{"id":"407.101.3.a","row":1032,"stored":{"file":"master_catalog.json","row":1032,"construction":null,"columns_sha256":null},"parameters":{"n":407,"k":101,"d":3,"N":113,"r":12,"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":[[0,3,5,6,7,9,10,11,12,13,14,16,17,18,19,20,21,22,23,25,28,29,30,34,35,37,38,39,40,52,53,54,57,58,59,62,64,66,67,70,71,72,73,75,76,78,80,82,83,84,87,89,91,93,94,95,97,98,100,101,102,103,104,107,108,109,110,111],[41,105,106],[0,1,2,3,4,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,102,106,108,112],[40,105,106,107],[87,105,108],[0,1,4,6,7,9,10,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,104,106,107,108,110,111],[1,2,3,7,12,19,21,23,24,26,27,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,103,105,106,110],[0,2,7,8,9,11,12,13,14,15,17,18,19,21,22,26,27,28,29,33,34,35,36,39,40,42,43,47,49,50,53,54,56,57,61,62,65,66,67,70,71,73,74,76,79,80,81,82,85,86,91,95,96,98,100,101,102,103,104,105,108,109,110],[76,101,102,105,109],[0,1,2,5,7,9,10,11,13,17,20,24,25,27,29,30,32,34,37,38,39,41,42,44,45,46,47,48,50,51,56,57,58,60,62,64,65,66,70,71,73,75,77,78,79,80,81,83,84,85,87,88,92,95,96,99,100,102,103,104,109,111],[0,1,2,6,7,8,16,18,22,23,24,28,29,31,34,35,37,38,39,40,41,42,44,45,46,47,49,51,53,54,55,57,60,67,69,71,75,76,77,78,79,81,82,87,88,89,90,91,92,93,95,98,99,103,104,105,110,111,112],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,70,73,80,82,83,84,90,91,93,97,98,100,101,103,107,110,112],[29,105,106,108,109],[89,105,107,108,109],[84,105,110],[2,105,106,110],[4,5,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,99,101,102,104,105,107,108,109,112],[1,4,14,17,19,21,23,24,27,30,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,103,106,109,110,111],[1,3,6,7,8,10,11,13,15,16,18,20,22,24,25,26,28,29,31,32,33,34,35,36,42,44,46,50,51,52,54,55,58,59,60,61,63,65,69,71,72,73,74,76,78,80,87,90,91,92,94,95,96,97,100,101,102,104,107,108,110,112],[44,105,106,108,110],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,55,57,58,61,63,64,65,68,69,71,72,73,74,77,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,103,104,107,108,109],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,101,102,105,108,109,110,111,112],[8,105,109,110],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,103,108,109,110,111,112],[4,5,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,71,72,74,79,80,81,82,85,86,89,91,95,96,101,104,105,107,108,112],[0,1,2,3,4,5,11,12,13,14,17,18,22,23,24,26,27,28,29,31,35,37,38,39,40,41,43,46,51,52,55,56,57,59,61,63,65,69,75,77,80,83,85,89,91,92,95,97,99,101,103,104,106,107,109,112],[97,105,106,108,109,110],[55,105,107,108,109,110],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,106,107,109,111,112],[0,1,6,7,10,13,17,18,20,21,23,24,25,27,28,29,30,32,33,34,35,37,38,41,43,45,46,47,48,54,55,56,59,64,66,69,71,72,74,77,80,82,84,86,89,91,93,95,96,99,100,101,102,103,106,107,108,110,112],[1,2,3,4,7,9,12,13,16,18,21,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,102,104,105,106,108,110,112],[1,2,7,9,11,12,13,14,17,22,23,24,27,30,37,38,39,43,46,47,52,53,54,55,56,58,59,60,61,63,65,68,69,71,74,75,76,77,81,83,86,87,89,91,92,93,95,97,99,103,105,108,112],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,50,51,52,53,54,56,57,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,102,103,104,111,112],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,62,65,67,69,71,72,73,77,83,86,89,90,92,95,96,97,98,99,101,105,111],[7,105,107,108,111],[91,105,106,107,108,111],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,60,66,71,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,102,104,107,110,111],[0,1,7,10,13,17,18,20,21,23,24,25,27,28,29,30,32,33,34,35,37,38,41,43,45,46,47,48,54,55,56,59,64,66,69,71,72,77,80,82,84,86,89,91,93,95,96,99,100,101,103,105,107,108,109,110,111,112],[1,2,4,7,9,12,13,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,104,106,107,108,110,111,112],[0,1,2,3,9,10,14,15,16,17,18,20,24,25,29,30,34,35,38,39,40,43,44,48,49,50,51,54,55,57,59,62,63,65,66,67,69,73,75,77,78,79,82,84,89,90,91,93,94,96,99,101,102,104,107,108,110],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,103,104,111,112],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,62,65,67,69,71,72,73,77,80,83,86,89,90,95,96,97,98,99,101,102,105,109,111],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,75,76,77,84,85,86,87,90,97,99,100,101,102,103,104,105,106,107,109],[28,105,106,107,108,109,111],[1,2,3,5,9,11,12,14,16,17,19,21,22,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,105,106,107,109,110],[2,3,7,9,12,13,14,16,17,18,19,21,23,26,27,28,29,33,34,35,39,45,47,49,50,51,53,56,57,58,61,62,63,67,71,72,73,75,79,80,85,86,90,91,92,96,98,101,102,103,104,107,108,109,112],[0,1,3,4,6,9,10,11,13,17,18,22,23,24,25,26,28,29,30,31,33,35,41,45,47,48,49,53,54,56,58,64,66,68,71,72,75,80,82,83,84,86,90,91,93,96,100,101,102,103,105,109,110,111],[64,105,106,107,110,111],[0,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,59,60,61,63,65,66,69,72,76,77,79,80,81,82,84,87,89,90,91,95,96,97,99,100,101,102,103,106,109,110,111,112],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,23,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,93,96,97,100,101,104,108,109,110],[5,7,9,11,14,16,17,20,22,23,27,30,31,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,103,108,109,110,111],[0,1,2,3,4,7,9,11,13,14,15,16,17,19,20,23,27,28,29,31,32,33,37,39,45,46,47,49,51,55,57,61,62,63,65,67,71,72,73,76,78,80,84,85,86,87,90,91,92,94,95,96,99,102,103,104,106,107,110,111,112],[2,3,4,9,12,16,17,18,19,21,23,28,29,33,35,36,37,39,44,45,48,49,50,51,53,57,58,59,60,62,65,66,70,72,73,78,79,80,85,86,87,88,91,92,93,97,98,101,102,103,104,106,107,108,109,110,111],[0,4,6,7,10,11,13,14,18,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,107,108,109,111,112],[1,2,4,7,9,12,13,14,16,18,19,23,24,26,28,29,31,34,35,37,38,40,42,44,45,47,48,49,51,54,57,58,60,61,63,64,65,67,68,70,71,72,73,74,75,77,79,80,81,82,83,85,87,88,90,91,93,94,95,97,98,99,100,102,105,107,109,111,112],[0,2,3,5,7,9,11,12,13,14,16,17,19,20,22,23,24,27,28,29,32,33,39,45,46,47,48,50,53,56,58,59,61,62,63,67,69,73,76,77,78,80,83,84,85,86,87,89,91,92,94,96,98,102,103,104,106,108,109,112],[0,2,3,4,5,6,7,10,11,12,14,17,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,93,96,97,100,101,102,104,105,106,111],[5,7,9,11,14,16,17,22,23,27,30,31,36,38,39,41,42,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,102,103,108,109,110,111],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,104,106,109,110,112],[27,101,104],[5,6,9,10,12,14,15,22,26,33,37,39,42,46,47,48,49,50,51,52,53,54,55,56,57,58,63,65,66,68,69,71,72,74,77,78,80,82,83,90,92,94,95,96,98,99,100,102,104,106,107,111,112],[72,105,107,112],[0,3,4,5,8,9,11,12,14,15,19,23,24,25,27,28,30,31,32,33,34,35,36,40,41,44,46,48,49,54,55,56,59,61,66,67,68,72,78,82,83,84,85,86,87,90,92,93,94,95,96,97,98,101,102,103,105,106,107,109,111],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,90,91,93,97,98,100,101,102,103,104,105,107,108,110],[0,1,4,6,7,9,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,106,107,108,110,111],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,103,104,105,106,110,112],[2,5,8,9,10,12,13,14,15,17,19,20,21,24,26,28,30,31,35,36,38,39,41,42,45,46,51,52,53,57,58,59,60,61,64,66,69,70,74,77,80,81,82,83,89,90,92,93,94,96,97,99,100,101,105,106,110],[34,101,102,104,105,109,112],[82,105,106,109,112],[0,1,2,3,4,5,6,7,9,10,11,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,104,105,106,107,108,109],[1,2,6,7,8,9,10,12,13,14,15,16,19,21,25,27,28,29,31,34,35,36,37,38,39,40,41,42,43,44,45,47,50,51,57,60,61,62,64,65,67,68,70,71,72,73,74,75,79,80,81,82,83,86,90,93,94,95,98,99,100,101,104,105,107,111,112],[38,105,108,109,112],[48,105,107,108,109,112],[0,1,2,5,7,8,9,12,13,15,16,18,19,20,23,26,27,31,32,33,34,37,39,42,46,47,51,52,53,54,55,57,63,65,67,68,69,72,73,78,81,84,86,87,90,91,92,93,94,95,96,97,99,102,103,106,107,112],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,103,104,108,109,110,111,112],[4,5,7,11,13,14,15,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,101,102,108,109,110,112],[9,105,108,110,112],[0,1,2,3,5,6,10,11,12,13,19,20,22,24,25,27,33,36,38,39,42,45,47,48,51,53,57,59,60,61,62,68,70,71,74,75,76,77,81,84,85,86,88,89,93,94,99,101,103,105,106,107,111],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,88,91,92,96,97,98,99,100,101,102,104,105