{"id":"512.84.6.a","row":1112,"stored":{"file":"master_catalog.json","row":1112,"construction":null,"columns_sha256":null},"parameters":{"n":512,"k":84,"d":6,"N":130,"r":46,"level":3},"gate":{"string":"0,64,83+0,65,82+0,66,81+0,67,80+0,68,79+0,69,78+0,70,77+0,71,76+0,72,75+0,73,74+1,54,83+1,55,82+1,56,81+1,57,80+1,58,79+1,59,78+1,60,77+1,61,76+1,62,75+1,63,74+2,50,83+2,51,82+2,52,81+2,53,80+2,58,73+2,59,72+2,60,71+2,61,70+2,62,69+2,63,68+3,49,83+3,51,79+3,52,78+3,53,77+3,55,73+3,56,72+3,57,71+3,61,67+3,62,66+3,63,65+4,49,82+4,50,79+4,52,76+4,53,75+4,54,73+4,56,70+4,57,69+4,59,67+4,60,66+4,63,64+5,49,81+5,50,78+5,51,76+5,53,74+5,54,72+5,55,70+5,57,68+5,58,67+5,60,65+5,62,64+6,49,80+6,50,77+6,51,75+6,52,74+6,54,71+6,55,69+6,56,68+6,58,66+6,59,65+6,61,64+7,39,83+7,40,82+7,41,81+7,42,80+7,43,79+7,44,78+7,45,77+7,46,76+7,47,75+7,48,74+8,35,83+8,36,82+8,37,81+8,38,80+8,43,73+8,44,72+8,45,71+8,46,70+8,47,69+8,48,68+9,34,83+9,36,79+9,37,78+9,38,77+9,40,73+9,41,72+9,42,71+9,46,67+9,47,66+9,48,65+10,34,82+10,35,79+10,37,76+10,38,75+10,39,73+10,41,70+10,42,69+10,44,67+10,45,66+10,48,64+11,34,81+11,35,78+11,36,76+11,38,74+11,39,72+11,40,70+11,42,68+11,43,67+11,45,65+11,47,64+12,34,80+12,35,77+12,36,75+12,37,74+12,39,71+12,40,69+12,41,68+12,43,66+12,44,65+12,46,64+13,30,83+13,31,82+13,32,81+13,33,80+13,43,63+13,44,62+13,45,61+13,46,60+13,47,59+13,48,58+14,29,83+14,31,79+14,32,78+14,33,77+14,40,63+14,41,62+14,42,61+14,46,57+14,47,56+14,48,55+15,29,82+15,30,79+15,32,76+15,33,75+15,39,63+15,41,60+15,42,59+15,44,57+15,45,56+15,48,54+16,29,81+16,30,78+16,31,76+16,33,74+16,39,62+16,40,60+16,42,58+16,43,57+16,45,55+16,47,54+17,29,80+17,30,77+17,31,75+17,32,74+17,39,61+17,40,59+17,41,58+17,43,56+17,44,55+17,46,54+18,28,83+18,31,73+18,32,72+18,33,71+18,36,63+18,37,62+18,38,61+18,46,53+18,47,52+18,48,51+19,28,82+19,30,73+19,32,70+19,33,69+19,35,63+19,37,60+19,38,59+19,44,53+19,45,52+19,48,50+20,28,81+20,30,72+20,31,70+20,33,68+20,35,62+20,36,60+20,38,58+20,43,53+20,45,51+20,47,50+21,28,80+21,30,71+21,31,69+21,32,68+21,35,61+21,36,59+21,37,58+21,43,52+21,44,51+21,46,50+22,28,79+22,29,73+22,32,67+22,33,66+22,34,63+22,37,57+22,38,56+22,41,53+22,42,52+22,48,49+23,28,78+23,29,72+23,31,67+23,33,65+23,34,62+23,36,57+23,38,55+23,40,53+23,42,51+23,47,49+24,28,77+24,29,71+24,31,66+24,32,65+24,34,61+24,36,56+24,37,55+24,40,52+24,41,51+24,46,49+25,28,76+25,29,70+25,30,67+25,33,64+25,34,60+25,35,57+25,38,54+25,39,53+25,42,50+25,45,49+26,28,75+26,29,69+26,30,66+26,32,64+26,34,59+26,35,56+26,37,54+26,39,52+26,41,50+26,44,49+27,28,74+27,29,68+27,30,65+27,31,64+27,34,58+27,35,55+27,36,54+27,39,51+27,40,50+27,43,49","human":"CCZ0,64,83\u00b7CCZ0,65,82\u00b7CCZ0,66,81\u00b7CCZ0,67,80\u00b7CCZ0,68,79\u00b7CCZ0,69,78\u00b7CCZ0,70,77\u00b7CCZ0,71,76\u00b7CCZ0,72,75\u00b7CCZ0,73,74\u00b7CCZ1,54,83\u00b7CCZ1,55,82\u00b7CCZ1,56,81\u00b7CCZ1,57,80\u00b7CCZ1,58,79\u00b7CCZ1,59,78\u00b7CCZ1,60,77\u00b7CCZ1,61,76\u00b7CCZ1,62,75\u00b7CCZ1,63,74\u00b7CCZ2,50,83\u00b7CCZ2,51,82\u00b7CCZ2,52,81\u00b7CCZ2,53,80\u00b7CCZ2,58,73\u00b7CCZ2,59,72\u00b7CCZ2,60,71\u00b7CCZ2,61,70\u00b7CCZ2,62,69\u00b7CCZ2,63,68\u00b7CCZ3,49,83\u00b7CCZ3,51,79\u00b7CCZ3,52,78\u00b7CCZ3,53,77\u00b7CCZ3,55,73\u00b7CCZ3,56,72\u00b7CCZ3,57,71\u00b7CCZ3,61,67\u00b7CCZ3,62,66\u00b7CCZ3,63,65\u00b7CCZ4,49,82\u00b7CCZ4,50,79\u00b7CCZ4,52,76\u00b7CCZ4,53,75\u00b7CCZ4,54,73\u00b7CCZ4,56,70\u00b7CCZ4,57,69\u00b7CCZ4,59,67\u00b7CCZ4,60,66\u00b7CCZ4,63,64\u00b7CCZ5,49,81\u00b7CCZ5,50,78\u00b7CCZ5,51,76\u00b7CCZ5,53,74\u00b7CCZ5,54,72\u00b7CCZ5,55,70\u00b7CCZ5,57,68\u00b7CCZ5,58,67\u00b7CCZ5,60,65\u00b7CCZ5,62,64\u00b7CCZ6,49,80\u00b7CCZ6,50,77\u00b7CCZ6,51,75\u00b7CCZ6,52,74\u00b7CCZ6,54,71\u00b7CCZ6,55,69\u00b7CCZ6,56,68\u00b7CCZ6,58,66\u00b7CCZ6,59,65\u00b7CCZ6,61,64\u00b7CCZ7,39,83\u00b7CCZ7,40,82\u00b7CCZ7,41,81\u00b7CCZ7,42,80\u00b7CCZ7,43,79\u00b7CCZ7,44,78\u00b7CCZ7,45,77\u00b7CCZ7,46,76\u00b7CCZ7,47,75\u00b7CCZ7,48,74\u00b7CCZ8,35,83\u00b7CCZ8,36,82\u00b7CCZ8,37,81\u00b7CCZ8,38,80\u00b7CCZ8,43,73\u00b7CCZ8,44,72\u00b7CCZ8,45,71\u00b7CCZ8,46,70\u00b7CCZ8,47,69\u00b7CCZ8,48,68\u00b7CCZ9,34,83\u00b7CCZ9,36,79\u00b7CCZ9,37,78\u00b7CCZ9,38,77\u00b7CCZ9,40,73\u00b7CCZ9,41,72\u00b7CCZ9,42,71\u00b7CCZ9,46,67\u00b7CCZ9,47,66\u00b7CCZ9,48,65\u00b7CCZ10,34,82\u00b7CCZ10,35,79\u00b7CCZ10,37,76\u00b7CCZ10,38,75\u00b7CCZ10,39,73\u00b7CCZ10,41,70\u00b7CCZ10,42,69\u00b7CCZ10,44,67\u00b7CCZ10,45,66\u00b7CCZ10,48,64\u00b7CCZ11,34,81\u00b7CCZ11,35,78\u00b7CCZ11,36,76\u00b7CCZ11,38,74\u00b7CCZ11,39,72\u00b7CCZ11,40,70\u00b7CCZ11,42,68\u00b7CCZ11,43,67\u00b7CCZ11,45,65\u00b7CCZ11,47,64\u00b7CCZ12,34,80\u00b7CCZ12,35,77\u00b7CCZ12,36,75\u00b7CCZ12,37,74\u00b7CCZ12,39,71\u00b7CCZ12,40,69\u00b7CCZ12,41,68\u00b7CCZ12,43,66\u00b7CCZ12,44,65\u00b7CCZ12,46,64\u00b7CCZ13,30,83\u00b7CCZ13,31,82\u00b7CCZ13,32,81\u00b7CCZ13,33,80\u00b7CCZ13,43,63\u00b7CCZ13,44,62\u00b7CCZ13,45,61\u00b7CCZ13,46,60\u00b7CCZ13,47,59\u00b7CCZ13,48,58\u00b7CCZ14,29,83\u00b7CCZ14,31,79\u00b7CCZ14,32,78\u00b7CCZ14,33,77\u00b7CCZ14,40,63\u00b7CCZ14,41,62\u00b7CCZ14,42,61\u00b7CCZ14,46,57\u00b7CCZ14,47,56\u00b7CCZ14,48,55\u00b7CCZ15,29,82\u00b7CCZ15,30,79\u00b7CCZ15,32,76\u00b7CCZ15,33,75\u00b7CCZ15,39,63\u00b7CCZ15,41,60\u00b7CCZ15,42,59\u00b7CCZ15,44,57\u00b7CCZ15,45,56\u00b7CCZ15,48,54\u00b7CCZ16,29,81\u00b7CCZ16,30,78\u00b7CCZ16,31,76\u00b7CCZ16,33,74\u00b7CCZ16,39,62\u00b7CCZ16,40,60\u00b7CCZ16,42,58\u00b7CCZ16,43,57\u00b7CCZ16,45,55\u00b7CCZ16,47,54\u00b7CCZ17,29,80\u00b7CCZ17,30,77\u00b7CCZ17,31,75\u00b7CCZ17,32,74\u00b7CCZ17,39,61\u00b7CCZ17,40,59\u00b7CCZ17,41,58\u00b7CCZ17,43,56\u00b7CCZ17,44,55\u00b7CCZ17,46,54\u00b7CCZ18,28,83\u00b7CCZ18,31,73\u00b7CCZ18,32,72\u00b7CCZ18,33,71\u00b7CCZ18,36,63\u00b7CCZ18,37,62\u00b7CCZ18,38,61\u00b7CCZ18,46,53\u00b7CCZ18,47,52\u00b7CCZ18,48,51\u00b7CCZ19,28,82\u00b7CCZ19,30,73\u00b7CCZ19,32,70\u00b7CCZ19,33,69\u00b7CCZ19,35,63\u00b7CCZ19,37,60\u00b7CCZ19,38,59\u00b7CCZ19,44,53\u00b7CCZ19,45,52\u00b7CCZ19,48,50\u00b7CCZ20,28,81\u00b7CCZ20,30,72\u00b7CCZ20,31,70\u00b7CCZ20,33,68\u00b7CCZ20,35,62\u00b7CCZ20,36,60\u00b7CCZ20,38,58\u00b7CCZ20,43,53\u00b7CCZ20,45,51\u00b7CCZ20,47,50\u00b7CCZ21,28,80\u00b7CCZ21,30,71\u00b7CCZ21,31,69\u00b7CCZ21,32,68\u00b7CCZ21,35,61\u00b7CCZ21,36,59\u00b7CCZ21,37,58\u00b7CCZ21,43,52\u00b7CCZ21,44,51\u00b7CCZ21,46,50\u00b7CCZ22,28,79\u00b7CCZ22,29,73\u00b7CCZ22,32,67\u00b7CCZ22,33,66\u00b7CCZ22,34,63\u00b7CCZ22,37,57\u00b7CCZ22,38,56\u00b7CCZ22,41,53\u00b7CCZ22,42,52\u00b7CCZ22,48,49\u00b7CCZ23,28,78\u00b7CCZ23,29,72\u00b7CCZ23,31,67\u00b7CCZ23,33,65\u00b7CCZ23,34,62\u00b7CCZ23,36,57\u00b7CCZ23,38,55\u00b7CCZ23,40,53\u00b7CCZ23,42,51\u00b7CCZ23,47,49\u00b7CCZ24,28,77\u00b7CCZ24,29,71\u00b7CCZ24,31,66\u00b7CCZ24,32,65\u00b7CCZ24,34,61\