{"id":"405.101.3.a","row":1027,"stored":{"file":"master_catalog.json","row":1027,"construction":null,"columns_sha256":null},"parameters":{"n":405,"k":101,"d":3,"N":112,"r":11,"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+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100","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\u00b7T82\u00b7T83\u00b7T84\u00b7T85\u00b7T86\u00b7T87\u00b7T88\u00b7T89\u00b7T90\u00b7T91\u00b7T92\u00b7T93\u00b7T94\u00b7T95\u00b7T96\u00b7T97\u00b7T98\u00b7T99\u00b7T100","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],[82],[83],[84],[85],[86],[87],[88],[89],[90],[91],[92],[93],[94],[95],[96],[97],[98],[99],[100]],"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],[82],[83],[84],[85],[86],[87],[88],[89],[90],[91],[92],[93],[94],[95],[96],[97],[98],[99],[100]],"sk_fingerprint":"57dcd9f801964bf7","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2,3,5,6,7,8,9,10,11,14,15,16,17,18,21,22,25,33,38,39,40,45,46,50,53,54,57,59,60,63,64,66,69,71,72,73,76,78,83,85,87,91,93,95,96,98,99,100,101,103,107,108,111],[41,104,105],[3,4,5,6,7,8,9,10,11,15,16,17,18,19,21,22,23,24,25,26,34,36,42,44,45,46,47,50,52,56,60,62,63,64,67,68,69,70,71,72,73,74,77,79,81,82,85,86,89,90,91,92,93,94,97,98,100,101,102,105,106,107,109,110],[40,104,105,106],[87,104,107],[0,1,4,6,7,9,10,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,103,105,106,107,109,110],[1,2,3,7,12,19,21,23,24,26,27,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,102,104,105,109],[1,7,9,11,14,17,18,20,21,22,23,26,27,30,36,37,39,40,42,43,45,46,47,49,52,53,54,56,57,58,60,61,63,65,66,69,71,73,74,75,76,79,81,84,86,89,91,94,95,97,98,99,100,101,103,104,106,107,108,110,111],[0,1,2,8,12,13,15,19,20,23,28,29,30,33,34,35,37,45,46,50,52,58,60,62,63,67,69,70,75,76,80,82,84,85,89,94,96,97,99,101,102,104,106,108,109,110,111],[5,7,8,9,10,11,12,15,17,19,23,24,25,27,28,32,33,35,38,39,41,42,44,47,48,51,52,56,57,63,64,65,66,67,69,71,73,77,78,79,81,82,83,87,88,89,92,94,95,97,100,103,106,108,109,111],[0,1,2,6,7,8,16,18,22,23,24,28,29,31,34,35,37,38,39,40,41,42,44,45,46,47,49,51,53,54,55,57,60,67,69,71,75,76,77,78,79,81,82,87,88,89,90,91,92,93,95,98,99,102,103,104,109,110,111],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,70,73,80,82,83,84,90,91,93,97,98,100,101,102,106,109,111],[29,104,105,107,108],[89,104,106,107,108],[84,104,109],[2,104,105,109],[0,1,2,4,5,7,8,11,12,14,15,17,18,20,21,22,23,30,32,34,36,37,38,39,41,42,43,44,45,47,48,49,51,52,53,54,55,56,57,58,60,61,66,68,70,71,72,74,75,79,81,84,86,91,94,95,97,101,102,103,104,107,108,109,110],[1,4,14,17,19,21,23,24,27,30,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,102,105,108,109,110],[0,2,3,6,7,10,11,12,16,18,19,22,23,24,25,26,30,31,32,36,37,42,44,45,51,54,55,59,61,62,65,67,70,71,72,73,74,75,76,78,82,84,85,87,89,90,91,92,95,99,100,101,102,103,107,110],[44,104,105,107,109],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,55,57,58,61,63,64,65,68,69,71,72,73,74,77,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,102,103,106,107,108],[2,5,6,8,9,10,11,12,14,15,16,18,19,21,22,23,24,25,30,31,32,36,39,42,44,45,46,49,50,54,56,57,59,61,62,65,67,68,69,70,72,73,74,76,77,82,85,87,89,91,92,94,98,101,102,104,106,107,108],[8,104,108,109],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,107,108,109,110,111],[4,5,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,71,72,74,79,80,81,82,85,86,89,91,95,96,101,103,104,106,107,111],[0,1,2,3,4,5,11,12,13,14,17,18,22,23,24,26,27,28,29,31,35,37,38,39,40,41,43,46,51,52,55,56,57,59,61,63,65,69,75,77,80,83,85,89,91,92,95,97,99,101,102,103,105,106,108,111],[97,104,105,107,108,109],[55,104,106,107,108,109],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,105,106,108,110,111],[2,6,7,8,10,12,15,17,18,19,21,24,25,27,32,38,41,43,47,48,50,52,54,55,56,58,59,60,62,63,64,66,67,70,71,72,74,75,77,85,86,91,93,94,95,97,100,101,105,107,110],[0,3,4,7,8,9,15,16,18,19,20,21,23,24,26,33,34,36,40,42,44,46,47,48,49,50,51,52,56,59,62,63,64,66,67,68,69,70,71,73,74,75,76,77,83,84,86,87,89,91,93,94,96,97,98,101,102,103,104,105,106,107,110],[1,2,7,9,11,12,13,14,17,22,23,24,27,30,37,38,39,43,46,47,52,53,54,55,56,58,59,60,61,63,65,68,69,71,74,75,76,77,81,83,86,87,89,91,92,93,95,97,99,102,104,107,111],[0,1,2,4,8,9,12,15,16,18,20,21,27,31,32,34,37,46,51,53,54,56,57,63,64,65,69,70,72,73,76,79,81,82,84,87,89,91,92,93,94,98,99,101,103,106,109],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,62,65,67,69,71,72,73,77,83,86,89,90,92,95,96,97,98,99,101,104,110],[7,104,106,107,110],[91,104,105,106,107,110],[1,2,5,6,8,10,11,12,13,15,17,19,21,22,23,25,28,29,30,34,35,37,40,46,48,49,50,51,52,58,62,63,66,67,69,70,71,72,76,79,80,81,83,87,89,90,92,94,97,99,100,101,102,103,111],[0,1,7,10,13,17,18,20,21,23,24,25,27,28,29,30,32,33,34,35,37,38,41,43,45,46,47,48,54,55,56,59,64,66,69,71,72,77,80,82,84,86,89,91,93,95,96,99,100,101,102,104,106,107,108,109,110,111],[1,2,4,7,9,12,13,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,103,105,106,107,109,110,111],[3,8,9,10,12,13,14,16,17,18,19,23,24,25,28,33,37,38,39,40,43,44,45,46,48,49,51,52,54,55,57,58,59,60,65,66,70,73,77,78,79,80,85,90,91,93,97,101,102,103,107,110,111],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,102,103,110,111],[0,2,4,5,7,8,9,11,12,13,15,16,20,21,22,23,24,28,29,30,31,35,38,40,41,43,47,49,53,55,59,60,63,65,70,71,72,73,75,77,82,83,84,85,86,90,94,95,98,101,102,104,106,108,109,111],[3,5,6,7,8,10,11,13,15,17,22,24,25,26,27,28,29,30,31,32,33,34,35,36,42,44,46,47,51,53,54,58,59,63,65,68,69,70,71,74,76,77,80,82,86,87,89,90,94,96,100,101,103,104,105,108,109,110,111],[28,104,105,106,107,108,110],[1,2,3,5,9,11,12,14,16,17,19,21,22,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,104,105,106,108,109],[0,1,3,7,8,9,14,15,16,17,18,20,21,26,27,30,37,39,46,47,49,51,52,53,56,57,60,61,69,70,71,72,73,79,82,84,86,89,90,91,92,94,97,98,99,101,103,107,108,109,110],[2,3,4,6,8,9,10,11,12,15,17,18,19,20,22,24,25,26,31,34,37,41,46,47,48,49,50,52,53,54,56,60,62,63,64,66,67,68,69,70,71,72,83,85,86,89,90,91,93,94,97,99,100,101,104,106,108,111],[64,104,105,106,109,110],[1,3,4,6,8,10,14,15,18,19,21,24,25,26,27,30,31,34,38,39,41,43,48,49,50,55,56,57,58,59,61,62,65,66,67,70,72,75,76,77,79,81,85,87,90,91,94,95,100,101,105,106,108],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,23,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,93,96,97,100,101,103,107,108,109],[5,7,9,11,14,16,17,20,22,23,27,30,31,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,102,107,108,109,110],[3,4,7,8,9,11,12,14,16,17,27,30,31,32,34,35,39,47,49,50,51,52,55,57,58,60,61,65,69,70,71,72,73,75,76,78,82,86,87,89,90,91,92,95,97,103,105],[0,1,3,4,8,9,13,15,16,17,18,20,21,30,34,36,39,44,46,48,49,51,52,53,57,59,63,65,66,67,69,72,73,75,78,79,82,84,86,87,88,89,91,92,93,94,96,98,99,101,103,105,107,108,111],[0,4,6,7,10,11,13,14,18,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,106,107,108,110,111],[0,4,7,8,9,14,15,16,18,20,24,26,30,31,33,38,40,42,44,46,47,48,49,50,51,52,54,57,61,62,64,65,68,69,71,72,73,74,77,79,81,83,84,87,88,89,90,91,93,95,96,98,100,102,104,108,109],[1,3,5,7,8,9,11,14,15,16,17,22,24,27,30,32,34,35,37,39,47,48,52,53,56,59,60,61,70,73,75,76,77,78,82,83,86,87,91,92,97,98,99,103,105,106,107,108,109,110],[1,3,4,5,6,7,8,10,11,13,14,15,17,19,21,22,23,25,26,28,29,31,32,35,37,39,40,46,47,48,50,51,54,57,58,60,61,62,64,65,66,67,69,70,71,72,80,83,86,89,92,93,94,99,100,101,102,103,104,105,106,109,111],[0,1,2,5,7,8,9,11,12,13,14,15,16,17,19,20,22,27,28,29,31,33,34,35,36,37,38,39,41,42,44,47,48,49,50,55,57,61,62,64,65,66,67,68,70,71,73,74,76,80,84,85,86,87,92,93,94,95,96,98,99,101,106,107,108,111],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,103,105,108,109,111],[27,101,103],[0,1,2,5,6,8,9,10,13,14,19,20,22,23,26,28,29,30,34,35,39,42,45,47,48,49,51,53,54,55,56,57,60,62,65,66,67,68,70,71,72,74,75,77,78,83,84,85,89,90,92,95,97,98,100,102,103,105,109],[72,104,106,111],[1,2,3,4,5,9,11,13,14,20,24,25,27,29,31,32,36,37,40,41,44,45,48,49,50,52,54,55,56,58,59,60,61,62,63,66,68,69,70,72,75,78,80,83,86,87,89,90,92,93,95,98,99,101,104,105,108,109,111],[1,2,4,5,6,8,9,10,11,12,15,16,17,18,22,25,27,31,33,34,37,40,45,46,48,49,53,54,56,60,63,64,65,66,69,70,73,75,83,85,89,90,91,93,94,96,98,99,100,101,103,104,107,110,111],[0,1,4,6,7,9,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,105,106,107,109,110],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,102,103,104,105,109,111],[2,5,8,9,10,12,13,14,15,17,19,20,21,24,26,28,30,31,35,36,38,39,41,42,45,46,51,52,53,57,58,59,60,61,64,66,69,70,74,77,80,81,82,83,89,90,92,93,94,96,97,99,100,101,104,105,109],[0,1,2,8,12,13,15,19,20,23,28,29,30,33,35,37,45,46,50,52,58,60,62,63,67,69,70,75,80,82,84,85,89,94,96,97,99,101,102,103,104,106,108,109,110],[82,104,105,108,111],[0,1,2,3,4,5,6,7,9,10,11,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,103,104,105,106,107,108],[38,104,107,108,111],[48,104,106,107,108,111],[5,7,9,16,18,26,27,28,29,30,31,32,35,39,42,45,47,50,51,53,54,55,57,58,60,62,65,68,70,72,73,75,78,80,81,82,85,86,87,89,90,91,92,93,95,105,109,110],[1,3,5,6,7,8,9,10,11,14,15,16,18,22,25,26,27,30,33,37,39,40,45,46,47,48,52,53,56,57,60,61,66,69,70,71,73,75,76,79,81,83,85,86,87,89,91,94,96,97,98,99,100,101,103,106,107,108],[0,1,2,4,5,7,8,11,12,14,17,18,20,21,22,23,30,32,34,36,37,38,39,41,42,43,44,45,47,48,49,51,52,53,54,55,56,57,58,60,61,66,68,70,71,72,74,75,79,81,84,86,91,94,95,97,99,101,102,106,107,108,110],[9,104,107,109,111],[0,1,2,3,5,6,10,11,12,13,19,20,22,24,25,27,33,36,38,39,42,45,47,48,51,53,57,59,60,61,62,68,70,71,74,75,76,77,81,84,85,86,88,89,93,94,99,101,102,104,105,106,110],[2,5,6,8,9,10,11,12,14,15,16,18,19,21,22,23,24,25,30,31,32,36,39,42,44,45,46,49,50,54,56,57,59,61,62,65,67,68,69,70,72,73,74,76,77,82,85,87,88,89,91,92,94,98,100,101,102,103,104,106,107,108,111],[68,104,108,109,111],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