,108,109,110,111],[68,105,109,110,112],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,36,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,103,104,108,109,110,111,112],[5,105,107,109,110,112],[0,2,3,5,6,10,11,13,14,19,20,22,23,25,30,31,32,36,38,40,45,51,54,56,61,63,65,66,67,70,71,72,75,76,78,79,81,82,83,84,85,89,90,92,93,95,100,101,105,106,108,112],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,27,32,33,34,36,38,40,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,103,104,106,107,111],[98,105,107,108,109,110,112],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,26,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,104,106,107,109,111,112],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,60,66,72,75,76,79,81,82,83,84,85,87,90,92,95,96,100,101,105,107,110,112],[0,1,4,5,9,12,15,18,19,23,24,25,27,29,32,33,35,36,41,42,44,45,46,48,49,51,55,56,57,58,59,63,65,66,67,72,74,76,77,78,79,81,82,83,84,85,87,92,93,94,95,96,98,101,102,103,104,107,108,110,111],[1,2,3,4,7,9,12,13,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,78,80,82,83,85,86,87,91,93,98,99,101,102,106,107,108,110,111,112],[2,3,4,5,9,11,12,16,22,23,25,26,27,32,34,36,38,41,42,43,44,45,46,48,54,55,58,66,68,69,73,74,75,79,81,82,89,90,92,95,98,101,103,104,105,106,110,111,112],[90,105,108,111,112],[0,2,7,8,10,11,12,13,14,15,18,19,20,21,22,23,26,27,29,34,35,36,40,44,47,48,49,53,55,56,58,61,66,67,71,73,74,76,77,79,80,81,82,83,86,87,88,94,95,96,97,98,100,101,103,104,105,106,108,110,112],[0,1,4,10,13,14,19,20,23,24,32,33,34,36,41,43,44,45,47,50,51,52,53,54,56,58,59,61,62,63,66,68,70,73,74,76,78,79,80,81,82,84,85,86,88,90,93,95,96,98,100,102,105,109,110,111,112],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,51,60,66,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,102,105,107,109,110,112],[0,3,5,7,8,9,14,15,17,27,30,31,38,39,40,41,44,46,47,48,49,51,52,54,55,57,60,61,64,68,69,70,71,72,73,79,81,86,87,89,90,93,97,98,100,103,105],[1,2,3,4,7,9,12,13,14,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,106,107,108,110,111,112],[16,105,106,107,109,111,112],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,37,45,50,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,103,111,112],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,94,97,99,100,101,102,103,105,106,107,109,112],[0,2,4,8,9,13,14,17,18,22,23,26,28,29,32,38,40,41,48,49,51,52,53,55,61,63,65,69,70,76,78,80,85,89,91,92,95,97,98,102,103,104,105,106,107,108,111],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,47,49,50,51,53,57,59,61,62,63,64,67,68,74,77,79,81,84,85,93,99,100,101,103,105,109,110,111,112],[67,105,106,108,110,111,112],[35,105,107,108,110,111,112],[33,105,106,107,108,110,111,112],[1,2,3,5,9,11,12,14,16,17,19,21,22,24,26,30,32,33,37,38,39,40,41,43,45,46,50,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,102,104,105,106,107,110,112],[0,1,4,5,6,9,10,11,13,16,17,18,19,20,22,24,25,26,27,28,29,30,32,34,35,36,37,38,42,48,50,52,54,57,58,59,63,64,65,66,67,68,73,74,77,79,80,81,84,90,91,92,97,98,99,101,104,106,107,108,109,111],[18,105,107,109,110,111,112],[0,1,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,59,60,61,63,65,66,69,72,76,77,79,80,81,82,83,84,87,89,90,91,95,96,97,99,100,101,103,104,106,109,110,111,112],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,96,97,100,101,102,108,109,110],[1,2,4,6,8,9,10,11,12,14,15,16,17,18,20,21,22,23,24,25,27,31,32,33,36,40,41,42,44,46,49,54,55,56,57,59,60,65,69,70,73,74,75,77,83,84,85,87,89,90,94,96,98,99,100,103,104,105,106,110,111,112],[54,105,106,107,108,109,110,111,112],[0,3,5,6,7,9,10,11,12,13,14,16,17,18,19,20,21,22,23,25,28,29,30,34,35,37,38,39,40,52,53,54,57,58,59,62,64,66,67,70,71,72,73,75,76,78,80,82,83,84,87,89,91,93,94,95,97,98,100,102,103,104,107,108,109,110,111],[1,5,7,11,13,18,22,23,24,27,28,29,30,32,34,35,37,38,40,43,46,47,49,51,54,55,56,59,60,64,69,71,75,76,77,79,80,81,83,85,86,87,89,90,91,92,93,95,99,101,102,103,104,105,108,111,112],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,26,27,32,33,34,36,38,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,101,103,104,105,106,107,111],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,87,90,91,93,97,98,100,101,102,103,105,107,108,110,112],[31,105,107,108],[0,3,5,7,8,9,14,15,17,27,30,31,38,39,40,41,44,46,47,48,49,51,52,54,55,57,60,61,64,68,69,70,71,72,73,79,81,86,87,89,90,93,97,98,100,103,105,107,108,109,111,112],[76,105,109],[0,2,9,10,17,18,20,22,23,25,28,35,39,40,42,43,44,45,48,49,50,54,55,57,58,59,62,65,66,69,70,73,76,78,84,86,88,89,90,91,93,96,100,101,102,106,108,109,112],[0,1,2,3,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,106,108,112],[1,3,4,7,8,9,10,12,17,18,20,21,22,24,25,26,27,28,29,31,32,33,35,36,37,39,43,45,47,53,57,58,67,68,71,72,73,74,75,77,78,79,81,82,83,84,85,88,90,91,92,93,96,99,100,101,102,105,110,112],[0,1,4,6,7,9,10,16,17,19,20,24,25,29,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,102,104,105,107,109,110,111],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,89,92,96,97,99,101,102,103,105,106,109,110],[2,3,5,11,12,13,18,19,21,22,26,28,29,30,31,33,34,35,36,38,41,42,43,44,46,48,50,51,52,53,55,56,60,62,64,65,66,67,68,69,72,74,76,80,82,87,89,90,91,93,95,96,97,101,104,107,110,111,112],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,85,89,90,92,93,95,98,99,100,101,104,105,106,109],[0,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,103,105,106,108,109,111,112],[99,105,107,110],[2,4,5,6,7,8,10,12,14,15,16,17,20,23,25,27,32,33,34,36,37,38,39,40,41,42,43,44,50,54,56,57,58,60,71,72,73,74,75,76,77,78,83,85,87,89,90,94,96,99,100,103,106,108,109,110],[2,3,4,7,12,14,17,26,30,31,32,34,39,44,47,49,52,54,57,60,61,63,64,65,71,76,79,81,86,87,90,93,97,101,105,106,107,109,110,111],[100,105,106,107,108,110],[0,1,2,3,6,8,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,102,104,105,106],[69,105,107,109,110],[1,4,14,17,19,21,23,24,27,30,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,63,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,99,101,102,103,106,109,110,111],[2,3,4,7,12,14,17,26,30,31,32,34,39,47,49,52,54,57,60,61,63,64,65,71,76,79,81,86,87,90,93,101,102,105,106,107,110,111],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,102,103,104,105,110],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,56,60,66,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,104,107,110,111],[21,105,107,111],[1,3,4,5,7,13,14,16,17,24,26,30,32,34,36,37,39,41,42,44,45,47,48,52,53,56,59,60,61,63,65,66,71,73,76,77,79,82,83,86,87,90,91,93,97,98,99,101,105,107,108,110,112],[92,105,106,108,111],[0,1,2,3,5,6,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,103,104,105,106,107],[0,2,3,6,10,12,13,17,18,19,20,25,26,28,29,30,31,34,35,36,38,40,41,42,43,44,45,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,92,93,95,97,100,101,102,105,106,107,108,111,112],[6,105,106,109,111],[0,1,4,5,10,11,12,14,15,17,18,20,22,23,24,25,26,27,29,30,32,35,36,39,40,41,42,45,46,49,50,51,57,58,59,62,63,65,67,68,74,77,78,81,84,91,92,93,94,95,96,98,99,103,104,108],[80,105,106,108,109,111],[75,105,107,108,109,111],[0,2,3,6,10,12,13,17,18,19,20,25,26,29,30,31,34,35,36,38,40,41,42,43,44,45,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,105,106,107,108,109,111,112],[24,105,110,111],[1,3,7,9,11,14,17,19,20,22,23,24,26,30,31,32,33,36,38,39,40,42,43,44,46,48,49,50,55,57,58,60,61,62,63,64,66,67,69,72,74,76,82,87,89,92,93,95,96,103,105,107,108,110,112],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,49,50,51,53,57,59,61,62,63,67,68,74,77,79,81,84,85,93,99,100,101,103,104,105,109,110,111],[1,9,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,102,104,106,109,110,112],[0,4,5,7,12,13,15,20,21,22,23,24,26,27,28,29,30,31,38,40,41,43,47,49,50,51,53,54,58,59,60,64,65,69,71,77,78,79,80,81,83,84,85,86,89,90,91,92,93,94,98,101,103,104,109,110,112],[4,7,13,14,26,27,34,36,37,44,47,48,56,59,60,61,63,65,66,67,70,71,75,78,79,87,88,90,93,96,97,102,106,110,111,112],[0,2,5,6,7,9,10,11,12,13,16,18,20,22,25,26,27,28,29,30,31,35,36,38,39,40,47,48,50,53,54,58,59,60,62,65,70,71,72,73,75,80,82,83,84,87,88,90,91,94,95,97,98,101,103,104,105,106,111,112],[1,4,5,6,7,9,10,11,16,17,18,19,21,22,25,26,31,32,35,37,38,41,43,47,49,50,52,53,55,57,58,60,62,65,66,67,72,73,78,79,81,82,83,85,86,90,92,94,95,97,98,99,100,101,102,104,108,110,111],[17,105,106,108,109,110,111],[1,6,7,9,10,11,12,13,14,15,18,23,24,26,27,28,29,30,32,33,34,35,38