{"id":"428.80.4.a","row":1047,"stored":{"file":"master_catalog.json","row":1047,"construction":null,"columns_sha256":null},"parameters":{"n":428,"k":80,"d":4,"N":100,"r":20,"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","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","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]],"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]],"sk_fingerprint":"d11392ce54687804","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[46,91],[41,91,92],[35,91,93],[1,2,5,7,8,9,11,13,14,21,22,23,24,25,26,28,29,30,32,33,34,37,39,44,45,47,48,51,52,55,56,57,59,61,62,63,65,66,68,70,72,73,74,75,76,78,79,82,84,86,87,88,90,93,94,95,96,97,98],[0,5,7,12,17,18,19,20,25,26,27,28,31,33,34,44,45,47,48,49,51,52,54,55,57,58,60,62,65,66,68,70,71,73,74,77,79,80,81,82,85,87,90,91,98],[1,2,3,4,5,6,9,13,16,19,20,22,24,25,28,29,32,41,42,43,45,46,47,49,50,51,52,53,54,55,56,58,61,65,66,68,70,72,73,74,77,80,83,85,86,87,89,93,95,99],[0,1,5,9,14,16,18,20,22,23,24,27,28,30,32,33,35,38,41,42,45,46,47,48,50,53,55,57,58,60,63,65,66,68,69,70,73,75,77,81,82,84,87,88,89,90,92,96],[0,2,4,8,9,12,14,18,19,20,21,25,26,28,32,34,35,37,38,41,42,44,45,48,50,51,52,56,57,61,66,67,68,69,70,73,74,75,77,82,83,85,87,96,99],[1,2,4,6,8,9,12,13,14,19,20,21,25,26,31,32,34,37,39,40,41,42,43,44,45,46,48,50,52,57,60,61,64,68,71,74,75,76,77,80,81,83,85,87,88,89,95,98],[0,3,6,7,10,12,13,14,22,24,28,30,31,34,35,38,42,44,45,50,51,52,60,61,62,63,67,70,72,73,74,75,78,80,85,86,87,89,90,91,92,93,96,97],[62,91,94,95],[15,91,92,94,95],[2,5,9,10,11,12,13,14,15,16,19,21,22,27,30,31,35,37,38,39,40,42,45,46,47,48,49,52,54,55,56,57,62,65,66,68,73,74,75,76,78,80,82,83,84,87,88,91,97,98,99],[1,2,4,5,6,7,8,12,13,16,17,18,19,20,22,25,27,32,33,34,35,39,41,44,46,47,49,50,51,52,54,55,58,59,61,62,64,65,68,72,73,74,76,77,78,80,81,82,84,85,86,94,95,97,99],[0,5,7,8,9,10,11,15,16,17,18,20,26,27,28,29,30,31,33,37,38,39,40,42,44,45,46,48,49,52,54,56,58,59,60,61,66,67,69,70,71,77,79,81,83,84,85,86,88,89,91,97,98,99],[0,5,6,7,8,12,18,19,20,21,23,24,25,26,28,33,34,36,37,38,39,41,43,44,45,48,50,51,53,54,55,56,57,58,62,64,67,68,75,76,77,78,79,80,82,85,87,88,91,92,93,94,95,97],[2,3,5,6,9,11,13,16,17,19,20,22,23,24,25,29,31,34,41,43,45,47,49,50,51,52,53,54,55,61,62,64,65,66,67,69,73,74,76,77,79,81,88,90,92,96,97],[4,8,11,12,13,16,18,19,20,22,24,25,27,33,34,35,41,43,44,46,47,49,50,51,54,56,58,59,61,62,64,65,66,67,75,76,77,81,83,84,85,87,88,91,93,94,95,96,98,99],[0,2,4,5,6,7,8,9,10,12,13,14,15,18,21,24,25,27,28,29,30,33,34,36,39,40,41,43,44,48,49,50,51,54,56,58,59,62,67,68,72,73,74,75,76,80,83,87,90,94,96,97,98,99],[17,28,31,34,39,68,79,80,81,82,83,85,86,88,89,97,98],[1,2,7,9,12,13,16,18,22,24,26,27,28,29,33,39,43,44,45,46,48,50,54,56,57,58,60,64,72,73,76,80,85,88,90,91,93,99],[0,1,2,8,9,12,13,14,15,17,18,20,22,23,25,30,31,32,33,35,37,38,41,42,43,44,45,48,50,52,55,59,61,62,64,66,67,68,69,70,71,72,77,78,79,80,81,82,83,84,85,86,88,89,92,94,96],[0,2,4,5,8,10,11,12,14,15,16,18,20,21,22,23,25,28,29,31,32,34,38,41,42,43,44,49,51,52,54,57,59,60,63,65,66,69,70,71,73,76,78,80,81,82,83,86,88,89,90,92,94,95,96,97,98,99],[0,2,5,9,10,12,13,14,15,16,17,19,20,22,23,27,28,35,36,37,38,42,43,44,46,48,49,50,51,52,56,62,65,66,67,70,72,76,77,78,79,80,81,84,85,86,88,89,91,92,93,95],[20,91,92,93,95,96],[0,4,5,6,12,13,16,17,18,19,22,23,24,25,26,27,31,33,34,35,40,41,42,44,46,47,49,50,51,53,55,56,58,59,63,64,65,66,68,71,72,73,76,77,79,80,82,84,86,87,89,90,91,92,97,99],[0,1,3,4,5,10,11,12,13,14,15,16,19,20,21,22,24,27,30,31,32,33,35,37,39,40,42,45,46,48,49,51,52,53,54,55,57,58,60,63,65,66,67,69,70,71,73,74,75,76,77,78,79,80,81,82,86,88,89,91,93,94,97,98],[1,4,10,11,12,14,20,24,25,27,28,29,31,32,34,35,36,37,38,41,42,44,45,47,48,55,56,58,63,68,69,70,71,72,74,76,78,80,84,85,86,89,90,91,93,94,96],[42,91,92,93,94,95,96],[0,2,3,5,6,7,8,9,11,12,15,16,18,19,20,21,22,23,25,27,29,32,33,34,35,36,38,39,40,41,43,45,48,49,50,51,53,54,55,56,59,61,62,63,65,67,68,70,71,72,73,76,78,81,82,85,87,90,92,93,95,98,99],[0,2,4,6,7,9,10,13,15,21,23,24,29,30,33,34,35,38,39,40,44,45,47,48,51,53,54,55,58,59,63,64,66,68,70,71,72,73,75,77,78,80,81,84,88,90,91,92,94,96,97],[0,3,4,7,9,10,12,14,15,19,21,24,27,28,35,39,43,47,51,52,53,54,56,59,60,63,64,66,68,69,70,71,73,74,75,77,78,80,81,82,85,86,89,91,93,94,95,97,98,99],[1,4,6,7,9,10,11,17,18,20,21,22,23,25,27,28,29,31,32,34,36,37,38,39,41,42,44,45,48,52,54,56,57,58,62,64,69,70,71,74,75,76,77,78,79,81,84,86,87,89,91,92,94,95,98,99],[2,3,4,5,8,10,11,13,15,16,18,19,22,24,26,27,28,29,30,33,37,38,39,43,44,46,48,49,51,53,57,58,60,63,64,65,66,70,71,77,79,85,87,88,90,91,92,93,95,97,98,99],[4,91,95,97],[1,2,3,6,8,9,16,17,20,21,22,23,25,26,28,29,31,32,34,35,36,38,40,41,42,43,44,45,46,47,50,52,53,56,57,60,61,63,66,67,72,74,77,78,79,81,82,83,91,93,97,99],[0,1,3,5,7,8,9,13,14,16,19,21,22,23,25,26,28,30,31,32,34,39,40,41,42,43,44,50,51,52,53,54,56,60,64,65,67,68,71,73,74,75,78,81,82,84,86,87,88,90,92,94,96],[1,2,4,5,6,7,8,12,13,16,17,18,19,20,22,24,25,27,32,33,34,35,39,40,41,46,47,49,50,51,52,54,55,57,58,59,61,62,64,65,66,68,72,73,74,75,76,77,78,80,81,84,85,86,87,90,91,92,93,94,97,98],[0,1,2,4,5,6,7,10,11,12,13,14,15,16,21,22,23,27,29,32,34,35,39,46,49,50,55,60,61,62,64,65,69,71,72,75,78,80,87,92,94,97,98],[1,2,4,6,8,9,12,13,14,16,19,20,21,25,26,31,34,37,38,39,40,41,42,43,44,45,46,48,50,52,57,60,61,64,68,69,70,71,72,74,75,76,77,80,81,82,84,85,88,89,90,94,95,96,99],[0,2,3,5,6,7,9,10,12,15,16,17,20,22,23,28,30,36,37,45,46,48,56,57,61,63,65,66,67,73,75,76,77,78,79,80,82,83,84,85,89,91,92,93,94,96,97],[0,3,4,6,7,8,9,10,11,12,14,15,17,19,21,24,31,32,35,38,40,42,44,45,50,52,53,57,59,60,61,63,64,66,67,69,71,78,79,80,83,84,87,89,91,93,94,95,96,97,98],[1,3,5,9,11,12,14,16,17,19,21,22,23,24,26,28,29,30,31,32,34,36,37,40,42,44,46,47,49,53,54,55,57,60,62,65,66,67,69,71,79,81,82,87,88,93,94,95,96,97,98],[0,6,8,9,10,11,13,14,18,19,23,33,36,38,39,40,42,43,46,48,51,58,59,60,61,62,71,72,75,80,81,85,87,91,92,94,95,96,97,98],[0,2,3,4,5,6,7,9,11,13,15,16,24,28,29,37,39,40,44,46,47,48,49,51,52,54,55,56,60,61,63,65,66,67,70,72,73,76,79,82,83,84,85,86,90,92,93,95],[17,28,31,39,59,68,79,85,86,88,89,98],[1,2,4,5,8,9,12,14,17,18,19,21,23,24,25,27,28,31,32,34,35,37,39,40,42,44,45,47,48,52,53,55,56,57,59,61,62,63,70,71,73,78,79,80,82,83,84,86,90,92,94,96],[1,2,9,10,11,12,13,14,15,16,19,21,22,27,29,30,31,32,35,37,38,42,43,45,47,48,50,51,54,55,56,60,62,64,65,67,68,69,70,71,72,73,74,75,76,78,79,80,82,88,90,91,93,96,97,98],[0,3,4,5,7,8,9,13,17,20,24,25,26,29,34,35,37,40,42,43,48,49,52,53,56,57,63,64,65,66,68,69,75,76,77,78,79,81,83,84,85,86,89,91,94,95,96],[0,1,7,9,10,11,15,16,18,20,22,23,26,27,28,29,30,32,35,36,37,40,42,43,44,46,48,52,56,57,59,61,62,63,64,65,67,70,74,77,78,81,82,83,85,88,92,93,95,97],[5,6,9,10,11,12,13,15,16,18,20,23,24,25,26,29,31,33,34,37,40,43,45,46,48,50,54,56,57,59,60,61,63,64,66,67,68,69,71,72,73,75,77,80,81,83,84,86,88,91,92,94,95,99],[0,2,5,9,10,12,13,14,15,16,17,19,20,22,23,27,28,32,35,36,37,38,42,43,44,46,48,49,50,51,52,62,65,66,69,76,77,78,79,80,81,82,84,85,86,87,88,89,90,91,92,93,95,97,98,99],[3,4,6,7,9,11,17,20,21,25,28,29,31,32,34,36,37,38,39,41,42,43,44,45,48,51,52,54,56,60,66,67,68,69,70,71,75,77,79,81,84,85,86,87,88,89,91,93,95],[1,5,8,15,17,21,22,26,28,32,35,36,38,39,44,45,49,54,56,58,59,60,62,63,64,65,66,68,71,73,74,78,79,80,81,83,84,86,89,90,92,96,97,98,99],[17,18,35,39,49,68,79,85,86,87,88,90,98,99],[0,1,3,8,11,12,17,18,19,20,21,24,25,26,27,31,32,33,34,35,36,37,38,39,41,43,44,45,48,51,52,53,54,57,58,60,62,66,68,69,70,72,73,75,77,83,87,89,91,92,94,95,96,97,98,99],[0,2,4,5,8,11,12,16,18,19,20,22,25,27,33,34,35,37,40,41,44,49,50,52,54,56,58,59,60,61,65,66,67,71,75,77,78,80,81,82,83,84,85,87,93,94,96,97,98],[3,4,6,7,9,10,11,12,14,15,17,19,20,21,23,24,27,35,42,43,47,51,52,53,55,56,60,61,62,64,66,69,70,73,74,75,77,78,79,80,81,82,88,91,93,95,98,99],[1,2,3,5,6,8,11,14,20,24,25,26,29,31,32,33,34,36,38,39,41,47,48,49,50,51,52,53,54,55,56,57,58,59,61,65,67,68,73,77,78,81,85,86,88,90,91,94,95,96,98],[0,2,3,4,5,10,12,14,16,20,22,23,27,28,34,37,40,42,44,46,48,50,52,53,54,58,60,62,63,65,69,72,73,75,76,77,78,80,81,83,84,85,87,89,96],[1,3,6,7,9,10,11,12,13,14,15,20,21,22,23,27,32,34,35,40,42,43,47,52,53,55,56,57,60,61,71,72,75,77,78,80,81,82,83,84,86,89,98