,36,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,103,107,108,109,110,111],[5,104,106,108,109,111],[0,2,3,5,6,10,11,13,14,19,20,22,23,25,30,31,32,36,38,40,45,51,54,56,61,63,65,66,67,70,71,72,75,76,78,79,81,82,83,84,85,89,90,92,93,95,100,101,104,105,107,111],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,27,32,33,34,36,38,40,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,102,103,105,106,110],[98,104,106,107,108,109,111],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,26,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,103,105,106,108,110,111],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,60,66,72,75,76,79,81,82,83,84,85,87,90,92,95,96,100,101,104,106,109,111],[2,4,5,8,9,13,18,20,24,25,27,28,30,32,34,36,37,41,42,44,48,49,50,51,52,55,56,57,59,60,62,65,66,69,70,72,74,75,76,77,78,79,80,81,83,87,89,92,93,95,97,98,99,101,103,107,111],[0,3,4,7,8,9,15,16,18,19,20,23,24,26,33,34,36,40,42,44,46,47,48,49,50,51,52,56,59,62,63,64,66,67,68,69,70,71,73,74,75,76,77,78,83,84,86,87,89,91,93,94,96,97,98,101,102,105,107],[2,3,4,5,9,11,12,16,22,23,25,26,27,32,34,36,38,41,42,43,44,45,46,48,54,55,58,66,68,69,73,74,75,79,81,82,89,90,92,95,98,101,102,103,104,105,109,110,111],[90,104,107,110,111],[0,2,7,8,10,11,12,13,14,15,18,19,20,21,22,23,26,27,29,34,35,36,40,44,47,48,49,53,55,56,58,61,66,67,71,73,74,76,77,79,80,81,82,83,86,87,88,94,95,96,97,98,100,101,102,103,104,105,107,109,111],[2,4,8,10,12,14,15,24,28,29,30,32,35,36,37,41,43,44,46,47,51,53,54,56,59,60,61,66,67,68,69,73,74,75,76,78,79,81,86,88,89,90,93,94,95,97,98,99,100,102,104,106,108],[1,2,5,6,8,10,11,12,13,15,17,19,21,22,23,25,28,29,30,34,35,37,40,46,48,50,51,52,58,62,63,66,67,69,70,72,76,79,80,81,83,87,89,90,92,94,97,99,100,101,102,104,108,110],[0,3,5,7,8,9,14,15,17,27,30,31,38,39,40,41,44,46,47,48,49,51,52,54,55,57,60,61,64,68,69,70,71,72,73,79,81,86,87,89,90,93,97,98,100,102,104],[1,2,3,4,7,9,12,13,14,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,105,106,107,109,110,111],[16,104,105,106,108,110,111],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,37,45,50,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,102,110,111],[3,5,6,7,8,10,11,13,15,17,22,24,25,26,27,28,29,30,31,32,33,34,35,36,42,44,46,47,51,53,54,58,59,63,65,68,69,70,71,74,75,76,77,80,82,86,87,89,90,96,100,101,104,105,108,109,110],[1,4,9,12,14,15,17,18,19,20,22,26,30,32,33,34,35,37,38,40,41,45,46,48,49,50,51,53,55,58,60,61,62,65,67,75,76,78,82,84,91,92,94,95,96,98,99,103,104,105,107,109,111],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,47,49,50,51,53,57,59,61,62,63,64,67,68,74,77,79,81,84,85,93,99,100,101,102,104,108,109,110,111],[67,104,105,107,109,110,111],[35,104,106,107,109,110,111],[33,104,105,106,107,109,110,111],[0,3,5,8,9,11,13,14,15,16,17,20,21,22,23,24,26,28,29,32,34,35,38,39,40,41,43,52,54,55,57,59,61,64,70,72,73,75,76,77,79,80,81,82,83,84,85,87,93,94,95,97,98,101,102,103,104,105,110],[0,1,4,5,6,9,10,11,13,16,17,18,19,20,22,24,25,26,27,28,29,30,32,34,35,36,37,38,42,48,50,52,54,57,58,59,63,64,65,66,67,68,73,74,77,79,80,81,84,90,91,92,97,98,99,101,103,105,106,107,108,110],[18,104,106,108,109,110,111],[0,1,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,59,60,61,63,65,66,69,72,76,77,79,80,81,82,83,84,87,89,90,91,95,96,97,99,100,101,102,103,105,108,109,110,111],[1,3,4,5,6,7,8,10,11,13,14,15,19,21,22,23,25,26,28,29,31,32,35,37,39,40,46,47,48,50,51,54,57,58,60,61,62,64,65,66,67,69,70,71,72,80,83,86,89,92,94,99,100,101,102,106,107,108,110,111],[1,2,4,6,8,9,10,11,12,14,15,16,17,18,20,21,22,23,24,25,27,31,32,33,36,40,41,42,44,46,49,54,55,56,57,59,60,65,69,70,73,74,75,77,83,84,85,87,89,90,94,96,98,99,100,102,103,104,105,109,110,111],[54,104,105,106,107,108,109,110,111],[1,2,3,5,6,7,8,9,10,11,14,15,16,17,18,21,22,25,33,38,39,40,45,46,50,53,54,57,59,60,63,64,66,69,71,72,73,76,78,83,85,87,91,93,95,96,98,99,100,103,107,108,111],[0,2,5,7,8,11,12,15,18,19,20,22,24,27,32,33,38,40,43,45,47,49,50,51,52,54,55,56,58,59,62,63,64,67,70,71,76,77,79,81,82,83,84,86,87,90,91,92,93,94,95,96,97,101,103,104,106,107,109],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,26,27,32,33,34,36,38,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,101,102,103,104,105,106,110],[1,2,4,5,6,8,9,10,11,12,15,16,17,18,22,25,27,31,32,33,34,37,40,45,46,48,49,53,54,56,60,63,64,65,66,69,70,73,75,83,85,87,89,90,91,93,94,96,98,99,100,101,104,107,110],[31,104,106,107],[0,3,5,7,8,9,14,15,17,27,30,31,38,39,40,41,44,46,47,48,49,51,52,54,55,57,60,61,64,68,69,70,71,72,73,79,81,86,87,89,90,93,97,98,100,102,104,106,107,108,110,111],[76,104,108],[1,8,9,10,12,13,15,17,18,19,22,25,29,30,33,34,37,39,40,42,43,44,46,48,49,52,54,55,57,59,60,63,65,66,67,73,75,76,78,80,82,85,86,88,90,91,93,94,97,99,100,101,102,105,106,107,108,109,110],[0,1,2,3,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,105,107,111],[0,2,3,4,7,9,10,13,15,17,18,19,21,22,23,24,25,26,27,30,31,32,34,36,39,43,46,47,50,52,53,57,60,62,63,68,69,70,71,72,73,74,77,78,79,80,81,83,88,89,90,91,92,93,94,97,100,101,102,104,106,110],[2,4,6,7,8,9,10,12,13,15,16,17,23,24,25,28,30,31,33,35,38,41,43,45,47,48,51,53,55,59,63,65,66,70,71,73,76,77,79,80,81,86,87,92,94,95,96,98,100,101,102,103,104,108,111],[0,3,7,8,13,15,20,21,24,26,27,28,29,30,31,32,34,35,36,40,42,44,45,46,47,48,49,53,54,58,59,60,63,65,66,68,69,70,71,72,74,77,79,80,81,83,84,85,86,92,94,101,104,105,106,108,110,111],[2,3,5,11,12,13,18,19,21,22,26,28,29,30,31,33,34,35,36,38,41,42,43,44,46,48,50,51,52,53,55,56,60,62,64,65,66,67,68,69,72,74,76,80,82,87,89,90,91,93,95,96,97,101,103,106,109,110,111],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,85,89,90,92,93,95,98,99,100,101,103,104,105,108],[1,2,3,5,6,7,8,9,10,11,14,15,16,18,22,25,26,27,30,33,37,39,40,45,46,47,48,52,53,56,57,61,66,69,70,71,73,75,76,79,81,83,85,86,87,89,91,94,96,97,98,99,100,101,104,105,106,107,108,109],[99,104,106,109],[2,4,5,6,7,8,10,12,14,15,16,17,20,23,25,27,32,33,34,36,37,38,39,40,41,42,43,44,50,54,56,57,58,60,71,72,73,74,75,76,77,78,83,85,87,89,90,94,96,99,100,102,105,107,108,109],[2,3,4,7,12,14,17,26,30,31,32,34,39,44,47,49,52,54,57,60,61,63,64,65,71,76,79,81,86,87,90,93,97,101,104,105,106,108,109,110],[100,104,105,106,107,109],[3,6,9,10,13,14,15,16,23,24,25,26,28,29,32,33,34,35,38,39,41,43,45,48,49,51,52,53,54,55,57,59,60,61,64,66,70,73,77,80,90,92,93,94,95,96,97,98,100,101,102,103,104,105,106,109,110,111],[69,104,106,108,109],[0,2,4,8,12,13,14,15,17,20,21,24,27,28,29,35,36,39,40,42,44,45,46,48,52,53,57,58,59,61,64,66,68,69,70,72,74,76,77,80,83,84,85,87,89,90,92,93,94,96,97,101,105,106,108,111],[0,1,3,4,7,8,13,14,15,17,19,20,23,26,28,29,31,32,33,35,37,39,45,46,47,49,50,54,57,58,61,62,64,65,67,69,70,71,75,76,79,80,81,82,84,85,86,87,89,90,93,94,96,97,99,101,102,104,105,111],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,56,60,66,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,103,106,109,110],[21,104,106,110],[1,3,4,5,7,13,14,16,17,24,26,30,32,34,36,37,39,41,42,44,45,47,48,52,53,56,59,60,61,63,65,66,71,73,76,77,79,82,83,86,87,90,91,93,97,98,99,101,104,106,107,109,111],[92,104,105,107,110],[0,1,2,3,5,6,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,102,103,104,105,106],[1,3,6,8,10,15,17,18,23,25,26,31,33,36,37,38,40,41,42,43,44,49,53,55,56,58,60,63,64,65,68,70,74,79,81,82,83,85,92,93,94,95,96,99,100,101,102,104,105,107,109],[6,104,105,108,110],[0,1,4,5,10,11,12,14,15,17,18,20,22,23,24,25,26,27,29,30,32,35,36,39,40,41,42,45,46,49,50,51,57,58,59,62,63,65,67,68,74,77,78,81,84,91,92,93,94,95,96,98,99,102,103,107],[80,104,105,107,108,110],[75,104,106,107,108,110],[0,2,3,6,10,12,13,17,18,19,20,25,26,29,30,31,34,35,36,38,40,41,42,43,44,45,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,104,105,106,107,108,110,111],[24,104,109,110],[1,3,7,9,11,14,17,19,20,22,23,24,26,30,31,32,33,36,38,39,40,42,43,44,46,48,49,50,55,57,58,60,61,62,63,64,66,67,69,72,74,76,82,87,89,92,93,95,96,102,104,106,107,109,111],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,49,50,51,53,57,59,61,62,63,67,68,74,77,79,81,84,85,93,99,100,101,102,103,104,108,109,110],[0,2,8,9,12,13,14,15,16,17,18,19,20,23,24,30,31,32,33,36,39,40,42,44,46,48,50,51,54,56,57,59,60,61,62,65,66,67,68,69,70,73,74,75,77,79,81,83,84,89,90,91,94,96,98,101,102,103,105,106,108,110],[0,4,5,7,12,13,15,20,21,22,23,24,26,27,28,29,30,31,38,40,41,43,47,49,50,51,53,54,58,59,60,64,65,69,71,77,78,79,80,81,83,84,85,86,89,90,91,92,93,94,98,101,102,103,108,109,111],[0,1,2,4,7,8,12,14,15,19,20,23,26,27,28,29,30,33,35,36,44,45,46,47,48,50,52,56,58,59,61,62,65,66,69,71,78,79,80,82,84,85,87,88,89,90,93,94,99,102,105,106],[0,2,5,6,7,9,10,11,12,13,16,18,20,22,25,26,27,28,29,30,31,35,36,38,39,40,47,48,50,53,54,58,59,60,62,65,70,71,72,73,75,80,82,83,84,87,88,90,91,94,95,97,98,101,102,103,104,105,110,111],[0,2,4,5,6,7,8,9,10,11,12,13,15,16,17,18,20,21,22,23,25,26,28,29,30,31,32,33,34,38,41,43,45,46,47,49,53,55,57,63,65,66,69,70,72,73,75,78,79,80,81,83,84,86,89,90,92,95,96,98,100,101,102,103,106,107,111],[17,104,105,107,108,109,110],[1,6,7,9,10,11,12,13,14,15,18,23,24,26,27,28,29,30,32,33,34,35,38,39,40,41,42,43,48,50,52,53,57,58,59,60,63,64,65,66,68,72,74,75,76,78,79,81,82,85,86,87,89,91,93,94,96,98,100,101,102,103,106,107],[3,4,5,6,7,8,9,10,11,15,16,17,18,19,21,22,23,24,25,26,34,36,42,44,45,46,47,50,52,56,59,60,62,63,64,67,68,69,70,71,73,74,77,79,81,82,85,86,89,90,91,92,93,94,97,98,100,101,102,103,104,105,107,109,110,111],[0,1,5,6,10,11,12,13,14,16,17,21,23,24,26,29,31,33,34,37,38,42,43,45,46,48,50,51,52,56,59,61,62,63,66,70,73,74,75,76,78,80,84,85,86,90,92,93,96,99,100,102,104,105,108,109,110,111],[32,104,107,111],[65,104,106,107,111],[0,1,2,3,9,10,11,12,13,14,17,18,19,22,23,24,28,30,35,37,39,43,44,46,48,52,55,56,57,59,60,61,63,65,68,69,72,75,76,77,80,81,82,83,84,87,89,91,92,95,96,97,100,102,104,105,109],[34,104,108,111],[1,5,7,11,13,18,22,23,24,27,28,29,30,32,34,35,37,38,40,