,39,40,41,42,43,48,50,52,53,57,58,59,60,63,64,65,66,68,72,74,75,76,78,79,81,82,85,86,87,89,91,93,94,96,98,100,101,103,104,107,108],[0,1,2,3,4,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,102,104,105,106,107,108],[2,5,6,8,10,11,14,15,16,17,19,20,21,24,26,28,30,31,35,38,42,43,48,51,56,58,59,60,61,66,67,69,73,74,76,78,82,86,89,90,92,93,94,97,100,102,105,106,107,109],[32,105,108,112],[65,105,107,108,112],[3,8,9,10,11,14,15,17,18,20,22,24,29,33,34,39,43,44,45,48,50,55,56,57,58,59,61,62,65,67,68,70,72,76,77,81,83,85,87,91,92,94,95,99,100,102,105,106,107,111,112],[34,105,109,112],[1,5,7,11,13,18,22,23,24,27,28,29,30,32,34,35,37,38,40,41,43,46,47,49,51,54,55,56,59,60,64,69,71,75,76,77,79,80,81,82,83,85,86,87,89,90,91,92,93,95,99,101,103,105,108,109,111],[12,105,107,109,112],[0,1,3,4,7,8,13,14,15,17,19,20,23,26,28,29,31,32,33,35,37,39,45,46,47,49,50,54,55,57,58,61,62,64,65,67,69,70,71,75,76,79,80,81,82,84,85,86,87,89,90,93,94,96,99,102,103,104,105,107,112],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,38,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,90,91,93,97,98,100,101,103,104,105,107,108,109,110],[0,1,4,6,7,9,10,16,17,19,20,24,25,31,34,37,38,41,42,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,102,106,107,108,110,111],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,102,103,104,105,106,109,110,112],[0,1,3,7,8,9,11,15,16,20,21,22,23,27,28,29,30,32,35,36,37,38,39,41,43,44,47,48,50,54,56,57,60,62,63,64,66,73,74,76,78,80,81,82,84,85,86,89,92,94,99,101,102,103,106,110,111],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,106,109,110],[1,4,14,17,19,21,23,24,27,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,63,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,103,104,106,109,110,111],[1,2,3,4,5,9,11,12,13,14,17,18,22,23,24,26,27,28,29,31,35,37,38,39,40,41,43,46,51,52,55,56,57,59,61,63,65,69,75,77,80,83,85,89,91,92,95,97,99,101,102,103,105,106,107,108,109,110],[0,1,4,5,6,7,10,11,13,14,17,19,20,22,24,25,26,27,30,31,32,33,34,36,38,42,45,48,49,51,52,53,54,59,62,63,64,65,68,70,74,75,77,79,84,85,87,88,89,90,94,97,99,103,104,105,106,108,109],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,52,55,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,103,107,108,109],[88,105,106,107,108,110,112],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,68,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,102,105,106,112],[4,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,101,105,107,108],[0,1,2,3,4,5,6,10,11,13,17,20,21,22,24,25,27,31,32,33,34,37,38,39,42,44,45,48,50,51,53,54,56,57,59,60,62,64,65,68,70,71,74,77,78,79,81,84,85,87,89,95,96,99,100,102,103,104,105,108,109,110,111,112],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,26,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,104,109,111,112],[2,3,4,7,12,14,17,26,30,31,32,34,39,47,49,52,54,57,60,61,63,64,65,71,76,79,86,87,90,93,97,101,102,104,107,108,109,111],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,55,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,100,101,102,103,105,110,112],[95,105,111,112],[4,5,6,7,9,10,12,13,15,17,19,20,21,28,30,34,36,37,38,42,43,44,47,49,51,54,57,58,63,64,65,67,69,71,74,76,78,79,80,81,83,85,86,87,89,91,92,94,98,99,100,106,111,112],[25,105,106,107,111,112],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,50,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,90,91,92,93,96,97,98,101,102,103,105,108],[0,1,2,4,5,8,9,10,12,13,14,15,16,18,20,23,24,26,27,29,31,33,35,36,37,38,41,43,44,45,46,48,50,52,56,59,61,62,65,66,69,72,74,76,79,80,81,82,87,88,89,90,94,99,100,103,105,110,112],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,39,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,103,106,108,111],[1,2,3,4,6,12,14,17,18,23,24,25,26,28,29,30,31,32,33,35,38,40,42,46,47,49,51,54,55,58,59,61,63,64,65,66,67,69,70,73,75,76,78,82,83,85,86,88,89,90,91,92,96,97,98,101,104,105,109,110,111],[49,105,109,111,112],[1,3,5,6,8,9,10,13,14,15,18,20,21,23,24,25,28,29,31,32,33,34,35,37,39,40,43,44,45,49,51,52,56,57,59,60,61,66,68,70,73,77,79,80,81,82,84,87,90,91,95,96,97,98,99,101,104,105,106,107,108,110,112],[2,3,4,5,9,11,12,22,23,26,27,32,34,36,38,41,42,43,44,45,46,48,54,55,58,66,68,69,73,74,75,79,81,82,89,90,92,95,98,101,102,103,104,105,106,109,110,111,112],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,65,67,69,71,72,73,77,83,86,89,90,95,96,97,98,99,101,102,104,106,108],[94,105,107,108,109,111,112],[0,2,3,6,10,12,13,17,18,19,20,25,26,28,29,30,31,34,35,36,38,40,41,42,43,44,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,104,112],[1,2,3,5,9,11,12,14,16,17,19,21,24,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,104,106,107,109,111],[2,3,7,9,12,13,14,16,17,18,19,21,23,26,27,28,29,33,34,35,39,45,47,49,50,51,53,56,57,58,61,62,63,67,71,72,73,75,80,85,90,91,92,96,98,101,102,103,107,108,109,112],[2,6,7,8,9,10,17,19,20,22,23,25,26,35,36,39,42,43,44,45,46,47,48,49,50,51,52,54,56,57,60,62,65,67,68,70,71,74,75,78,83,84,85,86,87,90,97,98,100,101,103,105,106,109,112],[47,105,106,107,110,111,112],[0,1,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,58,59,60,61,63,65,66,69,72,76,77,79,80,81,82,84,87,89,90,91,95,96,97,99,100,101,102,103,104,106,109,110,111,112],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,67,71,72,75,82,83,84,85,86,92,93,96,97,100,101,105,106,109,111,112],[5,7,9,11,14,16,17,22,23,27,30,31,35,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,103,104,105,107,109,112],[1,9,13,14,16,17,18,24,28,29,31,32,33,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,102,105,107,108,109,111],[53,105,109,110,111,112],[0,1,2,3,4,5,6,7,10,11,12,14,20,21,22,23,24,25,30,32,33,36,37,38,39,42,45,47,48,49,51,52,53,54,56,59,61,62,64,65,66,68,71,72,74,75,77,79,81,84,85,86,96,97,99,103,104,106,111,112],[0,4,6,7,10,13,14,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,104,105,108,110],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,49,50,51,53,57,59,61,62,63,64,66,67,68,74,77,79,81,84,85,93,99,100,101,102,103,106,107,109],[1,2,4,5,6,7,8,10,12,15,18,20,21,24,25,30,32,33,38,39,40,43,45,47,48,52,54,56,58,59,61,63,64,66,68,70,71,76,77,82,83,84,85,86,90,92,93,94,95,96,97,99,100,101,102,105,106,108,109,112],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,105,107,108,111],[0,3,5,6,7,9,10,11,12,13,14,16,17,18,19,20,21,22,23,25,28,29,30,34,35,37,38,39,40,52,53,54,57,58,59,62,64,66,67,70,71,72,73,75,76,78,80,82,83,84,87,89,91,93,94,95,97,98,100,101,102,103,104,105,107,108,109,110,111],[0,1,2,3,4,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,102,105,106,107,108,112],[0,1,4,6,7,9,10,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,104,105,107,110,111],[1,2,3,7,12,19,21,23,24,26,27,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,103,106,107,108,110],[0,2,7,8,9,11,12,13,14,15,17,18,19,21,22,26,27,28,29,33,34,35,36,39,40,42,43,47,49,50,53,54,56,57,61,62,65,66,67,70,71,73,74,76,79,80,81,82,85,86,91,95,96,98,100,101,102,103,104,106,107,109,110],[76,101,102],[0,1,2,5,7,9,10,11,13,17,20,24,25,27,29,30,32,34,37,38,39,41,42,44,45,46,47,48,50,51,56,57,58,60,62,64,65,66,70,71,73,75,77,78,79,80,81,83,84,85,87,88,92,95,96,99,100,102,103,104,105,106,111],[4,105,107,109],[0,1,2,6,7,8,16,18,22,23,24,28,29,31,34,35,37,38,39,40,41,42,44,45,46,47,49,51,53,54,55,57,60,67,69,71,75,76,77,78,79,81,82,87,88,89,90,91,92,93,95,98,99,103,104,106,107,109,110,111,112],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,70,73,80,82,83,84,90,91,93,97,98,100,101,103,105,107,108,109,110,112],[85,105,106,107,108,109],[4,5,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,99,101,102,104,108,109,110,112],[1,4,14,17,19,21,23,24,27,30,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,103,105,107,109,111],[1,3,6,7,8,10,11,13,15,16,18,20,22,24,25,26,28,29,31,32,33,34,35,36,42,44,46,50,51,52,54,55,58,59,60,61,63,65,69,71,72,73,74,76,78,80,87,90,91,92,94,95,96,97,100,101,102,104,105,107,112],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,55,57,58,61,63,64,65,68,69,71,72,73,74,77,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,103,104,105,109,110],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,101,102,106,107,109,111,112],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,103,105,106,108,111,112],[4,5,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,71,72,74,79,80,81,82,85,86,89,91,95,96,101,104,108,109,110,112],[96,105,106,107,109,110