,99],[53,91,92,94,95,98],[0,1,4,5,6,8,10,15,16,17,21,22,23,25,26,28,31,34,35,36,39,40,41,45,49,51,57,60,61,62,64,65,66,67,68,70,71,74,75,78,79,83,86,87,89,91,92,93,94,96],[1,2,4,5,6,7,8,9,12,13,16,18,19,20,22,25,27,32,33,34,35,41,44,46,47,49,50,51,52,54,55,58,59,61,62,64,65,72,73,74,75,76,77,78,79,80,81,82,84,85,90,94,95,97,99],[3,6,7,8,9,10,11,13,14,15,16,18,21,22,23,25,27,28,31,32,33,34,38,39,43,44,45,46,47,49,51,52,53,55,58,59,60,61,65,67,68,72,76,77,78,80,81,86,92,94,96,97,99],[1,2,4,5,8,9,10,11,12,14,15,17,18,23,25,28,29,32,33,34,36,37,38,40,41,42,43,47,48,49,50,54,57,58,59,60,61,64,66,67,69,71,75,80,84,86,89,90,92,97],[0,2,7,8,10,11,12,13,14,16,17,20,23,25,26,27,28,29,31,34,36,38,42,44,45,46,50,54,56,59,61,62,66,68,69,72,74,75,79,81,83,84,86,87,89,90,91,92,96,98,99],[0,2,3,4,5,6,7,10,11,13,18,19,23,24,25,27,28,31,33,35,36,37,41,43,44,45,47,48,49,50,51,53,54,57,58,62,63,64,66,75,78,83,86,87,88,89,90,91,92,93,94,95,96,98,99],[1,2,3,5,6,9,12,13,16,18,19,22,23,29,31,32,33,35,41,42,43,46,47,48,50,51,52,53,54,55,56,58,59,61,62,68,70,72,73,74,77,80,83,85,86,90,91,93,97],[73,91,93,94,96,98],[0,1,2,5,7,8,9,11,12,16,17,18,20,21,22,23,27,28,29,31,32,33,35,36,38,40,41,43,48,49,50,51,53,56,58,59,61,62,63,65,67,72,73,78,79,80,83,86,87,88,89,90,95,96,98,99],[1,2,3,4,5,7,8,10,12,13,15,16,17,19,22,24,26,27,28,31,32,33,35,37,39,40,43,44,46,47,48,49,50,53,54,56,58,60,61,62,63,65,68,69,71,72,74,76,79,80,81,83,88,89,90,96,98,99],[14,91,92,95,96,98],[1,2,3,4,5,6,7,10,12,14,15,16,17,19,21,24,25,27,29,31,32,35,40,41,45,46,49,50,51,54,56,57,58,60,65,66,67,68,69,71,72,74,75,78,79,80,82,83,84,86,88,89,90,93,95,98,99],[1,2,3,8,11,13,14,17,18,19,21,24,25,29,31,32,33,34,35,37,41,42,46,47,48,50,51,53,56,57,58,59,61,62,63,68,70,71,73,81,82,84,85,86,87,90,93,95,97],[0,91,92,93,94,95,96,98],[1,3,4,8,9,11,12,13,18,24,25,27,28,29,31,32,33,35,37,40,41,42,43,44,45,47,53,54,56,58,60,61,63,68,69,70,71,74,75,76,78,80,82,83,84,86,87,89,90,91,93,95],[6,91,92,97,98],[0,1,2,4,11,12,18,19,20,21,23,25,28,32,33,34,35,36,37,38,40,41,43,44,45,50,51,52,57,61,62,64,67,68,73,74,75,76,77,80,81,82,88,89,90,92,93,95,98],[1,5,8,9,10,13,14,15,16,18,19,21,22,23,26,27,28,29,31,32,36,37,39,43,44,46,47,48,49,55,56,57,62,63,64,65,66,67,68,69,71,81,83,84,85,86,88,89,90,92,94,97,98],[1,2,5,6,7,11,16,21,23,31,32,36,37,38,40,44,47,48,49,50,53,55,57,58,60,61,64,65,66,67,68,70,71,75,76,80,81,86,89,91,92,93,94,97,99],[55,91,92,94,97,98],[12,91,93,94,97,98],[1,2,6,7,10,12,15,17,19,20,21,23,33,35,36,40,44,45,47,50,51,52,54,55,56,57,58,59,64,66,68,70,77,80,81,86,91,92,93,94,96,98,99],[51,91,95,97,98],[0,1,3,4,6,7,9,10,12,14,15,17,19,21,24,27,31,35,39,41,43,45,47,51,52,54,60,63,64,66,67,70,71,72,74,75,77,78,79,80,81,87,88,90,95,96,97,98],[10,91,93,95,97,98],[0,1,2,3,7,9,11,12,13,14,16,17,18,21,22,23,26,27,28,29,31,32,33,35,37,40,41,42,43,46,48,49,50,51,52,53,56,58,59,61,66,68,72,73,77,80,82,83,84,85,87,88,89,92,95,96,97],[1,3,4,5,7,8,9,10,12,14,19,22,23,24,25,26,27,28,32,34,36,38,39,43,44,47,49,52,53,61,63,65,68,69,70,75,77,80,81,84,86,88,89,90,92,93,96,97,98],[0,5,7,8,9,10,12,13,15,16,17,19,22,24,25,26,27,28,29,31,35,36,37,38,39,40,48,51,52,54,60,61,64,65,69,70,74,75,76,77,79,80,82,83,86,87,88,90,93,94],[21,91,96,97,98],[48,91,92,96,97,98],[3,4,6,7,9,10,11,12,14,15,17,19,20,21,23,24,27,35,42,43,47,51,52,53,55,56,60,61,62,64,66,69,70,73,74,75,77,78,79,80,81,82,88,91,92,94,95,96,97,98,99],[0,2,3,4,5,8,10,14,15,16,17,18,19,20,22,24,25,29,33,36,38,40,41,42,45,46,47,48,49,50,51,52,55,58,60,63,64,65,66,67,68,69,71,72,74,75,76,77,79,81,82,83,85,87,88,90,93,95,96,97],[1,2,6,7,12,14,20,24,26,27,32,36,38,39,42,43,44,45,47,50,51,52,54,55,57,59,61,63,64,66,67,70,73,75,76,77,79,82,83,84,85,88,90,93,94,99],[2,3,5,6,9,16,17,19,20,23,25,28,29,32,34,40,41,43,45,47,49,50,51,52,53,54,55,57,61,62,64,65,67,70,72,73,76,77,79,80,82,84,85,88,90,91,93,94,96,97,98],[0,4,5,6,7,8,10,11,12,14,17,18,23,24,27,29,31,32,35,36,39,43,44,45,54,56,58,59,61,64,68,70,71,73,75,76,78,80,84,85,87,88,90,91,94,95,96,98],[70,91,93,95,96,97,98],[0,1,2,3,5,9,11,13,16,17,19,20,22,23,24,25,29,31,32,34,39,41,43,45,46,47,49,50,52,53,54,55,56,61,62,65,66,70,71,72,74,77,79,81,82,87,88,91,93,94,97,98,99],[1,3,6,7,9,10,11,12,13,15,16,20,21,22,23,24,27,32,33,34,35,38,43,44,47,51,52,53,55,58,60,61,65,66,67,68,72,77,78,80,81,86,87,89,90,92,96],[0,1,4,5,6,8,15,17,21,22,23,25,26,28,31,32,34,35,36,38,39,41,42,44,45,49,51,56,58,60,62,64,65,66,68,71,74,78,79,82,84,86,89,90,91,92,93,94,97,98,99],[0,2,4,5,8,12,16,17,18,19,20,22,25,27,28,31,32,33,34,35,39,40,41,44,46,47,49,51,52,54,56,58,59,60,61,62,65,66,67,68,69,70,71,72,74,75,77,78,79,80,84,86,87,89,91,93,94,95,96,99],[7,11,17,24,28,31,39,40,41,47,50,51,55,57,62,66,68,74,79,80,81,82,84,86,89,90,91,95,96,98,99],[5,6,8,9,10,12,13,14,15,17,19,20,22,25,29,30,31,34,35,36,37,39,48,50,54,57,58,61,62,63,64,65,66,69,70,73,75,76,77,78,79,83,84,85,87,88,89,90,93,94,95,97,98,99],[2,4,7,8,11,16,22,26,28,31,35,39,40,41,45,47,48,50,51,55,56,57,59,61,62,67,70,73,74,75,78,83,84,85,88,91,93,94,96,97],[0,2,3,5,8,10,13,14,15,16,17,18,19,20,22,23,24,29,33,34,36,37,38,40,45,46,48,49,50,51,52,53,55,56,59,64,65,66,67,68,69,70,72,75,77,82,86,89,91,92,94,95,98],[0,1,5,9,11,14,16,17,20,22,23,24,27,30,31,32,33,38,39,41,42,45,46,47,48,50,53,55,57,58,60,63,65,66,69,70,73,74,75,77,79,81,85,86,87,90,92,94,97,98,99],[0,2,5,9,10,12,13,14,15,16,17,19,20,22,23,27,28,35,36,37,38,42,43,44,46,48,49,52,62,63,65,66,67,69,72,76,77,78,79,80,83,84,85,88,92,93,99],[1,17,24,32,40,47,50,51,57,62,66,68,69,70,72,83,84,85,87,92,94,96,98,99],[0,3,6,7,10,12,13,14,17,22,28,30,31,34,35,38,39,42,44,45,50,51,52,57,60,61,62,63,67,68,70,72,73,74,75,78,79,80,85,89,95,96,97,98,99],[1,2,4,5,6,7,8,12,13,15,16,18,19,20,22,25,27,32,33,34,35,39,40,41,44,46,47,49,50,51,52,54,55,58,59,61,62,64,65,66,72,73,74,75,76,77,78,80,82,84,85,91,92,97,99],[0,1,2,4,6,8,9,11,12,13,14,19,23,25,26,28,30,34,36,37,38,39,41,42,46,47,48,51,52,54,55,56,60,61,64,67,68,70,71,73,76,80,82,84,85,88,89,90,91,92,95,96,97],[3,4,5,6,12,14,16,18,19,20,21,24,26,27,28,29,30,32,33,35,37,39,46,48,49,50,52,53,54,56,57,58,63,64,70,77,78,81,83,85,86,87,88,91,93,94,95,97],[0,1,2,5,8,11,14,17,18,19,21,23,24,25,27,29,31,32,33,34,37,39,40,41,42,48,50,51,52,53,56,57,58,59,61,63,70,73,74,78,79,81,82,84,86,87,92,94],[11,45,74,80,81,83],[0,3,6,7,9,10,11,13,14,15,16,17,18,20,21,22,25,27,28,33,34,38,40,41,42,43,45,46,49,50,53,54,56,57,58,60,63,65,70,71,72,74,75,76,77,78,79,82,84,85,86,90,91,95,96,97,98,99],[5,6,7,13,14,17,20,21,23,26,30,36,37,43,45,49,52,54,56,57,59,62,63,66,67,68,69,70,72,73,75,77,79,84,88,89,98,99],[34,91,93,94,96,99],[0,3,4,5,8,9,10,12,13,14,15,19,20,24,26,27,28,36,37,38,39,42,43,44,46,49,51,52,53,54,56,59,60,62,64,65,69,70,73,74,75,77,79,80,81,84,85,86,87,89,91,92,93,96,97,99],[0,2,3,4,5,7,9,10,14,16,17,18,19,20,23,24,25,26,27,28,30,38,40,41,42,45,46,47,49,52,53,54,55,56,58,59,60,63,64,65,66,67,68,70,74,76,77,78,79,82,84,86,87,89,91,92,94,95,96],[56,91,93,95,96,99],[0,3,4,6,7,8,9,11,12,18,20,23,24,27,29,31,33,35,40,43,44,45,51,53,56,58,59,60,64,68,70,71,73,75,76,78,79,80,82,83,84,85,86,88,89,91,93,95,97,99],[1,2,3,5,6,7,8,9,12,13,14,16,18,19,20,22,25,27,32,34,35,36,38,41,44,46,47,49,51,52,54,55,59,60,61,62,64,65,67,68,72,73,74,76,78,80,81,82,84,86,89,90,91,93,94,97],[3,4,5,6,7,12,16,17,20,22,23,28,29,30,37,38,40,43,45,48,49,52,53,54,57,61,64,65,67,68,69,70,73,76,77,78,79,80,82,84,87,90,91,93,97,98,99],[1,4,10,11,12,14,17,20,24,25,27,28,29,31,34,35,36,37,38,39,41,42,44,45,47,48,55,56,58,63,69,70,71,74,76,78,79,80,84,91,93,94,96],[0,1,2,3,5,9,11,13,16,19,20,22,23,25,29,31,32,34,40,41,42,43,45,46,47,49,50,52,53,54,55,56,57,60,61,62,65,68,70,71,72,74,77,81,83,84,86,87,88,89,90,92,95,98,99],[3,4,6,7,9,11,15,17,21,23,28,29,31,36,38,43,44,45,47,48,50,52,53,55,58,60,63,66,69,73,74,75,76,77,79,81,82,84,85,86,89,90,92,94,96,98],[0,1,4,6,8,9,10,11,14,15,17,18,24,25,31,32,33,34,36,37,38,41,42,43,48,50,51,54,57,58,59,61,62,64,66,67,69,73,75,81,82,83,84,85,86,87,88,89,90,91,93,94,95,96,99],[0,2,4,6,7,9,10,13,15,18,21,23,24,29,30,33,34,38,39,40,44,45,47,48,51,53,54,55,58,59,63,64,66,68,70,71,72,73,75,77,78,84,88,90,92,93,94,96,97],[0,2,4,8,9,11,12,14,17,18,19,20,21,24,25,26,31,34,35,37,38,39,40,41,42,43,44,45,48,50,51,52,56,61,67,72,73,75,77,78,79,80,81,82,86,