41,43,46,47,49,51,54,55,56,59,60,64,69,71,75,76,77,79,80,81,82,83,85,86,87,89,90,91,92,93,95,99,101,102,104,107,108,110],[12,104,106,108,111],[2,3,4,7,12,14,17,26,30,31,32,34,39,47,49,52,54,55,57,60,61,63,64,65,71,76,79,81,86,87,90,93,97,103,104,109,110],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,38,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,90,91,93,97,98,100,101,102,103,104,106,107,108,109],[2,4,6,7,8,9,10,12,13,15,16,17,23,24,25,28,29,30,31,33,35,38,41,42,43,45,47,48,51,53,55,59,63,65,66,70,71,73,76,77,79,80,81,86,87,92,94,95,96,98,100,101,102,105,107,111],[0,3,7,8,13,15,20,21,24,26,27,28,29,30,31,32,34,35,36,40,42,44,45,46,47,49,53,54,58,59,60,63,65,66,68,69,70,71,72,74,77,79,80,81,83,84,85,86,89,92,94,101,103,104,105,106,108,110],[2,3,7,9,11,12,13,16,19,21,22,27,32,33,34,36,38,39,41,43,44,45,46,47,48,52,54,56,57,58,64,66,67,69,70,73,74,75,76,78,81,86,92,96,97,101,105,106,111],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,105,108,109],[1,4,14,17,19,21,23,24,27,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,63,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,102,103,105,108,109,110],[0,3,4,5,8,9,11,14,15,17,18,19,20,22,24,26,27,30,31,33,34,38,39,40,41,43,45,50,51,55,56,57,58,59,60,61,62,65,67,70,77,82,83,84,91,92,94,95,96,101,104,105,107,108,110,111],[0,1,4,5,6,7,10,11,13,14,17,19,20,22,24,25,26,27,30,31,32,33,34,36,38,42,45,48,49,51,52,53,54,59,62,63,64,65,68,70,74,75,77,79,84,85,87,88,89,90,94,97,99,102,103,104,105,107,108],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,52,55,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,102,106,107,108],[88,104,105,106,107,109,111],[3,6,8,9,10,13,14,15,16,23,24,25,26,28,29,32,33,34,35,38,39,41,43,45,48,49,51,52,53,54,55,57,59,60,61,64,66,68,70,73,77,80,90,92,93,94,95,96,97,98,100,101,102,104,105,106,109,110],[4,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,101,104,106,107],[3,4,5,6,8,10,11,12,15,17,19,21,22,23,24,25,27,28,29,30,31,32,35,38,39,42,44,46,48,51,52,53,54,56,57,58,59,63,64,65,67,68,69,71,74,75,77,78,79,80,81,82,87,94,95,97,100,103,104,106,107,108],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,26,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,103,108,110,111],[0,1,3,4,7,8,13,14,15,17,19,20,23,26,28,29,31,32,33,35,37,39,45,46,47,49,50,54,57,58,61,62,64,65,67,69,70,71,75,76,79,80,82,84,85,86,87,89,90,93,94,96,99,101,102,103,107,108,109,111],[1,2,6,7,8,9,10,12,13,14,15,16,19,21,25,27,28,29,31,34,35,36,37,38,39,40,41,42,43,44,45,47,50,51,55,57,60,61,62,64,65,67,68,70,71,72,73,74,75,79,80,81,82,83,86,90,93,94,95,99,100,101,104,106,110],[95,104,110,111],[4,5,6,7,9,10,12,13,15,17,19,20,21,28,30,34,36,37,38,42,43,44,47,49,51,54,57,58,63,64,65,67,69,71,74,76,78,79,80,81,83,85,86,87,89,91,92,94,98,99,100,105,110,111],[25,104,105,106,110,111],[0,1,2,4,8,9,12,15,16,18,20,21,27,31,32,34,37,46,51,53,54,56,63,64,65,69,70,72,73,76,79,81,82,84,87,89,90,91,92,93,94,98,99,101,104,106,107,109,110,111],[0,1,2,4,5,8,9,10,12,13,14,15,16,18,20,23,24,26,27,29,31,33,35,36,37,38,41,43,44,45,46,48,50,52,56,59,61,62,65,66,69,72,74,76,79,80,81,82,87,88,89,90,94,99,100,102,104,109,111],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,39,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,102,105,107,110],[1,2,3,4,6,12,14,17,18,23,24,25,26,28,29,30,31,32,33,35,38,40,42,46,47,49,51,54,55,58,59,61,63,64,65,66,67,69,70,73,75,76,78,82,83,85,86,88,89,90,91,92,96,97,98,101,103,104,108,109,110],[49,104,108,110,111],[1,3,5,6,8,9,10,13,14,15,18,20,21,23,24,25,28,29,31,32,33,34,35,37,39,40,43,44,45,49,51,52,56,57,59,60,61,66,68,70,73,77,79,80,81,82,84,87,90,91,95,96,97,98,99,101,103,104,105,106,107,109,111],[0,1,3,4,5,8,9,11,13,15,19,20,22,26,27,28,29,30,32,33,35,36,37,38,41,42,43,44,48,50,52,54,55,60,62,63,66,67,68,70,73,74,79,80,81,84,85,90,92,94,95,96,97,98,99,101,103,104,105,106,108],[0,2,4,5,7,8,9,11,12,13,15,16,20,21,22,23,24,28,29,30,31,35,38,40,41,43,47,49,53,55,59,60,62,63,65,70,71,72,73,75,77,80,82,83,84,85,86,90,94,95,98,101,102,103,105,106,107,109,110,111],[94,104,106,107,108,110,111],[0,2,3,6,10,12,13,17,18,19,20,25,26,28,29,30,31,34,35,36,38,40,41,42,43,44,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,103,111],[1,2,3,5,9,11,12,14,16,17,19,21,24,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,103,105,106,108,110],[0,1,3,7,8,9,14,15,16,17,18,20,21,26,27,30,37,39,46,47,49,51,52,53,56,57,60,61,69,70,71,72,73,82,84,89,90,91,92,94,97,98,99,101,107,108,109,110],[2,6,7,8,9,10,17,19,20,22,23,25,26,35,36,39,42,43,44,45,46,47,48,49,50,51,52,54,56,57,60,62,65,67,68,70,71,74,75,78,83,84,85,86,87,90,97,98,100,101,102,104,105,108,111],[47,104,105,106,109,110,111],[3,4,6,8,10,14,15,18,19,21,24,25,26,27,30,31,34,38,39,41,43,48,49,50,55,56,57,59,61,62,65,66,67,70,72,75,76,77,79,81,85,87,90,91,94,95,100,101,103,105,106,108],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,67,71,72,75,82,83,84,85,86,92,93,96,97,100,101,104,105,108,110,111],[5,7,9,11,14,16,17,22,23,27,30,31,35,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,102,103,104,106,108,111],[0,2,8,9,12,14,15,16,17,18,19,20,23,24,30,31,32,36,39,40,42,44,46,48,50,51,54,56,57,59,60,61,62,65,66,67,68,69,70,73,74,75,77,79,81,83,84,89,90,91,94,96,98,101,102,104,107,108,109,111],[53,104,108,109,110,111],[0,1,2,3,4,5,6,7,10,11,12,14,20,21,22,23,24,25,30,32,33,36,37,38,39,42,45,47,48,49,51,52,53,54,56,59,61,62,64,65,66,68,71,72,74,75,77,79,81,84,85,86,96,97,99,102,103,105,110,111],[0,4,6,7,10,13,14,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,103,104,107,109],[2,4,5,6,8,10,11,12,13,14,15,22,24,25,27,28,29,33,35,36,39,42,44,46,49,51,52,53,57,58,59,60,61,64,66,68,69,70,74,75,77,79,80,81,82,89,93,94,96,97,100,101,105,108,109,110,111],[0,4,5,6,7,10,13,18,19,21,23,24,25,28,29,32,34,35,37,38,39,40,43,46,47,48,50,54,56,59,60,61,62,64,66,67,68,69,71,75,76,77,80,83,86,89,90,92,93,95,100,101,102,104,105,106,107,108,109,110],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,104,106,107,110],[1,2,3,5,6,7,8,9,10,11,14,15,16,17,18,21,22,25,33,38,39,40,45,46,50,53,54,57,59,60,63,64,66,69,71,72,73,76,78,83,85,87,91,93,95,96,98,99,100,101,103,104,107,108,111],[3,4,5,6,7,8,9,10,11,15,16,17,18,19,21,22,23,24,25,26,34,36,42,44,45,46,47,50,52,56,60,62,63,64,67,68,69,70,71,72,73,74,77,79,81,82,85,86,89,90,91,92,93,94,97,98,100,101,102,104,105,107,109,110],[0,1,4,6,7,9,10,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,103,104,106,109,110],[1,2,3,7,12,19,21,23,24,26,27,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,102,105,106,107,109],[1,7,9,11,14,17,18,20,21,22,23,26,27,30,36,37,39,40,42,43,45,46,47,49,52,53,54,56,57,58,60,61,63,65,66,69,71,73,74,75,76,79,81,84,86,89,91,94,95,97,98,99,100,101,103,105,108,110,111],[0,1,2,8,12,13,15,19,20,23,28,29,30,33,34,35,37,45,46,50,52,58,60,62,63,67,69,70,75,76,80,82,84,85,89,94,96,97,99,101,102,106,109,110,111],[5,7,8,9,10,11,12,15,17,19,23,24,25,27,28,32,33,35,38,39,41,42,44,47,48,51,52,56,57,63,64,65,66,67,69,71,73,77,78,79,81,82,83,87,88,89,92,94,95,97,100,103,104,105,106,109,111],[4,104,106,108],[0,1,2,6,7,8,16,18,22,23,24,28,29,31,34,35,37,38,39,40,41,42,44,45,46,47,49,51,53,54,55,57,60,67,69,71,75,76,77,78,79,81,82,87,88,89,90,91,92,93,95,98,99,102,103,105,106,108,109,110,111],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,70,73,80,82,83,84,90,91,93,97,98,100,101,102,104,106,107,108,109,111],[85,104,105,106,107,108],[0,1,2,4,5,7,8,11,12,14,15,17,18,20,21,22,23,30,32,34,36,37,38,39,41,42,43,44,45,47,48,49,51,52,53,54,55,56,57,58,60,61,66,68,70,71,72,74,75,79,81,84,86,91,94,95,97,101,102,103,106,107,108,110],[1,4,14,17,19,21,23,24,27,30,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,102,104,106,108,110],[0,2,3,6,7,10,11,12,16,18,19,22,23,24,25,26,30,31,32,36,37,42,44,45,51,54,55,59,61,62,65,67,70,71,72,73,74,75,76,78,82,84,85,87,89,90,91,92,95,99,100,101,102,103,104,109,110],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,55,57,58,61,63,64,65,68,69,71,72,73,74,77,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,102,103,104,108,109],[2,5,6,8,9,10,11,12,14,15,16,18,19,21,22,23,24,25,30,31,32,36,39,42,44,45,46,49,50,54,56,57,59,61,62,65,67,68,69,70,72,73,74,76,77,82,85,87,89,91,92,94,98,101,102,105,108,109],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,104,105,107,110,111],[4,5,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,71,72,74,79,80,81,82,85,86,89,91,95,96,101,103,107,108,109,111],[96,104,105,106,108,109],[0,1,2,3,4,5,11,12,13,14,17,18,22,23,24,26,27,28,29,31,35,37,38,39,40,41,43,46,51,52,55,56,57,59,61,63,65,69,75,77,80,83,85,89,91,92,95,97,99,101,102,103,104,105,106,107,109,111],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,104,107,109,110,111],[56,104,110],[2,6,7,8,10,12,15,17,18,19,21,24,25,27,32,38,41,43,47,48,50,52,54,55,56,58,59,60,62,63,64,66,67,70,71,72,74,75,77,85,86,91,93,94,95,97,100,101,104,107],[0,3,4,7,8,9,15,16,18,19,20,21,23,24,26,33,34,36,40,42,44,46,47,48,49,50,51,52,56,59,62,63,64,66,67,68,69,70,71,73,74,75,76,77,83,84,86,87,89,91,93,94,96,97,98,101,102,103,105,107],[1,2,7,9,11,12,13,14,17,22,23,24,27,30,37,38,39,43,46,47,52,53,54,55,56,58,59,60,61,63,65,68,69,71,74,75,76,77,81,83,86,87,89,91,92,93,95,97,99,102,105,106,107,110,111],[0,1,2,4,8,9,12,15,16,18,20,21,27,31,32,34,37,46,51,53,54,56,57,63,64,65,69,70,72,73,76,79,81,82,84,87,89,91,92,93,94,98,99,101,103,104,106,107,109,110],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,62,65,67,69,71,72,73,77,83,86,89,90,92,95,96,97,98,99,101,105,107],[1,2,5,6,8,10,11,12,13,15,17,19,21,22,23,25,28,29,30,34,35,37,40,46,48,49,50,51,52,58,62,63,66,67,69,70,71,72,76,79,80,81,83,87,89,90,92,94,97,99,100,101,102,103,104,108,110,111],[0,1,7,10,13,17,18,20,21,23,24,25,27,28,29,30,32,33,34,35,37,38,41,43,45,46,47,48,54,55,56,59,64,66,69,71,72,77,80,82,84,86,89,91,93,95,96,99,100,101,102,105,106,107,109,111],[1,2,4,7,9,12,13,