,30,32,33,35,36,37,39,40,43,44,46,48,49,53,55,58,60,63,64,69,70,73,75,77,78,79,80,81,82,84,85,88,91,93,94,99,100],[1,6,7,10,14,15,17,19,20,21,22,26,29,30,31,37,38,39,42,44,45,48,52,53,54,60,62,65,67,68,71,72,73,74,76,77,78,79,81,82,83,84,86,87,88,91,93,95,96,97,98,99],[1,4,6,9,10,13,14,15,16,18,20,21,22,23,24,26,28,29,31,32,33,34,35,36,37,38,39,40,41,43,46,47,48,50,52,53,54,55,56,59,60,62,64,67,68,69,71,74,75,76,77,79,81,82,83,84,86,87,88,92,93,94,96,98,100],[0,5,7,8,9,10,11,12,14,15,18,20,21,23,24,27,29,30,31,35,36,38,39,42,43,46,51,53,56,58,60,61,62,65,71,74,75,76,77,79,80,84,86,87,88,89,90,91,92,93,94,95],[0,1,4,6,7,11,12,15,16,17,23,24,30,31,32,38,39,41,47,50,51,53,54,55,56,57,58,59,61,63,66,71,79,83,85,86,88,89,92,94,95,100],[0,1,3,5,12,15,17,21,23,24,26,30,32,33,34,35,37,38,39,41,42,43,44,48,50,52,53,54,57,62,65,66,68,69,72,73,74,80,81,82,83,84,85,87,88,89,90,91,96,97,98,99,100],[17,92,94,98,99],[0,6,8,9,10,14,17,18,19,21,25,28,29,31,32,34,35,36,38,41,43,45,46,48,51,52,53,55,57,60,65,66,67,70,73,76,77,78,79,80,81,82,83,86,87,90,92,94,96,97,99],[0,10,14,15,18,19,20,21,22,25,26,33,34,35,36,38,41,42,43,45,46,48,50,51,52,54,55,56,57,58,60,61,63,65,66,68,70,73,75,76,77,78,79,80,81,82,83,85,86,88,90,93,97,98,100],[0,1,4,9,10,15,16,19,21,22,23,26,28,29,31,32,34,37,38,39,40,42,45,47,48,51,52,53,54,58,59,62,63,66,67,68,70,71,72,73,74,75,76,78,79,83,84,85,87,89,90,95,98,100],[0,2,3,4,5,7,9,13,17,23,24,28,30,31,33,34,36,42,45,47,48,49,54,55,56,57,60,62,63,69,72,73,75,76,79,89,90,92,96,97,100],[2,4,6,8,10,12,14,17,21,22,24,26,28,29,33,34,35,38,39,41,42,45,50,52,55,57,58,60,62,63,64,68,69,70,71,74,75,77,81,83,84,87,89,91,93,98,99,100],[0,1,2,5,6,7,8,9,10,13,14,16,18,20,22,24,25,28,31,34,37,39,40,41,44,45,46,47,48,49,50,51,59,60,66,67,69,70,71,74,76,79,80,82,84,85,87,89,91,92,94,95,96,97,99,100],[1,2,3,4,5,8,11,12,14,15,18,19,22,23,25,26,29,30,31,35,45,52,54,56,58,59,62,65,68,69,73,74,75,76,78,84,85,88,89,90,91,93,98,100],[0,6,10,11,12,13,15,19,21,23,24,26,27,29,30,31,32,36,39,41,42,46,49,51,52,54,55,58,59,66,68,69,70,72,75,78,81,84,85,91,94,95,96,99],[29,92,93,94,96,98,99],[22,92,95,96,98,99],[0,2,3,4,6,9,11,13,14,15,17,18,23,24,27,28,30,33,34,36,39,43,45,47,48,49,51,52,53,55,56,57,60,62,63,69,72,73,76,77,79,83,85,88,90,92,93,94,96,97,98,99,100],[0,1,2,7,9,12,15,16,17,18,19,23,24,31,32,33,35,36,37,39,41,47,48,50,51,53,54,55,56,57,58,59,64,66,67,69,72,73,74,76,78,79,81,83,86,87,88,89,90,91,93,94,95,98,99,100],[1,3,4,5,10,11,14,17,24,25,27,28,29,30,42,44,47,48,49,50,51,52,53,54,55,56,58,59,61,62,65,66,68,71,73,75,76,77,78,82,83,84,86,87,90,91,92,93,94,95,97,98,100],[0,1,2,5,6,7,9,11,12,14,18,21,23,24,27,29,32,38,40,43,45,46,47,48,50,51,52,53,58,59,60,62,63,66,67,68,69,70,71,72,74,77,78,79,80,82,83,87,88,89,90,91,92,93,94,95,96,97,98,99,100],[2,4,5,