87,88,89,91,92,93,94,96,98,99],[0,2,4,5,8,11,12,16,17,18,19,20,22,25,27,33,34,35,39,40,41,44,49,50,52,54,56,58,59,60,61,65,66,67,68,71,75,76,77,78,79,81,83,84,87,88,90,93,94,96,97,98],[0,3,4,9,10,12,14,15,17,19,21,24,27,28,35,43,47,51,52,53,54,55,56,59,60,63,64,66,69,70,71,73,74,75,77,78,79,80,81,82,85,86,88,89,91,93,94,95,97,98],[1,4,6,7,9,10,20,21,22,23,25,27,29,32,34,35,36,37,38,41,42,44,45,48,52,54,56,57,58,62,64,68,69,70,71,75,76,77,78,80,85,87,88,91,92,95,96,97],[1,3,4,5,6,7,8,11,12,13,16,18,20,21,22,23,24,27,28,29,30,35,36,37,38,40,43,45,46,47,48,49,50,52,53,54,55,56,59,60,63,65,71,80,81,85,87,90,94,95,96,97],[4,17,39,50,51,68,79,85,87,98],[3,4,5,7,9,12,13,18,19,21,23,24,26,27,28,29,31,32,33,36,38,40,42,43,45,47,49,50,53,54,55,56,58,59,60,63,64,65,66,67,68,69,70,72,73,75,76,80,81,82,87,91,92,93,95,96,98,99],[3,4,6,7,9,10,13,14,15,19,27,30,35,36,39,42,43,44,45,49,50,52,53,54,56,57,61,62,66,68,69,72,73,81,82,85,86,87,88,89,90,91,93,94,96,97,99],[1,4,6,7,9,11,19,20,21,28,29,32,34,36,37,38,42,43,44,47,48,51,52,55,60,61,62,64,66,67,68,71,75,76,77,82,83,84,88,93,99],[16,91,93,94,95,97,99],[0,2,3,5,6,7,9,10,12,15,16,20,22,23,28,30,36,37,39,40,45,46,48,56,57,61,63,65,67,68,73,75,76,77,78,80,82,83,84,85,86,89,91,92,93,94,96,97],[52,91,96,97,99],[0,1,2,3,4,5,8,10,14,15,16,18,19,20,21,22,24,25,27,28,30,32,33,36,39,40,41,42,45,46,48,49,52,53,54,55,57,58,60,63,65,66,67,70,71,76,77,82,84,86,88,92,93,96],[1,2,3,4,5,6,7,9,13,15,16,17,20,22,23,24,28,29,31,32,37,43,45,46,49,50,52,53,60,61,65,66,68,71,72,76,77,81,90,92,93,95],[0,3,4,6,7,8,9,10,12,14,15,17,19,21,24,28,30,35,38,40,42,44,45,47,51,53,57,59,60,61,62,63,64,66,67,70,71,72,74,78,79,80,81,86,87,88,90,93,94,97],[0,1,3,4,5,9,11,12,13,14,15,16,17,20,26,27,28,32,36,37,38,39,40,42,43,45,46,48,49,50,56,57,59,60,64,65,68,72,75,77,79,86,89,91,95,96,97,98],[59,91,93,94,96,97,99],[2,3,5,6,9,16,19,20,22,23,25,28,29,32,34,39,40,41,43,45,47,49,50,51,52,53,54,55,57,61,62,65,67,68,70,72,73,76,77,80,82,84,85,86,89,90,91,93,94,96,97,98],[0,3,5,7,12,17,18,19,20,21,25,26,27,28,33,34,35,36,37,38,44,45,48,51,54,55,57,58,59,60,62,66,67,68,70,73,74,77,79,80,81,82,85,86,90,93,94,96,97,98,99],[0,2,6,7,9,12,16,22,23,28,30,32,33,37,40,45,46,48,51,54,56,57,58,61,63,65,67,68,73,76,78,80,81,84,85,86,89,91,92,93,97],[0,3,4,5,7,8,9,13,20,24,25,26,29,34,35,37,39,40,42,43,48,49,52,53,56,57,63,64,65,66,70,75,76,77,78,81,83,84,87,93,94,97,98],[0,1,2,3,5,9,11,13,16,19,20,22,23,24,25,29,31,32,34,41,43,45,46,47,49,50,52,53,54,55,56,58,60,61,62,65,66,68,70,71,72,74,77,81,82,86,88,89,92,94,95,96],[0,3,4,5,8,9,11,12,13,17,18,19,20,23,24,29,30,31,33,36,39,42,49,51,52,53,54,57,58,59,60,62,64,67,68,69,70,71,72,76,77,78,79,80,83,84,85,91,92,93,94,98],[0,2,4,6,8,9,13,14,17,21,22,26,28,33,37,38,39,41,42,44,45,46,47,48,49,52,56,57,61,62,64,65,66,67,69,75,76,78,79,82,84,85,87,89,90,91,92,94,97,99],[0,3,4,6,7,8,9,11,12,18,23,25,27,29,31,33,35,43,44,45,51,53,56,57,58,59,60,64,66,68,70,71,73,75,76,78,79,80,82,85,86,87,88,89,90,91,93,95,96,97,98],[0,2,3,5,6,7,8,9,11,12,16,17,18,19,21,22,27,29,33,35,36,37,38,39,40,42,43,45,47,48,49,58,59,61,62,65,68,72,74,78,79,80,81,87,90,91,94,96,99],[1,5,7,8,11,15,17,21,22,24,26,31,32,35,36,38,39,40,44,45,47,49,50,51,54,55,56,57,58,59,60,63,64,65,68,71,73,78,79,82,83,87,88,90,95,97],[49,91,93,98,99],[0,2,3,6,7,8,10,15,17,18,23,25,27,28,34,37,38,41,43,47,48,50,53,55,56,57,59,60,62,64,66,68,70,73,74,75,79,82,85,88,90,91,92,94,95,97,98],[0,1,3,7,8,11,12,17,18,19,20,21,24,25,27,28,32,33,34,35,36,37,38,39,40,41,48,51,52,53,54,55,56,58,59,60,62,66,67,68,70,77,78,81,83,85,87,90,92,94,95],[1,2,3,5,6,8,14,18,20,24,25,26,28,29,32,33,34,35,36,38,39,41,47,48,49,50,51,52,53,54,55,56,57,58,59,61,65,67,68,73,74,77,78,81,82,84,85,86,88,89,91,95,97,99],[3,5,8,9,10,16,17,18,19,21,22,23,25,26,27,32,35,38,39,40,41,43,45,46,51,53,54,56,57,58,60,61,62,63,65,66,67,70,72,74,76,78,79,80,81,82,84,86,88,89,90,99],[0,2,5,9,10,12,13,14,15,16,19,20,22,23,27,28,35,36,37,38,39,42,43,44,46,48,49,52,54,62,65,66,67,68,69,72,76,77,78,80,83,84,87,88,90,92,93,99],[1,3,6,7,9,10,11,12,13,14,15,20,21,22,23,24,27,34,35,39,42,43,50,51,52,53,55,56,60,61,62,66,69,70,71,75,77,78,79,80,81,82,85,86,89,90,92,94,96],[1,2,4,6,8,9,12,13,14,17,19,20,21,25,26,31,32,34,36,37,38,40,41,42,43,44,45,46,48,50,52,57,60,61,64,71,74,75,76,77,79,80,81,83,86,88,89,90,95,98],[57,91,92,93,95,98,99],[17,39,47,62,68,71,79,85,90,91,94,95],[1,2,4,5,6,7,8,12,13,16,17,18,19,20,22,25,27,32,33,34,35,40,41,44,46,47,49,50,51,52,53,54,55,58,59,61,62,64,65,66,68,72,73,74,75,76,77,78,79,80,82,84,85,90,91,92,97,98,99],[27,91,93,94,95,98,99],[0,4,12,13,16,18,19,22,23,24,25,27,28,33,34,35,40,42,43,46,47,49,50,51,52,55,57,58,63,64,65,66,69,71,72,76,77,80,81,84,85,86,88,90,92,93,95,96,97,98],[4,5,6,7,8,9,10,15,17,18,20,23,25,26,27,31,33,34,37,39,41,44,45,47,48,49,50,52,55,57,58,60,62,63,66,69,70,71,73,74,76,77,79,81,85,87,91,92,93,95],[0,2,7,8,10,12,13,14,16,20,23,25,26,27,28,29,31,34,36,38,39,42,44,45,46,50,54,56,59,61,62,66,69,72,75,80,84,85,88,91,92,96,98,99],[2,3,5,6,9,11,16,20,22,23,24,25,29,31,34,39,41,43,45,47,49,50,51,52,53,54,55,61,62,64,65,66,67,68,69,73,74,76,77,81,86,87,89,92,96,97],[2,5,8,9,11,12,13,14,15,18,21,23,25,27,31,33,36,37,38,39,40,41,42,43,48,49,50,54,58,59,60,61,67,68,70,71,72,74,75,81,82,85,88,90,91,92,95,96,97,98,99],[0,1,3,4,5,6,8,10,13,15,16,19,20,22,24,25,26,27,28,31,32,34,35,37,40,42,43,44,45,46,47,53,54,55,56,57,59,61,62,63,66,69,72,73,76,84,85,86,87,90,91,93,94,96],[28,31,73,80,81,82,83,90,97,99],[3,4,9,10,11,12,14,15,19,21,23,27,28,31,32,35,37,39,40,41,42,43,45,52,56,57,61,63,67,68,69,70,73,74,75,76,77,78,79,80,81,83,84,86,88,89,90,92,95,97,98,99],[2,91,95,96,98,99],[0,2,4,5,8,10,11,12,15,16,17,18,20,21,22,23,25,28,29,31,32,34,38,39,41,42,43,44,49,51,52,54,57,59,60,63,65,66,68,69,70,71,73,76,77,78,79,80,81,82,83,86,87,88,91,94,97,99],[0,1,3,4,6,7,9,13,17,20,21,22,23,24,25,28,29,31,32,36,37,38,39,40,41,42,43,44,45,48,52,54,56,57,58,60,62,69,70,71,74,75,76,77,79,81,82,83,86,87,89,92,93,95,96,98],[0,3,4,6,7,8,9,11,12,17,18,23,24,27,29,31,33,35,39,40,43,44,45,51,53,56,58,59,60,61,64,70,71,73,75,76,78,80,82,83,84,85,87,88,90,92,96,97,99],[0,1,2,3,4,7,8,9,14,20,23,24,26,31,32,36,38,39,40,42,50,52,53,54,56,58,60,61,62,63,66,67,68,71,74,77,78,81,85,87,89,90,92,93,94,99],[1,2,3,5,9,11,13,16,17,19,20,22,23,25,29,31,32,34,39,40,41,43,45,46,47,49,50,52,53,54,55,56,57,60,61,62,65,70,71,72,74,77,79,81,83,84,87,88,92,95,99],[0,1,2,3,5,9,11,13,16,19,20,22,24,29,34,37,42,43,45,49,51,52,53,59,62,63,65,66,67,68,72,76,77,80,82,83,85,87,88,90,91,94,96,99],[0,1,4,8,9,10,11,14,15,18,23,24,25,31,32,33,34,36,37,38,39,41,42,43,48,50,51,54,57,58,59,61,62,64,66,67,68,69,73,75,79,81,82,83,84,85,86,89,90,92,93,94,95,96,97,98,99],[0,1,2,4,11,12,17,19,20,21,23,25,28,32,33,34,36,37,38,39,40,41,43,44,45,50,51,52,57,61,62,64,67,73,74,75,76,77,79,82,85,86,87,89,90,91,92,95,98],[0,1,2,4,5,10,11,12,13,15,16,20,22,23,24,25,27,28,29,32,34,35,36,38,39,40,41,42,45,46,47,49,50,51,52,55,57,61,62,63,64,65,66,69,71,72,73,75,77,80,82,83,84,85,86,88,90,91,93,96,97,99],[0,1,4,6,7,8,12,18,19,20,21,22,23,25,27,31,32,33,34,35,36,37,38,41,47,48,52,53,54,55,56,57,59,64,68,70,76,77,78,80,83,84,85,86,87,89,90,91,92,96,98,99],[7,91,92,94,97,98,99],[11,12,18,28,31,35,74,80,81,84,89,91,93,96,99],[0,2,3,5,8,9,10,13,14,15,16,17,18,20,21,22,25,31,33,34,43,44,45,46,47,49,51,55,57,58,59,60,61,63,65,66,67,69,71,72,73,76,79,81,83,87,88,90,92],[0,1,4,5,6,8,15,16,17,21,22,23,25,26,27,28,31,32,34,35,36,39,40,41,45,49,51,57,60,61,62,64,65,66,67,68,69,71,72,74,75,78,79,84,86,87,89,92,95,98,99],[0,3,4,5,6,8,9,11,14,17,19,20,21,23,24,25,26,28,29,31,34,37,42,43,44,47,48,53,54,55,56,57,62,64,65,68,74,75,76,78,79,81,82,83,87,88,89,90,91,93,94,95,96,98],[0,1,2,3,4,7,8,13,15,16,17,20,24,25,26,32,34,35,37,39,42,46,48,50,51,53,61,63,66,67,68,70,72,75,76,78,79,81,82,83,85,86,87,89,90,94,96,99],[0,1,2,4,5,6,7,10,14,15,16,20,21,22,24,27,28,29,34,35,36,39,41,42,43,44,45,46,50,51,54,57,65,71,72,81,83,84,87,89,91,94,96,97],[0,3,4,6,7,8,9,10,11,12,14,15,19,24,31,32,35,38,39,40,42,44,45,50,53,57,59,60,61,63,64,66,67,68,69,71,78,80,83,84,85,88,91,93,94,95,96,97,99],[0,2,4,8,9,10,11,12,15,18,20,23,25,26,27,29,31,33,34,37,41,44,45,47,52,58,62,63,68,69,70,76,77,81,84,86,88,89,91,94,95,96],[3