u00b7CCZ24,36,56\u00b7CCZ24,37,55\u00b7CCZ24,40,52\u00b7CCZ24,41,51\u00b7CCZ24,46,49\u00b7CCZ25,28,76\u00b7CCZ25,29,70\u00b7CCZ25,30,67\u00b7CCZ25,33,64\u00b7CCZ25,34,60\u00b7CCZ25,35,57\u00b7CCZ25,38,54\u00b7CCZ25,39,53\u00b7CCZ25,42,50\u00b7CCZ25,45,49\u00b7CCZ26,28,75\u00b7CCZ26,29,69\u00b7CCZ26,30,66\u00b7CCZ26,32,64\u00b7CCZ26,34,59\u00b7CCZ26,35,56\u00b7CCZ26,37,54\u00b7CCZ26,39,52\u00b7CCZ26,41,50\u00b7CCZ26,44,49\u00b7CCZ27,28,74\u00b7CCZ27,29,68\u00b7CCZ27,30,65\u00b7CCZ27,31,64\u00b7CCZ27,34,58\u00b7CCZ27,35,55\u00b7CCZ27,36,54\u00b7CCZ27,39,51\u00b7CCZ27,40,50\u00b7CCZ27,43,49","monomials":[[0,64,83],[0,65,82],[0,66,81],[0,67,80],[0,68,79],[0,69,78],[0,70,77],[0,71,76],[0,72,75],[0,73,74],[1,54,83],[1,55,82],[1,56,81],[1,57,80],[1,58,79],[1,59,78],[1,60,77],[1,61,76],[1,62,75],[1,63,74],[2,50,83],[2,51,82],[2,52,81],[2,53,80],[2,58,73],[2,59,72],[2,60,71],[2,61,70],[2,62,69],[2,63,68],[3,49,83],[3,51,79],[3,52,78],[3,53,77],[3,55,73],[3,56,72],[3,57,71],[3,61,67],[3,62,66],[3,63,65],[4,49,82],[4,50,79],[4,52,76],[4,53,75],[4,54,73],[4,56,70],[4,57,69],[4,59,67],[4,60,66],[4,63,64],[5,49,81],[5,50,78],[5,51,76],[5,53,74],[5,54,72],[5,55,70],[5,57,68],[5,58,67],[5,60,65],[5,62,64],[6,49,80],[6,50,77],[6,51,75],[6,52,74],[6,54,71],[6,55,69],[6,56,68],[6,58,66],[6,59,65],[6,61,64],[7,39,83],[7,40,82],[7,41,81],[7,42,80],[7,43,79],[7,44,78],[7,45,77],[7,46,76],[7,47,75],[7,48,74],[8,35,83],[8,36,82],[8,37,81],[8,38,80],[8,43,73],[8,44,72],[8,45,71],[8,46,70],[8,47,69],[8,48,68],[9,34,83],[9,36,79],[9,37,78],[9,38,77],[9,40,73],[9,41,72],[9,42,71],[9,46,67],[9,47,66],[9,48,65],[10,34,82],[10,35,79],[10,37,76],[10,38,75],[10,39,73],[10,41,70],[10,42,69],[10,44,67],[10,45,66],[10,48,64],[11,34,81],[11,35,78],[11,36,76],[11,38,74],[11,39,72],[11,40,70],[11,42,68],[11,43,67],[11,45,65],[11,47,64],[12,34,80],[12,35,77],[12,36,75],[12,37,74],[12,39,71],[12,40,69],[12,41,68],[12,43,66],[12,44,65],[12,46,64],[13,30,83],[13,31,82],[13,32,81],[13,33,80],[13,43,63],[13,44,62],[13,45,61],[13,46,60],[13,47,59],[13,48,58],[14,29,83],[14,31,79],[14,32,78],[14,33,77],[14,40,63],[14,41,62],[14,42,61],[14,46,57],[14,47,56],[14,48,55],[15,29,82],[15,30,79],[15,32,76],[15,33,75],[15,39,63],[15,41,60],[15,42,59],[15,44,57],[15,45,56],[15,48,54],[16,29,81],[16,30,78],[16,31,76],[16,33,74],[16,39,62],[16,40,60],[16,42,58],[16,43,57],[16,45,55],[16,47,54],[17,29,80],[17,30,77],[17,31,75],[17,32,74],[17,39,61],[17,40,59],[17,41,58],[17,43,56],[17,44,55],[17,46,54],[18,28,83],[18,31,73],[18,32,72],[18,33,71],[18,36,63],[18,37,62],[18,38,61],[18,46,53],[18,47,52],[18,48,51],[19,28,82],[19,30,73],[19,32,70],[19,33,69],[19,35,63],[19,37,60],[19,38,59],[19,44,53],[19,45,52],[19,48,50],[20,28,81],[20,30,72],[20,31,70],[20,33,68],[20,35,62],[20,36,60],[20,38,58],[20,43,53],[20,45,51],[20,47,50],[21,28,80],[21,30,71],[21,31,69],[21,32,68],[21,35,61],[21,36,59],[21,37,58],[21,43,52],[21,44,51],[21,46,50],[22,28,79],[22,29,73],[22,32,67],[22,33,66],[22,34,63],[22,37,57],[22,38,56],[22,41,53],[22,42,52],[22,48,49],[23,28,78],[23,29,72],[23,31,67],[23,33,65],[23,34,62],[23,36,57],[23,38,55],[23,40,53],[23,42,51],[23,47,49],[24,28,77],[24,29,71],[24,31,66],[24,32,65],[24,34,61],[24,36,56],[24,37,55],[24,40,52],[24,41,51],[24,46,49],[25,28,76],[25,29,70],[25,30,67],[25,33,64],[25,34,60],[25,35,57],[25,38,54],[25,39,53],[25,42,50],[25,45,49],[26,28,75],[26,29,69],[26,30,66],[26,32,64],[26,34,59],[26,35,56],[26,37,54],[26,39,52],[26,41,50],[26,44,49],[27,28,74],[27,29,68],[27,30,65],[27,31,64],[27,34,58],[27,35,55],[27,36,54],[27,39,51],[27,40,50],[27,43,49]],"sk_key":null,"sk_fingerprint":"893f13b8fe1f06f0","sk_canonical_frame":false,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[0,1,2,3,4,5,7,8,9,10,11,13,14,15,16,18,19,20,22,23,25,28,29,30,31,32,34,35,36,37,39,40,41,43,44,46,49,50,51,52,54,55,56,58,59,61,64,65,66,68,69,71,74,75,77,80,84,85,86,87,88,89,90,91,92,94,95,96,97,98,99,100,102,103,104,105,106,107,109,110,111,112,113,115,116,117,118,120,121,122,124,125,127],[0,1,2,3,4,6,7,8,9,10,12,13,14,15,17,18,19,21,22,24,26,28,29,30,31,33,34,35,36,38,39,40,42,43,45,47,49,50,51,53,54,55,57,58,60,62,64,65,67,68,70,72,74,76,78,81,84,85,86,87,88,89,90,91,93,94,95,96,97,98,99,101,102,103,104,105,106,108,109,110,111,112,114,115,116,117,119,120,121,123,124,126,128],[0,1,2,3,4,7,8,9,10,13,14,15,18,19,22,28,29,30,31,34,35,36,39,40,43,49,50,51,54,55,58,64,65,68,74,84,85,86,87,88,89,90,91,94,95,96,97,98,99,102,103,104,105,106,109,110,111,112,115,116,117,120,121,124],[0,1,2,3,5,6,7,8,9,11,12,13,14,16,17,18,20,21,23,24,27,28,29,30,32,33,34,35,37,38,39,41,42,44,45,48,49,50,52,53,54,56,57,59,60,63,64,66,67,69,70,73,75,76,79,82,84,85,86,87,88,89,90,92,93,94,95,96,97,98,100,101,102,103,104,105,107,108,109,110,111,113,114,115,116,118,119,120,122,123,125,126,129],[0,1,2,3,5,7,8,9,11,13,14,16,18,20,23,28,29,30,32,34,35,37,39,41,44,49,50,52,54,56,59,64,66,69,75,84,85,86,87,88,89,90,92,94,95,96,97,98,100,102,103,104,105,107,109,110,111,113,115,116,118,120,122,125],[0,1,2,3,6,7,8,9,12,13,14,17,18,21,24,28,29,30,33,34,35,38,39,42,45,49,50,53,54,57,60,64,67,70,76,84,85,86,87,88,89,90,93,94,95,96,97,98,101,102,103,104,105,108,109,110,111,114,115,116,119,120,123,126],[0,1,2,3,7,8,9,13,14,18,28,29,30,34,35,39,49,50,54,64,84,85,86,87,88,89,90,94,95,96,97,98,102,103,104,105,109,110,111,115,116,120],[0,1,2,4,5,6,7,8,10,11,12,13,15,16,17,19,20,21,25,26,27,28,29,31,32,33,34,36,37,38,40,41,42,46,47,48,49,51,52,53,55,56,57,61,62,63,65,66,67,71,72,73,77,78,79,83,84,85,86,87,88,89,91,92,93,94,95,96,97,99,100,101,102,103,104,106,107,108,109,110,112,113,114,115,117,118,119,121,122,123,127,128,129],[0,1,2,4,5,7,8,10,11,13,15,16,19,20,25,28,29,31,32,34,36,37,40,41,46,49,51,52,55,56,61,65,66,71,77,84,85,86,87,88,89,91,92,94,95,96,97,99,100,102,103,104,106,107,109,110,112,113,115,117,118,121,122,127],[0,1,2,4,6,7,8,10,12,13,15,17,19,21,26,28,29,31,33,34,36,38,40,42,47,49,51,53,55,57,62,65,67,72,78,84,85,86,87,88,89,91,93,94,95,96,97,99,101,102,103,104,106,108,109,110,112,114,115,117,119,121,123,128],[0,1,2,4,7,8,10,13,15,19,28,29,31,34,36,40,49,51,55,65,84,85,86,87,88,89,91,94,95,96,97,99,102,103,104,106,109,110,112,115,117,121],[0,1,2,5,6,7,8,11,12,13,16,17,20,21,27,28,29,32,33,34,37,38,41,42,48,49,52,53,56,57,63,66,67,73,79,84,85,86,87,88,89,92,93,94,95,96,97,100,101,102,103,104,107,108,109,110,113,114,115,118,119,122,123,129],[0,1,2,5,7,8,11,13,16,20,28,29,32,34,37,41,49,52,56,66,84,85,86,87,88,89,92,94,95,96,97,100,102,103,104,107,109,110,113,115,118,122],[0,1,2,6,7,8,12,13,17,21,28,29,33,34,38,42,49,53,57,67,84,85,86,87,88,89,93,94,95,96,97,101,102,103,104,108,109,110,114,115,119,123],[0,1,2,7,8,13,28,29,34,49,84,85,86,87,88,89,94,95