6,10,12,13,14,19,24,25,26,27,30,31,32,35,36,38,40,42,43,45,46,48,49,50,56,57,60,67,68,69,72,74,75,76,79,80,84,86,87,90,92,93,94,95,97,99,100],[0,5,9,11,13,15,16,18,24,25,26,28,29,30,32,33,35,37,39,40,42,46,48,50,51,52,53,54,56,59,61,62,63,64,65,67,68,71,76,77,80,85,86,88,90,91,93,95,97,99,100],[0,2,7,8,10,11,15,17,22,25,27,29,30,31,34,35,37,38,41,42,43,44,50,52,53,56,57,62,63,67,70,71,72,74,75,78,80,82,84,85,90,91,92,93,94,96,99,100],[0,1,2,3,6,8,9,10,11,12,13,16,20,23,29,30,32,33,34,35,38,39,41,42,44,45,46,47,48,49,50,51,52,54,56,59,65,66,69,71,72,75,76,79,80,87,88,93,94,96,98,100],[0,1,2,3,10,11,12,13,15,16,23,26,28,29,30,31,34,35,36,39,44,45,46,47,48,49,51,52,53,56,58,59,61,62,65,66,67,68,69,70,72,76,81,87,91,94,95,96,97,98,99,100],[0,1,2,5,8,9,12,14,15,18,21,22,24,30,31,32,34,35,38,40,41,42,43,44,46,47,48,50,51,57,59,60,63,65,66,68,69,75,77,84,85,87,88,89,91,92,93,97,100],[0,7,9,10,12,17,18,20,21,25,28,29,30,35,37,39,40,42,43,45,46,49,52,54,61,63,64,65,66,67,70,72,73,74,79,80,81,82,83,84,86,88,89,92,95,96,99,100],[0,2,4,6,9,13,16,19,22,24,25,27,28,31,33,34,36,37,38,41,42,43,44,46,48,49,62,64,65,67,68,69,73,74,76,78,79,80,81,84,87,89,90,92,93,94,95,97,98,99,100],[0,5,10,12,13,18,19,20,22,23,24,25,27,28,31,33,34,35,37,40,41,42,43,48,49,53,55,61,62,64,65,67,71,72,78,79,80,85,86,87,88,91,96,97,98],[0,2,4,6,8,10,11,12,13,16,17,19,20,22,25,26,27,29,34,36,37,41,43,44,49,52,53,54,56,57,58,62,63,68,72,73,74,78,81,83,84,85,88,90,94,96,97,100],[1,3,6,7,11,13,16,18,21,22,24,27,32,34,41,42,44,45,47,48,50,53,54,56,60,61,62,72,75,84,85,86,88,90,91,92,95,96,97,99,100],[2,7,9,12,14,15,17,19,21,22,23,24,25,27,30,31,32,33,34,35,37,39,41,43,44,45,46,48,57,59,62,64,70,74,75,76,77,78,79,82,83,84,85,87,88,89,90,92,93,94,98,100],[0,1,4,9,10,16,19,20,21,22,23,28,29,31,32,33,34,37,38,39,40,42,43,45,47,48,50,53,54,56,58,59,62,63,66,71,72,73,74,75,76,77,78,79,81,83,84,87,89,90,91,92,94,95,100],[0,1,2,5,6,7,8,9,11,12,13,16,18,19,20,21,25,26,29,31,32,39,40,42,44,46,47,49,51,52,55,56,57,58,59,62,63,66,68,69,70,71,72,73,74,75,77,78,79,80,81,82,83,85,90,93,94,97,100],[0,5,6,7,9,12,14,15,16,17,18,19,20,21,23,24,27,33,34,35,37,39,42,44,50,60,61,65,67,70,74,76,77,78,79,82,86,88,89,90,91,93,96,97,98,100],[52,92,95,100],[15,33,54,85,87,88,99],[0,1,4,6,7,8,9,10,14,15,16,18,19,21,22,23,26,28,29,31,32,34,36,37,38,40,43,45,47,48,51,52,53,54,56,59,60,61,62,63,66,67,68,70,71,72,73,74,75,76,77,78,79,83,84,85,87,90,92,93,98,99,100],[0,2,10,11,13,17,18,22,25,26,29,32,33,34,35,36,37,39,44,45,48,49,51,52,54,55,57,58,62,63,64,66,68,69,70,72,74,76,79,82,83,85,88,90,92,94],[28,92,93,96,100],[30,92,94,96,100],[0,2,4,5,7,10,11,12,14,16,17,19,21,22,23,26,27,29,33,34,36,39,40,42,46,50,55,59,60,67,68,70,72,73,75,76,77,78,81,82,83,86,87,89,94,97],[0,5,7,10,11,18,19,20,21,25,26,27,33,34,35,38,