,4,6,7,9,10,12,14,15,19,20,21,23,24,27,35,39,42,43,47,51,52,53,55,56,60,61,62,64,66,68,69,70,73,75,77,78,80,81,82,85,86,87,89,91,92,94,95,96,97,98,99],[1,7,11,17,25,28,31,32,37,41,46,47,53,55,59,60,62,63,64,67,68,69,71,72,74,80,81,82,83,86,87,89,91,94,95,98],[0,3,4,6,7,9,10,12,14,15,19,21,24,28,35,38,39,40,42,44,45,47,51,53,57,59,60,61,62,63,64,66,67,68,70,71,72,74,78,80,81,85,86,87,89,90,93,94,97],[29,91,92,94,96,97,98,99],[28,91,93,94,96,97,98,99],[0,1,2,3,4,7,8,9,14,17,20,23,24,26,31,32,33,36,38,40,42,47,51,52,53,54,56,58,60,61,63,65,66,67,71,74,77,78,79,81,83,84,87,89,92,93,97,98,99],[1,4,5,8,12,13,15,18,19,21,24,28,32,33,36,38,40,42,44,45,46,47,50,54,55,56,57,59,60,62,63,69,72,73,74,76,78,80,81,82,86,91,92,94,95],[60,91,92,93,95,96,97,98,99],[1,3,4,7,8,10,12,13,15,16,19,22,24,26,27,28,31,32,33,35,37,40,43,44,46,48,49,51,53,54,56,58,60,61,63,65,69,71,72,74,76,80,81,82,84,85,88,89,91,94,95,97,98],[0,1,2,3,4,5,6,7,8,9,13,14,18,25,27,28,29,31,32,33,35,40,41,42,49,50,51,53,54,55,58,59,61,62,63,66,67,68,71,73,76,82,83,85,88,89,92,95,96,97],[0,2,3,5,9,10,12,13,14,15,16,19,20,22,23,27,28,32,35,36,37,38,39,42,43,44,46,48,49,50,51,52,62,65,66,67,68,69,76,77,78,80,81,82,84,87,88,90,91,92,93,95,97,98,99],[1,3,5,7,9,11,12,15,18,21,22,25,26,27,28,29,32,33,34,36,38,41,42,43,49,53,57,59,62,65,68,70,73,74,75,76,79,80,84,85,86,87,88,89,92,94,95,96,99],[1,2,5,7,8,9,11,13,14,21,22,23,24,25,26,28,29,30,32,33,34,37,39,44,45,47,48,51,52,55,56,57,59,61,62,63,65,66,68,70,72,73,74,75,76,78,79,82,84,86,87,88,90,91,92,94,95,96,97,98],[0,5,7,12,17,18,19,20,25,26,27,28,31,33,34,44,45,47,48,49,51,52,54,55,57,58,60,62,65,66,68,70,71,73,74,77,79,80,81,82,85,87,90,94,98],[1,2,3,4,5,6,9,13,16,19,20,22,24,25,28,29,32,41,42,43,45,46,47,49,50,51,52,53,54,55,56,58,61,65,66,68,70,72,73,74,77,80,83,85,86,87,89,91,92,93,94,95,99],[0,1,5,9,14,16,18,20,22,23,24,27,28,30,32,33,35,38,41,42,45,46,47,48,50,53,55,57,58,60,63,65,66,68,69,70,73,75,77,81,82,84,87,88,89,90,91,92,93,94,96],[0,2,4,8,9,12,14,18,19,20,21,25,26,28,32,34,35,37,38,41,42,44,45,48,50,51,52,56,57,61,66,67,68,69,70,73,74,75,77,82,83,85,87,91,92,93,94,96,99],[63,91,95],[1,91,92,95],[1,2,4,6,8,9,12,13,14,19,20,21,25,26,31,32,34,37,39,40,41,42,43,44,45,46,48,50,52,57,60,61,64,68,71,74,75,76,77,80,81,83,85,87,88,89,91,93,98],[0,3,6,7,10,12,13,14,22,24,28,30,31,34,35,38,42,44,45,50,51,52,60,61,62,63,67,70,72,73,74,75,78,80,85,86,87,89,90,95,96,97],[2,5,9,10,11,12,13,14,15,16,19,21,22,27,30,31,35,37,38,39,40,42,45,46,47,48,49,52,54,55,56,57,62,65,66,68,73,74,75,76,78,80,82,83,84,87,88,93,94,95,97,98,99],[1,2,4,5,6,7,8,12,13,16,17,18,19,20,22,25,27,32,33,34,35,39,41,44,46,47,49,50,51,52,54,55,58,59,61,62,64,65,68,72,73,74,76,77,78,80,81,82,84,85,86,91,92,93,97,99],[0,5,7,8,9,10,11,15,16,17,18,20,26,27,28,29,30,31,33,37,38,39,40,42,44,45,46,48,49,52,54,56,58,59,60,61,66,67,69,70,71,77,79,81,83,84,85,86,88,89,96,97,98,99],[0,5,6,7,8,12,18,19,20,21,23,24,25,26,28,33,34,36,37,38,39,41,43,44,45,48,50,51,53,54,55,56,57,58,62,64,67,68,75,76,77,78,79,80,82,85,87,88,93,94,95,96,97],[45,91,93,96],[2,3,5,6,9,11,13,16,17,19,20,22,23,24,25,29,31,34,41,43,45,47,49,50,51,52,53,54,55,61,62,64,65,66,67,69,73,74,76,77,79,81,88,90,91,93,97],[4,8,11,12,13,16,18,19,20,22,24,25,27,33,34,35,41,43,44,46,47,49,50,51,54,56,58,59,61,62,64,65,66,67,75,76,77,81,83,84,85,87,88,93,95,98,99],[0,2,4,5,6,7,8,9,10,12,13,14,15,18,21,24,25,27,28,29,30,33,34,36,39,40,41,43,44,48,49,50,51,54,56,58,59,62,67,68,72,73,74,75,76,80,83,87,90,91,92,97,98,99],[17,28,31,34,39,68,79,80,81,82,83,85,86,88,89,91,93,94,96,97,98],[1,2,7,9,12,13,16,18,22,24,26,27,28,29,33,39,43,44,45,46,48,50,54,56,57,58,60,64,72,73,76,80,85,88,90,92,94,96,99],[0,1,2,8,9,12,13,14,15,17,18,20,22,23,25,30,31,32,33,35,37,38,41,42,43,44,45,48,50,52,55,59,61,62,64,66,67,68,69,70,71,72,77,78,79,80,81,82,83,84,85,86,88,89,91,92,94,95],[0,2,4,5,8,10,11,12,14,15,16,18,20,21,22,23,25,28,29,31,32,34,38,41,42,43,44,49,51,52,54,57,59,60,63,65,66,69,70,71,73,76,78,80,81,82,83,86,88,89,90,91,94,97,98,99],[0,2,5,9,10,12,13,14,15,16,17,19,20,22,23,27,28,35,36,37,38,42,43,44,46,48,49,50,51,52,56,62,65,66,67,70,72,76,77,78,79,80,81,84,85,86,88,89,92,96],[0,4,5,6,12,13,16,17,18,19,22,23,24,25,26,27,31,33,34,35,40,41,42,44,46,47,49,50,51,53,55,56,58,59,63,64,65,66,68,71,72,73,76,77,79,80,82,84,86,87,89,90,92,94,95,96,97,99],[0,1,3,4,5,10,11,12,13,14,15,16,19,20,21,22,24,27,30,31,32,33,35,37,39,40,42,45,46,48,49,51,52,53,54,55,57,58,60,63,65,66,67,69,70,71,73,74,75,76,77,78,79,80,81,82,86,88,89,92,93,95,96,97,98],[1,4,10,11,12,14,20,24,25,27,28,29,31,32,34,35,36,37,38,41,42,44,45,47,48,55,56,58,63,68,69,70,71,72,74,76,78,80,84,85,86,89,90,95],[0,2,3,5,6,7,8,9,11,12,15,16,18,19,20,21,22,23,25,27,29,32,33,34,35,36,38,39,40,41,43,45,48,49,50,51,53,54,55,56,59,61,62,63,65,67,68,70,71,72,73,76,78,81,82,85,87,90,91,92,93,95,97,98,99],[23,91,92,97],[0,2,4,6,7,9,10,13,15,21,23,24,29,30,33,34,35,38,39,40,44,45,47,48,51,53,54,55,58,59,63,64,66,68,70,71,72,73,75,77,78,80,81,84,88,90,92,93,94,96],[78,91,92,93,97],[76,91,94,97],[0,3,4,7,9,10,12,14,15,19,21,24,27,28,35,39,43,47,51,52,53,54,56,59,60,63,64,66,68,69,70,71,73,74,75,77,78,80,81,82,85,86,89,92,93,95,98,99],[1,4,6,7,9,10,11,17,18,20,21,22,23,25,27,28,29,31,32,34,36,37,38,39,41,42,44,45,48,52,54,56,57,58,62,64,69,70,71,74,75,76,77,78,79,81,84,86,87,89,92,93,95,97,98,99],[2,3,4,5,8,10,11,13,15,16,18,19,22,24,26,27,28,29,30,33,37,38,39,43,44,46,48,49,51,53,57,58,60,63,64,65,66,70,71,77,79,85,87,88,90,94,95,98,99],[1,2,3,6,8,9,16,17,20,21,22,23,25,26,28,29,31,32,34,35,36,38,40,41,42,43,44,45,46,47,50,52,53,56,57,60,61,63,66,67,72,74,77,78,79,81,82,83,92,93,95,99],[0,1,3,5,7,8,9,13,14,16,19,21,22,23,25,26,28,30,31,32,34,39,40,41,42,43,44,50,51,52,53,54,56,60,64,65,67,68,71,73,74,75,78,81,82,84,86,87,88,90,91,92,93,94,95,96,97],[1,2,4,5,6,7,8,12,13,16,17,18,19,20,22,24,25,27,32,33,34,35,39,40,41,46,47,49,50,51,52,54,55,57,58,59,61,62,64,65,66,68,72,73,74,75,76,77,78,80,81,84,85,86,87,90,94,95,98],[0,1,2,4,5,6,7,10,11,12,13,14,15,16,21,22,23,27,29,32,34,35,39,46,49,50,55,60,61,62,64,65,69,71,72,75,78,80,87,91,92,95,98],[39,91,92,94,95,97],[1,2,4,6,8,9,12,13,14,16,19,20,21,25,26,31,34,37,38,39,40,41,42,43,44,45,46,48,50,52,57,60,61,64,68,69,70,71,72,74,75,76,77,80,81,82,84,85,88,89,90,91,93,96,97,99],[0,2,3,5,6,7,9,10,12,15,16,17,20,22,23,28,30,36,37,45,46,48,56,57,61,63,65,66,67,73,75,76,77,78,79,80,82,83,84,85,89,95,96],[0,3,4,6,7,8,9,10,11,12,14,15,17,19,21,24,31,32,35,38,40,42,44,45,50,52,53,57,59,60,61,63,64,66,67,69,71,78,79,80,83,84,87,89,93,94,95,98],[1,3,5,9,11,12,14,16,17,19,21,22,23,24,26,28,29,30,31,32,34,36,37,40,42,44,46,47,49,53,54,55,57,60,62,65,66,67,69,71,79,81,82,87,88,91,92,93,94,95,98],[11,91,93,96,97],[0,6,8,9,10,11,13,14,18,19,23,33,36,38,39,40,42,43,46,48,51,58,59,60,61,62,71,72,75,80,81,85,87,93,94,95,98],[30,91,94,96,97],[0,2,3,4,5,6,7,9,11,13,15,16,24,28,29,37,39,40,44,46,47,48,49,51,52,54,55,56,60,61,63,65,66,67,70,72,73,76,79,82,83,84,85,86,90,91,93,94,95,96,97],[17,28,31,39,59,68,79,85,86,88,89,91,93,94,96,97,98],[64,91,92,93,94,96,97],[1,2,4,5,8,9,12,14,17,18,19,21,23,24,25,27,28,31,32,34,35,37,39,40,42,44,45,47,48,52,53,55,56,57,59,61,62,63,70,71,73,78,79,80,82,83,84,86,90,91,92,94,95,97],[1,2,9,10,11,12,13,14,15,16,19,21,22,27,29,30,31,32,35,37,38,42,43,45,47,48,50,51,54,55,56,60,62,64,65,67,68,69,70,71,72,73,74,75,76,78,79,80,82,88,90,92,93,95,98],[0,3,4,5,7,8,9,13,17,20,24,25,26,29,34,35,37,40,42,43,48,49,52,53,56,57,63,64,65,66,68,69,75,76,77,78,79,81,83,84,85,86,89,93,94,97],[58,91,92,93,95,96,97],[0,1,7,9,10,11,15,16,18,20,22,23,26,27,28,29,30,32,35,36,37,40,42,43,44,46,48,52,56,57,59,61,62,63,64,65,67,70,74,77,78,81,82,83,85,88,91,92,93,94,96],[5,6,9,10,11,12,13,15,16,18,20,23,24,25,26,29,31,33,34,37,40,43,45,46,48,50,54,56,57,59,60,61,63,64,66,67,68,69,71,72,73,75,77,80,81,83,84,86,88,96,97,99],[0,2,5,9,10,12,13,14,15,16,17,19,20,22,23,27,28,32,35,36,37,38,42,43,44,46,48,49,50,51,52,62,65,66,69,76,77,78,79,80,81,82,84,85,86,87,88,89,90,92,94,96,98,99],[25,91,92,93,94,95,96,97],[3,4,6,7,9,11,17,20,21,25,28,29,31,32,34,36,37,38,39,41,42,43,44,45,48,51,52,54,56,60,66,67,68,69,70,71,75,77,79,81,84,85,86,87,88,89,93,95,98],[1,5,8,15,17,21,22,26,28,32,35,36,38,39,44,45,49,54,56,58