,96,97,102,103,104,109,110,115],[0,1,3,4,5,6,7,9,10,11,12,14,15,16,17,22,23,24,25,26,27,28,30,31,32,33,35,36,37,38,43,44,45,46,47,48,50,51,52,53,58,59,60,61,62,63,68,69,70,71,72,73,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,101,102,103,105,106,107,108,109,111,112,113,114,116,117,118,119,124,125,126,127,128,129],[0,1,3,4,5,7,9,10,11,14,15,16,22,23,25,28,30,31,32,35,36,37,43,44,46,50,51,52,58,59,61,68,69,71,80,84,85,86,87,88,90,91,92,94,95,96,98,99,100,102,103,105,106,107,109,111,112,113,116,117,118,124,125,127],[0,1,3,4,6,7,9,10,12,14,15,17,22,24,26,28,30,31,33,35,36,38,43,45,47,50,51,53,58,60,62,68,70,72,81,84,85,86,87,88,90,91,93,94,95,96,98,99,101,102,103,105,106,108,109,111,112,114,116,117,119,124,126,128],[0,1,3,4,7,9,10,14,15,22,28,30,31,35,36,43,50,51,58,68,84,85,86,87,88,90,91,94,95,96,98,99,102,103,105,106,109,111,112,116,117,124],[0,1,3,5,6,7,9,11,12,14,16,17,23,24,27,28,30,32,33,35,37,38,44,45,48,50,52,53,59,60,63,69,70,73,82,84,85,86,87,88,90,92,93,94,95,96,98,100,101,102,103,105,107,108,109,111,113,114,116,118,119,125,126,129],[0,1,3,5,7,9,11,14,16,23,28,30,32,35,37,44,50,52,59,69,84,85,86,87,88,90,92,94,95,96,98,100,102,103,105,107,109,111,113,116,118,125],[0,1,3,6,7,9,12,14,17,24,28,30,33,35,38,45,50,53,60,70,84,85,86,87,88,90,93,94,95,96,98,101,102,103,105,108,109,111,114,116,119,126],[0,1,3,7,9,14,28,30,35,50,84,85,86,87,88,90,94,95,96,98,102,103,105,109,111,116],[0,1,4,5,6,7,10,11,12,15,16,17,25,26,27,28,31,32,33,36,37,38,46,47,48,51,52,53,61,62,63,71,72,73,83,84,85,86,87,88,91,92,93,94,95,96,99,100,101,102,103,106,107,108,109,112,113,114,117,118,119,127,128,129],[0,1,4,5,7,10,11,15,16,25,28,31,32,36,37,46,51,52,61,71,84,85,86,87,88,91,92,94,95,96,99,100,102,103,106,107,109,112,113,117,118,127],[0,1,4,6,7,10,12,15,17,26,28,31,33,36,38,47,51,53,62,72,84,85,86,87,88,91,93,94,95,96,99,101,102,103,106,108,109,112,114,117,119,128],[0,1,4,7,10,15,28,31,36,51,84,85,86,87,88,91,94,95,96,99,102,103,106,109,112,117],[0,1,5,6,7,11,12,16,17,27,28,32,33,37,38,48,52,53,63,73,84,85,86,87,88,92,93,94,95,96,100,101,102,103,107,108,109,113,114,118,119,129],[0,1,5,7,11,16,28,32,37,52,84,85,86,87,88,92,94,95,96,100,102,103,107,109,113,118],[0,1,6,7,12,17,28,33,38,53,84,85,86,87,88,93,94,95,96,101,102,103,108,109,114,119],[0,1,7,28,84,85,86,87,88,94,95,96,102,103,109],[0,2,3,4,5,6,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,29,30,31,32,33,39,40,41,42,43,44,45,46,47,48,54,55,56,57,58,59,60,61,62,63,74,75,76,77,78,79,80,81,82,83,84,85,86,87,89,90,91,92,93,94,95,97,98,99,100,101,102,104,105,106,107,108,110,111,112,113,114,120,121,122,123,124,125,126,127,128,129],[0,2,3,4,5,8,9,10,11,18,19,20,22,23,25,29,30,31,32,39,40,41,43,44,46,54,55,56,58,59,61,74,75,77,80,84,85,86,87,89,90,91,92,94,95,97,98,99,100,102,104,105,106,107,110,111,112,113,120,121,122,124,125,127],[0,2,3,4,6,8,9,10,12,18,19,21,22,24,26,29,30,31,33,39,40,42,43,45,47,54,55,57,58,60,62,74,76,78,81,84,85,86,87,89,90,91,93,94,95,97,98,99,101,102,104,105,106,108,110,111,112,114,120,121,123,124,126,128],[0,2,3,4,8,9,10,18,19,22,29,30,31,39,40,43,54,55,58,74,84,85,86,87,89,90,91,94,95,97,98,99,102,104,105,106,110,111,112,120,121,124],[0,2,3,5,6,8,9,11,12,18,20,21,23,24,27,29,30,32,33,39,41,42,44,45,48,54,56,57,59,60,63,75,76,79,82,84,85,86,87,89,90,92,93,94,95,97,98,100,101,102,104,105,107,108,110,111,113,114,120,122,123,125,126,129],[0,2,3,5,8,9,11,18,20,23,29,30,32,39,41,44,54,56,59,75,84,85,86,87,89,90,92,94,95,97,98,100,102,104,105,107,110,111,113,120,122,125],[0,2,3,6,8,9,12,18,21,24,29,30,33,39,42,45,54,57,60,76,84,85,86,87,89,90,93,94,95,97,98,101,102,104,105,108,110,111,114,120,123,126],[0,2,3,8,9,18,29,30,39,54,84,85,86,87,89,90,94,95,97,98,102,104,105,110,111,120],[0,2,4,5,6,8,10,11,12,19,20,21,25,26,27,29,31,32,33,40,41,42,46,47,48,55,56,57,61,62,63,77,78,79,83,84,85,86,87,89,91,92,93,94,95,97,99,100,101,102,104,106,107,108,110,112,113,114,121,122,123,127,128,129],[0,2,4,5,8,10,11,19,20,25,29,31,32,40,41,46,55,56,61,77,84,85,86,87,89,91,92,94,95,97,99,100,102,104,106,107,110,112,113,121,122,127],[0,2,4,6,8,10,12,19,21,26,29,31,33,40,42,47,55,57,62,78,84,85,86,87,89,91,93,94,95,97,99,101,102,104,106,108,110,112,114,121,123,128],[0,2,4,8,10,19,29,31,40,55,84,85,86,87,89,91,94,95,97,99,102,104,106,110,112,121],[0,2,5,6,8,11,12,20,21,27,29,32,33,41,42,48,56,57,63,79,84,85,86,87,89,92,93,94,95,97,100,101,102,104,107,108,110,113,114,122,123,129],[0,2,5,8,11,20,29,32,41,56,84,85,86,87,89,92,94,95,97,100,102,104,107,110,113,122],[0,2,6,8,12,21,29,33,42,57,84,85,86,87,89,93,94,95,97,101,102,104,108,110,114,123],[0,2,8,29,84,85,86,87,89,94,95,97,102,104,110],[0,3,4,5,6,9,10,11,12,22,23,24,25,26,27,30,31,32,33,43,44,45,46,47,48,58,59,60,61,62,63,80,81,82,83,84,85,86,87,90,91,92,93,94,95,98,99,100,101,102,105,106,107,108,111,112,113,114,124,125,126,127,128,129],[0,3,4,5,9,10,11,22,23,25,30,31,32,43,44,46,58,59,61,80,84,85,86,87,90,91,92,94,95,98,99,100,102,105,106,107,111,112,113,124,125,127],[0,3,4,6,9,10,12,22,24,26,30,31,33,43,45,47,58,60,62,81,84,85,86,87,90,91,93,94,95,98,99,101,102,105,106,108,111,112,114,124,126,128],[0,3,4,9,10,22,30,31,43,58,84,85,86,87,90,91,94,95,98,99,102,105,106,111,112,124],[0,3,5,6,9,11,12,23,24,27,30,32,33,44,45,48,59,60,63,82,84,85,86,87,90,92,93,94,95,98,100,101,102,105,107,108,111,113,114,125,126,129],[0,3,5,9,11,23,30,32,44,59,84,85,86,87,90,92,94,95,98,100,102,105,107,111,113,125],[0,3,6,9,12,24,30,33,45,60,84,85,86,87,90,93,94,95,98,101,102,105,108,111,114,126],[0,3,9,30,84,85,86,87,90,94,95,98,102,105,111],[0,4,5,6,10,11,12,25,26,27,31,32,33,46,47,48,61,62,63,83,84,85,86,87,91,92,93,94,95,99,100,101,102,106,107,108,112,113,114,127,128,129],[0,4,5,10,11,25,31,32,46,61,84,85,86,87,91,92,94,95,99,100,102,106,107,112,113,127],[0,4,6,10,12,26,31,33,47,62,84,85,86,87,91,93,94,95,99,101,102,106,108,112,114,128],[0,4,10,31,84,85,86,87,91,94,95,99,102,106,112],[0,5,6,11,12,27,32,33,48,63,84,85,86,87,92,93,94,95,100,101,102,107,108,113,114,129],[0,5,11,32,84,85,86,87,92,94,95,100,102,107,113],[0,6,12,33,84,85,86,87,93,94,95,101,102,108,114],[0,84,85,86,87,94,95,102],[1,2,3,4,5,6,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,88,89,90,91,92,93,94,96,97,98,99,100,101,103,104,105,106,107,108,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[1,2,3,4,5,13,14,15,16,18,19,20,22,23,25,34,35,36,37,39,40,41,43,44,46,64,65,66,68,69,71,74,75,77,80,84,85,86,88,89,90,91,92,94,96,97,98,99,100,103,104,105,106,107,115,116,117,118,120,121,122,124,125,127],[1,2,3,4,6,13,14,15,17,18,19,21,22,24,26,34,35,36,38,39,40,42,43,45,47,64,65,67,68,70,72,74,76,78,81,84,85,86,88,89,90,91,93,94,96,97,98,99,101,103,104,105,106,108,115,116,117,119,120,121,123,124,126,128],[1,2,3,4,13,14,15,