40,41,45,46,48,50,51,54,55,57,58,63,65,66,68,70,73,74,75,76,77,78,79,80,81,82,83,87,89,90,94,97,99],[0,1,4,6,9,10,16,19,21,22,23,26,28,29,32,33,34,36,37,38,39,40,43,45,47,48,54,56,59,62,63,66,67,68,70,71,72,73,74,76,77,78,79,83,84,85,89,90,95,98,99,100],[60,92,93,94,95,96,100],[1,2,7,8,9,11,12,16,21,23,28,29,33,34,37,38,40,41,43,44,46,48,50,51,52,56,57,59,61,63,65,66,67,69,70,72,73,74,77,82,83,84,85,86,87,88,90,91,93,94,96,97,98,99,100],[0,1,4,6,8,9,10,11,16,19,21,26,27,28,30,32,35,36,38,41,42,44,45,47,48,51,54,59,63,66,68,73,74,76,77,79,80,82,83,87,89,91,92,93,95,98],[0,2,4,5,6,7,8,9,10,11,13,15,20,22,23,26,29,30,32,33,34,39,40,42,44,45,49,50,51,52,53,55,57,61,62,63,64,65,66,68,69,76,79,83,84,85,86,87,88,90,91,93,95],[0,2,4,6,7,8,9,10,11,12,14,15,17,21,22,27,28,29,31,32,34,35,37,38,39,40,41,42,46,49,52,53,54,55,56,57,58,60,61,62,63,69,71,73,76,77,78,79,80,82,83,87,88,89,94,96,97,99,100],[1,4,6,7,8,9,10,13,14,17,21,22,25,28,29,31,32,34,36,38,41,45,46,47,48,49,51,52,55,57,60,66,67,68,70,71,72,73,76,77,78,79,81,82,83,88,91,92,95],[0,2,4,8,9,10,11,12,13,14,17,18,22,28,30,32,34,38,40,44,45,48,49,56,57,58,60,61,63,65,66,67,69,70,74,76,80,82,84,85,88,90,91,93,95,98,100],[2,3,4,6,8,10,11,12,13,16,20,21,22,23,27,28,29,31,34,37,41,43,44,49,52,53,56,58,62,63,65,68,69,72,73,74,77,78,81,83,84,86,87,88,89,93,94,95,96,97,99,100],[2,3,5,8,9,11,12,13,16,17,18,20,23,25,27,31,32,36,37,38,40,43,45,46,47,48,53,54,56,57,58,60,62,63,65,67,70,71,74,76,79,84,85,87,88,91,93,95,97,99],[1,2,3,6,11,14,15,16,17,18,19,21,23,25,26,30,31,36,37,40,43,44,46,49,51,53,54,55,58,59,61,63,64,66,68,69,70,72,73,74,76,77,78,79,80,82,85,86,87,88,90,91,92,93,94,95,96,98],[1,3,4,5,8,12,13,15,16,18,19,21,27,28,30,32,33,35,37,39,40,42,45,47,49,50,51,58,59,61,62,63,64,66,67,73,74,75,76,77,78,79,81,85,94,95,100],[5,7,12,14,18,23,29,31,39,48,51,52,54,60,62,63,64,70,71,74,75,82,83,85,86,88,93,94,95,96,98],[65,92,93,94,96,97,100],[0,2,4,6,8,15,16,17,22,24,25,28,30,32,34,35,39,41,42,46,49,51,54,55,56,65,66,68,70,72,73,74,76,83,90,92,93,94,97,98],[55,92,93,95,96,97,100],[1,4,6,7,11,12,13,15,17,18,19,22,23,25,27,28,30,32,33,34,39,42,43,44,46,47,48,49,50,51,53,54,55,56,57,58,59,61,62,63,64,65,66,67,68,78,80,83,84,85,86,87,88,90,92,95,96,97,99,100],[0,4,9,11,13,14,16,17,20,21,22,23,24,25,26,28,30,32,40,43,44,46,47,48,49,51,54,55,56,57,58,59,60,61,62,63,64,66,68,70,72,74,76,77,79,80,81,82,83,89,91,92,93,95,99],[0,1,4,6,7,11,12,15,16,17,20,23,24,30,31,32,38,39,41,47,51,53,54,55,56,57,58,59,61,63,66,71,79,83,86,88,89,91,92,94,95,99],[17,70,81,85,87,91,92,94,98,100],[0,3,4,5,8,12,15,16,18,20,21,22,25,30,32,34,38,39,40,42,43,44,46,47,48,51,53,55,56,59,61,63,66,69,70,71,73,75,81,83,85,86,87,89,90,91,92,93,94,95,100],[1,2,3,5,9,10,20,21,24,26,27,31,32,34,35,36,41,48,51,53,55,56,57,58,59,60,61,63,64,67,