],[0,1,2,3,4,5,11,12,13,14,17,18,22,23,24,26,27,28,29,31,35,37,38,39,40,41,43,46,51,52,55,56,57,59,61,63,65,69,75,77,80,83,85,89,91,92,95,97,99,101,103,104,105,106,107,108,110,112],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,91,92,96,97,98,99,100,101,105,108,110,111,112],[56,105,111],[0,1,6,7,10,13,17,18,20,21,23,24,25,27,28,29,30,32,33,34,35,37,38,41,43,45,46,47,48,54,55,56,59,64,66,69,71,72,74,77,80,82,84,86,89,91,93,95,96,99,100,101,102,103,105,107,108,110,111,112],[1,2,3,4,7,9,12,13,16,18,21,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,102,104,106,107,108,110,111,112],[1,2,7,9,11,12,13,14,17,22,23,24,27,30,37,38,39,43,46,47,52,53,54,55,56,58,59,60,61,63,65,68,69,71,74,75,76,77,81,83,86,87,89,91,92,93,95,97,99,103,106,107,108,111,112],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,50,51,52,53,54,56,57,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,102,103,104,105,108,112],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,62,65,67,69,71,72,73,77,83,86,89,90,92,95,96,97,98,99,101,106,108],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,60,66,71,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,102,104,105,107,109,110],[0,1,7,10,13,17,18,20,21,23,24,25,27,28,29,30,32,33,34,35,37,38,41,43,45,46,47,48,54,55,56,59,64,66,69,71,72,77,80,82,84,86,89,91,93,95,96,99,100,101,103,106,107,108,110,112],[1,2,4,7,9,12,13,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,104,105,106,108,109,110,112],[0,1,2,3,9,10,14,15,16,17,18,20,24,25,29,30,34,35,38,39,40,43,44,48,49,50,51,54,55,57,59,62,63,65,66,67,69,73,75,77,78,79,82,84,89,90,91,93,94,96,99,101,102,104,105,106,108,109,110,111],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,103,104,105,108,109,112],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,62,65,67,69,71,72,73,77,80,83,86,89,90,95,96,97,98,99,101,102,106,108],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,75,76,77,84,85,86,87,90,97,99,100,101,102,103,104,106,108,111],[1,2,3,5,9,11,12,14,16,17,19,21,22,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,106,107,109,111],[2,3,7,9,12,13,14,16,17,18,19,21,23,26,27,28,29,33,34,35,39,45,47,49,50,51,53,56,57,58,61,62,63,67,71,72,73,75,79,80,85,86,90,91,92,96,98,101,102,103,104,105,106,107,108,109,110,111,112],[0,1,3,4,6,9,10,11,13,17,18,22,23,24,25,26,28,29,30,31,33,35,41,45,47,48,49,53,54,56,58,64,66,68,71,72,75,80,82,83,84,86,90,91,93,96,100,101,102,103,107,109],[0,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,59,60,61,63,65,66,69,72,76,77,79,80,81,82,84,87,89,90,91,95,96,97,99,100,101,102,103,105,106,108,109,112],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,23,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,93,96,97,100,101,104,105,106,109,111],[5,7,9,11,14,16,17,20,22,23,27,30,31,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,103,105,107,109],[13,105,106,107,108,110,111],[0,1,2,3,4,7,9,11,13,14,15,16,17,19,20,23,27,28,29,31,32,33,37,39,45,46,47,49,51,55,57,61,62,63,65,67,71,72,73,76,78,80,84,85,86,87,90,91,92,94,95,96,99,102,103,104,105,106,107,109,112],[2,3,4,9,12,16,17,18,19,21,23,28,29,33,35,36,37,39,44,45,48,49,50,51,53,57,58,59,60,62,65,66,70,72,73,78,79,80,85,86,87,88,91,92,93,97,98,101,102,103,104,105,107,108],[0,4,6,7,10,11,13,14,18,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,105,108,110,112],[1,2,4,7,9,12,13,14,16,18,19,23,24,26,28,29,31,34,35,37,38,40,42,44,45,47,48,49,51,54,57,58,60,61,63,64,65,67,68,70,71,72,73,74,75,77,79,80,81,82,83,85,87,88,90,91,93,94,95,97,98,99,100,102,106,110,112],[0,2,3,5,7,9,11,12,13,14,16,17,19,20,22,23,24,27,28,29,32,33,39,45,46,47,48,50,53,56,58,59,61,62,63,67,69,73,76,77,78,80,83,84,85,86,87,89,91,92,94,96,98,102,103,104,105,106,110,111,112],[0,2,3,4,5,6,7,10,11,12,14,17,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,93,96,97,100,101,102,104,108,109,110],[5,7,9,11,14,16,17,22,23,27,30,31,36,38,39,41,42,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,102,103,105,107],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,104,105,107,108,111,112],[27,101,104,105,112],[5,6,9,10,12,14,15,22,26,33,37,39,42,46,47,48,49,50,51,52,53,54,55,56,57,58,63,65,66,68,69,71,72,74,77,78,80,82,83,90,92,94,95,96,98,99,100,102,104,105,107,111],[0,3,4,5,8,9,11,12,14,15,19,23,24,25,27,28,30,31,32,33,34,35,36,40,41,44,46,48,49,54,55,56,59,61,66,67,68,72,78,82,83,84,85,86,87,90,92,93,94,95,96,97,98,101,102,103,109,111,112],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,90,91,93,97,98,100,101,102,103,104,107,110,112],[0,1,4,6,7,9,16,17,19,20,24,25,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,105,107,110,111,112],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,103,104,106,107,108,110],[2,5,8,9,10,12,13,14,15,17,19,20,21,24,26,28,30,31,35,36,38,39,41,42,45,46,51,52,53,57,58,59,60,61,64,66,69,70,74,77,80,81,82,83,89,90,92,93,94,96,97,99,100,101,107,108,110,112],[34,101,102,104],[0,1,2,3,4,5,6,7,9,10,11,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,104,106,108,112],[1,2,6,7,8,9,10,12,13,14,15,16,19,21,25,27,28,29,31,34,35,36,37,38,39,40,41,42,43,44,45,47,50,51,57,60,61,62,64,65,67,68,70,71,72,73,74,75,79,80,81,82,83,86,90,93,94,95,98,99,100,101,104,106,109,111],[42,105,106,108,109,112],[0,1,2,5,7,8,9,12,13,15,16,18,19,20,23,26,27,31,32,33,34,37,39,42,46,47,51,52,53,54,55,57,63,65,67,68,69,72,73,78,81,84,86,87,90,91,92,93,94,95,96,97,99,102,103,105,108,109],[46,105,110,112],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,103,104,105,106,108,109,111],[4,5,7,11,13,14,15,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,101,102,105,107,108,109],[30,105,106,107,110,112],[0,1,2,3,5,6,10,11,12,13,19,20,22,24,25,27,33,36,38,39,42,45,47,48,51,53,57,59,60,61,62,68,70,71,74,75,76,77,81,84,85,86,88,89,93,94,99,101,103,107,108,110,111,112],[51,105,107,108,110,112],[0,1,5,6,9,10,11,13,14,16,18,20,21,22,24,25,28,29,31,32,33,34,35,36,37,39,42,44,49,52,54,56,57,58,59,60,61,63,65,68,72,73,74,75,76,77,80,84,87,88,91,92,96,97,98,99,100,101,102,104,106,107,109,111,112],[0,2,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,36,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,103,104,105,106,108,111],[0,2,3,5,6,10,11,13,14,19,20,22,23,25,30,31,32,36,38,40,45,51,54,56,61,63,65,66,67,70,71,72,75,76,78,79,81,82,83,84,85,89,90,92,93,95,100,101,107,108,109,110],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,27,32,33,34,36,38,40,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,103,104,105,106,107,108,109,110,111,112],[81,105,106,108,109,110,112],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,60,66,72,75,76,79,81,82,83,84,85,87,90,92,95,96,100,101,107,110,111],[0,1,4,5,9,12,15,18,19,23,24,25,27,29,32,33,35,36,41,42,44,45,46,48,49,51,55,56,57,58,59,63,65,66,67,72,74,76,77,78,79,81,82,83,84,85,87,92,93,94,95,96,98,101,102,103,104,105,106,107,108,110,112],[1,2,3,4,7,9,12,13,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,78,80,82,83,85,86,87,91,93,98,99,101,102,105,106,108,110],[2,3,4,5,9,11,12,16,22,23,25,26,27,32,34,36,38,41,42,43,44,45,46,48,54,55,58,66,68,69,73,74,75,79,81,82,89,90,92,95,98,101,103,104,107,110],[0,2,7,8,10,11,12,13,14,15,18,19,20,21,22,23,26,27,29,34,35,36,40,44,47,48,49,53,55,56,58,61,66,67,71,73,74,76,77,79,80,81,82,83,86,87,88,94,95,96,97,98,100,101,103,104,110,111],[39,105,107,108,111,112],[0,1,4,10,13,14,19,20,23,24,32,33,34,36,41,43,44,45,47,50,51,52,53,54,56,58,59,61,62,63,66,68,70,73,74,76,78,79,80,81,82,84,85,86,88,90,93,95,96,98,100,102,106,107,108,109,110],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,51,60,66,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,102,107,110,111],[1,2,3,4,7,9,12,13,14,16,18,24,26,28,29,30,35,36,37,40,42,44,45,47,48,49,51,56,58,59,60,64,66,68,71,73,74,76,77,80,82,83,85,86,87,91,93,98,99,101,105,106,108,109,110],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,37,45,50,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,91,92,93,96,97,98,101,103,105,108,109],[62,105,106,108,109,111,112],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,94,97,99,100,101,102,103,106,108,111],[45,105,106,107,108,109,111,112],[22,105,110,111,112],[86,105,106,110,111,112],[0,2,4,8,9,13,14,17,18,22,23,26,28,29,32,38,40,41,48,49,51,52,53,55,61,63,65,69,70,76,78,80,85,89,91,92,95,97,98,102,103,104,106,108,110,112],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,47,49,50,51,53,57,59,61,62,63,64,67,68,74,77,79,81,84,85,93,99,100