18,19,22,34,35,36,39,40,43,64,65,68,74,84,85,86,88,89,90,91,94,96,97,98,99,103,104,105,106,115,116,117,120,121,124],[1,2,3,5,6,13,14,16,17,18,20,21,23,24,27,34,35,37,38,39,41,42,44,45,48,64,66,67,69,70,73,75,76,79,82,84,85,86,88,89,90,92,93,94,96,97,98,100,101,103,104,105,107,108,115,116,118,119,120,122,123,125,126,129],[1,2,3,5,13,14,16,18,20,23,34,35,37,39,41,44,64,66,69,75,84,85,86,88,89,90,92,94,96,97,98,100,103,104,105,107,115,116,118,120,122,125],[1,2,3,6,13,14,17,18,21,24,34,35,38,39,42,45,64,67,70,76,84,85,86,88,89,90,93,94,96,97,98,101,103,104,105,108,115,116,119,120,123,126],[1,2,3,13,14,18,34,35,39,64,84,85,86,88,89,90,94,96,97,98,103,104,105,115,116,120],[1,2,4,5,6,13,15,16,17,19,20,21,25,26,27,34,36,37,38,40,41,42,46,47,48,65,66,67,71,72,73,77,78,79,83,84,85,86,88,89,91,92,93,94,96,97,99,100,101,103,104,106,107,108,115,117,118,119,121,122,123,127,128,129],[1,2,4,5,13,15,16,19,20,25,34,36,37,40,41,46,65,66,71,77,84,85,86,88,89,91,92,94,96,97,99,100,103,104,106,107,115,117,118,121,122,127],[1,2,4,6,13,15,17,19,21,26,34,36,38,40,42,47,65,67,72,78,84,85,86,88,89,91,93,94,96,97,99,101,103,104,106,108,115,117,119,121,123,128],[1,2,4,13,15,19,34,36,40,65,84,85,86,88,89,91,94,96,97,99,103,104,106,115,117,121],[1,2,5,6,13,16,17,20,21,27,34,37,38,41,42,48,66,67,73,79,84,85,86,88,89,92,93,94,96,97,100,101,103,104,107,108,115,118,119,122,123,129],[1,2,5,13,16,20,34,37,41,66,84,85,86,88,89,92,94,96,97,100,103,104,107,115,118,122],[1,2,6,13,17,21,34,38,42,67,84,85,86,88,89,93,94,96,97,101,103,104,108,115,119,123],[1,2,13,34,84,85,86,88,89,94,96,97,103,104,115],[1,3,4,5,6,14,15,16,17,22,23,24,25,26,27,35,36,37,38,43,44,45,46,47,48,68,69,70,71,72,73,80,81,82,83,84,85,86,88,90,91,92,93,94,96,98,99,100,101,103,105,106,107,108,116,117,118,119,124,125,126,127,128,129],[1,3,4,5,14,15,16,22,23,25,35,36,37,43,44,46,68,69,71,80,84,85,86,88,90,91,92,94,96,98,99,100,103,105,106,107,116,117,118,124,125,127],[1,3,4,6,14,15,17,22,24,26,35,36,38,43,45,47,68,70,72,81,84,85,86,88,90,91,93,94,96,98,99,101,103,105,106,108,116,117,119,124,126,128],[1,3,4,14,15,22,35,36,43,68,84,85,86,88,90,91,94,96,98,99,103,105,106,116,117,124],[1,3,5,6,14,16,17,23,24,27,35,37,38,44,45,48,69,70,73,82,84,85,86,88,90,92,93,94,96,98,100,101,103,105,107,108,116,118,119,125,126,129],[1,3,5,14,16,23,35,37,44,69,84,85,86,88,90,92,94,96,98,100,103,105,107,116,118,125],[1,3,6,14,17,24,35,38,45,70,84,85,86,88,90,93,94,96,98,101,103,105,108,116,119,126],[1,3,14,35,84,85,86,88,90,94,96,98,103,105,116],[1,4,5,6,15,16,17,25,26,27,36,37,38,46,47,48,71,72,73,83,84,85,86,88,91,92,93,94,96,99,100,101,103,106,107,108,117,118,119,127,128,129],[1,4,5,15,16,25,36,37,46,71,84,85,86,88,91,92,94,96,99,100,103,106,107,117,118,127],[1,4,6,15,17,26,36,38,47,72,84,85,86,88,91,93,94,96,99,101,103,106,108,117,119,128],[1,4,15,36,84,85,86,88,91,94,96,99,103,106,117],[1,5,6,16,17,27,37,38,48,73,84,85,86,88,92,93,94,96,100,101,103,107,108,118,119,129],[1,5,16,37,84,85,86,88,92,94,96,100,103,107,118],[1,6,17,38,84,85,86,88,93,94,96,101,103,108,119],[1,84,85,86,88,94,96,103],[2,3,4,5,6,18,19,20,21,22,23,24,25,26,27,39,40,41,42,43,44,45,46,47,48,74,75,76,77,78,79,80,81,82,83,84,85,86,89,90,91,92,93,94,97,98,99,100,101,104,105,106,107,108,120,121,122,123,124,125,126,127,128,129],[2,3,4,5,18,19,20,22,23,25,39,40,41,43,44,46,74,75,77,80,84,85,86,89,90,91,92,94,97,98,99,100,104,105,106,107,120,121,122,124,125,127],[2,3,4,6,18,19,21,22,24,26,39,40,42,43,45,47,74,76,78,81,84,85,86,89,90,91,93,94,97,98,99,101,104,105,106,108,120,121,123,124,126,128],[2,3,4,18,19,22,39,40,43,74,84,85,86,89,90,91,94,97,98,99,104,105,106,120,121,124],[2,3,5,6,18,20,21,23,24,27,39,41,42,44,45,48,75,76,79,82,84,85,86,89,90,92,93,94,97,98,100,101,104,105,107,108,120,122,123,125,126,129],[2,3,5,18,20,23,39,41,44,75,84,85,86,89,90,92,94,97,98,100,104,105,107,120,122,125],[2,3,6,18,21,24,39,42,45,76,84,85,86,89,90,93,94,97,98,101,104,105,108,120,123,126],[2,3,18,39,84,85,86,89,90,94,97,98,104,105,120],[2,4,5,6,19,20,21,25,26,27,40,41,42,46,47,48,77,78,79,83,84,85,86,89,91,92,93,94,97,99,100,101,104,106,107,108,121,122,123,127,128,129],[2,4,5,19,20,25,40,41,46,77,84,85,86,89,91,92,94,97,99,100,104,106,107,121,122,127],[2,4,6,19,21,26,40,42,47,78,84,85,86,89,91,93,94,97,99,101,104,106,108,121,123,128],[2,4,19,40,84,85,86,89,91,94,97,99,104,106,121],[2,5,6,20,21,27,41,42,48,79,84,85,86,89,92,93,94,97,100,101,104,107,108,122,123,129],[2,5,20,41,84,85,86,89,92,94,97,100,104,107,122],[2,6,21,42,84,85,86,89,93,94,97,101,104,108,123],[2,84,85,86,89,94,97,104],[3,4,5,6,22,23,24,25,26,27,43,44,45,46,47,48,80,81,82,83,84,85,86,90,91,92,93,94,98,99,100,101,105,106,107,108,124,125,126,127,128,129],[3,4,5,22,23,25,43,44,46,80,84,85,86,90,91,92,94,98,99,100,105,106,107,124,125,127],[3,4,6,22,24,26,43,45,47,81,84,85,86,90,91,93,94,98,99,101,105,106,108,124,126,128],[3,4,22,43,84,85,86,90,91,94,98,99,105,106,124],[3,5,6,23,24,27,44,45,48,82,84,85,86,90,92,93,94,98,100,101,105,107,108,125,126,129],[3,5,23,44,84,85,86,90,92,94,98,100,105,107,125],[3,6,24,45,84,85,86,90,93,94,98,101,105,108,126],[3,84,85,86,90,94,98,105],[4,5,6,25,26,27,46,47,48,83,84,85,86,91,92,93,94,99,100,101,106,107,108,127,128,129],[4,5,25,46,84,85,86,91,92,94,99,100,106,107,127],[4,6,26,47,84,85,86,91,93,94,99,101,106,108,128],[4,84,85,86,91,94,99,106],[5,6,27,48,84,85,86,92,93,94,100,101,107,108,129],[5,84,85,86,92,94,100,107],[6,84,85,86,93,94,101,108],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,87,88,89,90,91,92,93,95,96,97,98,99,100,101,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[7,8,9,10,11,13,14,15,16,18,19,20,22,23,25,49,50,51,52,54,55,56,58,59,61,64,65,66,68,69,71,74,75,77,80,84,85,87,88,89,90,91,92,95,96,97,98,99,100,109,110,111,112,113,115,116,117,118,120,121,122,124,125,127],[7,8,9,10,12,13,14,15,17,18,19,21,22,24,26,49,50,51,53,54,55,57,58,60,62,64,65,67,68,70,72,74,76,78,81,84,85,87,88,89,90,91,93,95,96,97,98,99,101,109,110,111,112,114,115,116,117,119,120,121,123,124,126,128],[7,8,9,10,13,14,15,18,19,22,49,50,51,54,55,58,64,65,68,74,84,85,87,88,89,90,91,95,96,97,98,99,109,110,111,112,115,116,117,120,121,124],[7,8,9,11,12,13,14,16,17,18,20,21,23,24,27,49,50,52,53,54,56,57,59,60,63,64,66,67,69,70,73,75,76,79,82,84,85,87,88,89,90,92,93,95,96,97,98,100,101,109,110,111,113,114,115,116,118,119,120,122,123,125,126,129],[7,8,9,11,13,14,16,18,20,23,49,50,52,54,56,59,64,66,69,75,84,85,87,88,89,90,92,95,96,97,98,100,109,110,111,113,115,116,118,120,122,125],[7,8,9,12,13,14,17,18,21,24,49,50,53,54,57,60,64,67,70,76,84,85,87,88,89,90,93,95,96,97,98,101,109,110,111,114,115,116,119,120,123,126],[7,8,9,13,14,18,49,50,54,64,84,85,87,88,89,90,95,96,97,98,109,110,111,115,116,120],[7,8,10,11,12,13,15,16,17