69,70,72,77,81,82,83,85,86,88,90,91,92,93,96,98,99],[56,92,93,95,98,100],[1,4,6,7,13,17,18,19,22,23,25,27,28,30,32,33,34,38,39,42,43,46,47,48,49,50,51,53,55,56,57,58,59,61,62,63,64,65,66,67,68,78,80,86,90,92,95,98,100],[2,4,6,8,10,12,14,17,21,22,24,26,28,29,33,34,35,38,39,41,42,43,45,50,52,55,57,58,60,62,63,64,68,69,70,71,74,75,81,83,84,85,86,88,89,93,98],[0,2,4,5,6,7,8,10,11,12,14,18,25,27,30,31,38,39,42,43,44,51,53,55,56,58,59,60,62,66,73,77,80,82,83,84,85,87,89,90,94,95,97,99],[0,1,2,7,8,9,12,13,16,17,19,21,24,25,27,28,29,30,32,33,40,44,46,47,49,50,51,52,55,57,59,62,66,67,69,70,71,72,73,74,77,78,79,80,81,82,87,88,89,90,95,97,100],[63,92,94,96,98,100],[0,3,4,5,7,9,11,13,16,17,18,20,21,22,23,24,26,27,28,29,31,32,35,39,40,44,45,46,47,49,52,54,55,56,57,58,60,61,65,66,67,68,71,72,75,76,77,79,80,82,84,87,88,91,92,93,94,95,97],[2,3,4,5,7,10,16,21,22,23,24,25,26,27,28,29,31,33,34,36,37,40,43,46,47,48,50,52,56,62,63,64,65,69,70,71,74,75,80,83,84,87,88,90,91,92,93,95,96,97,100],[36,92,93,95,96,98,100],[1,4,5,6,7,11,13,15,17,18,19,22,23,25,28,30,32,33,34,38,39,42,43,46,47,48,49,50,51,54,55,56,57,58,59,61,62,63,64,65,66,67,68,78,80,83,86,89,90,94,100],[0,1,2,6,7,9,12,15,16,17,18,19,23,24,31,32,33,35,36,37,39,41,42,47,48,50,51,53,54,55,56,57,58,59,64,66,67,69,72,73,74,76,78,79,81,83,85,90,93,94,95,98,99,100],[1,4,5,6,8,12,13,16,18,21,25,27,28,30,32,35,36,37,39,40,41,45,47,49,50,52,57,59,61,62,63,64,66,67,72,73,74,75,76,77,78,79,81,87,90,91,92,93,94,95,96,97,100],[19,92,94,97,98,100],[2,3,4,5,6,7,8,13,14,17,21,22,26,27,28,29,31,32,33,34,35,39,40,42,44,45,46,48,50,52,53,55,57,61,63,64,65,67,68,69,71,73,74,75,76,80,81,83,86,87,89,91,99],[0,1,6,7,11,16,17,18,20,21,22,24,25,26,27,28,29,30,33,34,35,36,41,42,44,46,47,48,51,52,53,57,58,59,64,66,67,68,69,73,74,75,77,82,85,87,89,90,91,92,93,95,97,99,100],[0,3,6,7,8,9,10,11,12,13,14,17,19,22,24,26,27,28,31,34,35,36,42,43,44,49,50,52,54,55,58,60,61,62,63,68,70,71,72,74,79,82,83,85,86,89,90,91,94,95,96,97],[1,2,6,7,8,10,11,12,14,17,19,26,29,30,34,37,40,41,45,47,48,49,50,51,52,55,56,57,60,61,66,67,68,69,70,72,74,75,77,82,84,86,87,88,92,95,96,100],[5,6,7,9,12,14,17,18,22,23,26,28,31,35,37,38,39,41,43,44,48,49,50,54,55,60,61,62,64,65,68,70,71,74,76,77,80,82,83,86,92,93,94,96,97,98,99],[80,92,93,96,97,98,100],[0,1,2,3,6,8,9,10,11,14,16,18,20,21,23,26,27,28,29,30,31,36,39,40,41,42,43,47,48,54,55,57,58,59,60,63,64,65,68,69,72,73,77,79,81,83,85,87,88,89,96],[45,92,93,94,96,97,98,100],[1,3,7,8,9,11,13,14,16,18,19,21,22,26,27,28,29,30,32,34,36,37,39,40,42,44,45,47,48,50,52,53,55,57,58,65,67,68,72,75,78,79,80,83,85,86,89,90,93,99],[0,5,8,9,11,15,17,18,19,20,22,23,24,25,28,32,33,34,35,36,38,39,41,46,48,51,53,54,55,56,61,63,64,65,66,67,70,71,72,78,81,83,85,86,87,92,93,94,95,96,98,100],[1,2,6,8,9,10,15,19,20,21,23,24,25,26,29