,101,103,106,107,109],[58,105,108,110,111,112],[1,2,3,5,9,11,12,14,16,17,19,21,22,24,26,30,32,33,37,38,39,40,41,43,45,46,50,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,102,104,106,107,109,111],[0,1,4,5,6,9,10,11,13,16,17,18,19,20,22,24,25,26,27,28,29,30,32,34,35,36,37,38,42,48,50,52,54,57,58,59,63,64,65,66,67,68,73,74,77,79,80,81,84,90,91,92,97,98,99,101,104,105,107,108,110,112],[66,105,106,107,109,110,111,112],[0,1,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,59,60,61,63,65,66,69,72,76,77,79,80,81,82,83,84,87,89,90,91,95,96,97,99,100,101,103,104,105,106,108],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,71,72,75,82,83,84,85,86,92,96,97,100,101,102,105,106,111,112],[1,2,4,6,8,9,10,11,12,14,15,16,17,18,20,21,22,23,24,25,27,31,32,33,36,40,41,42,44,46,49,54,55,56,57,59,60,65,69,70,73,74,75,77,83,84,85,87,89,90,94,96,98,99,100,103,104,106,107,108,109],[0,3,5,6,7,9,10,11,12,13,14,16,17,18,19,20,21,22,23,25,28,29,30,34,35,37,38,39,40,52,53,54,57,58,59,62,64,66,67,70,71,72,73,75,76,78,80,82,83,84,87,89,91,93,94,95,97,98,100,102,103,104,105,107,108,109,110,111],[1,5,7,11,13,18,22,23,24,27,28,29,30,32,34,35,37,38,40,43,46,47,49,51,54,55,56,59,60,64,69,71,75,76,77,79,80,81,83,85,86,87,89,90,91,92,93,95,99,101,102,103,104,106,108,111,112],[59,105,107],[0,2,3,4,6,9,10,12,16,17,20,21,23,25,26,27,32,33,34,36,38,41,42,43,44,46,49,51,54,55,58,60,68,69,72,73,74,76,83,84,85,87,89,95,96,98,100,101,103,104,111],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,87,90,91,93,97,98,100,101,102,103,107,110,112],[73,105,106,108],[0,2,9,10,17,18,20,22,23,25,28,35,39,40,42,43,44,45,48,49,50,54,55,57,58,59,62,65,66,69,70,73,76,78,84,86,88,89,90,91,93,96,100,101,102,105,108,112],[0,1,2,3,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,72,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,105,106,107,108,109,112],[1,3,4,7,8,9,10,12,17,18,20,21,22,24,25,26,27,28,29,31,32,33,35,36,37,39,43,45,47,53,57,58,67,68,71,72,73,74,75,77,78,79,81,82,83,84,85,88,90,91,92,93,96,99,100,101,102,106,107,109,110,112],[70,105,108,109],[0,1,4,6,7,9,10,16,17,19,20,24,25,29,31,34,37,38,41,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,102,104,106,107,108,110,111],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,48,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,89,92,96,97,99,101,102,103,106,107,108,110],[2,3,5,11,12,13,18,19,21,22,26,28,29,30,31,33,34,35,36,38,41,42,43,44,46,48,50,51,52,53,55,56,60,62,64,65,66,67,68,69,72,74,76,80,82,87,89,90,91,93,95,96,97,101,104,105,106,108,109,110,111,112],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,85,89,90,92,93,95,98,99,100,101,104,106,109,110],[0,3,5,6,7,9,10,11,12,13,14,16,18,19,20,22,23,25,26,27,28,29,34,35,39,40,47,48,50,53,56,57,58,60,61,62,63,66,67,71,73,76,79,80,81,82,83,84,86,87,91,98,100,101,102,103,108,109,110,111,112],[63,105,106,107,110],[2,4,5,6,7,8,10,12,14,15,16,17,20,23,25,27,32,33,34,36,37,38,39,40,41,42,43,44,50,54,56,57,58,60,71,72,73,74,75,76,77,78,83,85,87,89,90,94,96,99,100,103,105,106,109],[2,3,4,7,12,14,17,26,30,31,32,34,39,44,47,49,52,54,57,60,61,63,64,65,71,76,79,81,86,87,90,93,97,101,107,108,109,111],[77,105,107,108,110],[0,1,2,3,6,8,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,102,104,106,109,110],[19,105,106,109,110],[1,4,14,17,19,21,23,24,27,30,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,63,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,99,101,102,103,105,107,111],[0,105,108,109,110],[2,3,4,7,12,14,17,26,30,31,32,34,39,47,49,52,54,57,60,61,63,64,65,71,76,79,81,86,87,90,93,101,102,107,108,109,111],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,102,103,104,107,108,109],[52,105,106,107,108,109,110],[0,5,6,10,11,17,20,21,22,25,33,40,45,48,49,51,56,60,66,72,75,76,79,81,82,83,84,85,87,90,92,96,100,101,104,105,107,110],[74,105,106,111],[1,3,4,5,7,13,14,16,17,24,26,30,32,34,36,37,39,41,42,44,45,47,48,52,53,56,59,60,61,63,65,66,71,73,76,77,79,82,83,86,87,90,91,93,97,98,99,101,106,108,110,111,112],[57,105,108,111],[0,1,2,3,5,6,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,103,104,106,108,111],[0,2,3,6,10,12,13,17,18,19,20,25,26,28,29,30,31,34,35,36,38,40,41,42,43,44,45,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,92,93,95,97,100,101,102,112],[71,105,109,111],[3,105,107,109,111],[0,1,4,5,10,11,12,14,15,17,18,20,22,23,24,25,26,27,29,30,32,35,36,39,40,41,42,45,46,49,50,51,57,58,59,62,63,65,67,68,74,77,78,81,84,91,92,93,94,95,96,98,99,103,104,105,106,107,108,109,111],[50,105,108,109,111],[0,2,3,6,10,12,13,17,18,19,20,25,26,29,30,31,34,35,36,38,40,41,42,43,44,45,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,112],[79,105,106,110,111],[1,3,7,9,11,14,17,19,20,22,23,24,26,30,31,32,33,36,38,39,40,42,43,44,46,48,49,50,55,57,58,60,61,62,63,64,66,67,69,72,74,76,82,87,89,92,93,95,96,103,108,111,112],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,49,50,51,53,57,59,61,62,63,67,68,74,77,79,81,84,85,93,99,100,101,103,104,106,107,109],[1,105,108,110,111],[23,105,106,108,110,111],[20,105,107,108,110,111],[1,9,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,102,104,105,107,108,109,111,112],[0,4,5,7,12,13,15,20,21,22,23,24,26,27,28,29,30,31,38,40,41,43,47,49,50,51,53,54,58,59,60,64,65,69,71,77,78,79,80,81,83,84,85,86,89,90,91,92,93,94,98,101,103,104,105,111,112],[4,7,13,14,26,27,34,36,37,44,47,48,56,59,60,61,63,65,66,67,70,71,75,78,79,87,88,90,93,96,97,102,105,109,112],[11,105,107,109,110,111],[0,2,5,6,7,9,10,11,12,13,16,18,20,22,25,26,27,28,29,30,31,35,36,38,39,40,47,48,50,53,54,58,59,60,62,65,70,71,72,73,75,80,82,83,84,87,88,90,91,94,95,97,98,101,103,104,107,109,110,112],[1,4,5,6,7,9,10,11,16,17,18,19,21,22,25,26,31,32,35,37,38,41,43,47,49,50,52,53,55,57,58,60,62,65,66,67,72,73,78,79,81,82,83,85,86,90,92,94,95,97,98,99,100,101,102,104,105,109],[43,105,107,108,109,110,111],[61,105,106,107,108,109,110,111],[27,105,112],[1,6,7,9,10,11,12,13,14,15,18,23,24,26,27,28,29,30,32,33,34,35,38,39,40,41,42,43,48,50,52,53,57,58,59,60,63,64,65,66,68,72,74,75,76,78,79,81,82,85,86,87,89,91,93,94,96,98,100,101,103,104,105,106,107,108,112],[0,1,2,3,4,5,6,7,9,10,11,12,13,16,17,18,20,21,22,24,25,26,28,29,30,33,35,36,37,42,44,47,56,58,59,64,68,71,73,74,75,77,79,80,81,84,86,90,91,92,93,96,98,99,100,101,102,104,106,108,112],[2,5,6,8,10,11,14,15,16,17,19,20,21,24,26,28,30,31,35,38,42,43,48,51,56,58,59,60,61,66,67,69,73,74,76,78,82,86,89,90,92,93,94,97,100,102,109,112],[10,105,106,108,112],[3,8,9,10,11,14,15,17,18,20,22,24,29,33,34,39,43,44,45,48,50,55,56,57,58,59,61,62,65,67,68,70,72,76,77,81,83,85,87,91,92,94,95,99,100,102,108,111],[1,5,7,11,13,18,22,23,24,27,28,29,30,32,34,35,37,38,40,41,43,46,47,49,51,54,55,56,59,60,64,69,71,75,76,77,79,80,81,82,83,85,86,87,89,90,91,92,93,95,99,101,103,106,108,111,112],[0,1,3,4,7,8,13,14,15,17,19,20,23,26,28,29,31,32,33,35,37,39,45,46,47,49,50,54,55,57,58,61,62,64,65,67,69,70,71,75,76,79,80,81,82,84,85,86,87,89,90,93,94,96,99,102,103,104,106,109],[0,4,5,6,9,10,11,13,16,17,18,19,20,22,23,25,27,28,29,30,31,32,35,38,40,48,49,50,52,53,54,56,58,62,64,65,66,67,73,80,82,83,84,90,91,93,97,98,100,101,103,104,107,110,112],[0,1,4,6,7,9,10,16,17,19,20,24,25,31,34,37,38,41,42,43,46,47,48,50,51,52,53,55,58,59,60,62,65,66,67,69,71,73,75,76,77,79,81,82,84,85,86,87,89,92,95,97,98,99,100,101,102,105,107,109,110,111,112],[1,2,3,7,12,19,21,23,24,26,27,31,32,33,36,37,40,42,44,47,49,50,52,53,54,59,62,65,66,67,68,71,72,74,75,77,79,81,82,83,86,92,96,97,99,101,102,103,104,106,107,108,110],[0,1,3,7,8,9,11,15,16,20,21,22,23,27,28,29,30,32,35,36,37,38,39,41,43,44,47,48,50,54,56,57,60,62,63,64,66,73,74,76,78,80,81,82,84,85,86,89,92,94,99,101,102,103,105,107,108,109,110,111,112],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,105,106,109,112],[60,105,106,110,112],[15,105,107,110,112],[1,4,14,17,19,21,23,24,27,33,34,36,37,39,40,42,44,48,50,53,57,59,60,61,62,63,64,66,67,68,72,74,75,76,77,82,83,87,90,92,93,96,99,101,103,104,105,107,109,111,112],[1,2,3,4,5,9,11,12,13,14,17,18,22,23,24,26,27,28,29,31,35,37,38,39,40,41,43,46,51,52,55,56,57,59,61,63,65,69,75,77,80,83,85,89,91,92,95,97,99,101,102,103,106,107,109,112],[0,1,4,5,6,7,10,11,13,14,17,19,20,22,24,25,26,27,30,31,32,33,34,36,38,42,45,48,49,51,52,53,54,59,62,63,64,65,68,70,74,75,77,79,84,85,87,88,89,90,94,97,99,103,104,109,110,112],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,52,55,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,98