,59,60,62,63,64,65,66,68,71,73,74,78,79,80,81,83,84,86,89,90,91,96,97,99],[17,18,35,39,49,68,79,85,86,87,88,90,91,93,99],[0,1,3,8,11,12,17,18,19,20,21,24,25,26,27,31,32,33,34,35,36,37,38,39,41,43,44,45,48,51,52,53,54,57,58,60,62,66,68,69,70,72,73,75,77,83,87,89,93,94,95,96,97,99],[0,2,4,5,8,11,12,16,18,19,20,22,25,27,33,34,35,37,40,41,44,49,50,52,54,56,58,59,60,61,65,66,67,71,75,77,78,80,81,82,83,84,85,87,91,93,96,97],[1,2,3,5,6,8,11,14,20,24,25,26,29,31,32,33,34,36,38,39,41,47,48,49,50,51,52,53,54,55,56,57,58,59,61,65,67,68,73,77,78,81,85,86,88,90,93,95,96],[0,2,3,4,5,10,12,14,16,20,22,23,27,28,34,37,40,42,44,46,48,50,52,53,54,58,60,62,63,65,69,72,73,75,76,77,78,80,81,83,84,85,87,89,91,92,93,94,96,98],[54,91,95,98],[1,3,6,7,9,10,11,12,13,14,15,20,21,22,23,27,32,34,35,40,42,43,47,52,53,55,56,57,60,61,71,72,75,77,78,80,81,82,83,84,86,89,91,92,95,99],[36,91,93,95,98],[24,91,92,93,95,98],[71,91,94,95,98],[0,1,4,5,6,8,10,15,16,17,21,22,23,25,26,28,31,34,35,36,39,40,41,45,49,51,57,60,61,62,64,65,66,67,68,70,71,74,75,78,79,83,86,87,89,92,95,96,98],[1,2,4,5,6,7,8,9,12,13,16,18,19,20,22,25,27,32,33,34,35,41,44,46,47,49,50,51,52,54,55,58,59,61,62,64,65,72,73,74,75,76,77,78,79,80,81,82,84,85,90,91,92,93,97,98,99],[3,6,7,8,9,10,11,13,14,15,16,18,21,22,23,25,27,28,31,32,33,34,38,39,43,44,45,46,47,49,51,52,53,55,58,59,60,61,65,67,68,72,76,77,78,80,81,86,91,92,94,97,98,99],[1,2,4,5,8,9,10,11,12,14,15,17,18,23,25,28,29,32,33,34,36,37,38,40,41,42,43,47,48,49,50,54,57,58,59,60,61,64,66,67,69,71,75,80,84,86,89,90,91,96,97,98],[0,2,7,8,10,11,12,13,14,16,17,20,23,25,26,27,28,29,31,34,36,38,42,44,45,46,50,54,56,59,61,62,66,68,69,72,74,75,79,81,83,84,86,87,89,90,92,93,99],[19,91,92,93,96,98],[0,2,3,4,5,6,7,10,11,13,18,19,23,24,25,27,28,31,33,35,36,37,41,43,44,45,47,48,49,50,51,53,54,57,58,62,63,64,66,75,78,83,86,87,88,89,90,92,93,95,99],[1,2,3,5,6,9,12,13,16,18,19,22,23,29,31,32,33,35,41,42,43,46,47,48,50,51,52,53,54,55,56,58,59,61,62,68,70,72,73,74,77,80,83,85,86,90,92,93,94,96,97,98],[0,1,2,5,7,8,9,11,12,16,17,18,20,21,22,23,27,28,29,31,32,33,35,36,38,40,41,43,48,49,50,51,53,56,58,59,61,62,63,65,67,72,73,78,79,80,83,86,87,88,89,90,91,92,93,94,95,99],[1,2,3,4,5,7,8,10,12,13,15,16,17,19,22,24,26,27,28,31,32,33,35,37,39,40,43,44,46,47,48,49,50,53,54,56,58,60,61,62,63,65,68,69,71,72,74,76,79,80,81,83,88,89,90,91,95,99],[1,2,3,4,5,6,7,10,12,14,15,16,17,19,21,24,25,27,29,31,32,35,40,41,45,46,49,50,51,54,56,57,58,60,65,66,67,68,69,71,72,74,75,78,79,80,82,83,84,86,88,89,90,91,96,99],[61,91,92,93,95,96,98],[33,91,94,95,96,98],[1,2,3,8,11,13,14,17,18,19,21,24,25,29,31,32,33,34,35,37,41,42,46,47,48,50,51,53,56,57,58,59,61,62,63,68,70,71,73,81,82,84,85,86,87,90,91,92,93,94,96,97,98],[32,91,93,94,95,96,98],[1,3,4,8,9,11,12,13,18,24,25,27,28,29,31,32,33,35,37,40,41,42,43,44,45,47,53,54,56,58,60,61,63,68,69,70,71,74,75,76,78,80,82,83,84,86,87,89,90,93,95,97,98],[0,1,2,4,11,12,18,19,20,21,23,25,28,32,33,34,35,36,37,38,40,41,43,44,45,50,51,52,57,61,62,64,67,68,73,74,75,76,77,80,81,82,88,89,90,91,92,95,97],[1,5,8,9,10,13,14,15,16,18,19,21,22,23,26,27,28,29,31,32,36,37,39,43,44,46,47,48,49,55,56,57,62,63,64,65,66,67,68,69,71,81,83,84,85,86,88,89,90,91,93,94],[1,2,5,6,7,11,16,21,23,31,32,36,37,38,40,44,47,48,49,50,53,55,57,58,60,61,64,65,66,67,68,70,71,75,76,80,81,86,89,92,93,98,99],[1,2,6,7,10,12,15,17,19,20,21,23,33,35,36,40,44,45,47,50,51,52,54,55,56,57,58,59,64,66,68,70,77,80,81,86,96,97,99],[0,1,3,4,6,7,9,10,12,14,15,17,19,21,24,27,31,35,39,41,43,45,47,51,52,54,60,63,64,66,67,70,71,72,74,75,77,78,79,80,81,87,88,90,91,92,96],[0,1,2,3,7,9,11,12,13,14,16,17,18,21,22,23,26,27,28,29,31,32,33,35,37,40,41,42,43,46,48,49,50,51,52,53,56,58,59,61,66,68,72,73,77,80,82,83,84,85,87,88,89,91,93,96,98],[1,3,4,5,7,8,9,10,12,14,19,22,23,24,25,26,27,28,32,34,36,38,39,43,44,47,49,52,53,61,63,65,68,69,70,75,77,80,81,84,86,88,89,90,91,92,93,94,95,96],[68,91,92,94,95,97,98],[0,5,7,8,9,10,12,13,15,16,17,19,22,24,25,26,27,28,29,31,35,36,37,38,39,40,48,51,52,54,60,61,64,65,69,70,74,75,76,77,79,80,82,83,86,87,88,90,91,95,97,98],[66,91,92,93,94,95,97,98],[0,2,3,4,5,8,10,14,15,16,17,18,19,20,22,24,25,29,33,36,38,40,41,42,45,46,47,48,49,50,51,52,55,58,60,63,64,65,66,67,68,69,71,72,74,75,76,77,79,81,82,83,85,87,88,90,91,92,95,98],[8,91,94,96,97,98],[1,2,6,7,12,14,20,24,26,27,32,36,38,39,42,43,44,45,47,50,51,52,54,55,57,59,61,63,64,66,67,70,73,75,76,77,79,82,83,84,85,88,90,91,92,93,96,97,98,99],[31,91,93,94,96,97,98],[2,3,5,6,9,16,17,19,20,23,25,28,29,32,34,40,41,43,45,47,49,50,51,52,53,54,55,57,61,62,64,65,67,70,72,73,76,77,79,80,82,84,85,88,90,92],[65,91,95,96,97,98],[0,4,5,6,7,8,10,11,12,14,17,18,23,24,27,29,31,32,35,36,39,43,44,45,54,56,58,59,61,64,68,70,71,73,75,76,78,80,84,85,87,88,90,92,94,97],[0,1,2,3,5,9,11,13,16,17,19,20,22,23,24,25,29,31,32,34,39,41,43,45,46,47,49,50,52,53,54,55,56,61,62,65,66,70,71,72,74,77,79,81,82,87,88,92,94,95,96,99],[5,91,94,95,96,97,98],[1,3,6,7,9,10,11,12,13,15,16,20,21,22,23,24,27,32,33,34,35,38,43,44,47,51,52,53,55,58,60,61,65,66,67,68,72,77,78,80,81,86,87,89,90,91,94,95,97,98],[3,91,93,94,95,96,97,98],[0,1,4,5,6,8,15,17,21,22,23,25,26,28,31,32,34,35,36,38,39,41,42,44,45,49,51,56,58,60,62,64,65,66,68,71,74,78,79,82,84,86,89,90,95,96,99],[0,2,4,5,8,12,16,17,18,19,20,22,25,27,28,31,32,33,34,35,39,40,41,44,46,47,49,51,52,54,56,58,59,60,61,62,65,66,67,68,69,70,71,72,74,75,77,78,79,80,84,86,87,89,93,94,95,96],[7,11,17,24,28,31,39,40,41,47,50,51,55,57,62,66,68,74,79,80,81,82,84,86,89,90,92,95,96,98],[18,91,93,99],[5,6,8,9,10,12,13,14,15,17,19,20,22,25,29,30,31,34,35,36,37,39,48,50,54,57,58,61,62,63,64,65,66,69,70,73,75,76,77,78,79,83,84,85,87,88,89,90,91,92,94,95,97,98],[2,4,7,8,11,16,22,26,28,31,35,39,40,41,45,47,48,50,51,55,56,57,59,61,62,67,70,73,74,75,78,83,84,85,88,93,96,97,99],[0,2,3,5,8,10,13,14,15,16,17,18,19,20,22,23,24,29,33,34,36,37,38,40,45,46,48,49,50,51,52,53,55,56,59,64,65,66,67,68,69,70,72,75,77,82,86,89,95,98,99],[0,1,5,9,11,14,16,17,20,22,23,24,27,30,31,32,33,38,39,41,42,45,46,47,48,50,53,55,57,58,60,63,65,66,69,70,73,74,75,77,79,81,85,86,87,90,91,92,93,97,98],[43,91,92,93,94,99],[0,2,5,9,10,12,13,14,15,16,17,19,20,22,23,27,28,35,36,37,38,42,43,44,46,48,49,52,62,63,65,66,67,69,72,76,77,78,79,80,83,84,85,88,91,92,93,95],[1,17,24,32,40,47,50,51,57,62,66,68,69,70,72,83,84,85,87,91,94,95,96,98],[38,91,93,95,99],[0,3,6,7,10,12,13,14,17,22,28,30,31,34,35,38,39,42,44,45,50,51,52,57,60,61,62,63,67,68,70,72,73,74,75,78,79,80,85,89,91,92,93,96,97,98],[47,91,94,95,99],[1,2,4,5,6,7,8,12,13,15,16,18,19,20,22,25,27,32,33,34,35,39,40,41,44,46,47,49,50,51,52,54,55,58,59,61,62,64,65,66,72,73,74,75,76,77,78,80,82,84,85,94,95,97],[0,1,2,4,6,8,9,11,12,13,14,19,23,25,26,28,30,34,36,37,38,39,41,42,46,47,48,51,52,54,55,56,60,61,64,67,68,70,71,73,76,80,82,84,85,88,89,90,92,93,94,96,97,99],[75,91,92,93,94,95,99],[3,4,5,6,12,14,16,18,19,20,21,24,26,27,28,29,30,32,33,35,37,39,46,48,49,50,52,53,54,56,57,58,63,64,70,77,78,81,83,85,86,87,88,93,94,95,96,97,99],[0,1,2,5,8,11,14,17,18,19,21,23,24,25,27,29,31,32,33,34,37,39,40,41,42,48,50,51,52,53,56,57,58,59,61,63,70,73,74,78,79,81,82,84,86,87,91,94,96,99],[11,45,74,80,81,83,91,93,96,99],[13,91,92,93,96,99],[0,3,6,7,9,10,11,13,14,15,16,17,18,20,21,22,25,27,28,33,34,38,40,41,42,43,45,46,49,50,53,54,56,57,58,60,63,65,70,71,72,74,75,76,77,78,79,82,84,85,86,90,94,95,97,98],[5,6,7,13,14,17,20,21,23,26,30,36,37,43,45,49,52,54,56,57,59,62,63,66,67,68,69,70,72,73,75,77,79,84,88,89,91,92,94,96,98],[0,3,4,5,8,9,10,12,13,14,15,19,20,24,26,27,28,36,37,38,39,42,43,44,46,49,51,52,53,54,56,59,60,62,64,65,69,70,73,74,75,77,79,80,81,84,85,86,87,89,94,97],[0,2,3,4,5,7,9,10,14,16,17,18,19,20,23,24,25,26,27,28,30,38,40,41,42,45,46,47,49,52,53,54,55,56,58,59,60,63,64,65,66,67,68,70,74,76,77,78,79,82,84,86,87,89,92,94,99],[77,91,92,95,96,99],[0,3,4,6,7,8,9,11,12,18,20,23,24,27,29,31,33,35,40,43,44,45,51,53,56,58,59,60,64,68,70,71,73,75,76,78,79,80,82,83,84,85,86,88,89,92,96,97],[1,2,3,5,6,7,8,9,12,13,14,16,18,19,20,22,25,27,32,34,35,36,38,41,44,46,47,49,51,52,54,55,59,60,61,62,64,65,67,68,72,73,74,76,78,80,81,82,84,86,89,90,93,95,96,97,99],[3,4,5,6,7,12,16,17,20,22,23,28,29,30,37,38,40,43,45,48,49,52,53,54,57,61,64,65,67,68,69,70,73,76,77,78,79,80,82,84,87,90,92,93,94,95,96,97,98],[1,4,10,11,12,14