,30,33,38,40,42,43,44,45,46,47,48,51,55,59,62,63,65,68,71,75,76,77,78,79,84,85,89,93,95,97,98,100],[7,9,10,11,13,17,20,24,25,26,28,29,32,33,35,37,41,44,45,48,50,52,54,55,56,57,62,63,64,68,70,72,73,74,79,84,88,90,91,94,95,97,98,99],[16,92,93,99,100],[1,2,4,6,7,9,10,16,18,20,24,27,36,37,41,42,43,44,47,53,56,57,60,62,65,70,71,73,79,80,81,83,84,85,87,88,92,93,94,95,97,98,99],[67,92,93,94,99,100],[0,1,2,6,10,12,13,16,17,18,20,23,25,27,29,30,31,33,34,35,36,37,38,41,43,44,45,47,48,49,50,51,52,54,59,61,62,63,69,70,71,72,75,76,81,82,86,87,88,89,90,91,92,93,94,95,96,99,100],[7,13,18,85,86,88,99],[0,1,4,6,7,9,10,14,15,16,18,19,21,22,23,26,28,29,31,32,34,36,37,38,40,43,45,47,48,51,52,53,54,56,59,60,61,62,63,66,67,68,70,71,72,73,75,76,77,78,79,83,84,86,88,90,94,95,98,100],[0,2,4,5,7,8,9,12,14,15,18,20,22,23,24,26,29,30,32,33,34,35,38,40,41,46,49,50,52,53,58,60,61,62,64,67,68,69,72,73,76,79,80,82,86,87,90,92,94,95,96,99,100],[2,4,6,7,9,16,17,19,20,21,22,24,25,27,29,33,34,37,38,41,42,43,44,45,48,50,51,52,54,56,57,58,59,61,66,72,76,77,78,80,81,82,85,87,88,89,93,94,96,97,98,100],[4,92,94,96,99,100],[1,2,10,12,13,15,16,18,20,23,25,26,27,28,29,30,31,34,35,36,37,38,41,44,45,47,48,49,51,52,53,56,58,59,61,62,68,69,70,71,72,76,81,82,85,86,89,90,91,98,100],[0,2,4,8,9,10,11,12,17,22,28,30,32,34,38,40,44,45,46,48,49,55,56,57,58,60,61,63,65,67,69,70,74,76,80,84,86,89,90,91,93,95,97,98],[6,8,12,14,15,21,27,30,34,35,39,40,41,42,44,45,48,51,52,53,54,57,60,63,64,67,73,76,77,78,79,84,85,88,89,91,95,97,100],[1,4,5,6,13,15,16,18,19,25,28,32,34,37,39,41,44,49,50,51,53,54,58,59,62,66,74,75,81,84,86,87,90,91,93,96,97,100],[0,1,2,3,6,9,12,14,17,18,22,24,25,26,29,30,31,32,33,34,36,37,38,41,42,46,47,48,49,52,53,54,55,57,59,60,62,64,65,69,70,73,76,79,80,84,85,89,90,91,92,97,100],[0,2,3,6,7,8,13,14,16,18,19,20,22,24,25,26,31,32,35,38,39,44,47,51,52,53,55,57,61,62,63,65,66,68,70,71,72,73,75,76,79,80,81,83,84,86,87,90,91,94,98,99,100],[1,4,5,6,7,11,12,13,17,18,19,22,23,25,27,28,30,32,33,34,39,42,43,46,47,48,49,50,51,55,56,57,58,61,62,63,64,65,66,67,68,78,80,82,83,84,86,89,94,100],[78,92,93,94,95,97,99,100],[0,1,4,5,7,10,13,14,15,16,17,18,21,22,25,29,30,32,33,34,41,43,45,47,49,50,51,52,53,54,55,58,59,60,65,66,72,73,76,77,80,82,83,92,93,94,96],[0,5,8,9,10,11,12,14,18,21,23,26,27,29,30,31,33,35,36,38,39,42,45,49,50,52,53,58,60,61,64,68,70,71,73,75,76,77,79,80,81,84,85,86,87,88,89,90,92,95,100],[0,3,7,8,9,10,15,17,20,22,25,27,28,30,33,35,36,37,39,43,46,47,49,51,52,53,54,60,62,66,67,71,72,76,79,80,81,84,85,87,88,90,93,95,99],[3,92,93,94,96,97,99,100],[0,5,7,8,11,13,14,16,17,18,19,21,22,23,24,33,34,36,37,40,41,42,43,44,48,51,53,54,56,58,60,63,64,65,66,68,72,74,75,76,77,78,79,80,81,82,83,84,89,91,95,96,98,99,100],[1,6,7,10,14,15,17,19,20,21,22,26,29,30,31,37,38,39,42,44,45,46,48,52,53,54,55