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,103,104,105,107,108,109,111],[3,8,9,10,12,13,14,16,17,18,19,23,24,25,28,33,37,38,39,40,43,44,45,46,48,49,51,52,54,55,57,58,59,60,65,66,70,73,77,78,79,80,85,90,91,93,97,101,102,103,104,105,106,107,108,111],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,102,103,104,107,108,111],[0,2,4,5,7,8,9,11,12,13,15,16,20,21,22,23,24,28,29,30,31,35,38,40,41,43,47,49,53,55,59,60,63,65,70,71,72,73,75,77,82,83,84,85,86,90,94,95,98,101,102,105,106,107,109,110,111],[3,5,6,7,8,10,11,13,15,17,22,24,25,26,27,28,29,30,31,32,33,34,35,36,42,44,46,47,51,53,54,58,59,63,65,68,69,70,71,74,76,77,80,82,86,87,89,90,94,96,100,101,103,105,106,107,109,111],[1,2,3,5,9,11,12,14,16,17,19,21,22,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,105,106,108,110],[0,1,3,7,8,9,14,15,16,17,18,20,21,26,27,30,37,39,46,47,49,51,52,53,56,57,60,61,69,70,71,72,73,79,82,84,86,89,90,91,92,94,97,98,99,101,103,104,105,107,108],[2,3,4,6,8,9,10,11,12,15,17,18,19,20,22,24,25,26,31,34,37,41,46,47,48,49,50,52,53,54,56,60,62,63,64,66,67,68,69,70,71,72,83,85,86,89,90,91,93,94,97,99,100,101,108,109,110,111],[1,3,4,6,8,10,14,15,18,19,21,24,25,26,27,30,31,34,38,39,41,43,48,49,50,55,56,57,58,59,61,62,65,66,67,70,72,75,76,77,79,81,85,87,90,91,94,95,100,101,104,105,106,107,108,109,110],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,23,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,93,96,97,100,101,103,104,105,108,110],[5,7,9,11,14,16,17,20,22,23,27,30,31,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,102,104,106,108],[13,104,105,106,107,109,110],[3,4,7,8,9,11,12,14,16,17,27,30,31,32,34,35,39,47,49,50,51,52,55,57,58,60,61,65,69,70,71,72,73,75,76,78,82,86,87,89,90,91,92,95,97,103,104,105,108,109,110],[0,1,3,4,8,9,13,15,16,17,18,20,21,30,34,36,39,44,46,48,49,51,52,53,57,59,63,65,66,67,69,72,73,75,78,79,82,84,86,87,88,89,91,92,93,94,96,98,99,101,103,104,107,109,110,111],[0,4,6,7,10,11,13,14,18,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,104,107,109,111],[0,4,7,8,9,14,15,16,18,20,24,26,30,31,33,38,40,42,44,46,47,48,49,50,51,52,54,57,61,62,64,65,68,69,71,72,73,74,77,79,81,83,84,87,88,89,90,91,93,95,96,98,100,102,105,106,110],[1,3,5,7,8,9,11,14,15,16,17,22,24,27,30,32,34,35,37,39,47,48,52,53,56,59,60,61,70,73,75,76,77,78,82,83,86,87,91,92,97,98,99,103,104,105,106],[1,3,4,5,6,7,8,10,11,13,14,15,17,19,21,22,23,25,26,28,29,31,32,35,37,39,40,46,47,48,50,51,54,57,58,60,61,62,64,65,66,67,69,70,71,72,80,83,86,89,92,93,94,99,100,101,102,103,106,107,108,110,111],[0,1,2,5,7,8,9,11,12,13,14,15,16,17,19,20,22,27,28,29,31,33,34,35,36,37,38,39,41,42,44,47,48,49,50,55,57,61,62,64,65,66,67,68,70,71,73,74,76,80,84,85,86,87,92,93,94,95,96,98,99,101,104,109,110,111],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,103,104,106,107,110,111],[27,101,103,104,111],[0,1,2,5,6,8,9,10,13,14,19,20,22,23,26,28,29,30,34,35,39,42,45,47,48,49,51,53,54,55,56,57,60,62,65,66,67,68,70,71,72,74,75,77,78,83,84,85,89,90,92,95,97,98,100,102,103,104,109,111],[1,2,3,4,5,9,11,13,14,20,24,25,27,29,31,32,36,37,40,41,44,45,48,49,50,52,54,55,56,58,59,60,61,62,63,66,68,69,70,72,75,78,80,83,86,87,89,90,92,93,95,98,99,101,106,108,109],[1,2,4,5,6,8,9,10,11,12,15,16,17,18,22,25,27,31,33,34,37,40,45,46,48,49,53,54,56,60,63,64,65,66,69,70,73,75,83,85,89,90,91,93,94,96,98,99,100,101,103,110],[0,1,4,6,7,9,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,104,106,109,110,111],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,102,103,105,106,107,109],[2,5,8,9,10,12,13,14,15,17,19,20,21,24,26,28,30,31,35,36,38,39,41,42,45,46,51,52,53,57,58,59,60,61,64,66,69,70,74,77,80,81,82,83,89,90,92,93,94,96,97,99,100,101,106,107,109,111],[0,1,2,8,12,13,15,19,20,23,28,29,30,33,35,37,45,46,50,52,58,60,62,63,67,69,70,75,80,82,84,85,89,94,96,97,99,101,102,103,106,109,110,111],[0,1,2,3,4,5,6,7,9,10,11,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,103,105,107,111],[1,2,6,7,8,9,10,12,13,14,15,16,19,21,25,27,28,29,31,34,35,36,37,38,39,40,41,42,43,44,45,47,50,51,57,60,61,62,64,65,67,68,70,71,72,73,74,75,79,80,81,82,83,86,90,93,94,95,98,99,100,101,103,105,108,110],[42,104,105,107,108,111],[5,7,9,16,18,26,27,28,29,30,31,32,35,39,42,45,47,50,51,53,54,55,57,58,60,62,65,68,70,72,73,75,78,80,81,82,85,86,87,89,90,91,92,93,95,104,106,107,108,109,110,111],[46,104,109,111],[1,3,5,6,7,8,9,10,11,14,15,16,18,22,25,26,27,30,33,37,39,40,45,46,47,48,52,53,56,57,60,61,66,69,70,71,73,75,76,79,81,83,85,86,87,89,91,94,96,97,98,99,100,101,103,104,105,106,107,108,109,111],[0,1,2,4,5,7,8,11,12,14,17,18,20,21,22,23,30,32,34,36,37,38,39,41,42,43,44,45,47,48,49,51,52,53,54,55,56,57,58,60,61,66,68,70,71,72,74,75,79,81,84,86,91,94,95,97,99,101,102,104,107,108,109,110,111],[30,104,105,106,109,111],[0,1,2,3,5,6,10,11,12,13,19,20,22,24,25,27,33,36,38,39,42,45,47,48,51,53,57,59,60,61,62,68,70,71,74,75,76,77,81,84,85,86,88,89,93,94,99,101,102,106,107,109,110,111],[51,104,106,107,109,111],[2,5,6,8,9,10,11,12,14,15,16,18,19,21,22,23,24,25,30,31,32,36,39,42,44,45,46,49,50,54,56,57,59,61,62,65,67,68,69,70,72,73,74,76,77,82,85,87,88,89,91,92,94,98,100,101,102,103,105,108,109],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,36,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,103,104,105,107,110],[0,2,3,5,6,10,11,13,14,19,20,22,23,25,30,31,32,36,38,40,45,51,54,56,61,63,65,66,67,70,71,72,75,76,78,79,81,82,83,84,85,89,90,92,93,95,100,101,106,107,108,109],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,27,32,33,34,36,38,40,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,102,103,104,105,106,107,108,109,110,111],[81,104,105,107,108,109,111],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,60,66,72,75,76,79,81,82,83,84,85,87,90,92,95,96,100,101,106,109,110],[2,4,5,8,9,13,18,20,24,25,27,28,30,32,34,36,37,41,42,44,48,49,50,51,52,55,56,57,59,60,62,65,66,69,70,72,74,75,76,77,78,79,80,81,83,87,89,92,93,95,97,98,99,101,103,104,105,107,110],[0,3,4,7,8,9,15,16,18,19,20,23,24,26,33,34,36,40,42,44,46,47,48,49,50,51,52,56,59,62,63,64,66,67,68,69,70,71,73,74,75,76,77,78,83,84,86,87,89,91,93,94,96,97,98,101,102,104,105,106,107,110,111],[2,3,4,5,9,11,12,16,22,23,25,26,27,32,34,36,38,41,42,43,44,45,46,48,54,55,58,66,68,69,73,74,75,79,81,82,89,90,92,95,98,101,102,103,106,109],[0,2,7,8,10,11,12,13,14,15,18,19,20,21,22,23,26,27,29,34,35,36,40,44,47,48,49,53,55,56,58,61,66,67,71,73,74,76,77,79,80,81,82,83,86,87,88,94,95,96,97,98,100,101,102,103,109,110],[39,104,106,107,110,111],[2,4,8,10,12,14,15,24,28,29,30,32,35,36,37,41,43,44,46,47,51,53,54,56,59,60,61,66,67,68,69,73,74,75,76,78,79,81,86,88,89,90,93,94,95,97,98,99,100,102,105,107,108,110,111],[1,2,5,6,8,10,11,12,13,15,17,19,21,22,23,25,28,29,30,34,35,37,40,46,48,50,51,52,58,62,63,66,67,69,70,72,76,79,80,81,83,87,89,90,92,94,97,99,100,101,102,111],[1,2,3,4,7,9,12,13,14,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,104,105,107,108,109],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,37,45,50,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,102,104,107,108],[62,104,105,107,108,110,111],[3,5,6,7,8,10,11,13,15,17,22,24,25,26,27,28,29,30,31,32,33,34,35,36,42,44,46,47,51,53,54,58,59,63,65,68,69,70,71,74,75,76,77,80,82,86,87,89,90,96,100,101,105,106,107,109,111],[45,104,105,106,107,108,110,111],[22,104,109,110,111],[86,104,105,109,110,111],[1,4,9,12,14,15,17,18,19,20,22,26,30,32,33,34,35,37,38,40,41,45,46,48,49,50,51,53,55,58,60,61,62,65,67,75,76,78,82,84,91,92,94,95,96,98,99,103,105,106,107,110],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,47,49,50,51,53,57,59,61,62,63,64,67,68,74,77,79,81,84,85,93,99,100,101,102,105,106,108],[58,104,107,109,110,111],[0,3,5,8,9,11,13,14,15,16,17,20,21,22,23,24,26,28,29,32,34,35,38,39,40,41,43,52,54,55,57,59,61,64,70,72,73,75,76,77,79,80,81,82,83,84,85,87,93,94,95,97,98,101,102,103,105,108,109,111],[0,1,4,5,6,9,10,11,13,16,17,18,19,20,22,24,25,26,27,28,29,30,32,34,35,36,37,38,42,48,50,52,54,57,58,59,63,64,65,66,67,68,73,74,77,79,80,81,84,90,91,92,97,98,99,101,103,104,106,107,109,111],[66,104,105,106,108,109,110,111],[0,1,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,59,60,61,63,65,66,69,72,76,77,79,80,81,82,83,84,87,89,90,91,95,96,97,99,100,101,102,103,104,105,107],[1,3,4,5,6,7,8,10,11,13,14,15,19,21,22,23,25,26,28,29,31,32,35,37,39,40,46,47,48,50,51,54,57,58,60,61,62,64,65,66,67,69,70,71,72,80,83,86,89,92,94,99,100,101,102,104,105,106,109],[1,2,4,6,8,9,10,11,12,14,15,16,17,18,20,21,22,23,24,25,27,31,32,33,36,40,41,42,44,46,49,54,55,56,57,59,60,65,69,70,73,74,75,77,83,84,85,87,89,90,94,96,98,99,100,102,103,105,106,107,108],[1,2,3,5,6,7,8,9,10,11,14,15,16,17,18,21,22,25,33,38,39,40,45,46,50,53,54,57,59,60,63,64,66,69,71,72,73,76,78,83,85,87,91,93,95,96,98,99,100,103,104,107,108,111],[0,2,5,7,8,11,12,15,18,19,20,22,24,27,32,33,38,40,43,45,47,49,50,51,52,54,55,56,58,59,62,63,64,67,70,71,76,77,79,81,82,83,84,86,87,90,91,92,93,94,95,96,97,101,103,105,106,107,109],[59,104,106],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,26,27,32,33,34,36,38,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,101,102,103,110],[1,2,4,5,6,8,9,10,11,12,15,16,17,18,22,25,27,31,32,33,34,37,40,45,46,48,49,53,54,56,60,63,64,65,66,69,70,73,75,83,85,87,89,90,91,93,94,96,98,99,100,101,110],[73,104,105,107],[1,8,9,10,12,13,15,17,18,19,22,25,29,30,33,34,37,39,40,42,43,44,46,48,49,52,54,55,57,59,60,63,65,66,67,73,75,76,78,80,82,85,86,88,90,91,93,94,97,99,100,101,102,104,106,107,109,110],[0,1,2,3,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,104,105,106,107,108,111],[0,2,3,4,7,9,10,13,15,17,18,19,21,22,23,24,25,26,27,30,31,32,34,36,39,43,46,47,50,52,53,57,60,62,63,68,69,70,71,72,73,74,77,78,79,80,81,83,88,89,90,91,92,93,94,97,100,101,102,105,108,110],[70,104,107,108],[2,4,6,7,8,9,10,12,13,15,16,17,23,24,25,28,30,31,33,35,38,41,43,45,47,48,51,53,55,59,63,65,66,70,71,73,76,77,79,80,81,86,87,92,94,95,96,98,100,101,102,103,105,107,111],[0,3,7,8