,17,20,24,25,27,28,29,31,34,35,36,37,38,39,41,42,44,45,47,48,55,56,58,63,69,70,71,74,76,78,79,80,84,95,99],[0,1,2,3,5,9,11,13,16,19,20,22,23,25,29,31,32,34,40,41,42,43,45,46,47,49,50,52,53,54,55,56,57,60,61,62,65,68,70,71,72,74,77,81,83,84,86,87,88,89,90,91,93,94,96,98],[3,4,6,7,9,11,15,17,21,23,28,29,31,36,38,43,44,45,47,48,50,52,53,55,58,60,63,66,69,73,74,75,76,77,79,81,82,84,85,86,89,90,91,92,94,96,97,98,99],[0,1,4,6,8,9,10,11,14,15,17,18,24,25,31,32,33,34,36,37,38,41,42,43,48,50,51,54,57,58,59,61,62,64,66,67,69,73,75,81,82,83,84,85,86,87,88,89,90,92,93,94,95,96,97],[0,2,4,6,7,9,10,13,15,18,21,23,24,29,30,33,34,38,39,40,44,45,47,48,51,53,54,55,58,59,63,64,66,68,70,71,72,73,75,77,78,84,88,90,91,92,94,96,99],[0,2,4,8,9,11,12,14,17,18,19,20,21,24,25,26,31,34,35,37,38,39,40,41,42,43,44,45,48,50,51,52,56,61,67,72,73,75,77,78,79,80,81,82,86,87,88,89,94,96,97,98],[0,2,4,5,8,11,12,16,17,18,19,20,22,25,27,33,34,35,39,40,41,44,49,50,52,54,56,58,59,60,61,65,66,67,68,71,75,76,77,78,79,81,83,84,87,88,90,91,93,96,98,99],[0,3,4,9,10,12,14,15,17,19,21,24,27,28,35,43,47,51,52,53,54,55,56,59,60,63,64,66,69,70,71,73,74,75,77,78,79,80,81,82,85,86,88,89,92,93,95,98,99],[1,4,6,7,9,10,20,21,22,23,25,27,29,32,34,35,36,37,38,41,42,44,45,48,52,54,56,57,58,62,64,68,69,70,71,75,76,77,78,80,85,87,88,92,93,94,95,96,99],[1,3,4,5,6,7,8,11,12,13,16,18,20,21,22,23,24,27,28,29,30,35,36,37,38,40,43,45,46,47,48,49,50,52,53,54,55,56,59,60,63,65,71,80,81,85,87,90,91,92,93,95,96,99],[4,17,39,50,51,68,79,85,87,91,95,97,98,99],[3,4,5,7,9,12,13,18,19,21,23,24,26,27,28,29,31,32,33,36,38,40,42,43,45,47,49,50,53,54,55,56,58,59,60,63,64,65,66,67,68,69,70,72,73,75,76,80,81,82,87,93,96,97,98],[3,4,6,7,9,10,13,14,15,19,27,30,35,36,39,42,43,44,45,49,50,52,53,54,56,57,61,62,66,68,69,72,73,81,82,85,86,87,88,89,90,94,95,96],[44,91,92,93,95,97,99],[1,4,6,7,9,11,19,20,21,28,29,32,34,36,37,38,42,43,44,47,48,51,52,55,60,61,62,64,66,67,68,71,75,76,77,82,83,84,88,91,93,94,95,97],[79,91,92,94,95,97,99],[0,2,3,5,6,7,9,10,12,15,16,20,22,23,28,30,36,37,39,40,45,46,48,56,57,61,63,65,67,68,73,75,76,77,78,80,82,83,84,85,86,89,95,96,99],[0,1,2,3,4,5,8,10,14,15,16,18,19,20,21,22,24,25,27,28,30,32,33,36,39,40,41,42,45,46,48,49,52,53,54,55,57,58,60,63,65,66,67,70,71,76,77,82,84,86,88,91,93,97,99],[74,91,93,96,97,99],[1,2,3,4,5,6,7,9,13,15,16,17,20,22,23,24,28,29,31,32,37,43,45,46,49,50,52,53,60,61,65,66,68,71,72,76,77,81,90,91,95,96,97,99],[0,3,4,6,7,8,9,10,12,14,15,17,19,21,24,28,30,35,38,40,42,44,45,47,51,53,57,59,60,61,62,63,64,66,67,70,71,72,74,78,79,80,81,86,87,88,90,91,93,96,99],[0,1,3,4,5,9,11,12,13,14,15,16,17,20,26,27,28,32,36,37,38,39,40,42,43,45,46,48,49,50,56,57,59,60,64,65,68,72,75,77,79,86,89,92,94,95,98,99],[2,3,5,6,9,16,19,20,22,23,25,28,29,32,34,39,40,41,43,45,47,49,50,51,52,53,54,55,57,61,62,65,67,68,70,72,73,76,77,80,82,84,85,86,89,90,92,98,99],[0,3,5,7,12,17,18,19,20,21,25,26,27,28,33,34,35,36,37,38,44,45,48,51,54,55,57,58,59,60,62,66,67,68,70,73,74,77,79,80,81,82,85,86,90,91,93,94,95,98],[0,2,6,7,9,12,16,22,23,28,30,32,33,37,40,45,46,48,51,54,56,57,58,61,63,65,67,68,73,76,78,80,81,84,85,86,89,93,95,96,99],[0,3,4,5,7,8,9,13,20,24,25,26,29,34,35,37,39,40,42,43,48,49,52,53,56,57,63,64,65,66,70,75,76,77,78,81,83,84,87,91,94,95,96,98,99],[0,1,2,3,5,9,11,13,16,19,20,22,23,24,25,29,31,32,34,41,43,45,46,47,49,50,52,53,54,55,56,58,60,61,62,65,66,68,70,71,72,74,77,81,82,86,88,89,91,93,94,97,99],[0,3,4,5,8,9,11,12,13,17,18,19,20,23,24,29,30,31,33,36,39,42,49,51,52,53,54,57,58,59,60,62,64,67,68,69,70,71,72,76,77,78,79,80,83,84,85,92,93,95,96,97,98,99],[0,2,4,6,8,9,13,14,17,21,22,26,28,33,37,38,39,41,42,44,45,46,47,48,49,52,56,57,61,62,64,65,66,67,69,75,76,78,79,82,84,85,87,89,90,95,96],[67,91,93,94,95,96,97,99],[0,3,4,6,7,8,9,11,12,18,23,25,27,29,31,33,35,43,44,45,51,53,56,57,58,59,60,64,66,68,70,71,73,75,76,78,79,80,82,85,86,87,88,89,90,92,94,98,99],[0,2,3,5,6,7,8,9,11,12,16,17,18,19,21,22,27,29,33,35,36,37,38,39,40,42,43,45,47,48,49,58,59,61,62,65,68,72,74,78,79,80,81,87,90,94,96,98],[1,5,7,8,11,15,17,21,22,24,26,31,32,35,36,38,39,40,44,45,47,49,50,51,54,55,56,57,58,59,60,63,64,65,68,71,73,78,79,82,83,87,88,90,91,92,95,97,98,99],[37,91,94,98,99],[0,1,3,7,8,11,12,17,18,19,20,21,24,25,27,28,32,33,34,35,36,37,38,39,40,41,48,51,52,53,54,55,56,58,59,60,62,66,67,68,70,77,78,81,83,85,87,90,91,95,98,99],[1,2,3,5,6,8,14,18,20,24,25,26,28,29,32,33,34,35,36,38,39,41,47,48,49,50,51,52,53,54,55,56,57,58,59,61,65,67,68,73,74,77,78,81,82,84,85,86,88,89,93,94,95,97,98],[3,5,8,9,10,16,17,18,19,21,22,23,25,26,27,32,35,38,39,40,41,43,45,46,51,53,54,56,57,58,60,61,62,63,65,66,67,70,72,74,76,78,79,80,81,82,84,86,88,89,90,91,92,93,94,98],[0,2,5,9,10,12,13,14,15,16,19,20,22,23,27,28,35,36,37,38,39,42,43,44,46,48,49,52,54,62,65,66,67,68,69,72,76,77,78,80,83,84,87,88,90,91,92,93,95,98],[1,3,6,7,9,10,11,12,13,14,15,20,21,22,23,24,27,34,35,39,42,43,50,51,52,53,55,56,60,61,62,66,69,70,71,75,77,78,79,80,81,82,85,86,89,90,91,94,95,96,98,99],[1,2,4,6,8,9,12,13,14,17,19,20,21,25,26,31,32,34,36,37,38,40,41,42,43,44,45,46,48,50,52,57,60,61,64,71,74,75,76,77,79,80,81,83,86,88,89,90,91,93,99],[17,39,47,62,68,71,79,85,90,98,99],[1,2,4,5,6,7,8,12,13,16,17,18,19,20,22,25,27,32,33,34,35,40,41,44,46,47,49,50,51,52,53,54,55,58,59,61,62,64,65,66,68,72,73,74,75,76,77,78,79,80,82,84,85,90,94,95,97],[9,91,92,93,94,95,98,99],[0,4,12,13,16,18,19,22,23,24,25,27,28,33,34,35,40,42,43,46,47,49,50,51,52,55,57,58,63,64,65,66,69,71,72,76,77,80,81,84,85,86,88,90,91,92,93,95,97,99],[4,5,6,7,8,9,10,15,17,18,20,23,25,26,27,31,33,34,37,39,41,44,45,47,48,49,50,52,55,57,58,60,62,63,66,69,70,71,73,74,76,77,79,81,85,87,93,95,96,98,99],[0,2,7,8,10,12,13,14,16,20,23,25,26,27,28,29,31,34,36,38,39,42,44,45,46,50,54,56,59,61,62,66,69,72,75,80,84,85,88,92,93],[2,3,5,6,9,11,16,20,22,23,24,25,29,31,34,39,41,43,45,47,49,50,51,52,53,54,55,61,62,64,65,66,67,68,69,73,74,76,77,81,86,87,89,91,93,97,98,99],[2,5,8,9,11,12,13,14,15,18,21,23,25,27,31,33,36,37,38,39,40,41,42,43,48,49,50,54,58,59,60,61,67,68,70,71,72,74,75,81,82,85,88,90,92,94,95,97],[0,1,3,4,5,6,8,10,13,15,16,19,20,22,24,25,26,27,28,31,32,34,35,37,40,42,43,44,45,46,47,53,54,55,56,57,59,61,62,63,66,69,72,73,76,84,85,86,87,90,92,93,98,99],[28,31,73,80,81,82,83,90,91,93,94,96,97,98],[3,4,9,10,11,12,14,15,19,21,23,27,28,31,32,35,37,39,40,41,42,43,45,52,56,57,61,63,67,68,69,70,73,74,75,76,77,78,79,80,81,83,84,86,88,89,90,91,93,94,95,96,97],[0,2,4,5,8,10,11,12,15,16,17,18,20,21,22,23,25,28,29,31,32,34,38,39,41,42,43,44,49,51,52,54,57,59,60,63,65,66,68,69,70,71,73,76,77,78,79,80,81,82,83,86,87,88,92,94,95,96,97,98],[0,1,3,4,6,7,9,13,17,20,21,22,23,24,25,28,29,31,32,36,37,38,39,40,41,42,43,44,45,48,52,54,56,57,58,60,62,69,70,71,74,75,76,77,79,81,82,83,86,87,89,91,92,99],[0,3,4,6,7,8,9,11,12,17,18,23,24,27,29,31,33,35,39,40,43,44,45,51,53,56,58,59,60,61,64,70,71,73,75,76,78,80,82,83,84,85,87,88,90,91,93,95,97,98],[0,1,2,3,4,7,8,9,14,20,23,24,26,31,32,36,38,39,40,42,50,52,53,54,56,58,60,61,62,63,66,67,68,71,74,77,78,81,85,87,89,90,91,92,93,95,96,98],[0,2,3,6,7,8,10,15,17,18,23,25,27,28,34,37,38,41,43,47,48,50,53,55,56,57,59,60,62,64,66,68,70,73,74,75,79,82,85,88,90,91,92,93,96,97,98],[72,91,93,94,95,96,98,99],[1,2,3,5,9,11,13,16,17,19,20,22,23,25,29,31,32,34,39,40,41,43,45,46,47,49,50,52,53,54,55,56,57,60,61,62,65,70,71,72,74,77,79,81,83,84,87,88,91,93,94,96,98],[0,1,2,3,5,9,11,13,16,19,20,22,24,29,34,37,42,43,45,49,51,52,53,59,62,63,65,66,67,68,72,76,77,80,82,83,85,87,88,90,94,96,97,98],[0,1,4,8,9,10,11,14,15,18,23,24,25,31,32,33,34,36,37,38,39,41,42,43,48,50,51,54,57,58,59,61,62,64,66,67,68,69,73,75,79,81,82,83,84,85,86,89,90,91,93,94,95,96],[0,1,2,4,11,12,17,19,20,21,23,25,28,32,33,34,36,37,38,39,40,41,43,44,45,50,51,52,57,61,62,64,67,73,74,75,76,77,79,82,85,86,87,89,90,92,93,95,97,99],[0,1,2,4,5,10,11,12,13,15,16,20,22,23,24,25,27,28,29,32,34,35,36,38,39,40,41,42,45,46,47,49,50,51,52,55,57,61,62,63,64,65,66,69,71,72,73,75,77,80,82,83,84,85,86,88,90,92,96,98],[0,1,4,6,7,8,12,18,19,20,21,22,23,25,27,31,32,33,34,35,36,37,38,41,47,48,52,53,54,55,56,57,59,64,68,70,76,77,78,80,83,84,85,86,87,89,90,92,94,96,97],[11,12,18,28,31,35,74,80,81,84,89,94,96,97,98],[26,91,92,93,94,97,98,99],[50,91,95,97,98,99],[0,2,3,5,8,9,10,13,14,15,16,17,18,20,21,22,25,31,33,34,43,44