,60,62,65,67,68,71,72,73,74,76,77,78,79,81,82,83,84,85,87,89,90,91,93,95,96,97,98,99,100],[7,9,10,11,12,14,16,17,19,20,21,24,25,26,27,29,30,31,35,36,37,38,40,41,42,49,51,52,57,58,60,61,63,65,66,69,71,74,75,76,77,78,79,80,81,82,87,88,89,93,94,95,97,98,99],[1,4,5,7,8,10,12,13,15,16,17,18,22,25,26,27,28,29,31,32,35,36,38,39,40,42,44,47,48,49,53,54,55,57,59,63,64,65,66,68,70,71,72,75,81,82,83,84,85,89,92,93,95,96,97,99],[20,92,98,99,100],[0,2,3,5,10,11,12,16,17,21,22,27,29,30,35,36,37,38,40,42,45,46,47,49,50,51,54,57,58,59,61,62,63,64,70,71,72,73,74,76,79,82,85,86,87,88,89,93,95,96,98,99],[81,92,94,98,99,100],[1,4,5,8,14,18,20,21,22,26,29,32,33,39,40,42,43,44,47,48,49,53,54,55,57,58,59,60,61,64,65,67,70,72,74,76,77,83,84,85,86,93,95,96,98],[1,4,5,8,10,11,13,16,17,20,21,24,25,26,29,31,33,35,36,37,40,41,42,45,47,49,52,56,58,59,61,62,64,65,68,73,74,75,76,79,81,83,85,88,89,90,91,92,93,94,97,98,100],[0,1,2,3,5,6,9,11,18,19,22,24,25,27,31,32,36,38,39,43,45,46,50,51,53,54,58,59,60,61,64,65,66,67,68,69,72,73,75,76,78,79,80,85,86,87,88,89,91,95,96,97,98],[43,92,93,94,95,98,99,100],[1,2,3,4,5,6,7,8,10,11,13,14,15,17,18,21,24,26,27,29,32,33,34,35,39,41,48,52,55,56,57,58,59,63,64,68,69,70,72,77,81,82,83,85,86,87,88,89,90,91,93,95,98,99],[1,4,5,7,8,9,11,12,13,14,15,16,17,18,22,23,24,25,27,28,30,34,38,39,41,42,43,45,46,47,48,49,54,55,56,58,60,62,63,65,67,69,71,73,76,77,79,82,87,88,89,91,92,93,94,95,98,100],[0,6,8,9,10,14,17,18,19,21,23,28,31,32,34,35,36,37,38,41,43,45,46,48,51,52,53,55,57,60,64,66,67,70,73,76,77,78,79,80,81,85,89,93,97,98,100],[0,2,4,6,7,8,10,11,12,13,15,16,17,21,22,23,25,26,30,31,32,34,35,37,38,39,41,43,45,50,53,55,56,57,58,61,62,63,64,65,67,69,71,77,81,82,84,85,86,88,89,90,91,92,93,96,98],[2,4,5,10,12,14,15,18,19,20,23,24,25,30,33,35,36,39,40,41,44,45,46,51,53,54,55,57,60,64,66,69,71,72,74,76,78,80,81,83,85,87,89,90,93,94,95,98],[0,1,2,3,5,7,9,14,19,22,24,25,32,36,38,42,45,46,50,52,53,54,58,59,60,61,64,65,66,67,68,69,72,73,76,77,78,79,80,86,87,91,93,94,95,97,99],[0,2,4,6,7,8,10,11,13,15,21,25,26,30,31,32,34,35,39,40,43,45,46,50,53,56,57,58,62,63,64,65,67,68,69,71,77,82,84,85,87,88,89,90,92,93,94,96,97,98,99,100],[0,1,3,4,6,7,8,9,10,13,16,18,19,22,26,27,28,30,32,34,35,36,38,41,44,47,51,56,59,60,63,66,68,72,73,74,75,76,77,79,80,82,83,85,86,87,88,89,91,93,94,95,97,98,99],[35,92,94,97,98,99,100],[0,1,2,6,8,9,10,11,14,15,16,18,20,21,23,25,26,28,31,33,36,39,40,41,42,44,47,55,57,58,59,60,61,62,63,64,67,68,69,70,71,72,73,77,78,79,81,82,84,85,86,87,90,92,93,94,95,96,97],[0,1,4,5,7,10,11,12,13,14,16,17,18,19,20,21,22,28,29,31,32,33,34,38,40,41,43,44,45,47,49,50,51,52,53,56,58,59,60,64,66,72,73,76,77,79,80,82,84,86,88,89,90,92,94,95,97,98],[0,2,4,9,10,11,12,14,16,18,19,20,23,26,28,29,32,36,37,41,42,44,45,46,48,50,52,56,57,58,59,60,61,62,63,65,66,67