,13,15,20,21,24,26,27,28,29,30,31,32,34,35,36,40,42,44,45,46,47,48,49,53,54,58,59,60,63,65,66,68,69,70,71,72,74,77,79,80,81,83,84,85,86,92,94,101,105,107,110,111],[2,3,5,11,12,13,18,19,21,22,26,28,29,30,31,33,34,35,36,38,41,42,43,44,46,48,50,51,52,53,55,56,60,62,64,65,66,67,68,69,72,74,76,80,82,87,89,90,91,93,95,96,97,101,103,104,105,107,108,109,110,111],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,85,89,90,92,93,95,98,99,100,101,103,105,108,109],[1,2,3,5,6,7,8,9,10,11,14,15,16,18,22,25,26,27,30,33,37,39,40,45,46,47,48,52,53,56,57,61,66,69,70,71,73,75,76,79,81,83,85,86,87,89,91,94,96,97,98,99,100,101,106,107,108],[63,104,105,106,109],[2,4,5,6,7,8,10,12,14,15,16,17,20,23,25,27,32,33,34,36,37,38,39,40,41,42,43,44,50,54,56,57,58,60,71,72,73,74,75,76,77,78,83,85,87,89,90,94,96,99,100,102,104,105,108],[2,3,4,7,12,14,17,26,30,31,32,34,39,44,47,49,52,54,57,60,61,63,64,65,71,76,79,81,86,87,90,93,97,101,106,107,108,110],[77,104,106,107,109],[3,6,9,10,13,14,15,16,23,24,25,26,28,29,32,33,34,35,38,39,41,43,45,48,49,51,52,53,54,55,57,59,60,61,64,66,70,73,77,80,90,92,93,94,95,96,97,98,100,101,102,103,105,106,108,110,111],[19,104,105,108,109],[0,2,4,8,12,13,14,15,17,20,21,24,27,28,29,35,36,39,40,42,44,45,46,48,52,53,57,58,59,61,64,66,68,69,70,72,74,76,77,80,83,84,85,87,89,90,92,93,94,96,97,101,104,109,111],[0,104,107,108,109],[0,1,3,4,7,8,13,14,15,17,19,20,23,26,28,29,31,32,33,35,37,39,45,46,47,49,50,54,57,58,61,62,64,65,67,69,70,71,75,76,79,80,81,82,84,85,86,87,89,90,93,94,96,97,99,101,102,107,108,109,111],[1,2,6,7,8,9,10,12,13,14,15,16,19,21,25,27,28,29,31,34,35,36,37,38,39,40,41,42,43,44,45,47,50,51,57,60,61,62,64,65,67,68,70,71,72,73,74,75,79,80,81,82,83,86,90,93,94,95,98,99,100,101,103,107,108,109,110,111],[52,104,105,106,107,108,109],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,56,60,66,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,103,104,106,109],[74,104,105,110],[1,3,4,5,7,13,14,16,17,24,26,30,32,34,36,37,39,41,42,44,45,47,48,52,53,56,59,60,61,63,65,66,71,73,76,77,79,82,83,86,87,90,91,93,97,98,99,101,105,107,109,110,111],[57,104,107,110],[0,1,2,3,5,6,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,102,103,105,107,110],[1,3,6,8,10,15,17,18,23,25,26,31,33,36,37,38,40,41,42,43,44,49,53,55,56,58,60,63,64,65,68,70,74,79,81,82,83,85,92,93,94,95,96,99,100,101,102,106,109,110],[71,104,108,110],[3,104,106,108,110],[0,1,4,5,10,11,12,14,15,17,18,20,22,23,24,25,26,27,29,30,32,35,36,39,40,41,42,45,46,49,50,51,57,58,59,62,63,65,67,68,74,77,78,81,84,91,92,93,94,95,96,98,99,102,103,104,105,106,107,108,110],[50,104,107,108,110],[0,2,3,6,10,12,13,17,18,19,20,25,26,29,30,31,34,35,36,38,40,41,42,43,44,45,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,111],[79,104,105,109,110],[1,3,7,9,11,14,17,19,20,22,23,24,26,30,31,32,33,36,38,39,40,42,43,44,46,48,49,50,55,57,58,60,61,62,63,64,66,67,69,72,74,76,82,87,89,92,93,95,96,102,107,110,111],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,49,50,51,53,57,59,61,62,63,67,68,74,77,79,81,84,85,93,99,100,101,102,103,105,106,108],[1,104,107,109,110],[23,104,105,107,109,110],[20,104,106,107,109,110],[0,2,8,9,12,13,14,15,16,17,18,19,20,23,24,30,31,32,33,36,39,40,42,44,46,48,50,51,54,56,57,59,60,61,62,65,66,67,68,69,70,73,74,75,77,79,81,83,84,89,90,91,94,96,98,101,102,103,104,107,108,109],[0,4,5,7,12,13,15,20,21,22,23,24,26,27,28,29,30,31,38,40,41,43,47,49,50,51,53,54,58,59,60,64,65,69,71,77,78,79,80,81,83,84,85,86,89,90,91,92,93,94,98,101,102,103,104,110,111],[0,1,2,4,7,8,12,14,15,19,20,23,26,27,28,29,30,33,35,36,44,45,46,47,48,50,52,56,58,59,61,62,65,66,69,71,78,79,80,82,84,85,87,88,89,90,93,94,99,102,104,106,108,109,110],[11,104,106,108,109,110],[0,2,5,6,7,9,10,11,12,13,16,18,20,22,25,26,27,28,29,30,31,35,36,38,39,40,47,48,50,53,54,58,59,60,62,65,70,71,72,73,75,80,82,83,84,87,88,90,91,94,95,97,98,101,102,103,106,108,109,111],[0,2,4,5,6,7,8,9,10,11,12,13,15,16,17,18,20,21,22,23,25,26,28,29,30,31,32,33,34,38,41,43,45,46,47,49,53,55,57,63,65,66,69,70,72,73,75,78,79,80,81,83,84,86,89,90,92,95,96,98,100,101,102,103,104,106,108,109,110,111],[43,104,106,107,108,109,110],[61,104,105,106,107,108,109,110],[27,104,111],[1,6,7,9,10,11,12,13,14,15,18,23,24,26,27,28,29,30,32,33,34,35,38,39,40,41,42,43,48,50,52,53,57,58,59,60,63,64,65,66,68,72,74,75,76,78,79,81,82,85,86,87,89,91,93,94,96,98,100,101,102,103,104,105,106,107,111],[3,4,5,6,7,8,9,10,11,15,16,17,18,19,21,22,23,24,25,26,34,36,42,44,45,46,47,50,52,56,59,60,62,63,64,67,68,69,70,71,73,74,77,79,81,82,85,86,89,90,91,92,93,94,97,98,100,101,102,103,105,106,107,109,110],[0,1,5,6,10,11,12,13,14,16,17,21,23,24,26,29,31,33,34,37,38,42,43,45,46,48,50,51,52,56,59,61,62,63,66,70,73,74,75,76,78,80,84,85,86,90,92,93,96,99,100,102,106,108,109,110],[10,104,105,107,111],[0,1,2,3,9,10,11,12,13,14,17,18,19,22,23,24,28,30,35,37,39,43,44,46,48,52,55,56,57,59,60,61,63,65,68,69,72,75,76,77,80,81,82,83,84,87,89,91,92,95,96,97,100,102,106,107,109,111],[1,5,7,11,13,18,22,23,24,27,28,29,30,32,34,35,37,38,40,41,43,46,47,49,51,54,55,56,59,60,64,69,71,75,76,77,79,80,81,82,83,85,86,87,89,90,91,92,93,95,99,101,102,105,107,110,111],[2,3,4,7,12,14,17,26,30,31,32,34,39,47,49,52,54,55,57,60,61,63,64,65,71,76,79,81,86,87,90,93,97,103,105,106,108,109,110,111],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,38,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,90,91,93,97,98,100,101,102,103,106,109,111],[2,4,6,7,8,9,10,12,13,15,16,17,23,24,25,28,29,30,31,33,35,38,41,42,43,45,47,48,51,53,55,59,63,65,66,70,71,73,76,77,79,80,81,86,87,92,94,95,96,98,100,101,102,104,108],[0,3,7,8,13,15,20,21,24,26,27,28,29,30,31,32,34,35,36,40,42,44,45,46,47,49,53,54,58,59,60,63,65,66,68,69,70,71,72,74,77,79,80,81,83,84,85,86,89,92,94,101,103,105,107,110,111],[2,3,7,9,11,12,13,16,19,21,22,27,32,33,34,36,38,39,41,43,44,45,46,47,48,52,54,56,57,58,64,66,67,69,70,73,74,75,76,78,81,86,92,96,97,101,104,107,108],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,104,105,108,111],[60,104,105,109,111],[15,104,106,109,111],[1,4,14,17,19,21,23,24,27,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,63,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,102,103,104,106,108,110,111],[0,3,4,5,8,9,11,14,15,17,18,19,20,22,24,26,27,30,31,33,34,38,39,40,41,43,45,50,51,55,56,57,58,59,60,61,62,65,67,70,77,82,83,84,91,92,94,95,96,101,105,108,109,110],[0,1,4,5,6,7,10,11,13,14,17,19,20,22,24,25,26,27,30,31,32,33,34,36,38,42,45,48,49,51,52,53,54,59,62,63,64,65,68,70,74,75,77,79,84,85,87,88,89,90,94,97,99,102,103,108,109,111],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,52,55,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,102,104,108,109,111],[3,6,8,9,10,13,14,15,16,23,24,25,26,28,29,32,33,34,35,38,39,41,43,45,48,49,51,52,53,54,55,57,59,60,61,64,66,68,70,73,77,80,90,92,93,94,95,96,97,98,100,101,102,105,106,108,110,111],[36,104,105,108,109,111],[4,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,101,107,108,109,111],[3,4,5,6,8,10,11,12,15,17,19,21,22,23,24,25,27,28,29,30,31,32,35,38,39,42,44,46,48,51,52,53,54,56,57,58,59,63,64,65,67,68,69,71,74,75,77,78,79,80,81,82,87,94,95,97,100,103,105,107,109,111],[0,1,3,4,7,8,13,14,15,17,19,20,23,26,28,29,31,32,33,35,37,39,45,46,47,49,50,54,57,58,61,62,64,65,67,69,70,71,75,76,79,80,82,84,85,86,87,89,90,93,94,96,99,101,102,103,104,105],[1,2,6,7,8,9,10,12,13,14,15,16,19,21,25,27,28,29,31,34,35,36,37,38,39,40,41,42,43,44,45,47,50,51,55,57,60,61,62,64,65,67,68,70,71,72,73,74,75,79,80,81,82,83,86,90,93,94,95,99,100,101,107,108,109,110,111],[26,104,105,106,107,108,109,111],[4,5,6,7,9,10,12,13,15,17,19,20,21,28,30,34,36,37,38,42,43,44,47,49,51,54,57,58,63,64,65,67,69,71,74,76,78,79,80,81,83,85,86,87,89,91,92,94,98,99,100,104],[78,104,106,110,111],[0,1,2,4,8,9,12,15,16,18,20,21,27,31,32,34,37,46,51,53,54,56,63,64,65,69,70,72,73,76,79,81,82,84,87,89,90,91,92,93,94,98,99,101,106,109],[0,1,2,4,5,8,9,10,12,13,14,15,16,18,20,23,24,26,27,29,31,33,35,36,37,38,41,43,44,45,46,48,50,52,56,59,61,62,65,66,69,72,74,76,79,80,81,82,87,88,89,90,94,99,100,102,105,107,109,110],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,39,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,102,104,105,106,111],[1,2,3,4,6,12,14,17,18,23,24,25,26,28,29,30,31,32,33,35,38,40,42,46,47,49,51,54,55,58,59,61,63,64,65,66,67,69,70,73,75,76,78,82,83,85,86,88,89,90,91,92,96,97,98,101,103,105,106,107,108,109,111],[1,3,5,6,8,9,10,13,14,15,18,20,21,23,24,25,28,29,31,32,33,34,35,37,39,40,43,44,45,49,51,52,56,57,59,60,61,66,68,70,73,77,79,80,81,82,84,87,90,91,95,96,97,98,99,101,103,106,107,108,109,110],[14,104,106,108,110,111],[0,1,3,4,5,8,9,11,13,15,19,20,22,26,27,28,29,30,32,33,35,36,37,38,41,42,43,44,48,50,52,54,55,60,62,63,66,67,68,70,73,74,79,80,81,84,85,90,92,94,95,96,97,98,99,101,103,110,111],[37,104,107,108,110,111],[0,2,4,5,7,8,9,11,12,13,15,16,20,21,22,23,24,28,29,30,31,35,38,40,41,43,47,49,53,55,59,60,62,63,65,70,71,72,73,75,77,80,82,83,84,85,86,90,94,95,98,101,102,103,104,106,108,109],[0,2,3,6,10,12,13,17,18,19,20,25,26,28,29,30,31,34,35,36,38,40,41,42,43,44,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,103,104,105,106,107,108,110],[1,2,3,5,9,11,12,14,16,17,19,21,24,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,103,104,105,106,108,109,111],[0,1,3,7,8,9,14,15,16,17,18,20,21,26,27,30,37,39,46,47,49,51,52,53,56,57,60,61,69,70,71,72,73,82,84,89,90,91,92,94,97,98,99,101,104,105,107,108,111],[2,6,7,8,9,10,17,19,20,22,23,25,26,35,36,39,42,43,44,45,46,47,48,49,50,51,52,54,56,57,60,62,65,67,68,70,71,74,75,78,83,84,85,86,87,90,97,98,100,101,102,105,106,108,109,110],[3,4,6,8,10,14,15,18,19,21,24,25,26,27,30,31,34,38,39,41,43,48,49,50,55,56,57,59,61,62,65,66,67,70,72,75,76,77,79,81,85,87,90,91,94,95,100,101,103,104,105,106,107,108,109,110,111],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,67,71,72,75,82,83,84,85,86,92,93,96,97,100,101,107,108,109],[5,7,9,11,14,16,17,22,23,27,30,31,35,