,19,20,21,25,26,27,49,51,52,53,55,56,57,61,62,63,65,66,67,71,72,73,77,78,79,83,84,85,87,88,89,91,92,93,95,96,97,99,100,101,109,110,112,113,114,115,117,118,119,121,122,123,127,128,129],[7,8,10,11,13,15,16,19,20,25,49,51,52,55,56,61,65,66,71,77,84,85,87,88,89,91,92,95,96,97,99,100,109,110,112,113,115,117,118,121,122,127],[7,8,10,12,13,15,17,19,21,26,49,51,53,55,57,62,65,67,72,78,84,85,87,88,89,91,93,95,96,97,99,101,109,110,112,114,115,117,119,121,123,128],[7,8,10,13,15,19,49,51,55,65,84,85,87,88,89,91,95,96,97,99,109,110,112,115,117,121],[7,8,11,12,13,16,17,20,21,27,49,52,53,56,57,63,66,67,73,79,84,85,87,88,89,92,93,95,96,97,100,101,109,110,113,114,115,118,119,122,123,129],[7,8,11,13,16,20,49,52,56,66,84,85,87,88,89,92,95,96,97,100,109,110,113,115,118,122],[7,8,12,13,17,21,49,53,57,67,84,85,87,88,89,93,95,96,97,101,109,110,114,115,119,123],[7,8,13,49,84,85,87,88,89,95,96,97,109,110,115],[7,9,10,11,12,14,15,16,17,22,23,24,25,26,27,50,51,52,53,58,59,60,61,62,63,68,69,70,71,72,73,80,81,82,83,84,85,87,88,90,91,92,93,95,96,98,99,100,101,109,111,112,113,114,116,117,118,119,124,125,126,127,128,129],[7,9,10,11,14,15,16,22,23,25,50,51,52,58,59,61,68,69,71,80,84,85,87,88,90,91,92,95,96,98,99,100,109,111,112,113,116,117,118,124,125,127],[7,9,10,12,14,15,17,22,24,26,50,51,53,58,60,62,68,70,72,81,84,85,87,88,90,91,93,95,96,98,99,101,109,111,112,114,116,117,119,124,126,128],[7,9,10,14,15,22,50,51,58,68,84,85,87,88,90,91,95,96,98,99,109,111,112,116,117,124],[7,9,11,12,14,16,17,23,24,27,50,52,53,59,60,63,69,70,73,82,84,85,87,88,90,92,93,95,96,98,100,101,109,111,113,114,116,118,119,125,126,129],[7,9,11,14,16,23,50,52,59,69,84,85,87,88,90,92,95,96,98,100,109,111,113,116,118,125],[7,9,12,14,17,24,50,53,60,70,84,85,87,88,90,93,95,96,98,101,109,111,114,116,119,126],[7,9,14,50,84,85,87,88,90,95,96,98,109,111,116],[7,10,11,12,15,16,17,25,26,27,51,52,53,61,62,63,71,72,73,83,84,85,87,88,91,92,93,95,96,99,100,101,109,112,113,114,117,118,119,127,128,129],[7,10,11,15,16,25,51,52,61,71,84,85,87,88,91,92,95,96,99,100,109,112,113,117,118,127],[7,10,12,15,17,26,51,53,62,72,84,85,87,88,91,93,95,96,99,101,109,112,114,117,119,128],[7,10,15,51,84,85,87,88,91,95,96,99,109,112,117],[7,11,12,16,17,27,52,53,63,73,84,85,87,88,92,93,95,96,100,101,109,113,114,118,119,129],[7,11,16,52,84,85,87,88,92,95,96,100,109,113,118],[7,12,17,53,84,85,87,88,93,95,96,101,109,114,119],[7,84,85,87,88,95,96,109],[8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,54,55,56,57,58,59,60,61,62,63,74,75,76,77,78,79,80,81,82,83,84,85,87,89,90,91,92,93,95,97,98,99,100,101,110,111,112,113,114,120,121,122,123,124,125,126,127,128,129],[8,9,10,11,18,19,20,22,23,25,54,55,56,58,59,61,74,75,77,80,84,85,87,89,90,91,92,95,97,98,99,100,110,111,112,113,120,121,122,124,125,127],[8,9,10,12,18,19,21,22,24,26,54,55,57,58,60,62,74,76,78,81,84,85,87,89,90,91,93,95,97,98,99,101,110,111,112,114,120,121,123,124,126,128],[8,9,10,18,19,22,54,55,58,74,84,85,87,89,90,91,95,97,98,99,110,111,112,120,121,124],[8,9,11,12,18,20,21,23,24,27,54,56,57,59,60,63,75,76,79,82,84,85,87,89,90,92,93,95,97,98,100,101,110,111,113,114,120,122,123,125,126,129],[8,9,11,18,20,23,54,56,59,75,84,85,87,89,90,92,95,97,98,100,110,111,113,120,122,125],[8,9,12,18,21,24,54,57,60,76,84,85,87,89,90,93,95,97,98,101,110,111,114,120,123,126],[8,9,18,54,84,85,87,89,90,95,97,98,110,111,120],[8,10,11,12,19,20,21,25,26,27,55,56,57,61,62,63,77,78,79,83,84,85,87,89,91,92,93,95,97,99,100,101,110,112,113,114,121,122,123,127,128,129],[8,10,11,19,20,25,55,56,61,77,84,85,87,89,91,92,95,97,99,100,110,112,113,121,122,127],[8,10,12,19,21,26,55,57,62,78,84,85,87,89,91,93,95,97,99,101,110,112,114,121,123,128],[8,10,19,55,84,85,87,89,91,95,97,99,110,112,121],[8,11,12,20,21,27,56,57,63,79,84,85,87,89,92,93,95,97,100,101,110,113,114,122,123,129],[8,11,20,56,84,85,87,89,92,95,97,100,110,113,122],[8,12,21,57,84,85,87,89,93,95,97,101,110,114,123],[8,84,85,87,89,95,97,110],[9,10,11,12,22,23,24,25,26,27,58,59,60,61,62,63,80,81,82,83,84,85,87,90,91,92,93,95,98,99,100,101,111,112,113,114,124,125,126,127,128,129],[9,10,11,22,23,25,58,59,61,80,84,85,87,90,91,92,95,98,99,100,111,112,113,124,125,127],[9,10,12,22,24,26,58,60,62,81,84,85,87,90,91,93,95,98,99,101,111,112,114,124,126,128],[9,10,22,58,84,85,87,90,91,95,98,99,111,112,124],[9,11,12,23,24,27,59,60,63,82,84,85,87,90,92,93,95,98,100,101,111,113,114,125,126,129],[9,11,23,59,84,85,87,90,92,95,98,100,111,113,125],[9,12,24,60,84,85,87,90,93,95,98,101,111,114,126],[9,84,85,87,90,95,98,111],[10,11,12,25,26,27,61,62,63,83,84,85,87,91,92,93,95,99,100,101,112,113,114,127,128,129],[10,11,25,61,84,85,87,91,92,95,99,100,112,113,127],[10,12,26,62,84,85,87,91,93,95,99,101,112,114,128],[10,84,85,87,91,95,99,112],[11,12,27,63,84,85,87,92,93,95,100,101,113,114,129],[11,84,85,87,92,95,100,113],[12,84,85,87,93,95,101,114],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,88,89,90,91,92,93,96,97,98,99,100,101,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[13,14,15,16,18,19,20,22,23,25,64,65,66,68,69,71,74,75,77,80,84,85,88,89,90,91,92,96,97,98,99,100,115,116,117,118,120,121,122,124,125,127],[13,14,15,17,18,19,21,22,24,26,64,65,67,68,70,72,74,76,78,81,84,85,88,89,90,91,93,96,97,98,99,101,115,116,117,119,120,121,123,124,126,128],[13,14,15,18,19,22,64,65,68,74,84,85,88,89,90,91,96,97,98,99,115,116,117,120,121,124],[13,14,16,17,18,20,21,23,24,27,64,66,67,69,70,73,75,76,79,82,84,85,88,89,90,92,93,96,97,98,100,101,115,116,118,119,120,122,123,125,126,129],[13,14,16,18,20,23,64,66,69,75,84,85,88,89,90,92,96,97,98,100,115,116,118,120,122,125],[13,14,17,18,21,24,64,67,70,76,84,85,88,89,90,93,96,97,98,101,115,116,119,120,123,126],[13,14,18,64,84,85,88,89,90,96,97,98,115,116,120],[13,15,16,17,19,20,21,25,26,27,65,66,67,71,72,73,77,78,79,83,84,85,88,89,91,92,93,96,97,99,100,101,115,117,118,119,121,122,123,127,128,129],[13,15,16,19,20,25,65,66,71,77,84,85,88,89,91,92,96,97,99,100,115,117,118,121,122,127],[13,15,17,19,21,26,65,67,72,78,84,85,88,89,91,93,96,97,99,101,115,117,119,121,123,128],[13,15,19,65,84,85,88,89,91,96,97,99,115,117,121],[13,16,17,20,21,27,66,67,73,79,84,85,88,89,92,93,96,97,100,101,115,118,119,122,123,129],[13,16,20,66,84,85,88,89,92,96,97,100,115,118,122],[13,17,21,67,84,85,88,89,93,96,97,101,115,119,123],[13,84,85,88,89,96,97,115],[14,15,16,17,22,23,24,25,26,27,68,69,70,71,72,73,80,81,82,83,84,85,88,90,91,92,93,96,98,99,100,101,116,117,118,119,124,125,126,127,128,129],[14,15,16,22,23,25,68,69,71,80,84,85,88,90,91,92,96,98,99,100,116,117,118,124,125,127],[14,15,17,22,24,26,68,70,72,81,84,85,88,90,91,93,96,98,99,101,116,117,119,124,126,128],[14,15,22,68,84,85,88,90,91,96,98,99,116,117,124],[14,16,17,23,24,27,69,70,73,82,84,85,88,90,92,93,96,98,100,101,116,118,119