,100,101,103,105,109,110,112],[0,1,2,3,6,9,10,12,14,16,19,20,24,25,26,30,32,37,38,39,41,43,46,48,49,50,51,53,54,55,57,58,59,61,62,63,64,66,67,68,69,73,75,77,82,84,85,89,90,92,93,95,98,99,100,101,102,106,109,110],[36,105,106,109,110,112],[4,7,11,13,14,17,18,19,21,22,28,29,32,33,35,36,38,39,41,42,43,44,46,47,48,49,50,51,53,54,55,56,57,61,62,63,66,67,68,69,71,72,74,79,80,81,82,85,86,89,91,95,96,101,108,109,110,112],[0,1,2,3,4,5,6,10,11,13,17,20,21,22,24,25,27,31,32,33,34,37,38,39,42,44,45,48,50,51,53,54,56,57,59,60,62,64,65,68,70,71,74,77,78,79,81,84,85,87,89,95,96,99,100,102,103,104,106,107,108,111],[2,3,4,7,12,14,17,26,30,31,32,34,39,47,49,52,54,57,60,61,63,64,65,71,76,79,86,87,90,93,97,101,102,104,105,106,107,110,111,112],[0,6,7,9,10,14,16,20,21,23,25,27,30,31,33,36,38,39,40,41,42,43,44,46,47,51,52,55,57,58,61,63,64,65,68,69,71,72,73,74,79,81,83,84,85,86,89,90,93,95,96,97,100,101,102,103,107,108,109],[26,105,106,107,108,109,110,112],[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],[78,105,107,111,112],[4,9,13,16,18,19,21,23,27,28,29,30,31,32,33,35,45,50,51,52,53,54,56,58,60,62,64,65,67,72,73,75,76,79,80,81,85,87,90,91,92,93,96,97,98,101,102,103,111,112],[0,1,2,4,5,8,9,10,12,13,14,15,16,18,20,23,24,26,27,29,31,33,35,36,37,38,41,43,44,45,46,48,50,52,56,59,61,62,65,66,69,72,74,76,79,80,81,82,87,88,89,90,94,99,100,103,106,108,110,111],[0,1,2,3,5,6,7,10,11,12,17,19,20,22,23,24,25,26,27,31,32,36,37,39,42,44,45,47,50,51,52,53,54,59,60,62,65,67,68,71,74,76,77,84,85,86,87,90,97,99,100,101,103,105,106,107,112],[1,2,3,4,6,12,14,17,18,23,24,25,26,28,29,30,31,32,33,35,38,40,42,46,47,49,51,54,55,58,59,61,63,64,65,66,67,69,70,73,75,76,78,82,83,85,86,88,89,90,91,92,96,97,98,101,104,106,107,108,109,110,112],[1,3,5,6,8,9,10,13,14,15,18,20,21,23,24,25,28,29,31,32,33,34,35,37,39,40,43,44,45,49,51,52,56,57,59,60,61,66,68,70,73,77,79,80,81,82,84,87,90,91,95,96,97,98,99,101,104,107,108,109,110,111],[14,105,107,109,111,112],[2,3,4,5,9,11,12,22,23,26,27,32,34,36,38,41,42,43,44,45,46,48,54,55,58,66,68,69,73,74,75,79,81,82,89,90,92,95,98,101,102,103,104,107,110],[37,105,108,109,111,112],[1,4,5,7,9,11,16,19,21,22,24,31,33,34,37,38,40,41,43,45,46,47,49,50,52,53,55,58,59,65,67,69,71,72,73,77,83,86,89,90,95,96,97,98,99,101,102,104,105,109,111,112],[0,2,3,6,10,12,13,17,18,19,20,25,26,28,29,30,31,34,35,36,38,40,41,42,43,44,46,49,50,52,53,55,56,62,64,65,67,68,69,74,75,79,80,81,83,84,89,91,92,93,95,97,100,101,104,105,106,107,108,109,111],[1,2,3,5,9,11,12,14,16,17,19,21,24,26,30,32,33,37,38,39,40,41,43,45,46,50,53,54,55,57,58,59,60,61,62,63,64,67,69,72,73,76,77,79,81,83,87,89,93,95,96,98,99,101,104,105,106,107,109,110,112],[2,3,7,9,12,13,14,16,17,18,19,21,23,26,27,28,29,33,34,35,39,45,47,49,50,51,53,56,57,58,61,62,63,67,71,72,73,75,80,85,90,91,92,96,98,101,102,103,105,106,107,108,109,110,111],[2,6,7,8,9,10,17,19,20,22,23,25,26,35,36,39,42,43,44,45,46,47,48,49,50,51,52,54,56,57,60,62,65,67,68,70,71,74,75,78,83,84,85,86,87,90,97,98,100,101,103,106,107,109,110,111],[0,1,2,3,4,6,10,12,13,14,18,20,21,23,24,25,26,27,28,29,31,33,35,37,38,39,41,43,45,46,48,49,52,55,56,57,58,59,60,61,63,65,66,69,72,76,77,79,80,81,82,84,87,89,90,91,95,96,97,99,100,101,102,103,104,105,106,108,109],[0,2,3,4,5,6,7,10,11,12,14,20,21,22,25,26,30,31,32,33,34,39,40,45,47,48,51,52,54,57,61,63,64,65,66,67,71,72,75,82,83,84,85,86,92,93,96,97,100,101,108,109,110],[5,7,9,11,14,16,17,22,23,27,30,31,35,36,38,39,41,42,43,44,45,46,47,48,49,52,55,57,58,60,61,63,64,65,66,68,69,71,73,74,75,76,82,86,87,89,92,93,95,97,98,101,103,104,108,109,110,111],[1,9,13,14,16,17,18,24,28,29,31,32,33,34,35,36,37,39,40,42,44,45,48,51,52,54,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,102,106,109,110,112],[0,1,2,3,4,5,6,7,10,11,12,14,20,21,22,23,24,25,30,32,33,36,37,38,39,42,45,47,48,49,51,52,53,54,56,59,61,62,64,65,66,68,71,72,74,75,77,79,81,84,85,86,96,97,99,103,104,105,109,110],[0,4,6,7,10,13,14,19,20,25,28,29,32,35,36,38,39,40,41,42,43,44,45,46,47,50,53,54,55,56,57,60,61,62,63,67,68,69,71,74,75,76,80,83,84,86,87,89,90,91,92,95,100,101,104,107,108,109,111,112],[0,1,4,5,6,10,11,14,19,20,22,23,24,25,27,30,34,36,37,39,42,44,45,49,50,51,53,57,59,61,62,63,64,66,67,68,74,77,79,81,84,85,93,99,100,101,102,103,105,110,111,112],[83,105,108,109,110,111,112],[93,105,106,108,109,110,111,112],[1,2,4,5,6,7,8,10,12,15,18,20,21,24,25,30,32,33,38,39,40,43,45,47,48,52,54,56,58,59,61,63,64,66,68,70,71,76,77,82,83,84,85,86,90,92,93,94,95,96,97,99,100,101,102,106,107,110,111],[1,9,13,14,16,17,18,24,28,29,31,32,34,35,36,37,39,40,42,44,45,48,51,52,56,57,58,59,61,63,65,66,68,73,74,77,79,80,81,82,83,85,90,91,97,98,99,101,106,109,110,112]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,2,216],"A_d":2352,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,2],[2,1],[3,2],[4,1],[5,3],[6,2],[7,2],[8,2],[9,3],[10,2],[11,2],[12,1],[13,2],[14,3],[15,2],[16,2],[17,2],[18,2],[19,1],[20,2],[21,2],[22,2],[23,1],[24,2],[25,2],[26,2],[27,2],[28,2],[29,2],[30,2],[31,3],[32,2],[33,2],[34,2],[35,2],[36,2],[37,2],[38,2],[39,3],[40,2],[41,2],[42,2],[43,1],[44,3],[45,1],[46,2],[47,2],[48,2],[49,3],[50,1],[51,2],[52,3],[53,1],[54,3],[55,2],[56,2],[57,3],[58,2],[59,2],[60,3],[61,3],[62,1],[63,2],[64,2],[65,2],[66,1],[67,1],[68,3],[69,2],[70,2],[71,2],[72,3],[73,3],[74,2],[75,2],[76,2],[77,2],[78,1],[79,2],[80,2],[81,2],[82,1],[83,1],[84,2],[85,1],[86,2],[87,3],[88,1],[89,2],[90,2],[91,2],[92,2],[93,2],[94,1],[95,1],[96,2],[97,3],[98,3],[99,2],[100,3],[101,1],[103,1],[104,1],[105,1],[106,1],[108,1],[109,1],[110,1],[111,2],[112,1]],"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],[0,103],[0,104],[0,105],[0,106],[0,108],[0,109],[0,110],[0,112],[1,5],[1,6],[1,9],[1,10],[1,11],[1,13],[1,14],[1,16],[1,18],[1,20],[1,21],[1,22],[1,24],[1,25],[1,26],[1,28],[1,29],[1,31],[1,32],[1,33],[1,34],[1,35],[1,36],[1,37],[1,39],[1,42],[1,44],[1,49],[1,52],[1,54],[1,56],[1,57],[1,58],[1,59],[1,60],[1,61],[1,63],[1,65],[1,68],[1,72],[1,73],[1,74],[1,75],[1,76],[1,77],[1,80],[1,84],[1,87],[1,91],[1,92],[1,96],[1,97],[1,98],[1,99],[1,100],[1,101],[1,104],[1,105],[1,108],[1,110],[1,111],[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],[3,103],[3,106],[3,109],[3,111],[3,112],[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],[5,103],[5,104],[5,105],[5,106],[5,108],[5,109],[5,110],[5,112],[6,9],[6,10],[6,11],[6,13],[6,14],[6,16],[6,18],[6,20],[6,21],[6,22],[6,24],[6,25],[6,26],[6,28],[6,29],[6,31],[6,32],[6,33],[6,34],[6,35],[6,36],[6,37],[6,39],[6,42],[6,44],[6,49],[6,52],[6,54],[6,56],[6,57],[6,58],[6,59],[6,60],[6,61],[6,63],[6,65],[6,68],[6,72],[6,73],[6,74],[6,75],[6,76],[6,77],[6,80],[6,84],[6,87],[6,91],[6,92],[6,96],[6,97],[6,98],[6,99],[6,100],[6,101],[6,104],[6,105],[6,108],[6,110],[6,111],[7,8],[7,9],[7,14],[7,15],[7,17],[7,27],[7,30],[7,31],[7,38],[7,39],[7,40],[7,41],[7,44],[7,46],[7,47],[7,48],[7,49],[7,51],[7,52],[7,54],[7,55],[7,57],[7,60],[7,61],[7,64],[7,68],[7,69],[7,70],[7,71],[7,72],[7,73],[7,79],[7,81],[7,86],[7,87],[7,89],[7,90],[7,93],[7,97],[7,98],[7,100],[7,103],[7,106],[7,109],[7,111],[7,112],[8,9],[8,14],[8,15],[8,17],[8,27],[8,30],[8,31],[8,38],[8,39],[8,40],[8,41],[8,44],[8,46],[8,47],[8,48],[8,49],[8,51],[8,52],[8,54],[8,55],[8,57],[8,60],[8,61],[8,64],[8,68],[8,69],[8,70],[8,71],[8,72],[8,73],[8,79],[8,81],[8,86],[8,87],[8,89],[8,90],[8,93],[8,97],[8,98],[8,100],[8,103],[8,106],[8,109],[8,111],[8,112],[9,10],[9,11],[9,13],[9,15],[9,16],[9,17],[9,18],[9,20],[9,21],[9,22],[9,24],[9,25],[9,26],[9,27],[9,28],[9,29],[9,30],[9,32],[9,33],[9,34],[9,35],[9,36],[9,37],[9,38],[9,40],[9,41],[9,42],[9,46],[9,47],[9,48],[9,51],[9,55],[9,56],[9,58],[9,59],[9,63],[9,64],[9,65],[9,69],[9,70],[9,71],[9,74],[9,75],[9,76],[9,77],[9,79],[9,80],[9,81],[9,84],[9,86],[9,89],[9,90],[9,91],[9,92],[9,93],[9,96],[9,99],[9,101],[9,103],[9,104],[9,105],[9,106],[9,108],[9,109],[9,110],[9,112],[10,11],[10,13],[10,14],[10,16],[10,18],[10,20],[10,21],[10,22],[10,24],[10,25],[10,26],[10,28],[10,29],[10,31],[10,32],[10,33],[10,34],[10,35],[10,36],[10,37],[10,39],[10,42],[10,44],[10,49],[10,52],[10,54],[10,56],[10,57],[10,58],[10,59],[10,60],[10,61],[10,63],[10,65],[10,68],[10,72],[10,73],[10,74],[10,75],[10,76],[10,77],[10,80],[10,84],[10,87],[10,91],[10,92],[10,96],[10,97],[10,98],[10,99],[10,100],[10,101],[10,104],[10,105],[10,108],[10,110],[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],[11,104],[11,105],[11,108],[11,110],[11