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,102,103,107,108,109,110],[0,2,8,9,12,14,15,16,17,18,19,20,23,24,30,31,32,36,39,40,42,44,46,48,50,51,54,56,57,59,60,61,62,65,66,67,68,69,70,73,74,75,77,79,81,83,84,89,90,91,94,96,98,101,102,105,106,108,110],[0,1,2,3,4,5,6,7,10,11,12,14,20,21,22,23,24,25,30,32,33,36,37,38,39,42,45,47,48,49,51,52,53,54,56,59,61,62,64,65,66,68,71,72,74,75,77,79,81,84,85,86,96,97,99,102,103,104,108,109],[0,4,6,7,10,13,14,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,103,106,107,108,110,111],[2,4,5,6,8,10,11,12,13,14,15,22,24,25,27,28,29,33,35,36,39,42,44,46,49,51,52,53,57,58,59,60,61,64,66,68,69,70,74,75,77,79,80,81,82,89,93,94,96,97,100,101,104,106],[83,104,107,108,109,110,111],[93,104,105,107,108,109,110,111],[0,4,5,6,7,10,13,18,19,21,23,24,25,28,29,32,34,35,37,38,39,40,43,46,47,48,50,54,56,59,60,61,62,64,66,67,68,69,71,75,76,77,80,83,86,89,90,92,93,95,100,101,102,105,111],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,105,108,109,111]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,2,214],"A_d":4698,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,3],[2,2],[3,2],[4,1],[5,3],[6,3],[7,3],[8,3],[10,3],[11,2],[12,2],[13,3],[15,3],[16,3],[17,2],[18,2],[19,2],[20,2],[21,3],[22,2],[23,1],[24,2],[25,3],[26,2],[27,3],[28,3],[29,3],[30,2],[32,2],[33,2],[34,3],[35,3],[36,3],[37,3],[38,3],[40,3],[41,3],[42,3],[43,2],[45,2],[46,2],[47,3],[48,2],[49,3],[50,2],[51,3],[52,3],[53,1],[54,3],[55,2],[56,2],[58,2],[59,2],[62,2],[63,2],[64,3],[65,3],[66,1],[67,2],[69,2],[70,3],[71,3],[74,3],[75,3],[76,2],[77,2],[78,1],[79,3],[80,3],[81,3],[82,2],[83,2],[84,2],[85,1],[86,3],[87,3],[88,1],[89,2],[90,3],[91,2],[92,2],[93,3],[94,2],[95,2],[96,2],[97,3],[99,3],[101,2],[102,1],[103,2],[104,2],[105,1],[106,1],[107,1],[108,1],[109,1],[110,3],[111,2]],"CZ":[[0,1],[0,3],[0,6],[0,7],[0,8],[0,10],[0,11],[0,13],[0,15],[0,16],[0,17],[0,18],[0,20],[0,21],[0,22],[0,24],[0,25],[0,26],[0,27],[0,28],[0,29],[0,30],[0,32],[0,33],[0,34],[0,35],[0,36],[0,37],[0,38],[0,40],[0,41],[0,42],[0,46],[0,47],[0,48],[0,51],[0,55],[0,56],[0,58],[0,59],[0,63],[0,64],[0,65],[0,69],[0,70],[0,71],[0,74],[0,75],[0,76],[0,77],[0,79],[0,80],[0,81],[0,84],[0,86],[0,89],[0,90],[0,91],[0,92],[0,93],[0,96],[0,99],[0,101],[0,102],[0,103],[0,104],[0,105],[0,107],[0,108],[0,109],[0,111],[1,2],[1,5],[1,7],[1,8],[1,11],[1,12],[1,15],[1,18],[1,19],[1,20],[1,22],[1,24],[1,26],[1,27],[1,32],[1,33],[1,38],[1,40],[1,41],[1,43],[1,45],[1,47],[1,49],[1,50],[1,51],[1,52],[1,54],[1,56],[1,58],[1,59],[1,62],[1,63],[1,64],[1,67],[1,70],[1,71],[1,76],[1,77],[1,79],[1,81],[1,82],[1,83],[1,84],[1,86],[1,87],[1,90],[1,91],[1,92],[1,93],[1,94],[1,95],[1,96],[1,97],[1,106],[1,107],[1,109],[1,111],[2,6],[2,7],[2,8],[2,9],[2,10],[2,12],[2,13],[2,14],[2,15],[2,16],[2,19],[2,21],[2,25],[2,27],[2,28],[2,29],[2,31],[2,34],[2,35],[2,36],[2,37],[2,38],[2,39],[2,40],[2,41],[2,42],[2,43],[2,44],[2,45],[2,47],[2,50],[2,51],[2,57],[2,60],[2,61],[2,62],[2,64],[2,65],[2,67],[2,68],[2,70],[2,71],[2,72],[2,73],[2,74],[2,75],[2,79],[2,80],[2,81],[2,82],[2,83],[2,86],[2,90],[2,93],[2,94],[2,95],[2,98],[2,99],[2,100],[2,101],[2,103],[2,104],[2,106],[2,110],[2,111],[3,5],[3,7],[3,8],[3,9],[3,14],[3,15],[3,17],[3,27],[3,30],[3,31],[3,38],[3,39],[3,40],[3,41],[3,44],[3,46],[3,47],[3,48],[3,49],[3,51],[3,52],[3,54],[3,55],[3,57],[3,60],[3,61],[3,64],[3,68],[3,69],[3,70],[3,71],[3,72],[3,73],[3,79],[3,81],[3,86],[3,87],[3,89],[3,90],[3,93],[3,97],[3,98],[3,100],[3,102],[3,105],[3,108],[3,110],[3,111],[5,6],[5,7],[5,8],[5,10],[5,11],[5,13],[5,15],[5,16],[5,17],[5,18],[5,20],[5,21],[5,22],[5,24],[5,25],[5,26],[5,27],[5,28],[5,29],[5,30],[5,32],[5,33],[5,34],[5,35],[5,36],[5,37],[5,38],[5,40],[5,41],[5,42],[5,46],[5,47],[5,48],[5,51],[5,55],[5,56],[5,58],[5,59],[5,63],[5,64],[5,65],[5,69],[5,70],[5,71],[5,74],[5,75],[5,76],[5,77],[5,79],[5,80],[5,81],[5,84],[5,86],[5,89],[5,90],[5,91],[5,92],[5,93],[5,96],[5,99],[5,101],[5,102],[5,103],[5,104],[5,105],[5,107],[5,108],[5,109],[5,111],[6,7],[6,8],[6,11],[6,12],[6,15],[6,18],[6,19],[6,20],[6,22],[6,24],[6,26],[6,27],[6,32],[6,33],[6,38],[6,40],[6,41],[6,43],[6,45],[6,47],[6,49],[6,50],[6,51],[6,52],[6,54],[6,56],[6,58],[6,59],[6,62],[6,63],[6,64],[6,67],[6,70],[6,71],[6,76],[6,77],[6,79],[6,81],[6,82],[6,83],[6,84],[6,86],[6,87],[6,90],[6,91],[6,92],[6,93],[6,94],[6,95],[6,96],[6,97],[6,106],[6,107],[6,109],[6,111],[7,10],[7,12],[7,13],[7,16],[7,17],[7,19],[7,21],[7,25],[7,28],[7,29],[7,30],[7,34],[7,35],[7,36],[7,37],[7,42],[7,43],[7,45],[7,46],[7,48],[7,49],[7,50],[7,52],[7,54],[7,55],[7,62],[7,65],[7,67],[7,69],[7,74],[7,75],[7,80],[7,82],[7,83],[7,87],[7,89],[7,94],[7,95],[7,97],[7,99],[7,101],[7,102],[7,103],[7,104],[7,105],[7,106],[7,108],[8,10],[8,12],[8,13],[8,16],[8,17],[8,19],[8,21],[8,25],[8,28],[8,29],[8,30],[8,34],[8,35],[8,36],[8,37],[8,42],[8,43],[8,45],[8,46],[8,48],[8,49],[8,50],[8,52],[8,54],[8,55],[8,62],[8,65],[8,67],[8,69],[8,74],[8,75],[8,80],[8,82],[8,83],[8,87],[8,89],[8,94],[8,95],[8,97],[8,99],[8,101],[8,102],[8,103],[8,104],[8,105],[8,106],[8,108],[9,11],[9,12],[9,14],[9,17],[9,18],[9,19],[9,20],[9,22],[9,24],[9,26],[9,30],[9,31],[9,32],[9,33],[9,39],[9,43],[9,44],[9,45],[9,46],[9,48],[9,50],[9,55],[9,56],[9,57],[9,58],[9,59],[9,60],[9,61],[9,62],[9,63],[9,67],[9,68],[9,69],[9,72],[9,73],[9,76],[9,77],[9,82],[9,83],[9,84],[9,89],[9,91],[9,92],[9,94],[9,95],[9,96],[9,98],[9,100],[9,102],[9,105],[9,106],[9,107],[9,108],[9,109],[9,110],[10,11],[10,12],[10,15],[10,18],[10,19],[10,20],[10,22],[10,24],[10,26],[10,27],[10,32],[10,33],[10,38],[10,40],[10,41],[10,43],[10,45],[10,47],[10,49],[10,50],[10,51],[10,52],[10,54],[10,56],[10,58],[10,59],[10,62],[10,63],[10,64],[10,67],[10,70],[10,71],[10,76],[10,77],[10,79],[10,81],[10,82],[10,83],[10,84],[10,86],[10,87],[10,90],[10,91],[10,92],[10,93],[10,94],[10,95],[10,96],[10,97],[10,106],[10,107],[10,109],[10,111],[11,13],[11,14],[11,16],[11,18],[11,20],[11,21],[11,22],[11,24],[11,25],[11,26],[11,28],[11,29],[11,31],[11,32],[11,33],[11,34],[11,35],[11,36],[11,37],[11,39],[11,42],[11,44],[11,49],[11,52],[11,54],[11,56],[11,57],[11,58],[11,59],[11,60],[11,61],[11,63],[11,65],[11,68],[11,72],[11,73],[11,74],[11,75],[11,76],[11,77],[11,80],[11,84],[11,87],[11,91],[11,92],[11,96],[11,97],[11,98],[11,99],[11,100],[11,101],[11,103],[11,104],[11,107],[11,109],[11,110],[12,13],[12,14],[12,15],[12,16],[12,19],[12,21],[12,25],[12,27],[12,28],[12,29],[12,31],[12,34],[12,35],[12,36],[12,37],[12,38],[12,39],[12,40],[12,41],[12,42],[12,43],[12,44],[12,45],[12,47],[12,50],[12,51],[12,57],[12,60],[12,61],[12,62],[12,64],[12,65],[12,67],[12,68],[12,70],[12,71],[12,72],[12,73],[12,74],[12,75],[12,79],[12,80],[12,81],[12,82],[12,83],[12,86],[12,90],[12,93],[12,94],[12,95],[12,98],[12,99],[12,100],[12,101],[12,103],[12,104],[12,106],[12,110],[12,111],[13,15],[13,18],[13,19],[13,20],[13,22],[13,24],[13,26],[13,27],[13,32],[13,33],[13,38],[13,40],[13,41],[13,43],[13,45],[13,47],[13,49],[13,50],[13,51],[13,52],[13,54],[13,56],[13,58],[13,59],[13,62],[13,63],[13,64],[13,67],[13,70],[13,71],[13,76],[13,77],[13,79],[13,81],[13,82],[13,83],[13,84],[13,86],[13,87],[13,90],[13,91],[13,92],[13,93],[13,94],[13,95],[13,96],[13,97],[13,106],[13,107],[13,109],[13,111],[14,17],[14,18],[14,19],[14,20],[14,22],[14,24],[14,26],[14,30],[14,31],[14,32],[14,33],[14,39],[14,43],[14,44],[14,45],[14,46],[14,48],[14,50],[14,55],[14,56],[14,57],[14,58],[14,59],[14,60],[14,61],[14,62],[14,63],[14,67],[14,68],[14,69],[14,72],[14,73],[14,76],[14,77],[14,82],[14,83],[14,84],[14,89],[14,91],[14,92],[14,94],[14,95],[14,96],[14,98],[14,100],[14,102],[14,105],[14,106],[14,107],[14,108],[14,109],[14,110],[15,16],[15,17],[15,19],[15,21],[15,25],[15,28],[15,29],[15,30],[15,34],[15,35],[15,36],[15,37],[15,42],[15,43],[15,45],[15,46],[15,48],[15,49],[15,50],[15,52],[15,54],[15,55],[15,62],[15,65],[15,67],[15,69],[15,74],[15,75],[15,80],[15,82],[15,83],[15,87],[15,89],[15,94],[15,95],[15,97],[15,99],[15,101],[15,102],[15,103],[15,104],[15,105],[15,106],[15,108],[16,18],[16,19],[16,20],[16,22],[16,24],[16,26],[16,27],[16,32],[16,33],[16,38],[16,40],[16,41],[16,43],[16,45],[16,47],[16,49],[16,50],[16,51],[16,52],[16,54],[16,56],[16,58],[16,59],[16,62],[16,63],[16,64],[16,67],[16,70],[16,71],[16,76],[16,77],[16,79],[16,81],[16,82],[16,83],[16,84],[16,86],[16,87],[16,90],[16,91],[16,92],[16,93],[16,94],[16,95],[16,96],[16,97],[16,106],[16,107],[16,109],[16,111],[17,27],[17,30],[17,31],[17,38],[17,39],[17,40],[17,41],[17,44],[17,46],[17,47],[17,48],[17,49],[17,51],[17,52],[17,54],[17,55],[17,57],[17,60],[17,61],[17,64],[17,68],[17,69],[17,70],[17,71],[17,72],[17,73],[17,79],[17,81],[17,86],[17,87],[17,89],[17,90],[17,93],[17,97],[17,98],[17,100],[17,102],[17,105],[17,108],[17,110],[17,111],[18,20],[18,21],[18,22],[18,24],[18,25],[18,26],[18,28],[18,29],[18,31],[18,32],[18,33],[18,34],[18,35],[18,36],[18,37],[18,39],[18,42],[18,44],[18,49],[18,52],[18,54],[18,56],[18,57],[18,58],[18,59],[18,60],[18,61],[18,63],[18,65],[18,68],[18,72],[18,73],[18,74],[18,75],[18,76],[18,77],[18,80],[18,84],[18,87],[18,91],[18,92],[18,96],[18,97],[18,98],[18,99],[18,100],[18,101],[18,103],[18,104],[18,107],[18,109],[18,110],[19,21],[19,25],[19,27],[19,28],[19,29],[19,31],[19,34],[19,35],[19,36],[19,37],[19,38],[19,39],[19,40],[19,41],[19,42],[19,43],[19,44],[19,45],[19,47],[19,50],[19,51],[19,57],[19,60],[19,61],[19,62],[19,64],[19,65],[19,67],[19,68],[19,70],[19,71],[19,72],[19,73],[19,74],[19,75],[19,79],[19,80],[19,81],[19,82],[19,83],[19,86],[19,90],[19,93],[19,94],[19,95],[19,98],[19,99],[19,100],[19,101],[19,103],[19,104],[19,106],[19,110],[19,111],[20,21],[20,22],[20,24],[20,25],[20,26],[20,28],[20,29],[20,31],[20,32],[20,33],[20,34],[20,35],[20,36],[20,37],[20,39],[20,42],[20,44],[20,49],[20,52],[20,54],[20,56],[20,57],[20,58],[20,59],[20,60],[20,61],[20,63],[20,65],[20,68],