,125,126,129],[14,16,23,69,84,85,88,90,92,96,98,100,116,118,125],[14,17,24,70,84,85,88,90,93,96,98,101,116,119,126],[14,84,85,88,90,96,98,116],[15,16,17,25,26,27,71,72,73,83,84,85,88,91,92,93,96,99,100,101,117,118,119,127,128,129],[15,16,25,71,84,85,88,91,92,96,99,100,117,118,127],[15,17,26,72,84,85,88,91,93,96,99,101,117,119,128],[15,84,85,88,91,96,99,117],[16,17,27,73,84,85,88,92,93,96,100,101,118,119,129],[16,84,85,88,92,96,100,118],[17,84,85,88,93,96,101,119],[18,19,20,21,22,23,24,25,26,27,74,75,76,77,78,79,80,81,82,83,84,85,89,90,91,92,93,97,98,99,100,101,120,121,122,123,124,125,126,127,128,129],[18,19,20,22,23,25,74,75,77,80,84,85,89,90,91,92,97,98,99,100,120,121,122,124,125,127],[18,19,21,22,24,26,74,76,78,81,84,85,89,90,91,93,97,98,99,101,120,121,123,124,126,128],[18,19,22,74,84,85,89,90,91,97,98,99,120,121,124],[18,20,21,23,24,27,75,76,79,82,84,85,89,90,92,93,97,98,100,101,120,122,123,125,126,129],[18,20,23,75,84,85,89,90,92,97,98,100,120,122,125],[18,21,24,76,84,85,89,90,93,97,98,101,120,123,126],[18,84,85,89,90,97,98,120],[19,20,21,25,26,27,77,78,79,83,84,85,89,91,92,93,97,99,100,101,121,122,123,127,128,129],[19,20,25,77,84,85,89,91,92,97,99,100,121,122,127],[19,21,26,78,84,85,89,91,93,97,99,101,121,123,128],[19,84,85,89,91,97,99,121],[20,21,27,79,84,85,89,92,93,97,100,101,122,123,129],[20,84,85,89,92,97,100,122],[21,84,85,89,93,97,101,123],[22,23,24,25,26,27,80,81,82,83,84,85,90,91,92,93,98,99,100,101,124,125,126,127,128,129],[22,23,25,80,84,85,90,91,92,98,99,100,124,125,127],[22,24,26,81,84,85,90,91,93,98,99,101,124,126,128],[22,84,85,90,91,98,99,124],[23,24,27,82,84,85,90,92,93,98,100,101,125,126,129],[23,84,85,90,92,98,100,125],[24,84,85,90,93,98,101,126],[25,26,27,83,84,85,91,92,93,99,100,101,127,128,129],[25,84,85,91,92,99,100,127],[26,84,85,91,93,99,101,128],[27,84,85,92,93,100,101,129],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,86,87,88,89,90,91,92,93,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[28,29,30,31,32,34,35,36,37,39,40,41,43,44,46,49,50,51,52,54,55,56,58,59,61,64,65,66,68,69,71,74,75,77,80,84,86,87,88,89,90,91,92,102,103,104,105,106,107,109,110,111,112,113,115,116,117,118,120,121,122,124,125,127],[28,29,30,31,33,34,35,36,38,39,40,42,43,45,47,49,50,51,53,54,55,57,58,60,62,64,65,67,68,70,72,74,76,78,81,84,86,87,88,89,90,91,93,102,103,104,105,106,108,109,110,111,112,114,115,116,117,119,120,121,123,124,126,128],[28,29,30,31,34,35,36,39,40,43,49,50,51,54,55,58,64,65,68,74,84,86,87,88,89,90,91,102,103,104,105,106,109,110,111,112,115,116,117,120,121,124],[28,29,30,32,33,34,35,37,38,39,41,42,44,45,48,49,50,52,53,54,56,57,59,60,63,64,66,67,69,70,73,75,76,79,82,84,86,87,88,89,90,92,93,102,103,104,105,107,108,109,110,111,113,114,115,116,118,119,120,122,123,125,126,129],[28,29,30,32,34,35,37,39,41,44,49,50,52,54,56,59,64,66,69,75,84,86,87,88,89,90,92,102,103,104,105,107,109,110,111,113,115,116,118,120,122,125],[28,29,30,33,34,35,38,39,42,45,49,50,53,54,57,60,64,67,70,76,84,86,87,88,89,90,93,102,103,104,105,108,109,110,111,114,115,116,119,120,123,126],[28,29,30,34,35,39,49,50,54,64,84,86,87,88,89,90,102,103,104,105,109,110,111,115,116,120],[28,29,31,32,33,34,36,37,38,40,41,42,46,47,48,49,51,52,53,55,56,57,61,62,63,65,66,67,71,72,73,77,78,79,83,84,86,87,88,89,91,92,93,102,103,104,106,107,108,109,110,112,113,114,115,117,118,119,121,122,123,127,128,129],[28,29,31,32,34,36,37,40,41,46,49,51,52,55,56,61,65,66,71,77,84,86,87,88,89,91,92,102,103,104,106,107,109,110,112,113,115,117,118,121,122,127],[28,29,31,33,34,36,38,40,42,47,49,51,53,55,57,62,65,67,72,78,84,86,87,88,89,91,93,102,103,104,106,108,109,110,112,114,115,117,119,121,123,128],[28,29,31,34,36,40,49,51,55,65,84,86,87,88,89,91,102,103,104,106,109,110,112,115,117,121],[28,29,32,33,34,37,38,41,42,48,49,52,53,56,57,63,66,67,73,79,84,86,87,88,89,92,93,102,103,104,107,108,109,110,113,114,115,118,119,122,123,129],[28,29,32,34,37,41,49,52,56,66,84,86,87,88,89,92,102,103,104,107,109,110,113,115,118,122],[28,29,33,34,38,42,49,53,57,67,84,86,87,88,89,93,102,103,104,108,109,110,114,115,119,123],[28,29,34,49,84,86,87,88,89,102,103,104,109,110,115],[28,30,31,32,33,35,36,37,38,43,44,45,46,47,48,50,51,52,53,58,59,60,61,62,63,68,69,70,71,72,73,80,81,82,83,84,86,87,88,90,91,92,93,102,103,105,106,107,108,109,111,112,113,114,116,117,118,119,124,125,126,127,128,129],[28,30,31,32,35,36,37,43,44,46,50,51,52,58,59,61,68,69,71,80,84,86,87,88,90,91,92,102,103,105,106,107,109,111,112,113,116,117,118,124,125,127],[28,30,31,33,35,36,38,43,45,47,50,51,53,58,60,62,68,70,72,81,84,86,87,88,90,91,93,102,103,105,106,108,109,111,112,114,116,117,119,124,126,128],[28,30,31,35,36,43,50,51,58,68,84,86,87,88,90,91,102,103,105,106,109,111,112,116,117,124],[28,30,32,33,35,37,38,44,45,48,50,52,53,59,60,63,69,70,73,82,84,86,87,88,90,92,93,102,103,105,107,108,109,111,113,114,116,118,119,125,126,129],[28,30,32,35,37,44,50,52,59,69,84,86,87,88,90,92,102,103,105,107,109,111,113,116,118,125],[28,30,33,35,38,45,50,53,60,70,84,86,87,88,90,93,102,103,105,108,109,111,114,116,119,126],[28,30,35,50,84,86,87,88,90,102,103,105,109,111,116],[28,31,32,33,36,37,38,46,47,48,51,52,53,61,62,63,71,72,73,83,84,86,87,88,91,92,93,102,103,106,107,108,109,112,113,114,117,118,119,127,128,129],[28,31,32,36,37,46,51,52,61,71,84,86,87,88,91,92,102,103,106,107,109,112,113,117,118,127],[28,31,33,36,38,47,51,53,62,72,84,86,87,88,91,93,102,103,106,108,109,112,114,117,119,128],[28,31,36,51,84,86,87,88,91,102,103,106,109,112,117],[28,32,33,37,38,48,52,53,63,73,84,86,87,88,92,93,102,103,107,108,109,113,114,118,119,129],[28,32,37,52,84,86,87,88,92,102,103,107,109,113,118],[28,33,38,53,84,86,87,88,93,102,103,108,109,114,119],[28,84,86,87,88,102,103,109],[29,30,31,32,33,39,40,41,42,43,44,45,46,47,48,54,55,56,57,58,59,60,61,62,63,74,75,76,77,78,79,80,81,82,83,84,86,87,89,90,91,92,93,102,104,105,106,107,108,110,111,112,113,114,120,121,122,123,124,125,126,127,128,129],[29,30,31,32,39,40,41,43,44,46,54,55,56,58,59,61,74,75,77,80,84,86,87,89,90,91,92,102,104,105,106,107,110,111,112,113,120,121,122,124,125,127],[29,30,31,33,39,40,42,43,45,47,54,55,57,58,60,62,74,76,78,81,84,86,87,89,90,91,93,102,104,105,106,108,110,111,112,114,120,121,123,124,126,128],[29,30,31,39,40,43,54,55,58,74,84,86,87,89,90,91,102,104,105,106,110,111,112,120,121,124],[29,30,32,33,39,41,42,44,45,48,54,56,57,59,60,63,75,76,79,82,84,86,87,89,90,92,93,102,104,105,107,108,110,111,113,114,120,122,123,125,126,129],[29,30,32,39,41,44,54,56,59,75,84,86,87,89,90,92,102,104,105,107,110,111,113,120,122,125],[29,30,33,39,42,45,54,57,60,76,84,86,87,89,90,93,102,104,105,108,110,111,114,120,123,126],[29,30,39,54,84,86,87,89,90,102,104,105,110,111,120],[29,31,32,33,40,41,42,46,47,48,55,56,57,61,62,63,77,78,79,83