,111],[13,14],[13,16],[13,18],[13,20],[13,21],[13,22],[13,24],[13,25],[13,26],[13,28],[13,29],[13,31],[13,32],[13,33],[13,34],[13,35],[13,36],[13,37],[13,39],[13,42],[13,44],[13,49],[13,52],[13,54],[13,56],[13,57],[13,58],[13,59],[13,60],[13,61],[13,63],[13,65],[13,68],[13,72],[13,73],[13,74],[13,75],[13,76],[13,77],[13,80],[13,84],[13,87],[13,91],[13,92],[13,96],[13,97],[13,98],[13,99],[13,100],[13,101],[13,104],[13,105],[13,108],[13,110],[13,111],[14,15],[14,16],[14,17],[14,18],[14,20],[14,21],[14,22],[14,24],[14,25],[14,26],[14,27],[14,28],[14,29],[14,30],[14,32],[14,33],[14,34],[14,35],[14,36],[14,37],[14,38],[14,40],[14,41],[14,42],[14,46],[14,47],[14,48],[14,51],[14,55],[14,56],[14,58],[14,59],[14,63],[14,64],[14,65],[14,69],[14,70],[14,71],[14,74],[14,75],[14,76],[14,77],[14,79],[14,80],[14,81],[14,84],[14,86],[14,89],[14,90],[14,91],[14,92],[14,93],[14,96],[14,99],[14,101],[14,103],[14,104],[14,105],[14,106],[14,108],[14,109],[14,110],[14,112],[15,17],[15,27],[15,30],[15,31],[15,38],[15,39],[15,40],[15,41],[15,44],[15,46],[15,47],[15,48],[15,49],[15,51],[15,52],[15,54],[15,55],[15,57],[15,60],[15,61],[15,64],[15,68],[15,69],[15,70],[15,71],[15,72],[15,73],[15,79],[15,81],[15,86],[15,87],[15,89],[15,90],[15,93],[15,97],[15,98],[15,100],[15,103],[15,106],[15,109],[15,111],[15,112],[16,18],[16,20],[16,21],[16,22],[16,24],[16,25],[16,26],[16,28],[16,29],[16,31],[16,32],[16,33],[16,34],[16,35],[16,36],[16,37],[16,39],[16,42],[16,44],[16,49],[16,52],[16,54],[16,56],[16,57],[16,58],[16,59],[16,60],[16,61],[16,63],[16,65],[16,68],[16,72],[16,73],[16,74],[16,75],[16,76],[16,77],[16,80],[16,84],[16,87],[16,91],[16,92],[16,96],[16,97],[16,98],[16,99],[16,100],[16,101],[16,104],[16,105],[16,108],[16,110],[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],[17,103],[17,106],[17,109],[17,111],[17,112],[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],[18,104],[18,105],[18,108],[18,110],[18,111],[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],[20,104],[20,105],[20,108],[20,110],[20,111],[21,22],[21,24],[21,25],[21,26],[21,28],[21,29],[21,31],[21,32],[21,33],[21,34],[21,35],[21,36],[21,37],[21,39],[21,42],[21,44],[21,49],[21,52],[21,54],[21,56],[21,57],[21,58],[21,59],[21,60],[21,61],[21,63],[21,65],[21,68],[21,72],[21,73],[21,74],[21,75],[21,76],[21,77],[21,80],[21,84],[21,87],[21,91],[21,92],[21,96],[21,97],[21,98],[21,99],[21,100],[21,101],[21,104],[21,105],[21,108],[21,110],[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],[22,104],[22,105],[22,108],[22,110],[22,111],[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],[24,104],[24,105],[24,108],[24,110],[24,111],[25,26],[25,28],[25,29],[25,31],[25,32],[25,33],[25,34],[25,35],[25,36],[25,37],[25,39],[25,42],[25,44],[25,49],[25,52],[25,54],[25,56],[25,57],[25,58],[25,59],[25,60],[25,61],[25,63],[25,65],[25,68],[25,72],[25,73],[25,74],[25,75],[25,76],[25,77],[25,80],[25,84],[25,87],[25,91],[25,92],[25,96],[25,97],[25,98],[25,99],[25,100],[25,101],[25,104],[25,105],[25,108],[25,110],[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],[26,104],[26,105],[26,108],[26,110],[26,111],[27,30],[27,31],[27,38],[27,39],[27,40],[27,41],[27,44],[27,46],[27,47],[27,48],[27,49],[27,51],[27,52],[27,54],[27,55],[27,57],[27,60],[27,61],[27,64],[27,68],[27,69],[27,70],[27,71],[27,72],[27,73],[27,79],[27,81],[27,86],[27,87],[27,89],[27,90],[27,93],[27,97],[27,98],[27,100],[27,103],[27,106],[27,109],[27,111],[27,112],[28,29],[28,31],[28,32],[28,33],[28,34],[28,35],[28,36],[28,37],[28,39],[28,42],[28,44],[28,49],[28,52],[28,54],[28,56],[28,57],[28,58],[28,59],[28,60],[28,61],[28,63],[28,65],[28,68],[28,72],[28,73],[28,74],[28,75],[28,76],[28,77],[28,80],[28,84],[28,87],[28,91],[28,92],[28,96],[28,97],[28,98],[28,99],[28,100],[28,101],[28,104],[28,105],[28,108],[28,110],[28,111],[29,31],[29,32],[29,33],[29,34],[29,35],[29,36],[29,37],[29,39],[29,42],[29,44],[29,49],[29,52],[29,54],[29,56],[29,57],[29,58],[29,59],[29,60],[29,61],[29,63],[29,65],[29,68],[29,72],[29,73],[29,74],[29,75],[29,76],[29,77],[29,80],[29,84],[29,87],[29,91],[29,92],[29,96],[29,97],[29,98],[29,99],[29,100],[29,101],[29,104],[29,105],[29,108],[29,110],[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],[30,103],[30,106],[30,109],[30,111],[30,112],[31,32],[31,33],[31,34],[31,35],[31,36],[31,37],[31,38],[31,40],[31,41],[31,42],[31,46],[31,47],[31,48],[31,51],[31,55],[31,56],[31,58],[31,59],[31,63],[31,64],[31,65],[31,69],[31,70],[31,71],[31,74],[31,75],[31,76],[31,77],[31,79],[31,80],[31,81],[31,84],[31,86],[31,89],[31,90],[31,91],[31,92],[31,93],[31,96],[31,99],[31,101],[31,103],[31,104],[31,105],[31,106],[31,108],[31,109],[31,110],[31,112],[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],[32,104],[32,105],[32,108],[32,110],[32,111],[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],[33,104],[33,105],[33,108],[33,110],[33,111],[34,35],[34,36],[34,37],[34,39],[34,42],[34,44],[34,49],[34,52],[34,54],[34,56],[34,57],[34,58],[34,59],[34,60],[34,61],[34,63],[34,65],[34,68],[34,72],[34,73],[34,74],[34,75],[34,76],[34,77],[34,80],[34,84],[34,87],[34,91],[34,92],[34,96],[34,97],[34,98],[34,99],[34,100],[34,101],[34,104],[34,105],[34,108],[34,110],[34,111],[35,36],[35,37],[35,39],[35,42],[35,44],[35,49],[35,52],[35,54],[35,56],[35,57],[35,58],[35,59],[35,60],[35,61],[35,63],[35,65],[35,68],[35,72],[35,73],[35,74],[35,75],[35,76],[35,77],[35,80],[35,84],[35,87],[35,91],[35,92],[35,96],[35,97],[35,98],[35,99],[35,100],[35,101],[35,104],[35,105],[35,108],[35,110],[35,111],[36,37],[36,39],[36,42],[36,44],[36,49],[36,52],[36,54],[36,56],[36,57],[36,58],[36,59],[36,60],[36,61],[36,63],[36,65],[36,68],[36,72],[36,73],[36,74],[36,75],[36,76],[36,77],[36,80],[36,84],[36,87],[36,91],[36,92],[36,96],[36,97],[36,98],[36,99],[36,100],[36,101],[36,104],[36,105],[36,108],[36,110],[36,111],[37,39],[37,42],[37,44],[37,49],[37,52],[37,54],[37,56],[37,57],[37,58],[37,59],[37,60],[37,61],[37,63],[37,65],[37,68],[37,72],[37,73],[37,74],[37,75],[37,76],[37,77],[37,80],[37,84],[37,87],[37,91],[37,92],[37,96],[37,97],[37,98],[37,99],[37,100],[37,101],[37,104],[37,105],[37,108],[37,110],[37,111],[38,39],[38,40],[38,41],[38,44],[38,46],[38,47],[38,48],[38,49],[38,51],[38,52],[38,54],[38,55],[38,57],[38,60],[38,61],[38,64],[38,68],[38,69],[38,70],[38,71],[38,72],[38,73],[38,79],[38,81],[38,86],[38,87],[38,89],[38,90],[38,93],[38,97],[38,98],[38,100],[38,103],[38,106],[38,109],[38,111],[38,112],[39,40],[39,41],[39,42],[39,46],[39,47],[39,48],[39,51],[39,55],[39,56],[39,58],[39,59],[39,63],[39,64],[39,65],[39,69],[39,70],[39,71],[39,74],[39,75],[39,76],[39,77],[39,79],[39,80],[39,81],[39,84],[39,86],[39,89],[39,90],[39,91],[39,92],[39,93],[39,96],[39,99],[39,101],[39,103],[39,104],[39,105],[39,106],[39,108],[39,109],[39,110],[39,112],[40,41],[40,44],[40,46],[40,47],[40,48],[40,49],[40,51],[40,52],[40,54],[40,55],[40,57],[40,60],[40,61],[40,64],[40,68],[40,69],[40,70],[40,71],[40,72],[40,73],[40,79],[40,81],[40,86],[40,87],[40,89],[40,90],[40,93],[40,97],[40,98],[40,100],[40,103],[40,106],[40,109],[40,111],[40,112],[41,44],[41,46],[41,47],[41,48],[41,49],[41,51],[41,52],[41,54],[41,55],[41,57],[41,60],[41,61],[41,64],[41,68],[41,69],[41,70],[41,71],[41,72],[41,73],[41,79],[41,81],[41,86],[41,87],[41,89],[41,90],[41,93],[41,97],[41,98],[41,100],[41,103],[41,106],[41,109],[41,111],[41,112],[42,44],[42,49],[42,52],[42,54],[42,56],[42,57],[42,58],[42,59],[42,60],[42,61],[42,63],[42,65],[42,68],[42,72],[42,73],[42,74],[42,75],[42,76],[42,77],[42,80],[42,84],[42,87],[42,91],[42,92],[42,96],[42,97],[42,98],[42,99],[42,100],[42,101],[42,104],[42,105],[42,108],[42,110],[42,111],[44,46],[44,47],[44,48],[44,51],[44,55],[44,56],[44,58],[44,59],[44,63],[44,64],[44,65],[44,69],[44,70],[44,71],[44,74],[44,75],[44,76],[44,77],[44,79],[44,80],[44,81],[44,84],[44,86],[44,89],[44,90],[44,91],[44,92],[44,93],[44,96],[44,99],[44,101],[44,103],[44,104],[44,105],[44,106],[44,108],[44,109],[44,110],[44,112],[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],[46,103],[46,106],[46,109],[46,111],[46,112],[47,48],[47,49],[47,51],[47,52],[47,54],[47,55],[47,57],[47,60],[47,61],[47,64],[47,68],[47,69],[47,70],[47,71],[47,72],[47,73],[47,79],[47,81],[47,86],[47,87],[47,89],[47,90],[47,93],[47,97],[47,98],[47,100],[47,103],[47,106],[47,109],[47,111],[47,112],[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],[48,103],[48,106],[48