[20,72],[20,73],[20,74],[20,75],[20,76],[20,77],[20,80],[20,84],[20,87],[20,91],[20,92],[20,96],[20,97],[20,98],[20,99],[20,100],[20,101],[20,103],[20,104],[20,107],[20,109],[20,110],[21,22],[21,24],[21,26],[21,27],[21,32],[21,33],[21,38],[21,40],[21,41],[21,43],[21,45],[21,47],[21,49],[21,50],[21,51],[21,52],[21,54],[21,56],[21,58],[21,59],[21,62],[21,63],[21,64],[21,67],[21,70],[21,71],[21,76],[21,77],[21,79],[21,81],[21,82],[21,83],[21,84],[21,86],[21,87],[21,90],[21,91],[21,92],[21,93],[21,94],[21,95],[21,96],[21,97],[21,106],[21,107],[21,109],[21,111],[22,24],[22,25],[22,26],[22,28],[22,29],[22,31],[22,32],[22,33],[22,34],[22,35],[22,36],[22,37],[22,39],[22,42],[22,44],[22,49],[22,52],[22,54],[22,56],[22,57],[22,58],[22,59],[22,60],[22,61],[22,63],[22,65],[22,68],[22,72],[22,73],[22,74],[22,75],[22,76],[22,77],[22,80],[22,84],[22,87],[22,91],[22,92],[22,96],[22,97],[22,98],[22,99],[22,100],[22,101],[22,103],[22,104],[22,107],[22,109],[22,110],[24,25],[24,26],[24,28],[24,29],[24,31],[24,32],[24,33],[24,34],[24,35],[24,36],[24,37],[24,39],[24,42],[24,44],[24,49],[24,52],[24,54],[24,56],[24,57],[24,58],[24,59],[24,60],[24,61],[24,63],[24,65],[24,68],[24,72],[24,73],[24,74],[24,75],[24,76],[24,77],[24,80],[24,84],[24,87],[24,91],[24,92],[24,96],[24,97],[24,98],[24,99],[24,100],[24,101],[24,103],[24,104],[24,107],[24,109],[24,110],[25,26],[25,27],[25,32],[25,33],[25,38],[25,40],[25,41],[25,43],[25,45],[25,47],[25,49],[25,50],[25,51],[25,52],[25,54],[25,56],[25,58],[25,59],[25,62],[25,63],[25,64],[25,67],[25,70],[25,71],[25,76],[25,77],[25,79],[25,81],[25,82],[25,83],[25,84],[25,86],[25,87],[25,90],[25,91],[25,92],[25,93],[25,94],[25,95],[25,96],[25,97],[25,106],[25,107],[25,109],[25,111],[26,28],[26,29],[26,31],[26,32],[26,33],[26,34],[26,35],[26,36],[26,37],[26,39],[26,42],[26,44],[26,49],[26,52],[26,54],[26,56],[26,57],[26,58],[26,59],[26,60],[26,61],[26,63],[26,65],[26,68],[26,72],[26,73],[26,74],[26,75],[26,76],[26,77],[26,80],[26,84],[26,87],[26,91],[26,92],[26,96],[26,97],[26,98],[26,99],[26,100],[26,101],[26,103],[26,104],[26,107],[26,109],[26,110],[27,28],[27,29],[27,30],[27,34],[27,35],[27,36],[27,37],[27,42],[27,43],[27,45],[27,46],[27,48],[27,49],[27,50],[27,52],[27,54],[27,55],[27,62],[27,65],[27,67],[27,69],[27,74],[27,75],[27,80],[27,82],[27,83],[27,87],[27,89],[27,94],[27,95],[27,97],[27,99],[27,101],[27,102],[27,103],[27,104],[27,105],[27,106],[27,108],[28,32],[28,33],[28,38],[28,40],[28,41],[28,43],[28,45],[28,47],[28,49],[28,50],[28,51],[28,52],[28,54],[28,56],[28,58],[28,59],[28,62],[28,63],[28,64],[28,67],[28,70],[28,71],[28,76],[28,77],[28,79],[28,81],[28,82],[28,83],[28,84],[28,86],[28,87],[28,90],[28,91],[28,92],[28,93],[28,94],[28,95],[28,96],[28,97],[28,106],[28,107],[28,109],[28,111],[29,32],[29,33],[29,38],[29,40],[29,41],[29,43],[29,45],[29,47],[29,49],[29,50],[29,51],[29,52],[29,54],[29,56],[29,58],[29,59],[29,62],[29,63],[29,64],[29,67],[29,70],[29,71],[29,76],[29,77],[29,79],[29,81],[29,82],[29,83],[29,84],[29,86],[29,87],[29,90],[29,91],[29,92],[29,93],[29,94],[29,95],[29,96],[29,97],[29,106],[29,107],[29,109],[29,111],[30,31],[30,38],[30,39],[30,40],[30,41],[30,44],[30,46],[30,47],[30,48],[30,49],[30,51],[30,52],[30,54],[30,55],[30,57],[30,60],[30,61],[30,64],[30,68],[30,69],[30,70],[30,71],[30,72],[30,73],[30,79],[30,81],[30,86],[30,87],[30,89],[30,90],[30,93],[30,97],[30,98],[30,100],[30,102],[30,105],[30,108],[30,110],[30,111],[31,32],[31,33],[31,39],[31,43],[31,44],[31,45],[31,46],[31,48],[31,50],[31,55],[31,56],[31,57],[31,58],[31,59],[31,60],[31,61],[31,62],[31,63],[31,67],[31,68],[31,69],[31,72],[31,73],[31,76],[31,77],[31,82],[31,83],[31,84],[31,89],[31,91],[31,92],[31,94],[31,95],[31,96],[31,98],[31,100],[31,102],[31,105],[31,106],[31,107],[31,108],[31,109],[31,110],[32,33],[32,34],[32,35],[32,36],[32,37],[32,39],[32,42],[32,44],[32,49],[32,52],[32,54],[32,56],[32,57],[32,58],[32,59],[32,60],[32,61],[32,63],[32,65],[32,68],[32,72],[32,73],[32,74],[32,75],[32,76],[32,77],[32,80],[32,84],[32,87],[32,91],[32,92],[32,96],[32,97],[32,98],[32,99],[32,100],[32,101],[32,103],[32,104],[32,107],[32,109],[32,110],[33,34],[33,35],[33,36],[33,37],[33,39],[33,42],[33,44],[33,49],[33,52],[33,54],[33,56],[33,57],[33,58],[33,59],[33,60],[33,61],[33,63],[33,65],[33,68],[33,72],[33,73],[33,74],[33,75],[33,76],[33,77],[33,80],[33,84],[33,87],[33,91],[33,92],[33,96],[33,97],[33,98],[33,99],[33,100],[33,101],[33,103],[33,104],[33,107],[33,109],[33,110],[34,38],[34,40],[34,41],[34,43],[34,45],[34,47],[34,49],[34,50],[34,51],[34,52],[34,54],[34,56],[34,58],[34,59],[34,62],[34,63],[34,64],[34,67],[34,70],[34,71],[34,76],[34,77],[34,79],[34,81],[34,82],[34,83],[34,84],[34,86],[34,87],[34,90],[34,91],[34,92],[34,93],[34,94],[34,95],[34,96],[34,97],[34,106],[34,107],[34,109],[34,111],[35,38],[35,40],[35,41],[35,43],[35,45],[35,47],[35,49],[35,50],[35,51],[35,52],[35,54],[35,56],[35,58],[35,59],[35,62],[35,63],[35,64],[35,67],[35,70],[35,71],[35,76],[35,77],[35,79],[35,81],[35,82],[35,83],[35,84],[35,86],[35,87],[35,90],[35,91],[35,92],[35,93],[35,94],[35,95],[35,96],[35,97],[35,106],[35,107],[35,109],[35,111],[36,38],[36,40],[36,41],[36,43],[36,45],[36,47],[36,49],[36,50],[36,51],[36,52],[36,54],[36,56],[36,58],[36,59],[36,62],[36,63],[36,64],[36,67],[36,70],[36,71],[36,76],[36,77],[36,79],[36,81],[36,82],[36,83],[36,84],[36,86],[36,87],[36,90],[36,91],[36,92],[36,93],[36,94],[36,95],[36,96],[36,97],[36,106],[36,107],[36,109],[36,111],[37,38],[37,40],[37,41],[37,43],[37,45],[37,47],[37,49],[37,50],[37,51],[37,52],[37,54],[37,56],[37,58],[37,59],[37,62],[37,63],[37,64],[37,67],[37,70],[37,71],[37,76],[37,77],[37,79],[37,81],[37,82],[37,83],[37,84],[37,86],[37,87],[37,90],[37,91],[37,92],[37,93],[37,94],[37,95],[37,96],[37,97],[37,106],[37,107],[37,109],[37,111],[38,42],[38,43],[38,45],[38,46],[38,48],[38,49],[38,50],[38,52],[38,54],[38,55],[38,62],[38,65],[38,67],[38,69],[38,74],[38,75],[38,80],[38,82],[38,83],[38,87],[38,89],[38,94],[38,95],[38,97],[38,99],[38,101],[38,102],[38,103],[38,104],[38,105],[38,106],[38,108],[39,43],[39,44],[39,45],[39,46],[39,48],[39,50],[39,55],[39,56],[39,57],[39,58],[39,59],[39,60],[39,61],[39,62],[39,63],[39,67],[39,68],[39,69],[39,72],[39,73],[39,76],[39,77],[39,82],[39,83],[39,84],[39,89],[39,91],[39,92],[39,94],[39,95],[39,96],[39,98],[39,100],[39,102],[39,105],[39,106],[39,107],[39,108],[39,109],[39,110],[40,42],[40,43],[40,45],[40,46],[40,48],[40,49],[40,50],[40,52],[40,54],[40,55],[40,62],[40,65],[40,67],[40,69],[40,74],[40,75],[40,80],[40,82],[40,83],[40,87],[40,89],[40,94],[40,95],[40,97],[40,99],[40,101],[40,102],[40,103],[40,104],[40,105],[40,106],[40,108],[41,42],[41,43],[41,45],[41,46],[41,48],[41,49],[41,50],[41,52],[41,54],[41,55],[41,62],[41,65],[41,67],[41,69],[41,74],[41,75],[41,80],[41,82],[41,83],[41,87],[41,89],[41,94],[41,95],[41,97],[41,99],[41,101],[41,102],[41,103],[41,104],[41,105],[41,106],[41,108],[42,43],[42,45],[42,47],[42,49],[42,50],[42,51],[42,52],[42,54],[42,56],[42,58],[42,59],[42,62],[42,63],[42,64],[42,67],[42,70],[42,71],[42,76],[42,77],[42,79],[42,81],[42,82],[42,83],[42,84],[42,86],[42,87],[42,90],[42,91],[42,92],[42,93],[42,94],[42,95],[42,96],[42,97],[42,106],[42,107],[42,109],[42,111],[43,44],[43,45],[43,47],[43,50],[43,51],[43,57],[43,60],[43,61],[43,62],[43,64],[43,65],[43,67],[43,68],[43,70],[43,71],[43,72],[43,73],[43,74],[43,75],[43,79],[43,80],[43,81],[43,82],[43,83],[43,86],[43,90],[43,93],[43,94],[43,95],[43,98],[43,99],[43,100],[43,101],[43,103],[43,104],[43,106],[43,110],[43,111],[44,45],[44,46],[44,48],[44,50],[44,55],[44,56],[44,57],[44,58],[44,59],[44,60],[44,61],[44,62],[44,63],[44,67],[44,68],[44,69],[44,72],[44,73],[44,76],[44,77],[44,82],[44,83],[44,84],[44,89],[44,91],[44,92],[44,94],[44,95],[44,96],[44,98],[44,100],[44,102],[44,105],[44,106],[44,107],[44,108],[44,109],[44,110],[45,47],[45,50],[45,51],[45,57],[45,60],[45,61],[45,62],[45,64],[45,65],[45,67],[45,68],[45,70],[45,71],[45,72],[45,73],[45,74],[45,75],[45,79],[45,80],[45,81],[45,82],[45,83],[45,86],[45,90],[45,93],[45,94],[45,95],[45,98],[45,99],[45,100],[45,101],[45,103],[45,104],[45,106],[45,110],[45,111],[46,47],[46,48],[46,49],[46,51],[46,52],[46,54],[46,55],[46,57],[46,60],[46,61],[46,64],[46,68],[46,69],[46,70],[46,71],[46,72],[46,73],[46,79],[46,81],[46,86],[46,87],[46,89],[46,90],[46,93],[46,97],[46,98],[46,100],[46,102],[46,105],[46,108],[46,110],[46,111],[47,48],[47,49],[47,50],[47,52],[47,54],[47,55],[47,62],[47,65],[47,67],[47,69],[47,74],[47,75],[47,80],[47,82],[47,83],[47,87],[47,89],[47,94],[47,95],[47,97],[47,99],[47,101],[47,102],[47,103],[47,104],[47,105],[47,106],[47,108],[48,49],[48,51],[48,52],[48,54],[48,55],[48,57],[48,60],[48,61],[48,64],[48,68],[48,69],[48,70],[48,71],[48,72],[48,73],[48,79],[48,81],[48,86],[48,87],[48,89],[48,90],[48,93],[48,97],[48,98],[48,100],[48,102],[48,105],[48,108],[48,110],[48,111],[49,51],[49,55],[49,56],[49,58],[49,59],[49,63],[49,64],[49,65],[49,69],[49,70],[49,71],[49,74],[49,75],[49,76],[49,77],[49,79],[49,80],[49,81],[49,84],[49,86],[49,89],[49,90],[49,91],[49,92],[49,93],[49,96],[49,99],[49,101],[49,102],[49,103],[49,104],[49,105],[49,107],[49,108],[49,109],[49,111],[50,51],[50,57],[50,60],[50,61],[50,62],[50,64],[50,65],[50,67],[50,68],[50,70],[50,71],[50,72],[50,73],[50,74],[50,75],[50,79],[50,80],[50,81],[50,82],[50,83],[50,86],[50,90],[50,93],[50,94],[50,95],[50,98],[50,99],[50,100],[50,101],[50,103],[50,104],[50,106],[50,110],[50,111],[51,52],[51,54],[51,55],[51,62],[51,65],[51,67],[51,69],[51,74],[51,75],[51,80],[51,82],[51,83],[51,87],[51,89],[51,94],[51,95],[51,97],[51,99],[51,101],[51,102],[51,103],[51,104],[51,105],[51,106],[51,108],[52,55],[52,56],[52,58],[52,59],[52,63],[52,64],[52,65],[52,69],[52,70],[52,71],[52,74],[52,75],[52,76],[52,77],[52,79],[52,80],[52,81],[52,84],[52,86],[52,89],[52,90],[52,91],[52,92],[52,93],