,84,86,87,89,91,92,93,102,104,106,107,108,110,112,113,114,121,122,123,127,128,129],[29,31,32,40,41,46,55,56,61,77,84,86,87,89,91,92,102,104,106,107,110,112,113,121,122,127],[29,31,33,40,42,47,55,57,62,78,84,86,87,89,91,93,102,104,106,108,110,112,114,121,123,128],[29,31,40,55,84,86,87,89,91,102,104,106,110,112,121],[29,32,33,41,42,48,56,57,63,79,84,86,87,89,92,93,102,104,107,108,110,113,114,122,123,129],[29,32,41,56,84,86,87,89,92,102,104,107,110,113,122],[29,33,42,57,84,86,87,89,93,102,104,108,110,114,123],[29,84,86,87,89,102,104,110],[30,31,32,33,43,44,45,46,47,48,58,59,60,61,62,63,80,81,82,83,84,86,87,90,91,92,93,102,105,106,107,108,111,112,113,114,124,125,126,127,128,129],[30,31,32,43,44,46,58,59,61,80,84,86,87,90,91,92,102,105,106,107,111,112,113,124,125,127],[30,31,33,43,45,47,58,60,62,81,84,86,87,90,91,93,102,105,106,108,111,112,114,124,126,128],[30,31,43,58,84,86,87,90,91,102,105,106,111,112,124],[30,32,33,44,45,48,59,60,63,82,84,86,87,90,92,93,102,105,107,108,111,113,114,125,126,129],[30,32,44,59,84,86,87,90,92,102,105,107,111,113,125],[30,33,45,60,84,86,87,90,93,102,105,108,111,114,126],[30,84,86,87,90,102,105,111],[31,32,33,46,47,48,61,62,63,83,84,86,87,91,92,93,102,106,107,108,112,113,114,127,128,129],[31,32,46,61,84,86,87,91,92,102,106,107,112,113,127],[31,33,47,62,84,86,87,91,93,102,106,108,112,114,128],[31,84,86,87,91,102,106,112],[32,33,48,63,84,86,87,92,93,102,107,108,113,114,129],[32,84,86,87,92,102,107,113],[33,84,86,87,93,102,108,114],[34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,86,88,89,90,91,92,93,103,104,105,106,107,108,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[34,35,36,37,39,40,41,43,44,46,64,65,66,68,69,71,74,75,77,80,84,86,88,89,90,91,92,103,104,105,106,107,115,116,117,118,120,121,122,124,125,127],[34,35,36,38,39,40,42,43,45,47,64,65,67,68,70,72,74,76,78,81,84,86,88,89,90,91,93,103,104,105,106,108,115,116,117,119,120,121,123,124,126,128],[34,35,36,39,40,43,64,65,68,74,84,86,88,89,90,91,103,104,105,106,115,116,117,120,121,124],[34,35,37,38,39,41,42,44,45,48,64,66,67,69,70,73,75,76,79,82,84,86,88,89,90,92,93,103,104,105,107,108,115,116,118,119,120,122,123,125,126,129],[34,35,37,39,41,44,64,66,69,75,84,86,88,89,90,92,103,104,105,107,115,116,118,120,122,125],[34,35,38,39,42,45,64,67,70,76,84,86,88,89,90,93,103,104,105,108,115,116,119,120,123,126],[34,35,39,64,84,86,88,89,90,103,104,105,115,116,120],[34,36,37,38,40,41,42,46,47,48,65,66,67,71,72,73,77,78,79,83,84,86,88,89,91,92,93,103,104,106,107,108,115,117,118,119,121,122,123,127,128,129],[34,36,37,40,41,46,65,66,71,77,84,86,88,89,91,92,103,104,106,107,115,117,118,121,122,127],[34,36,38,40,42,47,65,67,72,78,84,86,88,89,91,93,103,104,106,108,115,117,119,121,123,128],[34,36,40,65,84,86,88,89,91,103,104,106,115,117,121],[34,37,38,41,42,48,66,67,73,79,84,86,88,89,92,93,103,104,107,108,115,118,119,122,123,129],[34,37,41,66,84,86,88,89,92,103,104,107,115,118,122],[34,38,42,67,84,86,88,89,93,103,104,108,115,119,123],[34,84,86,88,89,103,104,115],[35,36,37,38,43,44,45,46,47,48,68,69,70,71,72,73,80,81,82,83,84,86,88,90,91,92,93,103,105,106,107,108,116,117,118,119,124,125,126,127,128,129],[35,36,37,43,44,46,68,69,71,80,84,86,88,90,91,92,103,105,106,107,116,117,118,124,125,127],[35,36,38,43,45,47,68,70,72,81,84,86,88,90,91,93,103,105,106,108,116,117,119,124,126,128],[35,36,43,68,84,86,88,90,91,103,105,106,116,117,124],[35,37,38,44,45,48,69,70,73,82,84,86,88,90,92,93,103,105,107,108,116,118,119,125,126,129],[35,37,44,69,84,86,88,90,92,103,105,107,116,118,125],[35,38,45,70,84,86,88,90,93,103,105,108,116,119,126],[35,84,86,88,90,103,105,116],[36,37,38,46,47,48,71,72,73,83,84,86,88,91,92,93,103,106,107,108,117,118,119,127,128,129],[36,37,46,71,84,86,88,91,92,103,106,107,117,118,127],[36,38,47,72,84,86,88,91,93,103,106,108,117,119,128],[36,84,86,88,91,103,106,117],[37,38,48,73,84,86,88,92,93,103,107,108,118,119,129],[37,84,86,88,92,103,107,118],[38,84,86,88,93,103,108,119],[39,40,41,42,43,44,45,46,47,48,74,75,76,77,78,79,80,81,82,83,84,86,89,90,91,92,93,104,105,106,107,108,120,121,122,123,124,125,126,127,128,129],[39,40,41,43,44,46,74,75,77,80,84,86,89,90,91,92,104,105,106,107,120,121,122,124,125,127],[39,40,42,43,45,47,74,76,78,81,84,86,89,90,91,93,104,105,106,108,120,121,123,124,126,128],[39,40,43,74,84,86,89,90,91,104,105,106,120,121,124],[39,41,42,44,45,48,75,76,79,82,84,86,89,90,92,93,104,105,107,108,120,122,123,125,126,129],[39,41,44,75,84,86,89,90,92,104,105,107,120,122,125],[39,42,45,76,84,86,89,90,93,104,105,108,120,123,126],[39,84,86,89,90,104,105,120],[40,41,42,46,47,48,77,78,79,83,84,86,89,91,92,93,104,106,107,108,121,122,123,127,128,129],[40,41,46,77,84,86,89,91,92,104,106,107,121,122,127],[40,42,47,78,84,86,89,91,93,104,106,108,121,123,128],[40,84,86,89,91,104,106,121],[41,42,48,79,84,86,89,92,93,104,107,108,122,123,129],[41,84,86,89,92,104,107,122],[42,84,86,89,93,104,108,123],[43,44,45,46,47,48,80,81,82,83,84,86,90,91,92,93,105,106,107,108,124,125,126,127,128,129],[43,44,46,80,84,86,90,91,92,105,106,107,124,125,127],[43,45,47,81,84,86,90,91,93,105,106,108,124,126,128],[43,84,86,90,91,105,106,124],[44,45,48,82,84,86,90,92,93,105,107,108,125,126,129],[44,84,86,90,92,105,107,125],[45,84,86,90,93,105,108,126],[46,47,48,83,84,86,91,92,93,106,107,108,127,128,129],[46,84,86,91,92,106,107,127],[47,84,86,91,93,106,108,128],[48,84,86,92,93,107,108,129],[49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,87,88,89,90,91,92,93,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[49,50,51,52,54,55,56,58,59,61,64,65,66,68,69,71,74,75,77,80,84,87,88,89,90,91,92,109,110,111,112,113,115,116,117,118,120,121,122,124,125,127],[49,50,51,53,54,55,57,58,60,62,64,65,67,68,70,72,74,76,78,81,84,87,88,89,90,91,93,109,110,111,112,114,115,116,117,119,120,121,123,124,126,128],[49,50,51,54,55,58,64,65,68,74,84,87,88,89,90,91,109,110,111,112,115,116,117,120,121,124],[49,50,52,53,54,56,57,59,60,63,64,66,67,69,70,73,75,76,79,82,84,87,88,89,90,92,93,109,110,111,113,114,115,116,118,119,120,122,123,125,126,129],[49,50,52,54,56,59,64,66,69,75,84,87,88,89,90,92,109,110,111,113,115,116,118,120,122,125],[49,50,53,54,57,60,64,67,70,76,84,87,88,89,90,93,109,110,111,114,115,116,119,120,123,126],[49,50,54,64,84,87,88,89,90,109,110,111,115,116,120],[49,51,52,53,55,56,57,61,62,63,65,66,67,71,72,73,77,78,79,83,84,87,88,89,91,92,93,109,110,112,113,114,115,117,118,119,121,122,123,127,128,129],[49,51,52,55,56,61,65,66,71,77,84,87,88,89,91,92,109,110,112,113,115,117,118,121,122,127],[49,51,53,55,57,62,65,67,72,78,84,87,88,89,91,93,109,110,112,114,115,117,119,121,123,128],[49,51,55,65,84,87,88,89,91,109,110,112,115,117,121],[49,52,53,56,57,63,66,67,73,79,84,87,88,89,92,93,109,110,113,114,115,118,119,122,123,129],[49,52