,45,46,47,49,51,55,57,58,59,60,61,63,65,66,67,69,71,72,73,76,79,81,83,87,88,90,91,95,97,98,99],[0,1,4,5,6,8,15,16,17,21,22,23,25,26,27,28,31,32,34,35,36,39,40,41,45,49,51,57,60,61,62,64,65,66,67,68,69,71,72,74,75,78,79,84,86,87,89,91,92,93,97],[0,3,4,5,6,8,9,11,14,17,19,20,21,23,24,25,26,28,29,31,34,37,42,43,44,47,48,53,54,55,56,57,62,64,65,68,74,75,76,78,79,81,82,83,87,88,89,90,92,94,96,97,99],[0,1,2,3,4,7,8,13,15,16,17,20,24,25,26,32,34,35,37,39,42,46,48,50,51,53,61,63,66,67,68,70,72,75,76,78,79,81,82,83,85,86,87,89,90,91,95,96,97,98],[17,91,92,94,95,97,98,99],[0,1,2,4,5,6,7,10,14,15,16,20,21,22,24,27,28,29,34,35,36,39,41,42,43,44,45,46,50,51,54,57,65,71,72,81,83,84,87,89,93,95,96,98,99],[40,91,92,93,94,95,97,98,99],[0,3,4,6,7,8,9,10,11,12,14,15,19,24,31,32,35,38,39,40,42,44,45,50,53,57,59,60,61,63,64,66,67,68,69,71,78,80,83,84,85,88,93,94,95,98],[0,2,4,8,9,10,11,12,15,18,20,23,25,26,27,29,31,33,34,37,41,44,45,47,52,58,62,63,68,69,70,76,77,81,84,86,88,89,92,94,95,97,98,99],[3,4,6,7,9,10,12,14,15,19,20,21,23,24,27,35,39,42,43,47,51,52,53,55,56,60,61,62,64,66,68,69,70,73,75,77,78,80,81,82,85,86,87,89,92,93,94,95],[1,7,11,17,25,28,31,32,37,41,46,47,53,55,59,60,62,63,64,67,68,69,71,72,74,80,81,82,83,86,87,89,92,93,94,95,96,97,99],[0,3,4,6,7,9,10,12,14,15,19,21,24,28,35,38,39,40,42,44,45,47,51,53,57,59,60,61,62,63,64,66,67,68,70,71,72,74,78,80,81,85,86,87,89,90,91,93,96,98,99],[22,91,92,93,94,96,97,98,99],[0,1,2,3,4,7,8,9,14,17,20,23,24,26,31,32,33,36,38,40,42,47,51,52,53,54,56,58,60,61,63,65,66,67,71,74,77,78,79,81,83,84,87,89,91,92,93,95,96],[1,4,5,8,12,13,15,18,19,21,24,28,32,33,36,38,40,42,44,45,46,47,50,54,55,56,57,59,60,62,63,69,72,73,74,76,78,80,81,82,86,94,96,97,98,99],[69,91,93,95,96,97,98,99],[1,3,4,7,8,10,12,13,15,16,19,22,24,26,27,28,31,32,33,35,37,40,43,44,46,48,49,51,53,54,56,58,60,61,63,65,69,71,72,74,76,80,81,82,84,85,88,89,96,99],[0,1,2,3,4,5,6,7,8,9,13,14,18,25,27,28,29,31,32,33,35,40,41,42,49,50,51,53,54,55,58,59,61,62,63,66,67,68,71,73,76,82,83,85,88,89,91,94,98,99],[0,2,3,5,9,10,12,13,14,15,16,19,20,22,23,27,28,32,35,36,37,38,39,42,43,44,46,48,49,50,51,52,62,65,66,67,68,69,76,77,78,80,81,82,84,87,88,90,92,94,96],[1,3,5,7,9,11,12,15,18,21,22,25,26,27,28,29,32,33,34,36,38,41,42,43,49,53,57,59,62,65,68,70,73,74,75,76,79,80,84,85,86,87,88,89,91,93,97,98]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,10,11],"A_d":7936,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,1],[2,2],[3,3],[4,2],[5,1],[6,3],[7,3],[8,2],[9,2],[10,3],[11,2],[12,2],[13,1],[14,2],[15,3],[16,1],[17,3],[18,2],[19,2],[20,2],[21,2],[22,1],[23,3],[24,2],[25,2],[26,1],[27,3],[28,2],[29,1],[30,1],[31,1],[32,1],[33,1],[34,2],[35,2],[36,1],[37,2],[38,2],[39,1],[40,1],[41,2],[42,2],[43,3],[44,1],[45,1],[46,1],[47,3],[48,2],[49,1],[50,2],[51,2],[52,2],[53,3],[54,1],[55,3],[56,3],[57,2],[58,1],[59,2],[60,3],[61,2],[62,3],[63,1],[64,3],[65,1],[66,3],[67,1],[68,2],[69,2],[70,3],[71,1],[72,1],[73,3],[74,3],[75,3],[76,1],[77,2],[78,2],[79,3],[80,1],[81,1],[82,2],[85,1],[88,2],[90,1],[92,1],[93,2],[94,2],[95,2],[97,1],[99,2]],"CZ":[[0,2],[0,3],[0,6],[0,7],[0,8],[0,10],[0,15],[0,17],[0,18],[0,23],[0,25],[0,27],[0,28],[0,34],[0,37],[0,38],[0,41],[0,43],[0,47],[0,48],[0,50],[0,53],[0,55],[0,56],[0,57],[0,59],[0,60],[0,62],[0,64],[0,66],[0,68],[0,70],[0,73],[0,74],[0,75],[0,79],[0,82],[0,85],[0,88],[0,90],[0,93],[0,94],[0,95],[0,97],[0,99],[2,3],[2,6],[2,7],[2,8],[2,10],[2,15],[2,17],[2,18],[2,23],[2,25],[2,27],[2,28],[2,34],[2,37],[2,38],[2,41],[2,43],[2,47],[2,48],[2,50],[2,53],[2,55],[2,56],[2,57],[2,59],[2,60],[2,62],[2,64],[2,66],[2,68],[2,70],[2,73],[2,74],[2,75],[2,79],[2,82],[2,85],[2,88],[2,90],[2,93],[2,94],[2,95],[2,97],[2,99],[3,4],[3,8],[3,9],[3,11],[3,12],[3,14],[3,18],[3,19],[3,20],[3,21],[3,24],[3,25],[3,28],[3,34],[3,35],[3,37],[3,38],[3,41],[3,42],[3,48],[3,50],[3,51],[3,52],[3,57],[3,59],[3,61],[3,68],[3,69],[3,77],[3,78],[3,80],[3,81],[3,85],[3,90],[3,92],[3,97],[4,6],[4,7],[4,9],[4,10],[4,11],[4,12],[4,14],[4,15],[4,17],[4,19],[4,20],[4,21],[4,23],[4,24],[4,27],[4,35],[4,42],[4,43],[4,47],[4,51],[4,52],[4,53],[4,55],[4,56],[4,60],[4,61],[4,62],[4,64],[4,66],[4,69],[4,70],[4,73],[4,74],[4,75],[4,77],[4,78],[4,79],[4,80],[4,81],[4,82],[4,88],[4,92],[4,93],[4,94],[4,95],[4,99],[6,8],[6,9],[6,11],[6,12],[6,14],[6,18],[6,19],[6,20],[6,21],[6,24],[6,25],[6,28],[6,34],[6,35],[6,37],[6,38],[6,41],[6,42],[6,48],[6,50],[6,51],[6,52],[6,57],[6,59],[6,61],[6,68],[6,69],[6,77],[6,78],[6,80],[6,81],[6,85],[6,90],[6,92],[6,97],[7,8],[7,9],[7,11],[7,12],[7,14],[7,18],[7,19],[7,20],[7,21],[7,24],[7,25],[7,28],[7,34],[7,35],[7,37],[7,38],[7,41],[7,42],[7,48],[7,50],[7,51],[7,52],[7,57],[7,59],[7,61],[7,68],[7,69],[7,77],[7,78],[7,80],[7,81],[7,85],[7,90],[7,92],[7,97],[8,10],[8,15],[8,17],[8,18],[8,23],[8,25],[8,27],[8,28],[8,34],[8,37],[8,38],[8,41],[8,43],[8,47],[8,48],[8,50],[8,53],[8,55],[8,56],[8,57],[8,59],[8,60],[8,62],[8,64],[8,66],[8,68],[8,70],[8,73],[8,74],[8,75],[8,79],[8,82],[8,85],[8,88],[8,90],[8,93],[8,94],[8,95],[8,97],[8,99],[9,10],[9,11],[9,12],[9,14],[9,15],[9,17],[9,19],[9,20],[9,21],[9,23],[9,24],[9,27],[9,35],[9,42],[9,43],[9,47],[9,51],[9,52],[9,53],[9,55],[9,56],[9,60],[9,61],[9,62],[9,64],[9,66],[9,69],[9,70],[9,73],[9,74],[9,75],[9,77],[9,78],[9,79],[9,80],[9,81],[9,82],[9,88],[9,92],[9,93],[9,94],[9,95],[9,99],[10,11],[10,12],[10,14],[10,18],[10,19],[10,20],[10,21],[10,24],[10,25],[10,28],[10,34],[10,35],[10,37],[10,38],[10,41],[10,42],[10,48],[10,50],[10,51],[10,52],[10,57],[10,59],[10,61],[10,68],[10,69],[10,77],[10,78],[10,80],[10,81],[10,85],[10,90],[10,92],[10,97],[11,12],[11,14],[11,15],[11,17],[11,19],[11,20],[11,21],[11,23],[11,24],[11,27],[11,35],[11,42],[11,43],[11,47],[11,51],[11,52],[11,53],[11,55],[11,56],[11,60],[11,61],[11,62],[11,64],[11,66],[11,69],[11,70],[11,73],[11,74],[11,75],[11,77],[11,78],[11,79],[11,80],[11,81],[11,82],[11,88],[11,92],[11,93],[11,94],[11,95],[11,99],[12,14],[12,15],[12,17],[12,19],[12,20],[12,21],[12,23],[12,24],[12,27],[12,35],[12,42],[12,43],[12,47],[12,51],[12,52],[12,53],[12,55],[12,56],[12,60],[12,61],[12,62],[12,64],[12,66],[12,69],[12,70],[12,73],[12,74],[12,75],[12,77],[12,78],[12,79],[12,80],[12,81],[12,82],[12,88],[12,92],[12,93],[12,94],[12,95],[12,99],[14,15],[14,17],[14,19],[14,20],[14,21],[14,23],[14,24],[14,27],[14,35],[14,42],[14,43],[14,47],[14,51],[14,52],[14,53],[14,55],[14,56],[14,60],[14,61],[14,62],[14,64],[14,66],[14,69],[14,70],[14,73],[14,74],[14,75],[14,77],[14,78],[14,79],[14,80],[14,81],[14,82],[14,88],[14,92],[14,93],[14,94],[14,95],[14,99],[15,18],[15,19],[15,20],[15,21],[15,24],[15,25],[15,28],[15,34],[15,35],[15,37],[15,38],[15,41],[15,42],[15,48],[15,50],[15,51],[15,52],[15,57],[15,59],[15,61],[15,68],[15,69],[15,77],[15,78],[15,80],[15,81],[15,85],[15,90],[15,92],[15,97],[17,18],[17,19],[17,20],[17,21],[17,24],[17,25],[17,28],[17,34],[17,35],[17,37],[17,38],[17,41],[17,42],[17,48],[17,50],[17,51],[17,52],[17,57],[17,59],[17,61],[17,68],[17,69],[17,77],[17,78],[17,80],[17,81],[17,85],[17,90],[17,92],[17,97],[18,23],[18,25],[18,27],[18,28],[18,34],[18,37],[18,38],[18,41],[18,43],[18,47],[18,48],[18,50],[18,53],[18,55],[18,56],[18,57],[18,59],[18,60],[18,62],[18,64],[18,66],[18,68],[18,70],[18,73],[18,74],[18,75],[18,79],[18,82],[18,85],[18,88],[18,90],[18,93],[18,94],[18,95],[18,97],[18,99],[19,20],[19,21],[19,23],[19,24],[19,27],[19,35],[19,42],[19,43],[19,47],[19,51],[19,52],[19,53],[19,55],[19,56],[19,60],[19,61],[19,62],[19,64],[19,66],[19,69],[19,70],[19,73],[19,74],[19,75],[19,77],[19,78],[19,79],[19,80],[19,81],[19,82],[19,88],[19,92],[19,93],[19,94],[19,95],[19,99],[20,21],[20,23],[20,24],[20,27],[20,35],[20,42],[20,43],[20,47],[20,51],[20,52],[20,53],[20,55],[20,56],[20,60],[20,61],[20,62],[20,64],[20,66],[20,69],[20,70],[20,73],[20,74],[20,75],[20,77],[20,78],[20,79],[20,80],[20,81],[20,82],[20,88],[20,92],[20,93],[20,94],[20,95],[20,99],[21,23],[21,24],[21,27],[21,35],[21,42],[21,43],[21,47],[21,51],[21,52],[21,53],[21,55],[21,56],[21,60],[21,61],[21,62],[21,64],[21,66],[21,69],[21,70],[21,73],[21,74],[21,75],[21,77],[21,78],[21,79],[21,80],[21,81],[21,82],[21,88],[21,92],[21,93],[21,94],[21,95],[21,99],[23,24],[23,25],[23,28],[23,34],[23,35],[23,37],[23,38],[23,41],[23,42],[23,48],[23,50],