[52,96],[52,99],[52,101],[52,102],[52,103],[52,104],[52,105],[52,107],[52,108],[52,109],[52,111],[54,55],[54,56],[54,58],[54,59],[54,63],[54,64],[54,65],[54,69],[54,70],[54,71],[54,74],[54,75],[54,76],[54,77],[54,79],[54,80],[54,81],[54,84],[54,86],[54,89],[54,90],[54,91],[54,92],[54,93],[54,96],[54,99],[54,101],[54,102],[54,103],[54,104],[54,105],[54,107],[54,108],[54,109],[54,111],[55,57],[55,60],[55,61],[55,64],[55,68],[55,69],[55,70],[55,71],[55,72],[55,73],[55,79],[55,81],[55,86],[55,87],[55,89],[55,90],[55,93],[55,97],[55,98],[55,100],[55,102],[55,105],[55,108],[55,110],[55,111],[56,57],[56,58],[56,59],[56,60],[56,61],[56,63],[56,65],[56,68],[56,72],[56,73],[56,74],[56,75],[56,76],[56,77],[56,80],[56,84],[56,87],[56,91],[56,92],[56,96],[56,97],[56,98],[56,99],[56,100],[56,101],[56,103],[56,104],[56,107],[56,109],[56,110],[57,58],[57,59],[57,60],[57,61],[57,62],[57,63],[57,67],[57,68],[57,69],[57,72],[57,73],[57,76],[57,77],[57,82],[57,83],[57,84],[57,89],[57,91],[57,92],[57,94],[57,95],[57,96],[57,98],[57,100],[57,102],[57,105],[57,106],[57,107],[57,108],[57,109],[57,110],[58,59],[58,60],[58,61],[58,63],[58,65],[58,68],[58,72],[58,73],[58,74],[58,75],[58,76],[58,77],[58,80],[58,84],[58,87],[58,91],[58,92],[58,96],[58,97],[58,98],[58,99],[58,100],[58,101],[58,103],[58,104],[58,107],[58,109],[58,110],[59,60],[59,61],[59,63],[59,65],[59,68],[59,72],[59,73],[59,74],[59,75],[59,76],[59,77],[59,80],[59,84],[59,87],[59,91],[59,92],[59,96],[59,97],[59,98],[59,99],[59,100],[59,101],[59,103],[59,104],[59,107],[59,109],[59,110],[60,61],[60,62],[60,63],[60,67],[60,68],[60,69],[60,72],[60,73],[60,76],[60,77],[60,82],[60,83],[60,84],[60,89],[60,91],[60,92],[60,94],[60,95],[60,96],[60,98],[60,100],[60,102],[60,105],[60,106],[60,107],[60,108],[60,109],[60,110],[61,62],[61,63],[61,67],[61,68],[61,69],[61,72],[61,73],[61,76],[61,77],[61,82],[61,83],[61,84],[61,89],[61,91],[61,92],[61,94],[61,95],[61,96],[61,98],[61,100],[61,102],[61,105],[61,106],[61,107],[61,108],[61,109],[61,110],[62,64],[62,65],[62,67],[62,68],[62,70],[62,71],[62,72],[62,73],[62,74],[62,75],[62,79],[62,80],[62,81],[62,82],[62,83],[62,86],[62,90],[62,93],[62,94],[62,95],[62,98],[62,99],[62,100],[62,101],[62,103],[62,104],[62,106],[62,110],[62,111],[63,65],[63,68],[63,72],[63,73],[63,74],[63,75],[63,76],[63,77],[63,80],[63,84],[63,87],[63,91],[63,92],[63,96],[63,97],[63,98],[63,99],[63,100],[63,101],[63,103],[63,104],[63,107],[63,109],[63,110],[64,65],[64,67],[64,69],[64,74],[64,75],[64,80],[64,82],[64,83],[64,87],[64,89],[64,94],[64,95],[64,97],[64,99],[64,101],[64,102],[64,103],[64,104],[64,105],[64,106],[64,108],[65,67],[65,70],[65,71],[65,76],[65,77],[65,79],[65,81],[65,82],[65,83],[65,84],[65,86],[65,87],[65,90],[65,91],[65,92],[65,93],[65,94],[65,95],[65,96],[65,97],[65,106],[65,107],[65,109],[65,111],[67,68],[67,70],[67,71],[67,72],[67,73],[67,74],[67,75],[67,79],[67,80],[67,81],[67,82],[67,83],[67,86],[67,90],[67,93],[67,94],[67,95],[67,98],[67,99],[67,100],[67,101],[67,103],[67,104],[67,106],[67,110],[67,111],[68,69],[68,72],[68,73],[68,76],[68,77],[68,82],[68,83],[68,84],[68,89],[68,91],[68,92],[68,94],[68,95],[68,96],[68,98],[68,100],[68,102],[68,105],[68,106],[68,107],[68,108],[68,109],[68,110],[69,70],[69,71],[69,72],[69,73],[69,79],[69,81],[69,86],[69,87],[69,89],[69,90],[69,93],[69,97],[69,98],[69,100],[69,102],[69,105],[69,108],[69,110],[69,111],[70,74],[70,75],[70,80],[70,82],[70,83],[70,87],[70,89],[70,94],[70,95],[70,97],[70,99],[70,101],[70,102],[70,103],[70,104],[70,105],[70,106],[70,108],[71,74],[71,75],[71,80],[71,82],[71,83],[71,87],[71,89],[71,94],[71,95],[71,97],[71,99],[71,101],[71,102],[71,103],[71,104],[71,105],[71,106],[71,108],[72,73],[72,76],[72,77],[72,82],[72,83],[72,84],[72,89],[72,91],[72,92],[72,94],[72,95],[72,96],[72,98],[72,100],[72,102],[72,105],[72,106],[72,107],[72,108],[72,109],[72,110],[73,76],[73,77],[73,82],[73,83],[73,84],[73,89],[73,91],[73,92],[73,94],[73,95],[73,96],[73,98],[73,100],[73,102],[73,105],[73,106],[73,107],[73,108],[73,109],[73,110],[74,76],[74,77],[74,79],[74,81],[74,82],[74,83],[74,84],[74,86],[74,87],[74,90],[74,91],[74,92],[74,93],[74,94],[74,95],[74,96],[74,97],[74,106],[74,107],[74,109],[74,111],[75,76],[75,77],[75,79],[75,81],[75,82],[75,83],[75,84],[75,86],[75,87],[75,90],[75,91],[75,92],[75,93],[75,94],[75,95],[75,96],[75,97],[75,106],[75,107],[75,109],[75,111],[76,77],[76,80],[76,84],[76,87],[76,91],[76,92],[76,96],[76,97],[76,98],[76,99],[76,100],[76,101],[76,103],[76,104],[76,107],[76,109],[76,110],[77,80],[77,84],[77,87],[77,91],[77,92],[77,96],[77,97],[77,98],[77,99],[77,100],[77,101],[77,103],[77,104],[77,107],[77,109],[77,110],[79,80],[79,82],[79,83],[79,87],[79,89],[79,94],[79,95],[79,97],[79,99],[79,101],[79,102],[79,103],[79,104],[79,105],[79,106],[79,108],[80,81],[80,82],[80,83],[80,84],[80,86],[80,87],[80,90],[80,91],[80,92],[80,93],[80,94],[80,95],[80,96],[80,97],[80,106],[80,107],[80,109],[80,111],[81,82],[81,83],[81,87],[81,89],[81,94],[81,95],[81,97],[81,99],[81,101],[81,102],[81,103],[81,104],[81,105],[81,106],[81,108],[82,83],[82,86],[82,90],[82,93],[82,94],[82,95],[82,98],[82,99],[82,100],[82,101],[82,103],[82,104],[82,106],[82,110],[82,111],[83,86],[83,90],[83,93],[83,94],[83,95],[83,98],[83,99],[83,100],[83,101],[83,103],[83,104],[83,106],[83,110],[83,111],[84,87],[84,91],[84,92],[84,96],[84,97],[84,98],[84,99],[84,100],[84,101],[84,103],[84,104],[84,107],[84,109],[84,110],[86,87],[86,89],[86,94],[86,95],[86,97],[86,99],[86,101],[86,102],[86,103],[86,104],[86,105],[86,106],[86,108],[87,89],[87,90],[87,91],[87,92],[87,93],[87,96],[87,99],[87,101],[87,102],[87,103],[87,104],[87,105],[87,107],[87,108],[87,109],[87,111],[89,90],[89,93],[89,97],[89,98],[89,100],[89,102],[89,105],[89,108],[89,110],[89,111],[90,94],[90,95],[90,97],[90,99],[90,101],[90,102],[90,103],[90,104],[90,105],[90,106],[90,108],[91,92],[91,96],[91,97],[91,98],[91,99],[91,100],[91,101],[91,103],[91,104],[91,107],[91,109],[91,110],[92,96],[92,97],[92,98],[92,99],[92,100],[92,101],[92,103],[92,104],[92,107],[92,109],[92,110],[93,94],[93,95],[93,97],[93,99],[93,101],[93,102],[93,103],[93,104],[93,105],[93,106],[93,108],[94,95],[94,98],[94,99],[94,100],[94,101],[94,103],[94,104],[94,106],[94,110],[94,111],[95,98],[95,99],[95,100],[95,101],[95,103],[95,104],[95,106],[95,110],[95,111],[96,97],[96,98],[96,99],[96,100],[96,101],[96,103],[96,104],[96,107],[96,109],[96,110],[97,99],[97,101],[97,102],[97,103],[97,104],[97,105],[97,107],[97,108],[97,109],[97,111],[98,100],[98,102],[98,105],[98,106],[98,107],[98,108],[98,109],[98,110],[99,106],[99,107],[99,109],[99,111],[100,102],[100,105],[100,106],[100,107],[100,108],[100,109],[100,110],[101,106],[101,107],[101,109],[101,111],[102,105],[102,108],[102,110],[102,111],[103,106],[103,107],[103,109],[103,111],[104,106],[104,107],[104,109],[104,111],[105,108],[105,110],[105,111],[106,110],[106,111],[107,109],[107,110],[108,110],[108,111],[109,110]]},"rotation_powers":[[0,7],[2,5],[3,5],[4,5],[5,3],[6,5],[7,3],[8,3],[9,5],[10,5],[11,5],[12,7],[13,5],[14,3],[15,5],[16,5],[19,7],[20,3],[21,7],[22,3],[23,3],[24,7],[25,5],[26,3],[28,5],[29,5],[30,5],[31,7],[32,7],[33,3],[35,3],[36,3],[37,5],[38,7],[42,3],[43,7],[44,5],[47,5],[48,3],[49,3],[50,7],[53,3],[54,3],[55,7],[56,5],[59,5],[60,3],[62,5],[63,3],[64,3],[65,3],[66,3],[68,3],[70,7],[71,3],[72,5],[74,5],[75,3],[79,7],[81,7],[82,3],[83,7],[85,7],[86,5],[89,3],[90,7],[91,3],[94,3],[95,7],[96,5],[100,5],[101,3],[110,5],[111,3],[112,3],[113,5],[115,3],[116,7],[118,3],[121,3],[124,3],[125,3],[127,3],[128,3],[129,3],[130,3],[131,3],[134,3],[136,3],[138,3],[141,3],[144,3],[145,3],[146,3],[147,3],[150,3],[152,3],[153,5],[154,3],[155,3],[156,3],[157,3],[158,3],[160,3],[166,3],[169,3],[171,3],[175,3],[180,3],[181,3],[182,3],[183,3],[184,3],[185,3],[188,3],[190,3],[194,3],[195,3],[196,3],[198,3],[203,3],[204,3],[205,3],[206,7],[207,5],[208,7],[209,3],[210,3],[211,3],[212,3],[213,3],[214,3],[215,3],[216,3],[217,5],[218,3],[219,3],[221,3],[223,3],[225,3],[227,7],[228,3],[232,3],[233,3],[234,3],[235,3],[236,3],[237,3],[241,3],[244,3],[246,3],[248,3],[249,3],[253,3],[255,3],[256,3],[258,3],[260,3],[262,3],[263,3],[266,3],[269,3],[270,3],[271,3],[272,3],[273,3],[274,3],[275,3],[276,3],[280,3],[283,3],[285,3],[292,3],[293,3],[295,3],[296,3],[298,3],[300,3],[304,3],[306,3],[307,3],[308,3],[309,3],[310,3],[318,3],[319,3],[321,3],[327,3],[330,3],[332,3],[333,3],[334,3],[335,3],[336,3],[340,3],[343,3],[345,3],[347,3],[348,3],[350,3],[352,3],[356,3],[359,3],[362,3],[365,3],[366,3],[369,3],[370,3],[371,3],[372,3],[373,3],[374,3],[375,3],[376,3],[379,3],[381,3],[383,3],[387,3],[388,3],[389,3],[390,3],[391,3],[394,3],[395,3],[396,3],[397,3],[399,3],[400,3],[401,3],[403,3]]},"metrics":{"gamma":1.2641097906786891,"gamma_t":null,"gamma_rho":1.2641097906786891,"gamma_claim":1.2641097906786891,"gamma_t_claim":null,"gamma_rho_claim":1.2641097906786891,"v_ex":101,"rate":0.24938271604938272,"t_count":null,"poly_degree":null,"effective_width":101},"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_405_101_3_edbc6b23c2b6.json","label":"paired_column_contraction_405_101_3_edbc6b23c2b6","N":112,"d":3,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^7,3^2, cutoff 4), with searched graph punctures; 3 paired-column contractions","provenance":"gamma frontier release record paired_column_contraction_405_101_3_edbc6b23c2b6 (source catalogue id paired_column_contraction_405_101_3_edbc6b23c2b6); construction: Wills weighted Reed\u2013Muller parent (weights 1^7,3^2, cutoff 4), with searched graph punctures; 3 paired-column contractions; matrix edbc6b23c2b67106...; the release states d=3 (exact), gamma=1.2641097906786891 (exact)","notes":"matrix gamma_frontier_release/matrices/edbc6b23c2b67106c57449273b272620100146f25cebc24b4a68a1b73a9c585c.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"}]}