,56,66,84,87,88,89,92,109,110,113,115,118,122],[49,53,57,67,84,87,88,89,93,109,110,114,115,119,123],[49,84,87,88,89,109,110,115],[50,51,52,53,58,59,60,61,62,63,68,69,70,71,72,73,80,81,82,83,84,87,88,90,91,92,93,109,111,112,113,114,116,117,118,119,124,125,126,127,128,129],[50,51,52,58,59,61,68,69,71,80,84,87,88,90,91,92,109,111,112,113,116,117,118,124,125,127],[50,51,53,58,60,62,68,70,72,81,84,87,88,90,91,93,109,111,112,114,116,117,119,124,126,128],[50,51,58,68,84,87,88,90,91,109,111,112,116,117,124],[50,52,53,59,60,63,69,70,73,82,84,87,88,90,92,93,109,111,113,114,116,118,119,125,126,129],[50,52,59,69,84,87,88,90,92,109,111,113,116,118,125],[50,53,60,70,84,87,88,90,93,109,111,114,116,119,126],[50,84,87,88,90,109,111,116],[51,52,53,61,62,63,71,72,73,83,84,87,88,91,92,93,109,112,113,114,117,118,119,127,128,129],[51,52,61,71,84,87,88,91,92,109,112,113,117,118,127],[51,53,62,72,84,87,88,91,93,109,112,114,117,119,128],[51,84,87,88,91,109,112,117],[52,53,63,73,84,87,88,92,93,109,113,114,118,119,129],[52,84,87,88,92,109,113,118],[53,84,87,88,93,109,114,119],[54,55,56,57,58,59,60,61,62,63,74,75,76,77,78,79,80,81,82,83,84,87,89,90,91,92,93,110,111,112,113,114,120,121,122,123,124,125,126,127,128,129],[54,55,56,58,59,61,74,75,77,80,84,87,89,90,91,92,110,111,112,113,120,121,122,124,125,127],[54,55,57,58,60,62,74,76,78,81,84,87,89,90,91,93,110,111,112,114,120,121,123,124,126,128],[54,55,58,74,84,87,89,90,91,110,111,112,120,121,124],[54,56,57,59,60,63,75,76,79,82,84,87,89,90,92,93,110,111,113,114,120,122,123,125,126,129],[54,56,59,75,84,87,89,90,92,110,111,113,120,122,125],[54,57,60,76,84,87,89,90,93,110,111,114,120,123,126],[54,84,87,89,90,110,111,120],[55,56,57,61,62,63,77,78,79,83,84,87,89,91,92,93,110,112,113,114,121,122,123,127,128,129],[55,56,61,77,84,87,89,91,92,110,112,113,121,122,127],[55,57,62,78,84,87,89,91,93,110,112,114,121,123,128],[55,84,87,89,91,110,112,121],[56,57,63,79,84,87,89,92,93,110,113,114,122,123,129],[56,84,87,89,92,110,113,122],[57,84,87,89,93,110,114,123],[58,59,60,61,62,63,80,81,82,83,84,87,90,91,92,93,111,112,113,114,124,125,126,127,128,129],[58,59,61,80,84,87,90,91,92,111,112,113,124,125,127],[58,60,62,81,84,87,90,91,93,111,112,114,124,126,128],[58,84,87,90,91,111,112,124],[59,60,63,82,84,87,90,92,93,111,113,114,125,126,129],[59,84,87,90,92,111,113,125],[60,84,87,90,93,111,114,126],[61,62,63,83,84,87,91,92,93,112,113,114,127,128,129],[61,84,87,91,92,112,113,127],[62,84,87,91,93,112,114,128],[63,84,87,92,93,113,114,129],[64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,88,89,90,91,92,93,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129],[64,65,66,68,69,71,74,75,77,80,84,88,89,90,91,92,115,116,117,118,120,121,122,124,125,127],[64,65,67,68,70,72,74,76,78,81,84,88,89,90,91,93,115,116,117,119,120,121,123,124,126,128],[64,65,68,74,84,88,89,90,91,115,116,117,120,121,124],[64,66,67,69,70,73,75,76,79,82,84,88,89,90,92,93,115,116,118,119,120,122,123,125,126,129],[64,66,69,75,84,88,89,90,92,115,116,118,120,122,125],[64,67,70,76,84,88,89,90,93,115,116,119,120,123,126],[64,84,88,89,90,115,116,120],[65,66,67,71,72,73,77,78,79,83,84,88,89,91,92,93,115,117,118,119,121,122,123,127,128,129],[65,66,71,77,84,88,89,91,92,115,117,118,121,122,127],[65,67,72,78,84,88,89,91,93,115,117,119,121,123,128],[65,84,88,89,91,115,117,121],[66,67,73,79,84,88,89,92,93,115,118,119,122,123,129],[66,84,88,89,92,115,118,122],[67,84,88,89,93,115,119,123],[68,69,70,71,72,73,80,81,82,83,84,88,90,91,92,93,116,117,118,119,124,125,126,127,128,129],[68,69,71,80,84,88,90,91,92,116,117,118,124,125,127],[68,70,72,81,84,88,90,91,93,116,117,119,124,126,128],[68,84,88,90,91,116,117,124],[69,70,73,82,84,88,90,92,93,116,118,119,125,126,129],[69,84,88,90,92,116,118,125],[70,84,88,90,93,116,119,126],[71,72,73,83,84,88,91,92,93,117,118,119,127,128,129],[71,84,88,91,92,117,118,127],[72,84,88,91,93,117,119,128],[73,84,88,92,93,118,119,129],[74,75,76,77,78,79,80,81,82,83,84,89,90,91,92,93,120,121,122,123,124,125,126,127,128,129],[74,75,77,80,84,89,90,91,92,120,121,122,124,125,127],[74,76,78,81,84,89,90,91,93,120,121,123,124,126,128],[74,84,89,90,91,120,121,124],[75,76,79,82,84,89,90,92,93,120,122,123,125,126,129],[75,84,89,90,92,120,122,125],[76,84,89,90,93,120,123,126],[77,78,79,83,84,89,91,92,93,121,122,123,127,128,129],[77,84,89,91,92,121,122,127],[78,84,89,91,93,121,123,128],[79,84,89,92,93,122,123,129],[80,81,82,83,84,90,91,92,93,124,125,126,127,128,129],[80,84,90,91,92,124,125,127],[81,84,90,91,93,124,126,128],[82,84,90,92,93,125,126,129],[83,84,91,92,93,127,128,129],[84],[84,85],[84,85,86,94],[84,85,87,95],[84,85,88,96],[84,85,89,97],[84,85,90,98],[84,85,91,99],[84,85,92,100],[84,85,93,101],[84,86],[84,86,87,102],[84,86,88,103],[84,86,89,104],[84,86,90,105],[84,86,91,106],[84,86,92,107],[84,86,93,108],[84,87],[84,87,88,109],[84,87,89,110],[84,87,90,111],[84,87,91,112],[84,87,92,113],[84,87,93,114],[84,88],[84,88,89,115],[84,88,90,116],[84,88,91,117],[84,88,92,118],[84,88,93,119],[84,89],[84,89,90,120],[84,89,91,121],[84,89,92,122],[84,89,93,123],[84,90],[84,90,91,124],[84,90,92,125],[84,90,93,126],[84,91],[84,91,92,127],[84,91,93,128],[84,92],[84,92,93,129],[84,93]]},"distance":{"d":6,"is_exact":false,"upper":8,"witness":[127,147,200,220,411,421,498,503],"A_d":null,"certified":null},"clifford":{"kind":"none","correction":{"S":[],"CZ":[]},"rotation_powers":[]},"metrics":{"gamma":1.008789325374641,"gamma_t":null,"gamma_rho":null,"gamma_claim":1.008789325374641,"gamma_t_claim":null,"gamma_rho_claim":null,"v_ex":null,"rate":0.1640625,"t_count":null,"poly_degree":null,"effective_width":84},"provenance":{"regimes":["AI search"],"discovery":"AI search","strongest_claim":"found by an AI search campaign; a verified witness, not a maximum","sources":[{"regime":"AI search","file":"/private/tmp/claude-501/-Users-shubhamjain-Documents-Claude-remote-magic-states-AI/25937cc1-0367-40c1-acc9-031067b831d4/scratchpad/msai_for_merge.jsonl","label":"msAI:90ead2abdc2b7d71","N":130,"d":6,"d_is_exact":false,"origin":"magic-states-AI/master_catalogue/master_catalogue.jsonl","provenance":"magic-states-AI/master_catalogue/master_catalogue.jsonl","notes":"gamma_campaign"}]},"references":[{"key":"rengaswamy2020optimality","short":"Rengaswamy et al. (2020)","full":"N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, \"On Optimality of CSS Codes for Transversal T,\" IEEE J. Sel. Areas Inf. Theory 1, 499 (2020).","url":"https://doi.org/10.1109/JSAIT.2020.3012914","date":"2020-08"},{"key":"vuillot2022quantum","short":"Vuillot & Breuckmann (2022)","full":"C. Vuillot and N. P. Breuckmann, \"Quantum Pin Codes,\" IEEE Trans. Inf. Theory 68, 5955 (2022).","url":"https://doi.org/10.1109/TIT.2022.3170846","date":"2022-09"}]}