,68,69,72,74,77,78,81,82,84,86,87,88,90,91,92,93,94,95,97,98,99],[0,2,5,7,8,10,11,12,17,22,25,27,29,30,31,34,35,37,41,42,43,44,50,52,54,56,57,62,63,67,70,71,72,74,75,78,80,83,84,87,88,89,93,95,96,97,98,99,100],[3,25,65,85,86,87,89,90,92,93,94,95,97,98,99,100],[0,1,2,3,5,6,7,9,10,11,13,14,15,16,17,18,21,22,29,30,34,36,37,38,41,43,45,46,47,50,51,52,53,54,55,56,58,59,60,64,66,67,69,71,72,74,77,80,81,82,83,85,86,87,89,90,93,95,96,97,98,100],[1,4,5,6,8,12,14,16,17,19,20,22,26,30,31,32,34,36,37,38,39,40,42,46,47,48,49,51,54,56,59,60,61,62,64,68,71,72,74,75,76,77,78,80,81,82,83,85,86,87,92,93,94,95,97,99],[0,2,4,5,6,7,8,9,10,12,13,15,19,20,22,23,25,26,29,32,34,39,45,49,50,51,52,53,55,57,61,62,66,67,68,69,76,78,79,88,89,91,92,93,94,95,97,100],[2,4,5,6,9,10,12,13,15,16,18,23,24,26,27,28,29,32,33,35,37,38,39,43,44,46,48,51,52,55,57,58,61,62,64,65,66,67,68,70,71,73,74,84,85,87,89,91,96],[1,3,6,7,11,12,13,16,18,21,22,24,27,32,34,38,41,42,44,45,47,48,50,53,54,56,60,61,62,72,75,84,86,87,89,94,98,99,100],[2,4,7,11,12,13,14,15,18,19,20,21,22,25,26,28,30,31,33,35,36,37,39,41,42,43,44,46,49,50,53,60,63,67,68,69,70,73,77,78,80,82,84,85,89,93,95,96,97,98,100]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,3,16,144],"A_d":9650,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,2],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1],[11,1],[12,1],[13,1],[14,1],[15,1],[16,1],[17,1],[18,1],[19,1],[20,1],[21,1],[22,1],[23,1],[24,1],[25,2],[26,1],[27,1],[28,1],[29,1],[30,1],[31,1],[32,1],[33,1],[34,1],[35,1],[36,1],[37,1],[38,1],[39,1],[40,1],[41,1],[42,1],[43,1],[44,1],[45,1],[46,1],[47,1],[48,1],[49,1],[50,1],[51,1],[52,1],[53,1],[54,1],[55,1],[56,1],[57,1],[58,1],[59,1],[60,1],[61,1],[62,1],[63,1],[64,1],[65,2],[66,1],[67,1],[68,1],[69,1],[70,1],[71,1],[72,1],[73,1],[74,1],[75,1],[76,1],[77,1],[78,1],[79,1],[80,1],[81,1],[85,1],[86,1],[87,1],[89,1],[90,1]],"CZ":[[3,25],[3,65],[3,85],[3,86],[3,87],[3,89],[3,90],[25,65],[25,85],[25,86],[25,87],[25,89],[25,90],[65,85],[65,86],[65,87],[65,89],[65,90],[85,86],[85,87],[85,89],[85,90],[86,87],[86,89],[86,90],[87,89],[87,90],[89,90]]},"rotation_powers":[[0,5],[1,7],[2,5],[3,7],[4,5],[5,7],[6,7],[7,5],[9,5],[10,5],[12,7],[14,3],[16,7],[18,3],[20,3],[21,3],[23,5],[24,3],[26,3],[27,5],[28,7],[29,3],[30,5],[31,7],[32,7],[33,5],[35,5],[36,3],[39,3],[42,5],[46,5],[49,5],[51,5],[52,7],[55,7],[56,5],[57,5],[58,5],[60,5],[63,3],[65,3],[69,7],[70,3],[72,5],[81,3],[82,5],[84,3],[85,3],[86,3],[88,3],[89,3],[90,3],[92,3],[94,3],[96,3],[97,3],[98,3],[99,3],[100,3],[102,7],[103,5],[104,5],[105,7],[106,5],[107,5],[108,7],[110,7],[111,7],[112,3],[113,3],[115,3],[118,3],[124,7],[125,5],[126,7],[127,3],[128,3],[131,7],[132,3],[134,3],[135,3],[136,3],[139,3],[142,3],[144,3],[145,3],[147,3],[148,3],[149,3],[150,5],[152,7],[156,5