[23,51],[23,52],[23,57],[23,59],[23,61],[23,68],[23,69],[23,77],[23,78],[23,80],[23,81],[23,85],[23,90],[23,92],[23,97],[24,27],[24,35],[24,42],[24,43],[24,47],[24,51],[24,52],[24,53],[24,55],[24,56],[24,60],[24,61],[24,62],[24,64],[24,66],[24,69],[24,70],[24,73],[24,74],[24,75],[24,77],[24,78],[24,79],[24,80],[24,81],[24,82],[24,88],[24,92],[24,93],[24,94],[24,95],[24,99],[25,27],[25,28],[25,34],[25,37],[25,38],[25,41],[25,43],[25,47],[25,48],[25,50],[25,53],[25,55],[25,56],[25,57],[25,59],[25,60],[25,62],[25,64],[25,66],[25,68],[25,70],[25,73],[25,74],[25,75],[25,79],[25,82],[25,85],[25,88],[25,90],[25,93],[25,94],[25,95],[25,97],[25,99],[27,28],[27,34],[27,35],[27,37],[27,38],[27,41],[27,42],[27,48],[27,50],[27,51],[27,52],[27,57],[27,59],[27,61],[27,68],[27,69],[27,77],[27,78],[27,80],[27,81],[27,85],[27,90],[27,92],[27,97],[28,34],[28,37],[28,38],[28,41],[28,43],[28,47],[28,48],[28,50],[28,53],[28,55],[28,56],[28,57],[28,59],[28,60],[28,62],[28,64],[28,66],[28,68],[28,70],[28,73],[28,74],[28,75],[28,79],[28,82],[28,85],[28,88],[28,90],[28,93],[28,94],[28,95],[28,97],[28,99],[34,37],[34,38],[34,41],[34,43],[34,47],[34,48],[34,50],[34,53],[34,55],[34,56],[34,57],[34,59],[34,60],[34,62],[34,64],[34,66],[34,68],[34,70],[34,73],[34,74],[34,75],[34,79],[34,82],[34,85],[34,88],[34,90],[34,93],[34,94],[34,95],[34,97],[34,99],[35,42],[35,43],[35,47],[35,51],[35,52],[35,53],[35,55],[35,56],[35,60],[35,61],[35,62],[35,64],[35,66],[35,69],[35,70],[35,73],[35,74],[35,75],[35,77],[35,78],[35,79],[35,80],[35,81],[35,82],[35,88],[35,92],[35,93],[35,94],[35,95],[35,99],[37,38],[37,41],[37,43],[37,47],[37,48],[37,50],[37,53],[37,55],[37,56],[37,57],[37,59],[37,60],[37,62],[37,64],[37,66],[37,68],[37,70],[37,73],[37,74],[37,75],[37,79],[37,82],[37,85],[37,88],[37,90],[37,93],[37,94],[37,95],[37,97],[37,99],[38,41],[38,43],[38,47],[38,48],[38,50],[38,53],[38,55],[38,56],[38,57],[38,59],[38,60],[38,62],[38,64],[38,66],[38,68],[38,70],[38,73],[38,74],[38,75],[38,79],[38,82],[38,85],[38,88],[38,90],[38,93],[38,94],[38,95],[38,97],[38,99],[41,43],[41,47],[41,48],[41,50],[41,53],[41,55],[41,56],[41,57],[41,59],[41,60],[41,62],[41,64],[41,66],[41,68],[41,70],[41,73],[41,74],[41,75],[41,79],[41,82],[41,85],[41,88],[41,90],[41,93],[41,94],[41,95],[41,97],[41,99],[42,43],[42,47],[42,51],[42,52],[42,53],[42,55],[42,56],[42,60],[42,61],[42,62],[42,64],[42,66],[42,69],[42,70],[42,73],[42,74],[42,75],[42,77],[42,78],[42,79],[42,80],[42,81],[42,82],[42,88],[42,92],[42,93],[42,94],[42,95],[42,99],[43,48],[43,50],[43,51],[43,52],[43,57],[43,59],[43,61],[43,68],[43,69],[43,77],[43,78],[43,80],[43,81],[43,85],[43,90],[43,92],[43,97],[47,48],[47,50],[47,51],[47,52],[47,57],[47,59],[47,61],[47,68],[47,69],[47,77],[47,78],[47,80],[47,81],[47,85],[47,90],[47,92],[47,97],[48,50],[48,53],[48,55],[48,56],[48,57],[48,59],[48,60],[48,62],[48,64],[48,66],[48,68],[48,70],[48,73],[48,74],[48,75],[48,79],[48,82],[48,85],[48,88],[48,90],[48,93],[48,94],[48,95],[48,97],[48,99],[50,53],[50,55],[50,56],[50,57],[50,59],[50,60],[50,62],[50,64],[50,66],[50,68],[50,70],[50,73],[50,74],[50,75],[50,79],[50,82],[50,85],[50,88],[50,90],[50,93],[50,94],[50,95],[50,97],[50,99],[51,52],[51,53],[51,55],[51,56],[51,60],[51,61],[51,62],[51,64],[51,66],[51,69],[51,70],[51,73],[51,74],[51,75],[51,77],[51,78],[51,79],[51,80],[51,81],[51,82],[51,88],[51,92],[51,93],[51,94],[51,95],[51,99],[52,53],[52,55],[52,56],[52,60],[52,61],[52,62],[52,64],[52,66],[52,69],[52,70],[52,73],[52,74],[52,75],[52,77],[52,78],[52,79],[52,80],[52,81],[52,82],[52,88],[52,92],[52,93],[52,94],[52,95],[52,99],[53,57],[53,59],[53,61],[53,68],[53,69],[53,77],[53,78],[53,80],[53,81],[53,85],[53,90],[53,92],[53,97],[55,57],[55,59],[55,61],[55,68],[55,69],[55,77],[55,78],[55,80],[55,81],[55,85],[55,90],[55,92],[55,97],[56,57],[56,59],[56,61],[56,68],[56,69],[56,77],[56,78],[56,80],[56,81],[56,85],[56,90],[56,92],[56,97],[57,59],[57,60],[57,62],[57,64],[57,66],[57,68],[57,70],[57,73],[57,74],[57,75],[57,79],[57,82],[57,85],[57,88],[57,90],[57,93],[57,94],[57,95],[57,97],[57,99],[59,60],[59,62],[59,64],[59,66],[59,68],[59,70],[59,73],[59,74],[59,75],[59,79],[59,82],[59,85],[59,88],[59,90],[59,93],[59,94],[59,95],[59,97],[59,99],[60,61],[60,68],[60,69],[60,77],[60,78],[60,80],[60,81],[60,85],[60,90],[60,92],[60,97],[61,62],[61,64],[61,66],[61,69],[61,70],[61,73],[61,74],[61,75],[61,77],[61,78],[61,79],[61,80],[61,81],[61,82],[61,88],[61,92],[61,93],[61,94],[61,95],[61,99],[62,68],[62,69],[62,77],[62,78],[62,80],[62,81],[62,85],[62,90],[62,92],[62,97],[64,68],[64,69],[64,77],[64,78],[64,80],[64,81],[64,85],[64,90],[64,92],[64,97],[66,68],[66,69],[66,77],[66,78],[66,80],[66,81],[66,85],[66,90],[66,92],[66,97],[68,70],[68,73],[68,74],[68,75],[68,79],[68,82],[68,85],[68,88],[68,90],[68,93],[68,94],[68,95],[68,97],[68,99],[69,70],[69,73],[69,74],[69,75],[69,77],[69,78],[69,79],[69,80],[69,81],[69,82],[69,88],[69,92],[69,93],[69,94],[69,95],[69,99],[70,77],[70,78],[70,80],[70,81],[70,85],[70,90],[70,92],[70,97],[73,77],[73,78],[73,80],[73,81],[73,85],[73,90],[73,92],[73,97],[74,77],[74,78],[74,80],[74,81],[74,85],[74,90],[74,92],[74,97],[75,77],[75,78],[75,80],[75,81],[75,85],[75,90],[75,92],[75,97],[77,78],[77,79],[77,80],[77,81],[77,82],[77,88],[77,92],[77,93],[77,94],[77,95],[77,99],[78,79],[78,80],[78,81],[78,82],[78,88],[78,92],[78,93],[78,94],[78,95],[78,99],[79,80],[79,81],[79,85],[79,90],[79,92],[79,97],[80,81],[80,82],[80,88],[80,92],[80,93],[80,94],[80,95],[80,99],[81,82],[81,88],[81,92],[81,93],[81,94],[81,95],[81,99],[82,85],[82,90],[82,92],[82,97],[85,88],[85,90],[85,93],[85,94],[85,95],[85,97],[85,99],[88,90],[88,92],[88,97],[90,93],[90,94],[90,95],[90,97],[90,99],[92,93],[92,94],[92,95],[92,99],[93,97],[94,97],[95,97],[97,99]]},"rotation_powers":[[0,5],[1,5],[2,5],[3,7],[4,3],[5,7],[6,3],[7,5],[9,7],[10,5],[11,5],[12,5],[13,7],[15,3],[16,3],[17,3],[18,7],[19,7],[20,5],[21,7],[22,5],[25,5],[27,3],[30,7],[31,7],[32,5],[33,7],[34,5],[35,7],[36,5],[38,3],[40,7],[41,3],[42,7],[44,3],[46,5],[52,5],[53,3],[55,3],[56,3],[57,3],[60,3],[62,3],[64,3],[65,3],[66,7],[71,7],[76,3],[78,3],[80,7],[83,3],[84,5],[88,3],[89,3],[90,5],[98,3],[99,3],[100,3],[101,5],[102,3],[103,3],[105,5],[106,5],[107,3],[108,3],[109,5],[111,3],[112,5],[113,7],[114,7],[115,7],[119,7],[121,3],[125,3],[127,5],[128,7],[130,7],[131,3],[132,3],[134,7],[136,3],[140,5],[143,3],[148,3],[149,3],[150,3],[151,3],[152,3],[154,5],[155,7],[157,3],[158,5],[159,3],[161,3],[163,3],[165,3],[168,5],[169,3],[170,3],[177,3],[179,3],[180,3],[181,3],[182,3],[185,3],[188,3],[191,3],[192,3],[193,3],[195,3],[197,3],[198,3],[202,3],[205,3],[206,3],[212,3],[213,5],[215,3],[217,3],[219,3],[226,3],[228,3],[229,3],[230,3],[231,3],[233,3],[239,3],[242,3],[243,3],[246,3],[251,3],[254,3],[256,3],[257,3],[258,3],[260,3],[261,3],[262,3],[264,3],[266,3],[269,3],[270,3],[277,3],[282,3],[283,3],[284,3],[286,3],[289,3],[293,3],[296,3],[297,3],[302,3],[304,3],[306,3],[308,3],[314,3],[318,3],[319,3],[320,3],[325,3],[327,3],[330,3],[335,3],[336,3],[340,3],[341,3],[342,3],[344,3],[345,3],[347,3],[351,3],[353,3],[356,3],[358,3],[359,3],[361,3],[363,3],[364,3],[365,3],[372,3],[373,3],[376,3],[378,3],[380,3],[383,3],[385,3],[388,3],[389,3],[390,3],[391,3],[392,3],[394,3],[401,3],[402,3],[404,3],[408,3],[409,3],[415,3],[417,3],[421,3],[424,3],[427,3]]},"metrics":{"gamma":1.2097694457568924,"gamma_t":null,"gamma_rho":1.2097694457568924,"gamma_claim":1.2097694457568924,"gamma_t_claim":null,"gamma_rho_claim":1.2097694457568924,"v_ex":80,"rate":0.18691588785046728,"t_count":null,"poly_degree":null,"effective_width":80},"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_428_80_4_0c04f8eae387.json","label":"paired_column_contraction_428_80_4_0c04f8eae387","N":100,"d":4,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_428_80_4_0c04f8eae387 (source catalogue id paired_column_contraction_428_80_4_0c04f8eae387); construction: Existing triorthogonal code with physical paired-column contraction; matrix 0c04f8eae3877c2d...; the release states d=4 (exact), gamma=1.2097694457568924 (exact)","notes":"matrix gamma_frontier_release/matrices/0c04f8eae3877c2deb7a092b3925299febebe26abbd99949791717a0eeb9f6cb.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"}]}