,109],[48,111],[48,112],[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],[49,103],[49,104],[49,105],[49,106],[49,108],[49,109],[49,110],[49,112],[51,52],[51,54],[51,55],[51,57],[51,60],[51,61],[51,64],[51,68],[51,69],[51,70],[51,71],[51,72],[51,73],[51,79],[51,81],[51,86],[51,87],[51,89],[51,90],[51,93],[51,97],[51,98],[51,100],[51,103],[51,106],[51,109],[51,111],[51,112],[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],[52,103],[52,104],[52,105],[52,106],[52,108],[52,109],[52,110],[52,112],[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],[54,103],[54,104],[54,105],[54,106],[54,108],[54,109],[54,110],[54,112],[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],[55,103],[55,106],[55,109],[55,111],[55,112],[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],[56,104],[56,105],[56,108],[56,110],[56,111],[57,58],[57,59],[57,63],[57,64],[57,65],[57,69],[57,70],[57,71],[57,74],[57,75],[57,76],[57,77],[57,79],[57,80],[57,81],[57,84],[57,86],[57,89],[57,90],[57,91],[57,92],[57,93],[57,96],[57,99],[57,101],[57,103],[57,104],[57,105],[57,106],[57,108],[57,109],[57,110],[57,112],[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],[58,104],[58,105],[58,108],[58,110],[58,111],[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],[59,104],[59,105],[59,108],[59,110],[59,111],[60,63],[60,64],[60,65],[60,69],[60,70],[60,71],[60,74],[60,75],[60,76],[60,77],[60,79],[60,80],[60,81],[60,84],[60,86],[60,89],[60,90],[60,91],[60,92],[60,93],[60,96],[60,99],[60,101],[60,103],[60,104],[60,105],[60,106],[60,108],[60,109],[60,110],[60,112],[61,63],[61,64],[61,65],[61,69],[61,70],[61,71],[61,74],[61,75],[61,76],[61,77],[61,79],[61,80],[61,81],[61,84],[61,86],[61,89],[61,90],[61,91],[61,92],[61,93],[61,96],[61,99],[61,101],[61,103],[61,104],[61,105],[61,106],[61,108],[61,109],[61,110],[61,112],[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],[63,104],[63,105],[63,108],[63,110],[63,111],[64,68],[64,69],[64,70],[64,71],[64,72],[64,73],[64,79],[64,81],[64,86],[64,87],[64,89],[64,90],[64,93],[64,97],[64,98],[64,100],[64,103],[64,106],[64,109],[64,111],[64,112],[65,68],[65,72],[65,73],[65,74],[65,75],[65,76],[65,77],[65,80],[65,84],[65,87],[65,91],[65,92],[65,96],[65,97],[65,98],[65,99],[65,100],[65,101],[65,104],[65,105],[65,108],[65,110],[65,111],[68,69],[68,70],[68,71],[68,74],[68,75],[68,76],[68,77],[68,79],[68,80],[68,81],[68,84],[68,86],[68,89],[68,90],[68,91],[68,92],[68,93],[68,96],[68,99],[68,101],[68,103],[68,104],[68,105],[68,106],[68,108],[68,109],[68,110],[68,112],[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],[69,103],[69,106],[69,109],[69,111],[69,112],[70,71],[70,72],[70,73],[70,79],[70,81],[70,86],[70,87],[70,89],[70,90],[70,93],[70,97],[70,98],[70,100],[70,103],[70,106],[70,109],[70,111],[70,112],[71,72],[71,73],[71,79],[71,81],[71,86],[71,87],[71,89],[71,90],[71,93],[71,97],[71,98],[71,100],[71,103],[71,106],[71,109],[71,111],[71,112],[72,74],[72,75],[72,76],[72,77],[72,79],[72,80],[72,81],[72,84],[72,86],[72,89],[72,90],[72,91],[72,92],[72,93],[72,96],[72,99],[72,101],[72,103],[72,104],[72,105],[72,106],[72,108],[72,109],[72,110],[72,112],[73,74],[73,75],[73,76],[73,77],[73,79],[73,80],[73,81],[73,84],[73,86],[73,89],[73,90],[73,91],[73,92],[73,93],[73,96],[73,99],[73,101],[73,103],[73,104],[73,105],[73,106],[73,108],[73,109],[73,110],[73,112],[74,75],[74,76],[74,77],[74,80],[74,84],[74,87],[74,91],[74,92],[74,96],[74,97],[74,98],[74,99],[74,100],[74,101],[74,104],[74,105],[74,108],[74,110],[74,111],[75,76],[75,77],[75,80],[75,84],[75,87],[75,91],[75,92],[75,96],[75,97],[75,98],[75,99],[75,100],[75,101],[75,104],[75,105],[75,108],[75,110],[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],[76,104],[76,105],[76,108],[76,110],[76,111],[77,80],[77,84],[77,87],[77,91],[77,92],[77,96],[77,97],[77,98],[77,99],[77,100],[77,101],[77,104],[77,105],[77,108],[77,110],[77,111],[79,81],[79,86],[79,87],[79,89],[79,90],[79,93],[79,97],[79,98],[79,100],[79,103],[79,106],[79,109],[79,111],[79,112],[80,84],[80,87],[80,91],[80,92],[80,96],[80,97],[80,98],[80,99],[80,100],[80,101],[80,104],[80,105],[80,108],[80,110],[80,111],[81,86],[81,87],[81,89],[81,90],[81,93],[81,97],[81,98],[81,100],[81,103],[81,106],[81,109],[81,111],[81,112],[84,87],[84,91],[84,92],[84,96],[84,97],[84,98],[84,99],[84,100],[84,101],[84,104],[84,105],[84,108],[84,110],[84,111],[86,87],[86,89],[86,90],[86,93],[86,97],[86,98],[86,100],[86,103],[86,106],[86,109],[86,111],[86,112],[87,89],[87,90],[87,91],[87,92],[87,93],[87,96],[87,99],[87,101],[87,103],[87,104],[87,105],[87,106],[87,108],[87,109],[87,110],[87,112],[89,90],[89,93],[89,97],[89,98],[89,100],[89,103],[89,106],[89,109],[89,111],[89,112],[90,93],[90,97],[90,98],[90,100],[90,103],[90,106],[90,109],[90,111],[90,112],[91,92],[91,96],[91,97],[91,98],[91,99],[91,100],[91,101],[91,104],[91,105],[91,108],[91,110],[91,111],[92,96],[92,97],[92,98],[92,99],[92,100],[92,101],[92,104],[92,105],[92,108],[92,110],[92,111],[93,97],[93,98],[93,100],[93,103],[93,106],[93,109],[93,111],[93,112],[96,97],[96,98],[96,99],[96,100],[96,101],[96,104],[96,105],[96,108],[96,110],[96,111],[97,99],[97,101],[97,103],[97,104],[97,105],[97,106],[97,108],[97,109],[97,110],[97,112],[98,99],[98,101],[98,103],[98,104],[98,105],[98,106],[98,108],[98,109],[98,110],[98,112],[99,100],[99,101],[99,104],[99,105],[99,108],[99,110],[99,111],[100,101],[100,103],[100,104],[100,105],[100,106],[100,108],[100,109],[100,110],[100,112],[101,104],[101,105],[101,108],[101,110],[101,111],[103,106],[103,109],[103,111],[103,112],[104,105],[104,108],[104,110],[104,111],[105,108],[105,110],[105,111],[106,109],[106,111],[106,112],[108,110],[108,111],[109,111],[109,112],[110,111],[111,112]]},"rotation_powers":[[2,5],[4,5],[5,7],[6,7],[7,3],[8,3],[9,3],[10,7],[13,5],[16,7],[19,5],[20,5],[21,3],[22,5],[23,5],[24,5],[25,5],[28,3],[29,5],[32,5],[33,3],[34,5],[35,5],[36,3],[37,5],[39,7],[40,3],[42,7],[44,7],[46,5],[48,5],[49,5],[50,7],[51,3],[53,5],[54,7],[55,3],[60,5],[61,5],[62,3],[63,3],[67,5],[68,5],[69,7],[70,5],[71,5],[73,5],[75,7],[77,3],[80,7],[82,5],[83,3],[84,5],[87,3],[88,5],[89,7],[91,7],[92,3],[93,7],[94,7],[95,7],[97,5],[100,3],[101,5],[104,3],[111,5],[112,5],[113,7],[119,3],[120,3],[121,3],[123,3],[124,5],[130,3],[132,3],[133,3],[145,3],[149,3],[150,3],[153,3],[155,7],[157,3],[164,3],[166,3],[167,3],[168,3],[170,3],[171,3],[173,3],[176,3],[177,3],[178,3],[179,3],[180,3],[182,3],[185,3],[193,3],[194,3],[195,3],[196,3],[198,3],[200,3],[201,3],[203,3],[205,3],[208,7],[209,7],[210,5],[217,3],[219,5],[220,3],[221,3],[222,3],[224,3],[225,3],[227,3],[229,5],[230,3],[231,3],[232,3],[233,3],[236,3],[237,3],[240,3],[243,3],[244,3],[245,3],[246,3],[250,3],[251,3],[254,3],[255,3],[256,3],[257,3],[258,3],[261,3],[262,3],[263,3],[264,3],[266,3],[268,3],[270,3],[275,3],[277,3],[280,3],[282,3],[289,3],[291,3],[295,3],[299,3],[301,3],[302,3],[303,3],[304,3],[305,3],[308,3],[310,3],[315,3],[317,3],[318,3],[320,3],[321,3],[328,3],[330,3],[332,3],[334,3],[335,3],[338,3],[342,3],[343,3],[349,3],[351,3],[357,3],[360,3],[361,3],[363,3],[367,3],[372,3],[374,3],[383,3],[385,3],[386,3],[387,3],[389,3],[391,3],[397,3],[401,3],[405,3],[406,3]]},"metrics":{"gamma":1.2685937368231728,"gamma_t":null,"gamma_rho":1.2685937368231728,"gamma_claim":1.2685937368231728,"gamma_t_claim":null,"gamma_rho_claim":1.2685937368231728,"v_ex":101,"rate":0.24815724815724816,"t_count":null,"poly_degree":null,"effective_width":101},"provenance":{"regimes":["AI search (gamma frontier): contraction of an existing code"],"discovery":"AI search","strongest_claim":"a paired-column contraction of an existing triorthogonal code, 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): contraction of an existing code","file":"gamma_frontier_release/protocols/paired_column_contraction_407_101_3_513786cf4ac9.json","label":"paired_column_contraction_407_101_3_513786cf4ac9","N":113,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_407_101_3_513786cf4ac9 (source catalogue id paired_column_contraction_407_101_3_513786cf4ac9); construction: Existing triorthogonal code with physical paired-column contraction; matrix 513786cf4ac933a7...; the release states d=3 (exact), gamma=1.2685937368231728 (exact)","notes":"matrix gamma_frontier_release/matrices/513786cf4ac933a7e80072f0cc990c8f3e427894eed4ac4098ccc7d95dad4be0.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"}]}