],[157,3],[159,3],[160,3],[162,3],[163,3],[164,3],[165,3],[168,3],[170,3],[172,3],[173,3],[176,3],[179,3],[180,3],[184,3],[185,3],[186,3],[187,3],[189,3],[191,3],[192,3],[193,3],[197,3],[198,3],[199,3],[200,3],[201,3],[202,3],[203,3],[205,5],[206,3],[207,3],[208,5],[209,3],[210,3],[211,3],[213,3],[218,7],[219,3],[221,3],[222,3],[223,3],[224,3],[225,3],[226,3],[227,3],[229,3],[231,3],[233,7],[234,3],[245,3],[246,3],[248,3],[253,3],[254,3],[255,3],[256,3],[257,3],[259,3],[260,3],[261,3],[262,3],[263,7],[265,3],[266,3],[269,3],[275,3],[279,3],[284,3],[285,3],[286,3],[287,3],[290,3],[291,3],[292,3],[294,3],[295,3],[297,3],[301,3],[302,3],[303,3],[306,3],[307,3],[309,3],[312,3],[313,3],[314,3],[315,3],[317,7],[323,3],[324,3],[328,3],[331,3],[334,3],[335,3],[336,3],[338,3],[339,3],[340,3],[341,3],[342,3],[343,3],[344,3],[346,3],[347,3],[349,3],[351,3],[353,3],[354,3],[359,3],[360,3],[364,3],[365,3],[367,3],[368,3],[371,3],[372,3],[373,3],[375,3],[376,3],[379,3],[380,3],[382,3],[383,3],[384,3],[385,3],[388,3],[391,3],[392,3],[395,3],[397,3],[398,3],[399,3],[400,3],[403,3],[404,3],[406,3],[407,3],[409,3],[411,3],[413,3],[414,3],[415,3],[416,3],[418,3],[419,3],[420,3],[421,3],[422,3],[423,3],[427,3]]},"metrics":{"gamma":1.1919574908915316,"gamma_t":null,"gamma_rho":1.1919574908915316,"gamma_claim":1.1919574908915316,"gamma_t_claim":null,"gamma_rho_claim":1.1919574908915316,"v_ex":82,"rate":0.19158878504672897,"t_count":null,"poly_degree":null,"effective_width":82},"provenance":{"regimes":["AI search (gamma frontier): from Wills parent codes"],"discovery":"AI search","strongest_claim":"built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows","sources":[{"regime":"AI search (gamma frontier): from Wills parent codes","file":"gamma_frontier_release/protocols/paired_column_contraction_428_82_4_29a641c9409e.json","label":"paired_column_contraction_428_82_4_29a641c9409e","N":101,"d":4,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^8,2^1, cutoff 3), with searched graph punctures; 1 paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_428_82_4_29a641c9409e (source catalogue id paired_column_contraction_428_82_4_29a641c9409e); construction: Wills weighted Reed\u2013Muller parent (weights 1^8,2^1, cutoff 3), with searched graph punctures; 1 paired-column contraction; matrix 29a641c9409e8841...; the release states d=4 (exact), gamma=1.1919574908915316 (exact)","notes":"matrix gamma_frontier_release/matrices/29a641c9409e8841291a7548493afce96ab2fcf5617263f046da5e8d2b3d112f.matrix"}]},"references":[{"key":"jain2026symmetry","short":"Jain et al. (2026)","full":"S. P. Jain, A. Wills, and S. Singh, \"Symmetry and AI-assisted discovery of magic-state factories,\" arXiv:2610.06535 (2026).","url":"https://arxiv.org/abs/2610.06535","date":"2026-10-05"}]}